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authorTrupti Kini2017-01-28 23:30:35 +0600
committerTrupti Kini2017-01-28 23:30:35 +0600
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parent20b4cdb283d26cd07c04b0f41f0f95d3315953c7 (diff)
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Added(A)/Deleted(D) following books
A Machine_Design-I_by_Dr._Sadhu_Singh/chapter1.ipynb A Machine_Design-I_by_Dr._Sadhu_Singh/chapter3.ipynb A Machine_Design-I_by_Dr._Sadhu_Singh/chapter4.ipynb A Machine_Design-I_by_Dr._Sadhu_Singh/chapter5.ipynb A Machine_Design-I_by_Dr._Sadhu_Singh/chapter6.ipynb A Machine_Design-I_by_Dr._Sadhu_Singh/chapter7.ipynb A Machine_Design-I_by_Dr._Sadhu_Singh/chapter8.ipynb A Machine_Design-I_by_Dr._Sadhu_Singh/chapter9.ipynb A Machine_Design-I_by_Dr._Sadhu_Singh/screenshots/ch-4-dia-of-axlw.png A Machine_Design-I_by_Dr._Sadhu_Singh/screenshots/ch-4-endurance-limit.png A Machine_Design-I_by_Dr._Sadhu_Singh/screenshots/ch-4-thickness-of-plate.png
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-rw-r--r--Machine_Design-I_by_Dr._Sadhu_Singh/chapter3.ipynb649
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diff --git a/Machine_Design-I_by_Dr._Sadhu_Singh/chapter1.ipynb b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter1.ipynb
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 1 - Introduction"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 1.1 Pg 13"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The speeds of gear box are:\n",
+ "\n",
+ "\t\t\tN1 = 30.0 rpm\n",
+ "\n",
+ "\t\t\tN2 = 46.5 rpm\n",
+ "\n",
+ "\t\t\tN3 = 72.1 rpm\n",
+ "\n",
+ "\t\t\tN4 = 111.7 rpm\n",
+ "\n",
+ "\t\t\tN5 = 173.2 rpm\n",
+ "\n",
+ "\t\t\tN6 = 268.5 rpm\n",
+ "\n",
+ "\t\t\tN7 = 416.2 rpm\n",
+ "\n",
+ "\t\t\tN8 = 645.1 rpm\n",
+ "\n",
+ "\t\t\tN9 = 1000.0 rpm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "Nmax=1000## rpm\n",
+ "Nmin=30## rpm\n",
+ "z=9## no. of steps\n",
+ "\n",
+ "#Rn=Nmax/Nmin=fi**(z-1)\n",
+ "fi=(Nmax/Nmin)**(1/(z-1))## common ratio\n",
+ "\n",
+ "print 'The speeds of gear box are:'\n",
+ "N1=Nmin## rpm\n",
+ "for i in range(1,z+1):\n",
+ " print '\\n\\t\\t\\tN%d = %.1f rpm'%(i,N1)\n",
+ " N1=fi*N1##rpm\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 1.2 Pg 14"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The power of generating sets are:\n",
+ "\n",
+ "\t\t\tP1 = 10.0 kW\n",
+ "\n",
+ "\t\t\tP2 = 17.8 kW\n",
+ "\n",
+ "\t\t\tP3 = 31.6 kW\n",
+ "\n",
+ "\t\t\tP4 = 56.2 kW\n",
+ "\n",
+ "\t\t\tP5 = 100.0 kW\n",
+ "\n",
+ "Expanding for 10 models.\n",
+ "\n",
+ "The power of generating sets are:\n",
+ "\n",
+ "\t\t\tP1 = 10.0 kW\n",
+ "\n",
+ "\t\t\tP2 = 12.9 kW\n",
+ "\n",
+ "\t\t\tP3 = 16.7 kW\n",
+ "\n",
+ "\t\t\tP4 = 21.5 kW\n",
+ "\n",
+ "\t\t\tP5 = 27.8 kW\n",
+ "\n",
+ "\t\t\tP6 = 35.9 kW\n",
+ "\n",
+ "\t\t\tP7 = 46.4 kW\n",
+ "\n",
+ "\t\t\tP8 = 59.9 kW\n",
+ "\n",
+ "\t\t\tP9 = 77.4 kW\n",
+ "\n",
+ "\t\t\tP10 = 100.0 kW\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "Pmax=100## kW\n",
+ "Pmin=10## kW\n",
+ "z=5## no. of models\n",
+ "\n",
+ "#Rn=Pmax/Pmin=fi**(z-1)\n",
+ "fi=(Pmax/Pmin)**(1/(z-1))## common ratio\n",
+ "\n",
+ "print 'The power of generating sets are:'\n",
+ "P1=Pmin## kW\n",
+ "for i in range(1,z+1):\n",
+ " print '\\n\\t\\t\\tP%d = %.1f kW'%(i,P1)\n",
+ " P1=fi*P1##kW\n",
+ "\n",
+ "\n",
+ "print '\\nExpanding for 10 models.'\n",
+ "z=10## no. of models\n",
+ "\n",
+ "fi=(Pmax/Pmin)**(1/(z-1))## common ratio\n",
+ "\n",
+ "print '\\nThe power of generating sets are:'\n",
+ "P1=Pmin## kW\n",
+ "for i in range(1,z+1):\n",
+ " print '\\n\\t\\t\\tP%d = %.1f kW'%(i,P1)\n",
+ " P1=fi*P1##kW"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 1.4 Pg 15"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The models are:\n",
+ "\n",
+ "\t\t\tP0 = 5.0 kW\n",
+ "\n",
+ "\t\t\tP1 = 10.8 kW\n",
+ "\n",
+ "\t\t\tP2 = 23.2 kW\n",
+ "\n",
+ "\t\t\tP3 = 50.0 kW\n",
+ "\n",
+ " for 8 models.\n",
+ "The models are:\n",
+ "\n",
+ "\t\t\tP0 = 5.0 kW\n",
+ "\n",
+ "\t\t\tP1 = 6.9 kW\n",
+ "\n",
+ "\t\t\tP2 = 9.7 kW\n",
+ "\n",
+ "\t\t\tP3 = 13.4 kW\n",
+ "\n",
+ "\t\t\tP4 = 18.6 kW\n",
+ "\n",
+ "\t\t\tP5 = 25.9 kW\n",
+ "\n",
+ "\t\t\tP6 = 36.0 kW\n",
+ "\n",
+ "\t\t\tP7 = 50.0 kW\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "Pmax=50## kW\n",
+ "Pmin=5## kW\n",
+ "z=4## no. of models\n",
+ "\n",
+ "#Rn=Pmax/Pmin=fi**(z-1)\n",
+ "fi=(Pmax/Pmin)**(1/(z-1))## common ratio\n",
+ "\n",
+ "print 'The models are:'\n",
+ "\n",
+ "for i in range(0,z):\n",
+ " P1=fi**(i)*Pmin## kW\n",
+ " print '\\n\\t\\t\\tP%d = %.1f kW'%(i,P1)\n",
+ "\n",
+ "\n",
+ "print '\\n for 8 models.'\n",
+ "\n",
+ "z=8## no. of models\n",
+ "\n",
+ "#Rn=Pmax/Pmin=fi**(z-1)\n",
+ "fi=(Pmax/Pmin)**(1/(z-1))## common ratio\n",
+ "\n",
+ "print 'The models are:'\n",
+ "\n",
+ "for i in range(0,z):\n",
+ " P1=fi**(i)*Pmin## kW\n",
+ " print '\\n\\t\\t\\tP%d = %.1f kW'%(i,P1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 1.6 Pg 15"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The models are:\n",
+ "\n",
+ "\t\t\tP0 = 7.5 kW\n",
+ "\n",
+ "\t\t\tP1 = 13.3 kW\n",
+ "\n",
+ "\t\t\tP2 = 23.7 kW\n",
+ "\n",
+ "\t\t\tP3 = 42.2 kW\n",
+ "\n",
+ "\t\t\tP4 = 75.0 kW\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "Pmax=75## kW\n",
+ "Pmin=7.5## kW\n",
+ "z=5## no. of models\n",
+ "\n",
+ "#Rn=Pmax/Pmin=fi**(z-1)\n",
+ "fi=(Pmax/Pmin)**(1/(z-1))## common ratio\n",
+ "\n",
+ "print 'The models are:'\n",
+ "\n",
+ "for i in range(0,z):\n",
+ " P1=fi**(i)*Pmin## kW\n",
+ " print '\\n\\t\\t\\tP%d = %.1f kW'%(i,P1)\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Machine_Design-I_by_Dr._Sadhu_Singh/chapter3.ipynb b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter3.ipynb
new file mode 100644
index 00000000..3944ce95
--- /dev/null
+++ b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter3.ipynb
@@ -0,0 +1,649 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 3 - Design Against Static Load"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 3.1 Pg 62"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " dimension of cross section of link, t=19 mm. Adopt t=21 mm. \n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from sympy import symbols,solve\n",
+ "# Given Data\n",
+ "P=30## kN\n",
+ "Sut=350## MPa\n",
+ "n=2.5## factor of safety\n",
+ "\n",
+ "sigma_w=Sut/n## MPa (Working stress for the link)\n",
+ "\n",
+ "t=symbols('t')## thickness of link\n",
+ "A=2.5*t**2## mm.sq. \n",
+ "I=t*(2.5*t)**3/12## mm**4 (Moment of Inertia about N-A)\n",
+ "sigma_d=P/A## N/mm.sq.\n",
+ "e=10+1.25*t##mm\n",
+ "M=P*10**3*e## N.mm\n",
+ "sigma_t=M*1.25*t/I## N/mm.sq.\n",
+ "#maximum tensile stress at the top fibres = sigma_d+sigma_t=sigma_w ...eqn(1)\n",
+ "expr=sigma_d+sigma_t-sigma_w ## expression of polynomial from above eqn.\n",
+ "t=solve(expr)## solving the equation (as denominator will me be multiplied by zero on R.H.S)\n",
+ "t=t[0]## mm # discarding -ve roots\n",
+ "print ' dimension of cross section of link, t=%.f mm. Adopt t=21 mm. '%(t)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 3.2 Pg 63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " dimension of cross section of link, t=27 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from sympy import symbols,solve\n",
+ "from math import sin,cos,pi\n",
+ "# Given Data\n",
+ "P=6## kN\n",
+ "alfa=30## degree\n",
+ "Sut=250## MPa\n",
