Chapter 7: Belt, Rope and Chain Drive

Example 1, Page 228

import math

#Variable declaration
#given-belt is perfectly elastic and massless 
u=0.3
v=3600#ft/min
V=v/60#ft/sec
theta=165#degrees

#Calculations
x=theta*math.pi/180
k=math.e**(u*x)#k=T1/T2=e^(u*x)
To=500#lb
T1=2*k*To/(k+1)
T2=T1/k
T=T1-T2#effective tension
H=T*V/550#horsepower transmitted

#Result
print "The horse-power transmitted = %.2f"%H

The horse-power transmitted = 44.40

Example 2, Page 234

import math

#Variable declaration
w=1.2#lb/ft^2
u=0.3
v=3600#ft/min
V=v/60#ft/sec
theta=165#degrees
g=32.2#ft/s^2

#Calculations
x=theta*math.pi/180
k=math.e**(u*x)#k=T1/T2=e^(u*x)
To=500#lb
#Solution a)Vertical drive
Tc=w*V**2/g#equation 7.5
#solution a)
H=2*(k-1)*(To-Tc)*V/((k+1)*550)
Vmax=(To*g/(3*w))**(1./2)
Hmax=2*(k-1)*(To-Tc)*Vmax/((k+1)*550)
#Solution b)
To1=To+Tc
#from equation 7.15 2/To1^2=1/Tt^2+1/Ts^2
#T1/T2=k
T2=367 #lb - from trail and error
T1=k*T2
Tt=T1+Tc
Ts=T2+Tc
HP=(T1-T2)*V/550

#Results
print "Solution a)\nHorsepower transmitted= %.1f\nMaximum Horsepower transmitted= %.1f (at velocit = %.1f ft/s^2)"\
      "\n\nSolution b)\nTt=%.f lb\nTs=%.f lb\nHorsepower transmitted= %.1f"%(H,Hmax,Vmax,Tt,Ts,HP)

Solution a)
Horsepower transmitted= 32.5
Maximum Horsepower transmitted= 36.2 (at velocit = 66.9 ft/s^2)

Solution b)
Tt=1005 lb
Ts=501 lb
Horsepower transmitted= 54.9