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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/CH10 | |
| 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/CH10')
36 files changed, 907 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)
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