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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 9 - Power Screws"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.1 Pg 256"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " (a) Stress in the screw\n",
+ " \n",
+ " Direct compressive stress = 28.87 N/mm.sq\n",
+ " \n",
+ " Tortional shear stress = 36.72 N/mm.sq\n",
+ " \n",
+ " Maximum shear stress = 39.45 N/mm.sq\n",
+ " \n",
+ "\n",
+ " (b) number of threads of nut in engagement = 9\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,tan,atan,sqrt\n",
+ "\n",
+ "# Given Data\n",
+ "d=26## mm\n",
+ "p=5## mm\n",
+ "W=10## kN\n",
+ "Do=50## mm\n",
+ "Di=20## mm\n",
+ "mu=0.2## coefficient of thread friction\n",
+ "mu_c=0.15## coefficient of collar friction\n",
+ "N=15## rpm\n",
+ "pb=6## MPa\n",
+ "\n",
+ "dm=d-p/2## mm\n",
+ "dc=d-p## mm\n",
+ "t=p/2##mm\n",
+ "l=2*p## mm\n",
+ "alfa=atan(l/(pi*dm))*180/pi## degree\n",
+ "fi=atan(mu)*180/pi## degree\n",
+ "Tf=W*dm/2*tan(pi/180*(alfa+fi))## N.mm\n",
+ "Tc=mu_c*W/4*(Do+Di)## N.mm\n",
+ "T=Tf+Tc## N.mm\n",
+ "print ' \\n (a) Stress in the screw'\n",
+ "sigma_c=4*W*10**3/(pi*dc**2)## N/mm.sq.\n",
+ "print ' \\n Direct compressive stress = %.2f N/mm.sq'%(sigma_c)\n",
+ "tau=16*T*10**3/(pi*dc**3)##N/mm.sq.\n",
+ "print ' \\n Tortional shear stress = %.2f N/mm.sq'%(tau)\n",
+ "tau_max=sqrt(sigma_c**2/4+tau**2)##MPa\n",
+ "print ' \\n Maximum shear stress = %.2f N/mm.sq'%(tau_max)\n",
+ "n=W*10**3/(pi*dm*t*pb)#\n",
+ "print ' \\n\\n (b) number of threads of nut in engagement = %.f'%(n)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.2 Pg 257"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " (a) Power required = 0.045 kN\n",
+ " \n",
+ " (b) Efficiency of screw = 14.76 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import atan,tan,pi,sqrt,cos\n",
+ "# Given Data\n",
+ "d=50## mm\n",
+ "p=8## mm\n",
+ "W=2## kN\n",
+ "Do=100## mm\n",
+ "Di=50## mm\n",
+ "mu=0.15## coefficient of thread friction\n",
+ "mu_c=0.10## coefficient of collar friction\n",
+ "N=25## rpm\n",
+ "two_beta=29## degree\n",
+ "\n",
+ "dm=d-p/2## mm\n",
+ "dc=d-p## mm\n",
+ "t=p/2##mm\n",
+ "l=2*p## mm\n",
+ "alfa=atan(p/(pi*dm))*180/pi## degree\n",
+ "mu_e=mu/cos(pi/180*two_beta/2)## virtual coefficient of friction\n",
+ "fi=atan(mu_e)*180/pi## degree\n",
+ "Tf=W*dm/2*tan(pi/180*(alfa+fi))## N.mm\n",
+ "Tc=mu_c*W/4*(Do+Di)## N.mm\n",
+ "T=Tf+Tc## N.mm\n",
+ "P=2*pi*N*T/(60*10**3)## kW\n",
+ "print ' \\n (a) Power required = %.3f kN'%(P)\n",
+ "To=W*dm/2*tan(pi/180*alfa)## N.mm\n",
+ "eta=To/T*100## % (efficiency)\n",
+ "print ' \\n (b) Efficiency of screw = %.2f %%'%(eta)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.3 Pg 259"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " (a) Length of handle = -2422.0 mm\n",
+ " \n",
+ "\n",
+ " (b) Maximum shear stress in screw\n",
+ " \n",
+ " Section 1-1 : \n",
+ " \n",
+ " Maximum shear stress = 2161.89 MPa\n",
+ " \n",
+ " Section 2-2 : \n",
+ " \n",
+ " Maximum shear stress = 103.14 MPa\n",
+ " \n",
+ "\n",
+ " (b) Bearing pressure on threads = 11.1 MPa\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,atan,tan,cos,ceil\n",
+ "# Given Data\n",
+ "d=10## mm\n",
+ "p=3## mm\n",
+ "mu=0.15## coefficient of thread friction\n",
+ "mu_c=0.20## coefficient of collar friction\n",
+ "dc=15## mm\n",
+ "F=60## N\n",
+ "W=4## kN\n",
+ "two_beta=30## degree\n",
+ "h=25## mm\n",
+ "lf=150## mm (screw free length)\n",
+ "\n",
+ "dm=d-p/2## mm\n",
+ "alfa=atan(p/(pi*dm))*180/pi## degree\n",
+ "mu_e=mu/cos(pi/2*two_beta/2)## virtual coefficient of friction\n",
+ "fi=atan(mu_e)*180/pi## degree\n",
+ "Tf=W*10**3*dm/2*tan(pi/180*(alfa+fi))## N.mm\n",
+ "Tc=mu_c*W*10**3/2*dc## N.mm\n",
+ "T=Tf+Tc## N.mm\n",
+ "#F*l=T\n",
+ "l=T/F## mm (Length of handle)\n",
+ "print ' \\n (a) Length of handle = %.1f mm'%(l)\n",
+ "\n",
+ "print ' \\n\\n (b) Maximum shear stress in screw'\n",
+ "print ' \\n Section 1-1 : '\n",
+ "dc=d-p##mm\n",
+ "tau=16*T/(pi*dc**3)## N/mm.sq.\n",
+ "M=F*lf## N.mm\n",
+ "sigma_b=32*M/(pi*dc**3)## N/mm.sq.\n",
+ "tau_max=sqrt((sigma_b/2)**2+tau**2)## MPa\n",
