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| author | priyanka | 2015-06-24 15:03:17 +0530 |
|---|---|---|
| committer | priyanka | 2015-06-24 15:03:17 +0530 |
| commit | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch) | |
| tree | ab291cffc65280e58ac82470ba63fbcca7805165 /213 | |
| download | Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.gz Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.bz2 Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.zip | |
initial commit / add all books
Diffstat (limited to '213')
236 files changed, 6627 insertions, 0 deletions
diff --git a/213/CH10/EX10.1/10_1.sce b/213/CH10/EX10.1/10_1.sce new file mode 100755 index 000000000..7045af6e9 --- /dev/null +++ b/213/CH10/EX10.1/10_1.sce @@ -0,0 +1,22 @@ +//To find weight and coefficient of friction
+clc
+//Given:
+theta=30 //degrees
+P1=180 //Pulling force, N
+P2=220 //Pushing force, N
+//Solution:
+//Resolving the forces horizontally for the pull of 180N
+F1=P1*cosd(theta) //N
+//Resolving the forces for the push of 220 N
+F2=P2*cosd(theta) //N
+//Calculating the coefficient of friction
+//For the pull of 180N, F1=mu*W-90*mu, or F1/mu-W=-90 .....(i)
+//For the push of 220N, F2=W*mu+110*mu, or F2/mu-W=110 .....(ii)
+A=[F1 -1; F2 -1]
+B=[-90; 110]
+V=A \ B
+mu=1/V(1)
+W=V(2)
+//Results:
+printf("\n\n The weight of the body, W = %d N.\n",W)
+printf(" The coefficient of friction, mu = %.4f.\n\n",mu)
\ No newline at end of file diff --git a/213/CH10/EX10.10/10_10.sce b/213/CH10/EX10.10/10_10.sce new file mode 100755 index 000000000..28833e896 --- /dev/null +++ b/213/CH10/EX10.10/10_10.sce @@ -0,0 +1,26 @@ +//To find ratio of torques and efficiency
+clc
+//Given:
+d=50,p=12.5 //mm
+mu=0.13
+W=25*1000 //N
+//Solution:
+//Calculating the helix angle
+alpha=atan(p/(%pi*d)) //radians
+//Calculating the force required on the screw to raise the load
+phi=atan(mu) //Limiting angle of friction, radians
+P1=W*(alpha+phi) //N
+//Calculating the torque required on the screw to raise the load
+T1=P1*d/2 //N-mm
+//Calculating the force required on the screw to lower the load
+P2=W*tan(phi-alpha) //N
+//Calculating the torque required to lower the load
+T2=P2*d/2 //N
+//Calculating the ratio of the torques required
+r=T1/T2 //Ratio of the torques required, N-mm
+//Calculating the efficiency of the machine
+eta=tan(alpha)/tan(alpha+phi)*100 //%
+//Results:
+printf("\n\n Torque required on the screw to raise the load, T1 = %d N-mm.\n",T1)
+printf(" Ratio of the torque required to raise the load to the torque required to lower the load = %.1f.\n",r)
+printf(" Efficiency of the machine, eta = %.1f %c.\n\n",eta,"%")
\ No newline at end of file diff --git a/213/CH10/EX10.11/10_11.sce b/213/CH10/EX10.11/10_11.sce new file mode 100755 index 000000000..715599771 --- /dev/null +++ b/213/CH10/EX10.11/10_11.sce @@ -0,0 +1,37 @@ +//To find work done and efficiency
+clc
+//Given:
+p=10,d=50,D2=60,R2=D2/2,D1=10,R1=D1/2 //mm
+W=20*1000 //N
+mu=0.08,mu1=mu
+//Solution:
+//Calculating the helix angle
+alpha=atan(p/(%pi*d)) //radians
+//Calculating the force required at the circumference of the screw to lift the load
+phi=atan(mu) //Limiting angle of friction, radians
+P=W*tan(alpha+phi) //N
+//Calculating the torque required to overcome friction at the screw
+T=P*d/(2*1000) //N-m
+//Calculating the number of rotations made by the screw
+N=170/p
+//When the load rotates with the screw:
+//Calculating the work done in lifting the load
+W1=T*2*%pi*N //Work done in lifting the load, N-m
+//Calculating the efficiency of the screw jack
+eta1=tan(alpha)/tan(alpha+phi)*100 //%
+//When the load does not rotate with the screw:
+//Calculating the mean radius of the bearing surface
+R=(R1+R2)/2 //mm
+//Calculating the torque required to overcome friction at the screw and the collar
+T=(P*d/2+mu1*W*R)/1000 //N-m
+//Calculating the work done by the torque in lifting the load
+W2=T*2*%pi*N //Work done by the torque in lifting the load, N-m
+//Calculating the torque required to lift the load, neglecting frition
+T0=(W*tan(alpha)*d/2)/1000 //N-m
+//Calculating the efficiency of the screw jack
+eta2=T0/T*100 //%
+//Results:
+printf("\n\n When the load rotates with the screw, work done in lifting the load = %d N-m.\n",W1)
+printf(" Efficiency of the screw jack, eta = %.1f %c.\n",eta1,"%")
+printf(" When the load does not rotate with the screw, work done in lifting the load = %d N-m.\n",W2)
+printf(" Efficiency of the screw jack, eta = %.1f %c.\n\n",eta2,"%")
\ No newline at end of file diff --git a/213/CH10/EX10.12/10_12.sce b/213/CH10/EX10.12/10_12.sce new file mode 100755 index 000000000..149270d5d --- /dev/null +++ b/213/CH10/EX10.12/10_12.sce @@ -0,0 +1,28 @@ +//To find length of lever
+clc
+//Given:
+W=10*1000,P1=100 //N
+p=12,d=50 //mm
+mu=0.15
+//Solution:
+//Calculating the helix angle
+alpha=atan(p/(%pi*d)) //radians
+//Calculating the effort required at the circumference of the screw to raise the load
+phi=atan(mu) //Limiting angle of friction, radians
+P=W*tan(alpha+phi) //N
+//Calculating the torque required to overcome friction
+T=P*d/2 //N-mm
+//Calculating the length of the lever
+l=T/P1 //mm
+//Calculating the mechanical advantage
+MA=W/P1
+//Calculating the efficiency of the screw jack
+eta=tan(alpha)/tan(alpha+phi)*100 //%
+//Results:
+printf("\n\n The length of the lever to be used, l = %.1f mm.\n",l)
+printf(" Mechanical advantage obtained, M.A. = %d.\n",MA)
+if eta<50 then
+ printf(" The screw is a self locking screw.\n\n");
+else
+ printf(" The screw is not a self locking screw.");
+end
\ No newline at end of file diff --git a/213/CH10/EX10.13/10_13.sce b/213/CH10/EX10.13/10_13.sce new file mode 100755 index 000000000..b05ae275f --- /dev/null +++ b/213/CH10/EX10.13/10_13.sce @@ -0,0 +1,22 @@ +//To find the torque required
+clc
+//Given:
+d=22,p=3 //mm
+funcprot(0)
+beta=60/2 //degrees
+W=40*1000 //N
+mu=0.15
+//Solution:
+//Calculating the helix angle
+alpha=atan(p/(%pi*d)) //radians
+//Calculating the virtual coefficient of friction
+mu1=mu/cosd(beta)
+//Calculating the force required at the circumference of the screw
+phi1=atan(mu1) //Virtual limiting angle of friction, radians
+P=W*tan(alpha+phi1)
+//Calculating the torque on one rod
+T=P*d/(2*1000) //N-m
+//Calculating the torque required on the nut
+T1=2*T //N-m
+//Results:
+printf("\n\n The torque required on the nut, T1 = %.2f N-m.\n\n",T1)
\ No newline at end of file diff --git a/213/CH10/EX10.14/10_14.sce b/213/CH10/EX10.14/10_14.sce new file mode 100755 index 000000000..2b3be09d9 --- /dev/null +++ b/213/CH10/EX10.14/10_14.sce @@ -0,0 +1,23 @@ +//To find the forcr
+clc
+//Given:
+d=25,p=5,R=25 //mm
+funcprot(0)
+beta=27.5 //degrees
+mu=0.1,mu2=0.16
+l=0.5 //m
+W=10*1000 //N
+//Solution:
+//Calculating the virtual coefficient of friction
+mu1=mu/cosd(beta)
+//Calculating the helix angle
+alpha=atan(p/(%pi*d)) //radians
+//Calculating the force on the screw
+phi1=atan(mu1) //Virtual limiting angle of frcition, radians
+P=W*tan(alpha+phi1) //N
+//Calculating the total torque transmitted
+T=(P*d/2+mu2*W*R)/1000 //N-m
+//Calculating the force required at the end of a spanner
+P1=T/l //N
+//Results:
+printf("\n\n Force required at the end of a spanner, P1 = %.1f N.\n\n",P1)
\ No newline at end of file diff --git a/213/CH10/EX10.15/10_15.sce b/213/CH10/EX10.15/10_15.sce new file mode 100755 index 000000000..730b9bc91 --- /dev/null +++ b/213/CH10/EX10.15/10_15.sce @@ -0,0 +1,16 @@ +//To find power transmitted
+clc
+//Given:
+d=60,r=d/2 //mm
+W=2000 //N
+mu=0.03
+N=1440 //rpm
+//Solution:
+//Calculating the angular speed of the shaft
+omega=2*%pi*N/60 //rad/s
+//Calculating the torque transmitted
+T=mu*W*(r/1000) //N-m
+//Calculating the power transmitted
+P=T*omega //W
+//Results:
+printf("\n\n The power transmitted, P = %.1f W.\n\n",P)
\ No newline at end of file diff --git a/213/CH10/EX10.16/10_16.sce b/213/CH10/EX10.16/10_16.sce new file mode 100755 index 000000000..49a5029b7 --- /dev/null +++ b/213/CH10/EX10.16/10_16.sce @@ -0,0 +1,16 @@ +//To estimate power lost in friction
+clc
+//Given:
+D=150/1000,R=D/2 //m
+N=100 //rpm
+W=20*1000 //N
+mu=0.05
+//Solution:
+//Calculating the angular speed of the shaft
+omega=2*%pi*N/60 //rad/s
+//Calculating the total frictional torque for uniform pressure distribution
+T=2/3*mu*W*R //N-m
+//Calculating the power lost in friction
+P=T*omega //W
+//Results:
+printf("\n\n Power lost in friction, P = %.1f W.\n\n",P)
\ No newline at end of file diff --git a/213/CH10/EX10.17/10_17.sce b/213/CH10/EX10.17/10_17.sce new file mode 100755 index 000000000..5c6445f50 --- /dev/null +++ b/213/CH10/EX10.17/10_17.sce @@ -0,0 +1,21 @@ +//To find power absorbed in friction
+clc
+//Given:
+W=20*1000 //N
+alpha=120/2 //degrees
+Pn=0.3 //N/mm^2
+N=200 //rpm
+mu=0.1
+//Solution:
+//Calculating the angular speed of the shaft
+omega=2*%pi*N/60 //rad/s
+//Calculating the inner radius of the bearing surface
+r2=sqrt(W/(3*%pi*Pn)) //mm
+//Calculating the outer radius of the bearing surface
+r1=2*r2 //mm
+//Calculating the total frictional torque assuming uniform pressure
+T=2/3*mu*W*(1/sind(alpha))*(r1^3-r2^3)/(r1^2-r2^2)/1000 //N-m
+//Calculating the power absorbed in friction
+P=T*omega/1000 //kW
+//Results:
+printf("\n\n Power absorbed in friction, P = %.3f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH10/EX10.18/10_18.sce b/213/CH10/EX10.18/10_18.sce new file mode 100755 index 000000000..32f001d14 --- /dev/null +++ b/213/CH10/EX10.18/10_18.sce @@ -0,0 +1,24 @@ +//To find power lost in friction
+clc
+//Given:
+D=200/1000,R=D/2 //m
+W=30*1000 //N
+alpha=120/2 //degrees
+mu=0.025
+N=140 //rpm
+//Solution:
+//Calculating the angular speed of the shaft
+omega=2*%pi*N/60 //rad/s
+//Power lost in friction assuming uniform pressure:
+//Calculating the total frictional torque
+T=2/3*mu*W*R*(1/sind(alpha)) //N-m
+//Calculating the power lost in friction
+P1=T*omega //Power lost in friction, W
+//Power lost in friction assuming uniform wear:
+//Calculating the total frictional torque
+T=1/2*mu*W*R*(1/sind(alpha)) //N-m
+//Calculating the power lost in friction
+P2=T*omega //Power lost in friction, W
+//Resluts:
+printf("\n\n Power lost in friction assuming uniform pressure, P = %d W.\n",P1)
+printf(" Power lost in friction assuming uniform wear, P = %.1f W.\n\n",P2)
\ No newline at end of file diff --git a/213/CH10/EX10.19/10_19.sce b/213/CH10/EX10.19/10_19.sce new file mode 100755 index 000000000..77f5b7207 --- /dev/null +++ b/213/CH10/EX10.19/10_19.sce @@ -0,0 +1,24 @@ +//To find power absorbed in friction
+clc
+//Given:
+n=6
+d1=600,r1=d1/2,d2=300,r2=d2/2 //mm
+W=100*1000 //N
+mu=0.12
+N=90 //rpm
+//Solution:
+//Calculating the angular speed of the engine
+omega=2*%pi*N/60 //rad/s
+//Power absorbed in friction assuming uniform pressure:
+//Calculating the total frictional torque transmitted
+T=2/3*mu*W*(r1^3-r2^3)/(r1^2-r2^2)/1000 //N-m
+//Calculating the power absorbed in friction
+P1=T*omega/1000 //Power absorbed in friction assuming uniform pressure, kW
+//Power absorbed in friction assuming uniform wear:
+//Calculating the total frictional torque transmitted
+T=1/2*mu*W*(r1+r2)/1000 //N-m
+//Calculating the power absorbed in friction
+P2=T*omega/1000 //Power absorbed in friction assuming uniform wear, kW
+//Results:
+printf("\n\n Power absorbed in friction assuming uniform pressure, P = %.1f kW.\n",P1)
+printf(" Power absorbed in friction assuming uniform wear, P = %.2f kW.\n\n",P2)
\ No newline at end of file diff --git a/213/CH10/EX10.2/10_2.sce b/213/CH10/EX10.2/10_2.sce new file mode 100755 index 000000000..a40061a05 --- /dev/null +++ b/213/CH10/EX10.2/10_2.sce @@ -0,0 +1,17 @@ +//To find weight and coefficient of friction
+clc
+//Given:
+P1=1500,P2=1720 //N
+alpha1=12,alpha2=15 //degrees
+//Solution:
+//Refer Fig. 10.10
+//Effort applied parallel to the plane, P1=W*(sind(alpha1)+mu*cosd(alpha1)), or P1/W-mu*cosd(alpha1)=sind(alpha1) .....(i)
+//Effort applied parallel to the plane, P2=W*(sind(alpha2)+mu*cosd(alpha2)), or P2/W-mu*cosd(alpha2)=sind(alpha2) .....(ii)
+A=[P1 -cosd(alpha1); P2 -cosd(alpha2)]
+B=[sind(alpha1); sind(alpha2)]
+V=A \ B
+W=1/V(1)
+mu=V(2)
+//Results:
+printf("\n\n Coefficient of friction, mu = %.3f.\n",mu)
+printf(" Weight of the body, W = %d N.\n\n",W)
\ No newline at end of file diff --git a/213/CH10/EX10.20/10_20.sce b/213/CH10/EX10.20/10_20.sce new file mode 100755 index 000000000..b886d6564 --- /dev/null +++ b/213/CH10/EX10.20/10_20.sce @@ -0,0 +1,20 @@ +//To find power absorbed
+clc
+//Given:
+d1=400,r1=d1/2,d2=250,r2=d2/2 //mm
+p=0.35 //N/mm^2
+mu=0.05
+N=105 //rpm
+W=150*1000 //N
+//Solution:
+//Calculating the angular speed of the shaft
+omega=2*%pi*N/60 //rad/s
+//Calculating the total frictional torque transmitted for uniform pressure
+T=2/3*mu*W*(r1^3-r2^3)/(r1^2-r2^2)/1000 //N-m
+//Calculating the power absorbed
+P=T*omega/1000 //kW
+//Calculating the number of collars required
+n=W/(p*%pi*(r1^2-r2^2))
+//Results:
+printf("\n\n Power absorbed, P = %.2f kW.\n",P)
+printf(" Number of collars required, n = %d.\n\n",n+1)
\ No newline at end of file diff --git a/213/CH10/EX10.21/10_21.sce b/213/CH10/EX10.21/10_21.sce new file mode 100755 index 000000000..43d9c48e2 --- /dev/null +++ b/213/CH10/EX10.21/10_21.sce @@ -0,0 +1,24 @@ +//To find diameter and number of collars
+clc
+//Given:
+d2=300/1000,r2=d2/2 //m
+W=200*1000 //N
+N=75 //rpm
+mu=0.05
+p=0.3 //N/mm^2
+P=16*1000 //W
+//Solution:
+//Calculating the angular velocity of the shaft
+omega=2*%pi*N/60 //rad/s
+//Calculating the total frictional torque transmitted
+T=P/omega //N-m
+//Calculating the external diameter of the collar
+//We have, T=2/3*mu*W*(r1^3-r2^3)/(r1^2-r2^2), or (2*mu*W)*r1^2-(3*T-2*mu*W*r2)*r1+(2*mu*W*r2^2-3*T*r2)=0
+A=2*mu*W, B=-(3*T-2*mu*W*r2), C=2*mu*W*r2^2-3*T*r2
+r1=(-B+sqrt(B^2-4*A*C))/(2*A)*1000 //mm
+d1=2*r1 //mm
+//Calculating the number of collars
+n=W/(p*%pi*(r1^2-(r2*1000)^2))
+//Results:
+printf("\n\n External diameter of the collar, d1 = %d mm.\n",d1)
+printf(" Number of collars, n = %d.\n\n",n+1)
\ No newline at end of file diff --git a/213/CH10/EX10.22/10_22.sce b/213/CH10/EX10.22/10_22.sce new file mode 100755 index 000000000..0d10306f2 --- /dev/null +++ b/213/CH10/EX10.22/10_22.sce @@ -0,0 +1,16 @@ +//To find the pressure
+clc
+//Given:
+W=4*1000 //N
+r2=50,r1=100 //mm
+//Solution:
+//Calculating the maximum pressure
+pmax=W/(2*%pi*r2*(r1-r2)) //N/mm^2
+//Calculating the minimum pressure
+pmin=W/(2*%pi*r1*(r1-r2)) //N/mm^2
+//Calculating the average pressure
+pav=W/(%pi*(r1^2-r2^2)) //N/mm^2
+//Results:
+printf("\n\n Maximum pressure, pmax = %.4f N/mm^2.\n",pmax)
+printf(" Minimum pressure, pmin = %.4f N/mm^2.\n",pmin)
+printf(" Average pressure, pav = %.2f N/mm^2.\n\n",pav)
\ No newline at end of file diff --git a/213/CH10/EX10.23/10_23.sce b/213/CH10/EX10.23/10_23.sce new file mode 100755 index 000000000..97c8c6f65 --- /dev/null +++ b/213/CH10/EX10.23/10_23.sce @@ -0,0 +1,23 @@ +//To find power transmitted
+clc
+//Given:
+d1=300, r1=d1/2, d2=200, r2=d2/2 //mm
+p=0.1 //N/mm^2
+mu=0.3
+N=2500 //rpm
+n=2
+//Solution:
+//Calculating the radial speed of the clutch
+omega=2*%pi*N/60 //rad/s
+//Calculating the intensity of pressure
+C=p*r2 //N/mm
+//Calculating the axial thrust
+W=2*%pi*C*(r1-r2) //N
+//Calculating the mean radius of the friction surfaces for uniform wear
+R=(r1+r2)/(2*1000) //m
+//Calculating the torque transmitted
+T=n*mu*W*R //N-m
+//Calculating the power transmitted by a clutch
+P=T*omega/1000 //kW
+//Results:
+printf("\n\n Power transmitted by a clutch, P = %.3f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH10/EX10.24/10_24.sce b/213/CH10/EX10.24/10_24.sce new file mode 100755 index 000000000..a0950ab1d --- /dev/null +++ b/213/CH10/EX10.24/10_24.sce @@ -0,0 +1,24 @@ +//To find radii and axial thrust
+clc
+//Given:
+n=2, mu=0.255
+P=25*1000 //W
+N=3000 //rpm
+r=1.25 //Ratio of radii, r1/r2
+p=0.1 //N/mm^2
+//Solution:
+//Calculating the angular speed of the clutch
+omega = 2*%pi*N/60 //rad/s
+//Calculating the torque transmitted
+T=P/omega*1000 //N-mm
+//Calculating the inner radius
+r2=(T/(n*mu*2*%pi*0.1*(1.25-1)*(1.25+1)/2))^(1/3) //mm
+//Calculating the outer radius
+r1=r*r2 //mm
+//Calculating the axial thrust to be provided by springs
+C=0.1*r2 //Intensity of pressure, N/mm
+W=2*%pi*C*(r1-r2) //N
+//Results:
+printf("\n\n Outer radius of the frictional surface, r1 = %d mm.\n",r1)
+printf(" Inner radius of the frictional surface, r2 = %d mm.\n",r2)
+printf(" Axial thrust to be provided by springs, W = %d N.\n\n",W)
\ No newline at end of file diff --git a/213/CH10/EX10.25/10_25.sce b/213/CH10/EX10.25/10_25.sce new file mode 100755 index 000000000..c0db37152 --- /dev/null +++ b/213/CH10/EX10.25/10_25.sce @@ -0,0 +1,30 @@ +//To find dimensions of clutch plate
+clc
+//Given:
+P=7.5*1000 //W
+N=900 //rpm
+p=0.07 //N/mm^2
+mu=0.25
+n=2
+//Solution:
+//Calculating the angular speed of the clutch
+omega=2*%pi*N/60 //rad/s
+//Calculating the torque transmitted
+T=P/omega*1000 //N-mm
+//Calculating the mean radius of the friction lining
+R=(T/(%pi/2*n*mu*p))^(1/3) //mm
+//Calculating the face width of the friction lining
+w=R/4 //mm
+//Calculating the outer and inner radii of the clutch plate
+//We have, w = r1-r2, or r1-r2 = w .....(i)
+//Also, R = (r1+r2)/2, or r1+r2 = 2*R .....(ii)
+A=[1 -1; 1 1]
+B=[w; 2*R]
+V=A \ B
+r1=V(1)
+r2=V(2)
+//Results:
+printf("\n\n Mean radius of the friction lining, R = %d mm.\n",R)
+printf(" Face width of the friction lining, w = %.2f mm.\n",w)
+printf(" Outer radius of the clutch plate, r1 = %.3f mm.\n",r1)
+printf(" Inner radius of the clutch plate, r2 = %.3f mm.\n\n",r2)
\ No newline at end of file diff --git a/213/CH10/EX10.26/10_26.sce b/213/CH10/EX10.26/10_26.sce new file mode 100755 index 000000000..d5c94a135 --- /dev/null +++ b/213/CH10/EX10.26/10_26.sce @@ -0,0 +1,28 @@ +//To find dimensions of clutch plate
+clc
+//Given:
+P=100 //kW
+N=2400 //rpm
+T=500*1000 //N-mm
+p=0.07 //N/mm^2
+mu=0.3
+Ns=8 //Number of springs
+k=40 //Stiffness, N/mm
+n=2
+//Solution:
+//Calculating the inner radius of the friction plate
+r2=(T/(n*mu*2*%pi*p*(1.25-1)*(1.25+1)/2))^(1/3) //mm
+//Calculating the outer radius of the friction plate
+r1=1.25*r2 //mm
+//Calculating the total stiffness of the springs
+s=k*Ns //N/mm
+//Calculating the intensity of pressure
+C=p*r2 //N/mm
+//Calculating the axial force required to engage the clutch
+W=2*%pi*C*(r1-r2) //N
+//Calculating the initial compression in the springs
+IC=W/s //Initial compression in the springs, mm
+//Results:
+printf("\n\n Outer radius of the friction plate, r1 = %.1f mm.\n",r1)
+printf(" Inner radius of the friction plate, r2 = %d mm.\n",r2)
+printf(" Initial compression in the springs = %.1f mm.\n\n",IC)
\ No newline at end of file diff --git a/213/CH10/EX10.27/10_27.sce b/213/CH10/EX10.27/10_27.sce new file mode 100755 index 000000000..79a44155b --- /dev/null +++ b/213/CH10/EX10.27/10_27.sce @@ -0,0 +1,56 @@ +//To find speed, time and KE lost
+clc
+//Given:
+d1=220, r1=d1/2, d2=160, r2=d2/2 //mm
+W=570 //N
+m1=800, m2=1300 //kg
+k1=200/1000, k2=180/1000 //m
+mu=0.35
+N1=1250 //rpm
+n=2
+//Solution:
+//Calculating the initial angular speed of the motor shaft
+omega1=2*%pi*N1/60 //rad/s
+//Calculating the moment of inertia for the motor armature and shaft
+I1=m1*k1^2 //kg-m^2
+//Calculating the moment of inertia for the rotor
+I2=m2*k2^2 //kg-m^2
+//Calculating the final speed of the motor and rotor
+omega2=0
+omega3=(I1*omega1+I2*omega2)/(I1+I2) //rad/s
+//Calculating the mean radius of the friction plate
+R=(r1+r2)/(2*1000) //m
+//Calculating the frictional torque
+T=n*mu*W*R //N-m
+//Calculating the angular acceleration of the rotor
+alpha2=T/I2 //rad/s^2
+//Calculating the time to reach the speed of omega3
+omegaF=omega3, omegaI=omega2
+t=(omegaF-omegaI)/alpha2 //seconds
+//Calculating the angular kinetic energy before impact
+E1=1/2*I1*omega1^2+1/2*I2*omega2^2 //N-m
+//Calculating the angular kinetic energy after impact
+E2=1/2*(I1+I2)*omega3^2 //N-m
+//Calculating the kinetic energy lost during the period of slipping
+E=E1-E2 //N-m
+//Calculating the torque on armature shaft
+T1=-60-T //N-m
+//Calculating the torque on rotor shaft
+T2=T //N-m
+//Calculating the time of slipping assuming constant resisting torque:
+//Considering armature shaft, omega3 = omega1+alpha1*t1, or omega3-(T1/I1)*t1 = omega1 .....(i)
+//Considering rotor shaft, omega3 = alpha2*t1, or omega3-(T2/I2)*t1 = 0 .....(ii)
+A=[1 -T1/I1; 1 -T2/I2]
+B=[omega1; 0]
+V=A \ B
+t11=V(2) //Time of slipping assuming constant resisting torque, seconds
+//Calculating the time of slipping assuming constant driving torque:
+//Calculating the torque on armature shaft
+T1=60-T //N-m
+t12=(omega2-omega1)/(T1/I1-T2/I2) //Time of slipping assuming constant driving torque, seconds
+//Results:
+printf("\n\n Final speed of the motor and rotor, omega3 = %.2f rad/s.\n",omega3)
+printf(" Time to reach the speed of %.2f rad/s, t = %.1f s.\n",omega3,t)
+printf(" Kinetic energy lost during the period of slipping = %d N-m.\n",E)
+printf(" Time of slipping assuming constant resisting torque, t1 = %.1f s.\n",t11)
+printf(" Time of slipping assuming constant driving torque, t1 = %d s.\n\n",t12)
\ No newline at end of file diff --git a/213/CH10/EX10.28/10_28.sce b/213/CH10/EX10.28/10_28.sce new file mode 100755 index 000000000..02eaca7fd --- /dev/null +++ b/213/CH10/EX10.28/10_28.sce @@ -0,0 +1,22 @@ +//To find the power transmitted
+clc
+//Given:
+n=4, mu=0.3
+p=0.127 //N/mm^2
+N=500 //rpm
+r1=125, r2=75 //mm
+//Solution:
+//Calculating the angular speed of the clutch
+omega=2*%pi*N/60 //rad/s
+//Calculating the maximum intensity of pressure
+C=p*r2 //N/mm
+//Calculating the axial force required to engage the clutch
+W=2*%pi*C*(r1-r2) //N
+//Calculating the mean radius of the friction surfaces
+R=(r1+r2)/(2*1000) //m
+//Calculating the torque transmitted
+T=n*mu*W*R //N-m
+//Calculating the power transmitted
+P=T*omega/1000 //kW
+//Results:
+printf("\n\n Power transmitted, P = %.1f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH10/EX10.29/10_29.sce b/213/CH10/EX10.29/10_29.sce new file mode 100755 index 000000000..9e384a02b --- /dev/null +++ b/213/CH10/EX10.29/10_29.sce @@ -0,0 +1,22 @@ +//To find maximum intensity of pressure
+clc
+//Given:
+n1=3, n2=2, mu=0.3
+d1=240, r1=d1/2, d2=120, r2=d2/2 //mm
+P=25*1000 //W
+N=1575 //rpm
+//Solution:
+//Calculating the angular speed of the shaft
+omega=2*%pi*N/60 //rad/s
+//Calculating the torque transmitted
+T=P/omega //N-m
+//Calculating the number of pairs of friction surfaces
+n=n1+n2-1
+//Calculating the mean radius of friction surfaces for uniform wear
+R=(r1+r2)/(2*1000) //m
+//Calculating the axial force on each friction surface
+W=T/(n*mu*R) //N
+//Calculating the maximum axial intensity of pressure
+p=W/(2*%pi*r2*(r1-r2)) //N/mm^2
+//Results:
+printf("\n\n Maximum axial intensity of pressure, p = %.3f N/mm^2.\n\n",p)
\ No newline at end of file diff --git a/213/CH10/EX10.3/10_3.sce b/213/CH10/EX10.3/10_3.sce new file mode 100755 index 000000000..e7a484f2a --- /dev/null +++ b/213/CH10/EX10.3/10_3.sce @@ -0,0 +1,25 @@ +//To estimate the power
+clc
+//Given:
+W=75*1000 //W
+v=300 //mm/min
+p=6,d0=40 //mm
+mu=0.1
+//Solution:
+//Calculating the mean diameter of the screw
+d=(d0-p/2)/1000 //m
+//Calculating the helix angle
+alpha=atan(p/(%pi*d*1000)) //radians
+//Calculating the force required at the circumference of the screw
+phi=atan(mu) //Limiting angle of friction, radians
+P=W*tan(alpha+phi) //N
+//Calculating the torque required to overcome the friction
+T=P*d/2 //N-m
+//Calculating the speed of the screw
+N=v/p //rpm
+//Calculating the angular speed
+omega=2*%pi*N/60 //rad/s
+//Calculating the power of the motor
+Power=T*omega/1000 //Power of the motor, kW
+//Results:
+printf("\n\n Power of the motor required = %.3f kW.\n\n",Power)
\ No newline at end of file diff --git a/213/CH10/EX10.30/10_30.sce b/213/CH10/EX10.30/10_30.sce new file mode 100755 index 000000000..bd9eefb71 --- /dev/null +++ b/213/CH10/EX10.30/10_30.sce @@ -0,0 +1,37 @@ +//To find maximum power transmitted
+clc
+//Given:
+n1=3, n2=2, n=4, mu=0.3
+d1=240, r1=d1/2, d2=120, r2=d2/2 //mm
+P=25*1000 //W
+N=1575 //rpm
+//Solution:
+//Calculating the angular speed of the shaft
+omega=2*%pi*N/60 //rad/s
+//Calculating the torque transmitted
+T=P/omega //N-m
+//Calculating the mean radius of the contact surface, for uniform pressure
+R=2/3*(r1^3-r2^3)/(r1^2-r2^2)/1000 //m
+//Calculating the total spring load
+W1=T/(n*mu*R) //N
+//Calculating the maximum power transmitted:
+//Given:
+ns=6 //Number of springs
+c=8 //Contact surfaces of the spring
+w=1.25 //Wear on each contact surface, mm
+k=13*1000 //Stiffness of each spring, N/m
+//Calculating the total wear
+Tw=c*w/1000 //Total wear, m
+//Calculating the reduction in spring force
+Rs=Tw*k*ns //N
+//Calculating the new axial load
+W2=W1-Rs //N
+//Calculating the mean radius of the contact surfaces for uniform wear
+R=(r1+r2)/(2*1000) //m
+//Calculating the torque transmitted
+T=n*mu*W2*R //N-m
+//Calculating the maximum power transmitted
+P=T*omega/1000 //kw
+//Results:
+printf("\n\n Total spring load, W = %d N.\n",W1)
+printf(" Maximum power that can be transmitted, P = %.2f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH10/EX10.31/10_31.sce b/213/CH10/EX10.31/10_31.sce new file mode 100755 index 000000000..1cfa863e9 --- /dev/null +++ b/213/CH10/EX10.31/10_31.sce @@ -0,0 +1,32 @@ +//To find dimensions and axial load
+clc
+//Given:
+P=90*1000 //W
+N=1500 //rpm
+alpha=20 //degrees
+mu=0.2
+D=375, R=D/2 //mm
+pn=0.25 //N/mm^2
+//SOlution:
+//Calculating the angular speed of the clutch
+omega=2*%pi*N/60 //rad/s
+//Calculating the torque transmitted
+T=P/omega*1000 //N-mm
+//Calculating the width of the bearing surface
+b=T/(2*%pi*mu*pn*R^2) //mm
+//Calculating the external and internal radii of the bearing surface
+//We know that, r1+r2 = 2*R, and r1-r2 = b*sind(alpha)
+A=[1 1; 1 -1]
+B=[2*R; b*sind(alpha)]
+V=A \ B
+r1=V(1) //mm
+r2=V(2) //mm
+//Calculating the intensity of pressure
+C=pn*r2 //N/mm
+//Calculating the axial load required
+W=2*%pi*C*(r1-r2) //N
+//Results:
+printf("\n\n Width of the bearing surface, b = %.1f mm.\n",b)
+printf(" External radius of the bearing surface, r1 = %.1f mm.\n",r1)
+printf(" Internal radius of the bearing surface, r2 = %.1f mm.\n",r2)
+printf(" Axial load required, W = %d N.\n\n",W)
\ No newline at end of file diff --git a/213/CH10/EX10.32/10_32.sce b/213/CH10/EX10.32/10_32.sce new file mode 100755 index 000000000..89669811a --- /dev/null +++ b/213/CH10/EX10.32/10_32.sce @@ -0,0 +1,23 @@ +//To find axial force and face width
+clc
+//Given:
+P=45*1000 //W
+N=1000 //rpm
+alpha=12.5 //degrees
+D=500/1000, R=D/2 //m
+mu=0.2
+pn=0.1 //N/mm^2
+//Solution:
+//Calculating the angular speed of the shaft
+omega=2*%pi*N/60 //rad/s
+//Calculating the torque developed by the clutch
+T=P/omega //N-m
+//Calculating the normal load acting on the friction surface
+Wn=T/(mu*R) //N
+//Calculating the axial spring force necessary to engage the clutch
+We=Wn*(sind(alpha)+mu*cosd(alpha)) //N
+//Calculating the face width required
+b=Wn/(pn*2*%pi*R*1000) //mm
+//Results:
+printf("\n\n Axial force necessary to engage the clutch, We = %d N.\n",We)
+printf(" Face width required, b = %.1f mm.\n\n",b)
\ No newline at end of file diff --git a/213/CH10/EX10.33/10_33.sce b/213/CH10/EX10.33/10_33.sce new file mode 100755 index 000000000..f942fc018 --- /dev/null +++ b/213/CH10/EX10.33/10_33.sce @@ -0,0 +1,29 @@ +//To find dimensions of contact surfaces
+clc
+//Given:
+alpha=30/2 //degrees
+pn=0.35 //N/mm^2
+P=22.5*1000 //W
+N=2000 //rpm
+mu=0.15
+//Solution:
+//Calculating the angular speed of the clutch
+omega=2*%pi*N/60 //rad/s
+//Calculating the torque transmitted by the clutch
+T=P/omega*1000 //N-mm
+//Calculating the mean radius of the contact surface
+R=(T/(2*%pi*mu*pn/3))^(1/3) //mm
+//Calculating the face width of the contact surface
+b=R/3
+//Calculating the outer and inner radii of the contact surface
+//Refer Fig. 10.27
+//We have, r1-r2 = b*sind(alpha), and r1+r2 = 2*R
+A=[1 -1; 1 1]
+B=[b*sind(alpha); 2*R]
+V=A \ B
+r1=V(1) //mm
+r2=V(2) //mm
+//Results:
+printf("\n\n Mean radius of the contact surface, R = %d mm.\n",R)
+printf(" Outer radius of the contact surface, r1 = %.2f mm.\n",r1)
+printf(" Inner radius of the contact surface, r2 = %.2f mm.\n\n",r2)
\ No newline at end of file diff --git a/213/CH10/EX10.34/10_34.sce b/213/CH10/EX10.34/10_34.sce new file mode 100755 index 000000000..d5ad17f31 --- /dev/null +++ b/213/CH10/EX10.34/10_34.sce @@ -0,0 +1,29 @@ +//To find time required and energy lost
+clc
+//Given:
+D=75/1000, R=D/2 //m
+alpha=15 //degrees
+mu=0.3
+W=180 //N
+NF=1000 //rpm
+m=13.5 //kg
+k=150/1000 //m
+//Solution:
+//Calculating the angular speed of the flywheel
+omegaF=2*%pi*NF/60 //rad/s
+//Calculating the torque required to produce slipping
+T=mu*W*R*(1/sind(alpha)) //N-m
+//Calculating the mass moment of inertia of the flywheel
+IF=m*k^2 //kg-m^2
+//Calculating the angular acceleration of the flywheel
+alphaF=T/IF //rad/s^2
+//Calculating the time required for the flywheel to attain full speed
+tF=omegaF/alphaF //seconds
+//Calculating the angle turned through by the motor and flywheel in time tF
+theta=1/2*omegaF*tF //rad
+//Calculating the energy lost in slipping of the clutch
+E=T*theta //Energy lost in slipping of the clutch, N-m
+//Results:
+printf("\n\n Torque required to produce slipping, T = %.1f N-m.\n",T)
+printf(" Time required for the flywheel to attain full speed, tF = %.1f s.\n",tF)
+printf(" Energy lost in slipping of the clutch = %d N-m.\n\n",E)
\ No newline at end of file diff --git a/213/CH10/EX10.35/10_35.sce b/213/CH10/EX10.35/10_35.sce new file mode 100755 index 000000000..a9e691810 --- /dev/null +++ b/213/CH10/EX10.35/10_35.sce @@ -0,0 +1,29 @@ +//To find mass and size of shoes
+clc
+//Given:
+P=15*1000 //W
+N=900 //rpm
+n=4, mu=0.25
+R=150/1000, r=120/1000 //m
+theta=60 //degrees
+p=0.1 //N/mm^2
+//Solution:
+//Calculating the angular speed of the clutch
+omega=2*%pi*N/60 //rad/s
+//Calculating the speed at which the engagement begins
+omega1=3/4*omega //rad/s
+//Calculating the torque transmitted at the running speed
+T=P/omega //N-m
+//Calculating the mass of the shoes
+m=T/(n*mu*(omega^2*r-omega1^2*r)*R) //kg
+//Calculating the contact length of shoes
+l=(theta*%pi/180)*R*1000 //mm
+//Calculating the centrifugal force acting on each shoe
+Pc=m*omega^2*r //N
+//Calculating the inward force on each shoe exerted by the spring
+Ps=m*omega1^2*r //N
+//Calculating the width of the shoes
+b=(Pc-Ps)/(l*p) //mm
+//Results:
+printf("\n\n Mass of the shoes, m = %.2f kg.\n",m)
+printf(" Width of the shoes, b = %.1f mm.\n\n",b)
\ No newline at end of file diff --git a/213/CH10/EX10.36/10_36.sce b/213/CH10/EX10.36/10_36.sce new file mode 100755 index 000000000..9767e61f1 --- /dev/null +++ b/213/CH10/EX10.36/10_36.sce @@ -0,0 +1,27 @@ +//To fnd power transmitted
+clc
+//Given:
+n=4, mu=0.3
+c=5, r=160 //mm
+S=500 //N
+D=400/1000, R=D/2 //m
+m=8 //kg
+s=50 //N/mm
+N=500 //rpm
+//Solution:
+//Calculating the angular speed of the clutch
+omega=2*%pi*N/60 //rad/s
+//Calculating the operating radius
+r1=(r+c)/1000 //m
+//Calculating the centrifugal force on each shoe
+Pc=m*omega^2*r1 //N
+//Calculating the inward force exerted by the spring
+Ps=S+c*s //N
+//Calculating the frictional force acting tangentially on each shoe
+F=mu*(Pc-Ps) //N
+//Calculating the total frictional torque transmitted by the clutch
+T=n*F*R //N-m
+//Calculating the power transmitted
+P=T*omega/1000 //kW
+//Results:
+printf("\n\n Power transmitted, P = %.1f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH10/EX10.4/10_4.sce b/213/CH10/EX10.4/10_4.sce new file mode 100755 index 000000000..82831d4f2 --- /dev/null +++ b/213/CH10/EX10.4/10_4.sce @@ -0,0 +1,24 @@ +//To find work done
+clc
+//Given:
+p=12,d=40 //mm
+mu=0.16
+W=2500 //N
+//Solutiom:
+//Work done in drawing the wagons together agianst a steady load of 2500 N:
+//Calculating the helix angle
+alpha=atan(p/(%pi*d)) //radians
+//Calculating the effort required at the circumference of the screw
+phi=atan(mu) //Limiting angle of friction, radians
+P=W*tan(alpha+phi) //N
+//Calculating the torque required to overcome friction between the screw and nut
+T=P*d/(2*1000) //N-m
+//Calculating the number of turns required
+N=240/(2*p)
+//Calculating the work done
+W1=T*2*%pi*N //Work done, N-m
+//Work done in drawing the wagons together when the load increases from 2500 N to 6000 N:
+W2=W1*(6000-2500)/2500 //Work done, N-m
+//Results:
+printf("\n\n Work done in drawing the wagons together agianst a steady load of 2500 N = %.1f N-m.\n",W1)
+printf(" Work done in drawing the wagons together when the load increases from 2500 N to 6000 N = %.1f N-m.\n\n",W2)
\ No newline at end of file diff --git a/213/CH10/EX10.5/10_5.sce b/213/CH10/EX10.5/10_5.sce new file mode 100755 index 000000000..008730c57 --- /dev/null +++ b/213/CH10/EX10.5/10_5.sce @@ -0,0 +1,21 @@ +//To find the torque required
+clc
+//Given:
+D=150/1000 //m
+ps=2*10^6 //N/m^2
+d0=50,p=6 //mm
+mu=0.12
+//Solution:
+//Calculating the load on the valve
+W=ps*%pi/4*D^2 //N
+//Calculating the mean diameter of the screw
+d=(d0-p/2)/1000 //m
+//Calculating the helix angle
+alpha=atan(p/(%pi*d*1000))
+//Calculating the force required to turn the handle
+phi=atan(mu) //Limiting angle of friction, radians
+P=W*tan(alpha+phi) //N
+//Calculating the torque required to turn the handle
+T=P*d/2 //N-m
+//Results:
+printf("\n\n The torque required to turn the handle, T = %.1f N-m.\n\n",T)
\ No newline at end of file diff --git a/213/CH10/EX10.6/10_6.sce b/213/CH10/EX10.6/10_6.sce new file mode 100755 index 000000000..e74318c1e --- /dev/null +++ b/213/CH10/EX10.6/10_6.sce @@ -0,0 +1,20 @@ +//To find force required
+clc
+//Given:
+dc=22.5,p=5,D=50,R=D/2,l=500 //mm
+mu=0.1,mu1=0.16
+W=10*1000 //N
+//Solution:
+//Calculating the mean diameter of the screw
+d=dc+p/2 //mm
+//Calculating the helix angle
+alpha=p/(%pi*d) //radians
+//Calculating the force required at the circumference of the screw
+phi=atan(mu) //Limiting angle of friction, radians
+P=W*tan(alpha+phi) //N
+//Calculating the total torque required
+T=P*d/2+mu1*W*R //N-mm
+//Calculating the force required at the end of a spanner
+P1=T/l //N
+//Results:
+printf("\n\n Force required at the end of a spanner, P1 = %.2f N.\n\n",P1)
\ No newline at end of file diff --git a/213/CH10/EX10.7/10_7.sce b/213/CH10/EX10.7/10_7.sce new file mode 100755 index 000000000..856381c1d --- /dev/null +++ b/213/CH10/EX10.7/10_7.sce @@ -0,0 +1,18 @@ +//To find diameter of hand wheel
+clc
+//Given:
+d=50,p=12.5,D=60,R=D/2 //mm
+W=10*1000,P1=100 //N
+mu=0.15,mu1=0.18
+//Solution:
+//Calculating the helix angle
+alpha=atan(p/(%pi*d)) //radians
+//Calculating the tangential force required at the circumference of the screw
+phi=atan(mu) //Limiting angle of friction, radians
+P=W*tan(alpha+phi) //N
+//Calculating the total torque required to turn the hand wheel
+T=P*d/2+mu1*W*R //N-mm
+//Calculating the diameter of the hand wheel
+D1=T/(2*P1*1000)*2 //m
+//Results:
+printf("\n\n Diameter of the hand wheel, D1 = %.3f m.\n\n",D1)
\ No newline at end of file diff --git a/213/CH10/EX10.8/10_8.sce b/213/CH10/EX10.8/10_8.sce new file mode 100755 index 000000000..ee374e289 --- /dev/null +++ b/213/CH10/EX10.8/10_8.sce @@ -0,0 +1,28 @@ +//To find the power required
+clc
+//Given:
+d0=55,D2=60,R2=D2/2,D1=90,R1=D1/2 //mm
+p=10/1000 //m
+W=400 //N
+mu=0.15
+v=6 //Cutting speed, m/min
+//Solution:
+//Calculating the mean diameter of the screw
+d=d0-p/2 //mm
+//Calculating the helix angle
+alpha=p/(%pi*d) //radians
+//Calculating the force required at the circumference of the screw
+phi=atan(mu) //Limiting angle of friction, radians
+P=W*tan(alpha+phi) //N
+//Calculating the mean radius of the flat surface
+R=(R1+R2)/2 //mm
+//Calculating the torque required
+T=(P*d/2+mu1*W*R)/1000 //N-m
+//Calculating the speed of the screw
+N=v/p //rpm
+//Calculating the angular speed
+omega=2*%pi*N/60 //rad/s
+//Calculating the power required to operate the nut
+Power=T*omega/1000 //Power required to operate the nut, kW
+//Results:
+printf("\n\n Power required to operate the nut = %.3f kW.\n\n",Power)
\ No newline at end of file diff --git a/213/CH10/EX10.9/10_9.sce b/213/CH10/EX10.9/10_9.sce new file mode 100755 index 000000000..65354d79a --- /dev/null +++ b/213/CH10/EX10.9/10_9.sce @@ -0,0 +1,24 @@ +//To find the force applied
+clc
+//Given:
+d=50/1000,l=0.7 //m
+p=10 //mm
+mu=0.15
+W=20*1000 //N
+//Solution:
+//Calculating the helix angle
+alpha=atan(p/(%pi*d*1000)) //radians
+//Force required to raise the load:
+//Calculating the force required at the circumference of the screw
+phi=atan(mu) //Limiting angle of friction, radians
