diff options
Diffstat (limited to '3532/CH8')
| -rw-r--r-- | 3532/CH8/EX8.1/Ex8_1.sce | 22 | ||||
| -rw-r--r-- | 3532/CH8/EX8.2.1/Ex8_1.sce | 22 | ||||
| -rw-r--r-- | 3532/CH8/EX8.2/Ex8_2.sce | 30 | ||||
| -rw-r--r-- | 3532/CH8/EX8.3.1/Ex8_2.sce | 30 | ||||
| -rw-r--r-- | 3532/CH8/EX8.3/Ex8_3.sce | 20 | ||||
| -rw-r--r-- | 3532/CH8/EX8.4.1/Ex8_3.sce | 20 | ||||
| -rw-r--r-- | 3532/CH8/EX8.4/Ex8_4.sce | 22 | ||||
| -rw-r--r-- | 3532/CH8/EX8.6.1/Ex8_4.sce | 22 |
8 files changed, 188 insertions, 0 deletions
diff --git a/3532/CH8/EX8.1/Ex8_1.sce b/3532/CH8/EX8.1/Ex8_1.sce new file mode 100644 index 000000000..f91c1baa5 --- /dev/null +++ b/3532/CH8/EX8.1/Ex8_1.sce @@ -0,0 +1,22 @@ +clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 8.2.1\n')
+//given data
+E=1.96*10^11//youngs modulus in N/m^2
+m=5//mass of rotor in kg
+d=0.01//dia of shaft in m
+I=(%pi/64)*d^4///moment of area in m^4
+l=0.4//bearing span in m
+e=0.02//distance of CG away from geometric centre of rotor in mm
+N=3000//speed of shaft in RPM
+//calculations
+k=48*E*I/l^3//stiffness of shaft in N/m
+Wn=sqrt(k/m)
+W=2*%pi*N/60
+bet=(W/Wn)
+r=(bet^2*e/(1-bet^2))//from Eqn 8.2.2 in Sec 8.2
+rabs=abs(r)//absolute value of displacement
+Rd=k*rabs/1000//total dynamic load in bearings in N(divide by 1000 since r is in mm)
+F=Rd/2//dynamic load on each bearings in N
+//output
+mprintf(' The amplitude of steady state vibration of shaft is %f mm\nNOTE:negetive sign shows that displacement is out of phase with centrifugal force\nThe dynamic force transmtted to the bearings is %4.4f N\n The dynamic load on each bearing is %4.4f N',r,Rd,F)
diff --git a/3532/CH8/EX8.2.1/Ex8_1.sce b/3532/CH8/EX8.2.1/Ex8_1.sce new file mode 100644 index 000000000..f91c1baa5 --- /dev/null +++ b/3532/CH8/EX8.2.1/Ex8_1.sce @@ -0,0 +1,22 @@ +clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 8.2.1\n')
+//given data
+E=1.96*10^11//youngs modulus in N/m^2
+m=5//mass of rotor in kg
+d=0.01//dia of shaft in m
+I=(%pi/64)*d^4///moment of area in m^4
+l=0.4//bearing span in m
+e=0.02//distance of CG away from geometric centre of rotor in mm
+N=3000//speed of shaft in RPM
+//calculations
+k=48*E*I/l^3//stiffness of shaft in N/m
+Wn=sqrt(k/m)
+W=2*%pi*N/60
+bet=(W/Wn)
+r=(bet^2*e/(1-bet^2))//from Eqn 8.2.2 in Sec 8.2
+rabs=abs(r)//absolute value of displacement
+Rd=k*rabs/1000//total dynamic load in bearings in N(divide by 1000 since r is in mm)
+F=Rd/2//dynamic load on each bearings in N
+//output
+mprintf(' The amplitude of steady state vibration of shaft is %f mm\nNOTE:negetive sign shows that displacement is out of phase with centrifugal force\nThe dynamic force transmtted to the bearings is %4.4f N\n The dynamic load on each bearing is %4.4f N',r,Rd,F)
diff --git a/3532/CH8/EX8.2/Ex8_2.sce b/3532/CH8/EX8.2/Ex8_2.sce new file mode 100644 index 000000000..61792beb2 --- /dev/null +++ b/3532/CH8/EX8.2/Ex8_2.sce @@ -0,0 +1,30 @@ +clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 8.3.1\n')
+//given data
+E=1.96*10^11//youngs modulus in N/m^2
+m=4//mass of rotor in kg
+g=9.81//acc due to gravity in m/sec^2
+d=0.009//dia of shaft in m
+I=(%pi/64)*d^4///moment of area in m^4
+l=0.48//bearing span in m
+e=0.003//distance of CG away from geometric centre of rotor in mm
+N=760//speed of shaft in RPM
+c=49//equivalent viscous damping in N-sec/m