+ "print ' \\n Maximum shear stress = %.2f MPa'%(tau_max)\n",
+ "print ' \\n Section 2-2 : '\n",
+ "sigma_c=4*W*10**3/(pi*dc**2)## N/mm.sq. (Direct compressive stress)\n",
+ "tau2=16*Tc/(pi*dc**3)#### N/mm.sq. (Tortional shear stress)\n",
+ "tau_max=sqrt((sigma_c/2)**2+tau2**2)## MPa\n",
+ "print ' \\n Maximum shear stress = %.2f MPa'%(tau_max)\n",
+ "\n",
+ "#h=n*p## height of nut\n",
+ "n=ceil(h/p)## no. of threads\n",
+ "t=p/2## mm (thickness of threads)\n",
+ "pb=W*10**3/(pi*dm*t*n)## MPa\n",
+ "print ' \\n\\n (b) Bearing pressure on threads = %.1f MPa'%(pb)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.4 Pg 260"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Power required to drive the slide = 1.67 kN\n",
+ " \n",
+ " factor of safety in tension = 6.42 \n",
+ " \n",
+ " factor of safety in shear = 4.57 \n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,atan,tan,cos,ceil\n",
+ "# Given Data\n",
+ "W=25## kN\n",
+ "two_beta=29## degree\n",
+ "v=0.96## m/min\n",
+ "mu=0.14## coefficient of thread friction\n",
+ "Di=30## mm\n",
+ "Do=66## mm\n",
+ "mu_c=0.15## coefficient of collar friction\n",
+ "d=36## mm\n",
+ "p=6## mm\n",
+ "Sut=630## MPa\n",
+ "Syt=380## MPa\n",
+ "\n",
+ "dm=d-p/2## mm\n",
+ "dc=d-p## mm\n",
+ "l=2*p## mm\n",
+ "alfa=atan(l/(pi*dm))*180/pi## degree\n",
+ "mu_e=mu/cos(pi/180*two_beta/2)## virtual coefficient of friction\n",
+ "fi=atan(mu_e)*180/pi## degree\n",
+ "Tf=W*10**3*dm/2*tan(pi/180*(alfa+fi))## N.mm\n",
+ "Tc=mu_c*W*10**3/4*(Do+Di)## N.mm\n",
+ "T=Tf+Tc## N.mm\n",
+ "N=v*10**3/l## rpm\n",
+ "\n",
+ "P=2*pi*N*T/(60*10**3)*10**-3## kW\n",
+ "print ' \\n Power required to drive the slide = %.2f kN'%(P)\n",
+ "sigma_c=4*W*10**3/(pi*dc**2)## MPa\n",
+ "tau=16*T/(pi*dc**3)## MPa\n",
+ "sigma1=1/2*(sigma_c+sqrt(sigma_c**2+4*tau**2))## MPa\n",
+ "tau_max=sqrt((sigma_c/2)**2+tau**2)## MPa\n",
+ "n_t=Syt/sigma1## factor of safety in tension\n",
+ "print ' \\n factor of safety in tension = %.2f '%(n_t)\n",
+ "n_s=Syt/2/tau_max## factor of safety in shear\n",
+ "print ' \\n factor of safety in shear = %.2f '%(n_s)\n",
+ "# Note- Answer in the textbook are not accurate."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.5 Pg 262"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " (a) Clamping force between the jaws = 8555 N\n",
+ " \n",
+ " (b) Efficiency of vice = 18.15 %\n",
+ " \n",
+ " (c) Torque at A-A, Tf = 9866.9 N.mm & Torque at B-B = 15000 N.mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,atan,tan,cos,ceil\n",
+ "\n",
+ "# Given Data\n",
+ "d=12## mm\n",
+ "dc=10## mm\n",
+ "p=2## mm\n",
+ "Do=10##mm\n",
+ "mu=0.15## coefficient of thread friction\n",
+ "mu_c=0.18## coefficient of collar friction\n",
+ "F=100## N\n",
+ "l=150## mm\n",
+ "\n",
+ "dm=dc+p/2## mm\n",
+ "alfa=atan(p/(pi*dm))*180/pi## degree\n",
+ "fi=atan(mu)*180/pi## degree\n",
+ "TfByW=dm/2*tan(pi/180*(alfa+fi))## where TfByW = Tf/W\n",
+ "TcByW=mu_c/3*Do## where TcByW = Tc/W\n",
+ "TByW=TfByW+TcByW## N.mm (total torque at B-B)\n",
+ "Tapplied=F*l## N.mm (torque applied by the operator)\n",
+ "#putting T= Tapplied\n",
+ "W= Tapplied/TByW## N\n",
+ "print ' \\n (a) Clamping force between the jaws = %.f N'%(W)\n",
+ "eta=W*dm/2*tan(pi/180*alfa)/Tapplied*100## % \n",
+ "print ' \\n (b) Efficiency of vice = %.2f %%'%(eta)\n",
+ "Tf=TfByW*W## N.mm\n",
+ "print ' \\n (c) Torque at A-A, Tf = %.1f N.mm & Torque at B-B = %.f N.mm'%(Tf,Tapplied)\n",
+ "# Note- Answer in the textbook are not accurate."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.6 Pg 267"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Screw Diameter-\n",
+ " Core diameter of screw, dc=35.68 mm. Use dc=40 mm\n",
+ " \n",
+ " outside diameter = 47 mm\n",
+ " \n",
+ " mean diameter = 43.5 mm\n",
+ " \n",
+ " thread thickness = 3.5 mm\n",
+ " \n",
+ " Maximum tensile & shear stress in screw -\n",
+ " \n",
+ " Maximum tensile stress = 99 MPa < 100 MPA. Hence design is safe.\n",
+ " \n",
+ " Maximum shear stress = 59.27 MPa < 60 MPA. Hence design is safe.\n",
+ " \n",
+ " Height of nut-\n",
+ " \n",
+ " h=98 mm\n",
+ " \n",
+ " Check for stress in screw and nut\n",
+ " \n",