+P1=W*tan(alpha+phi) //N
+//Calculating the force required at the end of the lever
+P11=P1*d/(2*l) //N
+//Calculating the force required at the circumference of the screw
+P2=W*(phi-alpha) //N
+//Foce rewuired to lower the load:
+//Calculating the force required at the end of the lever
+P21=P2*d/(2*l) //N
+//Results:
+printf("\n\n Force required at the end of the lever to raise the load, P1 = %d N.\n",P11)
+printf(" Force required at the end of the lever to lower the load, P1 = %d N.\n\n",P21)
\ No newline at end of file diff --git a/213/CH11/EX11.1/11_1.sce b/213/CH11/EX11.1/11_1.sce new file mode 100755 index 000000000..2070edfe3 --- /dev/null +++ b/213/CH11/EX11.1/11_1.sce @@ -0,0 +1,14 @@ +//To find speed of shaft
+clc
+//Given:
+N1=150 //rpm
+d1=750, d2=450, d3=900, d4=150 //mm
+//Solution:
+//Calculating the speed of the dynamo shaft when there is no slip
+N41=N1*(d1*d3)/(d2*d4) //rpm
+//Calculating the speed of the dynamo shaft whne there is a slip of 2% at each drive
+s1=2, s2=2 //%
+N42=N1*(d1*d3)/(d2*d4)*(1-s1/100)*(1-s2/100) //rpm
+//Results:
+printf("\n\n Speed of the dynamo shaft when there is no slip, N4 = %d rpm.\n\n",N41)
+printf(" Speed of the dynamo shaft when there is a slip of 2%c at each drive, N4 = %d rpm.\n\n","%",N42)
\ No newline at end of file diff --git a/213/CH11/EX11.10/11_10.sce b/213/CH11/EX11.10/11_10.sce new file mode 100755 index 000000000..f5839b99c --- /dev/null +++ b/213/CH11/EX11.10/11_10.sce @@ -0,0 +1,29 @@ +//To find greatest power transmitted
+clc
+//Given:
+theta=120*%pi/180 //radians
+b=100/1000, t=6/1000 //m
+rho=1000 //kg/m^3
+mu=0.3
+sigma=2*10^6 //N/m^2
+//Solution:
+//Speed of the belt for greatest power:
+//Calculating the maximum tension in the belt
+T=sigma*b*t //N
+//Calculating the mass of the belt per metre length
+l=1 //m
+m=b*t*l*rho //kg/m
+//Calculating the speed of the belt for greatest power
+v=sqrt(T/(3*m)) //m/s
+//Greatest power which the belt can transmit
+//Calculating the centrifugal tension for maximum power to be transmitted
+TC=T/3 //N
+//Calculating the tension in the tight side of the belt
+T1=T-TC //N
+//Calculating the tension in the slack side of the belt
+T2=T1/exp(mu*theta) //N
+//Calculating the greatest power which the belt can transmit
+P=(T1-T2)*v/1000 //kW
+//Results:
+printf("\n\n Speed of the belt for greatest power, v = %.2f m/s.\n\n",v)
+printf(" Greatest power which the belt can transmit, P = %.2f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH11/EX11.11/11_11.sce b/213/CH11/EX11.11/11_11.sce new file mode 100755 index 000000000..d018d1738 --- /dev/null +++ b/213/CH11/EX11.11/11_11.sce @@ -0,0 +1,42 @@ +//To find torque, power and efficiency
+clc
+//Given:
+d1=1.2, r1=d1/2, d2=0.5, r2=d2/2, x=4 //m
+m=0.9 //kg/m
+T=2000 //N
+mu=0.3
+N1=200, N2=450 //rpm
+//Solution:
+//Calculating the velocity of the belt
+v=%pi*d1*N1/60 //m/s
+//Calculating the centrifugal tension
+TC=m*v^2 //N
+//Calculating the tension in the tight side of the belt
+T1=T-TC //N
+//Calculating the angle alpha for an open belt drive
+alpha=asin((r1-r2)/x)*180/%pi //degrees
+//Calculating the angle of lap on the smaller pulley
+theta=(180-2*alpha)*%pi/180 //radians
+//Calculating the tension in the slack side of the belt
+T2=T1/exp(mu*theta) //N
+//Calculating the torque on the shaft of larger pulley
+TL=(T1-T2)*r1 //N-m
+//Calculating the torque on the shaft of smaller pulley
+TS=(T1-T2)*r2 //N-m
+//Calculating the power transmitted
+P=(T1-T2)*v/1000 //kW
+//Power lost in friction:
+//Calculating the input power
+P1=TL*2*%pi*N1/(60*1000) //kW
+//Calculating the output power
+P2=TS*2*%pi*N2/(60*1000) //kW
+//Calculating the power lost in friction
+Pf=P1-P2 //Power lost in friction, kW
+//Calculating the efficiency of the drive
+eta=P2/P1*100 //%
+//Results:
+printf("\n\n Torque on the shaft of larger pulley, TL = %.1f N-m.\n\n",TL)
+printf(" Torque on the shaft of smaller pulley, TS = %d N-m.\n\n",TS)
+printf(" Power transmitted, P = %.2f kW.\n\n",P)
+printf(" Power lost in friction = %.2f kW.\n\n",Pf)
+printf(" Efficiency of the drive, eta = %.1f %c.\n\n",eta,"%")
\ No newline at end of file diff --git a/213/CH11/EX11.12/11_12.sce b/213/CH11/EX11.12/11_12.sce new file mode 100755 index 000000000..a65ac94fb --- /dev/null +++ b/213/CH11/EX11.12/11_12.sce @@ -0,0 +1,23 @@ +//To find power transmitted
+clc
+//Given:
+T0=2000 //N
+mu0=0.3
+theta=150*%pi/180 //radians
+r2=200/1000, d2=2*r2 //m
+N2=500//rpm
+//Solution:
+//Calculating the velocity of the belt
+v=%pi*d2*N2/60 //m/s
+//Calculating the tensions in the belt
+//Initial tension, T0 = (T1+T2)/2, or T1+T2 = 2*T0
+//Ratio of the tensions in the belt, log(T1/T2) = mu*theta, or T1-T2*exp(mu*theta) = 0
+A=[1 1; 1 -exp(mu*theta)]
+B=[2*T0; 0]
+V=A \ B
+T1=V(1) //N
+T2=V(2) //N
+//Calculating the power transmitted
+P=(T1-T2)*v/1000 //kW
+//Results:
+printf("\n\n Power transmitted, P = %.1f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH11/EX11.13/11_13.sce b/213/CH11/EX11.13/11_13.sce new file mode 100755 index 000000000..ce01bbf34 --- /dev/null +++ b/213/CH11/EX11.13/11_13.sce @@ -0,0 +1,29 @@ +//To find power trnasmitted
+clc
+//Given:
+x=4.8, d1=1.5, d2=1 //m
+T0=3*1000 //N
+m=1.5 //kg/m
+mu=0.3
+N2=400 //rpm
+//Solution:
+//Calculating the velocity of the belt
+v=%pi*d2*N2/60 //m/s
+//Calculating the centrifugal tension
+TC=m*v^2 //N
+//Calculating the angle alpha
+alpha=asin((d1-d2)/(2*x))*180/%pi //degrees
+//Calculating the angle of lap for the smaller pulley
+theta=(180-2*alpha)*%pi/180 //radians
+//Calculating the tensions in the belt
+//Initial tension, T0 = (T1+T2+2*TC)/2, or T1+T2 = 2*(T0-TC)
+//Ratio of tensions in the belt, log(T1/T2) = mu*theta, or T1-T2*exp(mu*theta) = 0
+A=[1 1; 1 -exp(mu*theta)]
+B=[2*(T0-TC); 0]
+V=A \ B
+T1=V(1) //N
+T2=V(2) //N
+//Calculating the power transmitted
+P=(T1-T2)*v/1000 //kW
+//Results:
+printf("\n\n Power transmitted, P = %.1f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH11/EX11.14/11_14.sce b/213/CH11/EX11.14/11_14.sce new file mode 100755 index 000000000..ad315c46b --- /dev/null +++ b/213/CH11/EX11.14/11_14.sce @@ -0,0 +1,30 @@ +//To find diameter, power and tension
+clc
+//Given:
+x=1.2, d2=400/1000, t=5/1000, b=80/1000 //m
+N1=350, N2=140 //rpm
+mu=0.3
+sigma=1.4*10^6 //N/m^2
+//Solution:
+//Calculating the diameter of the driving pulley
+d1=d2*(N2/N1) //m
+//Maximum power transmitted by the belting:
+//Refer Fig. 11.18
+//Calculating the angle alpha
+alpha=asin((d2-d1)/(2*x))*180/%pi //degrees
+//Calculating the angle of contact of the belt on the driving pulley
+theta=(180-2*alpha)*%pi/180 //radians
+//Calculating the maximum tension to which the belt can be subjected
+T1=sigma*b*t //N
+//Calculating the tension in the slack side of the belt
+T2=T1/exp(mu*theta) //N
+//Calculating the velocity of the belt
+v=%pi*d1*N1/60 //m/s
+//Calculating the power transmitted
+P=(T1-T2)*v/1000 //kW
+//Calculating the required initial belt tension
+T0=(T1+T2)/2 //N
+//Results:
+printf("\n\n Diameter of the driving pulley, d1 = %.2f m.\n\n",d1)
+printf(" Maximum power transmitted by the belting, P = %.3f kW.\n\n",P)
+printf(" Required initial belt tension, T0 = %.1f N.\n\n",T0)
\ No newline at end of file diff --git a/213/CH11/EX11.15/11_15.sce b/213/CH11/EX11.15/11_15.sce new file mode 100755 index 000000000..bff97d8c8 --- /dev/null +++ b/213/CH11/EX11.15/11_15.sce @@ -0,0 +1,34 @@ +//To find width, tension and length
+clc
+//Given:
+d2=240/1000, d1=600/1000, x=3 //m
+P=4*1000 //W
+N2=300 //rpm
+mu=0.3
+T1s=10 //Safe working tension, N/mm width
+//Solution:
+//Minimum width of the belt:
+//Calculating the velocity of the belt
+v=%pi*d2*N2/60 //m/s
+//Calculating the angle alpha for an open belt drive
+alpha=asin((d1-d2)/(2*x))*180/%pi //degrees
+//Calculating the angle of lap on the smaller pulley
+theta=(180-2*alpha)*%pi/180 //radians
+//Calculating the tensions in the belt
+//Power transmitted, P = (T1-T2)*v, or T1-T2 = P/v
+//Ratio of tensions, log(T1/T2) = mu*theta, or T1-T2*exp(mu*theta) = 0
+A=[1 -1; 1 -exp(mu*theta)]
+B=[P/v; 0]
+V=A \ B
+T1=V(1) //N
+T2=V(2) //N
+//Calculating the minimum width of the belt
+b=T1/T1s //mm
+//Calculating the initial belt tension
+T0=(T1+T2)/2 //N
+//Calculating the length of the belt required
+L=%pi/2*(d1+d2)+2*x+(d1-d2)^2/(4*x) //m
+//Results:
+printf("\n\n Minimum width of the belt, b = %.1f mm.\n\n",b)
+printf(" Initial belt tension, T0 = %.1f N.\n\n",T0)
+printf(" Length of the belt required, L = %.2f m.\n\n",L)
\ No newline at end of file diff --git a/213/CH11/EX11.16/11_16.sce b/213/CH11/EX11.16/11_16.sce new file mode 100755 index 000000000..acfb26613 --- /dev/null +++ b/213/CH11/EX11.16/11_16.sce @@ -0,0 +1,62 @@ +//To find power transmitted
+clc
+//Given:
+d1=400/1000 ,d2=250/1000, x=2, mu=0.4 //m
+T=1200 //N
+v=10 //m/s
+//Solution:
+//Power transmitted:
+//Calculating the angle alpha for an open belt drive
+alpha=asin((d1-d2)/(2*x))*180/%pi //degrees
+//Calculating the angle of contact
+theta=(180-2*alpha)*%pi/180 //radians
+//Calculating the tension in the tight side of the belt
+T1=T //Neglecting centrifugal tension, N
+//Calculating the tension in the slack side of the belt
+T2=T1/exp(mu*theta) //N
+//Calculating the power transmitted
+P=(T1-T2)*v/1000 //kW
+//Results:
+printf("\n\n Power transmitted, P = %.2f kW.\n\n",P)
+//Power transmitted when initial tension is increased by 10%:
+//Calculating the initial tension
+T0=(T1+T2)/2 //N
+//Calculating the increased initial tension
+T0dash=T0+10/100*T0 //N
+//Calculating the corresponding tensions in the belt
+//We have, T0dash = (T1+T2)/2, or T1+T2 = 2*T0dash
+//Ratio of the tensions, log(T1/T2) = mu*theta, or T1-T2*exp(mu*theta) = 0
+A=[1 1; 1 -exp(mu*theta)]
+B=[2*T0dash; 0]
+V=A \ B
+T1=V(1) //N
+T2=V(2) //N
+//Calculating the power transmitted
+P1=(T1-T2)*v/1000 //kW
+//Power transmitted when coefficient of friction is increased by 10%:
+//Calculating the increased coefficient of friction
+mudash=mu+10/100*mu
+//Calculating the corresponding tensions in the belt
+//Ratio of the tensions, log(T1/T2) = mudash*theta, or T1-T2*exp(mudash*theta) = 0
+//Initial tension, T0 = (T1+T2)/2, or T1+T2 = 2*T0
+A=[1 -exp(mudash*theta); 1 1]
+B=[0; 2*T0]
+V=A \ B
+T1=V(1) //N
+T2=V(2) //N
+//Calculating the power transmitted
+P2=(T1-T2)*v/1000 //kW
+//Results:
+if P1>P2 then
+ printf(" Since the power transmitted by increasing the initial tension is more, therefore in order to increase the power transmitted we shall adopt the method of increasing the initial tension.\n\n")
+else
+ printf(" Since the power transmitted by increasing the coefficient of friction is more, therefore in order to increase the power transmitted we shall adopt the method of increasing the coefficient of friction.\n\n")
+end
+//Percentage increase in power:\
+//Calculating the percentage increase in power when the initial tension is increased
+I1=(P1-P)/P*100 //Percentage increase in power when the initial tension is increased, %
+//Calculating the percentage increase in power when coefficient of friction is increased
+I2=(P2-P)/P*100 //Percentage increase in power when coefficient of friction is increased, %
+//Results:
+printf(" Percentage increase in power when the initial tension is increased = %.2f %c.\n\n",I1,"%")
+printf(" Percentage increase in power when coefficient of friction is increased = %.1f %c.\n\n",I2,"%")
\ No newline at end of file diff --git a/213/CH11/EX11.17/11_17.sce b/213/CH11/EX11.17/11_17.sce new file mode 100755 index 000000000..a22a3eb7f --- /dev/null +++ b/213/CH11/EX11.17/11_17.sce @@ -0,0 +1,37 @@ +//To find power and shaft speed
+clc
+//Given:
+funcprot(0)
+beta=30/2 //degrees
+alpha=750*10^-6 //mm^2
+mu=0.12
+rho=1.2*1000 //kg/m^3
+sigma=7*10^6 //N/m^2
+d=300/1000 //m
+N=1500 //rpm
+//Solution:
+//Power transmitted:
+//Calculating the velocity of the belt
+v=%pi*d*N/60 //m/s
+//Calculating the mass of the belt per metre length
+l=1 //m
+m=alpha*l*rho //kg/m
+//Calculating the centrifugal tension
+TC=m*v^2 //N
+//Calculating the maximum tension in the belt
+T=sigma*alpha //N
+//Calculating the tension in the tight side of the belt
+T1=T-TC //N
+//Calculating the tension in the slack side of the belt
+theta=%pi //Angle of contact, radians
+T2=T1/exp(mu*theta*(1/sind(beta))) //N
+//Calculating the power transmitted
+P=(T1-T2)*v*2/1000 //kW
+//Shaft speed:
+//Calculating the belt speed for maximum power transmitted
+v1=sqrt(T/(3*m)) //m/s
+//Calculating the shaft speed for maximum power transmitted
+N1=v1*60/(%pi*d) //rpm
+//Results:
+printf("\n\n Power transmitted, P = %.3f kW.\n\n",P)
+printf(" Shaft speed at which the power transmitted would be maximum, N1 = %d rpm.\n\n",N1)
\ No newline at end of file diff --git a/213/CH11/EX11.18/11_18.sce b/213/CH11/EX11.18/11_18.sce new file mode 100755 index 000000000..a99ec1196 --- /dev/null +++ b/213/CH11/EX11.18/11_18.sce @@ -0,0 +1,25 @@ +//To find maximum power transmitted
+clc
+//Given:
+funcprot(0)
+beta=30/2 //degrees
+t=20/1000, b=20/1000 //m
+m=0.35 //kg/m
+sigma=1.4*10^6 //N/m^2
+theta=140*%pi/180 //radians
+mu=0.15
+//Solution:
+//Calculating the maximum tension in the belt
+T=sigma*b*t //N
+//Calculating the velocity of the belt for maximum power to be transmitted
+v=sqrt(T/(3*m)) //m/s
+//Calculating the centrifugal tension
+TC=T/3 //N
+//Calculating the tension in the tight side of the belt
+T1=T-TC //N
+//Calculating the tension in the slack side of the belt
+T2=T1/exp(mu*theta*(1/sind(beta))) //N
+//Calculating the maximum power transmitted
+P=(T1-T2)*v/1000 //kW
+//Results:
+printf("\n\n Maximum power transmitted, P = %.2f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH11/EX11.19/11_19.sce b/213/CH11/EX11.19/11_19.sce new file mode 100755 index 000000000..fa1e4896e --- /dev/null +++ b/213/CH11/EX11.19/11_19.sce @@ -0,0 +1,41 @@ +//To find number of V-belts
+clc
+//Given:
+P=90 //kW
+N2=250, N1=750 //rpm
+d2=1, x=1.75 //m
+v=1600/60 //m/s
+a=375*10^-6 //m^2
+rho=1000 //kg/m^3
+sigma=2.5*10^6 //N/m^2
+beta=35/2 //degrees
+mu=0.25
+//Solution:
+//Calculating the diameter of the pulley on the motor shaft
+d1=d2*(N2/N1) //m
+//Calculating the mass of the belt per metre length
+l=1 //m
+m=a*l*rho //kg/m
+//Calculating the centrifugal tension
+TC=m*v^2 //N
+//Calculating the maximum tension in the belt
+T=sigma*a //N
+//Calculating the tension in the tight side of the belt
+T1=T-TC //N
+//Refer Fig. 11.21
+//Calculating the angle alpha
+alpha=asin((d2-d1)/(2*x))*180/%pi //degrees
+//Calculating the angle of lap on smaller pulley
+theta=(180-2*alpha)*%pi/180 //radians
+//Calculating the tension in the slack side of the belt
+T2=T1/exp(mu*theta*(1/sind(beta))) //N
+//Number of V-belts:
+//Calculating the power transmitted per belt
+P1=(T1-T2)*v/1000 //Power transmitted per belt, kW
+//Calculating the number of V-belts
+n=P/P1 //Number of V-belts
+//Calculating the length each of belt for an open belt drive
+L=%pi/2*(d2+d1)+2*x+(d2-d1)^2/(4*x) //m
+//Results:
+printf("\n\n Number of V-belts = %d.\n\n",n+1)
+printf(" Length of each belt, L = %.3f m.\n\n",L)
\ No newline at end of file diff --git a/213/CH11/EX11.2/11_2.sce b/213/CH11/EX11.2/11_2.sce new file mode 100755 index 000000000..338f4ccb5 --- /dev/null +++ b/213/CH11/EX11.2/11_2.sce @@ -0,0 +1,15 @@ +//To find speed lost
+clc
+//Given:
+d1=1, d2=2.25 //m
+N1=200 //rpm
+sigma1=1.4*10^6, sigma2=0.5*10^6, E=100*10^6 //N/m^2
+//Solution:
+//Calculating the speed of the driven pulley
+N21=N1*(d1/d2) //rpm
+//Calculating the speed of the shaft considering creep
+N22=N1*(d1/d2)*(E+sqrt(sigma2))/(E+sqrt(sigma1)) //rpm
+//Calculating the speed lost by the driven pulley due to creep
+Nl=N21-N22 //Speed lost by the driven pulley due to creep, rpm
+//Results:
+printf("\n\n Speed lost by the driven pulley due to creep = %.4f rpm.\n\n",Nl)
\ No newline at end of file diff --git a/213/CH11/EX11.20/11_20.sce b/213/CH11/EX11.20/11_20.sce new file mode 100755 index 000000000..dcbb3dddd --- /dev/null +++ b/213/CH11/EX11.20/11_20.sce @@ -0,0 +1,27 @@ +//To find number of ropes required
+clc
+//Given:
+P=600 //kW
+d=4 //m
+N=90 //rpm
+theta=160*%pi/180 //radians
+funcprot(0)
+beta=45/2 //degrees
+mu=0.28
+m=1.5 //kg/m
+T=2400 //N
+//Solution:
+//Calculating the velocity of the rope
+v=%pi*d*N/60 //m/s
+//Calculating the centrifugal tension
+TC=m*v^2 //N
+//Calculating the tension in the tight side of the rope
+T1=T-TC //N
+//Calculating the tension in the slack side of the belt
+T2=T1/exp(mu*theta*(1/sind(beta))) //N
+//Calculating the power transmitted per rope
+P1=(T1-T2)*v/1000 //Power transmitted per rope, kW
+//Calculating the number of ropes
+n=P/P1 //Number of ropes
+//Results:
+printf("\n\n Number of ropes required = %d.\n\n",n+1)
\ No newline at end of file diff --git a/213/CH11/EX11.21/11_21.sce b/213/CH11/EX11.21/11_21.sce new file mode 100755 index 000000000..d9b98a7fa --- /dev/null +++ b/213/CH11/EX11.21/11_21.sce @@ -0,0 +1,31 @@ +//To find speed of pulley
+clc
+//Given:
+d=3.6 //m
+n=15 //Number of grooves
+funcprot(0)
+beta=45/2 //degrees
+theta=170*%pi/180 //radians
+mu=0.28
+T=960 //N
+m=1.5 //kg/m
+//Solution:
+//Speed of the pulley:
+//Calculating the velocity of the rope
+v=sqrt(T/(3*m)) //m/s
+//Calculating the speed of the pulley
+N=v*60/(%pi*d) //rpm
+//Power transmitted
+//Calculating the centrifugal tension for maximum power
+TC=T/3 //N
+//Calculating the tension in the tight side of the rope
+T1=T-TC //N
+//Calculating the tension in the slack side of the rope
+T2=T1/exp(mu*theta*(1/sind(beta))) //N
+//Calculating the power transmitted per rope
+P1=(T1-T2)*v/1000 //Power transmitted per rope, kW
+//Calculating the total power transmitted
+P=P1*n //Total power transmitted, kW
+//Results:
+printf("\n\n Speed of the pulley for maximum power, N = %.1f rpm.\n\n",N)
+printf(" Power transmitted = %.2f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH11/EX11.22/11_22.sce b/213/CH11/EX11.22/11_22.sce new file mode 100755 index 000000000..042212217 --- /dev/null +++ b/213/CH11/EX11.22/11_22.sce @@ -0,0 +1,35 @@ +//To find initial tension and diameter
+clc
+//Given:
+PT=24 //kW
+d=400/1000 //m
+N=110 //rpm
+funcprot(0)
+beta=45/2 //degrees
+theta=160*%pi/180 //radians
+mu=0.28
+n=10
+//Solution:
+//Initial tension:
+//Calculating the power transmitted per rope
+P=PT/n*1000 //W
+//Calculating the velocity of the rope
+v=%pi*d*N/60 //m/s
+//Calculating the tensions in the rope
+//Power transmitted, P = (T1-T2)*v, or T1-T2 = P/v
+//Ratio of tensions, log(T1/T2) = mu*theta*(1/sind(beta)), or T1-T2*exp(mu*theta*(1/sind(beta))) = 0
+A=[1 -1; 1 -exp(mu*theta*(1/sind(beta)))]
+B=[P/v; 0]
+V=A \ B
+T1=V(1) //N
+T2=V(2) //N
+//Calculating the initial tension in each rope
+T0=(T1+T2)/2 //N
+//Diameter of each rope:
+//Calculating the girth of rope
+C=sqrt(T1/(122*10^3-53*v^2))*1000 //mm
+//Calculating the diameter of each rope
+d1=C/%pi //mm
+//Results:
+printf("\n\n Initial tension, T0 = %.2f N.\n\n",T0)
+printf(" Diameter of each rope, d1 = %.2f mm.\n\n",d1)
\ No newline at end of file diff --git a/213/CH11/EX11.23/11_23.sce b/213/CH11/EX11.23/11_23.sce new file mode 100755 index 000000000..c9a71bbfd --- /dev/null +++ b/213/CH11/EX11.23/11_23.sce @@ -0,0 +1,21 @@ +//To find pitch and length of chain
+clc
+//Given:
+N1=240, N2=120 //rpm
+T1=20
+d2=600/1000, r2=d2/2, x=800/1000 //m
+//SOlution:
+//Calculating the number of teeth on the drive sprocket
+T2=T1*(N1/N2)
+//Calculating the pitch of the chain
+p=r2*2*sind(180/T2)*1000 //mm
+//Length of the chain:
+m=x*1000/p
+//Calculating the multiplying factor
+K=(T1+T2)/2+2*m+(1/sind(180/T1)-1/sind(180/T2))^2/(4*m)
+//Calculating the length of the chain
+L=p*K/1000 //m
+//Results:
+printf("\n\n Number of teeth on the driven sprocket, T2 = %d.\n\n",T2)
+printf(" Pitch of the chain, p = %.1f mm.\n\n",p)
+printf(" Length of the chain, L = %.4f m.\n\n",L)
\ No newline at end of file diff --git a/213/CH11/EX11.3/11_3.sce b/213/CH11/EX11.3/11_3.sce new file mode 100755 index 000000000..a9c5cd144 --- /dev/null +++ b/213/CH11/EX11.3/11_3.sce @@ -0,0 +1,63 @@ +//To find radii of stepped pulleys
+clc
+//Given:
+N1=160, N3=N1, N5=N3, N2=60, N4=80, N6=100 //rpm
+x=720, r1=40 //mm
+//Solution:
+//For a crossed belt:
+//Calcluating the radii of pulleys 2, 3, 4, 5, and 6
+r2=r1*(N1/N2) //mm
+//For pulleys 3 and 4, r4 = r3*(N3/N4), or r3*(N3/N4)-r4 = 0
+//For a crossed belt drive, r3+r4 = r1+r2
+A=[N3/N4 -1; 1 1]
+B=[0; r1+r2]
+V=A \ B
+r3=V(1) //mm
+r4=V(2) //mm
+//For pulleys 5 and 6, r6 = r5*(N5/N6), or r5*(N5/N6)-r6 = 0
+//For a crossed belt drive, r5+r6 = r1+r2
+A=[N5/N6 -1; 1 1]
+B=[0; r1+r2]
+V=A \ B
+r5=V(1) //mm
+r6=V(2) //mm
+//Results:
+printf("\n\n For a crossed belt,\n r2 = %.1fmm;\n",r2)
+printf(" r3 = %.1f mm;\n",r3)
+printf(" r4 = %.1f mm;\n",r4)
+printf(" r5 = %.1f mm;\n",r5)
+printf(" r6 = %.1f mm.\n\n",r6)
+//For an open belt:
+//Calcluating the radii of pulleys 2, 3, 4, 5, and 6
+r2=r1*(N1/N2) //mm
+//Calculating the length of belt for an open belt drive
+L=%pi*(r1+r2)+(r2-r1)^2/x+2*x //mm
+//For pulleys 3 and 4, r4 = r3*(N3/N4), or r3*(N3/N4)-r4 = 0
+//Since L is constant, for pulleys 3 and 4, %pi*(r3+r4)+(r4-r3)^2/x+2*x-L = 0
+funcprot(0)
+function y=f(a)
+ r3=a(1)
+ r4=a(2)
+ y(1)=r3*(N3/N4)-r4
+ y(2)=%pi*(r3+r4)+(r4-r3)^2/x+2*x-L
+endfunction
+z=fsolve([1,1],f)
+r3=z(1) //mm
+r4=z(2) //mm
+//For pulleys 5 and 6, r6 = r5*(N5/N6), or r5*(N5/N6)-r6 = 0
+//Since L is constant, for pulleys 5 and 6, %pi*(r5+r6)+(r6-r5)^2/x+2*x-L = 0
+function y=f(a)
+ r5=a(1)
+ r6=a(2)
+ y(1)=r5*(N5/N6)-r6
+ y(2)=%pi*(r5+r6)+(r6-r5)^2/x+2*x-L
+endfunction
+z=fsolve([1,1],f)
+r5=z(1) //mm
+r6=z(2) //mm
+//Results:
+printf(" For an open belt,\n r2 = %.1fmm,\n",r2)
+printf(" r3 = %.1f mm;\n",r3)
+printf(" r4 = %.1f mm;\n",r4)
+printf(" r5 = %d mm;\n",r5)
+printf(" r6 = %d mm.\n\n",r6)
\ No newline at end of file diff --git a/213/CH11/EX11.4/11_4.sce b/213/CH11/EX11.4/11_4.sce new file mode 100755 index 000000000..77e235ba9 --- /dev/null +++ b/213/CH11/EX11.4/11_4.sce @@ -0,0 +1,17 @@ +//To find the power transmitted
+clc
+//Given:
+d=600/1000 //m
+N=200 //rpm
+mu=0.25
+theta=160*%pi/180 //radians
+T1=2500 //N
+//Solution:
+//Calcluating the velocity of the belt
+v=%pi*d*N/60 //m/s
+//Calcluating the tension in the slack side of the belt
+T2=T1/exp(mu*theta) //N
+//Calcluating the power transmitted by the belt
+P=(T1-T2)*v/1000 //kW
+//Results:
+printf("\n\n Power transmitted by the belt, P = %.2f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH11/EX11.5/11_5.sce b/213/CH11/EX11.5/11_5.sce new file mode 100755 index 000000000..80ba46d10 --- /dev/null +++ b/213/CH11/EX11.5/11_5.sce @@ -0,0 +1,21 @@ +//To find force and power
+clc
+//Given:
+W=9*1000, T1=W //N
+d=300/1000 //m
+N=20 //rpm
+mu=0.25
+//Solution:
+//Force required by the man:
+//Calculating the angle of contact
+theta=2.5*2*%pi //rad
+//Calculating the force required by the man
+T2=T1/exp(mu*theta) //N
+//Power to raise the casting:
+//Calculating the velocity of the rope
+v=%pi*d*N/60 //m/s
+//Calculating the power to raise the casting
+P=(T1-T2)*v/1000 //kW
+//Results:
+printf("\n\n Force required by the man, T2 = %.2f N.\n\n",T2)
+printf(" Power to raise the casting, P = %.3f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH11/EX11.6/11_6.sce b/213/CH11/EX11.6/11_6.sce new file mode 100755 index 000000000..0dbbda7dc --- /dev/null +++ b/213/CH11/EX11.6/11_6.sce @@ -0,0 +1,27 @@ +//To find length and power transmitted
+clc
+//Given:
+d1=450/1000, r1=d1/2, d2=200/1000, r2=d2/2, x=1.95 //m
+N1=200 //rpm
+T1=1*1000 //N
+mu=0.25
+//Solution:
+//Calculating the speed of the belt
+v=%pi*d1*N1/60 //m/s
+//Length of the belt:
+//Calculating the length of the crossed belt
+L=%pi*(r1+r2)+2*x+(r1+r2)^2/x //m
+//Angle of contact between the belt and each pulley:
+//Calculating the angle alpha
+alpha=asin((r1+r2)/x)*180/%pi //degrees
+//Calculating the angle of contact between the belt and each pulley
+theta=(180+2*alpha)*%pi/180 //radians
+//Power transmitted:
+//Calculating the tension in the slack side of the belt
+T2=T1/exp(mu*theta) //N
+//Calculating the power transmitted
+P=(T1-T2)*v/1000 //kW
+//Results:
+printf("\n\n Length of the belt, L = %.3f m.\n\n",L)
+printf(" Angle of contact between the belt and each pulley, theta = %.3f rad.\n\n",theta)
+printf(" Power transmitted, P = %.2f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH11/EX11.7/11_7.sce b/213/CH11/EX11.7/11_7.sce new file mode 100755 index 000000000..fcaa7605f --- /dev/null +++ b/213/CH11/EX11.7/11_7.sce @@ -0,0 +1,46 @@ +//To find stress in the belt
+clc
+//Given:
+N1=200, N2=300 //rpm
+P=6*1000 //W
+b=100, t=10 //mm
+x=4, d2=0.5 //m
+mu=0.3
+//Solution:
+//Stress in the belt for an open belt drive:
+//Calculating the diameter of the larger pulley
+d1=d2*(N2/N1) //m
+//Calculating the velocity of the belt
+v=%pi*d2*N2/60 //m/s
+//Calculating the angle alpha for an open belt drive
+alphao=asin((r1-r2)/x)*180/%pi //degrees
+//Calculating the angle of contact on the smaller pulley
+thetao=(180-2*alphao)*%pi/180 //radians
+//Calculating the tensions in the belt
+//Ratio of the tensions in the belt, T1/T2 = exp(mu*thetao), or T1-T2*exp(mu*thetao) = 0
+//Power transmitted, P = (T1-T2)*v, or T1-T2 = P/v
+A=[1 -exp(mu*thetao); 1 -1]
+B=[0; P/v]
+V=A \ B
+T1o=V(1) //N
+T2o=V(2) //N
+//Calculating the stress in the belt
+sigmao=T1o/(b*t) //MPa
+//Stress in the belt for a cross belt drive:
+//Calculating the angle alpha for a cross belt drive
+alphac=asin((d1+d2)/(2*x))*180/%pi //degrees
+//Calculating the angle of contact
+thetac=(180+2*alphac)*%pi/180 //radians
+//Calculating the tensions in the belt
+//Ratio of the tensions in the belt, T1/T2 = exp(mu*thetac), or T1-T2*exp(mu*thetac) = 0
+//Power transmitted, P = (T1-T2)*v, or T1-T2 = P/v
+A=[1 -exp(mu*thetac); 1 -1]
+B=[0; P/v]
+V=A \ B
+T1c=V(1) //N
+T2c=V(2) //N
+//Calculating the stress in the belt
+sigmac=T1c/(b*t) //MPa
+//Results:
+printf("\n\n Stress in the belt for an open belt drive, sigma = %.3f MPa.\n\n",sigmao)
+printf(" Stress in the belt for a cross belt drive, sigma = %.3f MPa.\n\n",sigmac)
\ No newline at end of file diff --git a/213/CH11/EX11.8/11_8.sce b/213/CH11/EX11.8/11_8.sce new file mode 100755 index 000000000..5120e437d --- /dev/null +++ b/213/CH11/EX11.8/11_8.sce @@ -0,0 +1,25 @@ +//To find width of the belt
+clc
+//Given:
+P=7.5*1000 //W
+d=1.2, t=10/1000 //m
+N=250 //rpm
+theta=165*%pi/180 //radians
+mu=0.3
+sigma=1.5*10^6 //N/m^2
+rho=1*10^3 //kg/m^3
+//Solution:
+//Calculating the velocity of the belt
+v=%pi*d*N/60 //m/s
+//Calculating the tensions in the belt
+//Power transmitted, P = (T1-T2)*v, or T1-T2 = P/v
+//Ratio of tensions in the belt, log(T1/T2) = mu*theta, or T1-T2*exp(mu*theta) = 0
+A=[1 -1; 1 -exp(mu*theta)]
+B=[P/v; 0]
+V=A \ B
+T1=V(1) //N
+T2=V(2) //N
+//Calculating the width of the belt
+b=T1/(sigma*t-t*1*rho*v^2)*1000 //mm
+//Results:
+printf("\n\n Width of the belt, b = %.1f mm.\n\n",b)
\ No newline at end of file diff --git a/213/CH11/EX11.9/11_9.sce b/213/CH11/EX11.9/11_9.sce new file mode 100755 index 000000000..7fe763423 --- /dev/null +++ b/213/CH11/EX11.9/11_9.sce @@ -0,0 +1,30 @@ +//To find width of the belt
+clc
+//Given:
+t=9.75/1000, d1=300/1000, x=3 //m
+P=15*1000 //W
+N1=900, N2=300 //rpm
+rho=1000 //kg/m^3
+sigma=2.5*10^6 //N/m^2
+mu=0.3
+//Solution:
+//Calculating the diameter of the driven pulley
+d2=d1*(N1/N2) //m
+//Calculating the velocity of the belt
+v=%pi*d1*N1/60 //m/s
+//Calculating the angle alpha for an open belt drive
+alpha=asin((d2-d1)/(2*x))*180/%pi //degrees
+//Calculating the angle of lap
+theta=(180-2*alpha)*%pi/180 //radians
+//Calculating the tensions in the belt
+//Ratio of tensions, log(T1/T2) = mu*theta, or T1-T2*exp(mu*theta) = 0
+//Power transmitted, P = (T1-T2)*v, or T1-T2 = P/v
+A=[1 -exp(mu*theta); 1 -1]
+B=[0; P/v]
+V=A \ B
+T1=V(1) //N
+T2=V(2) //N
+//Calculating the width of the belt
+b=T1/(sigma*t-t*1*rho*v^2)*1000 //mm
+//Results:
+printf("\n\n Width of the belt, b = %d mm.\n\n",b)
\ No newline at end of file diff --git a/213/CH12/EX12.1/12_1.sce b/213/CH12/EX12.1/12_1.sce new file mode 100755 index 000000000..3df604dae --- /dev/null +++ b/213/CH12/EX12.1/12_1.sce @@ -0,0 +1,18 @@ +//To find total load
+clc
+//Given:
+P=120*1000 //W
+d=250/1000, r=d/2 //m
+N=650 //rpm
+phi=20 //degrees
+//Solution:
+//Calculating the angular speed of the gear
+omega=2*%pi*N/60 //rad/s
+//Calculating the torque transmitted
+T=P/omega //N-m
+//Calculating the tangential load on the pinion
+FT=T/r //N
+//Calculating the total load due to power transmitted
+F=FT/(cosd(phi)*1000) //kN
+//Results:
+printf("\n\n Total load due to power transmitted, F = %.3f kN.\n\n",F)
\ No newline at end of file diff --git a/213/CH12/EX12.10/12_10.sce b/213/CH12/EX12.10/12_10.sce new file mode 100755 index 000000000..5fb0b6db8 --- /dev/null +++ b/213/CH12/EX12.10/12_10.sce @@ -0,0 +1,14 @@ +//To find number of teeth
+clc
+//Given:
+G=4
+phi=14.5 //degrees
+//Solution:
+//Least number of teeth on each wheel:
+//Calculating the least number of teeth on the pinion
+t=2*%pi/tand(phi)
+//Calculating the least number of teeth on the gear
+T=G*t
+//Results:
+printf("\n\n Least number of teeth on the pinion, t = %d.\n\n",t+1)
+printf(" Least number of teeth on the gear, T = %d.\n\n",T+1)
\ No newline at end of file diff --git a/213/CH12/EX12.11/12_11.sce b/213/CH12/EX12.11/12_11.sce new file mode 100755 index 000000000..be73ff060 --- /dev/null +++ b/213/CH12/EX12.11/12_11.sce @@ -0,0 +1,43 @@ +//To find addenda and velocity
+clc
+//Given:
+phi=16 //degrees
+m=6 //mm
+t=16, G=1.75, T=G*t
+N1=240 //rpm
+//Solution:
+//Calculating the angular speed of the pinion
+omega1=2*%pi*N1/60 //rad/s
+//Addenda on pinion and gear wheel:
+//Calculating the addendum on pinion
+addendump=m*t/2*(sqrt(1+T/t*(T/t+2)*(sind(phi))^2)-1) //Addendum on pinion, mm
+//Calculating the addendum on wheel
+addendumg=m*T/2*(sqrt(1+t/T*(t/T+2)*(sind(phi))^2)-1) //Addendum on wheel, mm
+//Length of path of contact:
+//Calculating the pitch circle radius of wheel
+R=m*T/2 //mm
+//Calculating the pitch circle radius of pinion
+r=m*t/2 //mm
+//Calculating the addendum circle radius of wheel
+RA=R+addendump //mm
+//Calculating the addendum circle radius of pinion
+rA=r+addendumg //mm
+//Calculating the length of path of approach
+KP=sqrt(RA^2-R^2*(cosd(phi))^2)-R*sind(phi) //mm
+//Calculating the length of path of recess
+PL=sqrt(rA^2-r^2*(cosd(phi))^2)-r*sind(phi) //mm
+//Calculating the length of path of contact
+KL=KP+PL //mm
+//Maximum velocity of sliding of teeth on either side of pitch point:
+//Calculating the angular speed of gear wheel
+omega2=omega1/G //rad/s
+//Calculating the maximum velocity of sliding of teeth on the left side of pitch point
+vmaxl=(omega1+omega2)*KP //Maximum velocity of sliding of teeth on the left side of pitch point, mm/s
+//Calculating the maximum velocity of sliding of teeth on the right side of pitch point
+vmaxr=(omega1+omega2)*PL //Maximum velocity of sliding of teeth on the right side of pitch point, mm/s
+//Results:
+printf("\n\n Addendum on pinion = %.2f mm.\n\n",addendump)
+printf(" Addendum on wheel = %.2f mm.\n\n",addendumg)
+printf(" Length of path of contact, KL = %.2f mm.\n\n",KL)
+printf(" Maximum velocity of sliding of teeth on the left side of pitch point = %d mm/s.\n\n",vmaxl)
+printf(" Maximum velocity of sliding of teeth on the right side of pitch point = %d mm/s.\n\n",vmaxr)
\ No newline at end of file diff --git a/213/CH12/EX12.12/12_12.sce b/213/CH12/EX12.12/12_12.sce new file mode 100755 index 000000000..5a8126cbd --- /dev/null +++ b/213/CH12/EX12.12/12_12.sce @@ -0,0 +1,43 @@ +//To find sliding velocities and contact ratio
+clc
+//Given:
+phi=20 //degrees
+t=30, T=50, m=4
+N1=1000 //rpm
+//Solution:
+//Calculating the angular speed of thr pinion
+omega1=2*%pi*N1/60 //rad/s
+//Sliding velocities at engagement and at disengagement of a pair of teeth:
+//Calculating the addendum of the smaller gear
+addendump=m*t/2*(sqrt(1+T/t*(T/t+2)*(sind(phi))^2)-1) //Addendum of the smaller gear, mm
+//Calculating the addendum of the larger gear
+addendumg=m*T/2*(sqrt(1+t/T*(t/T+2)*(sind(phi))^2)-1) //Addendum of the larger gear, mm
+//Calculating the pitch circle radius of the smaller gear
+r=m*t/2 //mm
+//Calculating the radius of addendum circle of the smaller gear
+rA=r+addendump //mm
+//Calculating the pitch circle radius of the larer gear
+R=m*T/2 //mm
+//Calculating the radius of addendum circle of the larger gear
+RA=R+addendumg //mm
+//Calculating the path of approach
+KP=sqrt(RA^2-R^2*(cosd(phi))^2)-R*sind(phi) //mm
+//Calculating the path of recess
+PL=sqrt(rA^2-r^2*(cosd(phi))^2)-r*sind(phi) //mm
+//Calculating the angular speed of the larger gear
+omega2=omega1*t/T //rad/s
+//Calculating the sliding velocity at engagement of a pair of teeth
+v1=(omega1+omega2)*KP //Sliding velocity at engagement of a pair of teeth, mm/s
+//Calculating the sliding velocity at disengagement of a pair of teeth
+v2=(omega1+omega2)*PL //Sliding velocity at disengagement of a pair of teeth, mm/s
+//Contact ratio:
+//Calculating the length of the arc of contact
+Lac=(KP+PL)/cosd(phi) //mm
+//Calculating the circular pitch
+pc=%pi*m //Circular pitch, mm
+//Calculating the contact ratio
+CR=Lac/pc //Contact ratio
+//Results:
+printf("\n\n Sliding velocity at engagement of a pair of teeth = %.3f m/s.\n\n",v1/1000)
+printf(" Sliding velocity at disengagement of a pair of teeth = %.3f m/s.\n\n",v2/1000)
+printf(" Contact ratio = %d.\n\n",CR+1)
\ No newline at end of file diff --git a/213/CH12/EX12.13/12_13.sce b/213/CH12/EX12.13/12_13.sce new file mode 100755 index 000000000..faa6accff --- /dev/null +++ b/213/CH12/EX12.13/12_13.sce @@ -0,0 +1,48 @@ +//To find teeth and velocity
+clc
+//Given:
+G=3
+m=6, AP=1*m, AW=AP //mm
+phi=20 //degrees
+N1=90 //rpm
+//Solution:
+//Calculating the angular speed of the pinion
+omega1=2*%pi*N1/60 //rad/s
+//Calculating the number of teeth on the pinion to avoid interference on it
+t=2*AP/(sqrt(1+G*(G+2)*(sind(phi))^2)-1)
+//Calculating the corresponding number of teeth on the wheel
+T=G*t
+//Length of path and arc of contact:
+//Calculating the pitch circle radius of pinion
+r=m*t/2 //mm
+//Calculating the radius of addendum circle of pinion
+rA=r+AP //mm
+//Calculating the pitch circle radius of wheel
+R=m*T/2 //mm
+//Calculating the radius of addendum circle of wheel
+RA=R+AW //mm
+//Calculating the path of approach
+KP=sqrt(RA^2-R^2*(cosd(phi))^2)-R*sind(phi) //mm
+//Calculating the path of recess
+PL=sqrt(rA^2-r^2*(cosd(phi))^2)-r*sind(phi) //mm
+//Calculating the length of path of contact
+KL=KP+PL //mm
+//Calculating the length of arc of contact
+Lac=KL/cosd(phi) //Length of arc of contact, mm
+//Number of pairs of teeth in contact:
+//Calculating the circular pitch
+pc=%pi*m //mm
+//Calculating the number of pairs of teeth in contact
+n=Lac/pc //Number of pairs of teeth in contact
+//Maximum velocity of sliding:
+//Calculating the angular speed of wheel
+omega2=omega1*t/T //rad/s
+//Calculating the maximum velocity of sliding
+vs=(omega1+omega2)*KP //mm/s
+//Results:
+printf("\n\n Number of teeth on the pinion to avoid interference, t = %d.\n\n",t+1)
+printf(" Corresponding number of teeth on the wheel, T = %d.\n\n",T+1)
+printf(" Length of path of contact, KL = %.2f mm.\n\n",KL)
+printf(" Length of arc of contact = %.2f mm.\n\n",Lac)
+printf(" Number of pairs of teeth in contact = %d.\n\n",n+1)
+printf(" Maximum velocity of sliding, vs = %.2f mm/s.\n\n",vs)
\ No newline at end of file diff --git a/213/CH12/EX12.14/12_14.sce b/213/CH12/EX12.14/12_14.sce new file mode 100755 index 000000000..908bdbfa4 --- /dev/null +++ b/213/CH12/EX12.14/12_14.sce @@ -0,0 +1,23 @@ +//To find pressure angle and teeth
+clc
+//Given:
+T=20
+d=125, r=d/2, OP=r, LH=6.25 //mm
+//Calculating the least pressure angle to avoid interference
+phi=asin(sqrt(LH/r))*180/%pi //degrees
+//Length of arc of contact:
+//Calculating the length of path of contact
+KL=sqrt((OP+LH)^2-(OP*cosd(phi))^2) //mm
+//Calculating the length of arc of contact
+Lac=KL/cosd(phi) //Length of arc of contact, mm
+//Minimum number of teeth:
+//Calculating the circular pitch
+pc=%pi*d/T //mm
+//Calculating the number of pairs of teeth in contact
+n=Lac/pc //Number of pairs of teeth in contact
+//Calculating the minimum number of teeth in contact
+nmin=n //Mimimum number of teeth in contact
+//Results:
+printf("\n\n Least pressure angle to avoid interference, phi = %.3f degrees.\n\n",phi)
+printf(" Length of arc of contact = %.2f mm.\n\n",Lac)
+printf(" Minimum number of teeth in contact = %d or %d pair.\n\n",nmin+1,(nmin+1)/2)
\ No newline at end of file diff --git a/213/CH12/EX12.15/12_15.sce b/213/CH12/EX12.15/12_15.sce new file mode 100755 index 000000000..a6c782c7f --- /dev/null +++ b/213/CH12/EX12.15/12_15.sce @@ -0,0 +1,40 @@ +//To find axial thrust