+ "n=2.5## factor of safety\n",
+ "\n",
+ "sigma_w=Sut/n## MPa (Working stress for the link)\n",
+ "PH=P*10**3*cos(pi/180*alfa)## kN\n",
+ "PV=P*10**3*sin(pi/180*alfa)## kN\n",
+ "\n",
+ "t=symbols('t')## thickness of link\n",
+ "A=2*t*t## mm.sq. \n",
+ "sigma_d=PH/A## N/mm.sq.\n",
+ "M=PH*100+PV*250## N.mm\n",
+ "I=t*(2*t)**3/12## mm**4 (Moment of Inertia)\n",
+ "sigma_t=M*t/I## N/mm.sq.\n",
+ "#maximum tensile stress at the top fibres = sigma_d+sigma_t=sigma_w ...eqn(1)\n",
+ "expr=sigma_d+sigma_t-sigma_w ## expression of polynomial from above eqn.\n",
+ "t=solve(expr,'t')## solving the equation (as denominator will me be multiplied by zero on R.H.S)\n",
+ "t=t[0]## mm # discarding -ve roots\n",
+ "print ' dimension of cross section of link, t=%.f mm.'%(t)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 3.3 Pg 64"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " dimension of cross section of link, t=22.36 mm. Use 23 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from sympy import symbols,solve\n",
+ "# Given Data\n",
+ "P=20## kN\n",
+ "Sut=300## MPa\n",
+ "n=3## factor of safety\n",
+ "\n",
+ "sigma_w=Sut/n## MPa (Working stress for the link)\n",
+ "\n",
+ "t=symbols('t')## thickness of link\n",
+ "A=4*t*t## mm.sq. \n",
+ "sigma_d=P*10**3/A## N/mm.sq.\n",
+ "e=6*t##mm\n",
+ "M=P*10**3*e## N.mm\n",
+ "z=t*(4*t)**2/6## mm**3 (section modulus at x1-x2)\n",
+ "sigma_b=M/z## N/mm.sq.\n",
+ "#maximum tensile stress at x1 = sigma_d+sigma_b=sigma_w ...eqn(1)\n",
+ "expr=sigma_d+sigma_b-sigma_w ## expression of polynomial from above eqn.\n",
+ "t=solve(expr,'t')## solving the equation (as denominator will me be multiplied by zero on R.H.S)\n",
+ "t=t[1]## mm # discarding -ve roots\n",
+ "print ' dimension of cross section of link, t=%.2f mm. Use 23 mm.'%(t)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 3.4 Pg 65"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Equating resultant tensile stress gives, a = 21.85 mm\n",
+ " \n",
+ " Equating resultant compressive stress gives, a = 4.77 mm\n",
+ " \n",
+ " dimension of cross section of link, a=21.85 mm. adopt a=22 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from sympy import symbols,solve\n",
+ "from math import ceil\n",
+ "# Given Data\n",
+ "P=15## kN\n",
+ "sigma_t=20## MPa\n",
+ "sigma_c=60## MPa\n",
+ "n=3## factor of safety\n",
+ "\n",
+ "a=symbols('a')## from the diagram.\n",
+ "# Area of cross section\n",
+ "A1=2*a*a## mm.sq.\n",
+ "A2=2*a*a/2## mm.sq.\n",
+ "A=A1+A2## mm.sq. \n",
+ "\n",
+ "# Location of neutral axis\n",
+ "#3*a**2*y_bar=2*a**2*a/2+a**2*(a+a/2)\n",
+ "y_bar=(2*a**2*a/2+a**2*(a+a/2))/(3*a**2)## mm\n",
+ "\n",
+ "# Moment of Inertia about neutral axis N-A\n",
+ "I=2*a*a**3/12+2*a**2*(y_bar-0.5*a)**2+2*((a/2)*(a**3/12)+(a**2/2)*(1.5*a-y_bar)**2)## mm**4\n",
+ "yt=y_bar##mm\n",
+ "yc=2*a-y_bar## mm\n",
+ "e=y_bar-0.5*a##mm\n",
+ "M=P*10**3*e## N.mm\n",
+ "sigma_d=P*10**3/A## N/mm.sq.\n",
+ "sigma_t1=M*yt/I##N/mm.sq.\n",
+ "sigma_c1=M*yc/I##N/mm.sq.\n",
+ "sigma_r_t=sigma_d+sigma_t1## N/mm.sq. (sigma_r_t=resultant tensile stress at AB=sigma_d+sigma_t)\n",
+ "sigma_r_c=sigma_c1-sigma_d## N/mm.sq. (sigma_r_t=resultant tensile stress at AB=sigma_d+sigma_t)\n",
+ "\n",
+ "#equating resulting tensile stress with given value sigma_t-sigma_r_t=0...eqn(1)\n",
+ "expr1=sigma_t-sigma_r_t## expression of polynomial from above eqn.\n",
+ "a1=solve(expr1,'a')## solving the equation (as denominator will me be multiplied by zero on R.H.S)\n",
+ "a1=a1[1]## mm # discasrding -ve roots\n",
+ "print ' Equating resultant tensile stress gives, a = %.2f mm'%(a1)\n",
+ "\n",
+ "#equating resulting compressive stress with given value sigma_c-sigma_c_t=0...eqn(1)\n",
+ "expr2=sigma_c-sigma_r_c## expression of polynomial from above eqn.\n",
+ "a2=solve(expr2,'a')## solving the equation (as denominator will me be multiplied by zero on R.H.S)\n",
+ "a2=a2[1]## mm # discarding -ve roots\n",
+ "print ' \\n Equating resultant compressive stress gives, a = %.2f mm'%(a2)\n",
+ "a=ceil(a1)##mm\n",
+ "print ' \\n dimension of cross section of link, a=%.2f mm. adopt a=%.f mm.'%(a1,a)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 3.5 Pg 67"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " (i) Maximum shear stress theory\n",
+ " diameter of shaft, d=99.2 mm or 100 mm\n",
+ " \n",
+ " (ii) Maximum strain energy theory\n",
+ " diameter of shaft, d=94.0 mm\n",
+ " \n",
+ " Adopt d=100mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,sqrt,ceil\n",
+ "# Given Data\n",
+ "Syt=760## MPa\n",
+ "M=15## kN.m\n",
+ "T=25##kN.m\n",
+ "n=2.5## factor of safety\n",
+ "E=200## GPa\n",
+ "v=0.25## Poisson's ratio\n",
+ "\n",
+ "sigma_d=Syt/n## MPa\n",
+ "# let d is diameter of the shaft\n",
+ "sigma_b_into_d_cube=32*M*10**6/pi## N/mm.sq. (where sigma_b_into_d_cube = sigma_d*d**3)\n",
+ "tau_into_d_cube=16*T*10**6/pi#d**3## N/mm.sq. (where tau_into_d_cube = tau*d**3)\n",
+ "sigma1_into_d_cube=sigma_b_into_d_cube/2+1/2*sqrt(sigma_b_into_d_cube**2+4*tau_into_d_cube**2) # # (where sigma1_into_d_cube=sigma1*d**3)\n",
+ "sigma2_into_d_cube=sigma_b_into_d_cube/2-1/2*sqrt(sigma_b_into_d_cube**2+4*tau_into_d_cube**2)# # (where sigma2_into_d_cube=sigma2*d**3)\n",
+ "print ' \\n (i) Maximum shear stress theory'\n",
+ "tau_max_into_d_cube=(sigma1_into_d_cube-sigma2_into_d_cube)/2# #(where tau_max_into_d_cube = tau_max*d**3)\n",
+ "d=(tau_max_into_d_cube/(sigma_d/2))**(1/3)##mm\n",
+ "print ' diameter of shaft, d=%.1f mm or %.f mm'%(d,ceil(d))\n",
+ "\n",
+ "print ' \\n (ii) Maximum strain energy theory'\n",
+ "#sigma1**2+sigma2**2-2*v*sigma1*sigma2=sigma_d**2\n",
+ "d=((sigma1_into_d_cube**2+sigma2_into_d_cube**2-2*v*sigma1_into_d_cube*sigma2_into_d_cube)/sigma_d**2)**(1/6)\n",
+ "print ' diameter of shaft, d=%.1f mm'%(d)\n",
+ "print ' \\n Adopt d=100mm'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 3.6 Pg 69"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Using equivalent torque equation,\n",
+ " shaft diameter d = 105 mm\n",
+ " \n",
+ " Using equivalent bending moment equation,\n",
+ " shaft diameter d = 97.68 mm or 98 mm\n",
+ " \n",
+ " Adopt d=105 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "N=200## rpm\n",
+ "P=200## kW\n",
+ "tau_d=42## Mpa\n",
+ "W=900## N\n",
+ "L=3## m\n",
+ "sigma_t=56## MPa\n",
+ "sigma_c=56## MPa\n",
+ "\n",
+ "T=P*60*10**3/(2*pi*N)## N.m\n",
+ "M=W*L/4## N.m\n",
+ "Te=sqrt(M**2+T**2)## N.m\n",
+ "#Te=(pi/16)*d**3*tau_d\n",
+ "d=(Te/((pi/16)*tau_d)*1000)**(1/3)## mm\n",
+ "print ' \\n Using equivalent torque equation,\\n shaft diameter d = %.f mm'%(d)\n",
+ "\n",
+ "Me=(1/2)*(M+sqrt(M**2+T**2))## N.m\n",
+ "#Me=(pi/32)*d**3*sigma_d\n",
+ "d=(Me/((pi/32)*sigma_c)*10**3)**(1/3)##mm\n",
+ "print ' \\n Using equivalent bending moment equation,\\n shaft diameter d = %.2f mm or %.f mm'%(d, ceil(d))\n",
+ "print ' \\n Adopt d=105 mm.'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 3.8 Pg 70"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Using equivalent torque equation,\n",
+ " shaft diameter d = 23 mm\n",
+ " \n",
+ " Using equivalent bending moment equation,\n",
+ " shaft diameter d = 21.40 mm or 22 mm\n",
+ " \n",
+ " Adopt d=23 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "M=15## N.m\n",
+ "P=5## kW\n",
+ "N=500## rpm\n",
+ "tau_d=40## Mpa\n",
+ "sigma_d=58## MPa\n",
+ "\n",
+ "T=P*60*10**3/(2*pi*N)## N.m\n",
+ "Te=sqrt(M**2+T**2)## N.m\n",