+ " shear stress in screw = 16.24 MPa < 60 MPa\n",
+ " \n",
+ " shear stress in nut = 13.82 MPa < 40 MPa\n",
+ " \n",
+ " These are within permissible limits. Hence design is safe.\n",
+ " \n",
+ " Nut collar size-\n",
+ " \n",
+ " Inside diameter of collar = 68.96 mm. Use D1=70 mm\n",
+ " \n",
+ " Outside diameter of collar = 87.92 mm. Use D2=90 mm\n",
+ " \n",
+ " thickness of nut = 11.37 mm. Use tc=12 mm.\n",
+ " \n",
+ " Head Dimensions-\n",
+ " \n",
+ " Diameter of head on top of screw = 82.25 mm. use D3=84 mm.\n",
+ " \n",
+ " pin diameter in the cup = 21 mm\n",
+ " \n",
+ " Torque required between cup and head-\n",
+ " \n",
+ " Tc=441000 N.mm (acc. to uniform pressure theory)\n",
+ " \n",
+ " Total Torque, T=993064 N.mm\n",
+ " \n",
+ " length of lever = 3310 mm. Use 3300 mm\n",
+ " \n",
+ " Diameter of lever, dl=46.7 mm. Use dl=48 mm.\n",
+ " \n",
+ " Height of head, H=96 mm\n",
+ " \n",
+ " Check for screw in buckling-\n",
+ " \n",
+ " Buckling or critical load for screw, Wcr = 200 kN > 100kN\n",
+ " \n",
+ " Efficiency of screw = 11.2 %\n",
+ " \n",
+ " Body dimensions-\n",
+ " \n",
+ " Diameter of body at top, D5 = 135 mm\n",
+ " \n",
+ " Thickness of base, t2 = 24 mm\n",
+ " \n",
+ " Thickness of body, t3 = 12 mm\n",
+ " \n",
+ " Inside diameter of bottom, D6 = 202.5 mm. Use D6=205 mm.\n",
+ " \n",
+ " Outside diameter at the bottom, D7 = 358.75 mm. Use 360 mm.\n",
+ " \n",
+ " Height of body = 598 mm. Use 600mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,atan,tan,cos,ceil\n",
+ "\n",
+ "# Given Data\n",
+ "W=100## kN\n",
+ "lift=400## mm\n",
+ "sigma_ts=100## MPa\n",
+ "sigma_cs=100## MPa\n",
+ "tau_s=60## MPa\n",
+ "tau_tn=50## MPa\n",
+ "sigma_cn=45## MPa\n",
+ "tau_n=40## MPa\n",
+ "pb=15## MPa\n",
+ "mu=0.2## coefficient of thread friction\n",
+ "mu_c=0.15## coefficient of collar friction\n",
+ "\n",
+ "#sigma_cs=4*W/(pi*dc**2)\n",
+ "dc=sqrt(4*W*10**3/(pi*sigma_cs))## mm\n",
+ "print ' \\n Screw Diameter-\\n Core diameter of screw, dc=%.2f mm. Use dc=40 mm'%(dc)\n",
+ "dc=40## mm\n",
+ "p=7## mm (for normal series square threads)\n",
+ "d=dc+p##mm\n",
+ "print ' \\n outside diameter = %.f mm'%(d)\n",
+ "dm=dc+p/2## mm\n",
+ "print ' \\n mean diameter = %.1f mm'%(dm)\n",
+ "t=p/2## mm\n",
+ "print ' \\n thread thickness = %.1f mm'%(t)\n",
+ "\n",
+ "print ' \\n Maximum tensile & shear stress in screw -'\n",
+ "sigma_c=4*W*1000/pi/dc**2## MPa\n",
+ "alfa=atan(p/(pi*dm))*180/pi## degree\n",
+ "fi=atan(mu)*180/pi## degree\n",
+ "Tf=dm*W*10**3/2*tan(pi/180*(alfa+fi))## where TfByW = Tf/W\n",
+ "tau=16*Tf/(pi*dc**3)## MPa\n",
+ "sigma12=(1/2)*(sigma_c+sqrt(sigma_c**2+4*tau**2))## MPa\n",
+ "print ' \\n Maximum tensile stress = %.f MPa < %.f MPA. Hence design is safe.'%(sigma12,sigma_ts)\n",
+ "tau_max=sqrt((sigma_c/2)**2+tau**2)## MPa\n",
+ "print ' \\n Maximum shear stress = %.2f MPa < %.f MPA. Hence design is safe.'%(tau_max,tau_s)\n",
+ "\n",
+ "print ' \\n Height of nut-'\n",
+ "n=W*10**3/(pi/4)/pb/(d**2-dc**2)## no. of threads\n",
+ "n= ceil(n)## no. of threads (rounding)\n",
+ "h=n*p## mm\n",
+ "print ' \\n h=%.f mm'%(h)\n",
+ "\n",
+ "print ' \\n Check for stress in screw and nut'\n",
+ "tau_screw=W*10**3/(pi*n*dc*t)## MPa\n",
+ "print ' \\n shear stress in screw = %.2f MPa < %.f MPa'%(tau_screw,tau_s)\n",
+ "tau_nut=W*10**3/(pi*n*d*t)## MPa\n",
+ "print ' \\n shear stress in nut = %.2f MPa < %.f MPa'%(tau_nut,tau_n)\n",
+ "print ' \\n These are within permissible limits. Hence design is safe.'\n",
+ "\n",
+ "print ' \\n Nut collar size-'\n",
+ "# pi/4*(D1**2-d**2)*sigma_tn=W\n",
+ "D1=sqrt(W*10**3/(pi/4)/tau_tn+d**2)## mm\n",
+ "print ' \\n Inside diameter of collar = %.2f mm. Use D1=70 mm'%(D1)\n",
+ "D1=70##mm (adopted for design)\n",
+ "# pi/4*(D2**2-D1**2)*sigma_cn=W\n",
+ "D2=sqrt(W*10**3/(pi/4)/sigma_cn+D1**2)## mm\n",
+ "print ' \\n Outside diameter of collar = %.2f mm. Use D2=90 mm'%(D2)\n",
+ "D2=90##mm (adopted for design)\n",
+ "\n",
+ "# pi*D1*tc*tau_n=W\n",
+ "tc=W*10**3/(pi*D1*tau_n)## mm\n",
+ "print ' \\n thickness of nut = %.2f mm. Use tc=12 mm.'%(tc)\n",
+ "tc=12## mm (adopted for design)\n",
+ "\n",
+ "print ' \\n Head Dimensions-'\n",
