import math
#Initilization of Variables
N1=200 #r.p.m
d1=51 #cm #Dia. of engine
d2=30 #cm #Dia. of driven shaft
#Calculations
#Speed of driven shaft
N2=d1*d2**-1*N1 #r.p.m
#Result
print"Speed of driven shaft is",round(N2,2),"r.p.m"
import math
#Initilization of Variables
t=1 #cm #thickness
N1=200 #r.p.m
d1=51 #cm
d2=30 #cm
#Calculations
#Speed of shaft
N2=(d1+t)*(d2+t)**-1*N1 #r.p.m
#Result
print"speed of shaft is",round(N2,2),"r.p.m"
import math
#Initilization of Variables
N1=200 #r.p.m
N2=300
d1=60 #cm
t=0.5 #cm
s=4 #%
#Calculations
#Diameter of pulley
d2=N1*N2**-1*d1 #cm
#Taking belt thickness
d2_2=(d1+t)*N1*N2**-1-t
#Also considering slip
d2_3=(d1+t)*N1*N2**-1*(1-s*100**-1)-t #cm
#Result
print"Diameter of belt is:Neglecting belt thickness",round(d2,2),"cm"
print" :Belt thickness only",round(d2_2,2),"cm"
print" :Considering belt thickness and slip",round(d2_3,2),"cm"
import math
#Initilization of Variables
d1=1 #m #dia. of driver pulley
N1=200 #r.p.m #Speed of driver pulley
d2=2.5 #m #Dia. of driven pulley
f1=1.44 #N/mm**2 #strress
f2=0.49 #N/mm**2
E=100 #N/mm**2 #Young's Modulus
#Calculations
#Speed of driven pulley
N2=d1*d2**-1*(E+round((f2)**0.5,2))*(E+round((f1)**0.5,2))**-1*N1
#Speed if creep is neglected
N2_2=d1*d2**-1*N1 #r.p.m
#Speed lost by driven pulley due to creep
N=N2_2-N2
#Result
print"speed Lost by driven pulley due to creep is",round(N,3),"r.p.m"
import math
#Initilization of Variables
d1=1 #m #Diameter
N1=200 #r.p.m
d2=2.5 #m
b=500 #mm #width
t=10 #mm #thickness
E=100 #N/mm**2
#Calculations
#Area
A=b*t #mm**2
#Tension on tight side
T1=10*b
#Tension on slack side
T2=4*b #N
#Stress on tight side
f1=T1*A**-1 #N/mm**2
#Stress on slack side
f2=T2*A**-1 #N/mm**2
#Speed of driven pulley
N2=d1*d2**-1*(E+(f2)**0.5)*(E+(f1)**0.5)**-1*N1
#Speed if creep is neglected
N2_2=d1*d2**-1*N1 #r.p.m
#Speed lost by driven pulley due to creep
N=N2_2-N2
#Result
print"speed Lost by driven pulley due to creep is",round(N,2),"r.p.m"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
x=600 #cm #Distance between shafts
r1=30 #cm #radius
r2=20 #cm
#Calculations
#If belt is open
L1=pi*(r1+r2)+(r1-r2)**2*x**-3+2*x #cm
#If belt is crossed
L2=pi*(r1+r2)+(r1+r2)**2*x**-1+2*x #cm
#Result
print"If belt is open Length is",round(L1,2),"cm"
print"If belt is crossed length is",round(L2,2),"cm"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
#speed of shafts
N1=N3=N5=160 #r.p.m
N2=60 #r.p.m
N4=80 #r.p.m
N6=100 #r.p.m
x=180 #cm #Distance between shafts
r1=15 #cm #Radius of smallest pulley
#Calculations
#Radii of pulley 2
r2=r1*N1*N2**-1 #cm
#using same above equation for radii of pulley 3 we get and further simplifying we get
#r4=2*r3 ..................1
#but for crossed belt equation is
#r1+r2=r3+r4=r5+r6 .................2
#After further simplifying we get
r3=(r1+r2)*3**-1 #cm
r4=2*r3 #cm
#Using same above equation and further simplifying we get
#r6=1.6*r5 ...............3
#sub value of r6 in equation we get
r5=(r1+r2)*2.6**-1 #cm
r6=1.6*r5 #cm
#Length of open belt
L=pi*(r1+r2)+(r1-r2)**2*x**-1+2*x #cm
#For pulley 3 and 4 equation is
#L=pi*(r3+r4)+(r3-r4)**2*x**-1+2*x
#sub value in above equation we get an equation as
#r3**2+1696.5*r3-31710.6=0
a=1
b=1696.5
c=-31710.6
X=b**2-4*a*c
r3_2=(-b+X**0.5)*2**-1 #cm
r4_2=2*r3_2 #cm
#Sim for r5 & r6
#L=pi*(r6+r5)+(r6-r5)**2*x**-1+2*x