+ "#Te=(pi/16)*d**3*tau_d\n",
+ "d=(Te/((pi/16)*tau_d)*1000)**(1/3)## mm\n",
+ "print ' \\n Using equivalent torque equation,\\n shaft diameter d = %.f mm'%(d)\n",
+ "\n",
+ "Me=(1/2)*(M+sqrt(M**2+T**2))## N.m\n",
+ "#Me=(pi/32)*d**3*sigma_d\n",
+ "d=(Me/((pi/32)*sigma_d)*10**3)**(1/3)##mm\n",
+ "print ' \\n Using equivalent bending moment equation,\\n shaft diameter d = %.2f mm or %.f mm'%(d, ceil(d))\n",
+ "print ' \\n Adopt d=23 mm.'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 3.10 Pg 71"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " (i) Maximum Principal Stress Theory-\n",
+ " \n",
+ " Maximum value of torque, T = 235851 N.cm.\n",
+ " \n",
+ " (ii) Maximum Shear Stress Theory\n",
+ " \n",
+ " Maximum value of torque, T = 124765 N.cm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "from sympy import symbols,solve\n",
+ "# Given Data\n",
+ "d=4## cm\n",
+ "M=15000## N.cm\n",
+ "Syt=20000## N/cm.sq.\n",
+ "\n",
+ "print ' \\n (i) Maximum Principal Stress Theory-'\n",
+ "z=pi*d**3/32## cm.cube.\n",
+ "sigma_b=M/z## N/cm.sq.\n",
+ "T=symbols('T')\n",
+ "tau=16*T/(pi*d**3)## N/cm.sq.\n",
+ "#sigma1=(1/2)*(sigma_b+sqrt(sigma_b**2+4*tau**2)) # Maximum principal stress\n",
+ "#sigma1=(sigma_b/2+sqrt(sigma_b**2/4+tau**2)) # on solving\n",
+ "#tau=sqrt((sigma1-sigma_b/2)**2-sigma_b**2/4)\n",
+ "sigma1=Syt## N/cm.sq.\n",
+ "T=sqrt((sigma1-sigma_b/2)**2-sigma_b**2/4)*(pi*d**3)/16## N.cm.\n",
+ "print ' \\n Maximum value of torque, T = %.f N.cm.'%(T)\n",
+ "\n",
+ "print ' \\n (ii) Maximum Shear Stress Theory'\n",
+ "tau_d=0.5*Syt## N.cm.\n",
+ "#Te=sqrt(M**2+T**2)=(pi/16)*d**3*tau_d\n",
+ "T=sqrt(((pi/16)*d**3*tau_d)**2-M**2)## N.cm.\n",
+ "print ' \\n Maximum value of torque, T = %.f N.cm.'%(T)\n",
+ "# Answer in the textbook is not accurate."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 3.11 Pg 72"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " shaft diameter(using equivalent torque)-\n",
+ " d=55 mm.\n",
+ " \n",
+ " shaft diameter(using equivalent bending moment)-\n",
+ " d=57 mm.\n",
+ " \n",
+ " adopt d=57 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "N=200## rpm\n",
+ "P=25## kW\n",
+ "tau_d=42## MPa\n",
+ "W=900## N\n",
+ "L=3## m\n",
+ "Syt=56## MPa\n",
+ "Syc=56## MPa\n",
+ "sigma_d=56## MPa\n",
+ "\n",
+ "T=P*60*10**3/(2*pi*N)## N.m\n",
+ "M=W*L/4## N.m\n",
+ "Te=sqrt(M**2+T**2)## N.m\n",
+ "# Te=(pi/16)*d**3*tau_d\n",
+ "d=(Te*10**3/((pi/16)*tau_d))**(1/3)## mm\n",
+ "print ' \\n shaft diameter(using equivalent torque)-\\n d=%.f mm.'%(d)\n",
+ "\n",
+ "Me=(1/2)*(M+sqrt(M**2+T**2))##N.m\n",
+ "# Me=(pi/32)*d**3*sigma_d\n",
+ "d=(Me*10**3/((pi/32)*sigma_d))**(1/3)## mm\n",
+ "print ' \\n shaft diameter(using equivalent bending moment)-\\n d=%.f mm.'%(d)\n",
+ "print ' \\n adopt d=57 mm.'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 3.12 Pg 72"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " value of t = 36.9 mm\n",
+ " \n",
+ " Area of cross-section of Hanger, A = 2716 mm.sq.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,cos,sin\n",
+ "from sympy import symbols,solve\n",
+ "# Given Data\n",
+ "sigma_w=60## MPa\n",
+ "F=10## kN\n",
+ "alfa=30## degree\n",
+ "\n",
+ "FH=F*sin(pi/180*alfa)## kN\n",
+ "FV=F*cos(pi/180*alfa)## kN\n",
+ "t=symbols('t')## mm\n",
+ "A=t*t## mm.sq.\n",
+ "sigma_d=FV*10**3/A\n",
+ "M=FV*10**3*120+FH*10**3*150## N.mm\n",
+ "I=t*(2*t)**3/12## mm**4\n",
+ "sigma_t=M*t/I## N/mm.sq.\n",
+ "# Tensile stress at A=sigma_d+sigma_t=sigma_w ...eqn(1)\n",
+ "expr = sigma_d+sigma_t-sigma_w## polynomial from above eqn.\n",
+ "t=solve(expr,'t')## roots of the polynomial\n",
+ "t=t[0]## mm # discarding -ve roots\n",
+ "print ' \\n value of t = %.1f mm'%(t)\n",
+ "A=2*t**2## mm.sq.\n",
+ "print ' \\n Area of cross-section of Hanger, A = %.f mm.sq.'%(A)\n",
+ "# Note-Answer in the textbook is slighly wrong and cross section not calculated."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 3.13 Pg 74"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " shaft diameter is : 63 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import tan,pi,sqrt\n",
+ "# Given Data\n",
+ "P=15## kW\n",
+ "n1=200## rpm\n",
+ "l=600## mm\n",
+ "z2=18## no. of teeth\n",
+ "m2=5## mm\n",
+ "alfa2=14.5## degree\n",
+ "l2=120## mm\n",
+ "z1=72## no. of teeth\n",
+ "m1=5## mm\n",
+ "alfa1=14.5## degree\n",
+ "l1=150## mm\n",
+ "sigma_d=80## MPa\n",
+ "\n",
+ "d1=m1*z1## mm\n",
+ "v1=pi*d1*n1/(60*10**3)## m/s\n",
+ "Ft1=10**3*P/v1## N (outwards)\n",
+ "Fr1=Ft1*tan(pi/180*alfa1)## N (Downwards)\n",
+ "d2=m2*z2## mm\n",
+ "v2=pi*d2*n1/(60*10**3)## m/s\n",
+ "Ft2=10**3*P/v2## N (outwards)\n",
+ "Fr2=Ft2*tan(pi/180*alfa2)## N (Upwards)\n",
+ "\n",
+ "# RAV*600=Fr1*450+Fr2*120 (Taking moments about bearing B)\n",
+ "RAV=(Fr1*450+Fr2*120)/600## N (Downwards)\n",
+ "RBV=(Fr1-Fr2-RAV)## N (upwards)\n",
+ "MCV=RAV*l1## N.mm\n",
+ "MBV=Fr2*l2## N.mm\n",
+ "\n",
+ "# RAH*600=-Ft1*450+Ft2*120 (Taking moments about bearing B)\n",
+ "RAH=(-Ft1*450+Ft2*120)/600## N (Outwards)\n",
+ "RBH=Ft1+Ft2+RAH## N (inwards)\n",
+ "MCH=RAH*l1## N.mm\n",
+ "MBH=Ft2*l2## N.mm\n",
+ "\n",
+ "# Resultant Bending Moments\n",
+ "MC=sqrt(MCV**2+MCH**2)## N.mm\n",
+ "MB=sqrt(MBV**2+MBH**2)## N.mm\n",
+ "Mmax=max(MC,MB)## N.mm\n",
+ "T=10**3*P/(2*pi*n1)## N.m\n",
+ "Me=(1/2)*(Mmax+sqrt(Mmax**2+T**2))## N.mm\n",
+ "# Me=(pi/32)*d**3*sigma_d\n",
+ "d=(Me/((pi/32)*sigma_d))**(1/3)\n",
+ "print ' \\n shaft diameter is : %.f mm'%(d)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Machine_Design-I_by_Dr._Sadhu_Singh/chapter4.ipynb b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter4.ipynb
new file mode 100644
index 00000000..22b6f0a7
--- /dev/null
+++ b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter4.ipynb
@@ -0,0 +1,1019 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 4 - Design Against Fluctuating Load"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.1 Pg 102"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " for stepped plate under tension, Kt=1.75 for r/d = 0.125 & D/d = 1.25 \n",
+ " \n",
+ " for finite width plate under tension with a hole, Kt=2.42 for d0/w = 0.25\n",
+ " \n",
+ " Thickness of plate = 6.05 mm or 6 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from sympy import symbols,solve\n",
+ "P=6## kN\n",
+ "\n",
+ "#dimensions of plate\n",
+ "r=5##mm\n",
+ "d=40##mm\n",
+ "D=50##mm\n",
+ "d0=10##mm\n",
+ "w=40##mm\n",
+ "Sut=200##MPa\n",
+ "n=2.5## factor of safety\n",
+ "\n",
+ "#Fillet - \n",
+ "rBYd=r/d#\n",
+ "DBYd=D/d#\n",
+ "Kt=1.75## factor\n",
+ "print ' for stepped plate under tension, Kt=%.2f for r/d = %.3f & D/d = %.2f '%(Kt,rBYd,DBYd)\n",
+ "t=symbols('t')\n",
+ "sigma_max = Kt*P/t## N per mm sq.\n",
+ "\n",
+ "# Hole -\n",
+ "d0BYw=d0/w#\n",
+ "Kt=2.42## factor \n",
+ "print ' \\n for finite width plate under tension with a hole, Kt=%.2f for d0/w = %.2f'%(Kt,d0BYw)\n",
+ "sigma_max_into_t = Kt*P/(w-d0)##N/mm sq.\n",
+ "\n",
+ "#Design stress\n",
+ "sigma_d = Sut/n## MPa\n",
+ "#putting sigma_max=sigma_d\n",
+ "t=sigma_max_into_t/sigma_d*1000## mm\n",
+ "print ' \\n Thickness of plate = %.2f mm or %.f mm'%(t,t)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.2 Pg 104"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Diameter of axle = 46.5 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi\n",
+ "# Given Data\n",
+ "rBYd=0.1#\n",
+ "DBYd=1.2#\n",
+ "P=3## kN\n",
+ "Syt=300##MPa\n",