+ "D3=1.75*d## mm\n",
+ "print ' \\n Diameter of head on top of screw = %.2f mm. use D3=84 mm.'%(D3)\n",
+ "D3=84## mm (adopted for design)\n",
+ "D4=D3/4## mm\n",
+ "print ' \\n pin diameter in the cup = %.f mm'%(D4)\n",
+ "\n",
+ "print ' \\n Torque required between cup and head-'\n",
+ "Tc=mu_c*W*10**3/3*((D3**3-D4**3)/(D3**2-D4**2))## N.mm\n",
+ "print ' \\n Tc=%.f N.mm (acc. to uniform pressure theory)'%(Tc)\n",
+ "T=Tf+Tc## N.mm\n",
+ "print ' \\n Total Torque, T=%.f N.mm'%(T)\n",
+ "\n",
+ "F=300## N (as a normal person can apply 100-300 N)\n",
+ "l=T/F##mm\n",
+ "print ' \\n length of lever = %.f mm. Use 3300 mm'%(l)\n",
+ "\n",
+ "M=F*l## N.mm\n",
+ "dl=(32*M/pi/sigma12)**(1/3)## mm\n",
+ "print ' \\n Diameter of lever, dl=%.1f mm. Use dl=48 mm.'%(dl)\n",
+ "dl=48## mm (adopted for design)\n",
+ "\n",
+ "H=2*dl## mm\n",
+ "print ' \\n Height of head, H=%.f mm'%(H)\n",
+ "\n",
+ "print ' \\n Check for screw in buckling-'\n",
+ "L=lift+0.5*h## mm\n",
+ "K=dc/4## mm\n",
+ "C=0.25## spring index\n",
+ "sigma_y=200## MPa\n",
+ "Ac=pi/4*dc**2##mm.sq.\n",
+ "Wcr=Ac*sigma_y*(1-(sigma_y/4/C/pi**2/(200*10**3))*(L/K)**2)/1000## kN\n",
+ "print ' \\n Buckling or critical load for screw, Wcr = %.f kN > 100kN'%(Wcr)\n",
+ "\n",
+ "To=W*10**3*dm/2*tan(pi/180*alfa)## N.mm\n",
+ "eta=To/T*100## %\n",
+ "print ' \\n Efficiency of screw = %.1f %%'%(eta)\n",
+ "\n",
+ "print ' \\n Body dimensions-'\n",
+ "D5=1.5*D2## mm\n",
+ "t2=2*tc## mm\n",
+ "t3=0.25*d##mm\n",
+ "D6=2.25*D2## mm\n",
+ "print ' \\n Diameter of body at top, D5 = %.f mm'%( D5)\n",
+ "print ' \\n Thickness of base, t2 = %.f mm'%( t2)\n",
+ "print ' \\n Thickness of body, t3 = %.f mm'%( t3)\n",
+ "print ' \\n Inside diameter of bottom, D6 = %.1f mm. Use D6=205 mm.'%( D6)\n",
+ "D6=205## mm (adopted for design)\n",
+ "D7=1.75*D6## mm\n",
+ "hb=lift+h+100## mm\n",
+ "print ' \\n Outside diameter at the bottom, D7 = %.2f mm. Use 360 mm.'%( D7)\n",
+ "print ' \\n Height of body = %.f mm. Use 600mm'%(hb)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.7 Pg 267"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Efficiency during raising the load = 34.71 %\n",
+ " \n",
+ " Efficiency during lowering the load = 92.28 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,atan,tan,cos,ceil\n",
+ "\n",
+ "# Given Data\n",
+ "two_beta=30## degree\n",
+ "W=400*10**3## N\n",
+ "d=100## mm\n",
+ "p=12## mm\n",
+ "mu=0.15## coefficient of thread friction\n",
+ "\n",
+ "dm=d-p/2## mm\n",
+ "dc=d-p## mm\n",
+ "l=2*p## mm\n",
+ "alfa=atan(l/pi/dm)*180/pi## degree\n",
+ "mu_e=mu/cos(pi/180*two_beta/2)## virtual coefficient of friction\n",
+ "fi=atan(mu)*180/pi## degree\n",
+ "Tf=W*dm/2*tan(pi/180*(alfa+fi))## N.mm (Frictional torque for raising load)\n",
+ "T=W*dm/4*tan(pi/180*fi)## N.mm\n",
+ "To=W*dm/2*tan(pi/180*alfa)## N.mm (Torque without friction)\n",
+ "eta1=To/Tf*100## % \n",
+ "print ' \\n Efficiency during raising the load = %.2f %%'%(eta1)\n",
+ "eta2=T/To*100## %\n",
+ "print ' \\n Efficiency during lowering the load = %.2f %%'%(eta2)\n",
+ "# Note - answer & solution is wrong in the textbook."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.9 Pg 272"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " (a) Safe Capacity of press or critical load for the screw = 680052 N\n",
+ " \n",
+ " (b) Height of nut, h=450 mm\n",
+ " \n",
+ " (c) Necessary torsional moment or total torque = 6939.12 N.mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,atan,tan,cos,ceil\n",
+ "\n",
+ "# Given Data\n",
+ "d=70## mm\n",
+ "mu=0.13## coefficient of thread friction\n",
+ "mu_c=0.15## coefficient of collar friction\n",
+ "Do=90## mm\n",
+ "Di=26## mm\n",
+ "L=450## mm\n",
+ "# C-25 steel screw\n",
+ "sigma_t1=275## MPa\n",
+ "sigma_c1=275## MPa\n",
+ "tau1=137.5## MPa\n",
+ "# Phosphor bronze nut\n",
+ "sigma_t2=100## MPa\n",
+ "sigma_c2=90## MPa\n",
+ "tau2=80## MPa\n",
+ "pb=15##MPa\n",
+ "n=2## factor of safety\n",
+ "#screw\n",
+ "sigma_ts=137.5## MPa\n",
+ "sigma_cs=137.5## MPa\n",
+ "tau_s=68.75## MPa\n",
+ "#Nut\n",
+ "sigma_tn=50## MPa\n",
+ "sigma_cn=45## MPa\n",
+ "tau_n=40## MPa\n",
+ "\n",