+clc
+//Given:
+L=175/1000, d2=100/1000, r2=d2/2 //m
+theta=70 //degrees
+G=1.5, T2=80
+Tf=75 //Torque on faster wheel, N-m
+funcprot(0)
+//Solution:
+//Spiral angles for each wheel:
+//Calculating the number of teeth on slower wheel
+T1=T2*G
+//Calculating the pitch circle diameter of the slower wheel
+d1=(L*2)-d2 //m
+//Calculating the spiral angles
+//We have, d2/d1 = (T2*cos(alpha1))/(T1*cos(alpha2)), or T2*d1*cos(alpha1)-T1*d2*cos(alpha2) = 0 .....(i)
+//Also, alpha1+alpha2 = theta, or alpha1+alpha2-theta = 0 .....(ii)
+function y=f(x)
+ alpha1=x(1)
+ alpha2=x(2)
+ y(1)=T2*d1*cos(alpha1)-T1*d2*cos(alpha2)
+ y(2)=alpha1+alpha2-theta*%pi/180
+endfunction
+z=fsolve([1,1],f)
+alpha1=z(1)*180/%pi //Spiral angle for slower wheel, degrees
+alpha2=z(2)*180/%pi //Spiral angle for faster wheel, degrees
+//Axial thrust on each shaft:
+//Calculating the tangential force at faster wheel
+F2=Tf/r2 //N
+//Calculating the normal reaction at the point of contact
+RN=F2/cosd(alpha2) //N
+//Calculating the axial thrust on the shaft of slower wheel
+Fa1=RN*sind(alpha1) //N
+//Calculating the axial thrust on the shaft of faster wheel
+Fa2=RN*sind(alpha2) //N
+//Results:
+printf("\n\n Spiral angle for slower wheel, alpha1 = %.2f degrees.\n\n",alpha1)
+printf(" Spiral angle for faster wheel, alpha2 = %.2f degrees.\n\n",alpha2)
+printf(" Axial thrust on the shaft of slower wheel, Fa1= %d N.\n\n",Fa1+1)
+printf(" Axial thrust on the shaft of faster wheel, Fa2 = %d N.\n\n",Fa2+1)
\ No newline at end of file diff --git a/213/CH12/EX12.16/12_16.sce b/213/CH12/EX12.16/12_16.sce new file mode 100755 index 000000000..3ae63bd26 --- /dev/null +++ b/213/CH12/EX12.16/12_16.sce @@ -0,0 +1,25 @@ +//To find teeth, distance and efficiency
+clc
+//Given:
+L=400/1000 //m
+G=3
+theta=50, phi=6 //degrees
+pN=18 //mm
+//Solution:
+//Number of teeth on each wheel:
+//Calculating the spiral angles of the driving and driven wheels
+alpha1=theta/2 //degrees
+alpha2=alpha1 //degrees
+//Calculating the number of teeth on driver wheel
+T1=L*1000*2*%pi/(pN*(1/cosd(alpha1)+G/cosd(alpha2)))
+//Calculating the number of teeth on driven wheel
+T2=G*T1
+//Calculating the exact centre distance
+L1=pN*T1/(2*%pi)*(1/cosd(alpha1)+G/cosd(alpha2)) //mm
+//Calculating the efficiency of the drive
+eta=(cosd(alpha2+phi)*cosd(alpha1))/(cosd(alpha1-phi)*cosd(alpha2))*100 //%
+//Results:
+printf("\n\n Number of teeth on driver wheel, T1 = %d.\n\n",T1+1)
+printf(" Number of teeth on driven wheel, T2 = %d.\n\n", T2+1)
+printf(" Exact centre distance, L1 = %.1f mm.\n\n",L1)
+printf(" Efficiency of the drive, eta = %.1f %c.\n\n",eta,"%")
\ No newline at end of file diff --git a/213/CH12/EX12.17/12_17.sce b/213/CH12/EX12.17/12_17.sce new file mode 100755 index 000000000..5547bf310 --- /dev/null +++ b/213/CH12/EX12.17/12_17.sce @@ -0,0 +1,39 @@ +//To find angle, teeth and efficiency
+clc
+//Given:
+pN=12.5, L=134 //mm
+theta=80, phi=6 //degrees
+G=1.25
+//Solution:
+funcprot(0)
+//Spiral angle of each wheel:
+//Calculating the spiral angles of wheels 1 and 2
+//We have, d2/d1 = (T2*cos(alpha1))/(T1*cos(alpha2)), or cos(alpha1)-G*cos(alpha2) = 0 .....(i)
+//Also, alpha1+alpha2 = theta, or alpha1+alpha2-theta = 0 .....(ii)
+function y=f(x)
+ alpha1=x(1)
+ alpha2=x(2)
+ y(1)=cos(alpha1)-G*cos(alpha2)
+ y(2)=alpha1+alpha2-theta*%pi/180
+endfunction
+z=fsolve([1,1],f)
+alpha1=z(1)*180/%pi //Spiral angle for slower wheel, degrees
+alpha2=z(2)*180/%pi //Spiral angle for faster wheel, degrees
+//Number of teeth on each wheel:
+//Calculating the diameters of the wheels
+d1=L, d2 = d1 //mm
+//Calculating the number of teeth on wheel 1
+T1=d1*%pi*cosd(alpha1)/pN
+//Calculating the number of teeth on wheel 2
+T2=T1/G
+//Calculating the efficiency of the drive
+eta=(cosd(alpha2+phi)*cosd(alpha1))/(cosd(alpha1-phi)*cosd(alpha2))*100 //%
+//Calculating the maximum efficiency
+etamax=(cosd(theta+phi)+1)/(cosd(theta-phi)+1)*100 //%
+//Results:
+printf("\n\n Spiral angle for slower wheel, alpha1 = %.2f degrees.\n\n",alpha1)
+printf(" Spiral angle for faster wheel, alpha2 = %.2f degrees.\n\n",alpha2)
+printf(" Number of teeth on wheel 1, T1 = %d.\n\n",T1+1)
+printf(" Number of teeth on wheel 2, T2 = %d.\n\n",T2+1)
+printf(" Efficiency of the drive, eta = %d %c.\n\n",eta+1,"%")
+printf(" Maximum efficiency, etamax = %.1f %c.\n\n",etamax,"%")
\ No newline at end of file diff --git a/213/CH12/EX12.2/12_2.sce b/213/CH12/EX12.2/12_2.sce new file mode 100755 index 000000000..051303b2c --- /dev/null +++ b/213/CH12/EX12.2/12_2.sce @@ -0,0 +1,22 @@ +//To find addendum
+clc
+//Given:
+T=40, t=T
+phi=20 //degrees
+m=6 //mm
+//Solution:
+//Calculating the circular pitch
+pc=%pi*m //mm
+//Calculating the length of arc of contact
+Lac=1.75*pc //Length of arc of contact, mm
+//Calculating the length of path of contact
+Lpc=Lac*cosd(phi) //Length of path of contact, mm
+//Calculating the pitch circle radii of each wheel
+R=m*T/2 //mm
+r=R //mm
+//Calculating the radius of the addendum circle of each wheel
+RA=sqrt(R^2*(cosd(phi))^2+(Lpc/2+R*sind(phi))^2) //mm
+//Calculating the addendum of the wheel
+Ad=RA-R //Addendum of the wheel, mm
+//Results:
+printf("\n\n Addendum of the wheel = %.2f mm.\n\n",Ad)
\ No newline at end of file diff --git a/213/CH12/EX12.3/12_3.sce b/213/CH12/EX12.3/12_3.sce new file mode 100755 index 000000000..992afe861 --- /dev/null +++ b/213/CH12/EX12.3/12_3.sce @@ -0,0 +1,35 @@ +//To find length of path of contact
+clc
+//Given:
+t=30, T=80
+phi=20 //degrees
+m=12 //mm
+Addendum=10 //mm
+//Solution:
+//Length of path of contact:
+//Calculating the pitch circle radius of pinion
+r=m*t/2 //mm
+//Calculating the pitch circle radius of gear
+R=m*T/2 //mm
+//Calculating the radius of addendum circle of pinion
+rA=r+Addendum //mm
+//Calculating the radius of addendum circle of gear
+RA=R+Addendum //mm
+//Calculating the length of path of approach
+//Refer Fig. 12.11
+KP=sqrt(RA^2-R^2*(cosd(phi))^2)-R*sind(phi) //mm
+//Calculating the length of path of recess
+PL=sqrt(rA^2-r^2*(cosd(phi))^2)-r*sind(phi) //mm
+//Calculating the length of path of contact
+KL=KP+PL //mm
+//Calculating the length of arc of contact
+Lac=KL/cosd(phi) //Length of arc of contact, mm
+//Contact ratio:
+//Calculating the circular pitch
+Pc=%pi*m //mm
+//Calculating the contact ratio
+CR=Lac/pc //Contact ratio
+//Results:
+printf("\n\n Length of path of contact, KL = %.1f mm.\n\n",KL)
+printf(" Length of arc of contact = %.2f mm.\n\n",Lac)
+printf(" Contact ratio = %d.\n\n",CR)
\ No newline at end of file diff --git a/213/CH12/EX12.4/12_4.sce b/213/CH12/EX12.4/12_4.sce new file mode 100755 index 000000000..dcb5d38f3 --- /dev/null +++ b/213/CH12/EX12.4/12_4.sce @@ -0,0 +1,38 @@ +//To find angle and maximum velocity
+clc
+//Given:
+phi=20 //degrees
+t=20, G=2
+m=5 //mm
+v=1.2 //m/s
+addendum=1*m //mm
+//Solution:
+//Angle turned through by pinion when one pair of teeth is in mesh:
+//Calculating the pitch circle radius of pinion
+r=m*t/2 //mm
+//Calculating the pitch circle radius of wheel
+R=m*G*t/2 //mm
+//Calculating the radius of addendum circle of pinion
+rA=r+addendum //mm
+//Calculating the radius of addendum circle of wheel
+RA=R+addendum //mm
+//Calculating the length of path of approach
+KP=sqrt(RA^2-R^2*(cosd(phi))^2)-R*sind(phi) //mm
+//Calculating the length of path of recess
+PL=sqrt(rA^2-r^2*(cosd(phi))^2)-r*sind(phi) //mm
+//Calculating the length of path of contact
+KL=KP+PL //mm
+//Calculating the length of arc of contact
+Lac=KL/cosd(phi) //mm
+//Calculating the angle turned by the pinion
+angle=Lac*360/(2*%pi*r) //Angle turned by the pinion, degrees
+//Maximum velocity of sliding:
+//Calculating the angular speed of pinion
+omega1=v*1000/r //rad/s
+//Calculating the angular speed of wheel
+omega2=v*1000/R //rad/s
+//Calculating the maximum velocity of sliding
+vS=(omega1+omega2)*KP //mm/s
+//Results:
+printf("\n\n Angle turned through by pinion when one pair of teeth is in mesh = %.2f degrees.\n\n",angle)
+printf(" Maximum velocity of sliding, vS = %.1f mm/s.\n\n",vS)
\ No newline at end of file diff --git a/213/CH12/EX12.5/12_5.sce b/213/CH12/EX12.5/12_5.sce new file mode 100755 index 000000000..960de0ecf --- /dev/null +++ b/213/CH12/EX12.5/12_5.sce @@ -0,0 +1,42 @@ +//To find velocity and angle turned
+clc
+//Given:
+T=40, t=20
+N1=2000 //rpm
+phi=20 //degrees
+addendum=5, m=5 //mm
+//Solution:
+//Calculating the angular velocity of the smaller gear
+omega1=2*%pi*N1/60 //rad/s
+//Calculating the angular velocity of the larger gear
+omega2=omega1*t/T //rad/s
+//Calculating the pitch circle radius of the smaller gear
+r=m*t/2 //mm
+//Calculating the pitch circle radius of the larger gear
+R=m*T/2 //mm
+//Calculating the radius of aaddendum circle of smaller gear
+rA=r+addendum //mm
+//Calculating the radius of addendum circle of larger gear
+RA=R+addendum //mm
+//Calculating the length of path of approach
+KP=sqrt(RA^2-R^2*(cosd(phi))^2)-R*sind(phi) //mm
+//Calculating the length of path of recess
+PL=sqrt(rA^2-r^2*(cosd(phi))^2)-r*sind(phi) //mm
+//Calculating the velocity of sliding at the point of engagement
+vSK=(omega1+omega2)*KP //mm/s
+//Calculating the velocity of sliding at the point of disengagement
+vSL=(omega1+omega2)*PL //mm/s
+//Angle through which the pinion turns:
+//Calculating the length of path of contact
+KL=KP+PL //mm
+//Calculating the length of arc of contact
+Lac=KL/cosd(phi) //Length of arc of contact, mm
+//Calculating the circumference of pinion
+C=2*%pi*r //Circumference of pinion, mm
+//Calculating the angle through which the pinion turns
+angle=Lac*360/C //Angle through which the pinion turns, degrees
+//Results:
+printf("\n\n Velocity of sliding at the point of engagement, vSK = %d mm/s.\n\n",vSK)
+printf(" Since the velocity of sliding is proportional to the distance of the contact point from the pitch point, therefore the velocity of sliding at the pitch point is zero.\n\n")
+printf(" Velocity of sliding at the point of disengagement, vsL = %d mm/s.\n\n",vSL)
+printf(" Angle through which the pinion turns = %.2f degrees.\n\n",angle)
\ No newline at end of file diff --git a/213/CH12/EX12.6/12_6.sce b/213/CH12/EX12.6/12_6.sce new file mode 100755 index 000000000..1f666cba1 --- /dev/null +++ b/213/CH12/EX12.6/12_6.sce @@ -0,0 +1,46 @@ +//To find teeth, angle and ratio
+clc
+//Given:
+phi=20 //degrees
+m=6, addendum=1*m //mm
+t=17, T=49
+//Solution:
+//Number of pairs of teeth in contact:
+//Calculating the pitch circle radius of pinion
+r=m*t/2 //mm
+//Calculating the pitch circle radius of gear
+R=m*T/2 //mm
+//Calculating the radius of addendum circle of pinion
+rA=r+addendum //mm
+//Calculating the radius of addendum circle of gear
+RA=R+addendum //mm
+//Calculating the length of path of approach
+//Refer Fig. 12.11
+KP=sqrt(RA^2-R^2*(cosd(phi))^2)-R*sind(phi) //mm
+//Calculating the length of path of recess
+PL=sqrt(rA^2-r^2*(cosd(phi))^2)-r*sind(phi) //mm
+//Calculating the length of path of contact
+KL=KP+PL //mm
+//Calculating the length of arc of contact
+Lac=KL/cosd(phi) //Length of arc of contact, mm
+//Calculating the circular pitch
+pc=%pi*m //mm
+//Calculating the number of pairs of teeth in contact
+n=Lac/pc //Number of pairs of teeth in contact
+//Angle turned by the pinion and gear wheel when one pair of teeth is in contact:
+//Calculating the angle turned through by the pinion
+anglep=Lac*360/(2*%pi*r) //Angle turned through by the pinion, degrees
+//Calculating the angle turned through by the wheel
+angleg=Lac*360/(2*%pi*R) //Angle turned through by the gear wheel, degrees
+//Ratio of sliding to rolling motion:
+//At the instant when the tip of a tooth on the larger wheel is just making contact with its mating teeth
+r1=((1+t/T)*KP)/r //Ratio of sliding velocity to rolling velocity
+//At the instant when the tip of a tooth on a larger wheel is just leaving contact with its mating teeth
+r2=((1+t/T)*PL)/r //Ratio of sliding velocity to rolling velocity
+//Results:
+printf("\n\n Number of pairs of teeth in contact = %d.\n\n",n+1)
+printf(" Angle turned through by the pinion = %.1f degrees.\n\n",anglep)
+printf(" Angle turned through by the gear wheel = %d degrees.\n\n",angleg)
+printf(" At the instant when the tip of a tooth on the larger wheel is just making contact with its mating teeth, ratio of sliding velocity to rolling velocity = %.2f.\n\n",r1)
+printf(" At the instant when the tip of a tooth on a larger wheel is just leaving contact with its mating teeth, ratio of sliding velocity to rolling velocity = %.3f.\n\n",r2)
+printf(" Since at the pitch point, the sliding velocity is zero,, therefore the ratio of sliding velocity to rolling velocity is zero.\n\n")
\ No newline at end of file diff --git a/213/CH12/EX12.7/12_7.sce b/213/CH12/EX12.7/12_7.sce new file mode 100755 index 000000000..9790e6224 --- /dev/null +++ b/213/CH12/EX12.7/12_7.sce @@ -0,0 +1,30 @@ +//To find length of path of contact
+clc
+//Given:
+t=18, T=72
+phi=20 //degrees
+m=4 //mm
+addendump=8.5 //Addendum on pinion, mm
+addendumg=3.5 //Addendum on gear, mm
+//SOlution:
+//Refer Fig. 12.12
+//Calculating the pitch circle radius of the pinion
+r=m*t/2 //mm
+//Calculating the pitch circle radius of the gear
+R=m*T/2 //mm
+//Calculating the radius of addendum circle of the pinion
+rA=r+addendump //mm
+//Calculating the radius of addendum circle of the gear
+RA=R-addendumg //mm
+//Calculating the radius of the base circle of the pinion
+O1M=r*cosd(phi) //mm
+//Calculating the radius of the base circle of the gear
+O2N=R*cosd(phi) //mm
+//Calculating the length of path of approach
+KP=R*sind(phi)-sqrt(RA^2-O2N^2) //mm
+//Calculating the length of path of recess
+PL=sqrt(rA^2-O1M^2)-r*sind(phi) //mm
+//Calculating the length of the path of contact
+KL=KP+PL //mm
+//Results:
+printf("\n\n Length of the path of contact, KL = %.2f mm.\n\n",KL)
\ No newline at end of file diff --git a/213/CH12/EX12.8/12_8.sce b/213/CH12/EX12.8/12_8.sce new file mode 100755 index 000000000..43d4ba511 --- /dev/null +++ b/213/CH12/EX12.8/12_8.sce @@ -0,0 +1,35 @@ +//To find path and arc of contact
+clc
+//Given:
+t=20, T=40
+m=10 //mm
+phi=20 //degrees
+//Solution:
+//Addendum height for each gear wheel:
+//Calculating the pitch circle radius of the smaller gear wheel
+r=m*t/2 //mm
+//Calculating the pitch circle radius of the larger wheel
+R=m*T/2 //mm
+//Calculating the radius of addendum circle for the larger gear wheel
+RA=sqrt((r*sind(phi)/2+R*sind(phi))^2+R^2*(cosd(phi))^2) //mm
+//Calculating the addendum height for larger gear wheel
+addendumg=RA-R //mm
+//Calculating the radius of addendum circle for the smaller gear wheel
+rA=sqrt((R*sind(phi)/2+r*sind(phi))^2+r^2*(cosd(phi))^2) //mm
+//Calculating the addendum height for smaller gear wheel
+addendump=rA-r //mm
+//Calculating the length of the path of contact
+Lpc=(r+R)*sind(phi)/2 //Length of the path of contact, mm
+//Calculating the length of the arc of contact
+Lac=Lpc/cosd(phi) //Length of the arc of contact, mm
+//Contact ratio:
+//Calculating the circular pitch
+pc=%pi*m //mm
+//Calculating the contact ratio
+CR=Lpc/pc //Contact ratio
+//Results:
+printf("\n\n Addendum height for larger gear wheel = %.1f mm.\n\n",addendumg)
+printf(" Addendum height for smaller gear wheel = %.1f mm.\n\n",addendump)
+printf(" Length of the path of contact = %.1f mm.\n\n",Lpc)
+printf(" Length of the arc of contact = %.1f mm.\n\n",Lac)
+printf(" Contact ratio = %d.\n\n",CR+1)
\ No newline at end of file diff --git a/213/CH12/EX12.9/12_9.sce b/213/CH12/EX12.9/12_9.sce new file mode 100755 index 000000000..83efb753c --- /dev/null +++ b/213/CH12/EX12.9/12_9.sce @@ -0,0 +1,14 @@ +//To find number of teeth
+clc
+//Given:
+G=3
+phi=20 //degrees
+Aw=1 //module
+//Solution:
+//Calculating the minimum number of teeth for a gear ratio of 3:1
+t1=(2*Aw)/(G*(sqrt(1+1/G*(1/G+2)*(sind(phi))^2)-1))
+//Calculating the minimum number of teeth for equal wheel
+t2=(2*Aw)/(sqrt(1+3*(sind(phi))^2)-1)
+//Results:
+printf("\n\n Minimum number of teeth for a gear ratio of 3:1, t = %d.\n\n",t1+1)
+printf(" Minimum number of teeth for equal wheel, t = %d.\n\n",t2+1)
\ No newline at end of file diff --git a/213/CH13/EX13.1/13_1.sce b/213/CH13/EX13.1/13_1.sce new file mode 100755 index 000000000..6bb2f9b56 --- /dev/null +++ b/213/CH13/EX13.1/13_1.sce @@ -0,0 +1,10 @@ +//To find speed of gear F
+clc
+//Given:
+NA=975 //rpm
+TA=20, TB=50, TC=25, TD=75, TE=26, TF=65
+//Solution:
+//Calculating the speed of gear F
+NF=NA*(TA*TC*TE)/(TB*TD*TF) //rpm
+//Results:
+printf("\n\n Speed of gear F, NF = %d rpm.\n\n",NF)
\ No newline at end of file diff --git a/213/CH13/EX13.10/13_10.sce b/213/CH13/EX13.10/13_10.sce new file mode 100755 index 000000000..f01c34420 --- /dev/null +++ b/213/CH13/EX13.10/13_10.sce @@ -0,0 +1,22 @@ +//To find angular velocities
+clc
+//Given:
+TC=50, TD=20, TE=35
+NA=110 //rpm
+//Solution:
+//Calculating the number of teeth on internal gear G
+TG=TC+TD+TE
+//Speed of shaft B:
+//Calculating the values of x and y
+//From the fourth row of Table 13.9, y-x*(TC/TD)*(TE/TG) = 0 .....(i)
+//Also, x+y = 110, or y+x = 110 .....(ii)
+A=[1 -(TC/TD)*(TE/TG); 1 1]
+B=[0; 110]
+V=A \ B
+x=V(2)
+y=V(1)
+//Calculating the speed of shaft B
+NB=round(+y) //Speed of shaft B, rpm
+//Results:
+printf("\n\n Number of teeth on internal gear G, TG = %d.\n\n",TG)
+printf(" Speed of shaft B = %d rpm, anticlockwise.\n\n",NB)
\ No newline at end of file diff --git a/213/CH13/EX13.11/13_11.sce b/213/CH13/EX13.11/13_11.sce new file mode 100755 index 000000000..fb266fb58 --- /dev/null +++ b/213/CH13/EX13.11/13_11.sce @@ -0,0 +1,29 @@ +//To find angular velocities
+clc
+//Given:
+TA=12, TB=30, TC=14
+NA=1, ND=5 //rps
+//Solution:
+//Number of teeth on wheels D and E:
+//Calculating the number of teeth on wheel E
+TE=TA+2*TB
+//Calculating the number of teeth on wheel E
+TD=TE-(TB-TC)
+//Magnitude and direction of angular velocities of arm OP and wheel E:
+//Calculating the values of x and y
+//From the fourth row of Table 13.10, -x-y = -1, or x+y = 1 .....(i)
+//Also, x*(TA/TB)*(TC/TD)-y = 5 .....(ii)
+A=[1 1; (TA/TB)*(TC/TD) -1]
+B=[1; 5]
+V=A \ B
+x=V(1)
+y=V(2)
+//Calculating the angular velocity of arm OP
+omegaOP=-y*2*%pi //Angular velocity of arm OP, rad/s
+//Calculating the angular velocity of wheel E
+omegaE=(x*TA/TE-y)*2*%pi //Angular velocity of wheel E, rad/s
+//Results:
+printf("\n\n Number of teeth on wheel E, TE = %d.\n\n",TE)
+printf(" Number of teeth on wheel D, TD = %d.\n\n",TD)
+printf(" Angular velocity of arm OP = %.3f rad/s, counter clockwise.\n\n",omegaOP)
+printf(" Angular velocity of wheel E = %.2f rad/s, counter clockwise.\n\n",omegaE)
\ No newline at end of file diff --git a/213/CH13/EX13.12/13_12.sce b/213/CH13/EX13.12/13_12.sce new file mode 100755 index 000000000..3ec839da8 --- /dev/null +++ b/213/CH13/EX13.12/13_12.sce @@ -0,0 +1,15 @@ +//To find speed of shaft
+clc
+//Given:
+TB=80, TC=82, TD=28
+NA=500 //rpm
+//Solution:
+//Calculating the number of teeth on wheel E
+TE=TB+TD-TC
+//Calculating the values of x and y
+y=800
+x=-y*(TE/TB)*(TC/TD)
+//Calculating the speed of shaft F
+NF=x+y //Speed of shaft F, rpm
+//Results:
+printf("\n\n Speed of shaft F = %d rpm, anticlockwise.\n\n",NF)
\ No newline at end of file diff --git a/213/CH13/EX13.14/13_14.sce b/213/CH13/EX13.14/13_14.sce new file mode 100755 index 000000000..af75d66aa --- /dev/null +++ b/213/CH13/EX13.14/13_14.sce @@ -0,0 +1,27 @@ +//To find number of teeth and speed
+clc
+//Given:
+NA=300 //rpm
+TD=40, TE=30, TF=50, TG=80, TH=40, TK=20, TL=30
+//Solution:
+//Refer Fig. 13.18 and Table 13.13
+//Calculating the speed of wheel E
+NE=NA*(TD/TE) //rpm
+//Calculating the number of teeth on wheel C
+TC=TH+TK+TL
+//Speed and direction of rotation of shaft B:
+//Calculating the values of x and y
+//We have, -x-y = -400, or x+y = 400 .....(i)
+//Also, x*(TH/TK)*(TL/TC)-y = 0 .....(ii)
+A=[1 1; (TH/TK)*(TL/TC) -1]
+B=[400; 0]
+V=A \ B
+x=V(1)
+y=V(2)
+//Calculating the speed of wheel F
+NF=-y //rpm
+//Calculating the speed of shaft B
+NB=-NF*(TF/TG) //Speed of shaft B, rpm
+//Results:
+printf("\n\n Number of teeth on wheel C, TC = %d.\n\n",TC)
+printf(" Speed of shaft B = %d rpm, anticlockwise.\n\n",NB)
\ No newline at end of file diff --git a/213/CH13/EX13.15/13_15.sce b/213/CH13/EX13.15/13_15.sce new file mode 100755 index 000000000..31a76df2f --- /dev/null +++ b/213/CH13/EX13.15/13_15.sce @@ -0,0 +1,36 @@ +//To find velocity ratio
+clc
+//Given:
+T1=80, T8=160, T4=100, T3=120, T6=20, T7=66
+//Solution:
+//Refer Fig. 13.19 and Table 13.14
+//Calculating the number of teeth on wheel 2
+T2=(T3-T1)/2
+//Calculating the values of x and y
+//Assuming that wheel 1 makes 1 rps anticlockwise, x+y = 1 .....(i)
+//Also, y-x*(T1/T3) = 0, or x*(T1/T3)-y = 0 .....(ii)
+A=[1 1; 1 T1/T3]
+B=[1; 0]
+V=A \ B
+x=V(1)
+y=V(2)
+//Calculating the speed of casing C
+NC=y //Speed of casing C, rps
+//Calculating the speed of wheel 2
+N2=y-x*(T1/T2) //Speed of wheel 2, rps
+//Calculating the number of teeth on wheel 5
+T5=(T4-T6)/2
+//Calculating the values of x1 and y1
+y1=-2
+x1=(y1-0.4)*(T4/T6)
+//Calculating the speed of wheel 6
+N6=x1+y1 //Speed of wheel 6, rps
+//Calculating the values of x2 and y2
+y2=0.4
+x2=-(14+y2)*(T7/T8)
+//Calculating the speed of wheel 8
+N8=x2+y2 //Speed of wheel 8, rps
+//Calculating the velocity ratio of the output shaft B to the input shaft A
+vr=N8/1 //Velocity ratio
+//Results:
+printf("\n\n Velocity ratio of the output shaft B to the input shaft A = %.2f.\n\n",vr)
\ No newline at end of file diff --git a/213/CH13/EX13.16/13_16.sce b/213/CH13/EX13.16/13_16.sce new file mode 100755 index 000000000..ea27b8148 --- /dev/null +++ b/213/CH13/EX13.16/13_16.sce @@ -0,0 +1,15 @@ +//To find speed of shaft
+clc
+//Given:
+TA=40, TB=30, TC=50
+NX=100, NA=NX //rpm
+Narm=100 //Speed of arm, rpm
+//Solution:
+//Refer Fig. 13.22 and Table 13.18
+//Calculating the values of x and y
+y=+100
+x=-100-y
+//Calculating the speed of the driven shaft
+NY=y-x*(TA/TB) //rpm
+//Results:
+printf("\n\n Speed of the driven shaft, NY = %.1f rpm, anticlockwise.\n\n",NY)
\ No newline at end of file diff --git a/213/CH13/EX13.17/13_17.sce b/213/CH13/EX13.17/13_17.sce new file mode 100755 index 000000000..8ff336537 --- /dev/null +++ b/213/CH13/EX13.17/13_17.sce @@ -0,0 +1,32 @@ +//To find speed of output shaft
+clc
+//Given:
+TB=20, TC=80, TD=80, TE=30, TF=32
+NB=1000 //rpm
+//Solution:
+//Refer Fig. 13.23 and Table 13.19
+//Speed of the output shaft when gear C is fixed:
+//Calculating the values of x and y
+//From the fourth row of the table, y-x*(TB/TC) = 0 .....(i)
+//Also, x+y = +1000, or y+x = 1000 .....(ii)
+A=[1 -TB/TC; 1 1]
+B=[0; 1000]
+V=A \ B
+x=V(2)
+y=V(1)
+//Calculating the speed of output shaft
+NF1=y-x*(TB/TD)*(TE/TF) //Speed of the output shaft when gear C is fixed, rpm
+//Speed of the output shaft when gear C is rotated at 10 rpm counter clockwise:
+//Calculating the values of x and y
+//From the fourth row of te table, y-x*(TB/TC) = +10 .....(iii)
+//Also, x+y = +1000, or y+x = 1000 .....(iv)
+A=[1 -TB/TC; 1 1]
+B=[10; 1000]
+V=A \ B
+x=V(2)
+y=V(1)
+//Calculating the speed of output shaft
+NF2=y-x*(TB/TD)*(TE/TF) //Speed of the output shaft when gear C is rotated at 10 rpm counter clockwise, rpm
+//Results:
+printf("\n\n Speed of the output shaft when gear C is fixed = %.1f rpm, counter clockwise.\n\n",NF1)
+printf(" Speed of the output shaft when gear C is rotated at 10 rpm counter clockwise = %.1f rpm, counter clockwise.\n\n",NF2)
\ No newline at end of file diff --git a/213/CH13/EX13.18/13_18.sce b/213/CH13/EX13.18/13_18.sce new file mode 100755 index 000000000..8dded6a25 --- /dev/null +++ b/213/CH13/EX13.18/13_18.sce @@ -0,0 +1,16 @@ +//To find speed of road wheel
+clc
+//Given:
+TA=10, TB=60
+NA=1000, NQ=210, ND=NQ //rpm
+//Solution:
+//Refer Fig. 13.24 and Table 13.20
+//Calculating the speed of crown gear B
+NB=NA*(TA/TB) //rpm
+//Calculating the values of x and y
+y=200
+x=y-210
+//Calculating the speed of road wheel attached to axle P
+NC=x+y //Speed of road wheel attached to axle P, rpm
+//Results:
+printf("\n\n Speed of road wheel attached to axle P = %d rpm.\n\n",NC)
\ No newline at end of file diff --git a/213/CH13/EX13.19/13_19.sce b/213/CH13/EX13.19/13_19.sce new file mode 100755 index 000000000..9bf0a2781 --- /dev/null +++ b/213/CH13/EX13.19/13_19.sce @@ -0,0 +1,26 @@ +//To find torque exerted
+clc
+//Given:
+TA=15, TB=20, TC=15
+NA=1000 //rpm
+Tm=100 //Torque developed by motor, N-m
+//Solution:
+//Refer Fig. 13.26 and Table 13.21
+//Calculating the number of teeth on gears E and D
+TE=TA+2*TB
+TD=TE-(TB-TC)
+//Speed of the machine shaft:
+//From the fourth row of the table, x+y = 1000, or y+x = 1000 .....(i)
+//Also, y-x*(TA/TE) = 0 .....(ii)
+A=[1 1; 1 -TA/TE]
+B=[1000; 0]
+V=A \ B
+y=V(1)
+x=V(2)
+//Calculating the speed of machine shaft
+ND=y-x*(TA/TB)*(TC/TD) //rpm
+//Calculating the torque exerted on the machine shaft
+Ts=Tm*NA/ND //Torque exerted on the machine shaft, N-m
+//Results:
+printf("\n\n Speed of machine shaft, ND = %.2f rpm, anticlockwise.\n\n",ND)
+printf(" Torque exerted on the machine shaft = %d N-m.\n\n",Ts)
\ No newline at end of file diff --git a/213/CH13/EX13.2/13_2.sce b/213/CH13/EX13.2/13_2.sce new file mode 100755 index 000000000..9ccc357d4 --- /dev/null +++ b/213/CH13/EX13.2/13_2.sce @@ -0,0 +1,27 @@ +//To design the gears
+clc
+//Given:
+x=600, pc=25 //mm
+N1=360, N2=120 //rpm
+//Solution:
+//Calculating the pitch circle diameters of each gear
+//Speed ratio, N1/N2 = d2/d1, or N1*d1-N2*d2 = 0 .....(i)
+//Centre distance between the shafts, x = 1/2*(d1+d2), or d1+d2 = 600*2 .....(ii)
+A=[N1 -N2; 1 1]
+B=[0; 600*2]
+V=A \ B
+d1=V(1) //mm
+d2=V(2) //mm
+//Calculating the number of teeth on the first gear
+T1=round(%pi*d1/pc)
+//Calculating the number of teeth on the second gear
+T2=int(%pi*d2/pc+1)
+//Calculating the pitch circle diameter of the first gear
+d1dash=T1*pc/%pi //mm
+//Calculating the pitch circle diameter of the second gear
+d2dash=T2*pc/%pi //mm
+//Calculating the exact distance between the two shafts
+xdash=(d1dash+d2dash)/2 //mm
+//Results:
+printf("\n\n The number of teeth on the first and second gear must be %d and %d and their pitch circle diameters must be %.2f mm and %.1f mm respectively.\n\n",T1,T2,d1dash,d2dash)
+printf(" The exact distance between the two shafts must be %.2f mm.\n\n",xdash)
\ No newline at end of file diff --git a/213/CH13/EX13.20/13_20.sce b/213/CH13/EX13.20/13_20.sce new file mode 100755 index 000000000..c9550e416 --- /dev/null +++ b/213/CH13/EX13.20/13_20.sce @@ -0,0 +1,22 @@ +//To find teeth and torque
+clc
+//Given:
+Ts=100 //Torque on the sun wheel, N-m
+r=5 //Ratio of speeds of gear S to C, NS/NC
+//Refer Fig. 13.27 and Table 13.22
+//Number of teeth on different wheels:
+//Calculating the values of x and y
+y=1
+x=5-y
+//Calculating the number of teeth on wheel E
+TS=16
+TE=4*TS
+//Calculating the number of teeth on wheel P
+TP=(TE-TS)/2
+//Torque necessary to keep the internal gear stationary:
+Tc=Ts*r //Torque on CN-m
+//Caluclating the torque necessary to keep the internal gear stationary
+Ti=Tc-Ts //Torque necessary to keep the internal gear stationary, N-m
+//Results:
+printf("\n\n Number of teeth on different wheels, TE = %d.\n\n",TE)
+printf(" Torque necessary to keep the internal gear stationary = %d N-m.\n\n",Ti)
\ No newline at end of file diff --git a/213/CH13/EX13.21/13_21.sce b/213/CH13/EX13.21/13_21.sce new file mode 100755 index 000000000..948934810 --- /dev/null +++ b/213/CH13/EX13.21/13_21.sce @@ -0,0 +1,31 @@ +//To find speed, direction and torque
+clc
+//Given:
+TA=14, TC=100
+r=98/41 //TE/TD
+PA=1.85*1000 //W
+NA=1200 //rpm
+//Solution:
+//Refer Fig. 13.28 and Table 13.23
+//Calculating the number of teeth on wheel B
+TB=(TC-TA)/2
+//Calculating the values of x and y
+//From the fourth row of the table, -y+x*(TA/TC) = 0, or x*(TA/TC)-y = 0 .....(i)
+//Also, -x-y = 1200, or x+y = -1200 .....(ii)
+A=[TA/TC -1; 1 1]
+B=[0; -1200]
+V=A \ B
+x=V(1)
+y=V(2)
+//Calculating the speed of gear E
+NE=round(-y+x*(TA/TB)*(1/r)) //rpm
+//Fixing torque required at C:
+//Calculating the torque on A
+Ta=PA*60/(2*%pi*NA) //Torque on A, N-m
+//Calculating the torque on E
+Te=PA*60/(2*%pi*NE) //Torque on E
+//Calculating the fixing torque required at C
+Tc=Te-Ta //Fixing torque at C, N-m
+//Results:
+printf("\n\n Speed and direction of rotation of gear E, NE = %d rpm, anticlockwise.\n\n",NE)
+printf(" Fixing torque required at C = %.1f N-m.\n\n",Tc)
\ No newline at end of file diff --git a/213/CH13/EX13.22/13_22.sce b/213/CH13/EX13.22/13_22.sce new file mode 100755 index 000000000..5c3334122 --- /dev/null +++ b/213/CH13/EX13.22/13_22.sce @@ -0,0 +1,30 @@ +//To find holding torque
+clc
+//Given:
+TB=15, TA=60, TC=20
+omegaY=740, omegaA=omegaY //rad/s
+P=130*1000 //W
+//Solution:
+//Refer Fig. 13.29 and Table 13.24
+//Calculating the number of teeth on wheel D
+TD=TA-(TC+TB)
+//Calculating the values of x and y
+//From the fourth row of the table, y-x*(TD/TC)*(TB/TA) = 740 .....(i)
+//Also, x+y = 0, or y+x = 0 .....(ii)
+A=[1 -(TD/TC)*(TB/TA); 1 1]
+B=[740; 0]
+V=A \ B
+x=V(2)
+y=V(1)
+//Calculating the speed of shaft X
+omegaX=y //rad/s
+//Holding torque on wheel D:
+//Calculating the torque on A
+Ta=P/omegaA //Torque on A, N-m
+//Calculating the torque on X
+Tx=P/omegaX //Torque on X, N-m
+//Calculating the holding torque on wheel D
+Td=Tx-Ta //Holding torque on wheel D, N-m
+//Results:
+printf("\n\n Speed of shaft X, omegaX = %.1f rad/s.\n\n",omegaX)
+printf(" Holding torque on wheel D = %.1f N-m.\n\n",Td)
\ No newline at end of file diff --git a/213/CH13/EX13.23/13_23.sce b/213/CH13/EX13.23/13_23.sce new file mode 100755 index 000000000..8979893e1 --- /dev/null +++ b/213/CH13/EX13.23/13_23.sce @@ -0,0 +1,41 @@ +//To find speed, direction and torque
+clc
+//Given:
+TP=144, TQ=120, TR=120, TX=36, TY=24, TZ=30
+NI=1500 //rpm
+P=7.5*1000 //W
+eta=0.8
+//Solution:
+//Refer Fig. 13.30 and Table 13.25
+//Calculating the values of x and y
+//From the fourth row of the table, x+y = -1500 .....(i)
+//Also, y-x*(TZ/TR) = 0, or -x*(TZ/TR)+y = 0 .....(ii)
+A=[1 1; -TZ/TR 1]
+B=[-1500; 0]
+V=A \ B
+x=V(1)
+y=V(2)
+//Calculating the values of x1 and y1
+//We have, y1-x1*(TY/TQ) = y .....(iii)
+//Also, x1+y1 = x+y, or y1+x1 = x+y .....(iv)
+A=[1 -TY/TQ; 1 1]
+B=[y; x+y]
+V=A \ B
+x1=V(2)
+y1=V(1)
+//Speed and direction of the driven shaft O and the wheel P:
+//Calculating the speed of shaft O
+NO=y1 //rpm
+//Calculating the speed of wheel P
+NP=y1+x1*(TY/TQ)*(TX/TP) //rpm
+//Torque tending to rotate the fixed wheel R:
+//Calculating the torque on shaft I
+T1=P*60/(2*%pi*NI) //N-m
+//Calculating the torque on shaft O
+T2=eta*P*60/(2*%pi*(-NO)) //N-m
+//Calculating the torque tending to rotate the fixed wheel R
+T=T2-T1 //Torque tending to rotate the fixed wheel R, N-m
+//Results:
+printf("\n\n Speed of the driven shaft O, NO = %d rpm, clockwise.\n\n",-NO)
+printf(" Speed of the wheel P, NP = %d rpm, clockwise.\n\n",-NP)
+printf(" Torque tending to rotate the fixed wheel R = %.2f N-m.\n\n",T)
\ No newline at end of file diff --git a/213/CH13/EX13.24/13_24.sce b/213/CH13/EX13.24/13_24.sce new file mode 100755 index 000000000..3daef9bd1 --- /dev/null +++ b/213/CH13/EX13.24/13_24.sce @@ -0,0 +1,44 @@ +//To find torque and forces
+clc
+//Given:
+TA=34, TB=120, TC=150, TD=38, TE=50
+PX=7.5*1000 //W
+NX=500 //rpm
+m=3.5 //mm
+//Solution:
+//Refer Fig. 13.31 and Table 13.27
+//Output torque of shaft Y:
+//Calculating the values of x and y
+//From the fourth row of the table, x+y = 500, or y+x = 500 .....(i)
+//Also, y-x*(TA/TC) = 0 .....(ii)
+A=[1 1; 1 -TA/TC]
+B=[500; 0]
+V=A \ B
+y=V(1) //rpm
+x=V(2) //rpm
+//Calculating the speed of output shaft Y
+NY=y-x*(TA/TB)*(TD/TE) //rpm
+//Calculating the speed of wheel E
+NE=NY //rpm
+//Calculating the input power assuming 100 per cent efficiency
+PY=PX //W
+//Calculating the output torque of shaft Y
+Ty=PY*60/(2*%pi*NY*1000) //Output torque on shaft Y, kN-m
+//Tangential force between wheels D and E:
+//Calculating the pitch circle radius of wheel E
+rE=m*TE/(2*1000) //m
+//Calculating the tangential force between wheels D and E
+FtDE=Ty/rE //Tangential force between wheels D and E, kN
+//Tangential force between wheels B and C:
+//Calculating the input torque on shaft X
+Tx=PX*60/(2*%pi*NX) //Input torque on shaft X, N-m
+//Calculating the fixing torque on the fixed wheel C
+Tf=Ty-Tx/1000 //Fixing torque on the fixed wheel C, kN-m
+//Calculating the pitch circle radius of wheel C
+rC=m*TC/(2*1000) //m
+//Calculating the tangential forces between wheels B and C
+FtBC=Tf/rC //kN
+//Results:
+printf("\n\n Output torque of shaft Y = %.3f kN-m.\n\n",Ty)
+printf(" Tangential force between wheels D and E = %.1f kN.\n\n",FtDE)
+printf(" Tangential force between wheels B and C = %d kN.\n\n",FtBC)
\ No newline at end of file diff --git a/213/CH13/EX13.3/13_3.sce b/213/CH13/EX13.3/13_3.sce new file mode 100755 index 000000000..73ddee044 --- /dev/null +++ b/213/CH13/EX13.3/13_3.sce @@ -0,0 +1,34 @@ +//To find the number of teeth
+clc
+//Given:
+rAD=12 //Speed ratio, NA/ND
+mA=3.125, mB=mA, mC=2.5, mD=mC, x=200 //mm
+//Solution:
+//Calculating the speed ratio between the gears A and B, and C and D
+rAB=sqrt(rAD) //Speed ratio between the gears A and B
+rCD=sqrt(rAB) //Speed ratio between the gears C and D
+//Calculating the ratio of teeth on gear B to gear A
+rtBA=rAB //Ratio of teeth on gear B to gear A
+//Calculating the ratio of teeth on gear D to gear C
+rtDC=rCD //Ratio of teeth on gear D to gear C
+//Calculating the number of teeth on the gears A and B
+//Distance between the shafts, x = mA*TA/2+mB*TB/2, or (mA/2)*TA+(mB/2)*TB = x .....(i)
+//Ratio of teeth on gear B to gear A, TB/TA = sqrt(12), or sqrt(12)*TA-TB = 0 .....(ii)
+A=[mA/2 mB/2; sqrt(12) -1]
+B=[x; 0]
+V=A \ B
+TA=int(V(1))
+TB=round(V(2))
+//Calculating the number of teeth on the gears C and D
+//Distance between the shafts, x = mC*TC/2+mD*TD/2, or (mC/2)*TC+(mD/2)*TD = x .....(iii)
+//Ratio of teeth on gear D to gear C, TD/TC = sqrt(12), or sqrt(12)*TC-TD = 0 .....(iv)
+A=[mC/2 mD/2; sqrt(12) -1]
+B=[x; 0]
+V=A \ B
+TC=round(V(1))
+TD=int(V(2))
+//Results:
+printf("\n\n Number of teeth on gear A, TA = %d.\n\n",TA)
+printf(" Number of teeth on gear B, TB = %d.\n\n",TB)
+printf(" Number of teeth on gear C, TC = %d.\n\n",TC)
+printf(" Number of teeth on gear D, TD = %d.\n\n",TD)
\ No newline at end of file diff --git a/213/CH13/EX13.4/13_4.sce b/213/CH13/EX13.4/13_4.sce new file mode 100755 index 000000000..0042351ec --- /dev/null +++ b/213/CH13/EX13.4/13_4.sce @@ -0,0 +1,17 @@ +//To find speed of gear B
+clc
+//Given:
+TA=36, TB=45
+NC=150 //rpm, anticlockwise
+//Solution:
+//Refer Fig. 13.7
+//Algebraic method:
+//Calculating the speed of gear B when gear A is fixed
+NA=0, NC=150 //rpm
+NB1=(-TA/TB)*(NA-NC)+NC //rpm
+//Calculating the speed of gear B when gear A makes 300 rpm clockwise
+NA=-300 //rpm
+NB2=(-TA/TB)*(NA-NC)+NC //rpm
+//Results:
+printf("\n\n Speed of gear B when gear A is fixed, NB = %d rpm.\n\n",NB1)
+printf(" Speed of gear B when gear A makes 300 rpm clockwise, NB = %d rpm.\n\n",NB2)
\ No newline at end of file diff --git a/213/CH13/EX13.5/13_5.sce b/213/CH13/EX13.5/13_5.sce new file mode 100755 index 000000000..fd14423a4 --- /dev/null +++ b/213/CH13/EX13.5/13_5.sce @@ -0,0 +1,15 @@ +//To find speed of gear C
+clc
+//Given:
+TB=75, TC=30, TD=90
+NA=100 //rpm, clockwise
+//Solution:
+//Refer Table 13.3
+//Calculating the number of teeth on gear E
+TE=TC+TD-TB
+//Calculating the speed of gear C
+y=-100
+x=y*(TB/TE)
+NC=y-x*(TD/TC) //rpm
+//Results:
+printf("\n\n Speed of gear C, NC = %d rpm, anticlockwise.\n\n",NC)
\ No newline at end of file diff --git a/213/CH13/EX13.6/13_6.sce b/213/CH13/EX13.6/13_6.sce new file mode 100755 index 000000000..761ebd50c --- /dev/null +++ b/213/CH13/EX13.6/13_6.sce @@ -0,0 +1,19 @@ +//To find speed of gears B and C
+clc
+//Given:
+TA=72, TC=32
+NEF=18 //Speed of arm EF, rpm
+//Solution:
+//Refer Table 13.5
+//Speed of gear C:
+y=18 //rpm
+x=y*(TA/TC)
+NC=x+y //Speed of gear C, rpm
+//Speed of gear B:
+//Calculating the number of teeth on gear B
+TB=(TA-TC)/2
+//Calculating the speed of gear B
+NB=y-x*(TC/TB) //Speed of gear B, rpm
+//Solution:
+printf("\n\n Speed of gear C = %.1f rpm.\n\n",NC)
+printf(" Speed of gear B = %.1f rpm in the opposite direction of arm.\n\n",-NB)
\ No newline at end of file diff --git a/213/CH13/EX13.7/13_7.sce b/213/CH13/EX13.7/13_7.sce new file mode 100755 index 000000000..1a8a9f6fd --- /dev/null +++ b/213/CH13/EX13.7/13_7.sce @@ -0,0 +1,37 @@ +//To find revolutions of arm
+clc
+//Given:
+TA=40, TD=90
+//Solution:
+//Calculating the number of teeth on gears B and C
+//From geometry of the Fig. 13.11, dA+2*dB=dD.