+ "n=3## factor of safety\n",
+ "#dimensions of plate\n",
+ "l1=400##mm\n",
+ "l2=300##mm\n",
+ "l3=400##mm\n",
+ "\n",
+ "\n",
+ "sigma_d=Syt/n## MPa\n",
+ "Kt=1.65## factor for circular fillet radius member\n",
+ "Rp=P/2##kN (bearing reaction due to symmetry)\n",
+ "Mf=Rp*l1## kN.mm (bending moment at fillet)\n",
+ "Mc=P*(l1+l2+l3)/4## kN.mm (bending moment at centre)\n",
+ "\n",
+ "#Fillet\n",
+ "#sigma_max=Kt*32*Mf/(pi*d**3)\n",
+ "sigma_max_into_d_cube_1 = Kt*32*Mf*1000/pi\n",
+ "\n",
+ "\n",
+ "#Centre\n",
+ "#sigma_max=32*Mc/(pi*d**3)\n",
+ "sigma_max_into_d_cube_2 = Kt*32*Mf*1000/pi\n",
+ "sigma_max_into_d_cube=max(sigma_max_into_d_cube_1,sigma_max_into_d_cube_2)## (getting max)\n",
+ "\n",
+ "#putting sigma_max=sigma_d\n",
+ "t=(sigma_max_into_d_cube/sigma_d)**(1/3)## mm\n",
+ "print ' \\n Diameter of axle = %.1f mm'%(t)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.3 Pg 105"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Endurance limit = 45.50 MPa\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "\n",
+ "# Given Data\n",
+ "Sut=440##MPa\n",
+ "d=25##mm\n",
+ "R=95/100## reliability\n",
+ "Kt=1.8## stress concentration factor\n",
+ "q=0.86## sensitivity factor\n",
+ "\n",
+ "Se_dash = 0.5*Sut## MPa\n",
+ "\n",
+ "# for machined surface\n",
+ "ka=0.82## surface finish factor\n",
+ "kb=0.85## size factor\n",
+ "kc=0.868## reliability factor\n",
+ "kd=1## temperature factor\n",
+ "ke=0.577## load factor\n",
+ "\n",
+ "Kf=1+q*(Kt-1)## fatigue strength factor\n",
+ "kf=1/Kf ## fatigue strength reduction factor\n",
+ "Se=ka*kb*kc*kd*ke*kf*Se_dash## (MPa) Endurance limit\n",
+ "print ' \\n Endurance limit = %.2f MPa'%(Se)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.4 Pg 105"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Thickness of plate = 18.26 mm or 20 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "\n",
+ "# Given Data\n",
+ "Sut=440##MPa\n",
+ "w=60##mm\n",
+ "d=12## mm\n",
+ "P=20## kN\n",
+ "q=0.8## sensitivity factor\n",
+ "R=90/100## reliability\n",
+ "n=2## factor of safety\n",
+ "\n",
+ "Kt=2.52## stress concentration factor\n",
+ "Se_dash = 0.5*Sut## MPa\n",
+ "# for hot rollednormalized condition\n",
+ "ka=0.67## surface finish factor\n",
+ "kb=0.85## size factor (assuming t<50 mm)\n",
+ "kc=0.897## reliability factor\n",
+ "kd=1## temperature factor\n",
+ "ke=0.9## load factor\n",
+ "dBYw=d/w# #(for circular hole)\n",
+ "\n",
+ "Kf=1+q*(Kt-1)## fatigue strength factor\n",
+ "kf=1/Kf ## fatigue strength reduction factor\n",
+ "Se=ka*kb*kc*kd*ke*kf*Se_dash## (MPa) Endurance limit\n",
+ "sigma_d=Se/n## MPa (design stress)\n",
+ "# sigma_max=P/(w-d)/t\n",
+ "sigma_max_into_t = P*1000/(w-d)#\n",
+ "# putting sigma_max=sigma_d\n",
+ "t=sigma_max_into_t/sigma_d## mm\n",
+ "print ' \\n Thickness of plate = %.2f mm or 20 mm'%(t)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.5 Pg 107"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Endurance of specimen = 395.34 MPa\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import log10\n",
+ "# Given Data\n",
+ "Sut=650##MPa\n",
+ "N=10**5## cycles\n",
+ "Se_dash = 0.5*Sut## MPa\n",
+ "of=5## unit\n",
+ "ob=6##unit\n",
+ "bf=ob-of## unit\n",
+ "be=3##unit\n",
+ "\n",
+ "# calculating endurance section wise\n",
+ "OE=log10(Se_dash)#\n",
+ "OA=log10(0.9*Sut)#\n",
+ "AE=OA-OE#\n",
+ "#log10_Sf=OD=OE+ED=OE+FC\n",
+ "log10_Sf=OE+(bf/be)*AE#\n",
+ "Sf=10**log10_Sf# # (MPa) Endurance\n",
+ "print ' \\n Endurance of specimen = %.2f MPa'%(Sf)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.6 Pg 108"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " diameter of beam 20 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import log10,pi\n",
+ "# Given Data\n",
+ "Sut=540##MPa\n",
+ "N=10**4## cycles\n",
+ "q=0.85## sensitivity factor\n",
+ "R=90/100## reliability\n",
+ "P=1500## N\n",
+ "l=160## mm\n",
+ "\n",
+ "Se_dash = 0.5*Sut## MPa\n",
+ "# for cold drawn steel\n",
+ "ka=0.79## surface finish factor\n",
+ "kb=0.85## size factor (assuming t<50 mm)\n",
+ "kc=0.897## reliability factor\n",
+ "kd=1## temperature factor\n",
+ "ke=1## load factor\n",
+ "\n",
+ "Kt=1.33## under bending\n",
+ "\n",
+ "Kf=1+q*(Kt-1)## fatigue strength factor\n",
+ "kf=1/Kf ## fatigue strength reduction factor\n",
+ "Se=ka*kb*kc*kd*ke*kf*Se_dash## MPa( Endurance limit)\n",
+ "\n",
+ "of=4## unit\n",
+ "ob=6##unit\n",
+ "bf=ob-of## unit\n",
+ "be=3##unit\n",
+ "\n",
+ "# calculating endurance section wise\n",
+ "OE=log10(Se)#\n",
+ "OA=log10(0.9*Sut)#\n",
+ "AE=OA-OE#\n",
+ "#log10_Sf=OD=OE+ED=OE+FC\n",
+ "log10_Sf=OE+(bf/be)*AE#\n",
+ "Sf=10**log10_Sf# # (MPa) Endurance\n",
+ "\n",
+ "MB=P*l## N.mm\n",
+ "# 32*MB/pi/d**3 = Sf\n",
+ "d=(32*MB/pi/Sf)**(1/3)\n",
+ "print ' \\n diameter of beam %.f mm'%(d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.7 Pg 110"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " diameter d at fillet cross section = 16 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,atan\n",
+ "# Given Data\n",
+ "Sut=600##MPa\n",
+ "Syt=380##MPa\n",
+ "q=0.9## sensitivity factor\n",
+ "R=90/100## reliability\n",
+ "n=2## factor of safety\n",
+ "Pmin=-100## N\n",
+ "Pmax=200## N\n",
+ "l=150## mm\n",
+ "\n",
+ "Se_dash = 0.5*Sut## MPa\n",
+ "# for cold drawn steel\n",
+ "ka=0.76## surface finish factor\n",
+ "kb=0.85## size factor (assuming t<50 mm)\n",
+ "kc=0.897## reliability factor\n",
+ "kd=1## temperature factor\n",
+ "ke=1## load factor\n",
+ "\n",
+ "Kt=1.4## under bending\n",
+ "\n",
+ "Kf=1+q*(Kt-1)## fatigue strength factor\n",
+ "kf=1/Kf ## fatigue strength reduction factor\n",
+ "Se=ka*kb*kc*kd*ke*kf*Se_dash## MPa( Endurance limit)\n",
+ "Mmax=Pmax*l## N.mm\n",
+ "Mmin=Pmin*l## N.mm\n",
+ "Mm=(Mmax+Mmin)/2## N.mm\n",
+ "Ma=(Mmax-Mmin)/2## N.mm\n",
+ "theta=atan(Ma/Mm)*180/pi## degree\n",
+ "\n",
+ "#equation of Goodman - sigma_m/Sut+sigma_a/Se=1\n",
+ "#here sigma_a/sigma_m=3\n",
+ "sigma_m=1/(1/Sut+3/Se)##MPa\n",
+ "sigma_a=3*sigma_m## MPa\n",
+ "\n",
+ "sigma_da=sigma_a/n## MPa\n",
+ "#sigma_da=32*Ma/pi/d**3\n",
+ "d=(32*Ma/pi/sigma_da)**(1/3)## mm \n",
+ "print ' \\n diameter d at fillet cross section = %.f mm'%(d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.8 Pg 112"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " diameter of shaft = 34 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,tan,atan\n",
+ "# Given Data\n",
+ "Sut=500##MPa\n",
+ "Syt=300##MPa\n",
+ "R=90/100## reliability\n",
+ "n=2## factor of safety\n",
+ "Tmin=-200## N.m\n",
+ "Tmax=500## N.m\n",
+ "\n",
+ "Se_dash = 0.5*Sut## MPa\n",
+ "# for cold drawn steel\n",
+ "ka=0.80## surface finish factor\n",
+ "kb=0.85## size factor (assuming t<50 mm)\n",
+ "kc=0.897## reliability factor\n",
+ "kd=1## temperature factor\n",
+ "ke=0.577## load factor\n",
+ "\n",
+ "Ses=ka*kb*kc*kd*ke*Se_dash## MPa( Endurance limit)\n",
+ "Sys=ke*Syt## MPa\n",
+ "Tm=(Tmax+Tmin)/2## N.m\n",
+ "Ta=(Tmax-Tmin)/2## N.m\n",
+ "theta=atan(Ta/Tm)*180/pi## degree\n",
+ "Sms=Ses/tan(pi/180*theta)##MPa\n",
+ "Sas=Ses##MPa\n",
+ "tau_da=Sas/n##MPa\n",
+ "#tua_da=16*Ta/pi/d**3\n",
+ "d=(16*Ta*1000/pi/tau_da)**(1/3)##mm\n",
+ "print ' \\n diameter of shaft = %.f mm'%(d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.9 Pg 113"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " life of the spring, N = 215630 cycles\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,log10\n",
+ "# Given Data\n",
+ "Sut=860##MPa\n",
