# 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