+//Since the number of teeth are proportional to their pitch circle diameters,
+TB=(TD-TA)/2
+TC=TB
+//Refer Table 13.6
+//Speed of arm when A makes 1 revolution clockwise and D makes half revolution anticlockwise:
+//Calculating the values of x and y
+//From the fourth row of the table, -x-y = -1, or x+y = 1 .....(i)
+//The gear D makes half revolution anticlockwise, i.e., x*(TA/TD)-y = 1/2 .....(ii)
+A=[1 1; TA/TD -1]
+B=[1; 1/2]
+V=A \ B
+x=V(1)
+y=V(2)
+//Calculating the speed of arm
+varm=-y //Speed of arm, revolutions
+//Results:
+printf("\n\n Speed of arm when A makes 1 revolution clockwise and D makes half revolution anticlockwise = %.2f revolution anticlockwise.\n\n",varm)
+//Speed of arm when A makes 1 revolution clockwise and D is stationary:
+//Calculating the values of x and y
+//From the fourth row of the table, -x-y = -1, or x+y = 1 .....(iii)
+//The gear D is stationary, i.e., x*(TA/TD)-y = 0 .....(iv)
+A=[1 1; TA/TD -1]
+B=[1; 0]
+V=A \ B
+x=V(1)
+y=V(2)
+//Calculating the speed of arm
+varm=-y //Speed of arm, revolutions
+//Results:
+printf(" Speed of arm when A makes 1 revolution clockwise and D is stationary = %.3f revolution clockwise.\n\n",-varm)
\ No newline at end of file diff --git a/213/CH13/EX13.8/13_8.sce b/213/CH13/EX13.8/13_8.sce new file mode 100755 index 000000000..2deb4b7cb --- /dev/null +++ b/213/CH13/EX13.8/13_8.sce @@ -0,0 +1,28 @@ +//To find teeth and speed
+clc
+//Given:
+TC=28, TD=26, TE=18, TF=TE
+//Solution:
+//The sketch is as in Fig. 13.12
+//Number of teeth on wheels A and B:
+//From geometry, dA = dC+2*dE, and dB = dD+2*dF
+//Since the number of teeth are proportional to their pitch circle diameters,
+TA=TC+2*TE
+TB=TD+2*TF
+//Speed of wheel B when arm G makes 100 rpm clockwise and wheel A is fixed:
+//Since the arm G makes 100 rpm clockwise, therefore from the fourth row of Table 13.7,
+y=-100
+x=-y
+//Calculating the speed of wheel B
+NB1=y+x*(TA/TC)*(TD/TB) //Speed of wheel B when arm G makes 100 rpm clockwise and wheel A is fixed, rpm
+//Speed of wheel B when arm G makes 100 rpm clockwise and wheel A makes 10 rpm counter clockwise:
+//Since the arm G makes 100 rpm clockwise, therefore from the fourth row of Table 13.7,
+y=-100
+x=10-y
+//Calculating the speed of wheel B
+NB2=y+x*(TA/TC)*(TD/TB) //Speed of wheel B when arm G makes 100 rpm clockwise and wheel A makes 10 rpm counter clockwise, rpm
+//Solution:
+printf("\n\n Number of teeth on wheel A, TA = %d.\n\n",TA)
+printf(" Number of teeth on wheel B, TB = %d.\n\n",TB)
+printf(" Speed of wheel B when arm G makes 100 rpm clockwise and wheel A is fixed = %.1f rpm, clockwise.\n\n",-NB1)
+printf(" Speed of wheel B when arm G makes 100 rpm clockwise and wheel A makes 10 rpm counter clockwise = %.1f rpm, counter clockwise.\n\n",NB2)
\ No newline at end of file diff --git a/213/CH13/EX13.9/13_9.sce b/213/CH13/EX13.9/13_9.sce new file mode 100755 index 000000000..5b476cfac --- /dev/null +++ b/213/CH13/EX13.9/13_9.sce @@ -0,0 +1,19 @@ +//To find number of teeth
+clc
+//Given:
+dD=224, m=4 //mm
+//Solution:
+//Refer Table 13.8
+//Calculating the values of x and y
+y=+1
+x=+5-y
+//Calculating the number of teeth on gear D
+TD=dD/m
+//Calculating the number of teeth on gear B
+TB=y/x*TD
+//Calculating the number of teeth on gear C
+TC=(TD-TB)/2
+//Results:
+printf("\n\n Number of teeth on gear D, TD = %d.\n\n",TD)
+printf(" Number of teeth on gear B, TB = %d.\n\n",TB)
+printf(" Number of teeth on gear C, TC = %d.\n\n",TC)
\ No newline at end of file diff --git a/213/CH14/EX14.1/14_1.sce b/213/CH14/EX14.1/14_1.sce new file mode 100755 index 000000000..d4b64e676 --- /dev/null +++ b/213/CH14/EX14.1/14_1.sce @@ -0,0 +1,17 @@ +//To find speed of precession
+clc
+//Given:
+d=300/1000, r=d/2, l=600/1000 //m
+m=5 //kg
+N=300 //rpm
+//Solution:
+//Calculating the angular speed of the disc
+omega=2*%pi*N/60 //rad/s
+//Calculating the mass moment of inertia of the disc, about an axis through its centre of gravity and perpendicular to the plane of the disc
+I=m*r^2/2 //kg-m^2
+//Calculating the couple due to mass of disc
+C=m*9.81*l //N-m
+//Calculating the speed of precession
+omegaP=C/(I*omega) //rad/s
+//Results:
+printf("\n\n Speed of precession, omegaP = %.1f rad/s.\n\n",omegaP)
\ No newline at end of file diff --git a/213/CH14/EX14.10/14_10.sce b/213/CH14/EX14.10/14_10.sce new file mode 100755 index 000000000..a4f718b41 --- /dev/null +++ b/213/CH14/EX14.10/14_10.sce @@ -0,0 +1,36 @@ +//To find centrifugal and gyroscopic effects
+clc
+//Given:
+m=2500 //kg
+x=1.5, R=30, dW=0.75, rW=dW/2, h=0.9 //m
+v=24*1000/3600 //m/s
+G=5
+IW=18, IE=12 //kg-m^2
+//Solution:
+//Calculating the road reaction on each wheel
+r=m*9.81/4 //Road reaction on each wheel, N
+//Calculating the angular velocity o the wheels
+omegaW=v/rW //rad/s
+//Calculating the angular velocity of precession
+omegaP=v/R //rad/s
+//Calculating the gyroscopic couple due to one pair of wheels and axle
+CW=round(2*IW*omegaW*omegaP) //N-m
+//Calculating the gyroscopic couple due to the rotating parts of the motor and gears
+CE=round(2*IE*G*omegaW*omegaP) //N-m
+//Calculating the net gyroscopic couple
+C=CW-CE //N-m
+//Calculating the reaction due to gyroscopic couple at each of the outer or inner wheels
+P=2*(-C)/(2*x) //N
+//Calculating the centrifugal force
+FC=m*v^2/R //N
+//Calculating the overturning couple
+CO=FC*h //N-m
+//Calculating the reaction due to overturning couple at each of the outer and inner wheels
+Q=2*CO/(2*x) //N
+//Calculating the vertical force exerted on each outer wheel
+PO=m*9.81/4-P/2+Q/2 //N
+//Calculating the vertical force exerted on each inner wheel
+PI=m*9.81/4+P/2-Q/2 //N
+//Results:
+printf("\n\n Vertical force exerted on each outer wheel, PO = %.2f N.\n\n",PO)
+printf(" Vertical force exerted on each inner wheel, PI = %.2f N.\n\n",PI)
\ No newline at end of file diff --git a/213/CH14/EX14.12/14_12.sce b/213/CH14/EX14.12/14_12.sce new file mode 100755 index 000000000..5e589be0d --- /dev/null +++ b/213/CH14/EX14.12/14_12.sce @@ -0,0 +1,51 @@ +//To find load on each wheel
+clc
+//Given:
+m=2000, mE=75 //kg
+b=2.5, x=1.5, h=500/1000, L=1, dW=0.8, rW=dW/2, kE=100/1000, R=60 //m
+IW=0.8 //kg-m^2
+G=4
+v=60*1000/3600 //m/s
+//Solution:
+//Refer Fig. 14.12
+//Calculating the weight on the rear wheels
+W2=(m*9.81*1)/b //N
+//Calculating the weight on the front wheels
+W1=m*9.81-W2 //N
+//Calculating the weight on each of the front wheels
+Wf=W1/2 //Weight on each of the front wheels, N
+//Calculating the weight on each of the rear wheels
+Wr=W2/2 //Weight on each of the rear wheels, N
+//Calculating the angular velocity of wheels
+omegaW=v/rW //rad/s
+//Calculating the angular velocity of precession
+omegaP=v/R //rad/s
+//Calculating the gyroscopic couple due to four wheels
+CW=4*IW*omegaW*omegaP //N-m
+//Calculating the magnitude of reaction due to gyroscopic couple due to four wheels at each of the inner or outer wheel
+P=2*(CW/(2*x)) //N
+//Calculating the mass moment of inertia of rotating parts of the engine
+IE=mE*(kE)^2 //kg-m^2
+//Calculating the gyroscopic couple due to rotating parts of the engine
+CE=IE*(kE)^2*G*omegaW*omegaP //N-m
+//Calculating the magnitude of reaction due to gyroscopic couple due to rotating parts of the engine at each of the inner or outer wheel
+F=2*(CE/(2*b)) //N
+//Calculating the centrifugal force
+FC=m*v^2/R //N
+//Calculating the centrifugal couple tending to overturn the car
+CO=FC*h //N-m
+//Calculating the magnitude of reaction due to overturning couple at each of the inner or outer wheel
+Q=2*(CO/(2*x)) //N
+//Calculating the load on front wheel 1
+Fw1=W1/2-P/2-F/2-Q/2 //Load on front wheel 1, N
+//Calculating the load on front wheel 2
+Fw2=W1/2+P/2-F/2+Q/2 //Load on front wheel 2, N
+//Calculating the load on rear wheel 3
+Rw3=W2/2-P/2+F/2-Q/2 //Load on rear wheel 3, N
+//Calculating the load on rear wheel 4
+Rw4=W2/2+P/2+F/2+Q/2 //Load on rear wheel 4, N
+//Results:
+printf("\n\n Load on front wheel 1 = %.2f N.\n\n",Fw1)
+printf(" Load on front wheel 2 = %.2f N.\n\n",Fw2)
+printf(" Load on rear wheel 3 = %.2f N.\n\n",Rw3)
+printf(" Load on rear wheel 4 = %.2f N.\n\n",Rw4)
\ No newline at end of file diff --git a/213/CH14/EX14.13/14_13.sce b/213/CH14/EX14.13/14_13.sce new file mode 100755 index 000000000..cc09841dc --- /dev/null +++ b/213/CH14/EX14.13/14_13.sce @@ -0,0 +1,29 @@ +//To find pressure on each rail
+clc
+//Given:
+m=2000, mI=200 //kg
+x=1.6, R=30, dW=0.7, rW=dW/2, k=0.3, h=1 //m
+v=54*1000/3600 //m/s
+theta=8 //degrees
+//Solution:
+//Refer Fig. 14.13
+//Calculating the reactions at the wheels:
+//Taking moments about B
+RA=(m*9.81*cosd(theta)+m*v^2/R*sind(theta))*1/2+(m*9.81*sind(theta)-m*v^2/R*cosd(theta))*h/x //N
+//Resolving the forces perpendicular to the track
+RB=(m*9.81*cosd(theta)+m*v^2/R*sind(theta))-RA //N
+//Calculating the angular velocity of wheels
+omegaW=v/rW //rad/s
+//Calculating the angular velocity of precession
+omegaP=v/R //rad/s
+//Calculating the gyroscopic couple
+C=mI*k^2*omegaW*cosd(theta)*omegaP //N-m
+//Calculating the force at each pair of wheels due to the gyroscopic couple
+P=C/x //N
+//Calculating the pressure on the inner rail
+PI=RA-P //N
+//Calculating the pressure o the outer rail
+PO=RB+P //N
+//Results:
+printf("\n\n Pressure on the inner rail, PI = %.2f N.\n\n",PI)
+printf(" Pressure on the outer rail, PO = %.2f N.\n\n",PO)
\ No newline at end of file diff --git a/213/CH14/EX14.14/14_14.sce b/213/CH14/EX14.14/14_14.sce new file mode 100755 index 000000000..8ffc16bb4 --- /dev/null +++ b/213/CH14/EX14.14/14_14.sce @@ -0,0 +1,24 @@ +//To find gyroscopic couple and reaction
+clc
+//Given:
+I=180 //kg-m^2
+D=1.8, R=D/2, x=1.5 //m
+v=95*1000/3600 //m/s
+t=0.1 //s
+//Solution:
+//Gyroscopic couple set up:
+//Calculating the angular velocity of the locomotive
+omega=v/R //rad/s
+//Calculating the amplitude
+A=1/2*6 //mm
+//Calculating the maximum velocity while falling
+vmax=2*%pi/t*A/1000 //m/s
+//Calculating the maximum angular velocity of tilt of the axle or angular velocity of precession
+omegaPmax=vmax/x //rad/s
+//Calculating the gyroscopic couple set up
+C=I*omega*omegaPmax //N-m
+//Calculating the reaction between the wheel and rail due to the gyroscopic couple
+P==C/x //N
+//Results:
+printf("\n\n Gyroscopic couple set up, C = %.1f N-m.\n\n",C)
+printf(" Reaction between the wheel and rail due to the gyroscopic couple, P = %d N.\n\n",P)
\ No newline at end of file diff --git a/213/CH14/EX14.15/14_15.sce b/213/CH14/EX14.15/14_15.sce new file mode 100755 index 000000000..13ef91565 --- /dev/null +++ b/213/CH14/EX14.15/14_15.sce @@ -0,0 +1,14 @@ +//To find angle of inclination
+clc
+//Given:
+m=250 //kg
+IE=0.3, IW=1 //kg-m^2
+G=5
+h=0.6, rW=300/1000, R=50 //m
+v=90*1000/3600 //m/s
+//Solution:
+//Calculating the angle of inclination with respect to the vertical of a two wheeler
+//Equating total overturning couple to balancing couple,
+theta=atand((1/(m*9.81*h))*((v^2/(R*rW)*(2*IW+G*IE))+(m*v^2/R*h))) //degrees
+//Results:
+printf("\n\n Angle of inclination with respect to the vertical of a two wheeler, theta = %.2f degrees.\n\n",theta)
\ No newline at end of file diff --git a/213/CH14/EX14.16/14_16.sce b/213/CH14/EX14.16/14_16.sce new file mode 100755 index 000000000..005d3793b --- /dev/null +++ b/213/CH14/EX14.16/14_16.sce @@ -0,0 +1,26 @@ +//To find inclination of gyrowheel
+clc
+//Given:
+m1=0.5, m2=0.3 //kg
+k=20/1000, OG=10/1000, h=OG, R=50 //m
+N=3000 //rpm
+v=15 //m/s
+//Solution:
+//Refer Fig. 14.15 and Fig. 14.16
+//Calculating the angular speed of the wheel
+omega=2*%pi*N/60 //rad/s
+//Calculating the mass moment of inertia of the gyrowheel
+I=m1*k^2 //kg-m^2
+//Calculating the angular velocity of precession
+omegaP=v/R //rad/s
+//When the vehicle moves in the direction of arrow X taking a left turn along the curve:
+//Calculating the angle of inclination of the gyrowheel from the vertical
+//Equating the overturning couple to the balancing couple for equilibrium condition,
+theta1=atand((1/(m2*9.81*h))*(I*omega*omegaP-m2*v^2/R*h)) //degrees
+//When the vehicle reverses at the same speed in the direction of arrow Y along the same path:
+//Calculating the angle of inclination of the gyrowheel from the vertical
+//Equating the overturning couple to the balancing couple for equilibrium condition,
+theta2=atand((1/(m2*9.81*h))*(I*omega*omegaP+m2*v^2/R*h)) //degrees
+//Results:
+printf("\n\n Angle of inclination of the gyrowheel from the vertical when the vehicle moves in the direction of arrow X taking a left turn along the curve, theta = %.2f degrees.\n\n",theta1)
+printf(" Angle of inclination of the gyrowheel from the vertical when the vehicle reverses at the same speed in the direction of arrow Y along the same path, theta = %.2f degrees.\n\n",theta2)
\ No newline at end of file diff --git a/213/CH14/EX14.17/14_17.sce b/213/CH14/EX14.17/14_17.sce new file mode 100755 index 000000000..97aec7e98 --- /dev/null +++ b/213/CH14/EX14.17/14_17.sce @@ -0,0 +1,14 @@ +//To find the gyroscopic couple
+clc
+//Given:
+d=0.6, r=d/2 //m
+m=30 //kg
+theta=1 //degree
+N=1200 //rpm
+//Solution:
+//Calculating the angular speed of the shaft
+omega=2*%pi*N/60 //rad/s
+//Calculating the gyroscopic couple acting on the bearings
+C=round(m/8*omega^2*r^2*sind(2*theta)) //N-m
+//Results:
+printf("\n\n Gyroscopic couple acting on the bearings, C = %d N-m.\n\n",C)
\ No newline at end of file diff --git a/213/CH14/EX14.2/14_2.sce b/213/CH14/EX14.2/14_2.sce new file mode 100755 index 000000000..1ab0427bb --- /dev/null +++ b/213/CH14/EX14.2/14_2.sce @@ -0,0 +1,28 @@ +//To find the resultant reaction
+clc
+//Given:
+d=150/1000, r=d/2, x=100/1000 //m
+m=5 //kg
+N=1000, NP=60 //rpm
+//Solution:
+//Calculating the angular speed of the disc
+omega=2*%pi*N/60 //rad/s
+//Calculating the speed of precession of the axle
+omegaP=2*%pi*NP/60 //rad/s
+//Calculating the mass moment of inertia of the disc, about an axis through its centre of gravity and perpendicular to the plane of disc
+I=m*r^2/2 //kg-m^2
+//Calculating the gyroscopic couple acting on the disc
+C=I*omega*omegaP //N-m
+//Calculating the force at each bearing due to the gyroscopic couple
+F=C/x //N
+//Calculating the reactions at the bearings A and B
+RA=m/2*9.81 //N
+RB=RA //N
+//Resultant reaction at each bearing:
+//Calculating the resultant reaction at the bearing A
+RA1=F+RA //N
+//Calculating the resultant reaction at the bearing B
+RB1=F-RB //N
+//Results:
+printf("\n\n Resultant reaction at the bearing A, RA1 = %.1f N, upwards.\n\n",RA1)
+printf(" Resultant reaction at the bearing B, RB1 = %.1f N, downwards.\n\n", RB1)
\ No newline at end of file diff --git a/213/CH14/EX14.3/14_3.sce b/213/CH14/EX14.3/14_3.sce new file mode 100755 index 000000000..acf9bd52d --- /dev/null +++ b/213/CH14/EX14.3/14_3.sce @@ -0,0 +1,19 @@ +//To find gyroscopic couple
+clc
+//Given:
+R=50, k=0.3 //m
+v=200*1000/3600 //m/s
+m=400 //kg
+N=2400 //rpm
+//Solution:
+//Calculating the angular speed of the engine
+omega=2*%pi*N/60 //rad/s
+//Calculating the mass moment of inertia of the engine and the propeller
+I=m*k^2 //kg-m^2
+//Calculating the angular velocity of precession
+omegaP=v/R //rad/s
+//Calculating the gyroscopic couple acting on the aircraft
+C=I*omega*omegaP/1000 //kN-m
+//Results:
+printf("\n\n Gyroscopic couple acting on the aircraft, C = %.3f kN-m.\n\n",C)
+printf(" The effect of the gyroscopic couple is to lift the nose upwards and tail downwards.\n\n")
\ No newline at end of file diff --git a/213/CH14/EX14.4/14_4.sce b/213/CH14/EX14.4/14_4.sce new file mode 100755 index 000000000..712882a60 --- /dev/null +++ b/213/CH14/EX14.4/14_4.sce @@ -0,0 +1,18 @@ +//To find gyroscopic couple
+clc
+//Given:
+m=8*1000 //kg
+k=0.6, R=75 //m
+N=1800 //rpm
+v=100*1000/3600 //m/s
+//Solution:
+//Calculating the angular speed of the rotor
+omega=2*%pi*N/60 //rad/s
+//Calculating the mass moment of inertia of the rotor
+I=m*k^2 //kg-m^2
+//Calculating the angular velocity of precession
+omegaP=v/R //rad/s
+//Calculating the gyroscopic couple
+C=I*omega*omegaP/1000 //kN-m
+//Results:
+printf("\n\n Gyroscopic couple, C = %.3f kN-m.\n\n",C)
\ No newline at end of file diff --git a/213/CH14/EX14.5/14_5.sce b/213/CH14/EX14.5/14_5.sce new file mode 100755 index 000000000..4a856cfcf --- /dev/null +++ b/213/CH14/EX14.5/14_5.sce @@ -0,0 +1,17 @@ +//To find gyroscopic couple and direction
+clc
+//Given:
+N=1500 //rpm
+m=750 //kg
+omegaP=1 //rad/s
+k=250/1000 //m
+//Solution:
+//Calculating the angular speed of the rotor
+omega=2*%pi*N/60 //rad/s
+//Calculating the mass moment of inertia of the rotor
+I=m*k^2 //kg-m^2
+//Calculating the gyroscopic couple transmitted to the hull
+C=I*omega*omegaP/1000 //kN-m
+//Results:
+printf("\n\n Gyroscopic couple transmitted to the hull, C = %.3f kN-m.\n\n",C)
+printf(" When the pitching is upward, the relative gyroscopic couple acts in the clockwise direction.\n\n")
\ No newline at end of file diff --git a/213/CH14/EX14.6/14_6.sce b/213/CH14/EX14.6/14_6.sce new file mode 100755 index 000000000..82e7a48c6 --- /dev/null +++ b/213/CH14/EX14.6/14_6.sce @@ -0,0 +1,34 @@ +//To find gyroscopic couple and effect
+clc
+//Given:
+m=3500 //kg
+k=0.45 //m
+N=3000 //rpm
+//Solution:
+//Calculating the angular speed of the rotor
+omega=2*%pi*N/60 //rad/s
+//When the ship is steering to the left:
+R=100 //m
+v=36*1000/3600 //m/s
+//Calculating the mass moment of inertia of the rotor
+I=m*k^2 //kg-m^2
+//Calculating the angular velocity of precession
+omegaP=v/R //rad/s
+//Calculating the gyroscopic couple
+C=I*omega*omegaP/1000 //kN-m
+//Results:
+printf("\n\n Gyroscopic couple when the ship is steering to the left, C = %.2f kN-m.\n\n",C)
+printf(" When the rotor rotates clockwise and the ship takes a left turn, the effect of the reactive gyroscopic couple is to raise the bow and lower the stern.\n\n")
+//When the ship is pitching with the bow falling:
+tp=40 //s
+//Calculating the amplitude of swing
+phi=12/2*%pi/180 //rad
+//Calculating the angular velocity of the simple harmonic motion
+omega1=2*%pi/tp //rad/s
+//Calculating the maximum angular velocity of precession
+omegaP=phi*omega1 //rad/s
+//Calculating the gyroscopic couple
+C=I*omega*omegaP/1000 //kN-m
+//Results:
+printf(" Gyroscopic couple when the ship is pitching with the bow falling, C = %.3f kN-m.\n\n",C)
+printf(" When the bow is falling, the effect of the reactive gyroscopic couple is to move the ship towards port side.\n\n")
\ No newline at end of file diff --git a/213/CH14/EX14.7/14_7.sce b/213/CH14/EX14.7/14_7.sce new file mode 100755 index 000000000..4fc49e34f --- /dev/null +++ b/213/CH14/EX14.7/14_7.sce @@ -0,0 +1,26 @@ +//To find gyroscopic couple and acceleration
+clc
+//Given:
+m=20*1000 //kg
+k=0.6 //m
+N=2000 //rpm
+phi=6*%pi/180 //rad
+tp=30 //s
+//Solution:
+//Calculating the angular speed of the rotor
+omega=2*%pi*N/60 //rad/s
+//Maximum gyroscopic couple:
+//Calculating the mass moment of inertia of the rotor
+I=m*k^2 //kg-m^2
+//Calculating the angular velocity of the simple harmonic motion
+omega1=2*%pi/tp //rad/s
+//Calculating the maximum angular velocity of precession
+omegaPmax=phi*omega1 //rad/s
+//Calculating the maximum gyroscopic couple
+Cmax=I*omega*omegaPmax/1000 //kN-m
+//Calculating the maximum angular acceleration during pitching
+alphamax=phi*omega1^2 //Maximum angular acceleration during pitching, rad/s^2
+//Results:
+printf("\n\n Maximum gyroscopic couple, Cmax = %.3f kN-m.\n\n",Cmax)
+printf(" Maximum angular acceleration during pitching = %.4f rad/s^2.\n\n",alphamax)
+printf(" When the rotation of the rotor is clockwise when looking from the left and when the bow is rising, then the reactive gyroscopic couple acts in the direction which tends to turn the bow towrds right.\n\n")
\ No newline at end of file diff --git a/213/CH14/EX14.8/14_8.sce b/213/CH14/EX14.8/14_8.sce new file mode 100755 index 000000000..3d15be9bc --- /dev/null +++ b/213/CH14/EX14.8/14_8.sce @@ -0,0 +1,41 @@ +//To find the gyroscopic effects
+clc
+//Given:
+m=5*1000 //kg
+N=1000 //rpm
+k=0.5 //m
+//Solution:
+//Calculating the angular speed of the rotor
+omega=2*%pi*N/60 //rad/s
+//When the ship steers to the left:
+v=30*1000/3600 //m/s
+R=60 //m
+//Calculating the angular velocity of precession
+omegaP=v/R //rad/s
+//Calculating the mass moment of inertia of the rotor
+I=m*k^2 //kg-m^2
+//Calculating the gyroscopic couple
+C=I*omega*omegaP/1000 //kN-m
+//Results:
+printf("\n\n When the rotor rotates in a clockwise direction when viewed from from the stern and the ship steers to the left, the effect of reactive gyroscopic couple is to raise the bow and lower the stern.\n\n")
+//When the ship pitches with the bow descending:
+phi=6*%pi/180 //rad
+tp=20 //s
+//Calculating the angular velocity of simple harmonic motion
+omega1=2*%pi/tp //rad/s
+//Calculating the maximum velocity of precession
+omegaPmax=phi*omega1 //rad/s
+//Calculating the maximum gyroscopic couple
+Cmax=I*omega*omegaPmax //N-m
+//Results:
+printf(" Since the ship is pitching with the low bow descending, therefore the effect of this maximum gyroscopic couple is to turn the ship towards port side.\n\n")
+//When the ship rolls:
+omegaP=0.03 //rad/s
+//Calculating the gyroscopic couple
+C=I*omega*omegaP //N-m
+//Results:
+printf(" In case of rolling of a ship, the axis of precession is always parallel to the axis of spin for all positions, therefore there is no effect of gyroscopic couple.\n\n")
+//Calculating the maximum angular acceleration during pitching
+alphamax=phi*omega1^2 //rad/s^2
+//Results:
+printf(" Maximum angular acceleration during pitching, alphamax = %.2f rad/s^2.\n\n",alphamax)
\ No newline at end of file diff --git a/213/CH14/EX14.9/14_9.sce b/213/CH14/EX14.9/14_9.sce new file mode 100755 index 000000000..b1dbfa8c5 --- /dev/null +++ b/213/CH14/EX14.9/14_9.sce @@ -0,0 +1,32 @@ +//To find maximum acceleration during pitching
+clc
+//Given:
+m=2000 //kg
+N=3000 //rpm
+k=0.5, R=100 //m
+v=16.1*1855/3600 //m/s
+//Solution:
+//Calculating the angular speed of the rotor
+omega=2*%pi*N/60 //rad/s
+//Gyroscopic couple:
+//Calculating the mass moment of inertia of the rotor
+I=m*k^2 //kg-m^2
+//Calculating the angular velocity of precession
+omegaP=v/R //rad/s
+//Calculating the gyroscopic couple
+C=I*omega*omegaP/1000 //kN-m
+//Torque during pitching:
+tp=50 //s
+phi=12/2*%pi/180 //rad
+//Calculating the angular velocity of simple harmonic motion
+omega1=2*%pi/tp //rad/s
+//Calculating the maximum angular velocity of precession
+omegaPmax=phi*omega1 //rad/s
+//Calculating the maximum gyroscopic couple during pitching
+Cmax=I*omega*omegaPmax //N-m
+//Calculating the maximum acceleration during pitching
+alphamax=phi*omega1^2 //rad/s^2
+//Results:
+printf("\n\n When the rotor rotates clockwise when looking from a stern the ship steers to the right, the effect of the reactive gyroscopic couple is to raise the stern and lower the bow.\n\n")
+printf(" Torque during pitching, Cmax = %d N-m.\n\n",Cmax)
+printf(" Maximum acceleration during pitching, alphamax = %.5f rad/s^2.\n\n",alphamax)
\ No newline at end of file diff --git a/213/CH15/EX15.1/15_1.sce b/213/CH15/EX15.1/15_1.sce new file mode 100755 index 000000000..2e4caad3f --- /dev/null +++ b/213/CH15/EX15.1/15_1.sce @@ -0,0 +1,36 @@ +//To find linear and angular velocity and acceleration
+clc
+//Given:
+OC=200/1000, PC=700/1000 //m
+omega=120 //rad/s
+//Solution:
+//Refer Fig. 15.5
+OM=127/1000, CM=173/1000, QN=93/1000, NO=200/1000 //m
+//Velocity and acceleration of the piston:
+//Calculating the velocity of the piston P
+vP=omega*OM //m/s
+//Calculating the acceleration of the piston P
+aP=omega^2*NO //m/s^2
+//Velocity and acceleration of the mid-point of the connecting rod:
+//By measurement,
+OD1=140/1000, OD2=193/1000 //m
+//Calculating the velocity of D
+vD=omega*OD1 //m/s
+//Calculating the acceleration of D
+aD=omega^2*OD2 //m/s^2
+//Angular velocity and angular acceleration of the connecting rod:
+//Calculating the velocity of the connecting rod PC
+vPC=omega*CM //m/s
+//Calculating the angular velocity of the connecting rod PC
+omegaPC=vPC/PC //rad/s
+//Calculating the tangential component of the acceleration of P with respect to C
+atPC=omega^2*QN //m/s^2
+//Calculating the angular acceleration of the connecting rod PC
+alphaPC=atPC/PC //ra/s^2
+//Results:
+printf("\n\n Velocity of the piston P, vP = %.2f m/s.\n\n",vP)
+printf(" Acceleration of the piston P, aP = %d m/s^2.\n\n", aP)
+printf(" Velocity of D, vD = %.1f m/s.\n\n",vD)
+printf(" Acceleration of D, aD = %.1f m/s^2.\n\n",aD)
+printf(" Angular velocity of the connecting rod PC, omegaPC = %.2f rad/s.\n\n",omegaPC)
+printf(" Angular acceleration of the connecting rod PC, alphaPC = %.2f rad/s^2.\n\n",alphaPC)
\ No newline at end of file diff --git a/213/CH15/EX15.10/15_10.sce b/213/CH15/EX15.10/15_10.sce new file mode 100755 index 000000000..7b1db7075 --- /dev/null +++ b/213/CH15/EX15.10/15_10.sce @@ -0,0 +1,30 @@ +//To find reaction, thrust and turning moment
+clc
+//Given:
+aP=36 //m/s^2
+theta=30 //degrees
+p=0.5 //N/mm^2
+RF=600 //N
+D=300/1000, r=300/1000 //m
+mR=180 //kg
+n=4.5
+//Solution:
+//Reaction on the guide bars:
+//Calculating the load on the piston
+FL=round(p*%pi/4*(D*1000)^2) //N
+//Calculating the inertia force due to reciprocating parts
+FI=mR*aP //N
+//Calculating the piston effort
+FP=(FL-FI-RF)/1000 //kN
+//Calculating the angle of inclination of the connecting rod to the line of stroke
+phi=asind(sind(theta)/n) //degrees
+//Calculating the reaction on the guide bars
+FN=FP*tand(phi) //kN
+//Calculating the thrust on the crank shaft bearing
+FB=(FP*cosd(phi+theta))/cosd(phi) //kN
+//Calculating the turning moment on the crank shaft
+T=(FP*sind(theta+phi))/cosd(phi)*r //kN-m
+//Results:
+printf("\n\n Reaction on the guide bars, FN = %.2f kN.\n\n",FN)
+printf(" Thrust on the crank shaft bearing, FB = %.1f kN.\n\n",FB)
+printf(" Turning moment on the crank shaft, T = %.2f kN-m.\n\n",T)
\ No newline at end of file diff --git a/213/CH15/EX15.11/15_11.sce b/213/CH15/EX15.11/15_11.sce new file mode 100755 index 000000000..599b479f7 --- /dev/null +++ b/213/CH15/EX15.11/15_11.sce @@ -0,0 +1,37 @@ +//To find force, load, thrust and speed
+clc
+//Given:
+D=100/1000, L=120/1000, r=L/2, l=250/1000 //m
+mR=1.1 //kg
+N=2000 //rpm
+theta=20 //degrees
+p=700 //kN/m^2
+//Solution:
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Net force on the piston:
+//Calculating the force due to gas pressure
+FL=p*%pi/4*D^2 //kN
+//Calculating the ratio of lengths of the connecting rod and crank
+n=l/r
+//Calculating the inertia force on the piston
+FI=round(mR*omega^2*r*(cosd(theta)+cosd(2*theta)/n)) //N
+//Calculating the net force on the piston
+FP=(FL*1000)-FI+mR*9.81 //N
+//Resultant force on the gudgeon pin:
+//Calculating the angle of inclination of the connecting rod to the line of stroke
+phi=asind(sind(theta)/n) //degrees
+//Calculating the resultant load on the gudgeon pin
+FQ=round(FP/cosd(phi)) //N
+//Calculating the thrust on the cylinder walls
+FN=FP*tand(phi) //N
+//Speed, above which, the gudgeon pin load would be reversed in direction:
+//Calculating the minimum speed for FP to be negative
+omega1=sqrt((FL*1000+mR*9.81)/(mR*r*(cosd(theta)+cosd(2*theta)/n))) //rad/s
+//Calculating the corresponding speed in rpm
+N1=omega1*60/(2*%pi) //rpm
+//Results:
+printf("\n\n Net force on the piston, FP = %.1f N.\n\n",FP)
+printf(" Resultant load on the gudgeon pin, FQ = %d N.\n\n",FQ)
+printf(" Thrust on the cylinder walls, FN = %.1f N.\n\n",FN)
+printf(" Speed, above which, the gudgeon pin load would be reversed in direction, N1 > %d rpm.\n\n",N1)
\ No newline at end of file diff --git a/213/CH15/EX15.12/15_12.sce b/213/CH15/EX15.12/15_12.sce new file mode 100755 index 000000000..604498db2 --- /dev/null +++ b/213/CH15/EX15.12/15_12.sce @@ -0,0 +1,44 @@ +//To find turning moment, thrust and acceleration
+clc
+//Given:
+N=120 //rpm
+D=250/1000, L=400/1000, r=L/2, l=0.6, d=50/1000 //m
+mR=60 //kg
+theta=45 //degrees
+p1=550*1000, p2=70*1000 //N/m^2
+//Solution:
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Turning moment on the crankshaft:
+//Calculating the area of the piston on the cover end side
+A1=%pi/4*D^2 //m^2
+//Calculating the area of the piston rod
+a=%pi/4*d^2 //m^2
+//Calculating the net load on the piston
+FL=p1*A1-p2*(A1-a) //N
+//Calculating the ratio of lengths of the connecting rod and crank
+n=l/r
+//Calculating the inertia force on the reciprocating parts
+FI=mR*omega^2*r*(cosd(theta)+cosd(2*theta)/n) //N
+//Calculating the net force on the piston or piston effort
+FP=(FL-FI)/1000 //kN
+//Calculating the angle of inclination of the connecting rod to the line of stroke
+phi=asind(sind(theta)/n) //degrees
+//Calculating the turning moment on the crank shaft
+T=(FP*sind(theta+phi))/cosd(phi)*r*1000 //N-m
+//Calculating the thrust on the bearings
+FB=(FP*cosd(theta+phi))/cosd(phi) //kN
+//Acceleration of the flywheel:
+P=20*1000 //W
+m=60 //kg
+k=0.6 //m
+//Calculating the mass moment of inertia of the flywheel
+I=m*k^2 //kg-m^2
+//Calculating the resisting torque
+TR=P*60/(2*%pi*N) //N-m
+//Calculating the acceleration of the flywheel
+alpha=(T-TR)/I //rad/s^2
+//Results:
+printf("\n\n Turning moment on the crank shaft, T = %d N-m.\n\n",T)
+printf(" Thrust on the bearings, FB = %.2f kN.\n\n",FB)
+printf(" Acceleration of the flywheel, alpha = %.1f rad/s^2.\n\n",alpha)
\ No newline at end of file diff --git a/213/CH15/EX15.13/15_13.sce b/213/CH15/EX15.13/15_13.sce new file mode 100755 index 000000000..8f35db74d --- /dev/null +++ b/213/CH15/EX15.13/15_13.sce @@ -0,0 +1,50 @@ +//To find effort, thrust and turning moment
+clc
+//Given:
+D=300/1000, L=500/1000, r=L/2 //m
+n=4.5
+N=180 //rpm
+mR=280 //kg
+theta=45 //degrees
+p1=0.1 //N/mm^2
+CR=14 //Compression ration, V1/V2
+//Solution:
+//Refer Fig. 15.12
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Calculating the pressure corresponding to point 2
+p2=p1*(CR)^1.35 //N/mm^2
+//Calculating the swept volume
+VS=%pi/4*D^2*L //m^3
+//Calculating the clearance volume
+VC=VS/(CR-1) //m^3
+//Calculating the volume corresponding to point 3
+V3=VC+(1/10*VS) //m^3
+//Calculating the displacement of the piston corresponding to crank displacement of 45 degrees
+x=r*((1-cosd(theta))+(sind(theta))^2/(2*n)) //m
+//Calculating the volume corresponding to point 4'
+V4dash=VC+(%pi/4*D^2*x) //m^2
+//Calculating the pressure corresponding to point 4'
+p3=p2
+p4dash=p3*(V3/V4dash)^1.35 //N/mm^2
+//Calculating the difference of pressures on two sides of the piston
+p=(p4dash-p1)*10^6 //N/m^2
+//Calculating the net load on the piston
+FL=p*%pi/4*D^2 //N
+//Calculating the inertia force on the reciprocating parts
+FI=mR*omega^2*r*(cosd(theta)+cosd(2*theta)/n) //N
+//Calculating the net force on the piston or piston effort
+FP=FL-FI+mR*9.81 //N
+//Crank-pin effort:
+//Calculating the angle of inclination of the connecting rod to the line of stroke
+phi=asind(sind(theta)/n) //degrees
+//Calculating the crank-pin effort
+FT=(FP*sind(theta+phi))/(cosd(phi)*1000) //kN
+//Calculating the thrust on the bearings
+FB=(FP*cosd(theta+phi))/(cosd(phi)*1000) //kN
+//Calculating the turning moment on the crankshaft
+T=FT*r //kN-m
+//Results:
+printf("\n\n Crank-pin effort, FT = %.3f kN.\n\n",FT)
+printf(" Thrust on the bearings, FB = %.3f kN.\n\n",FB)
+printf(" Turning moment on the crankshaft, T = %.2f kN-m.\n\n",T)
\ No newline at end of file diff --git a/213/CH15/EX15.14/15_14.sce b/213/CH15/EX15.14/15_14.sce new file mode 100755 index 000000000..91eaf8b7c --- /dev/null +++ b/213/CH15/EX15.14/15_14.sce @@ -0,0 +1,41 @@ +//To find turning moment
+clc
+//Given:
+D=240/1000, L=360/1000, r=L/2, l=0.6 //m
+N=300 //rpm
+mR=160 //kg
+pA=(8+1.03)*10^5, pE=(-0.75+1.03)*10^5 //N/m^2
+FR=500 //N
+theta=75 //degrees
+//Solution:
+//Refer Fig. 15.13
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Calculating the stroke volume
+VS=%pi/4*D^2*L //m^3
+//Calculating the volume of steam at cut-off
+VB=VS/3 //m^3
+//Calculating the ratio of lengths of the connecting rod and crank
+n=l/r
+//Calculating the displacement of the piston when the crank position is 75 degrees from the top dead centre
+x=r*((1-cosd(theta))+(sind(theta))^2/(2*n)) //m^3
+//Calculating the volume corresponding to point C'
+VCdash=VS*x/L //m^3
+//Calculating the pressure corresponding to point C'
+pB=pA
+pCdash=round((pB*VB)/VCdash) //N/m^2
+//Calculating the difference of pressures on the two sides of the piston
+p=round(pCdash-pE) //N/m^2
+//Calculating the net load on the piston
+FL=round(%pi/4*D^2*p) //N
+//Calculating the inertia force on the reciprocating parts
+FI=round(mR*omega^2*r*(cosd(theta)+(cosd(2*theta)/n))) //N
+//Calculating the piston effort
+FP=FL-FI+mR*9.81-FR //N
+//Turning moment on the crankshaft:
+//Calculating the angle of inclination of the connecting rod to the line of stroke
+phi=asind(sind(theta)/n) //degrees
+//Calculating the turning moment on the crankshaft
+T=(FP*sind(theta+phi))/cosd(phi)*r //N-m
+//Results:
+printf("\n\n Turning moment on the crankshaft, T = %d N-m.\n\n",T)
\ No newline at end of file diff --git a/213/CH15/EX15.15/15_15.sce b/213/CH15/EX15.15/15_15.sce new file mode 100755 index 000000000..e8044f8f9 --- /dev/null +++ b/213/CH15/EX15.15/15_15.sce @@ -0,0 +1,19 @@ +//To find equivalent system
+clc
+//Given:
+l=300, l1=200 //mm
+m=15 //kg
+I=7000 //kg-mm^2
+//Solution:
+//Refer Fig. 15.16 and Fig. 15.17
+//Calculating the radius of gyration of the connecting rod about an axis passing through its centre of gravity
+kG=sqrt(I/m) //mm
+//Calculating the distance of other mass from the centre of gravity
+l2=(kG)^2/l1 //mm
+//Calculating the magnitude of mass placed at the small end centre
+m1=(l2*m)/(l1+l2) //kg
+//Calculating the magnitude of the mass placed at a distance l2 from the centre of gravity
+m2=(l1*m)/(l1+l2) //kg
+//Results:
+printf("\n\n Mass placed at the small end centre, m1 = %.2f kg.\n\n",m1)
+printf(" Mass placed at a distance %.2f mm from the centre of gravity, m2 = %.2f kg.\n\n",l2,m2)
\ No newline at end of file diff --git a/213/CH15/EX15.16/15_16.sce b/213/CH15/EX15.16/15_16.sce new file mode 100755 index 000000000..cc8ee3dc3 --- /dev/null +++ b/213/CH15/EX15.16/15_16.sce @@ -0,0 +1,19 @@ +//To find equivalent system
+clc
+//Given:
+h=650/1000, l1=(650-25)/1000 //m
+m=37.5 //kg
+tp=1.87 //seconds
+//Solution:
+//Refer Fig. 15.18 and Fig. 15.19
+//Calculating the radius of gyration of the connecting rod about an axis passing through its centre of gravity
+kG=sqrt((tp/(2*%pi))^2*(9.81*h)-h^2) //m
+//Calculating the distance of mass m2 from the centre of gravity
+l2=(kG)^2/l1 //m
+//Calculating the magnitude of mass placed at the small end centre
+m1=(l2*m)/(l1+l2) //kg
+//Calculating the magnitude of mass placed at a distance l2 from centre of gravity
+m2=(l1*m)/(l1+l2) //kg
+//Results:
+printf("\n\n Mass placed at the small end centre A, m1 = %d kg.\n\n",m1)
+printf(" Mass placed at a distance %.3f m from G, m2 = %.1f kg.\n\n",l2,m2)
\ No newline at end of file diff --git a/213/CH15/EX15.17/15_17.sce b/213/CH15/EX15.17/15_17.sce new file mode 100755 index 000000000..266a0f083 --- /dev/null +++ b/213/CH15/EX15.17/15_17.sce @@ -0,0 +1,42 @@ +//To find radius and MI
+clc
+//Given:
+m=55 //kg
+l=850/1000, d1=75/1000, d2=100/1000 //m
+tp1=1.83, tp2=1.68 //seconds
+//Solution:
+//Refer Fig. 15.20
+//Calculating the length of equivalent simple pendulum when suspended from the top of small end bearing
+L1=9.81*(tp1/(2*%pi))^2 //m
+//Calculating the length of equivalent simple pendulum when suspended from the top of big end bearing
+L2=9.81*(tp2/(2*%pi))^2 //m
+//Radius of gyration of the rod about an axis passing through the centre of gravity and perpendicular to the plane of oscillation:
+//Calculating the distances of centre of gravity from the top of small end and big end bearings
+//We have, h1*(L1-h1) = h2*(L2-h2), or h1^2-h2^2+h2*L2-h1*L1 = 0 .....(i)
+//Also, h1+h2 = d1/2+l+d2/2, or h1+h2-d1/2-l-d2/2 = 0 .....(ii)
+function y=f(x)
+ h1=x(1)
+ h2=x(2)
+ y(1)=h1^2-h2^2+h2*L2-h1*L1
+ y(2)=h1+h2-d1/2-l-d2/2
+endfunction
+z=fsolve([1,1],f)
+h1=z(1), h2=z(2) //m
+//Calculating the required radius of gyration of the rod
+kG=sqrt(h1*(L1-h1)) //m
+//Calculating the moment of inertia of the rod
+I=m*(kG)^2 //kg-m^2
+//Dynamically equivalent system for the rod:
+//Calculating the distance of the mass situated at the centre of small end bearing from the centre of gravity
+l1=h1-d1/2 //m
+//Calculating the distance of the second mass from the centre of gravity towards big end bearing
+l2=(kG)^2/l1 //m
+//Calculating the magnitude of the mass situated at the centre of small end bearing
+m1=(l2*m)/(l1+l2) //kg
+//Calculating the magnitude of the second mass
+m2=(l1*m)/(l1+l2) //kg
+//Results:
+printf("\n\n Radius of gyration of the rod about an axis passing through the centre of gravity and perpendicular to the plane of oscillation, kG = %.3f m.\n\n",kG)