+ "Syt=690##MPa\n",
+ "Pmin=60## N\n",
+ "Pmax=120## N\n",
+ "R=50/100## reliability\n",
+ "l=500##mm\n",
+ "d=10##mm\n",
+ "Se_dash = 0.5*Sut## MPa\n",
+ "# for machines surface\n",
+ "ka=0.70## surface finish factor\n",
+ "kb=0.85## size factor (assuming t<50 mm)\n",
+ "kc=1## reliability factor\n",
+ "kd=1## temperature factor\n",
+ "ke=1## load factor\n",
+ "\n",
+ "Se=ka*kb*kc*kd*ke*Se_dash## MPa( Endurance limit)\n",
+ "Mmax=Pmax*l## N.mm\n",
+ "Mmin=Pmin*l## N.mm\n",
+ "Mm=(Mmax+Mmin)/2## N.mm\n",
+ "Ma=(Mmax-Mmin)/2## N.mm\n",
+ "Sm=32*Mm/pi/d**3##MPa\n",
+ "sigma_m=Sm##MPa\n",
+ "Sa=32*Ma/pi/d**3##MPa\n",
+ "sigma_a=Sa##MPa\n",
+ "Sf=Sa*Sut/(Sut-Sm)##MPa\n",
+ "\n",
+ "#calculating section\n",
+ "OB=6##unit ref. o at 3\n",
+ "BE=OB-3##unit\n",
+ "OC=Sf## MPa\n",
+ "AE=log10(0.9*Sut)-log10(Se)##MPa\n",
+ "AC=log10(0.9*Sut)-log10(Sf)##MPa\n",
+ "CD=BE*AC/AE##\n",
+ "#log10(N)=3+CD\n",
+ "N=10**(3+CD)## cycle\n",
+ "print ' \\n life of the spring, N = %.f cycles'%(N)\n",
+ "#Note : answer in the textbook is wrong."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.10 Pg 116"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " factor of safety, n = 5.04\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,tan,pi,atan\n",
+ "# Given Data\n",
+ "Sut=600##MPa\n",
+ "Se=280##MPa\n",
+ "sigma_x_min=50## MPa\n",
+ "sigma_x_max=100## MPa\n",
+ "sigma_y_min=20## MPa\n",
+ "sigma_y_max=70## MPa\n",
+ "\n",
+ "sigma_xm=(sigma_x_max+sigma_x_min)/2## MPa\n",
+ "sigma_xa=(sigma_x_max-sigma_x_min)/2## MPa\n",
+ "sigma_ym=(sigma_y_max+sigma_y_min)/2## MPa\n",
+ "sigma_ya=(sigma_y_max-sigma_y_min)/2## MPa\n",
+ "\n",
+ "# distortion energy theory - \n",
+ "sigma_m=sqrt(sigma_xm**2+sigma_ym**2-sigma_xm*sigma_ym)## MPa\n",
+ "sigma_a=sqrt(sigma_xa**2+sigma_ya**2-sigma_xa*sigma_ya)## MPa\n",
+ "theta=atan(sigma_a/sigma_m)*180/pi## degree\n",
+ "# Sm/Sut+Sa/Se=1 where Sa=Sm*tan(theta)\n",
+ "Sm=1/(1/Sut+tan(pi/180*theta)/Se)## MPa\n",
+ "Sa=tan(pi/180*theta)*Sm## MPa\n",
+ "n=Sa/sigma_a## factor of safety\n",
+ "\n",
+ "print ' \\n factor of safety, n = %.2f'%(n)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.11 Pg 117"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " diameter of shaft, d = 32.71 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "Sut=600##MPa\n",
+ "Syt=400##MPa\n",
+ "Se=200##MPa\n",
+ "Mmin=200## N.m\n",
+ "Mmax=500## N.m\n",
+ "Tmin=60## N.m\n",
+ "Tmax=180## N.m\n",
+ "n=2## factor of safety\n",
+ "\n",
+ "Mm=(Mmax+Mmin)/2## N.mm\n",
+ "Ma=(Mmax-Mmin)/2## N.mm\n",
+ "Tm=(Tmax+Tmin)/2## N.mm\n",
+ "Ta=(Tmax-Tmin)/2## N.mm\n",
+ "# sigma_xm=32*Mm/pi/d**3\n",
+ "sigma_xm_into_d_cube=(32*Mm*1000)/pi#\n",
+ "# sigma_xa=32*Ma/pi/d**3\n",
+ "sigma_xa_into_d_cube=(32*Ma*1000)/pi#\n",
+ "#Txym=16*Tm/pi/d**3\n",
+ "Txym_into_d_cube=16*Tm*1000/pi#\n",
+ "#Txya=16*Ta/pi/d**3\n",
+ "Txya_into_d_cube=16*Ta*1000/pi#\n",
+ "# sigma_m=sqrt(sigma_xm**2+3*Txym**2)\n",
+ "sigma_m_dash=sqrt(sigma_xm_into_d_cube**2+3*Txym_into_d_cube**2)## taken sigma_m_dash = sigma_m*d**(-3) for calculation\n",
+ "# sigma_a=sqrt(sigma_xa**2+3*Txya**2)\n",
+ "sigma_a_dash=sqrt(sigma_xa_into_d_cube**2+3*Txya_into_d_cube**2)## taken sigma_a_dash = sigma_a*d**(-3) for calculation\n",
+ "#tan(theta) = sigma_a/sigma_m\n",
+ "theta = atan(sigma_a_dash/sigma_m_dash)## radian\n",
+ "#Sm/Sut+Sa/Se= 1 where Sa/Sm=0.4348 \n",
+ "Sm= 1/(1/Sut+0.4348/Se)## MPa\n",
+ "Sa=0.4348 * Sm## MPa\n",
+ "#sigma_a=Sa/n\n",
+ "d=(Sa/n/sigma_a_dash)**(1/3)*1000## mm\n",
+ "print ' \\n diameter of shaft, d = %.2f mm'%(d)\n",
+ "# Note - Ans in the textbook is wrong."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.12 Pg 119"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " diameter of shaft, d = 31.22 mm or 32 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,atan,ceil\n",
+ "# Given Data\n",
+ "Sut=620##MPa\n",
+ "Syt=380##MPa\n",
+ "R=90/100## Reliability\n",
+ "n=2.5## factor of safety\n",
+ "Tmin=-200## N.m\n",
+ "Tmax=400## N.m\n",
+ "\n",
+ "Se_dash=0.5*Sut##MPa\n",
+ "# for ground shaft\n",
+ "ka=0.92## surface finish factor\n",
+ "kb=0.85## size factor (assuming t<50 mm)\n",
+ "kc=0.897## reliability factor\n",
+ "kd=1## temperature factor\n",
+ "ke=0.577## load factor\n",
+ "Ses=ka*kb*kc*kd*ke*Se_dash## MPa( Endurance limit)\n",
+ "Sys=ke*Syt## MPa\n",
+ "Tm=(Tmax+Tmin)/2## N.mm\n",
+ "Ta=(Tmax-Tmin)/2## N.mm\n",
+ "theta=atan(Ta/Tm)##radian\n",
+ "Sas=Ses## MPa\n",
+ "Sms=Sas/3## MPa\n",
+ "#Tda=Sas/n=16*Ta/pi/d**3\n",
+ "d=(16*Ta*1000/pi/(Sas/n))**(1/3)## mm\n",
+ "print ' \\n diameter of shaft, d = %.2f mm or %d mm'%(d, ceil(d))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.14 Pg 121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Minimum required ultimate strength, Sut = 787.5 MPa\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "\n",
+ "# Given Data\n",
+ "sigma_max=300## MPa\n",
+ "sigma_min=-150## MPa\n",
+ "n=1.5## factor of safety\n",
+ "\n",
+ "\n",
+ "sigma_m=(sigma_max+sigma_min)/2## MPa\n",
+ "sigma_a=(sigma_max-sigma_min)/2## MPa\n",
+ "# Goodman failure line - sigma_m/Sut+sigma_a/Se=1/n\n",
+ "Sut=(sigma_m+sigma_a/(0.5))*n ## putted Se=0.5*Sut\n",
+ "print ' \\n Minimum required ultimate strength, Sut = %.1f MPa'%(Sut)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.16 Pg 122"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Size of piston rod, d = 25 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,sqrt\n",
+ "# Given Data\n",
+ "Pmin=-15## kN\n",
+ "Pmax=25## kN\n",
+ "Se_dash=360## MPa\n",
+ "Sy=400## MPa\n",
+ "Ki=1.25## impact factor\n",
+ "n=2.25## factor of safety\n",
+ "ka=0.88## surface finish factor\n",
+ "Kt=2.25## stress concentration factor\n",
+ "Pm=(Pmax+Pmin)/2## kN\n",
+ "Pa=(Pmax-Pmin)/2## kN\n",
+ "q=0.8## sensitivity factor\n",
+ "\n",
+ "# sigma_m=4*Pm/pi/d**2\n",
+ "sigma_m_into_d_sq = 4*Pm*1000/pi#\n",
+ "sigma_a_into_d_sq = 4*Pa*1000/pi#\n",
+ "Kf=1+q*(Kt-1)## fatigue strength factor\n",
+ "kf=1/Kf ## fatigue strength reduction factor\n",
+ "kb=0.85## size factor\n",
+ "ke=0.9##load factor\n",
+ "ki=1/Ki## reverse impact factor\n",
+ "Se=ka*kb*ke*kf*ki*Se_dash## MPa\n",
+ "#soderburg failure equation - sigma_m/Sy+sigma_a/Se=1/n\n",
+ "d=sqrt((sigma_m_into_d_sq/Sy+sigma_a_into_d_sq/Se)*n)\n",
+ "print ' \\n Size of piston rod, d = %.f mm'%(d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.18 Pg 123"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Suitable diameter of rod, d = 121 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,sqrt\n",
+ "# Given Data\n",
+ "Pmin=-300## kN\n",
+ "Pmax=700## kN\n",
+ "Se_dash=280## MPa\n",
+ "Sy=350## MPa\n",
+ "Kf=1.8##fatigue strength factor\n",
+ "n=2## factor of safety\n",
+ "\n",
+ "Pm=(Pmax+Pmin)/2## kN\n",
+ "Pa=(Pmax-Pmin)/2## kN\n",
+ "# sigma_m=4*Pm/pi/d**2\n",
+ "sigma_m_into_d_sq = 4*Pm*1000/pi#\n",
+ "sigma_a_into_d_sq = 4*Pa*1000/pi#\n",
+ "kf=1/Kf ## fatigue strength reduction factor\n",
+ "kb=0.85## size factor\n",
+ "ke=0.9##load factor\n",
+ "ka=0.93## surface finish factor\n",
+ "Se=ka*kb*ke*kf*Se_dash## MPa\n",
+ "#Goodman failure equation - sigma_m/Sy+sigma_a/Se=1/n\n",
+ "d=sqrt((sigma_m_into_d_sq/Sy+sigma_a_into_d_sq/Se)*2.25)\n",
+ "print ' \\n Suitable diameter of rod, d = %.f mm'%(d)\n",
+ "# Note - Ans in the textbook is wrong."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.19 Pg 124"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " thickness of plate, t = 12.5 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "\n",