+ "p=10## mm (for normal series square threads)\n",
+ "dc=d-p##mm\n",
+ "dm=d-p/2##mm\n",
+ "t=p/2##mm\n",
+ "alfa=atan(p/pi/dm)*180/pi## degree\n",
+ "fi=atan(mu)*180/pi## degree\n",
+ "\n",
+ "K=dc/4## mm\n",
+ "C=0.25## spring index\n",
+ "sigma_y=275## MPa\n",
+ "Ac=pi/4*dc**2##mm.sq.\n",
+ "Wcr=Ac*sigma_y*(1-(sigma_y/4/C/pi**2/(200*10**3))*(L/K)**2)## N\n",
+ "print ' \\n (a) Safe Capacity of press or critical load for the screw = %.f N'%(Wcr)\n",
+ "\n",
+ "n=Wcr/(pi*dm*t*pb)## no. of threads\n",
+ "n=ceil(n)## rounding \n",
+ "h=n*p## mm\n",
+ "print ' \\n (b) Height of nut, h=%.f mm'%(h)\n",
+ "\n",
+ "W=Wcr## N\n",
+ "Tf=W*dm/2*tan(pi/180*(alfa+fi))/1000## N.mm (Frictional torque)\n",
+ "Tc=mu_c*W/4*(Do+Di)/1000## N.mm (Collar torque)\n",
+ "T=Tf+Tc## N.mm\n",
+ "print ' \\n (c) Necessary torsional moment or total torque = %.2f N.mm'%(T)\n",
+ "# Note - answer in the textbook is wrong."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.11 Pg 273"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " The force required for the job is : 22733 N\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,tan,atan,sqrt\n",
+ "\n",
+ "# Given Data\n",
+ "d=26## mm\n",
+ "L=0.25##m\n",
+ "F=300## N\n",
+ "mu=0.14## coefficient of thread friction\n",
+ "p=5## mm (for normal series)\n",
+ "\n",
+ "dc=d-p## mm\n",
+ "dm=d-p/2## mm\n",
+ "l=2*p## mm\n",
+ "alfa=atan(l/pi/dm)*180/pi## degree\n",
+ "fi=atan(mu)*180/pi## degree\n",
+ "To=F*L## N.m (Torque applied by the operator)\n",
+ "#Tf=W*dm/2*tand(alfa+fi)## N.mm\n",
+ "# And Tf=To\n",
+ "W=To*1000/(dm/2*tan(pi/180*(alfa+fi)))## N\n",
+ "print ' The force required for the job is : %.f N'%(W)\n",
+ "# Note - answer in the textbook is wrong."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.13 Pg 274"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Screw diameter - \n",
+ " Core diameter, dc = 25.75 mm. Use 30 mm\n",
+ " \n",
+ " outside diameter = 36 mm\n",
+ " \n",
+ " mean diameter = 33.0 mm\n",
+ " \n",
+ " thread thickness = 3.0 mm\n",
+ " \n",
+ " Maximum tensile & shear tress in screw -\n",
+ " \n",
+ " Maximum tensile stress = 82.4 MPa < 96 MPA. Hence design is safe.\n",
+ " \n",
+ " Maximum shear stress = 47.06 MPa < 48 MPA. Hence design is safe.\n",
+ " \n",
+ " Height of nut-\n",
+ " \n",
+ " h=60 mm\n",
+ " \n",
+ " Check for stress in screw and nut\n",
+ " \n",
+ " shear stress in screw = 17.68 MPa\n",
+ "\n",
+ " \n",
+ " shear stress in nut = 14.74 MPa\n",
+ " \n",
+ " These are within permissible limits. Hence design is safe.\n",
+ " \n",
+ " Nut collar size-\n",
+ " \n",
+ " Inside diameter of collar = 50.69 mm. Use D1=52 mm\n",
+ " \n",
+ " Outside diameter of collar = 64.2 mm. Use D2=65 mm\n",
+ " \n",
+ " thickness of nut = 7.65 mm. Use tc=8 mm.\n",
+ " \n",
+ " Head Dimensions-\n",
+ " \n",
+ " Diameter of head on top of screw = 63.00 mm. use D3=64 mm.\n",
+ " \n",
+ " pin diameter in the cup = 16 mm\n",
+ " \n",
+ " Torque required between cup and head-\n",
+ " \n",
+ " Tc=156800 N.mm (acc. to uniform pressure theory)\n",
+ " \n",
+ " Total Torque, T=321380 N.mm\n",
+ " \n",
+ " length of lever = 1071 mm. Use 1075 mm\n",
+ " \n",
+ " Diameter of lever, dl=34.1 mm.\n",
+ " \n",
+ " Height of head, H=68 mm\n",
+ " \n",
+ " Check for screw in buckling-\n",
+ " \n",
+ " Buckling or critical load for screw, Wcr = 176 kN > 50kN\n",
+ " \n",
+ " Hence design is safe.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,tan,atan,sqrt\n",
+ "\n",
+ "# Given Data\n",
+ "W=50## kN\n",
+ "lift=200## mm\n",
+ "gc=300## mm (ground clearance)\n",
+ "pb=16## MPa\n",
+ "mu=0.14## coefficient of collar friction\n",
+ "\n",
+ "#Screw C-35\n",
+ "Sut=288## MPa\n",
+ "n=3## factor of safety for screw\n",
+ "# Nut : phosphor-bronze\n",
+ "sigma_t=100## MPa\n",
+ "sigma_c=90## MPa\n",
+ "tau=80## MPa\n",
+ "n2=3## factor of safety for nut\n",
+ "\n",
+ "sigma_ts=Sut/n## MPa\n",
+ "sigma_cs=Sut/n## MPa\n",
+ "tau_s=sigma_ts/2## MPa\n",
+ "# sigma_cs=4*W/(pi*dc**2)\n",
+ "dc= sqrt(4*W*10**3/(pi*sigma_cs))## mm\n",
+ "print ' \\n Screw diameter - \\n Core diameter, dc = %.2f mm. Use 30 mm'%(dc)\n",