+printf(" Moment of inertia of the rod, I = %.2f kg-m^2.\n\n",I)
+printf(" Magnitude of the mass situated at the centre of small end bearing, m1 = %.2f kg.\n\n",m1)
+printf(" Magnitude of the second mass, m2 = %.2f kg.\n\n",m2)
\ No newline at end of file diff --git a/213/CH15/EX15.18/15_18.sce b/213/CH15/EX15.18/15_18.sce new file mode 100755 index 000000000..f90cb27e5 --- /dev/null +++ b/213/CH15/EX15.18/15_18.sce @@ -0,0 +1,25 @@ +//To find correcting couple
+clc
+//Given:
+m=2 //kg
+l=250/1000, l1=100/1000, kG=110/1000 //m
+alpha=23000 //rad/s^2
+//Solution:
+//Equivalent dynamical system:
+//Calculating the distance of the second mass from the centre of gravity
+l2=(kG)^2/l1 //m
+//Calculating the magnitude of the mass placed at the gudgeon pin
+m1=(l2*m)/(l1+l2) //kg
+//Calculating the magnitude of the mass placed at a distance l2 from centre of gravity
+m2=(l1*m)/(l1+l2) //kg
+//Correction couple:
+//Calculating the magnitude of l3
+l3=l-l1 //m
+//Calculating the new radius of gyration
+k1=sqrt(l1*l3) //m^2
+//Calculating the correction couple
+Tdash=m*(k1^2-kG^2)*alpha //N-m
+//Results:
+printf("\n\n Mass placed at the gudgeon pin, m1 = %.1f kg.\n\n",m1)
+printf(" Mass placed at a distance %.3f m from the centre of gravity, m2 = %.1f kg.\n\n",l2,m2)
+printf(" Correction couple, Tdash = %.1f N-m.\n\n",Tdash)
\ No newline at end of file diff --git a/213/CH15/EX15.19/15_19.sce b/213/CH15/EX15.19/15_19.sce new file mode 100755 index 000000000..b64dab24d --- /dev/null +++ b/213/CH15/EX15.19/15_19.sce @@ -0,0 +1,24 @@ +//To find acceleration and inertia force
+clc
+//Given:
+r=125, OC=r, l=500, PC=l, PG=275, kG=150 //mm
+mC=60 //kg
+N=600 //rpm
+theta=45 //degrees
+//Solution:
+//Refer Fig. 15.24
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Acceleration of the piston:
+//By measurement,
+NO=90/1000 //m
+//Calculating the acceleration of the piston
+aP=omega^2*NO //m/s^2
+//The magnitude, position and direction of inertia force due to the mass of the connecting rod:
+//By measurement,
+gO=103/1000 //m
+//Calculating the magnitude of the inertia force of the connecting rod
+FC=mC*omega^2*gO/1000 //kN
+//Results:
+printf("\n\n Acceleration of the piston, aP = %.1f m/s^2.\n\n",aP)
+printf(" The magnitude of inertia force due to the mass of the connecting rod, FC = %.1f kN.\n\n",FC)
\ No newline at end of file diff --git a/213/CH15/EX15.2/15_2.sce b/213/CH15/EX15.2/15_2.sce new file mode 100755 index 000000000..d3489ab5a --- /dev/null +++ b/213/CH15/EX15.2/15_2.sce @@ -0,0 +1,41 @@ +//To find linear and angular velocity and acceleration
+clc
+//Given:
+OC=150/1000, PC=600/1000, CD=150/1000 //m
+N=450 //rpm
+//Solution:
+//Refer Fig. 15.6
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//By measurement,
+OM=145/1000, CM=78/1000, QN=130/1000, NO=56/1000 //m
+//Velocity and acceleration of alider:
+//Calculating the velocity of the slider P
+vP=omega*OM //m/s
+//Calculating the acceleration of the slider P
+aP=omega^2*NO //m/s^2
+//Velocity and acceleration of point D on the connecting rod:
+//Calculating the length od CD1
+CD1=CD/PC*CM //m
+//By measurement,
+OD1=145/1000, OD2=120/1000 //m
+//Calculating the velocity of point D
+vD=omega*OD1 //m/s
+//Calculating the acceleration of point D
+aD=omega^2*OD2 //m/s^2
+//Angular velocity and angular acceleration of the connecting rod:
+//Calculating the velocity of the connecting rod PC
+vPC=omega*CM //m/s
+//Calculating the angular velocity of the connecting rod
+omegaPC=vPC/PC //rad/s
+//Calculating the tangential component of the acceleration of P with respect to C
+atPC=omega^2*QN //m/s^2
+//Calculating the angular acceleration of the connecting rod PC
+alphaPC=atPC/PC //rad/s^2
+//Results:
+printf("\n\n Velocity of the slider P, vP = %.3f m/s.\n\n",vP)
+printf(" Acceleration of the slider P, aP = %.1f m/s^2.\n\n",aP)
+printf(" Velocity of point D, vD = %.3f m/s.\n\n",vD)
+printf(" Acceleration of point D, aD = %.2f m/s^2.\n\n",aD)
+printf(" Angular velocity of the connecting rod, omegaPC = %.3f rad/s.\n\n",omegaPC)
+printf(" Angular acceleration of the connecting rod PC, alphaPC = %.2f rad/s^2.\n\n",alphaPC)
\ No newline at end of file diff --git a/213/CH15/EX15.20/15_20.sce b/213/CH15/EX15.20/15_20.sce new file mode 100755 index 000000000..e18409780 --- /dev/null +++ b/213/CH15/EX15.20/15_20.sce @@ -0,0 +1,30 @@ +//To find torque exerted
+clc
+//Given:
+D=240/1000, L=600/1000, r=L/2, l=1.5, GC=500/1000, kG=650/1000 //m
+mR=300, mC=250 //kg
+N=125 //rpm
+theta=30 //degrees
+//Solution:
+//Refer Fig. 15.25
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Analytical method:
+//Calculating the distance of centre of gravity of the connecting rod from P
+l1=l-GC //m
+//Calculating the ratio of lengths of the connecting rod and crank
+n=l/r
+//Calculating the inertia force due to total mass of the reciprocating parts at P
+FI=(mR+(l-l1)/l*mC)*omega^2*r*(cosd(theta)+cosd(2*theta)/n) //N
+//Calculating the corresponding torque due to FI
+TI=FI*r*(sind(theta)+sind(2*theta)/(2*sqrt(n^2-(sind(theta))^2))) //N-m
+//Calculating the equivalent length of a simple pendulum when swung about an axis through P
+L=((kG)^2+(l1)^2)/l1 //m
+//Calculating the correcting torque
+TC=mC*l1*(l-L) //N-m
+//Calculating the torque due to the weight of the connecting rod at C
+TW=mC*9.81*(l1/n)*cosd(theta) //N-m
+//Calculating the total torque exerted on the crankshaft
+Tt=TI+TC+TW //Total torque exerted on the crankshaft, N-m
+//Results:
+printf("\n\n Total torque exerted on the crankshaft = %.1f N-m.\n\n",Tt)
\ No newline at end of file diff --git a/213/CH15/EX15.21/15_21.sce b/213/CH15/EX15.21/15_21.sce new file mode 100755 index 000000000..6a3d5639f --- /dev/null +++ b/213/CH15/EX15.21/15_21.sce @@ -0,0 +1,54 @@ +//To find acceleration and inertia torque
+clc
+//Given:
+N=1200 //rpm
+L=110/1000, r=L/2, l=250/1000, PC=l, CG=75/1000 //m
+mC=1.25 //kg
+theta=40 //degrees
+//Solution:
+//Refer Fig. 15.26
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Radius of gyration of the connecting rod about an axis through its mass centre:
+//Calculating the distance of the centre of gravity from the point of suspension
+l1=l-CG //m
+PG=l1
+//Calculating the frequency of oscillation
+n=21/20 //Hz
+//Calculating the radius of gyration of the connecting rod about an axis through its mass centre
+kG=round(sqrt((9.81*l1/(2*%pi*n)^2)-l1^2)*1000) //mm
+//Acceleration of the piston:
+//Calculating the ratio of lengths of the connecting rod and crank
+n=l/r
+//Calculating the acceleration of the piston
+aP=omega^2*r*(cosd(theta)+cosd(2*theta)/n) //m/s^2
+//Calculating the angular acceleration of the connecting rod
+alphaPC=(-omega^2*sind(theta))/n //rad/s^2
+//Inertia torque exerted on the crankshaft:
+//Calculating the mass of the connecting rod at P
+m1=(l-l1)/l*mC //kg
+//Calculating the vertical inertia force
+FI=round(m1*aP) //N
+//By measurement,
+OM=0.0425, NC=0.035 //m
+//Calculating the corresponding torque due to FI
+TI=FI*OM //N-m
+//Calculating the equivalent length of a simple pendulum when swung about an axis passing through P
+L=((kG/1000)^2+(l1)^2)/l1 //m
+//Calculating the correction couple
+Tdash=mC*l1*(l-L)*alphaPC //N-m
+//Calculating the corresponding torque on the crankshaft
+TC=-Tdash*cosd(theta)/n //N-m
+//Calculating the torque due to mass at P
+TP=m1*9.81*OM //N-m
+//Calculating the equivalent mass of the connecting rod at C
+m2=mC*(l1/l) //kg
+//Calculating the torque due to mass at C
+TW=m2*9.81*NC //N-m
+//Calculating the inertia force exerted on the crankshaft
+Ti=TI+TC-TP-TW //Inertia torque exerted on the crankshaft, N-m
+//Results:
+printf("\n\n Radius of gyration of the connecting rod about an axis through its mass centre, kG = %d mm.\n\n",kG)
+printf(" Acceleration of the piston, aP = %.1f m/s^2.\n\n",aP)
+printf(" Angular acceleration of the connecting rod, alphaPC = %.1f rad/s^2.\n\n",alphaPC)
+printf(" Inertia torque exerted on the crankshaft = %.3f N-m.\n\n",Ti)
\ No newline at end of file diff --git a/213/CH15/EX15.22/15_22.sce b/213/CH15/EX15.22/15_22.sce new file mode 100755 index 000000000..396d20b06 --- /dev/null +++ b/213/CH15/EX15.22/15_22.sce @@ -0,0 +1,28 @@ +//To find resultant force
+clc
+//Given:
+l=225/1000, PC=l, L=150/1000, r=L/2, D=112.5/1000, PG=150/1000, kG=87.5/1000 //m
+mC=1.6, mR=2.4 //kg
+theta=40 //degrees
+p=1.8*10^6 //N/m^2
+N=2000 //rpm
+//Solution:
+//Refer Fig. 15.27
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//By measurement,
+NO=0.0625, gO=0.0685, IC=0.29, IP=0.24, IY=0.148, IX=0.08 //m
+//Calculating the force due to gas pressure
+FL=%pi/4*D^2*p //N
+//Calculating the inertia force due to mass of the reciprocating parts
+FI=mR*omega^2*NO //N
+//Calculating the net force on the piston
+FP=FL-FI //N
+//Calculating the inertia force due to mass of the connecting rod
+FC=mC*omega^2*gO //N
+//Calculating the force acting perpendicular to the crank OC
+FT=((FP*IP)-((mC*9.81*IY)+(FC*IX)))/IC //N
+//By measurement,
+FN=3550, FR=7550, FQ=13750 //N
+//Results:
+printf("\n\n Resultant force on the crank pin, FQ = %d N.\n\n",FQ)
\ No newline at end of file diff --git a/213/CH15/EX15.3/15_3.sce b/213/CH15/EX15.3/15_3.sce new file mode 100755 index 000000000..64432cdc6 --- /dev/null +++ b/213/CH15/EX15.3/15_3.sce @@ -0,0 +1,23 @@ +//To find crank angle and velocity
+clc
+//Given:
+r=300/1000, l=1 //m
+N=200 //rpm
+//Solution:
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Crank angle at which the maximum velocity occurs:
+//Calculating the ratio of length of connecting rod to crank radius
+n=l/r
+//Velocity of the piston, vP = omega*r*(sind(theta)+sind(2*theta)/(2*n)) .....(i)
+//For maximum velocity, d(vP)/d(theta) = 0 .....(ii)
+//Substituting (i) in (ii), we get, 2(cosd(theta))^2+n*cosd(theta)-1 = 0
+a=2, b=n, c=-1
+costheta=(-b+sqrt(b^2-4*a*c))/(2*a)
+//Calculating the crank angle from the inner dead centre at which the maximum velocity occurs
+theta=round(acosd(costheta)) //degrees
+//Calculating the maximum velocity of the piston:
+vPmax=omega*r*(sind(theta)+sind(2*theta)/(2*n)) //m/s
+//Results:
+printf("\n\n Crank angle from the inner dead centre at which the maximum velocity occurs, theta = %d degrees.\n\n",theta)
+printf(" Maximum velocity of the piston, vP(max) = %.2f m/s.\n\n",vPmax)
\ No newline at end of file diff --git a/213/CH15/EX15.4/15_4.sce b/213/CH15/EX15.4/15_4.sce new file mode 100755 index 000000000..b61e95d0a --- /dev/null +++ b/213/CH15/EX15.4/15_4.sce @@ -0,0 +1,28 @@ +//To find velocity and acceleration
+clc
+//Given:
+r=0.3, l=1.5 //m
+N=180 //rpm
+theta=40 //degrees
+//Solution:
+//Calculating the angular speed of the piston
+omega=2*%pi*N/60 //rad/s
+//Velocity of the piston:
+//Calculating the ratio of lengths of the connecting rod and crank
+n=l/r
+//Calculating the velocity of the piston
+vP=omega*r*(sind(theta)+sind(2*theta)/(2*n)) //m/s
+//Calculating the acceleration of the piston
+aP=omega^2*r*(cosd(theta)+cosd(2*theta)/n) //m/s^2
+//Position of the crank for zero acceleration of the piston:
+ap1=0
+//Calculating the position of the crank from the inner dead centre for zero acceleration of the piston
+//We have, ap1 = omega^2*r*(cosd(theta1)+cosd(2*theta1)/n), or 2*(cosd(theta1))^2+n*cosd(theta1)-1 = 0
+a=2, b=n, c=-1
+costheta1=(-b+sqrt(b^2-4*a*c))/(2*a)
+//Calculating the crank angle from the inner dead centre for zero acceleration of the piston
+theta1=acosd(costheta1) //degrees
+//Results:
+printf("\n\n Velocity of the piston, vP = %.2f m/s.\n\n", vP)
+printf(" Acceleration of the piston, aP = %.2f m/s^2.\n\n",aP)
+printf(" Position of the crank for zero acceleration of the piston, theta1 = %.2f degrees or %.2f degrees.\n\n",theta1,360-theta1)
\ No newline at end of file diff --git a/213/CH15/EX15.5/15_5.sce b/213/CH15/EX15.5/15_5.sce new file mode 100755 index 000000000..f8d6d2883 --- /dev/null +++ b/213/CH15/EX15.5/15_5.sce @@ -0,0 +1,26 @@ +//To find linear and angualr velocity and acceleration
+clc
+//Given:
+r=150/1000, l=600/1000 //m
+theta=60 //degrees
+N=450 //rpm
+//Solution:
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Velocity and acceleration of the slider:
+//Calculating the ratio of length of connecting rod and crank
+n=l/r
+//Calculating the velocity of the slider
+vP=omega*r*(sind(theta)+sind(2*theta)/(2*n)) //m/s
+//Calculating the acceleration of the slider
+aP=omega^2*r*(cosd(theta)+cosd(2*theta)/n) //m/s^2
+//Angular velocity and angular acceleration of the connecting rod:
+//Calculating the angular velocity of the connecting rod
+omegaPC=omega*cosd(theta)/n //rad/s
+//Calculating the angular acceleration of the connecting rod
+alphaPC=round(omega^2*sind(theta)/n) //rad/s^2
+//Results:
+printf("\n\n Velocity of the slider, vP = %.1f m/s.\n\n",vP)
+printf(" Acceleration of the slider, aP = %.2f m/s^2.\n\n",aP)
+printf(" Angular velocity of the connecting rod, omegaPC = %.1f rad/s.\n\n",omegaPC)
+printf(" Angular acceleration of the connecting rod, alphaPC = %d rad/s^2.\n\n",alphaPC)
\ No newline at end of file diff --git a/213/CH15/EX15.6/15_6.sce b/213/CH15/EX15.6/15_6.sce new file mode 100755 index 000000000..1dd040dda --- /dev/null +++ b/213/CH15/EX15.6/15_6.sce @@ -0,0 +1,16 @@ +//To find inertia force
+clc
+//Given:
+D=175/1000, L=200/1000, r=L/2, l=400/1000 //m
+N=500 //rpm
+mR=180 //kg
+//Solution:
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Analytical method:
+//Calculating the ratio of lengths of connecting rod and crank
+n=l/r
+//Calculating the inertia force
+FI=mR*omega^2*r*(cosd(theta)+cosd(2*theta)/n)/1000 //kN
+//Results:
+printf("\n\n Inertia force, FI = %.2f kN.\n\n",FI)
\ No newline at end of file diff --git a/213/CH15/EX15.7/15_7.sce b/213/CH15/EX15.7/15_7.sce new file mode 100755 index 000000000..353186d52 --- /dev/null +++ b/213/CH15/EX15.7/15_7.sce @@ -0,0 +1,35 @@ +//To find pressure, thrust, force and moment
+clc
+//Given:
+r=300/1000, l=1.2, D=0.5 //m
+mR=250 //kg
+theta=60 //degrees
+dp=0.35 //p1-p2, N/mm^2
+N=250 //rpm
+//Solution:
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Calculating the net load on the piston
+FL=(dp)*%pi/4*(D*1000)^2 //N
+//Calculating the ratio of length of connecting rod and crank
+n=l/r
+//Calculating the accelerating or inertia force on reciprocating parts
+FI=mR*omega^2*r*(cosd(theta)+cosd(2*theta)/n) //N
+//Calculating the piston effort
+FP=(FL-FI)/1000 //kN
+//Pressure on slide bars:
+//Calculating the angle of inclination of the connecting rod to the line of stroke
+phi=asind(sind(theta)/n) //degrees
+//Calculating the pressure on the slide bars
+FN=FP*tand(phi) //kN
+//Calculating the thrust in the connecting rod
+FQ=FP/cosd(phi) //kN
+//Calculating the tangential force on the crank pin
+FT=FQ*sind(theta+phi) //kN
+//Calculating the turning moment on the crank shaft
+T=FT*r //kN-m
+//Results:
+printf("\n\n Pressure on the slide bars, FN = %.2f kN.\n\n",FN)
+printf(" Thrust in the connecting rod, FQ = %.2f kN.\n\n",FQ)
+printf(" Tangential force on the crank-pin, FT = %.2f kN.\n\n",FT)
+printf(" Turning moment on the crank shaft, T = %.3f kN-m.\n\n",T)
\ No newline at end of file diff --git a/213/CH15/EX15.8/15_8.sce b/213/CH15/EX15.8/15_8.sce new file mode 100755 index 000000000..2fd92e08a --- /dev/null +++ b/213/CH15/EX15.8/15_8.sce @@ -0,0 +1,29 @@ +//To find turning moment
+clc
+//Given:
+D=300/1000, L=450/1000, r=L/2, d=50/1000, l=1.2 //m
+N=200 //rpm
+mR=225 //kg
+theta=125 //degrees
+p1=30*1000, p2=1.5*1000 //N/m^2
+//Solution:
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Calculating the area of the piston
+A1=%pi/4*D^2 //m^2
+//Calculating the area of the piston rod
+a=%pi/4*d^2 //m^2
+//Calculating the force on the piston due to steam pressure
+FL=round(p1*A1-p2*(A1-a)) //N
+//Calculating the ratio of lengths of connecting rod and crank
+n=l/r
+//Calculating the inertia force on the reciprocating parts
+FI=mR*omega^2*r*(cosd(theta)+cosd(2*theta)/n) //N
+//Calculating the net force on the piston or piston effort
+FP=FL-FI+mR*9.81 //N
+//Calculating the angle of inclination of the connecting rod to the line of stroke
+phi=asind(sind(theta)/n) //degrees
+//Calculating the effective turning moment on the crank shaft
+T=FP*sind(theta+phi)/cosd(phi)*r //N-m
+//Results:
+printf("\n\n Effective turning moment of the crank shaft, T = %.1f N-m.\n\n",T)
\ No newline at end of file diff --git a/213/CH15/EX15.9/15_9.sce b/213/CH15/EX15.9/15_9.sce new file mode 100755 index 000000000..7b2bcc78c --- /dev/null +++ b/213/CH15/EX15.9/15_9.sce @@ -0,0 +1,39 @@ +//To find load, thrust, reaction and speed
+clc
+//Given:
+N=1800 //rpm
+r=50/1000, l=200/1000, D=80/1000, x=10/1000 //m
+mR=1 //kg
+p=0.7 //N/mm^2
+//Solution:
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Net load on the gudgeon pin:
+//Calculating the load on the piston
+FL=round(%pi/4*(D*1000)^2*p) //N
+//Refer Fig. 15.10
+//By measurement,
+theta=33 //degrees
+//Calculating the ratio of lengths of connecting rod and crank
+n=l/r
+//Calculating the inertia force on the reciprocating parts
+FI=mR*omega^2*r*(cosd(theta)+cosd(2*theta)/n) //N
+//Calculating the net load on the gudgeon pin
+FP=FL-FI //N
+//Thrust in the connecting rod:
+//Calculating the angle of inclination of the connecting rod to the line of stroke
+phi=asind(sind(theta)/n) //degrees
+//Calculating the thrust in the connecting rod
+FQ=FP/cosd(phi) //N
+//Calculating the reaction between the piston and cylinder
+FN=FP*tand(phi) //N
+//Engine speed at which the abov values will become zero:
+//Calculating the speed at which FI=FL
+omega1=sqrt((%pi/4*(D*1000)^2*p)/(mR*r*(cosd(theta)+cosd(2*theta)/n))) //rad/s
+//Calculating the corresponding speed in rpm
+N1=omega1*60/(2*%pi) //rpm
+//Results:
+printf("\n\n Net load on the gudgeon pin, FP = %d N.\n\n",FP)
+printf(" Thrust in the connecting rod, FQ = %.1f N.\n\n",FQ)
+printf(" Reaction between the piston and cylinder, FN = %d N.\n\n",FN)
+printf(" Engine speed at which the above values will become zero, N1 = %d rpm.\n\n",N1)
\ No newline at end of file diff --git a/213/CH16/EX16.1/16_1.sce b/213/CH16/EX16.1/16_1.sce new file mode 100755 index 000000000..828b56ce4 --- /dev/null +++ b/213/CH16/EX16.1/16_1.sce @@ -0,0 +1,19 @@ +//To find maximum and minimum speeds
+clc
+//Given:
+m=6.5*1000 //kg
+k=1.8 //m
+deltaE=56*1000 //N-m
+N=120 //rpm
+//Solution:
+//Calculating the maximum and minimum speeds
+//We know that fluctuation of energy, deltaE = %pi^2/900*m*k^2*N*(N1-N2), or N1-N2 = (deltaE/(%pi^2/900*m*k^2*N)) .....(i)
+//Also mean speed, N = (N1+N2)/2, or N1+N2 = 2*N .....(ii)
+A=[1 -1; 1 1]
+B=[deltaE/(%pi^2/900*m*k^2*N); 2*N]
+V=A \ B
+N1=round(V(1)) //rpm
+N2=round(V(2)) //rpm
+//Results:
+printf("\n\n Maximum speed, N1 = %d rpm.\n\n",N1)
+printf(" Minimum speed, N2 = %d rpm.\n\n",N2)
\ No newline at end of file diff --git a/213/CH16/EX16.10/16_10.sce b/213/CH16/EX16.10/16_10.sce new file mode 100755 index 000000000..f9c8feae2 --- /dev/null +++ b/213/CH16/EX16.10/16_10.sce @@ -0,0 +1,37 @@ +//To find mass of the rim
+clc
+//Given:
+a1=0.45*10^-3, a2=1.7*10^-3, a3=6.8*10^-3, a4=0.65*10^-3 //m^2
+N1=202, N2=198 //rpm
+R=1.2 //m
+//Solution:
+//Refer Fig. 16.12
+//Calculating the net area
+a=a3-(a1+a2+a4) //Net area, m^2
+//Calculating the energy scale constant
+c=3*10^6 //Energy scale constant, N-m
+//Calculating the net work done per cycle
+WD=a*c //Net work done per cycle, N-m
+//Calculating the mean torque
+Tmean=WD/(4*%pi) //N-m
+//Calculating the value of FG
+FG=Tmean //N-m
+//Calculating the work done during expansion stroke
+WDe=a3*c //Work done during expansion stroke, N-m
+//Calculating the value of AG
+AG=WDe/(1/2*%pi) //N-m
+//Calculating the excess torque
+Texcess=AG-FG //N-m
+//Calculating the value of AF
+AF=Texcess //N-m
+//Calculating the value of DE
+DE=AF/AG*%pi //rad
+//Calculating the maximum fluctuation of energy
+deltaE=1/2*DE*AF //N-m
+//Mass of the rim of a flywheel:
+//Calculating the mean speed of the flywheel
+N=(N1+N2)/2 //rpm
+//Calculating the mass of the rim of a flywheel
+m=deltaE/(%pi^2/900*R^2*N*(N1-N2)) //kg
+//Results:
+printf("\n\n Mass of the rim of the flywheel, m = %d kg.\n\n",m)
\ No newline at end of file diff --git a/213/CH16/EX16.12/16_12.sce b/213/CH16/EX16.12/16_12.sce new file mode 100755 index 000000000..6f9cab113 --- /dev/null +++ b/213/CH16/EX16.12/16_12.sce @@ -0,0 +1,39 @@ +//To find fluctuation of energy and speed
+clc
+//Given:
+m=500 //kg
+k=0.4 //m
+N=150 //rpm
+//Solution:
+//Refer Fig. 16.14
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Fluctuation of energy:
+//Equating the change in torque to zero and calculating the value of theta
+thetaA=asind(0), thetaC=asind(0)+180, thetaE=asind(0)+360 //degrees
+thetaB=acosd(1/(2*(600/500))), thetaD=360-acosd(1/(2*(600/500))) //degrees
+//Calculating the maximum fluctuation of energy
+deltaE=round(integrate('(5000+600*sin(2*theta))-(5000+500*sin(theta))','theta',thetaC*%pi/180,thetaD*%pi/180)) //N-m
+//Calculating the total percentage fluctuation of speed
+CS=deltaE/(m*k^2*omega^2)*100 //%
+//Maximum and minimum angular acceleration of the flywheel and the corresponding shaft positions:
+//Calculating the maximum or minimum values of theta
+//Differentiating (600*sin(2*theta))-500*sin(theta) = 0 with respect to theta and equating to zero, we get 12*2*(cosd(theta))^2-5*cosd(theta)-12 = 0
+a=12*2, b=-5, c=-12
+cosdtheta1=(-b+sqrt(b^2-4*a*c))/(2*a)
+cosdtheta2=(-b-sqrt(b^2-4*a*c))/(2*a)
+theta1=round(acosd(cosdtheta1)), theta2=acosd(cosdtheta2) //degrees
+//Calculating the maximum torque
+Tmax=600*sind(2*theta1)-500*sind(theta1) //N-m
+//Calculating the minimum torque
+Tmin=600*sind(2*theta2)-500*sind(theta2) //N-m
+//Calculating the maximum acceleration
+alphamax=Tmax/(m*k^2) //rad/s^2
+//Calculating the minimum acceleration
+alphamin=abs(Tmin)/(m*k^2) //rad/s^2
+//Results:
+printf("\n\n Fluctuation of energy, deltaE = %d N-m.\n\n",deltaE)
+printf(" Total percentage fluctuation of speed, CS = %.1f %c.\n\n",CS,"%")
+printf(" Shaft position corresponding to maximum and minimum accelerations, theta = %d degrees and %.1f degrees.\n\n",theta1,theta2)
+printf(" Maximum acceleration, alphamax = %.2f rad/s^2.\n\n",alphamax)
+printf(" Minimum acceleration, alphamin = %.1f rad/s^2.\n\n",alphamin)
\ No newline at end of file diff --git a/213/CH16/EX16.13/16_13.sce b/213/CH16/EX16.13/16_13.sce new file mode 100755 index 000000000..6e4450e47 --- /dev/null +++ b/213/CH16/EX16.13/16_13.sce @@ -0,0 +1,36 @@ +//To find power, fluctuation and torque
+clc
+//Given:
+I=1000 //kg-m^2
+N=300 //rpm
+//Solution:
+//Refer Fig. 16.15 and Fig. 16.16
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Power of the engine:
+//Calculating the work done per revolution
+WD=integrate('5000+1500*sin(3*theta)','theta',0,2*%pi) //Work done per cycle, N-m
+//Calculating the mean resisting torque
+Tmean=WD/(2*%pi) //N-m
+//Calculating the power of the engine
+P=Tmean*omega/1000 //kW
+//Maximum fluctuation of the speed of the flywheel when resisting torque is constant:
+//Calculating the value of theta
+sind3theta=(5000-5000)/1500
+theta=1/3*(asind(sind3theta)+180) //degrees
+//Calculating the maximum fluctuation of energy
+deltaE=integrate('5000+1500*sin(3*theta)-5000','theta',0,60*%pi/180) //N-m
+//Calculating the maximum fluctuation of speed of the flywheel
+CS1=deltaE/(I*omega^2)*100 //%
+//Maximum fluctuation of speed of the flywheel when resisting torque (5000+600*sin(theta)) N-m:
+//Calculating the values of theta, thetaB and thetaC
+thetaB=asind(sqrt((1/4*(3-600/1500)))) //degrees
+thetaC=180-thetaB //degrees
+//Calculating the maximum fluctuation of energy
+deltaE=round(integrate('(5000+1500*sin(3*theta))-(5000+600*sin(theta))','theta',thetaB*%pi/180,thetaC*%pi/180)) //N-m
+//Calculating the maximum fluctuation of speed of the flywheel
+CS2=abs(deltaE)/(I*omega^2)*100 //%
+//Results:
+printf("\n\n Power of the engine, P = %.1f kW.\n\n",P)
+printf(" Maximum fluctuation of the speed of the flywheel when resisting torque is constant, CS = %.1f %c.\n\n",CS1,"%")
+printf(" Maximum fluctuation of speed of the flywheel when resisting torque (5000+600*sin(theta)) N-m, CS = %.3f %c.\n\n",CS2,"%")
\ No newline at end of file diff --git a/213/CH16/EX16.14/16_14.sce b/213/CH16/EX16.14/16_14.sce new file mode 100755 index 000000000..9b89721e8 --- /dev/null +++ b/213/CH16/EX16.14/16_14.sce @@ -0,0 +1,33 @@ +//To find diameter and cross section
+clc
+//Given:
+N=800 //rpm
+stroke=300 //mm
+sigma=7*10^6 //N/m^2
+rho=7200 //kg/m^3
+//Solution:
+//Refer Fig. 16.18
+//Calculating the angular speed of the engine
+omega=2*%pi*N/60 //rad/s
+//Calculating the coefficient of fluctuation of speed
+CS=4/100
+//Diameter of the flywheel rim:
+//Calculating the peripheral velocity of the flywheel rim
+v=sqrt(sigma/rho) //m/s
+//Calculating the diameter of the flywheel rim
+D=v*60/(%pi*N) //m
+//Cross-section of the flywheel rim:
+//Calculating the value of 1 mm^2 on the turning moment diagram
+c=500*%pi/30 //Value of 1 mm^2 on the turning moment diagram, N-m
+//Calculating the maximum fluctuation of energy
+deltaE=round((420-(-30))*c) //N-m
+//Calculating the mass of the flywheel rim
+m=deltaE/(v^2*CS) //kg
+//Calculating the thickness of the flywheel rim
+t=sqrt(m/(%pi*D*5*rho))*1000 //mm
+//Calculating the width of the flywheel rim
+b=5*t //mm
+//Results:
+printf("\n\n Diameter of the flywheel rim, D = %.3f m.\n\n",D)
+printf(" Thickness of the flywheel rim, t = %d mm.\n\n",t)
+printf(" Width of the flywheel rim, b = %d mm.\n\n",b)
\ No newline at end of file diff --git a/213/CH16/EX16.15/16_15.sce b/213/CH16/EX16.15/16_15.sce new file mode 100755 index 000000000..52732a0de --- /dev/null +++ b/213/CH16/EX16.15/16_15.sce @@ -0,0 +1,30 @@ +//To find mass and cross section
+clc
+//Given:
+P=150*1000 //W
+N=80 //rpm
+CE=0.1
+D=2, R=D/2 //m
+rho=7200 //kg/m^3
+//Solution:
+//Calculating the angular speed of the engine
+omega=2*%pi*N/60 //rad/s
+//Calculating the coefficient of fluctuation of speed
+CS=4/100
+//Mass of the flywheel rim:
+//Calculating the work done per cycle
+WD=P*60/N //Work done per cycle, N-m
+//Calculating the maximum fluctuation of energy
+deltaE=WD*CE //N-m
+//Calculating the mass moment of inertia of the flywheel
+I=deltaE/(omega^2*CS) //kg-m^2
+//Calculating the mass moment of inertia of the flywheel rim
+Irim=0.95*I //kg-m^2
+//Calculating the mass of the flywheel rim
+k=R //Radius of gyration, m
+m=Irim/k^2 //kg
+//Calculating the cross-sectional area of the flywheel rim
+A=m/(2*%pi*R*rho) //m^2
+//Resilts:
+printf("\n\n Mass of the flywheel rim, m = %d kg.\n\n",m)
+printf(" Cross-sectional area of the flywheel rim, A = %.3f m^2.\n\n",A)
\ No newline at end of file diff --git a/213/CH16/EX16.16/16_16.sce b/213/CH16/EX16.16/16_16.sce new file mode 100755 index 000000000..1ce9bf254 --- /dev/null +++ b/213/CH16/EX16.16/16_16.sce @@ -0,0 +1,36 @@ +//To find MI and dimensions
+clc
+//Given:
+N=600 //rpm
+rho=7250 //kg/m^3
+sigma=6*10^6 //N/m^2
+//Solution:
+//Refer Fig. 16.19
+//Calculating the angular speed of the engine
+omega=2*%pi*N/60 //rad/s
+//Calculating the total fluctuation of speed
+CS=2/100
+//Moment of inertia of the flywheel:
+//Calculating the value of 1 mm^2 of turning moment diagram
+c=250*%pi/60 //Value of 1 mm^2 of turning moment diagram, N-m
+//Calculating the maximum fluctuation of energy
+deltaE=round((162-(-35))*c) //N-m
+//Calculating the moment of inertia of the flywheel
+I=deltaE/(omega^2*CS) //kg-m^2
+//Dimensions of the flywheel rim:
+//Calculating the peripheral velocity of the flywheel
+v=sqrt(sigma/rho) //m/s
+//Calculating the mean diameter of the flywheel
+D=v*60/(%pi*N) //m
+//Calculating the maximum fluctuation of energy of the flywheel rim
+deltaErim=0.92*deltaE //N-m
+//Calculating the mass of the flywheel rim
+m=deltaErim/(v^2*CS) //kg
+//Calculating the thickness of the flywheel rim
+t=sqrt(m/(%pi*D*2*rho))*1000 //mm
+//Calculating the breadth of the flywheel rim
+b=2*t //mm
+//Results:
+printf("\n\n Moment of inertia of the flywheel, I = %.1f kg-m^2.\n\n",I)
+printf(" Thickness of the flywheel rim, t = %.1f mm.\n\n",t)
+printf(" Breadth of the flywheel rim, b = %.1f mm.\n\n",b)
\ No newline at end of file diff --git a/213/CH16/EX16.17/16_17.sce b/213/CH16/EX16.17/16_17.sce new file mode 100755 index 000000000..572f6c36d --- /dev/null +++ b/213/CH16/EX16.17/16_17.sce @@ -0,0 +1,53 @@ +//To find MI and size
+clc
+//Given:
+a1=5*10^-5, a2=21*10^-5, a3=85*10^-5, a4=8*10^-5 //m^2
+N2=98, N1=102 //rpm
+rho=8150 //kg/m^3
+sigma=7.5*10^6 //N/m^2
+//Solution:
+//Refer Fig. 16.20
+//Calculating the net area
+a=a3-(a1+a2+a4) //Net area, m^2
+//Calculating the value of 1 m^2 on the turning moment diagram in terms of work
+c=14*10^6 //Value of 1 m^2 on the turning moment diagram, N-m
+//Calculating the net work done per cycle
+WD=a*c //Net work done per cycle, N-m
+//Calculating the mean torque on the flywheel
+Tmean=WD/(4*%pi) //N-m
+FG=Tmean //N-m
+//Calculating the work done during expansion stroke
+WDe=a3*c //Work done during expansion stroke, N-m
+//Calculating the value of AG
+AG=WDe/(1/2*%pi) //N-m
+//Calculating the excess torque
+Texcess=AG-FG //Excess torque, N-m
+AF=Texcess //N-m
+//Calculating the value of DE
+DE=AF/AG*%pi //rad
+//Calculating the maximum fluctuation of energy
+deltaE=1/2*DE*AF //N-m
+//Moment of inertia of the flywheel:
+//Calculating the mean speed during the cycle
+N=(N1+N2)/2 //rpm
+//Calculating the corresponding angular mean speed
+omega=2*%pi*N/60 //rad/s
+//Calculating the coefficient of fluctuation of speed
+CS=(N1-N2)/N
+//Calculating the moment of inertia of the flywheel
+I=deltaE/(omega^2*CS) //kg-m^2
+//Size of flywheel:
+//Calculating the peripheral velocity of the flywheel
+v=sqrt(sigma/rho) //m/s
+//Calculating the mean diameter of the flywheel
+D=v*60/(%pi*N) //m
+//Calculating the mass of the flywheel rim
+m=deltaE/(v^2*CS) //kg
+//Calculating the thickness of the flywheel rim
+t=sqrt(m/(%pi*D*4*rho))*1000 //mm
+//Calculating the width of the flywheel rim
+b=4*t //mm
+//Results:
+printf("\n\n Moment of inertia of the flywheel, I = %d kg-m^2.\n\n",I)
+printf(" Thickness of the flywheel rim, t = %.1f mm.\n\n",t)
+printf(" Width of the flywheel rim, b = %.1f mm.\n\n",b)
\ No newline at end of file diff --git a/213/CH16/EX16.18/16_18.sce b/213/CH16/EX16.18/16_18.sce new file mode 100755 index 000000000..810ec4a7e --- /dev/null +++ b/213/CH16/EX16.18/16_18.sce @@ -0,0 +1,51 @@ +//To find diameter and cross section
+clc
+//Given:
+P=50*1000 //W
+N=150 //rpm
+n=75
+sigma=4*10^6 //N/m^2
+rho=7200 //kg/m^3
+//Solution:
+//Refer Fig. 16.21
+//Calculating the angular speed of the engine
+omega=2*%pi*N/60 //rad/s
+//Calculating the mean torque transmitted by the flywheel
+Tmean=P/omega //N-m
+FG=Tmean //N-m
+//Calculating the work done per cycle
+WD=Tmean*4*%pi //Work done per cycle, N-m
+//Calculating the work done during power stroke
+WDp=1.4*WD //Work done during power stroke, N-m
+//Calculating the maximum torque transmitted by the flywheel
+Tmax=WDp/(1/2*%pi) //N-m
+BF=Tmax //N-m
+//Calculating the excess torque
+Texcess=Tmax-Tmean //N-m
+BG=Texcess //N-m
+//Calculating the value of DE
+DE=BG/BF*%pi //N-m
+//Calculating the maximum fluctuation of energy
+deltaE=1/2*DE*BG //N-m
+//Mean diameter of the flywheel:
+//Calculating the peripheral velocity of the flywheel
+v=sqrt(sigma/rho) //m/s
+//Calculating the mean diameter of the flywheel
+D=v*60/(%pi*N) //m
+//Cross-sectional dimensions of the rim:
+//Calculating the coefficient of fluctuation of speed
+CS=1/100
+//Calculating the total energy of the flywheel
+E=deltaE/(2*CS) //N-m
+//Calculating the energy of the rim
+Erim=15/16*E //N-m
+//Calculating the mass of the flywheel rim
+m=Erim/(1/2*v^2) //kg
+//Calculating the thickness of the rim
+t=round(sqrt(m/(%pi*D*4*rho))*1000) //mm
+//Calculating the width of the rim
+b=4*t //mm
+//Results:
+printf("\n\n Mean diameter of the flywheel, D = %d m.\n\n",D)
+printf(" Thickness of the flywheel rim, t = %d mm.\n\n",t)
+printf(" Width of the flywheel rim, b = %d mm.\n\n",b)
\ No newline at end of file diff --git a/213/CH16/EX16.19/16_19.sce b/213/CH16/EX16.19/16_19.sce new file mode 100755 index 000000000..23af608a0 --- /dev/null +++ b/213/CH16/EX16.19/16_19.sce @@ -0,0 +1,25 @@ +//To find power and mass
+clc
+//Given:
+N1=225, N2=200 //rpm
+k=0.5 //m
+E1=15*1000 //N-m
+HolePunched=720 //per hour
+//Solution:
+//Power of the motor:
+//Calculating the total energy required per second
+E=E1*HolePunched/3600 //N-m/s
+//Calculating the power of the motor
+P=E/1000 //kW
+//Minimum mass of the flywheel:
+//Calculating the energy supplied by the motor in 2 seconds
+E2=E*2 //N-m
+//Calculating the energy supplied by the flywheel during punching
+deltaE=E1-E2 //N-m
+//Calculating the mean speed of the flywheel
+N=(N1+N2)/2 //rpm
+//Calculating the minimum mass of the flywheel
+m=round(deltaE*900/(%pi^2*k^2*N*(N1-N2))) //kg
+//Results:
+printf("\n\n Power of the motor, P = %d kW.\n\n",P)
+printf(" Minimum mass of the flywheel, m = %d kg.\n\n",m)
\ No newline at end of file diff --git a/213/CH16/EX16.2/16_2.sce b/213/CH16/EX16.2/16_2.sce new file mode 100755 index 000000000..6c2a6da14 --- /dev/null +++ b/213/CH16/EX16.2/16_2.sce @@ -0,0 +1,21 @@ +//To find angular acceleration and KE
+clc
+//Given:
+k=1 //m
+m=2500 //kg
+T=1500 //N-m
+//Solution:
+//Angular acceleration of the flywheel:
+//Calculating the mass moment of inertia of the flywheel
+I=m*k^2 //kg-m^2
+//Calculating the angular acceleration of the flywheel
+alpha=T/I //rad/s^2
+//Kinetic energy of the flywheel:
+omega1=0 //Angular speed at rest
+//Calculating the angular speed after 10 seconds
+omega2=omega1+alpha*10 //rad/s
+//Calculating the kinetic energy of the flywheel
+KE=1/2*I*(omega2)^2/1000 //Kinetic energy of the flywheel, kN-m
+//Results:
+printf("\n\n Angular acceleration of the flywheel, alpha = %.1f rad/s^2.\n\n",alpha)
+printf(" Kinetic energy of the flywheel = %d kN-m.\n\n",KE)
\ No newline at end of file diff --git a/213/CH16/EX16.20/16_20.sce b/213/CH16/EX16.20/16_20.sce new file mode 100755 index 000000000..89e031e49 --- /dev/null +++ b/213/CH16/EX16.20/16_20.sce @@ -0,0 +1,30 @@ +//To find power and mass
+clc
+//Given:
+d=38, t=32, s=100 //mm
+E1=7 //N-m/mm^2 of sheared area
+v=25 //m/s
+//Solution:
+//Power of the motor required:
+//Calculating the sheared area
+A=round(%pi*d*t) //mm^2
+//Calculating the total energy required per hole
+E1=E1*A //N-m
+//Calculating the energy required for punching work per second
+E=E1/10 //Energy required for punching work per second, N-m/s
+//Calculating the power of the motor required
+P=E/1000 //Power of the motor required, kW
+//Mass of the flywheel required:
+//Calculating the time required to punch a hole in a 32 mm thick plate
+t32=10/(2*s)*t //Time required to punch a hole in 32 mm thick plate, seconds
+//Calculating the energy supplied by the motor in t32 seconds
+E2=E*t32 //N-m
+//Calculating the energy to be supplied by the flywheel during punching
+deltaE=E1-E2 //N-m
+//Calculating the coefficient of fluctuation of speed
+CS=3/100
+//Calculating the mass of the flywheel required
+m=round(deltaE/(v^2*CS)) //kg
+//Results:
+printf("\n\n Power of the motor required, P = %.3f kW.\n\n",P)
+printf(" Mass of the flywheel required, m = %d kg.\n\n",m)
\ No newline at end of file diff --git a/213/CH16/EX16.21/16_21.sce b/213/CH16/EX16.21/16_21.sce new file mode 100755 index 000000000..af910bb1a --- /dev/null +++ b/213/CH16/EX16.21/16_21.sce @@ -0,0 +1,26 @@ +//To find speed and number of rivets
+clc
+//Given:
+P=3 //kW
+m=150 //kg
+k=0.6 //m
+N1=300 //rpm
+//Solution:
+//Calculating the angular speed of the flywheel before riveting
+omega1=2*%pi*N1/60 //rad/s
+//Speed of the flywheel immediately after riveting:
+//Calculating the energy supplied by the motor
+E2=P*1000 //N-m/s
+//Calculating the energy absorbed during one riveting operation which takes 1 second
+E1=10000 //N-m
+//Calculating the energy to be supplied by the flywheel for each riveting operation per second
+deltaE=E1-E2 //N-m
+//Calculating the angular speed of the flywheel immediately after riveting
+omega2=sqrt(omega1^2-(2*deltaE/(m*k^2))) //rad/s
+//Calculating the corresponding speed in rpm
+N2=omega2*60/(2*%pi) //rpm
+//Calculating the number of rivets that can be closed per minute
+n=E2/E1*60 //Number of rivets that can be closed per minute
+//Results:
+printf("\n\n Speed of the flywheel immediately after riveting, N2 = %.1f rpm.\n\n",N2)
+printf(" Number of rivets that can be closed per minute = %d rivets.\n\n",n)
\ No newline at end of file diff --git a/213/CH16/EX16.22/16_22.sce b/213/CH16/EX16.22/16_22.sce new file mode 100755 index 000000000..46e410a85 --- /dev/null +++ b/213/CH16/EX16.22/16_22.sce @@ -0,0 +1,26 @@ +//To find mass of the flywheel
+clc
+//Given:
+d=40, t=15 //mm
+NoofHoles=30 //per minute
+EnergyRequired=6 //N-m/mm^2
+Time=1/10 //seconds
+N1=160, N2=140 //rpm
+k=1 //m
+//Solution:
+//Calculating the sheared area per hole
