from __future__ import division
from math import sqrt, pi
# Given Data
Sut=650## MPa
Syt=380## MPa
F1BYF2 = 2.5## ratio of tensions
Fmax=2.5## kN
da=200## mm
db=400## mm
L=1*1000##mm
Km=1.5## fatigue factor
Kt=1## shock factor
tau_d1=0.30*Syt## MPa
tau_d2=0.18*Sut## MPa
tau_d=min(tau_d1, tau_d2)## MPa (taking minimum value)
tau_d=0.75*tau_d##MPa (Accounting keyway effect)
# Pulley A
F1=2500## N
F2=1000## N
T=(F1-F2)*da/2## N.mm
Fa=F1+F2## N (resultant pull Downwards)
# Pulley B
# F3 & F4 are tension in belt (assumed)
#T=(F3-F4)*db/2
SUB_F3F4 = 2*T/db## N (where SUB_F3F4 = F3-F4) --eqn(1)
F3BYF4=F1BYF2## ratio of tensions --eqn(2)
F4 = SUB_F3F4/(F3BYF4-1)## N (using above 2 equations)
F3=F3BYF4*F4## N
Fb=F3+F4## N (resultant pull right side( -->))
# BENDING MOMENTS -
Mav=Fa*L/4## N.mm (vertical force)
Mc=Fb*da## N.mm
Mah=Mc/2## N.mm (vertical force)
M = sqrt(Mav**2+Mah**2)## N.mm (resultant bending moment at A)
d=((16/pi/tau_d)*sqrt((Km*M)**2+(Kt*T)**2))**(1/3)## mm
print ' shaft diameter = %.2f mm. Use diameter = 45 mm.'%(d)
from __future__ import division
from math import sqrt,pi
# Given Data
Tmax=400## N.m
Tmin=140## N.m
Mmax=500## N.m
Mmin=250## N.m
Sut=540## MPa
Syt=400## MPa
n=2## factor of safety
Kf=1.25## given
Se_dash=0.4*Sut## Mpa
Se=Se_dash/Kf##MPa
Sys=0.577*Syt## MPa
Ses=0.577*Se## MPa
Mm=(Mmax+Mmin)/2## N.m
Ma=(Mmax-Mmin)/2## N.m
Tm=(Tmax+Tmin)/2## N.m
Ta=(Tmax-Tmin)/2## N.m
# Max. Distortion energy theory - Syt/n = 32/pi/d**3*sqrt((Mm+Ma*(Syt/Se)**2)+0.75*(Tm+Ta*(Sys/Ses))**2)
d = (32/pi*sqrt((Mm+Ma*(Syt/Se))**2+0.75*(Tm+Ta*(Sys/Ses))**2)*1000/(Syt/n))**(1/3) # # mm
print ' shaft diameter = %.2f mm. Use %.f mm.'%(d,d)
from __future__ import division
from math import sqrt,pi, ceil
# Given Data
P=5## kW
N=1000## rpm
Syt=300## N/mm.sq.
n=2## factor of safety
v=0.25## Poisson's ratio
#P=2*pi*N*T/(60*1000)
T=P/(2*pi*N/(60*1000))## N.m
#tau = 16*T/pi/d**3 # shear stress & sigma1 = tau#sigma2=0#sigma3=-tau
# max. shear strain energy theory, sigma1**2+sigma3**2+(sigma3-sigma1)**2=2*(Syt/n)**2
d=(16*T*1000/pi/sqrt(2/6*(Syt/n)**2))**(1/3)## mm (putting values of tau)
print ' shaft diameter = %.1f mm. Use %.f mm.'%(d,ceil(d))
from __future__ import division
from math import sqrt,pi,tan
# Given Data
Sut=700## MPa
Syt=460## Mpa
F1BYF2=3## ratio of tensions
dg=300## mm
dp=400## mm
P=25## kW
N=600## rpm
alfa=20## degree
Km=1.5## fatigue factor
Kt=1.5## shock factor
tau_d1=0.30*Syt## MPa
tau_d2=0.18*Sut## MPa
tau_d=min(tau_d1, tau_d2)## MPa (taking minimum value)
tau_d=0.75*tau_d##MPa (Accounting keyway effect)
# Pulley D
# P= 2*pi*N*T/60
T=P/(2*pi*N/(60*1000))## N.m
# (F1-F2)*dp/2=T
SUB_F1F2 = T*2/dp## N (where SUB_F1F2 = F1-F2)
F2 = SUB_F1F2/(F1BYF2-1) ## N (putting value of ratio)
F1=F1BYF2*F2## N
F=F1+F2## N
# Gear B
Ft=T*2/dg## N
Fr=Ft*tan(alfa*pi/180)## N
# Bearing Reactions
#Vertical forces
#RA*2*dg+Fr*dg=F*dg#
RA=(F*dg-Fr*dg)/(2*dg)## N (downwards)
RC=RA+Fr+F## N (upwards)
MA=0;MB_v=-RA*dg## N.mm
MC=-F*dg## N.mm
#Horizontal forces
MB_h=Ft*2*dg/4## N.mm
#Resultant B.M at B
MB=sqrt(MB_v**2+MB_h**2)## N.mm