+//calculations
+K=48*E*I/l^3//stiffness of shaft in N/m
+Wn=sqrt(K/m)
+W=2*%pi*N/60
+bet=(W/Wn)
+zeta=c/(2*sqrt(K*m))
+r=e*(bet^2/sqrt(((1-bet^2)^2+(2*zeta*bet)^2)))//from Eqn 8.3.4 ,Sec 8.3
+Fd=sqrt((K*r)^2+(c*W*r)^2)//dynamic load on bearing in N
+Fs=m*g//static load in N
+Fmax=Fd+Fs//maximum static load on the shaft under dynamic condition in N
+smax=(Fmax*l/4)*(d/2)/I//maximum stress under dynamic condition in N/m^2
+ss=(Fs*l/4)*(d/2)/I//maximum stress under dead load condition in N/m^2
+Fdamp=(c*W*r)//damping force in N
+Tdamp=Fdamp*r//damping torque in N-m
+P=2*%pi*N*Tdamp/60//power in Watts
+//output
+mprintf(' The mamximum stress in the shaft under dynamic condition is %.3f N/(m^2)\n The dead load stress is %.3f N/(m^2)\n The power required to drive the shaft at 760 RPM is %4.4f Watts',smax,ss,P)
diff --git a/3532/CH8/EX8.3.1/Ex8_2.sce b/3532/CH8/EX8.3.1/Ex8_2.sce new file mode 100644 index 000000000..61792beb2 --- /dev/null +++ b/3532/CH8/EX8.3.1/Ex8_2.sce @@ -0,0 +1,30 @@ +clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 8.3.1\n')
+//given data
+E=1.96*10^11//youngs modulus in N/m^2
+m=4//mass of rotor in kg
+g=9.81//acc due to gravity in m/sec^2
+d=0.009//dia of shaft in m
+I=(%pi/64)*d^4///moment of area in m^4
+l=0.48//bearing span in m
+e=0.003//distance of CG away from geometric centre of rotor in mm
+N=760//speed of shaft in RPM
+c=49//equivalent viscous damping in N-sec/m
+//calculations
+K=48*E*I/l^3//stiffness of shaft in N/m
+Wn=sqrt(K/m)
+W=2*%pi*N/60
+bet=(W/Wn)
+zeta=c/(2*sqrt(K*m))
+r=e*(bet^2/sqrt(((1-bet^2)^2+(2*zeta*bet)^2)))//from Eqn 8.3.4 ,Sec 8.3
+Fd=sqrt((K*r)^2+(c*W*r)^2)//dynamic load on bearing in N
+Fs=m*g//static load in N
+Fmax=Fd+Fs//maximum static load on the shaft under dynamic condition in N
+smax=(Fmax*l/4)*(d/2)/I//maximum stress under dynamic condition in N/m^2
+ss=(Fs*l/4)*(d/2)/I//maximum stress under dead load condition in N/m^2
+Fdamp=(c*W*r)//damping force in N
+Tdamp=Fdamp*r//damping torque in N-m
+P=2*%pi*N*Tdamp/60//power in Watts
+//output
+mprintf(' The mamximum stress in the shaft under dynamic condition is %.3f N/(m^2)\n The dead load stress is %.3f N/(m^2)\n The power required to drive the shaft at 760 RPM is %4.4f Watts',smax,ss,P)
diff --git a/3532/CH8/EX8.3/Ex8_3.sce b/3532/CH8/EX8.3/Ex8_3.sce new file mode 100644 index 000000000..bb812c820 --- /dev/null +++ b/3532/CH8/EX8.3/Ex8_3.sce @@ -0,0 +1,20 @@ +clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 8.4.1\n')
+//given data
+E=1.96*10^11//youngs modulus in N/m^2
+I=4*10^-7//moment of area in m^4
+M1=100;M2=50//mass of discs 1 and 2 in Kgs
+c=0.18//distance of disc 1 from support in m
+l=0.3//distance of disc 2 from support in m
+g=9.81//aceleration due to gravity in m/sec^2
+//calculations
+a=[(c^3/(3*E*I)),(c^2/(6*E*I)*(3*l-c));(c^2/(6*E*I)*(3*l-c)),(l^3/(3*E*I))]//from SOM
+p=M1*a(1,1)+M2*a(2,2)//from Eqn 8.4.6 ,Sec 8.4
+q=M1*M2*(a(1,1)*a(2,2)-(a(1,2)^2))//from Eqn 8.4.6 ,Sec 8.4
+Wn1=sqrt((p-sqrt(p^2-4*q))/(2*q))//from Eqn 8.4.6 ,Sec 8.4
+Wn2=sqrt((p+sqrt(p^2-4*q))/(2*q))//from Eqn 8.4.6 ,Sec 8.4
+Nc1=Wn1*60/(2*%pi)//critical speed in RPM
+Nc2=Wn2*60/(2*%pi)//critical speed in RPM
+//output
+mprintf(' The critical speeds for the system shown in fig 7.2.1 are %4.4f RPM and %4.4f RPM',Nc1,Nc2)