+A=round(%pi*d*t) //Sheared area per hole, mm^2
+//Calculating the energy required to punch a hole
+E1=EnergyRequired*A //N-m
+//Calculating the energy required for punching work per second
+E=E1*NoofHoles/60 //Energy required for punching work per second, N-m/s
+//Calculating the energy supplied by the motor during the time of punching
+E2=E*Time //N-m
+//Calculating the energy to be supplied by the flywheel during punching a hole
+deltaE=E1-E2 //N-m
+//Calculating the mean speed of the flywheel
+N=(N1+N2)/2 //rpm
+//Calculating the mass of the flywheel required
+m=round(deltaE*900/(%pi^2*k^2*N*(N1-N2))) //kg
+//Results:
+printf("\n\n Mass of the flywheel required, m = %d kg.\n\n",m)
\ No newline at end of file diff --git a/213/CH16/EX16.23/16_23.sce b/213/CH16/EX16.23/16_23.sce new file mode 100755 index 000000000..4410f8d04 --- /dev/null +++ b/213/CH16/EX16.23/16_23.sce @@ -0,0 +1,40 @@ +//To find power and cross section
+clc
+//Given:
+n=25
+d1=25/1000, t1=18/1000, D=1.4, R=D/2 //m
+touu=300*10^6 //N/m^2
+etam=95/100, CS=0.1
+sigma=6*10^6 //N/m^2
+rho=7250 //kg/m^3
+//Solution:
+//Power needed for the driving motor:
+//Calculating the area of the plate sheared
+AS=%pi*d1*t1 //m^2
+//Calculating the maximum shearing force required for punching
+FS=AS*touu //N
+//Calculating the energy required per stroke
+E=1/2*FS*t1 //Energy required per stroke, N-m
+//Calculating the energy required per minute
+E1=E*n //Energy required per minute, N-m
+//Calculating the power required for the driving motor
+P=E1/(60*etam)/1000 //Energy required for the driving motor, kW
+//Dimensions for the rim cross-section:
+//Calculating the maximum fluctuation of energy
+deltaE=9/10*E //N-m
+//Calculating the maximum fluctuation of energy provided by the rim
+deltaErim=0.95*deltaE //N-m
+//Calculating the mean speed of the flywheel
+N=9*25 //rpm
+//Calculating the mean angular speed
+omega=2*%pi*N/60 //rad/s
+//Calculating the mass of the flywheel
+m=round(deltaErim/(R^2*omega^2*CS)) //kg
+//Calculating the thickness of rim
+t=sqrt(m/(%pi*D*2*rho))*1000 //mm
+//Calculating the width of rim
+b=2*t //mm
+//Results:
+printf("\n\n Power needed for the driving motor = %.3f kW.\n\n",P)
+printf(" Thickness of the flywheel rim, t = %d mm.\n\n",t)
+printf(" Width of the flywheel rim, b = %d mm.\n\n",b)
\ No newline at end of file diff --git a/213/CH16/EX16.3/16_3.sce b/213/CH16/EX16.3/16_3.sce new file mode 100755 index 000000000..e2b47f107 --- /dev/null +++ b/213/CH16/EX16.3/16_3.sce @@ -0,0 +1,20 @@ +//To find weight of flywheel
+clc
+//Given:
+P=300*1000 //W
+N=90 //rpm
+CE=0.1
+k=2 //m
+//Solution:
+//Calculating the mean angular speed
+omega=2*%pi*N/60 //rad/s
+//Calculating the coefficient of fluctuation of speed
+CS=1/100
+//Calculating the work done per cycle
+WD=P*60/N //Work done per cycle, N-m
+//Calculating the maximum fluctuation of energy
+deltaE=WD*CE //N-m
+//Calculating the mass of the flywheel
+m=deltaE/(k^2*omega^2*CS) //kg
+//Results:
+printf("\n\n Mass of the flywheel, m = %d kg.\n\n",m)
\ No newline at end of file diff --git a/213/CH16/EX16.4/16_4.sce b/213/CH16/EX16.4/16_4.sce new file mode 100755 index 000000000..d4681e2e9 --- /dev/null +++ b/213/CH16/EX16.4/16_4.sce @@ -0,0 +1,19 @@ +//To find coefficient of fluctuation of speed
+clc
+//Given:
+m=36 //kg
+k=150/1000 //m
+N=1800 //rpm
+//Solution:
+//Refer Fig. 16.6
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Calculating the value of 1 mm^2 on the turning moment diagram
+c=5*%pi/180 //Value of 1 mm^2 on turning miment diagram, N-m
+//Calculating the maximum fluctuation of energy
+//From the turning moment diagram, maximum energy = E+295, and minimum energy = E-690
+deltaE=(285-(-690))*c //N-m
+//Calculating the coefficient of fluctuation of energy
+CS=deltaE/(m*k^2*omega^2)*100 //%
+//Results:
+printf("\n\n Coefficient of fluctuation of speed, CS = %.1f %c.\n\n",CS,"%")
\ No newline at end of file diff --git a/213/CH16/EX16.5/16_5.sce b/213/CH16/EX16.5/16_5.sce new file mode 100755 index 000000000..57ae7f9f0 --- /dev/null +++ b/213/CH16/EX16.5/16_5.sce @@ -0,0 +1,20 @@ +//To find mass of the flywheel
+clc
+//Given:
+N=600 //rpm
+R=0.5 //m
+//Solution:
+//Refer Fig. 16.7
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Calculating the coefficient of fluctuation of speed
+CS=3/100
+//Calculating the value of 1 mm^2 on turning moment diagram
+c=600*%pi/60 //Value of 1 mm^2 on turning moment diagram, N-m
+//Calculating the maximum fluctuation of energy
+//From the turning moment diagram, maximum fluctuation = E+52, and minimum fluctuation = E-120
+deltaE=(52-(-120))*c //N-m
+//Calculating the mass of the flywheel
+m=deltaE/(R^2*omega^2*CS) //kg
+//Results:
+printf("\n\n Mass of the flywheel, m = %d kg.\n\n",m)
\ No newline at end of file diff --git a/213/CH16/EX16.6/16_6.sce b/213/CH16/EX16.6/16_6.sce new file mode 100755 index 000000000..5604daedd --- /dev/null +++ b/213/CH16/EX16.6/16_6.sce @@ -0,0 +1,33 @@ +//To find power and speed fluctuation
+clc
+//Given:
+N=250 //rpm
+m=500 //kg
+k=600/1000 //m
+//Solution:
+//Refer Fig. 16.8
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Calculating the torque required for one complete cycle
+T=(6*%pi*750)+(1/2*%pi*(3000-750))+(2*%pi*(3000-750))+(1/2*%pi*(3000-750)) //N-m
+//Calculating the mean torque
+Tmean=T/(6*%pi) //N-m
+//Calculating the power required to drive the machine
+P=Tmean*omega/1000 //kW
+//Coefficient of fluctuation of speed:
+//Calculating the value of LM
+LM=%pi*((3000-1875)/(3000-750))
+//Calculating the value of NP
+NP=%pi*((3000-1875)/(3000-750))
+//Calculating the value of BM
+BM=3000-1875 //N-m
+CN=BM
+//Calculating the value of MN
+MN=2*%pi
+//Calculating the maximum fluctuation of energy
+deltaE=(1/2*LM*BM)+(MN*BM)+(1/2*NP*CN) //N-m
+//Calculating the coefficient of fluctuation of speed
+CS=deltaE/(m*k^2*omega^2)
+//Results:
+printf("\n\n Power required to drive the machine, P = %.3f kW.\n\n",P)
+printf(" Coefficient of speed, CS = %.3f.\n\n",CS)
\ No newline at end of file diff --git a/213/CH16/EX16.7/16_7.sce b/213/CH16/EX16.7/16_7.sce new file mode 100755 index 000000000..9c07dad33 --- /dev/null +++ b/213/CH16/EX16.7/16_7.sce @@ -0,0 +1,39 @@ +//To find coefficient of fluctuation
+clc
+//Given:
+N=100 //rpm
+k=1.75 //m
+//Solution:
+//Refer Fig. 16.9
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Calculating the coefficient of fluctuation of speed
+CS=1.5/100
+//Coefficient of fluctuation of energy:
+AB=2000, LM=1500 //N-m
+//Calculating the work done per cycle
+WD=(1/2*%pi*AB)+(1/2*%pi*LM) //Work done per cycle, N-m
+//Calculating the mean resisting torque
+Tmean=WD/(2*%pi) //N-m
+//Calculating the value of CD
+CD=%pi/2000*(2000-875) //rad
+//Calculating the maximum fluctuation of energy
+deltaE=1/2*CD*(2000-875) //N-m
+//Calculating the coefficient of fluctuation of energy
+Ce=deltaE/WD*100 //%
+//Calculating the mass of the flywheel
+m=deltaE/(k^2*omega^2*CS) //kg
+//Crank angles for minimum and maximum speeds:
+//Calculating the value of CE
+CE=(2000-875)/2000*(4*%pi/9) //rad
+//Calculating the crank angle for minimum speed
+thetaC=((4*%pi/9)-CE)*180/%pi //degrees
+//Calculating the value of ED
+ED=(2000-875)/2000*(%pi-(4*%pi/9)) //rad
+//Calculating the crank angle for maximum speed
+thetaD=((4*%pi/9)+ED)*180/%pi //degrees
+//Results:
+printf("\n\n Coefficient of fluctuation of energy, CE = %d %c.\n\n",Ce,"%")
+printf(" Mass of the flywheel, m = %.1f kg.\n\n",m)
+printf(" Crank angle from IDC for the minimum speed, thetaC = %d degrees.\n\n",thetaC)
+printf(" Crank angle from IDC for the maximum speed, thetaD = %d degrees.\n\n",thetaD)
\ No newline at end of file diff --git a/213/CH16/EX16.8/16_8.sce b/213/CH16/EX16.8/16_8.sce new file mode 100755 index 000000000..fb40d5c3b --- /dev/null +++ b/213/CH16/EX16.8/16_8.sce @@ -0,0 +1,33 @@ +//To find power and coefficients
+clc
+//Given:
+N=600 //rpm
+Tmax=90 //N-m
+m=12 //kg
+k=80/1000 //m
+//Solution:
+//Refer Fig. 16.10
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //rad/s
+//Power developed:
+//Calculating the work done per cycle
+WD=3*1/2*%pi*90 //Work done per cycle, N-m
+//Calculating the mean torque
+Tmean=WD/(2*%pi) //N-m\
+//Calculating the power developed
+P=Tmean*omega/1000 //Power developed, kW
+//Coefficient of fluctuation of speed:
+//Calculating the maximum fluctuation of energy
+//From the torque-crank angle diagram, maximum energy=E+5.89, and minimum energy=E-5.89
+deltaE=5.89-(-5.89) //N-m
+//Calculating the coefficient of fluctuation of speed
+CS=round(deltaE/(m*k^2*omega^2)*100) //%
+//Calculating the coefficient of fluctuation of energy
+CE=deltaE/WD*100 //%
+//Calculating the maximum angular acceleration of the flywheel
+alpha=(Tmax-Tmean)/(m*k^2) //rad/s^2
+//Results:
+printf("\n\n Power developed = %.2f kW.\n\n",P)
+printf(" Coefficient of fluctuation of speed, CS = %d %c.\n\n",CS,"%")
+printf(" Coefficient of fluctuation of energy, CE = %.2f %c.\n\n",CE,"%")
+printf(" Maximum angular acceleration of the flywheel, alpha = %d rad/s^2.\n\n",alpha)
\ No newline at end of file diff --git a/213/CH16/EX16.9/16_9.sce b/213/CH16/EX16.9/16_9.sce new file mode 100755 index 000000000..1ea7b81e0 --- /dev/null +++ b/213/CH16/EX16.9/16_9.sce @@ -0,0 +1,31 @@ +//To find moment of inertia
+clc
+//Given:
+P=20*1000 //W
+N=300 //rpm
+//Solution:
+//Refer Fig. 16.11
+//Calculating the angular speed of the crank
+omega=2*%pi*N/60 //ra/s
+//Calculating the coefficient of fluctuation of speed
+CS=4/100
+//Calculating the number of working strokes per cycle for a four stroke engine
+n=N/2
+//Calculating the work done per cycle
+WD=P*60/n //Work done per cycle, N-m
+//Calculating the work done during expansion cycle
+WE=WD*3/2 //N-m
+//Calculating the maximum turning moment
+Tmax=WE*2/%pi //N-m
+//Calculating the mean turning moment
+Tmean=WD/(4*%pi) //N-m
+//Calculating the excess turning moment
+Texcess=Tmax-Tmean //N-m
+//Calculating the value of DE
+DE=Texcess/Tmax*%pi //rad
+//Calculating the maximum fluctuation of energy
+deltaE=(1/2*DE*Texcess) //N-m
+//Calculating the moment of inertia of the flywheel
+I=deltaE/(omega^2*CS) //kg-m^2
+//Results:
+printf("\n\n Moment of inertia of the flywheel, I = %.1f kg-m^2.\n\n",I)
\ No newline at end of file diff --git a/213/CH2/EX2.1/2_1.sce b/213/CH2/EX2.1/2_1.sce new file mode 100755 index 000000000..c2fd0d1f8 --- /dev/null +++ b/213/CH2/EX2.1/2_1.sce @@ -0,0 +1,28 @@ +//To Find the Acceleration and Distance
+clc
+//Given:
+u1=0,v1=72*1000/3600 //m/s
+s1=500 //m
+//Solution:
+//Calculating the initial acceleration of the car
+a1=(v1^2-u1^2)/(2*s1) //m/s^2
+//Calculating time taken by the car to attain the speed
+t1=(v1-u1)/a1 //seconds
+//Parameters for the second case
+u2=v1,v2=90*1000/3600 //m/s
+t2=10 //seconds
+//Calculating the acceleration for the second case
+a2=(v2-u2)/t2 //m/s^2
+//Calculating the distance moved by the car in the second case
+s2=(u2*t2)+(a2/2*t2^2)
+//Parameters for the third case
+u3=v2,v3=0 //m/s
+t3=5 //seconds
+//Calculating the distance moved by the car
+s3=(u3+v3)*t3/2 //m
+//Results:
+printf("\n\n The acceleration of the car, a = %.1f m/s^2. \n",a1)
+printf(" The car takes t = %d s to attain the speed.\n",t1)
+printf(" The acceleration of the car in the second case, a = %.1f m/s^2.",a2)
+printf("\n The distance moved by the car, s = %d m.\n",s2)
+printf(" The distance travelled by the car during braking, s = %.1f m.\n\n",s3)
\ No newline at end of file diff --git a/213/CH2/EX2.3/2_3.sce b/213/CH2/EX2.3/2_3.sce new file mode 100755 index 000000000..bcda83c83 --- /dev/null +++ b/213/CH2/EX2.3/2_3.sce @@ -0,0 +1,22 @@ +//To Find the Velocity
+clc
+//Given:
+//Initial parameters
+v0=100 //kmph
+t0=0
+//Parameters at the end of 40 seconds
+v1=90/100*v0 //kmph
+t1=40 //seconds
+//Solution:
+//The acceleration is given by, a=(-dv/dt)=k*v
+//Integrating, we get ln(v)=-k*t+C
+//Calculating the constant of integration
+C=integrate('1/v','v',1,100)
+//Calculating the constant of proportionality
+k=(C-2.3*log10(90))/40
+//Time after 120 seconds
+t2=120 //seconds
+//Calculating the velocity after 120 seconds
+v120=10^((-k*t2+C)/2.29)
+//Results:
+printf("\n\n The velocity at the end of 120 seconds, v120 = %.1f kmph.\n\n",v120)
\ No newline at end of file diff --git a/213/CH2/EX2.5/2_5.sce b/213/CH2/EX2.5/2_5.sce new file mode 100755 index 000000000..560a71a0c --- /dev/null +++ b/213/CH2/EX2.5/2_5.sce @@ -0,0 +1,20 @@ +//To Find the Maximum Cutting Speed
+clc
+//Given:
+s=500,s1=125,s2=250,s3=125 //mm
+t=1 //second
+//Solution:
+//Matrices for the velocity vs. time graph
+V=[0,750,750,0] //The velocity matrix
+T=[0,1/3,2/3,1] //The time matrix
+plot2d(T,V)
+//Calculating the time of uniform acceleration
+t1=rdivf('s1','v/2')
+//Calculating the time of constant speed
+t2=rdivf('s2','v')
+//Calculating the time of uniform retardation
+t3=rdivf('s3','v/2')
+//Equating the time taken to complete the stroke to 1 second
+v=(125/(1/2)+250/1+125/(1/2))/1 //mm/s
+//Results:
+printf("\n\n The maximum cutting speed, v = %d mm/s.\n\n",v)
\ No newline at end of file diff --git a/213/CH2/EX2.6/2_6.sce b/213/CH2/EX2.6/2_6.sce new file mode 100755 index 000000000..318f4ab30 --- /dev/null +++ b/213/CH2/EX2.6/2_6.sce @@ -0,0 +1,17 @@ +//To Find the Angular Acceleration
+clc
+//Given:
+N0=0,N=2000 //rpm
+t=20 //seconds
+//Solution:
+//Calculating the angular velocities
+omega0=0, omega=2*%pi*N/60 //rad/s
+//Calculating the angular acceleration
+alpha=(omega-omega0)/t //rad/s^2
+//Calculating the angular distance moved by the wheel during 2000 rpm
+theta=(omega0+omega)*t/2 //rad
+//Calculating the number of revolutions made by the wheel
+n=theta/(2*%pi)
+//Results:
+printf("\n\n The angular acceleration of the wheel, alpha = %.3f rad/s^2.\n",alpha)
+printf(" The wheel makes n = %.1f revolutions.\n\n",n)
\ No newline at end of file diff --git a/213/CH2/EX2.7/2_7.sce b/213/CH2/EX2.7/2_7.sce new file mode 100755 index 000000000..f87044b74 --- /dev/null +++ b/213/CH2/EX2.7/2_7.sce @@ -0,0 +1,24 @@ +//To Find Velocity and Acceleration
+clc
+//Given:
+r=1.5 //m
+N0=1200,N=1500 //rpm
+t=5 //seconds
+//Solution:
+//Calculating the angular velocities
+omega0=2*%pi*N0/60,omega=2*%pi*N/60 //rad/s
+//Calculating the linear velocity at the beginning
+v0=r*omega0 //m/s
+//Calculating the linear velocity at the end of 5 seconds
+v5=r*omega //m/s
+//Calculating the angular acceleration
+alpha=(omega-omega0)/t //ad/s^2
+//Calculating the tangential acceleration after 5 seconds
+TangentialAcceleration=alpha*(r/2) //m/s^2
+//Calculating the radial acceleration after 5 seconds
+RadialAcceleration=(omega^2)*(r/2) //m/s^2
+//Results:
+printf("\n\n The linear velocity at the beginning, v0 = %.1f m/s.\n",v0)
+printf(" The linear velocity after 5 seconds, v5 = %.1f m/s.\n",v5)
+printf(" The tangential acceleration after 5 seconds is %.1f m/s^2.\n",TangentialAcceleration)
+printf(" The radial acceleration after 5 seconds is %d m/s^2.",RadialAcceleration)
\ No newline at end of file diff --git a/213/CH3/EX3.1/3_1.sce b/213/CH3/EX3.1/3_1.sce new file mode 100755 index 000000000..20486fa11 --- /dev/null +++ b/213/CH3/EX3.1/3_1.sce @@ -0,0 +1,21 @@ +//To find the angular acceleration and KE
+clc
+//Given:
+k=1 //m
+m=2500 //kg
+T=1500 //N-m
+//Solution:
+//Calculating the mass moment of inertia of the flywheel
+I=m*k^2 //kg-m^2
+//Calculating the angular acceleration of the flywheel
+alpha=T/I //rad/s^2
+//The angular speed at start
+omega1=0
+t=10 //seconds
+//Calculating the angular speed of the flywheel after t=10 seconds from start
+omega2=omega1+alpha*t //rad/s
+//Calculating the kinetic energy of the flywheel after 10 seconds from start
+E=1/2*I*omega2^2/1000 //kJ
+//Results:
+printf("\n\n The angular acceleration of the flywheel, alpha = %.1f rad/s^2.\n",alpha)
+printf(" The kinetic energy of the flywheel, E = %d kJ.\n\n",E)
\ No newline at end of file diff --git a/213/CH3/EX3.10/3_10.sce b/213/CH3/EX3.10/3_10.sce new file mode 100755 index 000000000..8c0c178dc --- /dev/null +++ b/213/CH3/EX3.10/3_10.sce @@ -0,0 +1,22 @@ +//To find the angular velocities
+clc
+//Given:
+m1=0.7,m2=2.4 //kg
+k1=270/1000,k2=185/1000,h1=0.25,DL=0.2,CM=0.275 //m
+//Solution:
+//Calculating the angular velocity of hammer just before impact
+h=h1*(1-cos(20*%pi/180))
+omega=sqrt(m1*9.81*h*2/(m1*k1^2)) //rad/s
+//Calculating the relative linear velocity
+RLV=0.8*omega*CM
+//Calculating the values of angular velocities
+//The two equations we get in terms of omegaA and omegaB are
+//DL*omegaA-CM*omegaB=RLV .....(i)
+//m1*k1^2*(omega-omegaB)=.275/.2*m2*k2^2*omegaA, or
+//2.21*omegaA+omegaB=2.01 .....(ii)
+A=[DL -CM; 2.21 1]
+B=[RLV; 2.01]
+V=A \ B
+//Results:
+printf("\n\n The angular velocity of the anvil A, omegaA = %.2f rad/s.\n",V(1))
+printf(" The angular velocity of the hammer B, omegaB = %.2f rad/s, i.e. %.2f rad/s, in the reverse direction.\n\n",V(2),V(2)*-1)
\ No newline at end of file diff --git a/213/CH3/EX3.11/3_11.sce b/213/CH3/EX3.11/3_11.sce new file mode 100755 index 000000000..df8bc3ce1 --- /dev/null +++ b/213/CH3/EX3.11/3_11.sce @@ -0,0 +1,44 @@ +//To find the velocity, impulse, angle of swing and average force
+clc
+//Given:
+m=30 //kg
+AG=1,GB=150/1000,k1=1.1,k2=350/1000 //m
+theta=60*%pi/180 //rad
+t=0.005 //s
+a=AG,b=GB
+//Solution:
+//Calculating the mass moment of inertia of the pendulum about the point of suspension A
+IA=m*k1^2 //kg-m^2
+//Calculating the mass moment of inertia ofthe pendulum about centre of gravity G
+IG=m*k2^2 //kg-m^2
+//Calculating the angular velocity of the pendulum
+h1=a-a*cos(theta)
+omega=sqrt(2*m*9.81*h1/IA) //rad/s
+//Calculating the striking velocity of the pendulum
+v=omega*(a+b) //m/s
+//Calculating the angular velocity of the pendulum just after the breakage of the specimen
+omega1=sqrt(omega^2-2*54/IA)
+//Calculating the linear velocity of G just before the breakage of specimen
+vG=omega*AG //m/s
+//Calculating the linear velocity of G just after the breakage of specimen
+vGdash=omega1*AG //m/s
+//Calculating the impulses at pivot A and knife edge B
+//F1+F2=m*(vG-vGdash) .....(i)
+//b*F2-a*F1=IG*(omega-omega1) .....(ii)
+A=[1 1; -a b]
+B=[m*(vG-vGdash); IG*(omega-omega1)]
+V=A \ B
+F1=V(1),F2=V(2)
+//Calculating the angle of swing of the pendulum after impact
+theta1=acos(a-1/2*IA*omega1^2/(m*9.81))/a //radians
+//Calculating the average force exerted at the pivot
+Fp=F1/t //N
+//Calculating the average force exerted at the knife edge
+Fk=F2/t //N
+//Results:
+printf("\n\n The striking velocity of the pendulum, v = %.2f m/s.\n",v)
+printf(" Impulse at the pivot A, F1 = %.1f N.\n",F1)
+printf(" Impulse at the knife edge B, F2 = %.1f N.\n",F2)
+printf(" Angle of swing of the pendulum after impact, theta = %.2f degree.\n",theta1*180/%pi)
+printf(" Average force exerted at the pivot is %d N.\n",Fp)
+printf(" Average force exerted at the knife edge is %d N.\n\n",Fk)
\ No newline at end of file diff --git a/213/CH3/EX3.12/3_12.sce b/213/CH3/EX3.12/3_12.sce new file mode 100755 index 000000000..0d718d9d7 --- /dev/null +++ b/213/CH3/EX3.12/3_12.sce @@ -0,0 +1,29 @@ +//To find the speed, time and KE lost
+clc
+//Given:
+T=150 //N-m
+m1=60,m2=20 //kg
+k1=140/1000,k2=80/1000 //m
+N1=750,N2=0 //rpm
+//Sloution:
+//Calculating the angular speeds
+omega1=2*%pi*N1/60,omega2=0 //rad/s
+//Calculating the mass moment of inertia of the rotor on motor
+I1=m1*k1^2 //kg-m^2
+//Calculating the mass moment of inertia of the parts attached to machine
+I2=m2*k2^2 //kg-m^2
+//Calculating the speed after engagement of the clutch and the time taken
+//We know that impulsive torque = change in angular momentum
+//T*t = I1*(omega1-omega), or I1*omega+T*t = I1*omega1 .....(i)
+//T*t = I2*(omega-omega2), or I2*omega-T*t = I2*omega2 .....(ii)
+A=[I1 T; I2 -T]
+B=[I1*omega1; I2*omega2]
+V=A \ B
+omega=V(1) //rad/s
+t=V(2) //s
+//Calculating the kinetic energy lost during the operation
+E=I1*I2*(omega1-omega2)^2/(2*(I1+I2)) //N-m
+//Results:
+printf("\n\n The speed after engagement, omega = %.1f rad/s.\n",omega)
+printf(" The time taken, t = %.2f s.\n",t)
+printf(" The kinetic energy lost during the operation, E = %d N-m.\n\n",E)
\ No newline at end of file diff --git a/213/CH3/EX3.13/3_13.sce b/213/CH3/EX3.13/3_13.sce new file mode 100755 index 000000000..f91d49995 --- /dev/null +++ b/213/CH3/EX3.13/3_13.sce @@ -0,0 +1,26 @@ +//To find the acceleration
+clc
+//Given:
+M=75 //kg
+r=0.3 //m
+G=6
+IA=100,IB=5 //kg-m^2
+eta=90/100 //%
+//Solution:
+//Calculating the equivalent mass of the geared system
+me=1/r^2*(IA+G^2*IB) //kg
+//Calculating the total equivalent mass to be accelerated
+Me=me+M //kg
+//Calculating the acceleration when it is allowed to fall freely
+F=M*9.81 //Accelerating force provided by the pull of gravity, N
+a=F/Me //m/s^2
+//Calculating the equivalent mass of the geared system when the efficiency is 90%
+me1=1/r^2*(IA+G^2*IB/eta) //kg
+//Calculating the total equivalent mass to be accelerated
+Me1=me1+M //kg
+//Calculating the acceleration when the efficiency is 90%
+F1=M*9.81 //Accelerating force by the pull of gravity, N
+a1=F1/Me1 //m/s^2
+//Results:
+printf("\n\n The acceleration of the mass M if it is allowed to fall freely, a = %.3f m/s^2.\n",a)
+printf(" The acceleration of the mass M when the efficiency of the gearing system is 0.9, a = %.3f m/s^2.\n\n",a1)
\ No newline at end of file diff --git a/213/CH3/EX3.18/3_18.sce b/213/CH3/EX3.18/3_18.sce new file mode 100755 index 000000000..3dba10e73 --- /dev/null +++ b/213/CH3/EX3.18/3_18.sce @@ -0,0 +1,48 @@ +//To find the torque
+clc
+//Given:
+d=1.5,r=d/2,d1=1,kM=90/1000,kI=225/1000,kD=600/1000,kP=450/1000 //m
+NM=900,N1=275,ND=50 //rpm
+mM=200,mI=375,mD=2250,mP=200,m1=1150,m2=650 //kg
+FI=150, FD=1125, FP=150 //N-m
+F1=500,F2=350 //N
+a=0.9 //m/s^2
+//Solution:
+//Calculating the speed of guide pulley
+NP=ND*d/d1 //rpm
+//Calculating the gear ratio for intermediate gear and motor
+G1=N1/NM
+//Calculating the gear ratio for drum and motor
+G2=ND/NM
+//Calculating the gear ratio for the guide pulley and motor
+G3=NP/NM
+//Calculating the mass moment of inertia of the motor
+IM=mM*kM^2 //kg-m^2
+//Calculating the mass moment of inertia of the intermediate gear
+II=mI*kI^2 //kg-m^2
+//Calculating the mass moment of inertia of the drum and shaft
+ID=mD*kD^2 //kg-m^2
+//Calculating the mass moment of inertia of the guide pulley
+IP=mP*kP^2 //kg-m^2
+//Calculating the angular acceleration of the drum
+alphaD=a/r //rad/s^2
+//Calculating the angular acceleration of the motor
+alphaM=alphaD*NM/ND //rad/s^2
+//Calculating the equivalent mass moment of inertia of the system
+I=IM+G1^2*II+G2^2*ID+2*G3^2*IP //kg-m^2
+//Calculating the torque at motor to accelerate the system
+T1=I*alphaM //N-m
+//Calculating the torque at motor to overcome friction at intermediate gear, drum and two guide pulleys
+T2=G1*FI+G2*FD+2*G3*FP //N-m
+//Calculating the tension in the rising rope between the pulley and drum
+Q1=m1*9.81+m1*a+F1 //N
+//Calculating the tension in the falling rope between the pulley and drum
+Q2=m2*9.81-m2*a-F2 //N
+//Calculating the torque at drum
+TD=(Q1-Q2)*r //N-m
+//Calculating the torque at motor to raise and lower cages and ropes and to overcome frictional resistance
+T3=G2*TD //N-m
+//Calculating the total motor torque required
+T=T1+T2+T3 //N-m
+//Results:
+printf("\n\n The total motor torque required, T = %.1f N-m.\n\n",T)
\ No newline at end of file diff --git a/213/CH3/EX3.19/3_19.sce b/213/CH3/EX3.19/3_19.sce new file mode 100755 index 000000000..765a34f94 --- /dev/null +++ b/213/CH3/EX3.19/3_19.sce @@ -0,0 +1,35 @@ +//To find velocities and loss of KE
+clc
+//Given:
+m1=50,m2=25 //kg
+u1=3,u2=1.5 //m/s
+//Solution:
+//When the impact is inelastic
+//Calculating the common velocity after impact
+v=(m1*u1+m2*u2)/(m1+m2) //m/s
+//Calculating the loss of kinetic energy during impact
+EL=m1*m2/(2*(m1+m2))*(u1-u2)^2 //N-m
+//When the impact is elastic
+//Calculating the velocity of the first sphere immediately after impact
+v1=2*v-u1 //m/s
+//Calculating the velocity of the second sphere immediately after impact
+v2=2*v-u2 //m/s
+//Calculating the loss of kinetic energy
+EL1=0
+//When the coefficient of restitution, e=0.6
+e=0.6
+//Calculating the velocity of the first sphere immediately after impact
+v12=(1+e)*v-e*u1 //m/s
+//Calculating the velocity of the second sphere immediately after impact
+v22=(1+e)*v-e*u2 //m/s
+//Calculating the loss of kinetic energy
+EL2=m1*m2/(2*(m1+m2))*(u1-u2)^2*(1-e^2) //N-m
+//Results:
+printf("\n\n The common velocity after impact when the impact is inelastic, v = %.1f m/s.\n",v)
+printf(" The loss of kinetic energy during impact, EL = %.2f N-m.\n",EL)
+printf(" The velocity of the first sphere immediately after impact when the impact is elastic, v1 = %d m/s.\n",v1)
+printf(" The velocity of the second sphere immediately after impact, v2 = %.1f m/s.\n",v2)
+printf(" The loss of kinetic energy, EL = %d.\n",EL1)
+printf(" The velocity of the first sphere immediately after impact When the coefficient of restitution is 0.6, v1 = %.1f m/s.\n",v12)
+printf(" The velocity of the second sphere immediately after impact, v2 = %.1f m/s.\n",v22)
+printf(" The loss of kinetic energy during impactm EL = %d N-m.\n\n",EL2)
\ No newline at end of file diff --git a/213/CH3/EX3.2/3_2.sce b/213/CH3/EX3.2/3_2.sce new file mode 100755 index 000000000..db39ddd8a --- /dev/null +++ b/213/CH3/EX3.2/3_2.sce @@ -0,0 +1,56 @@ +//To find the time, torque and power
+clc
+//Given:
+mC=500,mD=250 //kg
+s=100,r=0.5,k=0.35 //m
+m=3 //kg/m
+//Solution:
+//Velocities of the cage
+u1=0,v1=10,v2=10,u3=10,v3=0 //m/s
+//Accelerations of the cage
+a1=1.5,a3=-6 //m/s^2
+s=100 //m
+//Calculating the time taken by the cage to reach the top
+t1=(v1-u1)/a1 //seconds
+//Calculating the distance moved by the cage during time t1
+s1=(v1+u1)/2*t1 //m
+//Calculating the time taken for the cage from initial velocity u3=10 m/s to final velocity of v3=0
+t3=(v3-u3)/a3 //seconds
+//Calculating the distance moved by the cage during time t3
+s3=(v3+u3)/2*t3 //m
+//Calculating the distance travelled during constant velocity of v2=10 m/s
+s2=s-s1-s3 //m
+//Calculating the time taken for the cage during constant velocity
+t2=s2/v2 //seconds
+//Calculating the time taken for the cage to reach the top
+t=t1+t2+t3 //seconds
+//Calculating the total mass of the rope for 100 metres
+mR=m*s //kg
+//Calculating the force to raise the cage and rope at uniform speed
+F1=(mC+mR)*9.81 //N
+//Calculating the torque to raise the cage and rope at uniform speed
+T1=F1*r //N-m
+//Calculating the force to accelerate the cage and rope
+F2=(mC+mR)*a1 //N
+//Calculating the torque to accelerate the cage and rope
+T2=F2*r //N-m
+//Calculating the mass moment of inertia of the drum
+I=mD*k^2 //kg-m^2
+//Calculating the angular acceleration of the drum
+alpha=a1/r //rad/s^2
+//Calculating the torque to accelerate the drum
+T3=I*alpha //N-m
+//Calculating the total torque which must be applied to the drum at starting
+T=T1+T2+T3 //N-m
+//Calculating the mass of 33.35 m rope
+m1=m*33.35 //kg
+//Calculating the reduction of torque
+T4=(m1*9.81+m1*a1)*r //N-m
+//Calculating the angular velocity of drum
+omega=v2/(2*%pi*r) //rad/s
+//Calculating the power
+P=T4*omega/1000 //Power, kW
+//Results:
+printf("\n\n The time taken for the cage to reach the top, t = %.2f s.\n",t)
+printf(" The total torque which must be applied to the drum during starting, T = %.1f N-m.\n",T)
+printf(" The power required is %.3f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH3/EX3.20/3_20.sce b/213/CH3/EX3.20/3_20.sce new file mode 100755 index 000000000..1ed3dae81 --- /dev/null +++ b/213/CH3/EX3.20/3_20.sce @@ -0,0 +1,35 @@ +//To find the speed and energy dissipated
+clc
+//Given:
+m1=15*1000,m2=5*1000 //kg
+u1=20*1000/3600,u2=12*1000/3600 //m/s
+s=1000*10^3 //N/m
+e=0.5
+//Solution:
+//Calculating the common speed
+v=(m1*u1+m2*u2)/(m1+m2) //m/s
+//Calculating the strain energy stored in one spring
+SE=mulf('1/2*s','x^2') //Strain energy, N-m
+//Calculating the strain energy stored in four buffer springs
+SE4=mulf('4*1/2*s','x^2') //Strain energy, N-m
+//Calculating the difference in kinetic energies before impact and during impact
+d=m1*m2/(2*(m1+m2))*(u1-u2)^2 //Difference in kinetic energies, N-m
+//Equating the difference between kinetic energies to the strain energy stored in the springs
+x=sqrt(d*2/(4*s))*1000 //mm
+//Calculating the speed of the loaded wagon immediately after impact ends
+v11=2*v-u1 //m/s
+//Calculating the speed of the empty wagon immediately after impact ends
+v21=2*v-u2 //m/s
+//Calculating the speeds of the wagons taking into account the coefficient of restitution, e=0.5
+v12=(1+e)*v-e*u1 //m/s
+v22=(1+e)*v-e*u2 //m/s
+//Calculating the amount of energy dissipated during impact
+EL=m1*m2/(2*(m1+m2))*(u1-u2)^2*(1-e^2) //N-m
+//Results:
+printf("\n\n The magnitude of common speed, v = %d m/s.\n",v)
+printf(" The maximum deflection of each buffer spring during impact, x = %d mm.\n",x)
+printf(" The speed of the loaded wagon immediately after the impact ends, v1 = %.2f m/s.\n",v11)
+printf(" The speed of the empty wagon immediately after the impact ends, v2 = %.2f m/s.\n",v21)
+printf(" When coefficient of restitution is taken into account, v1 = %.3f m/s.\n",v12)
+printf(" When coefficient of restitution is taken into account, v2 = %.3f m/s.\n",v22)
+printf(" The amount of energy dissipated during impact, EL = %d N-m.\n\n",EL)
\ No newline at end of file diff --git a/213/CH3/EX3.21/3_21.sce b/213/CH3/EX3.21/3_21.sce new file mode 100755 index 000000000..8f6d066fa --- /dev/null +++ b/213/CH3/EX3.21/3_21.sce @@ -0,0 +1,28 @@ +//To find strain energy, twist and speed
+clc
+//Given:
+IA=22.5,IB=67.5 //kg-m^2
+q=225 //N-m/rad
+NA=150,NB=0 //rpm
+//Calculating the angular speed of the flywheel
+omegaA=2*%pi*NA/60 //rad/s
+//Calculating the angular speed of both the flywheels at the instant their speeds are equal
+omega=IA*omegaA/(IA+IB) //rad/s
+//Calculating the kinetic energy of the system at that instant
+E2=1/2*(IA+IB)*omega^2 //N-m
+//Calculating the kinetic energy of the flywheel A
+E1=1/2*IA*omegaA^2 //N-m
+//Calculating the strain energy stored in the spring
+E=E1-E2 //Strain energy stored in the spring, N-m
+//Calculating the maximum twist of the spring
+theta=sqrt(E*2/q) //radians
+thetad=theta*180/%pi //Maximum twist, degrees
+//Calculating the speed of each flywheel when the spring regains its initial unstrained condition
+N=60*omega/(2*%pi)
+NA1=2*N-NA //rpm
+NB1=2*N-NB //rpm
+//Results:
+printf("\n\n The strain energy stored in the spring is %d N-m.\n",E)
+printf(" The maximum twist of the spring, theta = %.1f degrees.\n",thetad)
+printf(" The speed of flywheel A when the spring regains its initial unstrained condition, NA1 = %d rpm, i.e. %d rpm in the opposite direction.\n",NA1,-NA1)
+printf(" The speed of flywheel B when the spring regains its initial unstrained condition, NB1 = %d rpm.\n",NB1)
\ No newline at end of file diff --git a/213/CH3/EX3.3/3_3.sce b/213/CH3/EX3.3/3_3.sce new file mode 100755 index 000000000..b4220a226 --- /dev/null +++ b/213/CH3/EX3.3/3_3.sce @@ -0,0 +1,26 @@ +//To find the reduction of speed
+clc
+//Given:
+P=4*1000 //W
+I=140 //kg-m^2
+N1=240 //rpm
+//Solution:
+//Calculating the angular acceleration at the commencement of operation
+omega1=2*%pi*N1/60 //rad/s
+//Calculating the energy supplied by the motor (E1) and the energy consumed in closing a revet in 1 second
+E1=4000,E2=10000 //N-m
+//Calculating the loss of kinetic energy of the flywheel during the operation
+E=E2-E1 //N-m
+//Calculating the kinetic energy of the flywheel at the commencement of operation
+KEc=1/2*I*omega1^2 //Kinetic energy at the commencement, N-m
+//Calculating the kinetic energy of the flywheel at the end of operation
+KEe=KEc-E //Kinetic energy at the end, N-m
+//Calculating the angular speed of the flywheel immediately after closing a revet
+omega2=sqrt(KEe*2/I) //rad/s
+//Calculating the reduction of speed
+ReductionofSpeed=(omega1-omega2)*60/(2*%pi) //rpm
+//Calculating the maximum rate at which the revets can be closed per minute
+Rate=P*60/E2 //Maximum rate at which the revets can be closed per minute
+//Results:
+printf("\n\n The reduction of speed is %.1f rpm.\n",ReductionofSpeed)
+printf(" The maximum rate at which rivets can be closed per minute is %d.\n\n",Rate)
\ No newline at end of file diff --git a/213/CH3/EX3.4/3_4.sce b/213/CH3/EX3.4/3_4.sce new file mode 100755 index 000000000..b599ca966 --- /dev/null +++ b/213/CH3/EX3.4/3_4.sce @@ -0,0 +1,37 @@ +//To find the torque and power
+clc
+//Given:
+m=14*1000,m1=1.25*1000,m2=110 //kg
+d=1,r=d/2,k1=450/1000,k2=125/1000 //m
+F=1.2*1000 //N
+eta=0.85
+v=1.8 //m/s
+a=0.1 //m/s^2
+//Solution:
+//Calculating the forces opposing the motion
+P1=m*9.81*1/20+m*a+F //N
+//Calculating the torque on the drum shaft to accelerate the load
+T1=P1*r //N-m
+//Calculating the mass moment of inertia of the drum
+I1=m1*k1^2 //kg-m^2
+//Calculating the angular acceleration of the drum
+alpha1=a/r //rad/s
+//Calculating the torque on the drum to accelerate the drum shaft
+T2=I1*alpha1 //N-m
+//Calculating the torque on the armature to accelerate drum and load
+T3=(T1+T2)/(40*eta) //N-m
+//Calculating the mass moment of inertia of the armature
+I2=m2*k2^2 //kg-m^2
+//Calculating the angular acceleration of the armature
+alpha2=a/r*40 //rad/s^2
+//Calculating the torque on the armature to accelerate armature shaft
+T4=I2*alpha2 //N-m
+//Calculating the torque on the motor shaft
+T=T3+T4 //N-m
+//Calculating the angular speed of the motor
+omega=v/r*40 //rad/s
+//Calculating the power developed by the motor
+P=T*omega/1000 //Power developed by the motor, kW
+//Results:
+printf("\n\n The torque on the motor shaft, T = %.2f N-m.\n",T)
+printf(" The power developed by the motor is %.2f kW.\n\n",P)
\ No newline at end of file diff --git a/213/CH3/EX3.5/3_5.sce b/213/CH3/EX3.5/3_5.sce new file mode 100755 index 000000000..e2eedc6f2 --- /dev/null +++ b/213/CH3/EX3.5/3_5.sce @@ -0,0 +1,31 @@ +//To find the KE and braking force
+clc
+//Given:
+m=12*1000,m1=2*1000,m2=2.5*1000 //kg
+k1=0.4,d1=1.2,r1=d1/2,k2=0.6,d2=1.5,r2=d2/2,s=6 //m
+v=9*1000/3600 //m/s
+//Solution:
+//Calculating the mass moment of inertia of the front roller
+I1=m1*k1^2 //kg-m^2
+//Calculating the mass moment of inertia of the rear axle together with its wheels
+I2=m2*k2^2 //kg-m^2
+//Calculating the angular speed of the front roller
+omega1=v/r1 //rad/s
+//Calculating the angular speed of rear wheels
+omega2=v/r2 //rad/s
+//Calculating the kinetic energy of rotation of the front roller
+E1=1/2*I1*omega1^2 //N-m
+//Calculating the kinetic energy of rotation of the rear axle with its wheels
+E2=1/2*I2*omega2^2 //N-m
+//Calculating the total kinetic energy of rotation of the wheels
+E=E1+E2 //N-m
+//Calculating the kinetic energy of translation of the road roller
+E3=1/2*m*v^2 //N-m
+//Calculating the total kinetic energy of the road roller
+E4=E3+E //N-m
+//Calculating the braking force to bring the roller to rest
+F=E4/s //N
+//Results:
+printf("\n\n The total kinetic energy of rotation of the wheels, E = %d N-m.\n",E)
+printf(" The total kinetic energy of the road roller, E4 = %d N-m.\n",E4)
+printf(" The braking force required to bring the roller to rest, F = %.1f N.\n\n",F)
\ No newline at end of file diff --git a/213/CH3/EX3.7/3_7.sce b/213/CH3/EX3.7/3_7.sce new file mode 100755 index 000000000..f80400318 --- /dev/null +++ b/213/CH3/EX3.7/3_7.sce @@ -0,0 +1,22 @@ +//To Find the Speed and Energy Lost
+clc
+//Given:
+r=500/1000,k=450/1000 //m
+m1=500,m2=1250 //kg
+u=0.75 //m/s
+//Solution:
+//Calculating the mass moment of inertia of drum
+I2=m2*k^2 //kg-m^2
+//Calculating the speed of truck
+//Impulse, F=m1*v or, F-m1*v=0 .....(i)
+//Moment of impulse, F*r=I2*(omega2-omega2) or, F*r=I2*(u-v)/r or, F*r+I2*v/r=I2*u/r .....(ii)
+//Solving (i) and (ii)
+A=[1 -m1; r I2/r]
+B=[0; I2*u/r]
+V=A \ B
+v=V(2)
+//Calculating the energy lost to the system
+E=1/2*I2*(u^2-v^2)/r^2-1/2*m1*v^2 //Energy lost to the system, N-m
+//Results:
+printf("\n\n The speed of the truck when the motion becomes steady, v = %.3f m/s.\n",v)
+printf(" The energy lost to the system is %d N-m.\n\n",E)
\ No newline at end of file diff --git a/213/CH3/EX3.8/3_8.sce b/213/CH3/EX3.8/3_8.sce new file mode 100755 index 000000000..25d57ab82 --- /dev/null +++ b/213/CH3/EX3.8/3_8.sce @@ -0,0 +1,34 @@ +//To find the velocity, KE and compression
+clc
+//Given:
+s=0.7*10^6 //N/m
+m1=10*10^3,m2=15*10^3 //kg
+v1=1.8,v2=0.6 //m/s
+//Solution:
+//Calculating the common velocity when moving together during impact
+v=(m1*v1+m2*v2)/(m1+m2)
+//Calculating the kinetic energy lost to the system
+E=(1/2*m1*v1^2+1/2*m2*v2^2)-1/2*(m1+m2)*v^2
+//Calculating the compression of each buffer spring
+x=sqrt(E/(2*s))
+//Calculating the velocity of each truck on separation
+//Final KE after separation=KE at common velocity+Half of energy stored in springs.
