# Ch:28 Worm and worm wheel set¶

## exa 28-1 - Page 726¶

In [5]:
from __future__ import division
from math import sqrt, pi
Z1=1#
Z2=30#
q=10#
m=5#
d=q*m#
D=m*Z2#
#let the speed reduction ratio be G
G=Z2/Z1#
CD=(d+D)/2#
print "G is %0.0f   "%(G)#
print "\nCD is %0.0f mm  "%(CD)#
print "\nd  is %0.0f mm  "%(d)#
print "\nD  is %0.0f mm  "%(D)#

G is 30

CD is 100 mm

d  is 50 mm

D  is 150 mm


## exa 28-2 - Page 726¶

In [6]:
from math import tan, atan, cos,pi
Z1=1#
Z2=52#
q=10#
m=8#
i=Z2/Z1#
CD=((m*q)+(m*Z2))/2#
lamda=atan(Z1/q)#
d=q*m#
da=m*(q+2)#
df=m*(q+2-(4.4*cos(lamda)))#
pa=m*pi#
D=m*Z2#
Da=m*(Z2+(4*cos(lamda))-2)#
Df=m*(Z2-2-(0.4*cos(lamda)))#
print "i is %0.0f   "%(i)#
print "\nCD is %0.0f mm  "%(CD)#
print "\npa is %0.2f mm  "%(pa)#
print "\nda is %0.0f mm  "%(da)#
print "\ndf is %0.3f mm  "%(df)#
print "\nDa is %0.3f mm  "%(Da)#
print "\nDf is %0.3f mm  "%(Df)#

i is 52

CD is 248 mm

pa is 25.13 mm

da is 96 mm

df is 60.975 mm

Da is 431.841 mm

Df is 396.816 mm


## exa 28-3 - Page 727¶

In [7]:
from math import sqrt, pi,sin,cos,atan
Z1=2#
Z2=60#
q=10#
m=5#
P=6000#
N=1440#
u=0.08#
alpha=20*pi/180#
lamda=atan(Z1/q)#
d=m*q#
w=2*pi*N/60#
T=P/w#
Ptw=T*10**3/(d/2)#
a=cos(alpha)#
b=cos(lamda)#
x=sin(alpha)#
y=sin(lamda)#
Paw=Ptw*(((a*b)-(u*y))/((a*y)+(u*b)))#
Prw=Ptw*y/((a*y)+(u*b))#
#Paw=Ptw*((cos(alpha)*cos(lambda))-(u*sin(lambda)))/((cos(alpha)*sin(lambda))+(u*cos(lambda)))#
#Prw=Ptw*((sin(alpha))/((cos(alpha)*sin(lambda))+(u*cos(lambda))))#
print "Ptw=Pag is %0.1f N  "%(Ptw)#
print "\nPaw=Ptg is %0.0f N  "%(Paw)#
print "\nPrw=Prg  is %0.0f N  "%(Prw)#

#The difference in the value is due to rounding-off the values.

Ptw=Pag is 1591.5 N

Paw=Ptg is 5487 N

Prw=Prg  is 1188 N


## exa 28-4 - Page 728¶

In [8]:
from __future__ import division
from math import sqrt, pi, cos,atan,tan,sin
Z1=2#
Z2=40#
q=8#
m=5#
d=q*m#
P=1.2#
lamda=atan(Z1/q)#
N=1000#
Vt=2*pi*N*20/(60*1000)#
Vs=Vt/cos(lamda)#
u=0.032#
alpha=20*pi/180#
x=cos(alpha)#
y=tan(lamda)#
z=(cos(lamda))/sin(lamda)#
n=(x-(u*y))/(x+(u*z))#
#Let power output be Po
Po=P*n#
#Let power lost in friction be Pf
Pf=P-Po#
print "P is %0.1f kW  "%(P)#
print "\nPo is %0.3f kW  "%(Po)#
print "\nPf is %0.3f kW  "%(Pf)#


P is 1.2 kW

Po is 1.047 kW

Pf is 0.153 kW


## exa 28-5 - Page 729¶

In [9]:
from math import sqrt, pi, cos,atan,tan,sin
Z1=2#
Z2=54#
q=10#
m=8#
P=4000#
A=1.8#
K=16#
N=1000#
u=0.028#
lamda=atan(Z1/q)#
alpha=20*pi/180#
d=m*q#
Vt=2*pi*N*d/(2*60*1000)#
Vs=Vt/cos(lamda)#
x=cos(alpha)#
y=tan(lamda)#
z=(cos(lamda))/sin(lamda)#
n=(x-(u*y))/(x+(u*z))#
delT=P*(1-n)/(K*A)#
print "n is %0.3f   "%(n)#
print "\ndelT is %0.2f deg  "%(delT)#

n is 0.865

delT is 18.73 deg


## exa 28-6 - Page 729¶

In [10]:
from math import sqrt, pi, cos,atan,tan,sin
Z1=1#
Z2=30#
q=10#
m=6#
#Let the ultimate strength of gear is sigut
#Let the allowable strenth of wheel is sigb
sigut=450#
sigb=84#
N=1200#
n=N/Z2#
alpha=20*pi/180#
d=m*q#
D=Z2*m#
b=3*d/4#
V=2*pi*n*D/(2*60*1000)#
Cv=6/(6+V)#
y=0.154-(0.912/Z2)#
Y=pi*y#
Sb=sigb*b*Cv*m*Y#
K=0.415#
Sw=b*D*K#
print "Sb is %0.0f N  "%(Sb)#
print "\nSw is %0.0f N  "%(Sw)#

#The difference in the value of Sb is due to rounding-off the values.

Sb is 8286 N

Sw is 3362 N