+ "dc=30## mm (adopted for design)\n",
+ "p=6## mm (for normal series square threads)\n",
+ "d=dc+p##mm\n",
+ "print ' \\n outside diameter = %.f mm'%(d)\n",
+ "dm=dc+p/2## mm\n",
+ "print ' \\n mean diameter = %.1f mm'%(dm)\n",
+ "t=p/2## mm\n",
+ "print ' \\n thread thickness = %.1f mm'%(t)\n",
+ "\n",
+ "print ' \\n Maximum tensile & shear tress in screw -'\n",
+ "sigma_c=4*W*1000/pi/dc**2## MPa\n",
+ "alfa=atan(p/(pi*dm))*180/pi;# degree \n",
+ "fi=atan(mu)*180/pi; # degree \n",
+ "Tf=dm*W*10**3/2*tan(pi/180*(alfa+fi))## where TfByW = Tf/W\n",
+ "tau=16*Tf/(pi*dc**3)## MPa\n",
+ "sigma12=(1/2)*(sigma_c+sqrt(sigma_c**2+4*tau**2))## MPa\n",
+ "print ' \\n Maximum tensile stress = %.1f MPa < %.f MPA. Hence design is safe.'%(sigma12,sigma_ts)\n",
+ "tau_max=sqrt((sigma_c/2)**2+tau**2)## MPa\n",
+ "print ' \\n Maximum shear stress = %.2f MPa < %.f MPA. Hence design is safe.'%(tau_max,tau_s)\n",
+ "\n",
+ "print ' \\n Height of nut-'\n",
+ "n=W*10**3/(pi/4)/pb/(d**2-dc**2)## no. of threads\n",
+ "n= round(n)## no. of threads (rounding)\n",
+ "h=n*p## mm\n",
+ "print ' \\n h=%.f mm'%(h)\n",
+ "\n",
+ "print ' \\n Check for stress in screw and nut'\n",
+ "tau_screw=W*10**3/(pi*n*dc*t)## MPa\n",
+ "print ' \\n shear stress in screw = %.2f MPa\\n'%(tau_screw)\n",
+ "tau_nut=W*10**3/(pi*n*d*t)## MPa\n",
+ "print ' \\n shear stress in nut = %.2f MPa'%(tau_nut)\n",
+ "print ' \\n These are within permissible limits. Hence design is safe.'\n",
+ "\n",
+ "print ' \\n Nut collar size-'\n",
+ "# pi/4*(D1**2-d**2)*sigma_tn=W\n",
+ "D1=sqrt(W*10**3/(pi/4)/(50)+d**2)## mm\n",
+ "print ' \\n Inside diameter of collar = %.2f mm. Use D1=52 mm'%(D1)\n",
+ "D1=52##mm (adopted for design)\n",
+ "# pi/4*(D2**2-D1**2)*sigma_cn=W\n",
+ "D2=sqrt(W*10**3/(pi/4)/45+D1**2)## mm\n",
+ "print ' \\n Outside diameter of collar = %.1f mm. Use D2=65 mm'%(D2)\n",
+ "D2=65##mm (adopted for design)\n",
+ "\n",
+ "# pi*D1*tc*tau_cn=W\n",
+ "tau_cn=40## MPa\n",
+ "tc=W*10**3/(pi*D1*tau_cn)## mm\n",
+ "print ' \\n thickness of nut = %.2f mm. Use tc=8 mm.'%(tc)\n",
+ "tc=8## mm (adopted for design)\n",
+ "\n",
+ "print ' \\n Head Dimensions-'\n",
+ "D3=1.75*d## mm\n",
+ "print ' \\n Diameter of head on top of screw = %.2f mm. use D3=64 mm.'%(D3)\n",
+ "D3=64## mm (adopted for design)\n",
+ "D4=D3/4## mm\n",
+ "print ' \\n pin diameter in the cup = %.f mm'%(D4)\n",
+ "\n",
+ "print ' \\n Torque required between cup and head-'\n",
+ "Tc=mu*W*10**3/3*((D3**3-D4**3)/(D3**2-D4**2))## N.mm\n",
+ "print ' \\n Tc=%.f N.mm (acc. to uniform pressure theory)'%(Tc)\n",
+ "T=Tf+Tc## N.mm\n",
+ "print ' \\n Total Torque, T=%.f N.mm'%(T)\n",
+ "\n",
+ "F=300## N (as a normal person can apply 100-300 N)\n",
+ "l=T/F##mm\n",
+ "print ' \\n length of lever = %.f mm. Use 1075 mm'%(l)\n",
+ "\n",
+ "M=F*l## N.mm\n",
+ "dl=(32*M/pi/sigma12)**(1/3)## mm\n",
+ "print ' \\n Diameter of lever, dl=%.1f mm.'%(dl)\n",
+ "\n",
+ "H=2*dl## mm\n",
+ "print ' \\n Height of head, H=%.f mm'%(H)\n",
+ "\n",
+ "print ' \\n Check for screw in buckling-'\n",
+ "L=lift+0.5*h## mm\n",
+ "K=dc/4## mm\n",
+ "C=0.25## spring index\n",
+ "sigma_y=288## MPa\n",
+ "Ac=pi/4*dc**2##mm.sq.\n",
+ "Wcr=Ac*sigma_y*(1-(sigma_y/4/C/pi**2/(200*10**3))*(L/K)**2)/1000## kN\n",
+ "print ' \\n Buckling or critical load for screw, Wcr = %.f kN > 50kN'%(Wcr)\n",
+ "print ' \\n Hence design is safe.'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.14 Pg 278"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " (i) Torque required to rotate the screw = 88400 N.mm\n",
+ " \n",
+ " (ii) Stresses induced in screw - \n",
+ " \n",
+ " Direct compressive stress = 20.96 N/mm.sq\n",
+ " \n",
+ " Tortional shear stress = 22.87 N/mm.sq\n",
+ " \n",
+ " Maximum shear stress = 25.16 MPa < 30 MPa\n",
+ " \n",
+ " Hence design is safe.\n",
+ " \n",
+ " (iii) Height of nut = 45 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,tan,atan,sqrt,ceil\n",
+ "\n",
+ "# Given Data\n",
+ "d=32## mm\n",
+ "p=5## mm\n",
+ "W=12## kN\n",
+ "D3=50## mm\n",
+ "D4=20## mm\n",
+ "mu=0.15## coefficient of thread friction\n",
+ "mu_c=0.20## coefficient of collar friction\n",
+ "N=24## rpm\n",