#sub value in above equation we get an equation as
#r5**2+4084*r5-88085=0
a=1
b=4084
c=-88085
X=b**2-4*a*c
r5_2=(-b+X**0.5)*2**-1 #cm
r6_2=1.6*r5_2 #cm
#Result
print"Radii of two stepped pulleys is:For crossed belt:r3",round(r3,2),"cm"
print" :r4",round(r4,2),"cm"
print" :r5",round(r5,2),"cm"
print" :r6",round(r6,2),"cm"
print"Radii of two stepped pulleys is:For open belt:r3_2",round(r3_2,2),"cm"
print" :r4_2",round(r4_2,2),"cm"
print" :r5_2",round(r5_2,2),"cm"
print" :r6_2",round(r6_2,2),"cm"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
d=1.2 #m #Diameter
N=200 #r.p.m #Speed
theta=165*pi*180**-1 #radians
mu=0.3 #Coefficient of friction
T1=3000 #N #MAx Tension
#Calculations
#Velocity
v=pi*d*N*60**-1 #m/s
#From ration of tensions we get
#T1*T2=e**mu*theta
#After simplifying we get
#e**mu*theta =2.3714
T2=T1*2.3714**-1 #N
#Power transmitted
P=(T1-T2)*v*1000**-1 #KW
#Result
print"Power transmitted is",round(P,2),"KW"
import math
from math import sin, cos, tan, radians, pi
import numpy as np
#Initilization of Variables
d1=1.20 #m #Diameter
r1=0.6 #m #Radius
r2=0.25 #m
x=4 #m #Distance between shafts
T1=1855.3 #N #Max TRension
mu=0.3 #Coefficient of friction
N1=200 #r.p.m
#Calculations
#Velocity
v=pi*d1*N1*60**-1 #m/s
##Let sin(alpha)=X
X=(r1-r2)*x**-1
alpha=np.arcsin(X)*(pi**-1*180)
#Angle of contact
theta=180-2*alpha
#From equation of max tension and further simplifying we get
T2=1855.3*2.435**-1 #N
#Power transmitted
P=(T1-T2)*v*1000**-1 #KW
#Torque
t1=(T1-T2)*r1 #N*m
t2=(T1-T2)*r2 #Nm
#Result
print"Power transmitted is",round(P,2),"KN"
print"Torque Exerted on driving shaft is:t1",round(t1,2),"N*m"
print" :t2",round(t2,2),"N*m"
import math
#Initilization of Variables
theta=2.88
v=28.33 #m/s #velocity
b=20 #cm #Width
t=0.8 #cm #thickness
rho=10**-3 #Kg/cm**3 #density
f=250 #N/cm**2 #Stress
mu=0.25 #coefficient of friction
#Calculations
#Max Tension
Tm=f*b*t #N
#mass
m=rho*b*t*100 #Kg
#Centrifugal Tension
Tc=m*v**2 #N
#Tension on tight side
T1=Tm-Tc #N
#From ratio of tension equation we get
T2=T1*2.056**-1 #N
#MAx Power
P=(T1-T2)*v*1000**-1 #KW
#Result
print"Max Power transmitted is",round(P,2),"KW"
import math
#Initilization of Variables
rho=10**-3 #kg/cm**3 #density
f=250 #N/cm**2 #stress
b=20 #cm #width
t=1.2 #cm #thickness
#Calculations
#MAss
m=rho*b*t*100
#MAx tension
Tm=f*b*t #N
#Velocity
v=(Tm*(3*m)**-1)**0.5 #m/s
#From equation of max tension and further simplifying we get
T1=2*3**-1*Tm #N
T2=T1*2**-1 #N
#Power
P=(T1-T2)*v*(1000)**-1 #KW
#Result
print"Max Power transmitted is",round(P,2),"KW"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
P=9 #KW #Power
d1=1.2 #m #Diameter
N1=200 #r.p.m
theta=165*pi*180**-1 #radians
mu=0.3 #Coefficient of friction
f=140 #N/cm**2 #Stress
rho=10**-3 #kg/cm**3
t=1 #cm #thickness
#Calculations
#From Ratio of tension equation we get
#T1*T2=e**mu*theta
#After simplifying we get
#e**mu*theta =2.3714
#T1=2.3714*T2 ................1
#Max tension in belt
#Tm=f*b*t ..............2
#Centrifugal tension
#Tc=m*v**2 .....................3
#Velocity
v=pi*d1*N1*60**-1 #m/s
#mass
#m=rho*b*t*100
#After simplifying we get
#m=b*10**-1
#Sub value of m in equation 2 and further simplfying we get
#T1-T2=716.5
#After further simplifying equations 1,2,3 we get
T2=716.5*1.3714**-1 #N
T1=2.3714*T2 #N
#sub value in MAx tension and further simplifying we get
