Ch:16 Power screws

exa 16-1 - Page 450

In [3]:
from math import atan, pi, sqrt, tan
d=30#
W=20*10**3#
r1=8#
r2=16#
p=6#
u1=0.2#
u2=0.15#
dm=d-(p/2)#
alpha=atan(p/(pi*dm))#
phi=atan(u1)#
rm=(r1+r2)/2#
Ttr=W*((dm*tan(alpha+phi)/2)+(u2*rm))#
Ttr=Ttr*10**-3#
print "Ttr is %0.3f Nm     "%(Ttr)#
#The answer to Ttr is slightly different than in the book due to rounding-off of values.

Ttr is 110.148 Nm

exa 16-2 - Page 451

In [4]:
from math import cos,pi,atan,tan
d=50#
W=20*10**3#
r1=10#
r2=30#
p=7#
u1=0.12/cos(15*pi/180)#
u2=0.15#
dm=d-(p/2)#
alpha=atan(3*p/(pi*dm))#
phi=atan(u1)#
rm=(r1+r2)/2#
Tr=W*((dm*tan(alpha+phi)/2)+(u2*rm))#
Tr=Tr*10**-3#
Te=W*((dm*tan(phi-alpha)/2)+(u2*rm))#
Te=Te*10**-3#
n=dm/2*tan(alpha)/(dm*tan(alpha+phi)/2+(u2*rm))#
L=0.30#
Ph=Tr/L#
print " Tr is %0.2f Nm     "%(Tr)#
print "\n Te is %0.3f Nm     "%(Te)#
print "\n n is %0.4f      "%(n)#
print "\n Ph is %0.2f N     "%(Ph)#
#The answers to Tr, Te and Ph is slightly different than in the book due to rounding-off of values.

 Tr is 187.49 Nm     

 Te is 51.691 Nm     

 n is 0.3489      

 Ph is 624.96 N

exa 16-3 - Page 452

In [5]:
from math import sqrt, pi, atan,tan
d=30#
W=5*10**3#
p=5#
rm=45/2#
u1=0.15/cos(14.5*pi/180)#
u2=0.15#
dm=d-(p/2)#
alpha=atan(p/(pi*dm))#
phi=atan(u1)#
Tr1=W*((dm*tan(alpha+phi)/2)+(u2*rm))#
Tr1=Tr1*10**-3#
n1=dm/2*tan(alpha)/(dm*tan(alpha+phi)/2+(u2*rm))#
T1=W*((dm*tan(phi-alpha)/2)+(u2*rm))#
T1=T1*10**-3#
n2=dm/2*tan(alpha)/(dm*tan(phi-alpha)/2+(u2*rm))#
u2=0.02#
Tr2=W*((dm*tan(alpha+phi)/2)+(u2*rm))#
Tr2=Tr2*10**-3#
n3=dm/2*tan(alpha)/(dm*tan(alpha+phi)/2+(u2*rm))#
Te=W*((dm*tan(phi-alpha)/2)+(u2*rm))#
Te=Te*10**-3#
n4=dm/2*tan(alpha)/(dm*tan(phi-alpha)/2+(u2*rm))#
print " Tr1 is %0.3f Nm     "%(Tr1)#
print "\n n1 is %0.4f      "%(n1)#
print "\n T1 is %0.3f Nm     "%(T1)#
print "\n n2 is %0.4f      "%(n2)#
print "\n Tr2 is %0.3f Nm     "%(Tr2)#
print "\n n3 is %0.4f      "%(n3)#
print "\n Te is %0.3f Nm     "%(Te)#
print "\n n4 is %0.4f      "%(n4)#
  
  #The answer to T1 is misprinted in the book.