+ "# Given Data\n",
+ "w=110## mm\n",
+ "Pmin=98.1## kN\n",
+ "Pmax=250## kN\n",
+ "Se=225## N/mm.sq\n",
+ "Sy=300## N/mm.sq\n",
+ "n=1.5## factor of safety\n",
+ "\n",
+ "Pm=(Pmax+Pmin)/2## kN\n",
+ "Pa=(Pmax-Pmin)/2## kN\n",
+ "# sigma_m=Pm/w/t\n",
+ "sigma_m_into_t = Pm/w#\n",
+ "sigma_a_into_t = Pa/w#\n",
+ "#Soderburg failure equation - sigma_m/Sy+sigma_a/Se=1/n\n",
+ "d=(sigma_m_into_t/Sy+sigma_a_into_t/Se)*n*1000## mm\n",
+ "print ' \\n thickness of plate, t = %.1f mm'%(d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.20 Pg 124"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " shaft size, d = 34 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "Mmin=200## kN.mm\n",
+ "Mmax=600## kN.mm\n",
+ "Tmin=60## kN\n",
+ "Tmax=180## kN\n",
+ "Su=550## MPa\n",
+ "Sy=400## MPa\n",
+ "Se=0.5*Su## MPa\n",
+ "n=1.5## factor of safety\n",
+ "Ktb=1.5## stress concentration factor in blending\n",
+ "Kts=1.2## stress concentration factor in torsion\n",
+ "\n",
+ "Mm=(Mmax+Mmin)/2## kN.mm\n",
+ "Ma=(Mmax-Mmin)/2## kN.mm\n",
+ "\n",
+ "#sigma_xm=32*Mm/pi/d**3\n",
+ "sigma_xm_into_d_cube=32*Mm/pi#\n",
+ "#sigma_xa=32*Ma/pi/d**3\n",
+ "sigma_xa_into_d_cube=32*Ma/pi#\n",
+ "Tm=(Tmax+Tmin)/2## kN.mm\n",
+ "Ta=(Tmax-Tmin)/2## kN.mm\n",
+ "Txym_into_d_cube=16*Tm/pi#\n",
+ "Txya_into_d_cube=16*Ta/pi#\n",
+ "# using distortion energy theory\n",
+ "# sigma_m=sqrt(sigma_xm**2+3*Txym**2)\n",
+ "sigma_m_into_d_cube=sqrt(sigma_xm_into_d_cube**2+3*Txym_into_d_cube**2)#\n",
+ "# sigma_a=sqrt((Ktb*sigma_xa)**2+3*(Kts*Txym)**2)\n",
+ "sigma_a_into_d_cube=sqrt((Ktb*sigma_xa_into_d_cube)**2+3*(Kts*Txya_into_d_cube)**2)#\n",
+ "# Sodeburg equation - sigma_m + (Su/Se)*sigma_a=Sy/n\n",
+ "d=((sigma_m_into_d_cube + (Su/Se)*sigma_a_into_d_cube)*1000/(Sy/n))**(1/3)\n",
+ "print ' \\n shaft size, d = %.f mm'%(d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 4.21 Pg 126"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Calculating for hole - \n",
+ " thickness is : 10.24 mm\n",
+ " \n",
+ " Calculating for notch - \n",
+ " thickness is : 9.58 mm\n",
+ " Suggestion, Adopt t = 11 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "\n",
+ "# Given Data\n",
+ "# Hole -\n",
+ "d=25##mm\n",
+ "w=150##mm\n",
+ "Kt=2.56## stress concentration factor\n",
+ "P=50## kN\n",
+ "sigma_max=100## N/mm.sq\n",
+ "t=Kt*P*1000/(w-d)/sigma_max## mm\n",
+ "print ' Calculating for hole - \\n thickness is : %.2f mm'%(t)\n",
+ "\n",
+ "# Notch -\n",
+ "d=30##mm\n",
+ "w=120##mm\n",
+ "w=150##mm\n",
+ "Kt=2.3## stress concentration factor\n",
+ "P=50## kN\n",
+ "sigma_max=100## N/mm.sq\n",
+ "t=Kt*P*1000/(w-d)/sigma_max## mm\n",
+ "print ' \\n Calculating for notch - \\n thickness is : %.2f mm'%(t)\n",
+ "print ' Suggestion, Adopt t = 11 mm'"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Machine_Design-I_by_Dr._Sadhu_Singh/chapter5.ipynb b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter5.ipynb
new file mode 100644
index 00000000..208c11ea
--- /dev/null
+++ b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter5.ipynb
@@ -0,0 +1,671 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 5 - Riveted Joints"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 5.1 Pg 142"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " DESIGNING LONGITUDINAL JOINT - \n",
+ "\n",
+ " \n",
+ " Plate Thickness\n",
+ " , t = 30.30 mm\n",
+ " \n",
+ " use t = 32 mm\n",
+ " \n",
+ " Diameter of rivet hole, do = \n",
+ " 33.94 mm\n",
+ " \n",
+ " Use do = 34 mm\n",
+ " \n",
+ " Diameter of rivet, d = \n",
+ " 33.00 mm\n",
+ " \n",
+ " Pitch of rivets, p = \n",
+ " 220.7 mm\n",
+ " \n",
+ " as per IBR-\n",
+ " pitch, pmax = 232 mm\n",
+ " \n",
+ " Use p = 220 mm\n",
+ " \n",
+ " pitch of rivets in inner row, pi = 110 mm\n",
+ " \n",
+ " distance between outer and adjacent row = 82.5 mm\n",
+ " \n",
+ " take & use this distance = 85 mm\n",
+ " \n",
+ " distance between inner row for zig-zag riveting = 59.4 mm\n",
+ " \n",
+ " take & use this distance = 60 mm\n",
+ " \n",
+ " Thickness of wide butt strap, t= \n",
+ " 24 mm\n",
+ " \n",
+ " Thickness of narrow butt strap, t= 20 mm\n",
+ " \n",
+ " margin, m = 52 mm\n",
+ " \n",
+ " strength of the joint = 2350472 N\n",
+ " \n",
+ " strength of solid plate = 563200 N\n",
+ " \n",
+ " Efficiency of joint, eta_l = 417.3 %\n",
+ " \n",
+ "\n",
+ " DESIGNING CIRCUMFERENTIAL JOINT- \n",
+ "\n",
+ " \n",
+ " Plate Thickness\n",
+ " , t = 32.00 mm\n",
+ " \n",
+ " Diameter of rivet hole, do = \n",
+ " 34.50 mm\n",
+ " \n",
+ " Diameter of rivet, d = \n",
+ " 33.00 mm\n",
+ " \n",
+ " no. of rivets = 78.8\n",
+ " \n",
+ " take n = 80\n",
+ " \n",
+ " pitch of rivets, pc = 4213.00 mm\n",
+ " use pc = 4213 mm\n",
+ " \n",
+ " Efficiency of joint, eta_c = 99.18 %\n",
+ " \n",
+ " for zig-zag riveting, distance between rows of rivets = 1413.4 mm. use 65 mm\n",
+ " \n",
+ " margin, m = 52 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,sqrt,ceil\n",
+ "# Given Data\n",
+ "ps=2.5## MPa\n",
+ "D=1.5##m\n",
+ "sigma_t=80## MPa\n",
+ "tau=60## MPa\n",
+ "sigma_c=120## MPa\n",
+ "n=5## no. of rivets\n",
+ "\n",
+ "print ' DESIGNING LONGITUDINAL JOINT - \\n'\n",
+ "print ' \\n Plate Thickness'\n",
+ "eta_l=80## % (efficiency)\n",
+ "t = ps*D*1000/2/sigma_t/(eta_l/100)+1## mm\n",
+ "print ' , t = %.2f mm'%(t)\n",
+ "t=32##mm (adopted for design)\n",
+ "print ' \\n use t = %d mm'%(t)\n",
+ "print ' \\n Diameter of rivet hole, do = '\n",
+ "d0=6*sqrt(t)##mm (for t>8 mm)\n",
+ "print ' %.2f mm'%(d0)\n",
+ "d0=34.5## suggested for design\n",
+ "print ' \\n Use do = %.f mm'%(d0)\n",
+ "print ' \\n Diameter of rivet, d = '\n",
+ "d=d0-1.5##mm \n",
+ "print ' %.2f mm'%(d)\n",
+ "print ' \\n Pitch of rivets, p = '\n",
+ "Ps=(4*1.875+1)*pi/4*d0**2*tau## N\n",
+ "# Putting Pt=Ps where Pt=(p-d0)*t*sigma_t## N\n",
+ "Pt=Ps##N\n",
+ "p=Pt/(t*sigma_t)+d0## N\n",
+ "print ' %.1f mm'%(p)\n",
+ "C=6## for 5 no. of rivets\n",
+ "pmax=C*t+40## mm (as per IBR)\n",
+ "print ' \\n as per IBR-\\n pitch, pmax = %.f mm'%(pmax)\n",
+ "p=220## mm (adopted for design)\n",
+ "print ' \\n Use p = %.f mm'%(p)\n",
+ "pi=p/2## mm \n",
+ "print ' \\n pitch of rivets in inner row, pi = %.f mm'%(pi)\n",
+ "\n",
+ "#Distance between rows of rivets\n",
+ "dis1=0.2*p+1.115*d0## mm \n",
+ "print ' \\n distance between outer and adjacent row = %.1f mm'%(dis1)\n",
+ "dis1=85##mm (adopted for design)\n",
+ "print ' \\n take & use this distance = %.f mm'%( dis1)\n",
+ "dis2=0.165*p+0.67*d0## mm \n",
+ "print ' \\n distance between inner row for zig-zag riveting = %.1f mm'%( dis2)\n",
+ "dis2=60##mm (adopted for design)\n",
+ "print ' \\n take & use this distance = %.f mm'%( dis2)\n",
+ "print ' \\n Thickness of wide butt strap, t= '\n",
+ "t1=0.75*t## mm (wide butt strap)\n",
+ "print ' %.f mm'%(t1)\n",
+ "t2=0.625*t## mm (narrow butt strap)\n",
+ "print ' \\n Thickness of narrow butt strap, t= %.f mm'%(t2)\n",
+ "#margin\n",
+ "m=ceil(1.5*d0)## mm\n",
+ "print ' \\n margin, m = %.f mm'%(m)\n",
+ "# Efficiency of joint\n",
+ "Pt=(p-d0)*t*sigma_t## N\n",
+ "Ps=Ps## N (shearing resistance of rivets)\n",
+ "Pc=n*d0*t*sigma_c## N (crushing resistance of rivets)\n",
+ "sigma_com = (p-2*d0)*t*sigma_t+pi/4*d0**2*tau## N\n",
+ "print ' \\n strength of the joint = %d N'%(sigma_com)\n",
+ "P=p*t*sigma_t##N (strength of solid plate)\n",