b=1238.96*124**-1 #cm
#Result
print"Width of belt is",round(b,2),"cm"
import math
#Initilization of Variables
b=100 #mm #Width
t=10 #mm #thickness
theta=2.79 #radians
rho=10**-6 #kg/mm**3
mu=0.25 #coefficient of friction
f=1.5 #N/mm**2
g=9.81
#Calculations
#MAx tension
Tm=f*b*t #N
#From Ratio of tension equation we get
#T1*T2=e**mu*theta
#After simplifying we get
#e**mu*theta =2
#For Max power
Tc=Tm*3**-1 #N
#From max transmissiom equation
T1=Tm-Tc
T2=T1*2**-1 #N
#MAss
m=rho*b*t*1000 #Kg
#Weight
W=m*g #N
#Velocity
v=(Tm*(3*m)**-1)**0.5 #m/s
#Power transmitted
P=(T1-T2)*v*10**-3 #KW
#Result
print"Max Power that can be transmitted is",round(P,2),"KW"
import math
from math import sin, cos, tan, radians, pi
import numpy as np
#Initilization of Variables
d1=60 #cm #diameter
r1=30 #cm #Radius
d2=24 #cm
r2=12 #cm
x=300 #cm #dist between two shafs
N2=300 #r.p.m #speed of small pulley
mu=0.3 #coefficient of friction
m=0.6703 #kg
t=100 #N per cm width #Safe working tension
#Calculations
#LEt sin(Alpha)=X
alpha=np.arcsin((r1-r2)*x**-1)*(180*pi**-1)
#Using equation of ratio of tension
#T1*T2**-1=e**mu*theta ...........1
#Simplifying furter we get value of
#e**mu*theta=2.474
#T1=2.474*T2 ...................1
#Velocity
v=pi*d2*N2*60**-1*10**-2 #m/s
#Sub value of v and P in equation of power transmited and further simplifying we get
#(T1-T2)=994.7 .....................2
#Sub value of T1 from equation 1 we get
T2=994.7*1.474**-1 #N
T1=2.474*T2 #N
#Min width
b=T1*t**-1 #cm
#Initial belt tension
To=(T1+T2)*2**-1 #N
#Length of belt required
L=(pi*(r1+r2)+(r1+r2)**2*x**-1+2*x)*100**-1 #m
#Result
print"Minimum width of belt is",round(b,2),"cm"
print"Initial belt tension is",round(To,2),"N"
print"Length of belt required is",round(L,2),"m"
import math
from math import sin, cos, tan, radians, pi
import numpy as np
#Initilization of Variables
d1=1.5 #m #diameter
r1=0.75 #m #Radius
d2=1 #m
r2=0.5 #m
x=4.80 #dist between two shafs
To=3000 #N #Initial tension
N2=600 #r.p.m #speed of small pulley
mu=0.3 #coefficient of friction
m=0.6703 #kg
#Calculation
#Velocity
v=pi*d2*N2*60**-1 #m/s
#Centrifugal tension
Tc=m*v**2
#from Initial Tensiom
#T1+T2=4677 ..........1
#Let sin(alpha)=X
X=(r1-r2)*x**-1
alpha=np.arcsin(X)*(pi**-1*180)
#Angle of contact
theta=(180-2*alpha)*pi*180**-1
#From equation of ratio of tension we get
#t1=2.5*T2 ...................2
#sub value in equation 1 we get
T2=4677*3.5**-1 #N
T1=2.5*T2
#Power transmitted
P2=(T1-T2)*v*10**-3
#Result
print"Power transmitted is",round(P2,2),"KW"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
alpha=25 #degrees #Angle of groove
Tmax=T1=1500 #N #Max tension
theta=170*pi*180**-1 #radians
mu=0.27 #coefficient of friction
v=2 #m/s #belt speed
#Calculations
#From ratio of tension
#T1*T2**-1=e**mu*cosec(alpha)
#AFter further simplifying we get
#e**mu*cosec(alpha)=8.109
T2=T1*8.109**-1
#Net driving tension
T3=(T1-T2) #N
#Power transmitted
P=T3*v*10**-3 #W
#Result
print"Net driving tension is",round(T3,2),"N"
print"Power transmitted by the pulley is",round(P,2),"W"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
alpha=15 #Degrees
t=2 #cm #Depth pf belt
m=3.5*100*1000 #gm/l #mass
f=140 #N/cm**2 #Allowable stress
theta=140*pi*180**-1
mu=0.15 #coefficient of friction
#Calculations
CF=2*tan(15*pi*180**-1)
GC=1-2*tan(15*pi*180**-1)
BC=2*GC
ED=2