Mmax=MC##N.mm
T=T*1000## N.mm
# d**3=16/pi/tau_d*sqrt((Km*M)**2+(Kt*T)**2)
d=(16/pi/tau_d*sqrt((Km*Mmax*1000)**2+(Kt*T)**2))**(1/3)
print ' shaft diameter(using ASME Code) = %.1f mm. Use diameter = %.f mm.'%(d,d)
from __future__ import division
from math import sqrt,pi,tan
# Given Data
L=1000## mm
alfa=20## degree
dg=500## mm
L1=250## mm
L2=300## mm
dp=600## mm
Wp=2000## N
F1=2.5*1000## N
F1BYF2=3## ratio of tensions
tau_d=42## MPa
F2=F1/F1BYF2## N
T=(F1-F2)*dp/2## N.mm
Ftg=2*T/dg## N
Frg=Ftg*tan(alfa*pi/180)## N
F=F1+F2## N
# Vertical Loads
RAV=(Ftg*(L1+dg)+Wp*L2)/L## N
RBV=Ftg+Wp-RAV## N
MCV=RAV*L1##N.mm
MDV=RBV*L2## N.mm
# Horizontal Loads
RAH=(Frg*(L1+dg)+F*L2)/L##N
RBH=Frg+F-RAH## N
MCH=RAH*L1## N.mm
MDH=RBH*L2## N.mm
MD=sqrt(MDV**2+MDH**2)## N.mm
Mmax=MD##N.mm
Te=MCV+MDV;# N.mm
# d**3 = 16*Te/%pi/tau_d
d = (16*Te/pi/tau_d)**(1/3);# mm
print ' shaft diameter(using ASME Code) = %.1f mm.'%(d)
from __future__ import division
from math import sqrt,pi
# Given Data
Tmax=400## N.mm
Tmin=200## N.mm
Mmax=500## N.mm
Mmin=250## N.mm
Sut=540## MPa
Syt=420## MPa
n=2## factor of safety
Se=0.35*Sut## MPa
Mm=(Mmax+Mmin)/2## N.m
Ma=(Mmax-Mmin)/2## N.m
Tm=(Tmax+Tmin)/2## N.m
Ta=(Tmax-Tmin)/2## N.m
Sys=0.5*Syt# MPa
Ses=0.5*Se## MPa
# Max. Distortion energy theory - Syt/n = 32/pi/d**3*sqrt((Mm+Ma*(Syt/Se)**2)+0.75*(Tm+Ta*(Sys/Ses))**2)
d = (32/pi*sqrt((Mm+Ma*(Syt/Se))**2+0.75*(Tm+Ta*(Sys/Ses))**2)*1000/(Syt/n))**(1/3) # # mm
print ' shaft diameter = %.f mm.'%(d)
from __future__ import division
from math import sqrt,pi
# Given Data
Wmax=40## kN
Wmin=20## kN
L=500## mm
Se_dash=350## MPa
Sut=650## MPa
Syt=500## MPa
n=1.5## factor of safety
ka=0.9# # surface finish factor
kb=0.85## size factor
ke=1## load factor
Kf=1## fatigue strength factor
Wm=1/2*(Wmax+Wmin)## N
Wa=1/2*(Wmax-Wmin)## N
Se=ka*kb*ke*Se_dash##MPa
Mm=Wm*L/1000/4## kN.m
Ma=Wa*L/1000/4## kN.m
#sigma_m=32*Mm/pi/d**3# & sigma_a=32*Ma/pi/d**3
#soderburg failure criteria - 1/n=sigma_m/Syt+Kf*sigma_a/Se
#d=((32/pi*n/1000)*(Mm/Syt+Kf*Ma/Se))*(1/3)
d=((32/pi/1000)*(Mm/Syt+Kf*Ma/Se)*n)**(1/3)*1000## mm
print ' shaft diameter = %.f mm.'%(d)
from __future__ import division
from math import sqrt,pi
# Given Data
Tmax=300## N.mm
Tmin=-100## N.mm
Mmax=400## N.mm
Mmin=-200## N.mm
n=1.5## factor of safety
Sut=500## MPa
Syt=420## MPa
sigma_d=280## MPa
ka=0.62# # surface finish factor
kb=0.85## size factor
keb=1## load factor for bending
kes=0.58## load factor for torsion
Kfb=1## fatigue strength factor for bending
Kfs=1## fatigue strength factor for torsion
Se_dash=0.5*Sut## MPa
Se=ka*kb*keb*Se_dash## MPa
Ses_dash=0.5*Se_dash## MPa
Ses=ka*kb*kes*Ses_dash## MPa
Sys=0.5*Syt## MPa
Mm=(Mmax+Mmin)/2## N.m
Ma=(Mmax-Mmin)/2## N.m
Tm=(Tmax+Tmin)/2## N.m
Ta=(Tmax-Tmin)/2## N.m
# tau_d/n = (16/pi/d**3)*sqrt((Mm+Ma*(Syt/Se)**2)+(Tm+Ta*(Sys/Ses))**2)
tau_d=sigma_d/2## MPa
d = ((16/pi)*sqrt((Mm+Ma*(Syt/Se)**2)+(Tm+Ta*(Sys/Ses))**2)/(tau_d*10**6/n))**(1/3)*1000## mm
print ' shaft diameter = %.2f mm.'%(d)
# Note - answer in the from math import sqrt,pi textbook is not accurate.