 Tr1 is 31.456 Nm     

 n1 is 0.1265      

 T1 is 23.307 Nm     

 n2 is 0.1707      

 Tr2 is 17.156 Nm     

 n3 is 0.2319      

 Te is 9.007 Nm     

 n4 is 0.4418

exa 16-4 - Page 453

In [6]:
from math import tan,atan,pi
d=28#
P=300#
L=180#
p=8#
r1=16#
r2=46#
rm=(r1+r2)/2#
u1=0.12#
u2=0.15#
dm=d-(p/2)#
alpha=atan(p/(pi*dm))#
phi=atan(u1)#
T=P*L#
F=T/((dm*tan(alpha+phi)/2)+(u2*rm))#
F=F*10**-3#
print "F is %0.3f kN     "%(F)#

F is 7.299 kN

exa 16-5 - Page 453

In [7]:
from math import sqrt, pi, atan,tan
d=25#
p=8#
F=392.4#
L=250#
l=p*2#
u=0.14#
dm=d-(p/2)#
alpha=atan(l/(pi*dm))#
phi=atan(u)#
T=dm*tan(alpha+phi)/2#
M=F*L#
P=M/T*10**-3#
print "P is %0.1f kN     "%(P)#

P is 23.6 kN

exa 16-6 - Page 454

In [8]:
from math import sqrt, pi,atan,tan
d=52#
W=2.2*10**3#
p=8#
r1=15#
r2=30#
rm=(r1+r2)/2#
u1=0.15/cos(14.5*pi/180)#
dm=d-(p/2)#
alpha=atan(p/(pi*dm))#
phi=atan(u1)#
Ts=W*dm*tan(alpha+phi)/2#
u2=0.12#
Tc=u2*W*rm#
T=10**-3*(Ts+Tc)#
N=40#
w=2*pi*N/60#
P=T*w*10**-3#
To=W*dm/2*tan(alpha)#
n=To/(T*10**3)#
print "P is %0.2f KW     "%(P)#
print "\nn is %0.4f      "%(n)#

P is 0.07 KW     

n is 0.1659

exa 16-7 - Page 455

In [9]:
from math import sqrt, pi,atan,tan
alpha=atan(2*0.2/(pi*0.9))#
u1=0.15#
phi=atan(u1)#
P=200#
L=250#
Tt=P*L#
W=10*10**3#
u2=0.15#
x=Tt/W#
d=x/0.1716#
d=30#
p=6#
dr=0.8*d#
d=24#
p=5#
dr=d-p#
dm=d-(p/2)#
print "d is %0.0f mm     "%(d)#
print "\np is %0.0f mm     "%(p)#

d is 24 mm     

p is 5 mm

exa 16-8 - Page 456

In [10]:
from math import sqrt, pi,atan,tan
FOS=3#
sigut=380#
Ta=0.577*sigut/FOS#
d=25#
Tus=460#
Ps=pi*d*Tus#
siga=127#
dr=sqrt(Ps*4/(pi*siga))#
d=30#
p=6#
dr=d-p#
dm=d-(p/2)#
u1=0.15#
alpha=atan(p*2/(pi*dm))#
phi=atan(u1)#
T=Ps*dm*tan(alpha+phi)/2#
T1=16*T/(pi*dr**3)#
sigc=4*Ps/(pi*dr**2)#
sigmax=sigc/2+sqrt((sigc/2**2)+(T1**2))#
Tmax=sqrt((sigc/2**2)+(T1**2))#
n=tan(alpha)/tan(alpha+phi)#
Uo=Ps/2#
Ui=Uo/n#
wav=pi/2#
wmax=2*wav#
I=Ui*2/wmax**2#
k=0.4#
Ir=0.9*I*10**-3#
m=Ir/k**2#
R=0.4#
rho=7200#
a=sqrt(m/(2*pi*R*rho))#
T=T*10**-3#
print " T is %0.3f Nm     "%(T)#
print "\n n is %0.4f      "%(n)#
print "\n a is %0.5f mm      "%(a)#
  
#The difference in the answers of T is due to rounding-off of values.

 T is 145.242 Nm     

 n is 0.4751      

 a is 0.04894 mm