Chapter 14: Balancing¶

Example 1, Page 491¶

In [9]:
#Variable declaration
W=200#lb
r=9#in
b1=15#in
bm=b1
l=10#in
d=50#in

#Calculations
#case a
ma=d+l
Bm1=W*r*l/(d*bm)#From 14.2
B11=W*r*ma/(d*b1)#from 14.3
#case b
mb=d-l
Bm2=W*r*l/(d*bm)#from 14.2
B12=W*r*mb/(d*b1)#from 14.3

#Results
print "a) Bm= %.f lb ; B1= %.f lb\nb) Bm= %.f lb ; B1= %.f lb"%(Bm1,B11,Bm2,B12)

a) Bm= 24 lb ; B1= 144 lb
b) Bm= 24 lb ; B1= 96 lb


Example 2, Page 491¶

In [2]:
import math

#Variable declaration
Wa=200#lb
Wb=300#lb
Wc=240#lb
W1=260#lb
ra=9#in
rb=7#in
rc=10#in
r1=12#in
R=24#in

#Calculations
alpha=45*math.pi/180
bita=75*math.pi/180
gama=135*math.pi/180
Hb=Wa*ra+Wb*rb*math.cos(alpha)-Wc*rc*math.cos(gama-bita)-W1*r1*math.cos(bita)#horizontal component after resolving
Vb=Wb*rb*math.sin(alpha)+Wc*rc*math.sin(gama-bita)-W1*r1*math.sin(bita)#vertical component after resolving
Bb=(Hb**2+Vb**2)**(1./2)
B=Bb/R
theta=math.degrees(math.atan(Vb/Hb))

#Results
print "Balance weight required = %.1f lb\ntheta = %.2f degrees"%(B,theta)

Balance weight required = 57.9 lb
theta = 23.28 degrees


Example 5, Page 500¶

In [8]:
import math

#Variable declaration
W=180.#lb
R=150.#lb
c=.5
N=300.#rpm
r=7.5/12#ft
g = 32.2

#Calculations
Bb=(W+c*R)*r*12
b=6#in
B=Bb/b
w=(math.pi*N)/30
Uf=(1./2)*(R/g)*w**2*r
a=math.floor(Uf)

#Results
print "Balance weight required = %.1f lb\n The resultant unbalanced force = %.f lb\n"%(B,a)

Balance weight required = 318.8 lb
The resultant unbalanced force = 1436 lb



Example 12, Page 517¶

In [12]:
import math

#Variable declaration
N=1500 #rpm
R=4#lb
g=32.2#ft/s^2
w=math.pi*N/30
stroke=5.#in
r=stroke/2
l=9#in
b=3.5#in

#Calculations
B=(3./2)*R*r/b#primary force
n=l/r
F=(3./2)*R*w**2*r/(g*12*n)#secondary force

#Results
print "Resultant primary force = %.2f lb\nResultant secondary force = %.f lb"%(B,F)

Resultant primary force = 4.29 lb
Resultant secondary force = 266 lb


Example 13, Page 519¶

In [14]:
import math

#Variable declaration
g=32.2#ft/s^2
n=2000#rpm
R=6#lb
r=3.#in
L=11.#in

#Calculations
w=math.pi*n/30
n=L/r
#minimum secondary force
F1=2*R*w**2*r/(g*n*12)
a=math.floor(F1)
#maximum secondary force
F2=6*R*w**2*r/(g*n*12)
b=math.floor(F2)

#Results
print "Minimum secondary force = %.f lb\nMaximum secondary force = %.f lb"%(a,b)

Minimum secondary force = 1114 lb
Maximum secondary force = 3343 lb