# Ch:15 Shafts¶

## exa 15-2 - Page 421¶

In [1]:
from __future__ import division
from math import pi, sqrt, tan
dA=150#
dB=250#
alpha=20*pi/180#
W=400#
sigyt=400#
sigut=500#
Kb=1.5#
Kt=2#
T=W*dA/2#
Pt=T/(dB/2)#
Pr1=W*tan(alpha)#
Pr2=Pt*tan(alpha)#
RDH=((W*120)-(Pt*320))/440#
RcH=W-RDH-Pt#
#RcH=400+65.5-240#
McH=0#
MAH=RcH*120#
MBH=RDH*120#
RDV=((Pr1*120)-(Pr2*320))/440#
RcV=Pr1-RDV-Pr2#
MAV=RcV*120#
MBV=RDV*120#
Mmax=sqrt((MAH**2)+(MAV**2))#
T=30*10**3#
Ta=0.135*sigut#
d=16*sqrt((Kb*Mmax)**2+(Kt*T)**2)/(pi*Ta)#
d=d**(1/3)#
print "d is %0.2f mm    "%(d)#


d is 17.73 mm


## exa 15-3 - Page 421¶

In [2]:
from math import sqrt, pi
P=16*746#
N=3000#
w=2*pi*N/60#
T=P/w*10**3#
sigy=400#
Ty=sigy/2#
FOS=2#
Ta=Ty/FOS#
d=T*16/(pi*Ta)#
d1=d**(1/3)#
r=3#
D=d1+(2*r)#
SCF=1.196
Tys=Ta/SCF#
d=T*16/(pi*Tys)#
d2=d**(1/3)#
d=14#
D=d+(2*r)#
print "d1 is %0.2f mm    "%(d1)#
print "\nd2 is %0.2f mm    "%(d2)#


d1 is 12.46 mm

d2 is 13.23 mm


## exa 15-4 - Page 422¶

In [3]:
from math import sqrt, pi
P1=24*10**3#
P2=10*10**3#
sigyt=460#
Tya=sigyt*0.3#
SCF=2.84#
Ta=Tya/SCF#
N=400#
w=2*pi*N/60#
T1=P1/w#
T2=P2/w#
d1=T1*16*10**3/(pi*Ta)#
d1=d1**(1/3)#
d2=T2*16*10**3/(pi*Ta)#
d2=d2**(1/3)#
theta1=pi/3600#
l1=120#
G=84*10**3#
d3=T1*10**3*l1*32/(pi*G*theta1)#
d3=d3**(1/4)#
d4=T2*l1*10**3*32/(pi*G*theta1)#
d4=d4**(1/4)#
print " d1 is %0.2f mm    "%(d1)#
print "\n d2 is %0.2f mm    "%(d2)#
print "\n d3 is %0.1f mm    "%(d3)#
print "\n d4 is %0.2f mm    "%(d4)#

 d1 is 39.16 mm

d2 is 29.25 mm

d3 is 55.6 mm

d4 is 44.67 mm


## exa 15-5 - Page 423¶

In [4]:
from math import sin, exp
d=200#
r=d/2#
N=300#
P=5000#
D=500#
R=D/2#
u=0.3#
E=205*10**3#
G=84*10**3#
Ta=60#
Kb=1.5#
Kt=2#
w=2*pi*N/60#
beta1=20*pi/180#
V=r*w#
v=R*w#
# Let T1-T2 =T
T=P/V#
x=u*pi/sin(beta1)#
T2=T/((exp(x)-1))#
T1=T2*exp(x)#
t=P/v#
y=u*pi#
T3=t/((exp(x)-1))#
T4=T3*exp(x)#
T=P/w#
Rc=2612##
RA=645.1#
MB=96.76#
MC=-208.96#
d=16*10**3*sqrt((Kb*MC)**2+(Kt*T)**2)/(pi*Ta)#
d=d**(1/3)#
l=380#
J=pi*d**4/32#
theta=T*10**3*l/(G*J)#
theta=theta*180/pi#
print "d is %0.1f mm    "%(d)#
print "\ntheta is %0.2f degree    "%(theta)#

d is 33.6 mm

theta is 0.33 degree


## exa 15-6 - Page 423¶

In [5]:
from math import sqrt, pi
T=400#
Pt=4800#
Pg=3600#
sigyt=360#
E=205*10**3#
G=80*10**3#
Kb=2#
Kt=1.5#
FOS=3#
RC=((Pt*90)+(Pg*200))/140#
RA=8400-RC#
MB=RA*0.9#
MC=Pg*0.045#
Te=sqrt((Kb*MC)**2+(Kt*T)**2)#
Ta=0.577*sigyt/FOS#
d=16*10**3*Te/(pi*Ta)#
d=d**(1/3)#
L=110#
J=pi*d**4/32#
T=400#
theta=T*10**3*L/(G*J)#
theta=theta*180/pi#
print "d is %0.0f mm    "%(d)#
print "\ntheta is %0.4f deg    "%(theta)#

d is 37 mm

theta is 0.1735 deg


## exa 15-7 - Page 424¶

In [6]:
from math import sqrt, pi
T=47*10**3#
M=32*10**3#
d=20#
siga=32*M/(pi*d**3)#
Tm=16*T/(pi*d**3)#
sige=75#
Tys=165#
n=1/sqrt((siga/sige)**2+(Tm/Tys)**2)#
print "n is %0.2f     "%(n)#


n is 1.75