+//And initial and final momentum must be equal.
+//Simplifying the two equations, we get,
+//1/2*m1*v3^2+1/2*m2*v4^2=1/2*(m1+m2)*v^2+1/2*E .....(i)
+//m1*v3+m2*v4=(m1+m2)*v
+function y=f(x)
+ v3=x(1)
+ v4=x(2)
+ y(1)=1/2*m1*v3^2+1/2*m2*v4^2-1/2*(m1+m2)*v^2-1/2*E
+ y(2)=m1*v3+m2*v4-(m1+m2)*v
+endfunction
+z=fsolve([1,1],f)
+v3=z(1)
+v4=z(2)
+//Results:
+printf("\n\n The common velocity when moving together during impact, v = %.2f m/s.\n",v)
+printf(" The kinetic energy lost to the system is %.2f kN-m.\n",E/1000)
+printf(" The compression of each buffer spring, x = %d mm.\n",x*1000)
+printf(" The velocity of separation for 10 tonnes truck, v3 = %.1f m/s.\n",v3)
+printf(" The velocity of separation for 15 tonnes truck, v4 = %.1f m/s.\n",v4)
\ No newline at end of file diff --git a/213/CH3/EX3.9/3_9.sce b/213/CH3/EX3.9/3_9.sce new file mode 100755 index 000000000..beaa6ea0d --- /dev/null +++ b/213/CH3/EX3.9/3_9.sce @@ -0,0 +1,23 @@ +//To find energy lost and resistance
+clc
+//Given:
+m1=300,m2=500 //kg
+s=1,x=150/1000 //m
+//Solution:
+//Calculating the velocity with which mass m1 hits the pile
+u=0
+v1=sqrt(2*9.81*s+u^2) //m/s
+//Calculating the common velocity after impact
+v2=0
+v=(m1*v1+m2*v2)/(m1+m2) //m/s
+//Calculating the kinetic energy before impact
+KEb=m1*9.81*s //Kinetic energy before impact, N-m
+//Calculating the kinetic energy after impact
+KEa=1/2*(m1+m2)*v^2 //Kinetic energy after impact, N-m
+//Calculating the energy lost in the blow
+E=KEb-KEa //Energy lost in the blow, N-m
+//Calculating the average resistance against the pile
+R=KEa/x+m1*9.81+m2*9.81
+//Results:
+printf("\n\n The energy lost in the blow is %d N-m.\n",E)
+printf(" The average resistance against the pile, R = %.3f kN.\n\n",R/1000)
\ No newline at end of file diff --git a/213/CH4/EX4.1/4_1.sce b/213/CH4/EX4.1/4_1.sce new file mode 100755 index 000000000..ceb60d3bd --- /dev/null +++ b/213/CH4/EX4.1/4_1.sce @@ -0,0 +1,15 @@ +//To Find the Velocity and Acceleration
+clc
+//Given:
+N=120 //rpm
+r=1,x=0.75 //m
+//Solution:
+//Calculating Angular Velocity
+omega=2*%pi*N/60 //rad/s
+//Calculating Velocity of the Piston
+v=omega*sqrt(r^2-x^2) //m/s
+//Calculating Acceleration of the Piston
+a=omega^2*x
+//Results:
+printf("\n\n The Velocity of the Piston, v = %.2f m/s.\n",v)
+printf(" The Acceleration of the Piston, a = %.2f m/s^2.\n\n",a)
\ No newline at end of file diff --git a/213/CH4/EX4.10/4_10.sce b/213/CH4/EX4.10/4_10.sce new file mode 100755 index 000000000..c5bb2d0ec --- /dev/null +++ b/213/CH4/EX4.10/4_10.sce @@ -0,0 +1,11 @@ +//To Find the Radius of Gyration
+clc
+//Given:
+l=2.5,r=250*10^-3 //m
+//Solution:
+//Calculating the Frequency of Oscillation
+n=50/170 //Hz
+//Calculating the Radius of Gyration of the Wheel
+kG=r/(2*%pi*n)*sqrt(9.81/l) //m
+//Results:
+printf("\n\n The Radius of Gyration, kG = %d mm.\n\n",kG*10^3)
\ No newline at end of file diff --git a/213/CH4/EX4.11/4_11.sce b/213/CH4/EX4.11/4_11.sce new file mode 100755 index 000000000..441e14d08 --- /dev/null +++ b/213/CH4/EX4.11/4_11.sce @@ -0,0 +1,15 @@ +//To Find the Mass Moment of Inertia
+clc
+//Given:
+m1=5.5,m2=1.5 //kg
+l=1.25,r=125*10^-3 //m
+//Solution:
+//Calculating the Frequency of Oscillation
+n=10/30 //Hz
+//Calculating the Radius of Gyration About an Axis Through the c.g.
+kG=r/(2*%pi*n)*sqrt(9.81/l) //m
+//Calculating the Mass Moment of Inertia About an Axis Through its c.g.
+m=m1+m2 //Total Mass, kg
+I=m*kG^2 //kg-m^2
+//Results:
+printf("\n\n The Mass Moment of Inertia About an Axis Through its c.g., I = %.3f kg-m^2.\n\n",I)
\ No newline at end of file diff --git a/213/CH4/EX4.2/4_2.sce b/213/CH4/EX4.2/4_2.sce new file mode 100755 index 000000000..a6937da05 --- /dev/null +++ b/213/CH4/EX4.2/4_2.sce @@ -0,0 +1,26 @@ +//To Find the Angular Velocity, Time and Acceleration
+clc
+//Given:
+x1=.75,x2=2 //m
+v1=11,v2=3 //m/s
+//Solution:
+//We have, 11=omega*sqrt(r^2-.75^2) and 3=omega*sqrt(r^2-2^2).
+//These upon solving yield r^2-(121/omega^2)-0.5625=0 and r^2-(9/omega^2)-4=0.
+//Take r^2=x and (1/omega^2)=y and the equation become x-121y=0.5625 and x-9y=4.
+//Variables Matrix
+A=[1 -121; 1 -9]
+//Constants Matrix
+B=[.5625; 4]
+V=A \ B
+//Calculating Amplitude of the Particle
+r=sqrt(V(1)) //m
+//Calculating Angular Velocity of the Particle
+omega=sqrt(1/V(2)) //rad/s
+//Calculating Periodic Time
+tp=2*%pi/omega //seconds
+//Calculating Maximum Acceleration
+amax=omega^2*r //m/s^2
+//Results:
+printf("\n\n The Angular Velocity, omega = %.1f rad/s.\n",omega)
+printf(" The Periodic Time, tp = %.1f s.\n",tp)
+printf(" The Maximum Acceleration, amax = %.2f m/s^2.\n\n",amax)
\ No newline at end of file diff --git a/213/CH4/EX4.3/4_3.sce b/213/CH4/EX4.3/4_3.sce new file mode 100755 index 000000000..7e720a90f --- /dev/null +++ b/213/CH4/EX4.3/4_3.sce @@ -0,0 +1,17 @@ +//To Find the Frequency and Velocity
+clc
+//Given:
+m=60 //kg
+r=0.0125,x=0.005 //m
+//Solution:
+//Calculating the Extension of the Spring
+delta=(.25/1.5)*60*10^-3 //m
+//Calculating the Frequency of the System
+n=1/(2*%pi)*sqrt(9.81/delta) //Hz
+//Calculating the Angular Velocity of the Mass
+omega=sqrt(9.81/delta) //rad/s
+//Calculating the Linear Velocity of the Mass
+v=omega*sqrt(r^2-x^2)
+//Results:
+printf("\n\n The Frequency of Natural Vibration, n = %.2f Hz.\n",n)
+printf(" The Velocity of the Mass, v = %.2f m/s.\n\n",v)
\ No newline at end of file diff --git a/213/CH4/EX4.4/4_4.sce b/213/CH4/EX4.4/4_4.sce new file mode 100755 index 000000000..88ec9a5e6 --- /dev/null +++ b/213/CH4/EX4.4/4_4.sce @@ -0,0 +1,20 @@ +//To Find the Frequency of Oscillation
+clc
+//Given:
+m=1,m1=2.5 //kg
+s=1.8*10^3 //N/m
+l=(300+300)*10^-3 //m
+//Solution:
+//Calculating the Mass Moment of Inertia of the System
+IA=(m*l^2/3)+(m1*l^2) //kg-m^2
+//Calculating the Ratio of Alpha to Theta
+//delta=0.3*theta
+//Restoring Force=s*delta=540*theta
+//Restoring torque about A=540*theta*0.3=162*theta N-m ...(i)
+//Torque about A= IA*alpha=1.02*alpha N-m ...(ii)
+//Equating (i) and (ii), 1.02*alpha=162*theta
+alphabytheta=162/1.02
+//Calculating the Frequency of Oscillation
+n=1/(2*%pi)*sqrt(alphabytheta)
+//Results:
+printf("\n\n The Frequency of Oscillation, n = %.2f Hz.\n\n",n)
\ No newline at end of file diff --git a/213/CH4/EX4.5/4_5.sce b/213/CH4/EX4.5/4_5.sce new file mode 100755 index 000000000..1c4b0d32b --- /dev/null +++ b/213/CH4/EX4.5/4_5.sce @@ -0,0 +1,16 @@ +//To Find the Moment of Inertia
+clc
+//Given:
+m=85 //kg
+h=0.1 //m
+//Solution:
+//Calculating the Frequency of Oscillation
+n=100/145 //Hz
+//Calculating the Equivalent Length of Simple Pendulum
+L=(1/(2*%pi)/.69*sqrt(9.81))^2
+//Calculating the Radius of Gyration
+kG=sqrt((L-h)*h)
+//Calculating the Moment of Inertia of the Flywheel through the Centre of Gravity
+I=m*kG^2 //kg-m^2
+//Results:
+printf("\n\n The Moment of Inertia of the Flywheel Through its c.g., I = %.1f kg-m^2.\n\n",I)
\ No newline at end of file diff --git a/213/CH4/EX4.6/4_6.sce b/213/CH4/EX4.6/4_6.sce new file mode 100755 index 000000000..c1627261e --- /dev/null +++ b/213/CH4/EX4.6/4_6.sce @@ -0,0 +1,27 @@ +//To Find the Moment of Inertia
+clc
+//Given:
+m=60 //kg
+d1=75,d2=102 //mm
+//Solution:
+//Calculating the Frequencies of Oscillation
+n1=100/190,n2=100/165 //Hz
+//Calculating the Equivalent Lengths of Simple Pendulum
+L1=9.81/(2*%pi*n1)^2 //m
+L2=9.81/(2*%pi*n2)^2 //m
+//Calculating Distance of c.g. from the Small and Big End Centres (h1 and h2), and the Radius of Gyration
+function y=f(x)
+ h1=x(1)
+ h2=x(2)
+ kG=x(3)
+ y(1)=L1*h1-h1^2-kG^2
+ y(2)=L2*h2-h2^2-kG^2
+ y(3)=h1+h2-1
+endfunction
+z=fsolve([1,1,1],f)
+h1=z(1),h2=z(2),kG=z(3)
+//Calculating the Mass Moment of Inertia of the Rod
+I=m*kG^2 //kg-m^2
+//Results:
+printf("\n\n The Moment of Inertia of the Rod, I = %d kg-m^2.\n",I)
+printf(" The C.G is at a Distance of h1 = %.3f m from the Small End Centre.\n\n",h1)
\ No newline at end of file diff --git a/213/CH4/EX4.7/4_7.sce b/213/CH4/EX4.7/4_7.sce new file mode 100755 index 000000000..ba958153d --- /dev/null +++ b/213/CH4/EX4.7/4_7.sce @@ -0,0 +1,25 @@ +//To Find the Time of Swing
+clc
+//Given:
+l=1.2 //m
+theta=3*%pi/180 //rad
+//Solution:
+//Calculating the Distance Between the Knife Edge and C.G. of the Rod
+h=1.2/2-.05 //m
+//Calculating the Radius of Gyration of the Rod About C.G.
+kG=l/sqrt(12) //m
+//Calculating the Time of Swing of the Rod
+tp=2*%pi*sqrt((kG^2+h^2)/(9.81*h)) //seconds
+//Calculating the Minimum Time of Swing
+tpmin=2*%pi*sqrt((2*kG)/9.81) //seconds
+//Calculating Angular Velocity
+omega=2*%pi/tp //rad/s
+//Calculating Maximum Angular Velocity
+omegamax=omega*theta //rad/s
+//Calculating Maximum Angular Acceleration
+alphamax=omega^2*theta //rad/s^2
+//Results:
+printf("\n\n The Time of Swing of the Rod, tp = %.2f seconds.\n",tp)
+printf(" The Minimum Time of Swing, tp(min) = %.2f seconds.\n",tpmin)
+printf(" The Maximum Angular Velocity, omega(max) = %.4f rad/s.\n",omegamax)
+printf(" The Maximum Angular Acceleration, alpha(max) = %.3f rad/s^2.\n\n", alphamax)
\ No newline at end of file diff --git a/213/CH4/EX4.8/4_8.sce b/213/CH4/EX4.8/4_8.sce new file mode 100755 index 000000000..17197b02e --- /dev/null +++ b/213/CH4/EX4.8/4_8.sce @@ -0,0 +1,45 @@ +//To Find Centre of Percussion and Impulse
+clc
+//Given:
+m=30 //kg
+OG=1.05,h=OG,AG=0.15 //m
+//Solution:
+//Calculating the Frequency of Oscillation
+n=20/43.5 //Hz
+//Calculating the Equivalent Length of Simple Pendulum
+L=9.81/(2*%pi*n)^2 //m
+//Calculating the Distance of Centre of Percussion (C) from the Centre of Gravity (G)
+CG=L-OG //m
+//Calculating the Distance of Centre of Percussion (C) from the Knife Edge A
+AC=AG-CG //m
+//Calculating the Radius of Gyration of the Pendulum About O
+kO=sqrt(L*h) //m
+h1=h*(1-cos(60*%pi/180)) //m
+//Calculating the Angular Velocity of the Pendulum
+omega=sqrt(2*m*9.81*h1/(m*kO^2)) //rad/s
+OA=OG+AG
+//Calculating the Velocity of Striking
+v=omega*(OA) //Velocity of Striking
+//Calculating the Angular Velocity of the Pendulum Immediately After Impact
+I=m*kO^2
+LKE=55 //Loss of Kinetic Energy, N-m
+omega1=sqrt(omega^2-LKE*2/I)
+//Calculating the Impulses at Knife Edge A and at Pivot O (P and Q)
+CLM=m*h*(omega-omega1) //Change of Linear Momentum
+CAM=m*(kO^2-h^2)*(omega-omega1) //Change of Angular Momentum
+//P+Q=Change of Linear Momentum and, 0.15P-1.05Q=Change of Angular Momentum.
+//i.e., P+Q=CLM and 0.15P-1.05Q=CAM
+//Variables Matrix
+A=[1 1; 0.15 -1.05]
+B=[CLM; CAM]
+V=A \ B
+P=V(1)
+Q=V(2)
+//Calculating the Change in Axis Reaction When the Pendulum is Vertical
+CAR=m*(omega^2-omega1^2)*h //Change in Axis Reaction, N
+//Results:
+printf("\n\n The Distance of Centre of Percussion, AC = %.3f m.\n",AC)
+printf(" The Velocity of Striking = %.2f m/s.\n",v)
+printf(" The Impulse at the Knife Edge, P = %.1f N-s.\n",P)
+printf(" The Impulse at the Pivot, Q = %.2f N-s.\n",Q)
+printf(" The Change in Axis Reaction When the Pendulum is Vertical = %d N.\n\n",CAR)
\ No newline at end of file diff --git a/213/CH4/EX4.9/4_9.sce b/213/CH4/EX4.9/4_9.sce new file mode 100755 index 000000000..0158f2429 --- /dev/null +++ b/213/CH4/EX4.9/4_9.sce @@ -0,0 +1,15 @@ +//To Find the Radius of Gyration
+clc
+//Given:
+m=1.5 //kg
+l=1.25,x=120*10^-3,y=x //m
+//Solution:
+//Calculating the Frequency of Oscillation
+n=20/40 //Hz
+//Calculating the Radius of Gyration of the Connecting Rod
+kG=1/(2*%pi*n)*sqrt(9.81*x*y/l) //m
+//Calculating the Moment of Inertia of the Connecting Rod
+I=m*kG^2 //kg-m^2
+//Results:
+printf("\n\n The Radius of Gyration, kG = %d mm.\n",kG*1000)
+printf(" The Mass Moment of Inertia, I = %.3f kg-m^2.\n\n",I)
\ No newline at end of file diff --git a/213/CH5/EX5.1/5_1.sce b/213/CH5/EX5.1/5_1.sce new file mode 100755 index 000000000..b0a8f7b02 --- /dev/null +++ b/213/CH5/EX5.1/5_1.sce @@ -0,0 +1,16 @@ +//To find the time ratio
+clc
+//Given:
+AC=300,CB1=120 //mm
+//Solution:
+//Refer Fig. 5.28
+//Calculating the sine of inclination of the slotted bar with the vertical
+sineCAB1=CB1/AC
+//Calculating the inclination of the slotted bar with the vertical
+angleCAB1=asin(sineCAB1)*180/%pi //degrees
+//Calculating the angle alpha
+alpha=2*(90-angleCAB1) //degrees
+//Calculating the ratio of time of cutting stroke to time of return stroke
+r=(360-alpha)/alpha //Ratio of time of cutting stroke to time of return stroke
+//Results:
+printf("\n\n The ratio of the time of cutting stroke to the time of return stroke is %.2f.\n\n",r)
\ No newline at end of file diff --git a/213/CH5/EX5.2/5_2.sce b/213/CH5/EX5.2/5_2.sce new file mode 100755 index 000000000..aa39b364c --- /dev/null +++ b/213/CH5/EX5.2/5_2.sce @@ -0,0 +1,19 @@ +//To find the time ratio
+clc
+//Given:
+AC=240,CB1=120,AP1=450 //mm
+//Solution:
+//Refer Fig. 5.29
+//Calculating the sine of inclination of the slotted bar with the vertical
+sineCAB1=CB1/AC
+//Calculating the inclination of the slotted bar with the vertical
+angleCAB1=asin(sineCAB1)*180/%pi //degrees
+//Calculating the angle alpha
+alpha=2*(90-angleCAB1) //degrees
+//Calculating the time ratio of cutting stroke to the return stroke
+r=(360-alpha)/alpha //Time ratio of cutting stroke to the return stroke
+//Calculating the length of the stroke
+R1R2=2*AP1*sin(%pi/2-alpha/2*%pi/180) //mm
+//Results:
+printf("\n\n The time ratio of cutting stroke to the return stroke is %d.\n",r)
+printf(" The length of the stroke, R1R2 = P1P2 = %d mm.\n\n",R1R2)
\ No newline at end of file diff --git a/213/CH5/EX5.3/5_3.sce b/213/CH5/EX5.3/5_3.sce new file mode 100755 index 000000000..504d9cbb7 --- /dev/null +++ b/213/CH5/EX5.3/5_3.sce @@ -0,0 +1,18 @@ +//To find the dimensions of AC and AP
+clc
+//Given:
+//Refer Fig. 5.30 and Fig. 5.31
+BC=30,R1R2=120 //mm
+r=1.7 //Time ratio of working stroke to the return stroke
+//Solution:
+//Calculating the angle alpha
+alpha=360/(1.7+1) //degrees
+//Calculating the length of the link AC
+B1C=BC
+AC=B1C/cosd(alpha/2) //mm
+//Calculating the length of the link AP
+AP1=R1R2/(2*cosd(alpha/2)) //mm
+AP=AP1
+//Results:
+printf("\n\n The length of AC = %.1f mm.\n",AC)
+printf(" The length of AP = %.1f mm.\n\n",AP)
\ No newline at end of file diff --git a/213/CH5/EX5.4/5_4.sce b/213/CH5/EX5.4/5_4.sce new file mode 100755 index 000000000..1a7ef1009 --- /dev/null +++ b/213/CH5/EX5.4/5_4.sce @@ -0,0 +1,18 @@ +//To find the time ratio
+clc
+//Given:
+CD=50,CA=75,PA=150,PR=135 //mm
+//Solution:
+//Refer Fig. 5.32 and Fig. 5.33
+//Calculating the cosine of angle beta
+CA2=CA
+cosbeta=CD/CA2
+//Calculating the angle beta
+beta=2*acos(cosbeta)*180/%pi //degrees
+//Calculating the ratio of time of cutting stroke to time of return stroke
+r=(360-beta)/beta //Ratio of time of cutting stroke to time of return stroke
+//Calculating the length of effective stroke
+R1R2=87.5 //mm
+//Results:
+printf("\n\n The ratio of time of cutting stroke to time of return stroke is %.3f.\n",r)
+printf(" The length of effective stroke, R1R2 = %.1f mm.\n\n",R1R2)
\ No newline at end of file diff --git a/213/CH6/EX6.1/6_1.sce b/213/CH6/EX6.1/6_1.sce new file mode 100755 index 000000000..e6452c760 --- /dev/null +++ b/213/CH6/EX6.1/6_1.sce @@ -0,0 +1,17 @@ +//To find the angular velocity
+clc
+//Given:
+NAB=100 //rpm
+AB=300/1000,BC=360/1000,CD=BC //m
+//Solution:
+//Refer Fig. 6.9
+//Calculating the angular speed of link AB
+omegaAB=2*%pi*NAB/60 //rad/s
+//Calculating the velocity of point B on link AB
+vB=omegaAB*AB //m/s
+//Calculating the angular velocity of link BC
+//By measurement from instantaneous centre diagram, Fig. 6.10,
+I13B=500/1000 //m
+omegaBC=vB/I13B //rad/s
+//Results:
+printf("\n\n The angular velocity of the link BC, omegaBC = %.3f rad/s.\n\n",omegaBC)
\ No newline at end of file diff --git a/213/CH6/EX6.2/6_2.sce b/213/CH6/EX6.2/6_2.sce new file mode 100755 index 000000000..c959f134a --- /dev/null +++ b/213/CH6/EX6.2/6_2.sce @@ -0,0 +1,19 @@ +//To find velocity and angular velocity
+clc
+//Given:
+omegaOB=10 //rad/s
+OB=100/1000 //m
+//Solution:
+//Refer Fig. 6.12
+//Calculating the velocity of the crank OB
+vOB=omegaOB*OB //m/s
+vB=vOB
+//By measurement from the instantaneous cemtre diagram, Fig. 6.13,
+I13A=460/1000,I13B=560/1000 //m
+//Calculating the velocity of slider A
+vA=vB/I13B*I13A
+//Calculating the angular velocity of the connecting rod AB
+omegaAB=vB/I13B //rad/s
+//Results:
+printf("\n\n The velocity of slider A, vA = %.2f m/s.\n",vA)
+printf(" The angular velocity of connecting rod AB, omegaAB = %.2f rad/s.\n\n",omegaAB)
\ No newline at end of file diff --git a/213/CH6/EX6.3/6_3.sce b/213/CH6/EX6.3/6_3.sce new file mode 100755 index 000000000..fef2d78cb --- /dev/null +++ b/213/CH6/EX6.3/6_3.sce @@ -0,0 +1,33 @@ +//To find velocity and angular velocity
+clc
+//Given:
+NOA=120 //rpm
+OA=200/1000 //m/s
+//Results:
+//Refer Fig. 6.15
+//Calculating the angular velocity of the crank OA
+omegaOA=2*%pi*NOA/60 //rad/s
+//Calculating the velocity of crank OA
+vOA=omegaOA*OA //m/s
+vA=vOA
+//By measurement from the instantaneous cemtre diagram, Fig. 6.16,
+I13A=840/1000,I13B=1070/1000,I14B=400/1000,I14C=200/1000,I15C=740/1000,I15D=500/1000 //m
+//Calculating the velocity of point B
+vB=vA/I13A*I13B //m/s
+//Calculating the velocity of point C
+vC=vB/I14B*I14C //m/s
+//Calculating the velocity of point B
+vD=vC/I15C*I15D //m/s
+//Calculating the angular velocity of the link AB
+omegaAB=vA/I13A //rad/s
+//Calculating the angular velocity of the link BC
+omegaBC=vB/I14B //rad/s
+//Calculating the angular velocity of the link CD
+omegaCD=vC/I15C //rad/s
+//Results:
+printf("\n\n The velocity of point B, vB = %.1f m/s.\n",vB)
+printf(" The velocity of point C, vC = %.1f m/s.\n",vC)
+printf(" The velocity of point D, vD = %.2f m/s.\n",vD)
+printf(" The angular velocity of the link AB, omegaAB = %.2f rad/s.\n",omegaAB)
+printf(" The angular velocity of the link BC, omegaBC = %d rad/s.\n",omegaBC)
+printf(" The angular velocity of the link CD, omegaCD = %.2f rad/s.\n\n",omegaCD)
\ No newline at end of file diff --git a/213/CH6/EX6.4/6_4.sce b/213/CH6/EX6.4/6_4.sce new file mode 100755 index 000000000..500ec746f --- /dev/null +++ b/213/CH6/EX6.4/6_4.sce @@ -0,0 +1,22 @@ +//To find the velocity
+clc
+//Given:
+omegaO1A=100 //rad/s
+O1A=100/1000 //m
+//Solution:
+//Refer Fig. 6.18
+//Calculating the linear velocity of crank O1A
+vO1A=omegaO1A*O1A //m/s
+vA=vO1A
+//By measurement from the instantaneous cemtre diagram, Fig. 6.19,
+I13A=910/1000,I13B=820/1000,I15B=130/1000,I15D=50/1000,I16D=200/1000,I16E=400/1000 //m
+//Calculating the velocity of point B
+vB=vA/I13A*I13B //m/s
+//Calculating the velocity of point D
+vD=vB/I15B*I15D //m/s
+//Calculating the velocity of point E
+vE=vD/I16D*I16E //m/s
+//Results:
+printf("\n\n The velocity of point B, vB = %.2f m/s.\n",vB)
+printf(" The velocity of point D, vD = %.2f m/s.\n",vD)
+printf(" The velocity of point E, vE = %.2f m/s.\n",vE)
\ No newline at end of file diff --git a/213/CH6/EX6.5/6_5.sce b/213/CH6/EX6.5/6_5.sce new file mode 100755 index 000000000..1bcf5969a --- /dev/null +++ b/213/CH6/EX6.5/6_5.sce @@ -0,0 +1,22 @@ +//To find the velocity
+clc
+//Given:
+NO1A=400 //rpm
+O1A=16/1000 //m
+//Solution:
+//Refer Fig. 6.21
+//Calculating the angular velocity of the crank O1A
+omegaO1A=2*%pi*NO1A/60 //rad/s
+//Calculating the linear velocity of the crank O1A
+vO1A=omegaO1A*O1A //m/s
+vA=vO1A
+//By measurement from the instantaneous cemtre diagram, Fig. 6.22,
+I13A=41/1000,I13B=50/1000,I14B=23/1000,I14C=28/1000,I15C=65/1000,I15D=62/1000 //m
+//Calculating the velocity of point B
+vB=vA/I13A*I13B //m/s
+//Calculating the velocity of point C
+vC=vB/I14B*I14C //m/s
+//Calculating the velocity of of the needle at D
+vD=vC/I15C*I15D //m/s
+//Results:
+printf("\n\n The velocity of the needle at D, vD = %.2f m/s.\n\n",vD)
\ No newline at end of file diff --git a/213/CH6/EX6.6/6_6.sce b/213/CH6/EX6.6/6_6.sce new file mode 100755 index 000000000..12340017e --- /dev/null +++ b/213/CH6/EX6.6/6_6.sce @@ -0,0 +1,14 @@ +//To find velocity of ram
+clc
+//Given:
+NOA=120 //rpm
+//Solution:
+//Refer Fig. 6.24
+//Calculating the angular speed of crank OA
+omegaOA=2*%pi*NOA/60 //rad/s
+//By measurement from the instantaneous cemtre diagram, Fig. 6.25,
+I12I26=65/1000 //m
+//Calculating the velocity of the ram
+vD=omegaOA*I12I26 //m/s
+//Results:
+printf("\n\n The velocity of ram D, vD = %.3f m/s.\n\n",vD)
\ No newline at end of file diff --git a/213/CH7/EX7.1/7_1.sce b/213/CH7/EX7.1/7_1.sce new file mode 100755 index 000000000..dcf0b8310 --- /dev/null +++ b/213/CH7/EX7.1/7_1.sce @@ -0,0 +1,19 @@ +//To find the angular velocity
+clc
+//Given:
+NBA=120 //rpm
+AB=40/1000,CD=80/1000 //m
+//Solution:
+//Refer Fig. 7.7
+//Calculating the angular velocity of the crank AB
+omegaBA=2*%pi*NBA/60 //rad/s
+//Calculating the velocity of B with respect to A
+vBA=omegaBA*AB //m/s
+vB=vBA
+//By measurement from the velocity diagram, Fig. 7.7(b),
+vCD=0.385 //m/s
+vC=vCD
+//Calculating the angular velocity of link CD
+omegaCD=vCD/CD //rad/s
+//Results:
+printf("\n\n The angular velocity of link CD, omegaCD = %.1f rad/s, clockwise about D.\n\n",omegaCD)
\ No newline at end of file diff --git a/213/CH7/EX7.10/7_10.sce b/213/CH7/EX7.10/7_10.sce new file mode 100755 index 000000000..1a6709425 --- /dev/null +++ b/213/CH7/EX7.10/7_10.sce @@ -0,0 +1,29 @@ +//To find velocity and resisting torque
+clc
+//Given:
+NAD=100 //rpm
+TA=50 //N-m
+DA=300/1000,CB=360/1000,AB=CB,DC=600/1000 //m
+eta=70/100 //%
+//Solution:
+//Refer Fig. 7.25
+//Calculating the angular velocity of the crank AD
+omegaAD=2*%pi*NAD/60 //rad/s
+//Calculating the velocity of A with respect to D
+vAD=omegaAD*DA //m/s
+vA=vAD
+//By measurement from the velocity diagram, Fig. 7.25(b),
+vBC=2.25 //m/s
+vB=vBC
+//Calculating the angular velocity of the driven link CB
+omegaBC=vBC/CB //rad/s
+//Calculating the actual mechanical advantage
+omegaA=omegaAD,omegaB=omegaBC
+MAactual=eta*omegaA/omegaB
+//Calculating the resisting torque
+TB=eta*TA*omegaA/omegaB //N-m
+//Results:
+printf("\n\n The velocity of the point B, vB = %.2f m/s.\n",vB)
+printf(" The angular velocity of the driven link CB, omegaBC = %.2f rad/s.\n",omegaBC)
+printf(" The actual mechanical advantage, M.A.(actual) = %.2f.\n",MAactual)
+printf(" The resisting torque, TB = %.1f N-m.\n\n",TB)
\ No newline at end of file diff --git a/213/CH7/EX7.11/7_11.sce b/213/CH7/EX7.11/7_11.sce new file mode 100755 index 000000000..9608fa8eb --- /dev/null +++ b/213/CH7/EX7.11/7_11.sce @@ -0,0 +1,24 @@ +//To find velocity ratio
+clc
+//Given:
+WC=2.5*1000,WD=4*1000 //N
+OA=175/1000,AB=180/1000,AD=500/1000,BC=325/1000 //m
+//Solution:
+//Refer Fig. 7.26
+//Assuming the speed of crank OA to be 'N'
+//Calculating the angular velocity of crank OA
+omegaAO=mulf('2*%pi/60','N')
+//Calculating the velocity of A with respect to O
+vAO=mulf('omegaAO','OA')
+vA=vAO
+//Assume the vector oa (i.e. velocity of A) as 20 m/s
+N=20/(2*%pi/60*OA) //mm
+//By measurement from the velocity diagram, Fig. 7.27(b),
+vC=35,vD=21 //mm
+//Calculating the velocity ratio between C and the ram D
+r=vC/vD //The velocity ratio between C and the ram D
+//Calculating the efficiency of the machine
+eta=(WD*vD)/(WC*vC)*100 //%
+//Results:
+printf("\n\n The velocity ratio between C and the ram D is %.2f.\n",r)
+printf(" The efficiency of the machine, eta = %d %s.\n\n",eta,'%')
\ No newline at end of file diff --git a/213/CH7/EX7.12/7_12.sce b/213/CH7/EX7.12/7_12.sce new file mode 100755 index 000000000..cc3c3642a --- /dev/null +++ b/213/CH7/EX7.12/7_12.sce @@ -0,0 +1,40 @@ +//To find velocity, angular velocity and torque
+clc
+//Given:
+NAO=180 //rpm
+OA=180/1000,CB=240/1000,AB=360/1000,BD=540/1000 //m
+FD=2*1000 //N
+DA=30/1000,DD=DA,rA=DA/2,rD=DD/2 //m
+//Solution:
+//Refer Fig. 7.28
+//Calculating the angular velocity of the crank OA
+omegaAO=2*%pi*NAO/60 //rad/s
+//Calculating the velocity of A with respect to O
+vAO=omegaAO*OA
+vA=vAO
+//By measurement fro the velocity diagram, Fig. 7.29(b)
+vD=2.05,vBA=0.9,vBC=2.8,vDB=2.4 //m/s
+//Calculating the angular velocity of the link AB
+omegaAB=vBA/AB //rad/s
+//Calculating the angular velocity of the link CB
+omegaCB=vBC/CB //rad/s
+//Calculating the angular velocity of the link BD
+omegaBD=vDB/BD //rad/s
+//Calculating the relative angular velocity at A
+rvA=omegaCB-omegaAB+omegaBD //The relative angular velocity at A, rad/s
+//Calculating the relative angular velocity at D
+rvD=omegaBD //The relative angular velocity at D, rad/s
+//Calculating the velocity of rubbing on the pin A
+vrA=rvA*rA*1000 //The velocity of rubbing on the pin A, mm/s
+//Calculating the velocity of rubbing on the pin D
+vrD=rvD*rD*1000 //The velocity of rubbing on the pin D, mm/s
+//Calculating the torque applied to crank OA
+TA=FD*vD/omegaAO //N-m
+//Results:
+printf("\n\n The velocity of slider D, vD = %.2f m/s.\n",vD)
+printf(" The angular velocity of the link AB, omegaAB = %.1f rad/s, anticlockwise about A.\n",omegaAB)
+printf(" The angular velocity of the link CB, omegaCB = %.2f rad/s, anticlockwise about C.\n",omegaCB)
+printf(" The angular velocity of the link BD, omegaBD = %.2f rad/s, clockwise about B.\n",omegaBD)
+printf(" The velocity of rubbing on the pin A is %d mm/s.\n",vrA)
+printf(" The velocity of rubbing on the pin D is %d mm/s.\n",vrD)
+printf(" The torque applied to the crank OA, TA = %.1f N-m.\n\n",TA)
\ No newline at end of file diff --git a/213/CH7/EX7.13/7_13.sce b/213/CH7/EX7.13/7_13.sce new file mode 100755 index 000000000..7a1f93099 --- /dev/null +++ b/213/CH7/EX7.13/7_13.sce @@ -0,0 +1,23 @@ +//To find the velocities
+clc
+//Given:
+NBA=180 //rpm
+AB=0.45,BD=1.5,BC=0.9,CE=BC //m
+FD=500,FE=750 //N
+//Solution:
+//Refer Fig. 7.31
+//Calculating the angular velocity of the crank AB
+omegaBA=2*%pi*NBA/60 //rad/s
+//Calculating the velocity of B with respect to A
+vBA=omegaBA*AB //m/s
+vB=vBA
+//By measurement from the velocity diagram, Fig. 7.31(b),
+vD=9.5,vE=1.7 //m/s
+//Calculating the power input
+Pi=FD*vD-FE*vE //N-m/s
+//Calculating the turning moment at A
+TA=Pi/omegaBA //N-m
+//Results:
+printf("\n\n The velocity of slider D, vD = %.1f m/s.\n",vD)
+printf(" The velocity of slider E, vE = %.1f m/s.\n",vE)
+printf(" The turning moment at A, TA = %.1f N-m.\n\n",TA)
\ No newline at end of file diff --git a/213/CH7/EX7.2/7_2.sce b/213/CH7/EX7.2/7_2.sce new file mode 100755 index 000000000..de1ba4e03 --- /dev/null +++ b/213/CH7/EX7.2/7_2.sce @@ -0,0 +1,33 @@ +//To find velocities, angular velocities and position
+clc
+//Given:
+NBO=180 //rpm
+OB=0.5,PB=2,dO=50/1000,dB=60/1000,dC=30/1000 //m
+//Solution:
+//Refer Fig. 7.8
+//Calculating the angular velocity of the crank BO
+omegaBO=2*%pi*NBO/60 //rad/s
+//Calculating the linear velocity of B with respect to O
+vBO=omegaBO*OB //m/s
+vB=vBO
+//By measurement from the velocity diagram, Fig. 7.8(b),
+vP=8.15,vPB=6.8,vE=8.5,bg=5,bp=vPB,vG=8 //m/s
+//Calculating the angular velocity of the connecting rod PB
+omegaPB=vPB/PB //rad/s
+//Calculating the velocity of rubbing at the pin of crank-shaft
+vCS=dO/2*omegaBO //Velocity of rubbing at the pin of crank-shaft, m/s
+//Calculating the velocity of rubbing at the pin of crank
+vC=dB/2*(omegaBO+omegaPB) //Velocity of rubbing at the pin of crank, m/s
+//Calculating the velocity of rubbing at the pin of cross-head
+vPCH=dC/2*omegaPB //Velocity of rubbing at the pin of cross-head, m/s
+//Calculating the position of point G on the connecting rod
+BG=bg/bp*PB //m
+//Results:
+printf("\n\n The velocity of piston P, vP = %.2f m/s.\n",vP)
+printf(" The angular velocity of connecting rod, omegaPB = %.1f rad/s, anticlockwise.\n",omegaPB)
+printf(" The velocity of point E on the connecting rod, vE = %.1f m/s.\n",vE)
+printf(" The velocity of rubbing at the pin of crank-shaft is %.2f m/s.\n",vCS)
+printf(" The velocity of rubbing at the pin of crank is %.4f m/s.\n",vC)
+printf(" The velocity of rubbing at the pin of cross-head is %.3f m/s.\n",vPCH)
+printf(" The position of point G on the connecting rod, BG = %.2f m.\n",BG)
+printf(" The linear velocity of point G, vG = %d m/s.\n\n",vG)
\ No newline at end of file diff --git a/213/CH7/EX7.3/7_3.sce b/213/CH7/EX7.3/7_3.sce new file mode 100755 index 000000000..0a603fa2c --- /dev/null +++ b/213/CH7/EX7.3/7_3.sce @@ -0,0 +1,19 @@ +//To find the velocity
+clc
+//Given:
+NAO=600 //rpm
+OA=28/1000,BD=46/1000 //m
+//Solution:
+//Refer Fig. 7.10
+//Calculating the angular velocity of crank AO
+omegaAO=2*%pi*NAO/60 //rad/s
+//Calculating the velocity of A with respect to O
+vAO=omegaAO*OA //m/s
+vA=vAO
+//By measurement from the velocity diagram, Fig. 7.10(b),
+vD=1.6,vDB=1.7 //m/s
+//Calculating the angular velocity of D with respect to B
+omegaBD=vDB/BD //rad/s
+//Results:
+printf("\n\n The velocity of the slider D, vD = %.1f m/s.\n",vD)
+printf(" The angular velocity of the link BD, omegaBD = %.2f rad/s, clockwise sbout B.\n\n",omegaBD)
\ No newline at end of file diff --git a/213/CH7/EX7.4/7_4.sce b/213/CH7/EX7.4/7_4.sce new file mode 100755 index 000000000..64d2e0c22 --- /dev/null +++ b/213/CH7/EX7.4/7_4.sce @@ -0,0 +1,24 @@ +//To find velocity, angular velocity and rubbing speed
+clc
+//Given:
+NBA=120 //rpm
+AB=150/1000,DC=450/1000,BC=450/1000,dC=50/1000,rC=dC/2 //m
+//Sloution:
+//Refer Fig. 7.12
+//Calculating the angular velocity of the crank AB
+omegaBA=2*%pi*NBA/60 //rad/s
+//Calculating the linear velocity of B with respect to A
+vBA=omegaBA*AB //m/s
+vB=vBA
+//By measurement from the velocity diagram, Fig. 7.12(b),
+vF=0.7,vCD=2.25,vCB=2.25 //m/s
+//Calculating the angular velocity of DC
+omegaDC=vCD/DC //rad/s
+//Calculating the angular velocity of BC
+omegaCB=vCB/BC //rad/s
+//Calculating the rubbing speed at the pin C
+vr=(omegaCB-omegaDC)*rC //The rubbing speed at the pin C,m/s
+//Results:
+printf("\n\n The velocity of block F, vF = %.1f m/s.\n",vF)
+printf(" The angular velocity of DC, omegaDC = %d rad/s, anticlockwise about D.\n",omegaDC)
+printf(" The rubbing speed at the pin C is %d m/s.\n\n",vr)
\ No newline at end of file diff --git a/213/CH7/EX7.5/7_5.sce b/213/CH7/EX7.5/7_5.sce new file mode 100755 index 000000000..3ca22fb5f --- /dev/null +++ b/213/CH7/EX7.5/7_5.sce @@ -0,0 +1,20 @@ +//To find velocity and angular velocity
+clc
+//Given:
+NAO=120 //rpm
+OA=100/1000,CE=350/1000 //m
+//Solution:
+//Refer Fig. 7.13
+//Calculating the angular speed of the crank OA
+omegaAO=2*%pi*NAO/60 //rad/s
+//Calculating the velocity of A with respect to O
+vAO=omegaAO*OA //m/s
+vA=vAO
+//By measurement from the velocity diagram, Fig. 7.14(b),
+vF=0.53,od=1.08,vCE=0.44 //m/s
+//Calculating the angular velocity of CE
+omegaCE=vCE/CE //rad/s
+//Results:
+printf("\n\n The velocity of F, vF = %.2f m/s.\n",vF)
+printf(" The velocity of sliding of CE in the trunnion is %.2f m/s.\n",od)
+printf(" The angular velocity of CE, omegaCE = %.2f rad/s, clockwise about E.\n\n",omegaCE)
\ No newline at end of file diff --git a/213/CH7/EX7.6/7_6.sce b/213/CH7/EX7.6/7_6.sce new file mode 100755 index 000000000..d66973c47 --- /dev/null +++ b/213/CH7/EX7.6/7_6.sce @@ -0,0 +1,16 @@ +//To find the absolute velocity
+clc
+//Given:
+NCO=120 //rpm
+OC=125/1000 //m
+//Solution:
+//Refer Fig. 7.15
+//Calculating the angular velocity of the crank CO
+omegaCO=2*%pi*NCO/60 //rad/s
+//Calculating the linear velocity of C with respect to O
+vCO=omegaCO*OC //m/s
+vC=vCO
+//By measurement from the velocity diagram, Fig. 7.16(b),
+vCO=1.57,vE=0.7 //m/s
+//Results:
+printf("\n\n The absolute velocity of point E of the lever, vE = %.1f m/s.\n\n",vE)
\ No newline at end of file diff --git a/213/CH7/EX7.7/7_7.sce b/213/CH7/EX7.7/7_7.sce new file mode 100755 index 000000000..6acc329b0 --- /dev/null +++ b/213/CH7/EX7.7/7_7.sce @@ -0,0 +1,20 @@ +//To find linear and angular velocity
+clc
+//Given:
+NBO1=40 //rpm
+O1O2=800/1000,O1B=300/1000,O2D=1300/1000,DR=400/1000 //m
+//Solution:
+//Refer Fig. 7.18
+//Calculating the angular speed of the crank BO
+omegaBO1=2*%pi*NBO1/60 //rad/s
+//Calculating the velocity of B with respect to O1
+vBO1=omegaBO1*O1B //m/s
+vB=vBO1
+//By measurement from the velocity diagram, Fig. 7.18(b),
+vR=1.44, vDO2=1.32 //m/s
+vD=vDO2
+//Calculating the angular velocity of the link O2D
+omegaDO2=vDO2/O2D //rad/s
+//Results:
+printf("\n\n The velocity of the ram R, vR = %.2f m/s.\n",vR)
+printf(" The angular velocity of the link O2D, omegaDO2 = %.3f rad/s, anticlockwise about O2.\n\n",omegaDO2)
\ No newline at end of file diff --git a/213/CH7/EX7.8/7_8.sce b/213/CH7/EX7.8/7_8.sce new file mode 100755 index 000000000..d960fd903 --- /dev/null +++ b/213/CH7/EX7.8/7_8.sce @@ -0,0 +1,30 @@ +//To find speed and time ratio
+clc
+//Given:
+NAO1=60 //rpm
+O1A=85,rQ=50 //mm
+//Solution:
+//Refer Fig. 7.20 and Fig. 7.21
+//Calculating the angular velocity of AO1