DF=2
#Area of v-belt
A=(ED+BC)*2**-1*DF
#MAx permissible tension
Tmax=f*A #N
#Centrifugal tension
Tc=Tmax*3**-1 #N
#Velocity
v=(Tc*m**-1)**0.5*1000 #m/s
#tension on tight side
T1=Tmax-Tc #N
#From ratio of tensions
#T1*T2**-1=e*mu*thta*cosec(alpha)
#After substituting values and furter simplifying we get value of
#e*mu*thta*cosec(alpha)=4.12
T2=T1*4.12**-1 #N
#Power
P2=(T1-T2)*v*1000**-1
#Result
print"Max Power transmitted is",round(P2,2),"KW"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
P=75 #KW #Power
d1=1.50 #m #Dia. of driver pulley
N1=200 #r.p.m
alpha=22.5 #Angle of groove
mu=0.3 #coefficient of friction
theta=160*pi*180**-1
m=0.6 #kg #Mass
Tmax=800 #N #Max safe
#Calculations
#Velocity of rope
v=pi*d1*N1*60**-1 #m/s
#centrifugal Tension
Tc=m*v**2 #N
#Tension in tight side of rope
T1=Tmax-Tc #N
#Ratio of tension in rope
#T1*T2=e**mu*theta*cosec(alpha)
#After further simplifying we get value of e**mu*theta*cosec(alpha
#e**mu*theta*cosec(alpha=8.95
T2=T1*8.95**-1
#Power Transmitted by onr rope
P2=(T1-T2)*v*1000**-1 #KW
#No. of ropes required
n=P*P2**-1
#Initial rope tensuion
To=(T1+T2+2*Tc)*2**-1
#Result
print"No. of ropes required for drive is",round(n,2)
print"Initial Rope tension is",round(To,2),"N"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
d1=0.40 #Dia. of pulley
N1=110 #speed #r.p.m
alpha=22.5 #Angle of groove
mu=0.28 #coefficient of friction
N=10 #No.of ropes
P=23.628 #KW #Power
theta=160*pi*180**-1 #radians
#Calculations
#velocity
v=pi*d1*N1*60**-1 #m/s
#Power transmited by one rope
P2=P*N**-1 #KW
#Centrifugal Tension
#Tc=0.0281*C**2 ................1
#Ratio of tension in rope
#T1=7.71*T2 ...........................2
#From other formula of power transmited by one rope
#P2=(T1-T2)*v*1000**-1
#After further substituting and simplifying we get
T2=1026*6.71**-1 #N
T1=7.71*T2 #N
#Tmax=T1+T2
#After sub values and further simplifying we get
C=(96.86)**0.5 #cm #girth of rope
Tc=0.0281*C**2 #N
#Initial Tension
To=(T1+T2+2*Tc)*2**-1 #N
#Dia. of each rope
d=C*pi**-1 #cm
#Result
print"Initial Tension is",round(To,2),"N"
print"Dia. of each rope is",round(d,2),"cm"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
D=3.6 #m #Dia. of pulley
n=15 #No. of ropes
alpha=22.5 #Degrees
theta=170*pi*180**-1 #Angle of contact
mu=0.28 #angle of friction
Tmax=960 #N #MAx tension
m=1.5 #kg/l #mass of rope
#Calculations
#Centrifugal tension
Tc=Tmax*3**-1 #N
#Velocity
v=(Tmax*(3*m)**-1)**0.5 #m
N=60*v*(pi*D)**-1 #r.p.m
#equation
#T1*T2**-1=e**mu*theta*cosec(alpha)
#After simlifying further we get
#e**mu*theta*cosec(alpha)=8.756
#Tension in tight side of rope
T1=Tmax-Tc #N
#Tension in slack side
T2=T1*8.756**-1
#Max Power
P=(T1-T2)*v*1000**-1
#Total max power
P2=P*n
#Result
print"Speed of the pulley in r.p.m is",round(N,2),"r.p.m"
print"Total max power is",round(P2,2),"KW"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
W=9000 #N #Weight of casting
n=2.5 #turns
theta=5*pi #Total angle covered
D=0.3 #m #diameter
N=20 #Speed
mu=0.25 #Coefficient of friction
#Calculations
#equation
#W*P**-1=e**mu*theta
#After simlifying further we get
P=W*50.65**-1 #Tension in slack side of rope #N
#Velocity
v=pi*D*N*60**-1 #m/s
#Power to raise casting
P2=(W-P)*v*1000**-1
#Result
print"Force Required by the man is",round(P,2),"N"
print"Power to raise the casting is",round(P2,2),"N"