+ "print ' \\n strength of solid plate = %d N'%(P)\n",
+ "eta_l=sigma_com/P*100## % (efficiency)\n",
+ "print ' \\n Efficiency of joint, eta_l = %.1f %%'%(eta_l)\n",
+ "\n",
+ "print ' \\n\\n DESIGNING CIRCUMFERENTIAL JOINT- \\n'\n",
+ "t=32## mm\n",
+ "d0=34.5##mm\n",
+ "d=33##mm\n",
+ "print ' \\n Plate Thickness'\n",
+ "print ' , t = %.2f mm'%(t)\n",
+ "print ' \\n Diameter of rivet hole, do = '\n",
+ "print ' %.2f mm'%(d0)\n",
+ "print ' \\n Diameter of rivet, d = '\n",
+ "print ' %.2f mm'%(d) \n",
+ "n=(D*1000/d0)**2*(ps/tau)## no. of rivets\n",
+ "print ' \\n no. of rivets = %.1f'%(n)\n",
+ "n=80## adopted for design\n",
+ "print ' \\n take n = %d'%(n)\n",
+ "# Pitch of rivets\n",
+ "n1=n/2## no. of rivets per row\n",
+ "pc=pi*(D*1000+t)/n1## mm (pitch of rivets)\n",
+ "print ' \\n pitch of rivets, pc = %.2f mm\\n use pc = %.f mm'%(pc,pc)\n",
+ "eta_c=(pc-d0)/pc*100## % (efficiency of joint)\n",
+ "print ' \\n Efficiency of joint, eta_c = %.2f %%'%(eta_c)\n",
+ "dis=0.33*pc+0.67*d0## mm (distance between rows of rivets)\n",
+ "print ' \\n for zig-zag riveting, distance between rows of rivets = %.1f mm. use 65 mm'%( dis)\n",
+ "m=1.5*d0## mm (Margin)\n",
+ "print ' \\n margin, m = %.f mm'%(m)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 5.2 Pg 147"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Diameter of rivet, do = \n",
+ " 26.83 mm\n",
+ " \n",
+ " Standard diameter of rivet hole, do = 29 mm & corresponding diameter of rivet = 27 mm\n",
+ " \n",
+ " no. of rivets, n = 9.629. Use n = 10 \n",
+ " \n",
+ " thickness of inner butt strap, t1 = 15 mm\n",
+ " \n",
+ " thickness of outer butt strap, t2 = 15 mm\n",
+ " \n",
+ " efficiency of joint = 92.75 %\n",
+ " \n",
+ " pitch of rivets = 92 mm. Use 100 mm\n",
+ " \n",
+ " margin,\n",
+ " m = 43.5 mm. Use 50 mm\n",
+ " \n",
+ " w = 400 mm\n",
+ " \n",
+ " distance between rows = 72.5 mm. Use 75 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,ceil\n",
+ "# Given Data\n",
+ "w=400##mm\n",
+ "t=20##mm\n",
+ "sigma_t=90## MPa\n",
+ "tau=60## MPa\n",
+ "sigma_c=140## MPa\n",
+ "\n",
+ "print ' \\n Diameter of rivet, do = '\n",
+ "d0=6*sqrt(t)##mm (for t>8 mm)\n",
+ "print ' %.2f mm'%(d0)\n",
+ "d0=29##mm (standard)\n",
+ "print ' \\n Standard diameter of rivet hole, do = %.f mm & corresponding diameter of rivet = 27 mm'%(d0)\n",
+ "Pt=(w-d0)*t*sigma_t##N max. tearing strength of plate\n",
+ "Ps=1.75*pi/4*d0**2*tau## N (shearing strength of one rivet)\n",
+ "n1=Pt/Ps## no. of rivets\n",
+ "n=ceil(n1)#\n",
+ "print ' \\n no. of rivets, n = %.3f. Use n = %.f '%(n1,n)\n",
+ "t1=0.75*t## mm\n",
+ "t2=t1## mm\n",
+ "print ' \\n thickness of inner butt strap, t1 = %.f mm'%( t1)\n",
+ "print ' \\n thickness of outer butt strap, t2 = %.f mm'%( t2)\n",
+ "# section 1-1 \n",
+ "P1=(w-d0)*t*sigma_t##N\n",
+ "# section 2-2 \n",
+ "P2=(w-2*d0)*t*sigma_t+1.75*pi/4*d0**2*tau##N\n",
+ "# section 3-3 \n",
+ "P3=(w-3*d0)*t*sigma_t+1.75*3*pi/4*d0**2*tau##N\n",
+ "# section 4-4\n",
+ "P4=(w-4*d0)*t*sigma_t+1.75*6*pi/4*d0**2*tau##N\n",
+ "Ps=10*Ps## N (shearing stress of all rivets)\n",
+ "Pc=10*d0*t*sigma_c## N (shearing stress of all rivets)\n",
+ "Pj=P1## N (strength f joint)\n",
+ "P = w*t*sigma_t## N (strength of solid plate)\n",
+ "eta=P1/P*100# # % (efficiency of joint)\n",
+ "print ' \\n efficiency of joint = %.2f %%'%( eta)\n",
+ "p1=3*d0+5## mm (pitch of rivets)\n",
+ "p=100##mm (adopt for design)\n",
+ "print ' \\n pitch of rivets = %.f mm. Use %.f mm'%(p1,p)\n",
+ "m1=1.5*d0## mm (margin)\n",
+ "m=50##mm\n",
+ "w=3*p+2*m## mm\n",
+ "print ' \\n margin,\\n m = %.1f mm. Use %.f mm'%( m1,m)\n",
+ "print ' \\n w = %.f mm'%(w)\n",
+ "dis=2.5*d0## mm\n",
+ "print ' \\n distance between rows = %.1f mm. Use 75 mm'%(dis)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 5.3 Pg 150"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " diameter of rivets = 16.99 mm. Use d0 = 17.5 mm & d=16 mm for design.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,ceil,acos,cos\n",
+ "# Given Data\n",
+ "n=6## no. of rivets\n",
+ "P=54## kN\n",
+ "e=200##mm \n",
+ "a=50##mm (from fig.5.13(a))\n",
+ "b=100##mm (from fig.5.13(a))\n",
+ "tau=120## MPa\n",
+ "\n",
+ "Pd=P/n*1000## N (direct shear load in rivet)\n",
+ "C=P*e## kN.mm (Couple)\n",
+ "#l1=l3=l4=l6\n",
+ "l1=sqrt(a**2+b**2)## mm\n",
+ "l3=l1#l4=l1#l6=l1#mm\n",
+ "l2=a#l5=a##mm\n",
+ "# F1/l1*(4*l1**2+2*l2**2)=C\n",
+ "F1=C*1000/(4*l1**2+2*l2**2)*l1## N\n",
+ "theta1=acos(a/l1)## radian\n",
+ "R1=sqrt(Pd**2+F1**2+2*Pd*F1*cos(theta1))## N (resultant force in rivet 1)\n",
+ "#R1=pi/4*d0**2*tau\n",
+ "d0=sqrt(R1/(pi/4*tau))## mm\n",
+ "print ' \\n diameter of rivets = %.2f mm. Use d0 = 17.5 mm & d=16 mm for design.'%(d0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 5.4 Pg 151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " DESIGNING LONGITUDINAL JOINT - \n",
+ "\n",
+ " \n",
+ " Plate Thickness\n",
+ " , t = 9.61 mm\n",
+ " \n",
+ " use t = 10 mm\n",
+ " \n",
+ " Diameter of rivet hole, do = \n",
+ " 18.97 mm\n",
+ " \n",
+ " Use do = 19.5 mm\n",
+ " \n",
+ " Diameter of rivet, d = \n",
+ " 18.00 mm\n",
+ " \n",
+ " Pitch of rivets, p = \n",
+ " 89.18 mm\n",
+ " \n",
+ " as per IBR-\n",
+ " pitch, pmax = 75 mm\n",
+ " \n",
+ " Use p = 75 mm\n",
+ " \n",
+ " distance between rows of rivets = 37.8 mm\n",
+ " \n",
+ " take & use this distance = 40 mm\n",
+ " \n",
+ " Thickness of butt strap, t= \n",
+ " 6.25 mm\n",
+ " \n",
+ " Use thickness = 7 mm\n",
+ " \n",
+ " margin, m = 30 mm\n",
+ " \n",
+ " strength of the joint = 49950 N\n",
+ " \n",
+ " strength of solid plate = 67500 N\n",
+ " \n",
+ " Efficiency of joint, eta_l = 74.00 % = 75 % as given\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import ceil,sqrt,pi\n",
+ "# Given Data\n",
+ "D=0.75##m\n",
+ "ps=1.55## N/mm.sq\n",
+ "eta_l=0.75## efficiency\n",
+ "sigma_t=90## MPa\n",
+ "sigma_c=140## MPa\n",
+ "tau=56## MPa\n",
+ "n=2## no. of rivets\n",
+ "\n",
+ "print ' DESIGNING LONGITUDINAL JOINT - \\n'\n",
+ "print ' \\n Plate Thickness'\n",
+ "t = ps*D*1000/2/sigma_t/eta_l+1## mm\n",
+ "print ' , t = %.2f mm'%(t)\n",
+ "t=ceil(t)##mm (adopted for design)\n",
+ "print ' \\n use t = %d mm'%(t)\n",
+ "\n",
+ "print ' \\n Diameter of rivet hole, do = '\n",
+ "d0=6*sqrt(t)##mm (for t>8 mm)\n",
+ "print ' %.2f mm'%(d0)\n",
+ "d0=19.5## suggested for design\n",
+ "print ' \\n Use do = %.1f mm'%(d0)\n",
+ "print ' \\n Diameter of rivet, d = '\n",
+ "d=d0-1.5##mm \n",
+ "print ' %.2f mm'%(d)\n",
+ "\n",
+ "print ' \\n Pitch of rivets, p = '\n",
+ "Ps=(2*1.875)*pi/4*d0**2*tau## N\n",
+ "# Putting Pt=Ps where Pt=(p-d0)*t*sigma_t## N\n",
+ "Pt=Ps##N\n",
+ "p=Pt/(t*sigma_t)+d0## N\n",
+ "print ' %.2f mm'%(p)\n",
+ "C=3.5## for 2 no. of rivets\n",
+ "pmax=C*t+40## mm (as per IBR)\n",
+ "print ' \\n as per IBR-\\n pitch, pmax = %.f mm'%(pmax)\n",
+ "p=75## mm (adopted for design)\n",
+ "print ' \\n Use p = %.f mm'%(p)\n",
+ "\n",
+ "#Distance between rows of rivets\n",
+ "dis=0.33*p+0.67*d0## mm \n",
+ "print ' \\n distance between rows of rivets = %.1f mm'%(dis)\n",
+ "dis=40##mm (adopted for design)\n",
+ "print ' \\n take & use this distance = %.f mm'%( dis)\n",
+ "\n",
+ "print ' \\n Thickness of butt strap, t= '\n",
+ "t1=0.625*t## mm\n",
+ "print ' %.2f mm'%(t1)\n",
+ "t1=7## mm (adopted for design)\n",
+ "print ' \\n Use thickness = %.f mm'%(t1)\n",
+ "\n",
+ "#margin\n",
+ "m=ceil(1.5*d0)## mm\n",
