# Ch:25 Gears¶

## exa 25-1 - Page 669¶

In [8]:
from __future__ import division
from math import sqrt, pi
Zp=25#
Zg=60#
m=5#
dp=m*Zp#
dg=m*Zg#
CD=(dp+dg)/2#
ha=m#
hf=1.25*m#
c=hf-ha#
r=0.4*m#
print "dp is %0.0f mm  "%(dp)#
print "\ndg is %0.0f mm  "%(dg)#
print "\nCD is %0.1f mm   "%(CD)#
print "\nha is %0.0f mm   "%(ha)#
print "\nhf is %0.2f mm   "%(hf)#
print "\nc is %0.2f mm   "%(c)#
print "\nr is %0.0f mm   "%(r)#

dp is 125 mm

dg is 300 mm

CD is 212.5 mm

ha is 5 mm

hf is 6.25 mm

c is 1.25 mm

r is 2 mm


## exa 25-2 - Page 669¶

In [9]:
from math import sqrt, pi
from sympy import symbols, solve
N=800#
P=6000#
n=200#
Cs=1.4#
sigb=150#
FOS=2#
Zp=18#
Zg=Zp*N/n#
Y=pi*(0.154-(0.912/Zp))#
p=[1 ,0 ,-9.5846, -38.135]#
P = symbols('P')
expr = P**3*p[0]+P**2*p[1]+P*p[2]+p[3]
m=solve(expr, P)[0]#
dp=m*Zp#
dg=m*Zg#
# printing data in scilab o/p window
print "dp is %0.0f mm  "%(dp)#
print "\ndg is %0.0f mm  "%(dg)#
# Answer is given wrong in the textbook

dp is 77 mm

dg is 309 mm


## exa 25-3 - Page 670¶

In [10]:
from math import sqrt, pi
Zp=30#
N=1000#
Zg=75#
m=5#
b=60#
sigut=450#
BHN=350#
Cs=1.5#
FOS=2#
dp=m*Zp#
dg=m*Zg#
v=2*pi*N*dp/(60*1000*2)#
Cv=3/(3+v)#
sigb=450/3#
Y=0.358#
Sb=m*b*sigb*Y#
Q=(2*Zg)/(Zp+Zg)#
K=0.16*(BHN/100)**2#
Sw=b*dp*Q*K#
Pt=Sb*Cv/(Cs*FOS)#
P=Pt*v#
P=P*10**-3#
print "Sb is %0.0f N   "%(Sb)#
print "\nSw is %0.0f N  "%(Sw)#
print "\nP is %0.3f kW  "%(P)#

#The difference in the value of Sw is due to rounding-off of the value of Q.

Sb is 16110 N

Sw is 25200 N

P is 11.657 kW


## exa 25-4 - Page 670¶

In [11]:
from math import sqrt, pi
n=240#
P=8000#
N=1200#
CD=300#
Cs=1.5#
alpha=20*pi/180#
G=N/n#
dp=CD*2/6#
dg=5*dp#
v=2*pi*N*dp/(60*1000*2)#
Cv=3/(3+v)#
Pt=P/v#
Peff=Pt*Cs/Cv#
m=4#
b=10*m#
FOS=2#
Sb=Peff*FOS#
sigut=600#
sigb=sigut/3#
Zp=dp/m#
Zg=dg/m#
Q=(2*Zg)/(Zp+Zg)#
K=Sb/(b*dp*Q)#
BHN=sqrt(K/0.16)*100#
BHN=333#
print "BHN is %0.0f    "%(BHN)#

BHN is 333


## exa 25-5 - Page 671¶

In [12]:
from math import sqrt, pi
alpha=20*pi/180#
N=800#
P=6000#
sigut=450#
i=5#
Cs=1.3#
v=3.6#
FOS=2#
Pt=P/v#
Cv=3/(3+v)#
sigb=sigut/3#
dp=3.6*1000*2*60/(2*pi*N)#
dp=86#
Sb=Pt*Cs/Cv*FOS#
#Let x be m**2*Y
x=Sb/(10*sigb)#
m=5#
Zp=18#
dp=m*Zp#
Zg=i*Zp#
dg=m*Zg#
b=10*m#
phip=m+(0.25*sqrt(dp))#
ep=32+(2.5*phip)#
phig=m+(0.25*sqrt(dg))#
eg=32+(2.5*phig)#
e=ep+eg#
e=e*10**-3#
Ps=Cs*Pt#
r1=dp/2#
r2=dg/2#
Pd=e*N*Zp*b*r1*r2/(2530*sqrt(r1**2+r2**2))#
Q=(2*Zg)/(Zp+Zg)#
K=Sb/(b*dp*Q)#
BHN=sqrt(K/0.16)*100#
print "Ps is %0.2f N   "%(Ps)#
print "\nPd is %0.1f N   "%(Pd)#
print "\nBHN is %0.0f   "%(BHN)#

Ps is 2166.67 N

Pd is 1358.6 N

BHN is 282


## exa 25-4 - Page 672¶

In [13]:
from math import sqrt, pi
P=9000#
N=900#
n=150#
sigut=750#
BHN=300#
Cs=1.5#
FOS=2#
i=N/n#
x=sqrt(i)#
Zp=18#
Zg=x*Zp#
Zg=44#
#Let actual speed reduction be xa
xa=Zg/Zp#
n1=N/xa**2#
T1=P*60/(2*pi*N)#
i2=N/xa#
T2=N/i2*T1#
m=6#
dp=Zp*m#
dg=m*Zg#
phip=m+(0.25*sqrt(dp))#
ep=16+(1.25*phip)#
phig=m+(0.25*sqrt(dg))#
eg=16+(1.25*phig)#
e=ep+eg#
e=e*10**-3#
Pt=26000#
Ps=Cs*Pt#
r1=dp/2#
r2=dg/2#
b=10*m#
Pd=e*i2*Zp*b*r1*r2/(2530*sqrt(r1**2+r2**2))#
Q=(2*Zg)/(Zp+Zg)#
sigb=sigut/3#
Y=0.308#

Sb=b*m*sigb*Y#
K=0.16*(BHN/100)**2#
Sw=b*dp*K*Q#
print "m is %0.0f mm   "%(m)#
print "\nPd is %0.3f N   "%(Pd)#
print "\nSw is %0.0f N   "%(Sw)
#The difference in the values is due to rounding-off of the values.

m is 6 mm

Pd is 434.590 N

Sw is 13244 N