+omegaAO1=2*%pi*NAO1/60 //rad/s
+//Calculating the velocity of A with respect to O1
+vAO1=omegaAO1*O1A //mm/s
+vA=vAO1
+//By measurement from the velocity diagram, Fig. 7.20(b),
+vDO2=410 //mm/s
+O2D=264 //mm
+angleB1O2B2=60*%pi/180 //rad
+funcprot(0) //To vary the Scilab function 'beta'
+alpha=120,beta=240 //degrees
+//Calculating the angular velocity of the quadant Q
+omegaQ=vDO2/O2D //rad/s
+//Calculating the linear speed of the rack
+vR=omegaQ*rQ //mm/s
+//Calculating the ratio of times of lowering and raising the rack
+r=beta/alpha
+//Calculating the length of stroke of the rack
+L=rQ*angleB1O2B2 //mm
+//Results:
+printf("\n\n The linear speed of the rack, vR = %.1f mm/s.\n",vR)
+printf(" The ratio of times of lowering and raising the rack is %d.\n",r)
+printf(" The length of the stroke of the rack is %.2f mm.\n\n",L)
\ No newline at end of file diff --git a/213/CH7/EX7.9/7_9.sce b/213/CH7/EX7.9/7_9.sce new file mode 100755 index 000000000..107f172b3 --- /dev/null +++ b/213/CH7/EX7.9/7_9.sce @@ -0,0 +1,20 @@ +//To find velocity and angular velocity
+clc
+//Given:
+NPO=120 //rpm
+OQ=100/1000,OP=200/1000,RQ=150/1000,RS=500/1000 //m
+//Solution:
+//Refer Fig. 7.22
+//Calculating the angular speed of the crank PO
+omegaPO=2*%pi*NPO/60 //rad/s
+//Calculating the velocity of P with respect to O
+vPO=omegaPO*OP //m/s
+vP=vPO
+//By measurement from the velocity diagram, Fig. 7.23(b),
+vS=0.8,vSR=0.96,vTP=0.85 //m/s
+//Calculating the angular velocity of link RS
+omegaRS=vSR/RS //rad/s
+//Results:
+printf("\n\n The velocity of the slider S (cutting tool), vS = %.1f m/s.\n",vS)
+printf(" The angular velocity of the link RS, omegaRS = %.2f rad/s, clockwise about R.\n",omegaRS)
+printf(" The velocity of the sliding block T on the slotted lever QT, vTP = %.2f m/s.\n\n",vTP)
\ No newline at end of file diff --git a/213/CH8/EX8.1/8_1.sce b/213/CH8/EX8.1/8_1.sce new file mode 100755 index 000000000..6c763fb7d --- /dev/null +++ b/213/CH8/EX8.1/8_1.sce @@ -0,0 +1,30 @@ +//To find linear and agular velocity and acceleration
+clc
+//Given:
+NBO=300 //rpm
+OB=150/1000,BA=600/1000 //m
+//Solution:
+//Refer Fig. 8.4
+//Calculating the angular velocity of BO
+omegaBO=2*%pi*NBO/60 //rad/s
+//Calculating the linear velocity of B with respect to O
+vBO=omegaBO*OB //m/s
+vB=vBO
+//By measurement from the velocity diagram, Fig. 8.4(b),
+vAB=3.4,vD=4.1 //m/s
+//Calculating the radial component of the acceleration of B with respect of O
+arBO=vBO^2/OB //m/s^2
+aB=arBO
+//Calculating the radisla component of the accaleration of A with respect to B
+arAB=vAB^2/BA //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.4(c),
+aD=117,adashAB=103 //m/s^2
+//Calculating the angular velocity of the connecting rod
+omegaAB=vAB/BA //rad/s^2
+//Calculating the angular acceleration of the connecting rod
+alphaAB=adashAB/BA //rad/s^2
+//Results:
+printf("\n\n The linear velocity of the midpoint of the connecting rod, vD = %.1f m/s.\n",vD)
+printf(" The linear acceleration of the midpoint of the connecting rod, aD = %d m/s^2.\n",aD)
+printf(" The angular velocity of the connecting rod, omegaAB = %.2f rad/s, anticlockwise about B.\n",omegaAB)
+printf(" The angular acceleration of the connecting rod, alphaAB = %.2f rad/s^2, clockwise about B.\n\n",alphaAB)
\ No newline at end of file diff --git a/213/CH8/EX8.10/8_10.sce b/213/CH8/EX8.10/8_10.sce new file mode 100755 index 000000000..c6dd92db2 --- /dev/null +++ b/213/CH8/EX8.10/8_10.sce @@ -0,0 +1,51 @@ +//To find velocity, torque and acceleration
+clc
+//Given:
+NAO=100 //rpm
+OA=150/1000,AB=600/1000,BC=350/1000,CD=150/1000,DE=500/1000 //m
+dA=50/1000,dB=dA,rA=dA/2,rB=dB/2 //m
+pF=0.35 //N/mm^2
+DF=250 //mm
+//Solution:
+//Refer Fig. 8.21
+//Calculating the angular speed of the crank AO
+omegaAO=2*%pi*NAO/60 //rad/s
+//Calculating the velocity of A with respect to O
+vAO=omegaAO*OA //m/s
+vA=vAO
+//By measurement from the velocity diagram, Fig. 8.21(b),
+vBA=1.65,vBC=0.93,vB=vBC,vED=0.18,vEO=0.36,vE=vEO,vF=vE //m/s
+//Calculating the velocity of D with respect to C
+vDC=vBC*CD/BC //m/s
+//Calculating the angular velocity of B with respect to A
+omegaBA=vBA/AB //rad/s
+//Calculating the angular velocity of B with respect to C
+omegaBC=vBC/BC //rad/s
+//Calculating the rubbing velocity of pin at A
+vrA=(omegaAO-omegaBA)*rA //The rubbing velocity of pin at A, m/s
+//Calculating the rubbing velocity of pin at B
+vrB=(omegaBA+omegaBC)*rB //The rubbing velocity of pin at B, m/s
+//Calculating the force at the pump piston at F
+FF=pF*%pi/4*DF^2 //N
+//Calculating the force required at the crankshaft A
+FA=FF*vF/vA //N
+//Calculating the torque required at the crankshaft
+TA=FA*OA //N-m
+//Calculating the radial component of the acceleration of A with respect to O
+arAO=vAO^2/OA //m/s^2
+//Calculating the radial component of the acceleration of B with respect to A
+arBA=vBA^2/AB //m/s^2
+//Calculating the radial component of the acceleration of B with respect to C
+arBC=vBC^2/BC //m/s^2
+//Calculating the radial component of the acceleration of E with respect to D
+arED=vED^2/DE //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.21(c),
+aBC=9.2,aB=aBC,aBA=9,aE=3.8 //m/s^2
+//Calculating the acceleration of D
+aD=aBC*CD/BC //m/s^2
+//Results:
+printf("\n\n The velocity of the cross-head E, vE = %.2f m/s.\n",vE)
+printf(" The rubbing velocity of pin at A = %.3f m/s.\n",vrA)
+printf(" The rubbing velocity of pin at B = %.3f m/s.\n",vrB)
+printf(" The torque required at the crankshaft, TA = %d N-m.\n",TA)
+printf(" The acceleration of the crosshead E, aE = %.1f m/s^2.\n\n",aE)
\ No newline at end of file diff --git a/213/CH8/EX8.11/8_11.sce b/213/CH8/EX8.11/8_11.sce new file mode 100755 index 000000000..b994b8440 --- /dev/null +++ b/213/CH8/EX8.11/8_11.sce @@ -0,0 +1,28 @@ +//To find velocity and acceleration
+clc
+//Given:
+NAO=150 //rpm
+OA=150/1000,AB=550/1000,AC=450/1000,DC=500/1000,BE=350/1000 //m
+//Solution:
+//Refer Fig. 8.23
+//Calculating the angular speed of the crank AO
+omegaAO=2*%pi*NAO/60 //rad/s
+//Calculating the linear velocity of A with respect to O
+vAO=omegaAO*OA //m/s
+vA=vAO
+//By measurement from the velocity diagram, Fig. 8.23(b),
+vCA=0.53,vCD=1.7,vC=vCD,vEB=1.93,vE=1.05 //m/s
+//Calculating the radial component of the acceleration of A with respect to O
+arAO=vAO^2/OA //m/s^2
+aA=arAO
+//Calculating the radial component of the acceleration of C with respect to A
+arCA=vCA^2/AC //m/s^2
+//Calculating the radial component of the acceleration of C with respect to D
+arCD=vCD^2/DC //m/s^2
+//Calculating the radial component of the acceleration of E with respect to B
+arEB=vEB^2/BE //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.23(c),
+aE=3.1 //m/s^2
+//Results:
+printf("\n\n Velocity of the ram E, vE = %.2f m/s.\n",vE)
+printf(" Acceleration of the ram E, aE = %.1f m/s^2.\n\n",aE)
\ No newline at end of file diff --git a/213/CH8/EX8.12/8_12.sce b/213/CH8/EX8.12/8_12.sce new file mode 100755 index 000000000..99d4a87fd --- /dev/null +++ b/213/CH8/EX8.12/8_12.sce @@ -0,0 +1,34 @@ +//To find the velocity and acceleration
+clc
+//Given:
+NDC=1140 //rpm
+AB=80/1000,CD=40/1000,BE=150/1000,DE=BE,EP=200/1000 //m
+//Solution:
+//Refer Fig. 8.25
+//Calculating the angular speed of the link CD
+omegaDC=2*%pi*NDC/60 //rad/s
+//Calculating the velocity of D with respect to C
+vDC=omegaDC*CD //m/s
+vD=vDC
+//Calculating the angular speed of the larger wheel
+omegaBA=omegaDC*CD/AB //rad/s
+//Calculating the velocity of B with respect to A
+vBA=omegaBA*AB //m/s
+vB=vBA
+//By measurement from the velocity diagram, Fig. 8.25(b),
+vEB=8.1,vED=0.15,vPE=4.7,vP=0.35 //m/s
+//Calculating the radial component of the acceleration of B with respect to A
+arBA=vBA^2/AB //m/s^2
+//Calculating the radial component of the acceleration of D with respect to C
+arDC=vDC^2/CD //m/s^2
+//Calculating the radial component of the acceleration of E with respect to B
+arEB=vEB^2/BE //m/s^2
+//Calculating the radial component of the acceleration of E with respect to D
+arED=vED^2/DE //m/s^2
+//Calculating the radial component of the acceleration of P with respect to E
+arPE=vPE^2/EP //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.25(c),
+aP=655 //m/s^2
+//Results:
+printf("\n\n Velocity of P, vP = %.2f m/s.\n",vP)
+printf(" Acceleration of the piston P, aP = %d m/s^2.\n\n",aP)
\ No newline at end of file diff --git a/213/CH8/EX8.13/8_13.sce b/213/CH8/EX8.13/8_13.sce new file mode 100755 index 000000000..1cc0bf29b --- /dev/null +++ b/213/CH8/EX8.13/8_13.sce @@ -0,0 +1,33 @@ +//To find velocity and acceleration
+clc
+//Given:
+NBA=120 //rpm
+AB=150/1000,OC=700/1000,CD=200/1000 //m
+//Solution:
+//Refer Fig. 8.29
+//Calculating the angular speed of the crank AB
+omegaAB=2*%pi*NBA/AB //rad/s
+//Calculating the velocity of B with respect to A
+vBA=omegaBA*AB //m/s
+//By measurement from the velocity diagram, Fig. 8.29(b),
+vD=2.15,vBBdash=1.05,vDC=0.45,vBdashO=1.55,vCO=2.15 //m/s
+BdashO=0.52 //m
+//Calculating the angular velocity of the link OC or OB'
+omegaCO=vCO/OC //rad/s
+omegaBdashO=omegaCO //rad/s
+//Calculating the radial component of the acceleration of B with respect to A
+arBA=omegaAB^2/AB //m/s^2
+//Calculating the coriolis component of the acceleration of slider B with respect to the coincident point B'
+acBBdash=2*omegaCO*vBBdash //m/s^2
+//Calculating the radial component of the acceleration of D with respect to C
+arDC=vDC^2/CD //m/s^2
+//Calculating the radial component of the acceleration of B' with respect to O
+arBdashO=vBdashO^2/BdashO //m/s^2
+//By measurement fro the acceleration diagram, Fig. 8.29(c),
+aD=8.4,atBdashO=6.4 //m/s^2
+//Calculating the angular acceleration of the slotted lever
+alpha=atBdashO/BdashO //The angular acceleration of the slotted lever, rad/s^2
+//Results:
+printf("\n\n Velocity of the ram D, vD = %.2f m/s.\n",vD)
+printf(" Acceleration of the ram D, aD = %.1f m/s^2.\n",aD)
+printf(" Angular acceleration of the slotted lever = %.1f rad/s^2, anticlockwise.\n\n",alpha)
\ No newline at end of file diff --git a/213/CH8/EX8.14/8_14.sce b/213/CH8/EX8.14/8_14.sce new file mode 100755 index 000000000..5f4af9e79 --- /dev/null +++ b/213/CH8/EX8.14/8_14.sce @@ -0,0 +1,30 @@ +//To find the acceleration
+clc
+//Given:
+NBA=200 //rpm
+AB=75/1000,PQ=375/1000,QR=500/1000 //m
+//Solution:
+//Refer Fig. 8.31
+//Calculating the angular velocity of the crank AB
+omegaBA=2*%pi*NBA/60 //rad/s
+//Calculating the velocity of B with respect to A
+vBA=omegaBA*AB //m/s
+//By measurement from the velocity diagram, Fig. 8.31(b),
+vR=1.6,vBdashB=1.06,vBdashP=1.13,vRQ=0.4,vQP=1.7 //m/s
+PBdash=248/1000 //m
+//Calculating the angular velocity of the link PQ
+omegaPQ=vQP/PQ //rad/s
+//Calculating the radial component of the acceleration of B with respect to A
+arBA=omegaBA^2*AB //m/s^2
+//Calculating the coriolis component of the acceleration of B with respect to coincident point B'
+acBBdash=2*omegaPQ*vBdashB //m/s^2
+//Calculating the radial component of the acceleration of R with respect to Q
+arRQ=vRQ^2/QR //m/s^2
+//Calculating the radial component of the acceleration of B' with respect to P
+arBdashP=vBdashP^2/PBdash //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.31(d),
+aR=22,aBBdash=18 //m/s^2
+//Results:
+printf("\n\n Velocity of the tool-box R, vR = %.1f m/s.\n",vR)
+printf(" Acceleration of the tool-box R, aR = %d m/s^2.\n",aR)
+printf(" The acceleration of sliding of the block B along the slotted lever PQ, aBBdash = %d m/s^2.\n\n",aBBdash)
\ No newline at end of file diff --git a/213/CH8/EX8.15/8_15.sce b/213/CH8/EX8.15/8_15.sce new file mode 100755 index 000000000..2575f1862 --- /dev/null +++ b/213/CH8/EX8.15/8_15.sce @@ -0,0 +1,33 @@ +//To find linear and angular acceleration
+clc
+//Given:
+NAO=30 //rpm
+OA=150/1000,OC=100/1000,CD=125/1000,DR=500/1000 //m
+//Solution:
+//Refer Fig. 8.33
+//Calculating the angular speed of the crank OA
+omegaAO=2*%pi*NAO/60 //rad/s
+//Calculating the velocity of A with respect to O
+vAO=omegaAO*OA //m/s
+vA=vAO
+//By measurement from the velocity diagram, Fig. 8.33(b),
+vBC=0.46,vAB=0.15,vRD=0.12 //m/s
+CB=240/1000 //m
+//Calculating the angular velocity of the link BC
+omegaBC=vBC/CB //rad/s
+//Calculating the radial component of the acceleration of A with respect to O
+arAO=vAO^2/OA //m/s^2
+//Calculating the coriolis component of the acceleration of A with respect to coincident point B
+acAB=2*omegaBC*vAB //m/s^2
+//Calculating the radial component of the acceleration of B with respect to C
+arBC=vBC^2/CB //m/s^2
+//Calculating the radial component of the acceleration of R with respect to D
+arRD=vRD^2/DR //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.33(c),
+aR=0.18,atBC=0.14 //m/s^2
+//Calculating the angular acceleration of the slotted lever CA
+alphaCA=atBC/CB //rad/s^2
+alphaBC=alphaCA
+//Results:
+printf("\n\n Acceleration of the sliding block R, aR = %.2f m/s^2.\n",aR)
+printf(" Angular acceleration of the slotted lever CA, alphaCA = %.3f rad/s^2, anticlockwise.\n\n",alphaCA)
\ No newline at end of file diff --git a/213/CH8/EX8.16/8_16.sce b/213/CH8/EX8.16/8_16.sce new file mode 100755 index 000000000..1695928de --- /dev/null +++ b/213/CH8/EX8.16/8_16.sce @@ -0,0 +1,29 @@ +//To find linear and angular acceleration
+clc
+//Given:
+AB=125/1000 //m
+NCO=300 //rpm
+//Solution:
+//Refer Fig. 8.35
+//By measurement from the space diagram, Fig. 8.35(a),
+OC=85/1000 //m
+//Calculating the angular velocity of the link CO
+omegaCO=2*%pi*NCO/60 //rad/s
+//Calculating the velocity of C with respect to O
+vCO=omegaCO*OC //m/s
+vC=vCO
+//By measurement from the velocity diagram, Fig. 8.35(b),
+vBC=0.85,vBA=2.85,vB=vBA //m/s
+//Calculating the radial component of of the acceleration of C with respect to O
+arCO=vCO^2/OC //m/s^2
+//Calculating the coriolis component of of acceleration of the piston B with respect to the cylinder or the coincident point C
+acBC=2*omegaCO*vBC //m/s^2
+//Calculating the radial component of of the acceleration of B with respect to A
+arBA=vBA^2/AB //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.35(d),
+aBC=73.2,atBA=37.6 //m/s^2
+//Calculating the angular acceleration of the connecting rod AB
+alphaAB=atBA/AB //rad/s^2
+//Results:
+printf("\n\n Acceleration of the piston inside the cylinder, aBC = %.1f m/s^2.\n",aBC)
+printf(" Angular acceleration of the connecting rod AB, alphaAB = %d rad/s^2, clockwise.\n\n",alphaAB)
\ No newline at end of file diff --git a/213/CH8/EX8.17/8_17.sce b/213/CH8/EX8.17/8_17.sce new file mode 100755 index 000000000..040d2dda1 --- /dev/null +++ b/213/CH8/EX8.17/8_17.sce @@ -0,0 +1,38 @@ +//To find velocities and acceleration
+clc
+//Given:
+NAO=100 //rpm
+OA=50/1000,AB=350/1000,DE=250/1000,EF=DE,CB=125/1000 //m
+//Solution:
+//Refer Fig. 8.37
+//Calculating the angular velocity of the crank AO
+omegaAO=2*%pi*NAO/60 //rad/s
+//Calculating the velocity of A with respect to O
+vAO=omegaAO*OA //m/s
+vA=vAO
+//By measurement from the velocity diagram, Fig. 8.37(b),
+vBA=0.4,vBC=0.485,vB=vBC,vSD=0.265,vQS=0.4,vED=0.73,vFE=0.6,vF=0.27 //m/s
+DS=85/1000 //m
+//Calculating the angular velocity of the link DE
+omegaDE=vED/DE //rad/s
+//Calculating the velocity of sliding of the link DE in the swivel block
+vS=vQS //m/s
+//Calculating the radial component of the acceleration of A with respect to O
+arAO=vAO^2/OA //m/s^2
+//Calculating the radial component of the acceleration of B with respect to A
+arBA=vBA^2/AB //m/s^2
+//Calculating the radial component of the acceleration of B with respect to C
+arBC=vBC^2/CB //m/s^2
+//Calculating the radial component of the acceleration of S with respect to D
+arSD=vSD^2/DS //m/s^2
+//Calculating the coriolis component of the acceleration of Q with respect to S
+acQS=2*omegaDE*vQS //m/s^2
+//Calculating the radial component of the acceleration of F with respect to E
+arFE=vFE^2/EF //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.37(d),
+arQS=1.55 //m/s^2
+//Results:
+printf("\n\n Velocity of the slider block F, vF = %.2f m/s.\n",vF)
+printf(" Angular velocity of the link DE, omegaDE = %.2f rad/s, anticlockwise.\n",omegaDE)
+printf(" Velocity of sliding of the link DE in the swivel block, vS = %.1f m/s.\n",vS)
+printf(" Acceleration of sliding of the link DE in the trunnion, arQS = %.2f m/s^2.\n\n",arQS)
\ No newline at end of file diff --git a/213/CH8/EX8.2/8_2.sce b/213/CH8/EX8.2/8_2.sce new file mode 100755 index 000000000..deddbe2fb --- /dev/null +++ b/213/CH8/EX8.2/8_2.sce @@ -0,0 +1,29 @@ +//To find linear and angular velocity and acceleration
+clc
+//Given:
+omegaBC=75 //rad/s
+alphaBC=1200 //rad/s^2
+CB=100/1000,BA=300/1000 //m/
+//Solution:
+//Refer Fig. 8.5
+//Calculating the linear velocity of B with respect to C
+vBC=omegaBC*CB //m/s
+//Calculating the tangential component of the acceleration of B with respect to C
+alphatBC=alphaBC*CB //m/s^2
+//By measurement from the velocity diagram, Fig. 8.6(b),
+vG=6.8,vAB=4 //m/s
+//Calculating the angular velocity of AB
+omegaAB=vAB/BA //rad/s
+//Calculating the radial component of the acceleration of B with respect to C
+arBC=vBC^2/CB //m/s^2
+//Calculating the radial component of the acceleration of A with respect to B
+arAB=vAB^2/BA //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.6(c),
+arBC=120,arAB=53.3,aG=414,atAB=546 //m/s^2
+//Calculating the angular acceleration of AB
+alphaAB=atAB/BA //rad/s^2
+//Results:
+printf("\n\n The velocity of G, vG = %.1f m/s.\n",vG)
+printf(" The angular velocity of AB, omegaAB = %.1f rad/s, clockwise.\n",omegaAB)
+printf(" The acceleration of G, aG = %d m/s^2.\n",aG)
+printf(" The angular accaleration of AB, alphaAB = %d rad/s^2.\n\n",alphaAB)
\ No newline at end of file diff --git a/213/CH8/EX8.3/8_3.sce b/213/CH8/EX8.3/8_3.sce new file mode 100755 index 000000000..cd4d6d6ab --- /dev/null +++ b/213/CH8/EX8.3/8_3.sce @@ -0,0 +1,25 @@ +//To find linear and angular acceleration
+clc
+//Given:
+vC=1,vCD=vC //m/s
+aC=2.5 //m/s^2
+AB=3,BC=1.5 //m
+//Solution:
+//Refer Fig. 8.8
+//By measurement from the velocity diagram, Fig. 8.8(b),
+vBA=0.72,vBC=0.72 //m/s
+//Calculating the radial component of acceleration of B with respect to C
+arBC=vBC^2/BC //m/s^2
+//Calculating the radial component of acceleration of B with respect to A
+arBA=vBA^2/AB //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.8(c),
+aCD=2.5,aC=aCD,arBC=0.346,arBA=0.173, atBA=1.41,atBC=1.94,vectorbb=1.13,vectorab=0.9 //m/s^2
+//Calculating the angular accaleration of AB
+alphaAB=atBA/AB //rad/s^2
+//Calculating the angular acceleration of BC
+alphaBC=atBC/BC //rad/s^2
+//Results:
+printf("\n\n The magnitude of vertical component of the acceleration of the point B is %.2f m/s^2.\n",vectorbb)
+printf(" The magnitude of horizontal component of the acceleration of the point B is %.1f m/s^2.\n",vectorab)
+printf(" The angular acceleration of the link AB, alphaAB = %.2f rad/s^2.\n",alphaAB)
+printf(" The angular acceleration of the link BC, alphaBC = %.1f rad/s^2.\n\n",alphaBC)
\ No newline at end of file diff --git a/213/CH8/EX8.4/8_4.sce b/213/CH8/EX8.4/8_4.sce new file mode 100755 index 000000000..595f618fd --- /dev/null +++ b/213/CH8/EX8.4/8_4.sce @@ -0,0 +1,35 @@ +//To find the angular velocity and acceleration
+clc
+//Given:
+omegaQP=10 //rad/s
+PQ=62.5/1000,QR=175/1000,RS=112.5/1000,PS=200/1000 //m
+//Solution:
+//Refer Fig. 8.9
+//Calculating the velocity of Q with respect to P
+vQP=omegaQP*PQ //m/s
+vQ=vQP
+//By measurement from the velocity diagram, Fig. 8.9(b),
+vRQ=0.333,vRS=0.426,vR=vRS //m/s
+//Calculating the angular velocity of link QR
+omegaQR=vRQ/QR //rad/s
+//Calculating the angular velocity of link RS
+omegaRS=vRS/RS //rad/s
+//Calculating the radial component of the acceleration of Q with respect to P
+arQP=vQP^2/PQ //m/s^2
+aQP=arQP,aQ=aQP
+//Calculating the radial component of the acceleration of R with respect to Q
+arRQ=vRQ^2/QR //m/s^2
+//Calculating the radial component of the acceleration of R with respect to S
+arRS=vRS^2/RS //m/s^2
+aRS=arRS,aR=aRS
+//By measurement from the acceleration diagram, Fig. 8.9(c),
+atRQ=4.1,atRS=5.3 //m/s^2
+//Calculating the angular acceleration of link QR
+alphaQR=atRQ/QR //rad/s^2
+//Calculating the angular acceleration of link RS
+alphaRS=atRS/RS //rad/s^2
+//Results:
+printf("\n\n The angular velocity of link QR, omegaQR = %.1f rad/s, anticlockwise.\n",omegaQR)
+printf(" The angular velocity of link RS, omegaRS = %.2f rad/s, clockwise.\n",omegaRS)
+printf(" The angular acceleration of link QR, alphaQR = %.2f rad/s^2, anticlockwise.\n",alphaQR)
+printf(" The angular acceleration of link RS, alphaRS = %.1f rad/s^2, anticlockwise.\n\n",alphaRS)
\ No newline at end of file diff --git a/213/CH8/EX8.5/8_5.sce b/213/CH8/EX8.5/8_5.sce new file mode 100755 index 000000000..03082824b --- /dev/null +++ b/213/CH8/EX8.5/8_5.sce @@ -0,0 +1,38 @@ +//To find angular velocities and accelerations
+clc
+//Given:
+omegaAP1=10 //rad/s
+alphaAP1=30 //rad/s^2
+P1A=300/1000,P2B=360/1000,AB=P2B //m
+//Solution:
+//Refer Fig. 8.10
+//Calculating the velocity of A with respect to P1
+vAP1=omegaAP1/P1A //m/s
+vA=vAP1
+//By measurement from the velocity diagram, Fig. 8.11(b),
+vBP2=2.2,vBA=2.05 //m/s
+//Calculating the angular velocity of P2B
+omegaP2B=vBP2/P2B //rad/s
+//Calculating the angular velocity of AB
+omegaAB=vBA/AB //rad/s
+//Calculating the tangential component of the acceleration of A with respect to P1
+atAP1=alphaAP1*P1A //m/s^2
+//Calculating the radial component of the acceleration of A with respect to P1
+arAP1=vAP1^2/P1A //m/s^2
+//Calculating the radial component of the acceleration of B with respect to A
+arBA=vBA^2/AB //m/s^2
+//Calculating the radial component of B with respect to P2
+arBP2=vBP2^2/P2B //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.11(c),
+aBP2=29.6,aB=aBP2,atBA=13.6,atBP2=26.6 //m/s^2
+//Calculating the angular acceleration of P2B
+alphaP2B=atBP2/P2B //rad/s^2
+//Calculating the angular acceleration of AB
+alphaAB=atBA/AB //rad/s^2
+//Results:
+printf("\n\n The velocity of P2B, vBP2 = %.1f m/s.\n",vBP2)
+printf(" The angular velocity of P2B, omegaP2B = %.1f rad/s, clockwise.\n",omegaP2B)
+printf(" The angular velocity of AB, omegaAB = %.1f rad/s, anticlockwise.\n",omegaAB)
+printf(" The acceleration of the joint B, aB = %.1f m/s^2.\n",aB)
+printf(" The angular acceleration of P2B, alphaP2B = %.1f rad/s^2, anticlockwise.\n",alphaP2B)
+printf(" The angular acceleration of AB, alphaAB = %.1f rad/s^2, anticlockwise.\n\n",alphaAB)
\ No newline at end of file diff --git a/213/CH8/EX8.6/8_6.sce b/213/CH8/EX8.6/8_6.sce new file mode 100755 index 000000000..500db5984 --- /dev/null +++ b/213/CH8/EX8.6/8_6.sce @@ -0,0 +1,32 @@ +//To find velocities and accelerations
+clc
+//Given:
+NAO=20 //rpm
+OA=300/1000,AB=1200/1000,BC=450/1000,CD=BC //m
+//Solution:
+//Refer Fig. 8.13
+//Calculating the angular velocity of crank AO
+omegaAO=2*%pi*NAO/60 //rad/s
+//Calculating the linear velocity of A with respect to O
+vAO=omegaAO*OA //m/s
+vA=vAO
+//By measurement from the velocity diagram, Fig. 8.13(b),
+vB=0.4,vD=0.24,vDC=0.37,vBA=0.54 //m/s
+//Calculating the angular velocity of CD
+omegaCD=vDC/CD //rad/s
+//Calculating the radial component of the acceleration of A with respect to O
+arAO=vAO^2/OA //m/s^2
+//Calculating the radial component of the acceleration of B with respect to A
+arBA=vBA^2/AB //m/s^2
+//Calculating the radial component of the acceleration of D with respect to C
+arDC=vDC^2/CD //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.13(c),
+aD=0.16,atDC=1.28 //m/s^2
+//Calculating the angular acceleration of CD
+alphaCD=atDC/CD //rad/s^2
+//Results:
+printf("\n\n Velocity of sliding at B, vB = %.1f m/s.\n",vB)
+printf(" Velocity of sliding at D, vD = %.2f m/s.\n",vD)
+printf(" Angular velocity of CD, omegaCD = %.2f rad/s.\n",omegaCD)
+printf(" Linear acceleration of D, aD = %.2f m/s^2.\n",aD)
+printf(" Angular acceleration of CD, alphaCD = %.2f rad/s^2, clockwise.\n\n",alphaCD)
\ No newline at end of file diff --git a/213/CH8/EX8.7/8_7.sce b/213/CH8/EX8.7/8_7.sce new file mode 100755 index 000000000..a84ac0209 --- /dev/null +++ b/213/CH8/EX8.7/8_7.sce @@ -0,0 +1,29 @@ +//To find linear and angular acceleration
+clc
+//Given:
+NAO=180 //rpm
+OA=150/1000,AB=450/1000,PB=240/1000,CD=660/1000 //m
+//solution:
+//Refer Fig. 8.15
+//Calculating the angular speed of crank AO
+omegaAO=2*%pi*NAO/60 //rad/s
+//Calculating the velocity of A with respect to O
+vAO=omegaAO*OA //m/s
+vA=vAO
+//By measurement from the velocity diagram, Fig. 8.15(b),
+vD=2.36,vDC=1.2,vBA=1.8,vBP=1.5 //m/s
+//Calculating the radial component of the acceleration of B with respect to A
+arAO=vBA^2/AB //m/s^2
+//Calculating the radial component of the acceleration of B with respect to A
+arBA=vBA^2/AB //m/s^2
+//Calculating the radial component of the acceleration of B with respect to P
+arBP=vBP^2/PB //m/s^2
+//Calculating the radial component of D with respect to C
+arDC=vDC^2/CD //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.15(c),
+aD=69.6,atDC=17.4 //m/s^2
+//Calculating the angular acceleration of CD
+alphaCD=atDC/CD //rad/s^2
+//Results:
+printf("\n\n Acceleration of slider D, aD = %.1f m/s^2.\n",aD)
+printf(" Angular acceleration of link CD, alphaCD = %.1f rad/s^2.\n\n",alphaCD)
\ No newline at end of file diff --git a/213/CH8/EX8.8/8_8.sce b/213/CH8/EX8.8/8_8.sce new file mode 100755 index 000000000..26bdc319f --- /dev/null +++ b/213/CH8/EX8.8/8_8.sce @@ -0,0 +1,36 @@ +//To find linear and angular velocities and accelerations
+clc
+//Given:
+NAO=180 //rpm
+OA=180/1000,CB=240/1000,AB=360/1000,BD=540/1000 //m
+alphaAO=50 //rad/s^2
+//Solution:
+//Refer Fig. 8.17
+//Calculating the angular speed of crank AO
+omegaAO=2*%pi*NAO/60 //rad/s
+//Calculating the velcoity of A with respect to O
+vAO=omegaAO*OA //m/s
+vA=vAO
+//By measurement from the velocity diagram, Fig. 8.17(b),
+vBA=0.9,vBC=2.4,vDB=2.4,vD=2.05 //m/s
+//Calculating the angular velocity of BD
+omegaBD=vDB/BD //rad/s
+//Calculating the tangential component of the acceleration of A with respect to O
+atAO=alphaAO*OA //m/s^2
+//Calculating the radial component of the acceleration of A with respect to O
+arAO=vAO^2/OA //m/s^2
+//Calculating the radial component of the acceleration of B with respect to A
+arBA=vBA^2/AB //m/s^2
+//Calculating the radial component of the acceleration of B with respect to C
+arBC=vBC^2/AB //m/s^2
+//Calculating the radial component of the acceleration of D with respect to B
+arDB=vDB^2/BD //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.17(c),
+aD=13.3,atDB=38.5 //m/s^2
+//Calculating the angular acceleration of BD
+alphaBD=atDB/BD //rad/s^2
+//Results:
+printf("\n\n Velocity of slider D, vD = %.2f m/s.\n",vD)
+printf(" Angular velocity of BD, omegaBD = %.1f rad/s.\n",omegaBD)
+printf(" Acceleration of slider D, aD = %.1f m/s^2.\n",aD)
+printf(" Angular acceleration of BD, alphaBD = %.1f rad/s^2, clockwise.\n\n",alphaBD)
\ No newline at end of file diff --git a/213/CH8/EX8.9/8_9.sce b/213/CH8/EX8.9/8_9.sce new file mode 100755 index 000000000..1810d89ed --- /dev/null +++ b/213/CH8/EX8.9/8_9.sce @@ -0,0 +1,36 @@ +//To find velocity and accelerations
+clc
+//Given:
+omegaAO1=100 //rad/s
+O1A=100/1000,AC=700/1000,BC=200/1000,BD=150/1000,O2D=200/1000,O2E=400/1000,O3C=200/1000 //m
+//Solution:
+//Refer Fig. 8.19
+//Calculating the linear velocity of A with respect to O1
+vAO1=omegaAO1/O1A //m/s
+vA=vAO1
+//By measurement from the velocity diagram, Fig. 8.19(b),
+vCA=7,vCO3=10,vC=vCO3,vDB=10.2,vDO2=2.8,vD=vDO2,vE=5.8,vEO2=vE //m/s
+//Calculating the radial component of the acceleration of A with respect to O1
+arAO1=vAO1^2/O1A //m/s^2
+aAO1=arAO1,aA=aAO1
+//Calculating the radial component of the acceleration of C with respect to A
+arCA=vCA^2/AC //m/s^2
+//Calculating the radial component of the acceleration of C with respect to O3
+arCO3=vCO3^2/O3C //m/s^2
+//Calculating the radial component of the acceleration of D with respect to B
+arDB=vDB^2/BD //m/s^2
+//Calculating the radial component of the acceleration of D with respect to O2
+arDO2=vDO2^2/O2D //m/s^2
+//Calculating the radial component of the acceleration of E with respect to O2
+arEO2=vEO2^2/O2E //m/s^2
+//By measurement from the acceleration diagram, Fig. 8.19(c),
+aE=1200,atDO2=610 //m/s^2
+aEO2=aE
+aB=440 //Acceleration of point B, m/s^2
+//Calculating the angular acceleration of the bell crank lever
+alpha=atDO2/O2D //The angular acceleration of the bell crank lever, rad/s^2
+//Results:
+printf("\n\n Velocity of the point E on the bell crank lever, vE = %.1f m/s.\n",vE)
+printf(" Acceleration of point B = %d m/s^2.\n",aB)
+printf(" Acceleration of point E, aE = %d m/s^2.\n",aE)
+printf(" Angular acceleration of the bell crank lever = %d rad/s^2, anticlockwise.\n\n",alpha)
\ No newline at end of file diff --git a/213/CH9/EX9.1/9_1.sce b/213/CH9/EX9.1/9_1.sce new file mode 100755 index 000000000..6d4a6b32e --- /dev/null +++ b/213/CH9/EX9.1/9_1.sce @@ -0,0 +1,9 @@ +//To find inclination of track arm
+clc
+//Given:
+c=1.2,b=2.7 //m
+//Solution:
+//Calculating the inclination of the track arm to the longitudinal axis
+alpha=atan(c/(2*b))*180/%pi //degrees
+//Results:
+printf("\n\n Inclination of the track arm to the longitudinal axis, alpha = %.1f degrees.\n\n",alpha)
\ No newline at end of file diff --git a/213/CH9/EX9.3/9_3.sce b/213/CH9/EX9.3/9_3.sce new file mode 100755 index 000000000..d28eefb00 --- /dev/null +++ b/213/CH9/EX9.3/9_3.sce @@ -0,0 +1,13 @@ +//To find the angle turned
+clc
+//Given:
+alpha=18*%pi/180 //radians
+//Solution:
+//Maximum velocity is possible when
+theta1=0,theta2=180 //degrees
+//Calculating the angle turned by the driving shaft when the velocity ratio is unity
+theta3=acos(sqrt((1-cos(alpha))/(sin(alpha)^2)))*180/%pi //degrees
+theta4=180-theta3 //degrees
+//Results:
+printf("\n\n Angle turned by the driving shaft when the velocity ratio is maximum, theta = %d degrees or %d degrees.\n",theta1,theta2)
+printf(" Angle turned by the driving shaft when the velocity ratio is unity, theta = %.1f degrees or %.1f degrees.\n\n",theta3,theta4)
\ No newline at end of file diff --git a/213/CH9/EX9.4/9_4.sce b/213/CH9/EX9.4/9_4.sce new file mode 100755 index 000000000..36f82a206 --- /dev/null +++ b/213/CH9/EX9.4/9_4.sce @@ -0,0 +1,13 @@ +//To find the greatest permissible angle
+clc
+//Given:
+N=500 //rpm
+//Solution:
+//Calculating the angular velocity of the driving shaft
+omega=2*%pi*N/60 //rad/s
+//Calculating the total fluctuation of speed of the driven shaft
+q=12/100*omega //rad/s
+//Calculating the greatest permissible angle between the centre lines of the shafts
+alpha=acos((-(q/omega)+sqrt(0.12^2+4))/2)*180/%pi //degrees
+//Results:
+printf("\n\n Greatest permissible angle between the centre lines of the shafts, alpha = %.2f degrees.\n\n",alpha)
\ No newline at end of file diff --git a/213/CH9/EX9.5/9_5.sce b/213/CH9/EX9.5/9_5.sce new file mode 100755 index 000000000..a9b9a5f07 --- /dev/null +++ b/213/CH9/EX9.5/9_5.sce @@ -0,0 +1,15 @@ +//To find speeds and permissible angle
+clc
+//Given:
+N=1200,q=100 //rpm
+//Solution:
+//Calculating the greatest permissible angle between the centre lines of the shafts
+alpha=acos((-(100/1200)+sqrt(0.083^2+4))/2)*180/%pi //degrees
+//Calculating the maximum speed of the driven shaft
+N1max=N/cosd(alpha) //rpm
+//Calculating the minimum speed of the driven shaft
+N1min=N*cosd(alpha) //rpm
+//Results:
+printf("\n\n Greatest permissible angle between the centre lines of the shafts, alpha = %.1f degrees.\n",alpha)
+printf(" Maximum speed of the driven shaft, N1(max) = %d rpm.\n",N1max)
+printf(" Minimum speed of the driven shaft, N1(min) = %d rpm.\n\n",N1min)
\ No newline at end of file diff --git a/213/CH9/EX9.7/9_7.sce b/213/CH9/EX9.7/9_7.sce new file mode 100755 index 000000000..f8f4ebb92 --- /dev/null +++ b/213/CH9/EX9.7/9_7.sce @@ -0,0 +1,19 @@ +//To find speeds of shafts
+clc
+//Given:
+alpha=20 //degrees
+NA=500 //rpm
+//Solution:
+//Calculating the maximum speed of the intermediate shaft
+NBmax=NA/cosd(alpha) //rpm
+//Calculating the minimum speed of the intermediate shaft
+NBmin=NA*cosd(alpha) //rpm
+//Calculating the maximum speed of the driven shaft
+NCmax=NBmax/cosd(alpha) //rpm
+//Calculating the minimum speed of the driven shaft
+NCmin=NBmin*cosd(alpha) //rpm
+//Results:
+printf("\n\n Maximum speed of the intermediate shaft, NB(max) = %.1f rad/s.\n",NBmax)
+printf(" Minimum speed of the intermediate shaft, NB(min) = %.2f rad/s.\n",NBmin)
+printf(" Maximum speed of the driven shaft, NC(max) = %.2f rad/s.\n",NCmax)
+printf(" Minimum speed of the driven shaft, NC(min) = %.1f rad/s.\n",NCmin)
\ No newline at end of file |