Chapter17-Shaft Design

Ex1-pg379

In [1]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-17.1 Page No.379\n');

hp=5.;
n=1750.;
T=63000.*hp/n;

##Torsional stress in the shaft
D=0.75;
Z1=math.pi*D**3/16.;

Ss=T/Z1;

print'%s %.2f %s '%('\n Torsional stress in the shaft = ',Ss,' lb/in^2.');

##Load at the gear pitch circle
Nt=40.;
Pd=10.;
Dp=Nt/Pd;

Ft=2.*T/Dp;

print'%s %.2f %s '%('\n Load at gear pitch circle = ',Ft,' lb.');

##Resultant force on the shaft
theta=20.*math.pi/180.;
Fr=Ft/math.cos(theta);

print'%s %.2f %s '%('\n Resultant force = ',Fr,' lb.');

##Maximum moment
L=15.;
Mm=Fr*L/4.;

print'%s %.2f %s '%('\n Maximum moment = ',Mm,' in-lb.');

##Stress
D2=0.75;
Z2=math.pi*D2**3/32.;
Z2=round(Z2*1000.)*10**-3;

S=Mm/Z2;

print'%s %.2f %s '%('\n Stress = ',S,' lb/in^2.');

##Note-There is an error in the answer given in textbook

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-17.1 Page No.379


 Torsional stress in the shaft =  2173.00  lb/in^2. 

 Load at gear pitch circle =  90.00  lb. 

 Resultant force =  95.78  lb. 

 Maximum moment =  359.16  in-lb. 

 Stress =  8760.00  lb/in^2.

Ex2-pg383

In [2]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-17.2 Page No.383\n');

##Combined stress using the maximum shear stress theorem

Ss=2170.;
S=8780.;
Sr=math.sqrt(Ss**2+(S/2.)**2);

print'%s %.2f %s '%('\n Combined stress = ',Sr,' lb/in^2.');

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-17.2 Page No.383


 Combined stress =  4897.04  lb/in^2.

Ex3-pg383

In [3]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-17.3 Page No.383\n');

##Combined stress using the maximum normal stress theory
Ss=2170.;
S=8780.;
Sr=S/2.+math.sqrt(Ss**2+(S/2.)**2);

print'%s %.2f %s '%('\n Combined stress = ',Sr,' lb/in^2.');

##Note-There is an error in the answer given in textbook

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-17.3 Page No.383


 Combined stress =  9287.04  lb/in^2.

Ex4-pg385

In [4]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-17.4 Page No.385\n');

##Modifying factors for Sn
Su=88000.;
Csize=0.85;
Csurface=0.88;
Ctype=1.;

Sn=Csize*Csurface*Ctype*(0.5*Su);
Kt=2.3;
S=9300.;

N=Sn/(Kt*S);

if N>2:
    print('\n It would be an acceptable design.');
else:
    print('\n N<2,So this is not a suitable design for long term use.');

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-17.4 Page No.385


 N<2,So this is not a suitable design for long term use.

Ex5-pg388

In [5]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-17.5 Page No.388\n');
import numpy
##Deflection
D=0.75;
E=30.*10**6;
L=15.;
F=96.;
I=math.pi*D**4/64.;

delta=F*L**4/(48.*E*I);
delta=numpy.floor(100.*delta)*10**-2;
Nc=188./math.sqrt(delta);

print'%s %.2f %s '%('\n Critical speed = ',Nc,' rpm.');

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-17.5 Page No.388


 Critical speed =  410.25  rpm.