Chapter13-Helical Bevel and Worm Gears¶

Ex1-pg280¶

In [1]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-13.1 Page No.280\n');

##Pitch-line velocity
Nt=24.;
Pd=12.;
Dp=Nt/Pd;
n=1750.;
Vm=math.pi*Dp*n/12.;

print'%s %.2f %s '%('\n Pitch-line velocity = ',Vm,' ft/min.');

##Transmitted force
hp=5.;
Ft=33000.*hp/Vm;

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

##Axial force
psi=15.*math.pi/180.;
Fa=Ft*math.tan(psi);

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

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

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

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-13.1 Page No.280

Pitch-line velocity =  916.30  ft/min.

Transmitted force =  180.07  lb.

Axial force =  48.25  lb.

Separating force =  67.85  lb.


Ex2-pg282¶

In [2]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-13.2 Page No.282\n');

##Normal plane pitch
Pd=16.;
psi=45.*math.pi/180;
Pdn=Pd/math.cos(psi);

print'%s %.2f %s '%('\n Normal plane pitch =',Pdn,' in.');

N=24.;
S=30000.;
b=0.5;
Ne=N/math.cos(psi)**3;
Y=0.427;
Fs=S*b*Y/Pdn;

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

Dp=24./16.;
n=600.;
Vm=math.pi*Dp*n/12.;

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

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

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

P=Ft*Vm/33000.;

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

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

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-13.2 Page No.282

Normal plane pitch = 22.63  in.

Allowable force =  283.06  lb.

Surface speed =  235.62  ft/min.

Force transmitted =  203.25  lb.

Power rating =  1.45  hp.


Ex3-pg286¶

In [3]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-13.3 Page No.286\n');

Np=24.;
Ng=36.;
Pd=8.;
Yp=33.7*math.pi/180.;
Yg=56.3*math.pi/180.;
theta=14.5*math.pi/180.;

##Pitch diameter
Dp=Np/Pd;

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

##Transmitted force
n=2200.;
P=8.;
T=63000.*P/n;

Ft=2.*T/Dp;

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

##Separating force - Pinion
Fnp=Ft*math.tan(theta)*math.cos(Yp);

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

##Separating force-Gear
Fng=Ft*math.tan(theta)*math.cos(Yg);

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

##Axial force-Pinion
Fap=Ft*math.tan(theta)*math.sin(Yp);

print'%s %.2f %s '%('\n Axial force-Pinion= ',Fap,' lb.');

##Axial force-Gear
Fag=Ft*math.tan(theta)*math.sin(Yg);

print'%s %.2f %s '%('\n Axial force-Gear = ',Fag,' lb.');

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-13.3 Page No.286

Pitch diameter =  3.00  in.

Transmitted force =  152.73  lb.

Separating force-Pinion =  32.86  lb.

Separating force =  21.92  lb.

Axial force-Pinion=  21.92  lb.

Axial force-Gear =  32.86  lb.


Ex4-pg288¶

In [4]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-13.4 Page No.288\n');

##Pitch diameter
Ng=60.;
Pd=6.;
Dp=Ng/Pd;

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

##Circular pitch
Pc=math.pi*Dp/Ng;

print'%s %.2f %s '%('\n Circular pitch = ',Pc,' in.');

L=Pc;

D=2.;
LA=math.atan(L/(math.pi*D));
LA=LA*180./math.pi;

print'%s %.2f %s '%('\n Lead angle = ',LA,' deg.');

##Centerline distance
CC=(D+Dp)/2.;

print'%s %.2f %s '%('\n Centerline distance = ',CC,' in.');

##Velocity ratio
Ntgear=60.;
Nstarts_worm=1.;
Vr=Ntgear/Nstarts_worm;

print'%s %.2f %s '%('\n Velocity ratio = ',Vr,'');

##Output speed
nin=1750.;
nout=nin/Vr;

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

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-13.4 Page No.288

Pitch diameter =  10.00  in.

Circular pitch =  0.52  in.

Centerline distance =  6.00  in.

Velocity ratio =  60.00

Output speed =  29.17  rpm.


Ex5-pg292¶

In [5]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-13.5 Page No.292\n');

##Normal circular pitch
Pc=0.524;
LA=4.77*math.pi/180.;
Pcn=Pc*math.cos(LA);

print'%s %.2f %s '%('\n Normal circular pitch = ',Pcn,'in.');

##Force transmitted
hp=5.;
n=29.2;
T=63000.*hp/n;
Dp=10.;
Ft=2.*T/Dp;

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

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

Fd=(1200.+Vm)*Ft/1200.;

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

##Force allowable
Su=95.*10**3;
Y=0.392;
b=1.;
Sn=0.5*Su;
Fs=Sn*Y*b*Pcn/math.pi;

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

##Safty factor
Nsf=Fs/Fd;

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

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

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-13.5 Page No.292

Normal circular pitch =  0.52 in.

Force transmitted =  2157.53  lb.

Force allowable =  3094.95  lb.

Safty factor =  1.35


Ex6-pg294¶

In [6]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-13.6 Page No.294\n');

##Efficiency
LA=4.77*math.pi/180.;
f=0.03;
e=math.tan(LA)*(1-f*math.tan(LA))/(f+math.tan(LA));

print'%s %.2f %s '%('\n Efficiency =  ',e,'');

##Torque input
hp=5.;
n=1750.;
T=63000.*hp/n;

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

Vr=60.;
Tout=0.73*Vr*T;

print'%s %.2f %s '%('\n Output torque = ',Tout,' in-lb.');

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-13.6 Page No.294

Efficiency =   0.73

Torque input =  180.00  in-lb.

Output torque =  7884.00  in-lb.


Ex7-pg296¶

In [7]:
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-13.7 Page No.296\n');

hpin=5.
e=0.73;
Q=(1.-e)*hpin*2544.;

print'%s %.2f %s '%('\n Heat generated by system = ',Q,' Btu/hr.');

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

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-13.7 Page No.296

Heat generated by system =  3434.40  Btu/hr.