diff --git a/3532/CH8/EX8.4.1/Ex8_3.sce b/3532/CH8/EX8.4.1/Ex8_3.sce new file mode 100644 index 000000000..bb812c820 --- /dev/null +++ b/3532/CH8/EX8.4.1/Ex8_3.sce @@ -0,0 +1,20 @@ +clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 8.4.1\n')
+//given data
+E=1.96*10^11//youngs modulus in N/m^2
+I=4*10^-7//moment of area in m^4
+M1=100;M2=50//mass of discs 1 and 2 in Kgs
+c=0.18//distance of disc 1 from support in m
+l=0.3//distance of disc 2 from support in m
+g=9.81//aceleration due to gravity in m/sec^2
+//calculations
+a=[(c^3/(3*E*I)),(c^2/(6*E*I)*(3*l-c));(c^2/(6*E*I)*(3*l-c)),(l^3/(3*E*I))]//from SOM
+p=M1*a(1,1)+M2*a(2,2)//from Eqn 8.4.6 ,Sec 8.4
+q=M1*M2*(a(1,1)*a(2,2)-(a(1,2)^2))//from Eqn 8.4.6 ,Sec 8.4
+Wn1=sqrt((p-sqrt(p^2-4*q))/(2*q))//from Eqn 8.4.6 ,Sec 8.4
+Wn2=sqrt((p+sqrt(p^2-4*q))/(2*q))//from Eqn 8.4.6 ,Sec 8.4
+Nc1=Wn1*60/(2*%pi)//critical speed in RPM
+Nc2=Wn2*60/(2*%pi)//critical speed in RPM
+//output
+mprintf(' The critical speeds for the system shown in fig 7.2.1 are %4.4f RPM and %4.4f RPM',Nc1,Nc2)
diff --git a/3532/CH8/EX8.4/Ex8_4.sce b/3532/CH8/EX8.4/Ex8_4.sce new file mode 100644 index 000000000..4659fd16d --- /dev/null +++ b/3532/CH8/EX8.4/Ex8_4.sce @@ -0,0 +1,22 @@ +clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 8.6.1\n')
+//given data
+E=1.96*10^11//youngs modulus in N/m^2
+M=10//mass of rotor in kg
+g=9.81//acc due to gravity in m/sec^2
+ra=0.12//radius of gyration in m
+l=0.3//lenght of steel shaft in m
+b=0.06//thickness of rotor in m
+I=10*10^-8//moment of inertia of section in m^4
+//calculations
+r=sqrt((ra^2/2)+(b^2/12))
+h=3*(r^2)/l^2//from Eqn 8.6.4 ,Sec 8.6
+g1=sqrt((2/h)*((h+1)-sqrt((h+1)^2-h)))//natural frequency,from Eqn 8.6.4 ,Sec 8.6
+g2=sqrt((2/h)*((h+1)+sqrt((h+1)^2-h)))//natural frequency,from Eqn 8.6.4 ,Sec 8.6
+W1=g1*sqrt(3*E*I/(M*l^3))//from Eqn 8.6.4 ,Sec 8.6
+W2=g2*sqrt(3*E*I/(M*l^3))//from Eqn 8.6.4 ,Sec 8.6
+Nc1=W1*60/(2*%pi)//critical speed in RPM
+Nc2=W2*60/(2*%pi)//critical speed in RPM
+//output
+mprintf(' The operating speed of 10000 RPM is not near to either of \n the critical speeds i.e %4.4f RPM or %4.4f RPM.\n Therefore the operating speed is safe.',Nc1,Nc2)
diff --git a/3532/CH8/EX8.6.1/Ex8_4.sce b/3532/CH8/EX8.6.1/Ex8_4.sce new file mode 100644 index 000000000..4659fd16d --- /dev/null +++ b/3532/CH8/EX8.6.1/Ex8_4.sce @@ -0,0 +1,22 @@ +clc
+clear
+mprintf('Mechanical vibrations by G.K.Grover\n Example 8.6.1\n')
+//given data
+E=1.96*10^11//youngs modulus in N/m^2
+M=10//mass of rotor in kg
+g=9.81//acc due to gravity in m/sec^2
+ra=0.12//radius of gyration in m
+l=0.3//lenght of steel shaft in m
+b=0.06//thickness of rotor in m
+I=10*10^-8//moment of inertia of section in m^4
+//calculations
+r=sqrt((ra^2/2)+(b^2/12))
+h=3*(r^2)/l^2//from Eqn 8.6.4 ,Sec 8.6
+g1=sqrt((2/h)*((h+1)-sqrt((h+1)^2-h)))//natural frequency,from Eqn 8.6.4 ,Sec 8.6
+g2=sqrt((2/h)*((h+1)+sqrt((h+1)^2-h)))//natural frequency,from Eqn 8.6.4 ,Sec 8.6
+W1=g1*sqrt(3*E*I/(M*l^3))//from Eqn 8.6.4 ,Sec 8.6
+W2=g2*sqrt(3*E*I/(M*l^3))//from Eqn 8.6.4 ,Sec 8.6
+Nc1=W1*60/(2*%pi)//critical speed in RPM
+Nc2=W2*60/(2*%pi)//critical speed in RPM
+//output
+mprintf(' The operating speed of 10000 RPM is not near to either of \n the critical speeds i.e %4.4f RPM or %4.4f RPM.\n Therefore the operating speed is safe.',Nc1,Nc2)
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