+ "pb=6## N/mm.sq.\n",
+ "tau_s=30## MPa\n",
+ "tau_n=30## MPa\n",
+ "\n",
+ "dm=d-p/2## mm\n",
+ "dc=d-p## mm\n",
+ "t=p/2## mm\n",
+ "l=2*p##mm\n",
+ "alfa=atan(l/pi/dm)*180/pi## degree\n",
+ "fi=atan(mu)*180/pi## degree\n",
+ "Tf=W*10**3*dm/2*tan(pi/180*(alfa+fi))## N.mm\n",
+ "Tc=mu_c*W*10**3/4*(D3+D4)## N.mm\n",
+ "T=Tf+Tc## N.mm\n",
+ "print ' \\n (i) Torque required to rotate the screw = %.f N.mm'%(T)\n",
+ "\n",
+ "print ' \\n (ii) Stresses induced in screw - '\n",
+ "sigma_c=4*W*10**3/(pi*dc**2)## N/mm.sq.\n",
+ "print ' \\n Direct compressive stress = %.2f N/mm.sq'%(sigma_c)\n",
+ "tau=16*T/(pi*dc**3)## N/mm.sq.\n",
+ "print ' \\n Tortional shear stress = %.2f N/mm.sq'%(tau)\n",
+ "tau_max=sqrt((sigma_c/2)**2+tau**2)## MPa \n",
+ "print ' \\n Maximum shear stress = %.2f MPa < %.f MPa'%(tau_max,tau_s)\n",
+ "print ' \\n Hence design is safe.'\n",
+ "n=W*10**3/(pi*dm*t*pb)## no. of threads\n",
+ "n=ceil(n)## rounding\n",
+ "h=n*p##mm\n",
+ "print ' \\n (iii) Height of nut = %.f mm'%(h)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 9.15 Pg 279"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Screw Diameter-\n",
+ " Core diameter of screw, dc=25.23 mm. Use dc=33 mm\n",
+ " \n",
+ " outside diameter = 40 mm\n",
+ " \n",
+ " mean diameter = 36.5 mm\n",
+ " \n",
+ " thread thickness = 3.5 mm\n",
+ " \n",
+ " Maximum stresses in screw -\n",
+ " \n",
+ " Maximum tensile stress = 138.8 N/mm.sq. < 200 N/mm.sq.. Hence design is safe.\n",
+ " \n",
+ " Maximum shear stress = 80.33 N/mm.sq. < 85 N/mm.sq.. Hence design is safe.\n",
+ " \n",
+ " Height of nut-\n",
+ " \n",
+ " h=119 mm. Use 120 mm.\n",
+ " \n",
+ " Check for stress in screw and nut\n",
+ " \n",
+ " shear stress in screw = 16.21 MPa < 85 MPa\n",
+ " \n",
+ " shear stress in nut = 13.37 MPa < 52 MPa\n",
+ " \n",
+ " These are within permissible limits. Hence design is safe.\n",
+ " \n",
+ " Nut collar size-\n",
+ " \n",
+ " Inside diameter of collar = 52.47 mm. Use D1=55 mm\n",
+ " \n",
+ " Outside diameter of collar = 64.64 mm. Use D2=70 mm\n",
+ " \n",
+ " thickness of nut = 11 mm. Use tc=15 mm.\n",
+ " \n",
+ " Head Dimensions-\n",
+ " \n",
+ " Diameter of head on top of screw = 70.00 mm.\n",
+ " \n",
+ " pin diameter in the cup = 17.5 mm. Use 20 mm.\n",
+ " \n",
+ " Torque required between cup and head-\n",
+ " \n",
+ " Tc=496296 N.mm (acc. to uniform pressure theory)\n",
+ " \n",
+ " Total Torque, T=885014 N.mm\n",
+ " \n",
+ " length of lever = 2950 mm or 2.95 m\n",
+ " \n",
+ " Diameter of lever, dl=44.8 mm. Use dl=45 mm.\n",
+ " \n",
+ " Height of head, H=90 mm\n",
+ " \n",
+ " Check for screw in buckling-\n",
+ " \n",
+ " Buckling or critical load for screw, Wcr = 145 kN > 100kN\n",
+ " \n",
+ " Efficiency of screw = 12.59 %\n",
+ " \n",
+ " Body dimensions-\n",
+ " \n",
+ " Diameter of body at top, D5 = 105 mm\n",
+ " \n",
+ " Thickness of base, t2 = 30 mm\n",
+ " \n",
+ " Thickness of body, t3 = 10 mm\n",
+ " \n",
+ " Inside diameter of bottom, D6 = 157.5 mm. Use D6=160 mm.\n",
+ " \n",
+ " Outside diameter at the bottom, D7 = 280.00 mm.\n",
+ " \n",
+ " Height of body = 480 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,tan,atan,sqrt,ceil\n",
+ "\n",
+ "# Given Data\n",
+ "W=100## kN\n",
+ "lift=260## mm\n",
+ "pb=15## N/mm.sq.\n",
+ "mu=0.15## coefficient of thread friction\n",
+ "mu_c=0.20## coefficient of collar friction\n",
+ "#Screw\n",
+ "Suts=800## N/mm.sq.\n",
+ "sigma_ss=340## N/mm.sq.\n",
+ "ns=4## factor of safety\n",
+ "#Nut\n",
+ "Sutn=552## N/mm.sq.\n",
+ "sigma_sn=260## N/mm.sq.\n",
+ "nn=5## factor of safety\n",
+ "\n",
+ "sigma_ts=Suts/ns## N/mm.sq.\n",
+ "sigma_cs=Suts/ns## N/mm.sq.\n",
+ "tau_s=sigma_ss/ns## N/mm.sq.\n",
+ "sigma_tn=Sutn/nn## N/mm.sq.\n",
+ "sigma_cn=Sutn/nn## N/mm.sq.\n",
+ "tau_n=sigma_sn/nn## N/mm.sq.\n",
+ "\n",
+ "#sigma_cs=4*W/(pi*dc**2)\n",
+ "dc=sqrt(4*W*10**3/(pi*sigma_cs))## mm\n",
+ "print ' \\n Screw Diameter-\\n Core diameter of screw, dc=%.2f mm. Use dc=33 mm'%(dc)\n",
+ "dc=33## mm\n",
+ "p=7## mm (for normal series square threads)\n",
+ "d=dc+p##mm\n",
+ "print ' \\n outside diameter = %.f mm'%(d)\n",
+ "dm=dc+p/2## mm\n",
