Chapter12-Spur Gear Design and Selection

Ex1-pg245

In [1]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-12.1 Page No.254\n');

P=5.;
n=1725.;
T=63000.*P/n;

##Pitch circle diameter
Np=20.;
Pd=8.;
Dp=Np/Pd;

print'%s %.2f %s '%('\n Pitch circle diameter = ',Dp,' in.');

##Transmitted force
Ft=2.*T/Dp;

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

##Separating force
theta=20.*math.pi/180.;
Fn=Ft*math.tan(theta);

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

##Maximum force
Fr=Ft/math.cos(theta);

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

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-12.1 Page No.254


 Pitch circle diameter =  2.50  in. 

 Transmitted force =  146.09  lb. 

 Separating force =  53.17  lb. 

 Maximum force =  155.46  lb.

Ex2-pg256

In [2]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-12.2 Page No.256\n');

##Surface speed
Dp=2.5;
n=1725.;
Vm=math.pi*Dp*n/12.;

print'%s %.2f %s '%('\n Surface speed = ',Vm,' ft/min.');

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-12.2 Page No.256


 Surface speed =  1129.01  ft/min.

Ex3-pg258

In [3]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-12.3 Page No.258\n');
##Pinion
Su=95.*10**3;
Sn=0.5*Su;
Y=0.320;
b=1.;
Pd=8.;

Fsp=Sn*b*Y/Pd;

print'%s %.2f %s '%('\n Force allowable for pinion = ',Fsp,' lb.');

##Gear
Sn=0.5*88.*10**3;
Y=0.421;
Fsg=Sn*b*Y/Pd;

print'%s %.2f %s '%('\n Force allowable for gear = ',Fsg,' lb.');

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-12.3 Page No.258


 Force allowable for pinion =  1900.00  lb. 

 Force allowable for gear =  2315.50  lb.

Ex4-pg262

In [4]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-12.4 Page No.262\n');

##Dynamic load
Vm=1129.;
Ft=146.;
Fd=(600.+Vm)*Ft/600.;

print'%s %.2f %s '%('\n Dynamic load = ',Fd,' lb.');

Fs=1900.;
Nsf=2.;

##Comparing to the allowable stress

if (Fs/Nsf)>Fd:
    print('\n This is an acceptable design.');

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-12.4 Page No.262


 Dynamic load =  420.72  lb. 

 This is an acceptable design.

Ex5-pg263

In [5]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-12.5 Page No.263\n');

Su=55.*10**3;
Sn=0.5*Su;

Np=24.;
Pd=12.;
Dp=Np/Pd;

print'%s %.2f %s '%('\n Pitch circle diameter = ',Dp,' in.');

n=1800.;
Vm=math.pi*Dp*n/12.;

print'%s %.2f %s '%('\n Surface speed = ',Vm,' ft/min.');

b=3./4.;
Y=0.302;
Fs=Sn*b*Y/Pd;

print'%s %.2f %s '%('\n Allowable stress = ',Fs,' lb.');

Fd=Fs;
Ft=600.*Fd/(600.+Vm);

print'%s %.2f %s '%('\n Force transmitted = ',Ft,' lb.');

T=Ft*Dp/2.;

P=T*n/63000.;

print'%s %.2f %s '%('\n Power transmitted = ',P,' hp.');

##Compared to catalog
hp_catalog=4.14;

Nsf=P/hp_catalog;

print'%s %.2f %s '%('\n Safety factor =  .',Nsf,'');

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-12.5 Page No.263


 Pitch circle diameter =  2.00  in. 

 Surface speed =  942.48  ft/min. 

 Allowable stress =  519.06  lb. 

 Force transmitted =  201.91  lb. 

 Power transmitted =  5.77  hp. 

 Safety factor =  . 1.39

Ex6-pg266

In [6]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-12.6 Page No.266\n');

##Miscellaneous properties
Np=48.;
Pd=12.;
Dp=Np/Pd;
Vr=3.;
Ng=Np*Vr;

##Surface speed
n=900.;
Vm=math.pi*Dp*n/12.;

print'%s %.2f %s '%('\n Surface speed = ',Vm,' ft/min.');

##Force on teeth
hp=2.;
Ft=33000.*hp/Vm;

print'%s %.2f %s '%('\n Force on teeth = ',Ft,' lb.');

##Dynamic force
Fd=(600.+Vm)*Ft/600.;

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

##Width
Su=30.*10**3;
Sn=0.4*Su;
Y=0.344;
Nsf=2.;
b=Fd*Nsf*Pd/(Sn*Y);
b=round(b);

print'%s %.2f %s '%('\n Width = ',b,' in.');

if (8/Pd)<b:
	if b<(12.5/Pd):
		print('\n This is an acceptable design.');

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-12.6 Page No.266


 Surface speed =  942.48  ft/min. 

 Force on teeth =  70.03  lb. 

 Dynamic force =  180.03  lb. 

 Width =  1.00  in. 

 This is an acceptable design.

Ex7-pg270

In [7]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-12.7 Page No.270\n');

Su=95.*10**3;
Sn=0.5*Su;
Np=24.;
Pd=16.;
Dp=Np/Pd;

##Torque
n=3450.;
P=3.;
T=P*63000./n;

print'%s %.2f %s '%('\n Torque = ',T,' in-lb.');

##Force transmitted
Ft=2.*T/Dp;

print'%s %.2f %s '%('\n Force transmitted = ',Ft,' lb.');

##Surface speed
Vm=math.pi*Dp*n/12.;

print'%s %.2f %s '%('\n Surface speed = ',Vm,' ft/min.');

##Force allowable
Y=0.337;
b=1.;
Fs=Sn*b*Y/Pd;

print'%s %.2f %s '%('\n Force allowable = ',Fs,' lb.');

##Dynamic load using Buckingham's equation
C=830.;
Fd=Ft+0.05*Vm*(b*C+Ft)/(0.05*Vm+(b*C+Ft)**0.5);

Nsf=1.4;
if (Fs/Nsf)>Fd:
    print('\n This is a suitable design');

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-12.7 Page No.270


 Torque =  54.78  in-lb. 

 Force transmitted =  73.04  lb. 

 Surface speed =  1354.81  ft/min. 

 Force allowable =  1000.47  lb. 

 This is a suitable design

Ex8-pg272

In [8]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-12.8 Page No.272\n');

Ng=42.;
Np=24.;
Q=2.*Ng/(Ng+Np);

Kg=270.;
Dp=1.5;
b=1.;

Fw=Dp*b*Q*Kg;
Fd=699.;
Nsf=1.2;

if (Fw/Nsf)<Fd:
	print('\n (Fw/Nsf)<Fd So this would not be suitable design');


##If the surfaces each had a BHN = 450

Kg=470.;
Fw=Dp*b*Q*Kg;

if(Fw/Nsf)>Fd:
    print('\n\n If the surfaces each had a BHN = 450');
    print('\n (Fw/Nsf)>Fd So this would be suitable design.');

MACHINE DESIGN 
 Timothy H. Wentzell, P.E. 
 EXAMPLE-12.8 Page No.272


 (Fw/Nsf)<Fd So this would not be suitable design


 If the surfaces each had a BHN = 450

 (Fw/Nsf)>Fd So this would be suitable design.