+ "print ' \\n mean diameter = %.1f mm'%(dm)\n",
+ "t=p/2## mm\n",
+ "print ' \\n thread thickness = %.1f mm'%(t)\n",
+ "\n",
+ "print ' \\n Maximum stresses in screw -'\n",
+ "sigma_c=4*W*1000/pi/dc**2## MPa\n",
+ "alfa=atan(p/(pi*dm))*180/pi## degree\n",
+ "fi=atan(mu)*180/pi## degree\n",
+ "Tf=dm*W*10**3/2*tan(pi/180*(alfa+fi))## where TfByW = Tf/W\n",
+ "tau=16*Tf/(pi*dc**3)## MPa\n",
+ "sigma12=(1/2)*(sigma_c+sqrt(sigma_c**2+4*tau**2))## MPa\n",
+ "print ' \\n Maximum tensile stress = %.1f N/mm.sq. < %.f N/mm.sq.. Hence design is safe.'%(sigma12,sigma_ts)\n",
+ "tau_max=sqrt((sigma_c/2)**2+tau**2)## MPa\n",
+ "print ' \\n Maximum shear stress = %.2f N/mm.sq. < %.f N/mm.sq.. Hence design is safe.'%(tau_max,tau_s)\n",
+ "\n",
+ "print ' \\n Height of nut-'\n",
+ "n=W*10**3/(pi/4)/pb/(d**2-dc**2)## no. of threads\n",
+ "n= ceil(n)## no. of threads (rounding)\n",
+ "h=n*p## mm\n",
+ "print ' \\n h=%.f mm. Use 120 mm.'%(h)\n",
+ "h=120## mm\n",
+ "\n",
+ "print ' \\n Check for stress in screw and nut'\n",
+ "tau_screw=W*10**3/(pi*n*dc*t)## MPa\n",
+ "print ' \\n shear stress in screw = %.2f MPa < %.f MPa'%(tau_screw,tau_s)\n",
+ "tau_nut=W*10**3/(pi*n*d*t)## MPa\n",
+ "print ' \\n shear stress in nut = %.2f MPa < %.f MPa'%(tau_nut,tau_n)\n",
+ "print ' \\n These are within permissible limits. Hence design is safe.'\n",
+ "\n",
+ "print ' \\n Nut collar size-'\n",
+ "# pi/4*(D1**2-d**2)*sigma_tn=W\n",
+ "D1=sqrt(W*10**3/(pi/4)/sigma_tn+d**2)## mm\n",
+ "print ' \\n Inside diameter of collar = %.2f mm. Use D1=55 mm'%(D1)\n",
+ "D1=55##mm (adopted for design)\n",
+ "# pi/4*(D2**2-D1**2)*sigma_cn=W\n",
+ "D2=sqrt(W*10**3/(pi/4)/sigma_cn+D1**2)## mm\n",
+ "print ' \\n Outside diameter of collar = %.2f mm. Use D2=70 mm'%(D2)\n",
+ "D2=70##mm (adopted for design)\n",
+ "\n",
+ "# pi*D1*tc*tau_n=W\n",
+ "tc=W*10**3/(pi*D1*tau_n)## mm\n",
+ "print ' \\n thickness of nut = %.f mm. Use tc=15 mm.'%(tc)\n",
+ "tc=15## mm (adopted for design)\n",
+ "\n",
+ "print ' \\n Head Dimensions-'\n",
+ "D3=1.75*d## mm\n",
+ "print ' \\n Diameter of head on top of screw = %.2f mm.'%(D3)\n",
+ "D4=D3/4## mm\n",
+ "print ' \\n pin diameter in the cup = %.1f mm. Use 20 mm.'%(D4)\n",
+ "D4=20## mm (adopted for design)\n",
+ "\n",
+ "print ' \\n Torque required between cup and head-'\n",
+ "Tc=mu_c*W*10**3/3*((D3**3-D4**3)/(D3**2-D4**2))## N.mm\n",
+ "print ' \\n Tc=%.f N.mm (acc. to uniform pressure theory)'%(Tc)\n",
+ "T=Tf+Tc## N.mm\n",
+ "print ' \\n Total Torque, T=%.f N.mm'%(T)\n",
+ "\n",
+ "F=300## N (as a normal person can apply 100-300 N)\n",
+ "l=T/F##mm\n",
+ "print ' \\n length of lever = %.f mm or %.2f m'%(l,l/1000)\n",
+ "\n",
+ "M=F*l## N.mm\n",
+ "sigma_b=100## N/mm.sq. (assumed)\n",
+ "dl=(32*M/pi/sigma_b)**(1/3)## mm\n",
+ "print ' \\n Diameter of lever, dl=%.1f mm. Use dl=45 mm.'%(dl)\n",
+ "dl=45## mm (adopted for design)\n",
+ "\n",
+ "H=2*dl## mm\n",
+ "print ' \\n Height of head, H=%.f mm'%(H)\n",
+ "\n",
+ "print ' \\n Check for screw in buckling-'\n",
+ "L=lift+0.5*h## mm\n",
+ "K=dc/4## mm\n",
+ "C=0.25## spring index\n",
+ "sigma_y=200## MPa\n",
+ "Ac=pi/4*dc**2##mm.sq.\n",
+ "Wcr=Ac*sigma_y*(1-(sigma_y/4/C/pi**2/(200*10**3))*(L/K)**2)/1000## kN\n",
+ "print ' \\n Buckling or critical load for screw, Wcr = %.f kN > 100kN'%(Wcr)\n",
+ "\n",
+ "To=W*10**3*dm/2*tan(pi/180*alfa)## N.mm\n",
+ "eta=To/T*100## %\n",
+ "print ' \\n Efficiency of screw = %.2f %%'%(eta)\n",
+ "\n",
+ "print ' \\n Body dimensions-'\n",
+ "D5=1.5*D2## mm\n",
+ "t2=2*tc## mm\n",
+ "t3=0.25*d##mm\n",
+ "D6=2.25*D2## mm\n",
+ "print ' \\n Diameter of body at top, D5 = %.f mm'%( D5)\n",
+ "print ' \\n Thickness of base, t2 = %.f mm'%( t2)\n",
+ "print ' \\n Thickness of body, t3 = %.f mm'%( t3)\n",
+ "print ' \\n Inside diameter of bottom, D6 = %.1f mm. Use D6=160 mm.'%( D6)\n",
+ "D6=160## mm (adopted for design)\n",
+ "D7=1.75*D6## mm\n",
+ "hb=lift+h+100## mm\n",
+ "print ' \\n Outside diameter at the bottom, D7 = %.2f mm.'%( D7)\n",
+ "print ' \\n Height of body = %.f mm.'%(hb)"
+ ]
+ }
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generated by cgit (git 2.34.1) at 2025-05-18 03:50:20 +0000