+ "print ' \\n margin, m = %.f mm'%(m)\n",
+ "\n",
+ "# Efficiency of joint\n",
+ "Pt=(p-d0)*t*sigma_t## N\n",
+ "Ps=Ps## N (shearing resistance of rivets)\n",
+ "Pc=n*d0*t*sigma_c## N (crushing resistance of rivets)\n",
+ "sigma_com = (p-2*d0)*t*sigma_t+pi/4*d0**2*tau## N\n",
+ "print ' \\n strength of the joint = %d N'%(Pt)\n",
+ "P=p*t*sigma_t##N (strength of solid plate)\n",
+ "print ' \\n strength of solid plate = %d N'%(P)\n",
+ "eta_l=Pt/P*100## % (efficiency)\n",
+ "print ' \\n Efficiency of joint, eta_l = %.2f %% = 75 %% as given'%(eta_l)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 5.6 Pg 153"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " diameter of rivets = 22.81 mm. Use d0 = 21.5 mm & d=20 mm for design.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import cos,pi,sqrt,sin,atan,tan\n",
+ "# Given Data\n",
+ "n=5## no. of rivets\n",
+ "P=45## kN\n",
+ "alfa=30## degree\n",
+ "tau=120## MPa\n",
+ "\n",
+ "\n",
+ "Pd=P/n*1000## N (direct shear load in rivet)\n",
+ "# C.G. of rivet group\n",
+ "# values below are collected direct from figure\n",
+ "x_bar=(3*200)/5## mm\n",
+ "y_bar=(1*50+1*150+1*100+1*200)/5## mm\n",
+ "ex=300+x_bar+y_bar##mm\n",
+ "ey=100##mm\n",
+ "l1=sqrt(x_bar**2+(y_bar/2)**2)## mm\n",
+ "l2=l1##mm\n",
+ "l3=sqrt(100**2+80**2)## mm\n",
+ "l4=80##mm\n",
+ "l5=l3##mm\n",
+ "\n",
+ "#2*F1*l1+2*F3*l3+F4*l4=P*cos(alfa)*ex+P*sin(alfa)*ey\n",
+ "F1=(P*1000*cos(pi/180*alfa)*ex+P*1000*sin(pi/180*alfa)*ey)/(2*l1**2+2*l3**2+l4**2)*l1##N\n",
+ "# rivet 1 is nearest\n",
+ "Beta = atan(x_bar/(y_bar/2))*180/pi## degree\n",
+ "theta1=Beta-(90-alfa)## degree\n",
+ "R1=sqrt(Pd**2+F1**2+2*Pd*F1*cos(pi/180*theta1))## N (resultant force in rivet 1)\n",
+ "#R1=pi/4*d0**2*tau\n",
+ "d0=sqrt(R1/(pi/4*tau))## mm\n",
+ "print ' \\n diameter of rivets = %.2f mm. Use d0 = 21.5 mm & d=20 mm for design.'%(d0)\n",
+ "# Note - Ans in the textbook is wrong."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 5.7 Pg 155"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Diameter of rivets, d0 = 11.46 mm. Take d0=13.5 mm & d=12 mm\n",
+ " \n",
+ " Distance between rows of rivet = 35.2 mm = 35 mm\n",
+ " \n",
+ " back pitch = 21 mm\n",
+ " \n",
+ " tearing strength = 28380 N\n",
+ " \n",
+ " shearing strength = 28628 N\n",
+ " \n",
+ " crushing strength = 24300 N\n",
+ " \n",
+ " joint strength = 24300 N\n",
+ " \n",
+ " strength of solid plate = 46200 N\n",
+ " \n",
+ " efficiency of joint = 52.6 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,sqrt,floor\n",
+ "# Given Data\n",
+ "t=6##mm\n",
+ "sigma_t=220## MPa\n",
+ "tau=100## MPa\n",
+ "sigma_c=150## MPa\n",
+ "n=2## no. of rivets / pitch length\n",
+ "#Ps=n*pi/4**d0**2*tau## shearing strength of rivets\n",
+ "#Pc=2*d0*t*sigma_c## Crushing strength of rivets\n",
+ "d0=2*t*sigma_c/(n*pi/4*tau)## mm (equating Ps=Pc)\n",
+ "print ' Diameter of rivets, d0 = %.2f mm. Take d0=13.5 mm & d=12 mm'%(d0)\n",
+ "d0=13.5##mm\n",
+ "d=12##mm\n",
+ "#Pt=(p-d0)*t*sigma_t## tearing strength\n",
+ "# equating Pt=Ps\n",
+ "#p= n*pi/4**d0**2*tau/(t*sigma_t)+d0##mm\n",
+ "p= n*pi/4*d0**2*tau/(t*sigma_t)+d0\n",
+ "print ' \\n Distance between rows of rivet = %.1f mm = %.f mm'%(p,p)\n",
+ "p=floor(p)##mm\n",
+ "pb=0.6*p##mm (back pitch)\n",
+ "print ' \\n back pitch = %.f mm'%(pb)\n",
+ "Pt=(p-d0)*t*sigma_t## N (tearing strength)\n",
+ "print ' \\n tearing strength = %.f N'%(Pt)\n",
+ "Ps=n*pi/4*d0**2*tau## N ( shearing strength)\n",
+ "print ' \\n shearing strength = %.f N'%(Ps)\n",
+ "Pc=2*d0*t*sigma_c##N (Crushing strength of rivets)\n",
+ "print ' \\n crushing strength = %.f N'%(Pc)\n",
+ "joint_strength = Pc## N\n",
+ "print ' \\n joint strength = %.f N'%(joint_strength)\n",
+ "P=p*t*sigma_t##N (strength of solid plate)\n",
+ "print ' \\n strength of solid plate = %.f N'%(P)\n",
+ "eta = joint_strength/P*100## % (efficiency)\n",
+ "print ' \\n efficiency of joint = %.1f %%'%( eta)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 5.8 Pg 156"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Diameter of rivets - \n",
+ " d0 = 11.654 mm\n",
+ " \n",
+ " Use d0 = 13.5 mm & d = 12 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "P=20## kN\n",
+ "e=80##mm\n",
+ "tau=150## MPa\n",
+ "\n",
+ "\n",
+ "Pd=P/4## kN\n",
+ "C=P*e## kN.mm (Couple)\n",
+ "# As C.G. lies at 45mm from top rivet\n",
+ "l1=45;l4=45##mm \n",
+ "l2=15;l3=15##mm\n",
+ "#(F1/l1)*(2*l1*l4+2*l2*l3) = C\n",
+ "F1= C*1000/(2*l1*l4+2*l2*l3)*l1##N\n",
+ "R1=sqrt(Pd**2+F1**2)## N\n",
+ "#R1=pi/4*d0**2*tau\n",
+ "d0=sqrt(R1/(pi/4*tau))##mm\n",
+ "print ' Diameter of rivets - \\n d0 = %.3f mm'%(d0)\n",
+ "print ' \\n Use d0 = 13.5 mm & d = 12 mm'"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Machine_Design-I_by_Dr._Sadhu_Singh/chapter6.ipynb b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter6.ipynb
new file mode 100644
index 00000000..8ce118a6
--- /dev/null
+++ b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter6.ipynb
@@ -0,0 +1,478 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 6 - Shafts"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6.1 Pg 168"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " shaft diameter = 43.13 mm. Use diameter = 45 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt, pi\n",
+ "# Given Data\n",
+ "Sut=650## MPa\n",
+ "Syt=380## MPa\n",
+ "F1BYF2 = 2.5## ratio of tensions\n",
+ "Fmax=2.5## kN\n",
+ "da=200## mm\n",
+ "db=400## mm\n",
+ "L=1*1000##mm\n",
+ "Km=1.5## fatigue factor\n",
+ "Kt=1## shock factor\n",
+ "\n",
+ "\n",
+ "tau_d1=0.30*Syt## MPa\n",
+ "tau_d2=0.18*Sut## MPa\n",
+ "tau_d=min(tau_d1, tau_d2)## MPa (taking minimum value)\n",
+ "tau_d=0.75*tau_d##MPa (Accounting keyway effect)\n",
+ "\n",
+ "# Pulley A\n",
+ "F1=2500## N\n",
+ "F2=1000## N\n",
+ "T=(F1-F2)*da/2## N.mm\n",
+ "Fa=F1+F2## N (resultant pull Downwards)\n",
+ "\n",
+ "# Pulley B\n",
+ "# F3 & F4 are tension in belt (assumed)\n",
+ "#T=(F3-F4)*db/2\n",
+ "SUB_F3F4 = 2*T/db## N (where SUB_F3F4 = F3-F4) --eqn(1)\n",
+ "F3BYF4=F1BYF2## ratio of tensions --eqn(2)\n",
+ "F4 = SUB_F3F4/(F3BYF4-1)## N (using above 2 equations)\n",
+ "F3=F3BYF4*F4## N\n",
+ "\n",
+ "Fb=F3+F4## N (resultant pull right side( -->))\n",
+ "\n",
+ "# BENDING MOMENTS -\n",
+ "Mav=Fa*L/4## N.mm (vertical force)\n",
+ "Mc=Fb*da## N.mm\n",
+ "Mah=Mc/2## N.mm (vertical force)\n",
+ "M = sqrt(Mav**2+Mah**2)## N.mm (resultant bending moment at A)\n",
+ "d=((16/pi/tau_d)*sqrt((Km*M)**2+(Kt*T)**2))**(1/3)## mm \n",
+ "\n",
+ "print ' shaft diameter = %.2f mm. Use diameter = 45 mm.'%(d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6.2 Pg 170"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " shaft diameter = 34.81 mm. Use 35 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "Tmax=400## N.m\n",
+ "Tmin=140## N.m\n",
+ "Mmax=500## N.m\n",
+ "Mmin=250## N.m\n",
+ "Sut=540## MPa\n",
+ "Syt=400## MPa\n",
+ "n=2## factor of safety\n",
+ "Kf=1.25## given\n",
+ "\n",
+ "Se_dash=0.4*Sut## Mpa\n",
+ "Se=Se_dash/Kf##MPa\n",
+ "Sys=0.577*Syt## MPa\n",
+ "Ses=0.577*Se## MPa\n",
+ "Mm=(Mmax+Mmin)/2## N.m\n",
+ "Ma=(Mmax-Mmin)/2## N.m\n",
+ "Tm=(Tmax+Tmin)/2## N.m\n",
+ "Ta=(Tmax-Tmin)/2## N.m\n",
+ "# Max. Distortion energy theory - Syt/n = 32/pi/d**3*sqrt((Mm+Ma*(Syt/Se)**2)+0.75*(Tm+Ta*(Sys/Ses))**2)\n",
+ "d = (32/pi*sqrt((Mm+Ma*(Syt/Se))**2+0.75*(Tm+Ta*(Sys/Ses))**2)*1000/(Syt/n))**(1/3) # # mm\n",
+ "print ' shaft diameter = %.2f mm. Use %.f mm.'%(d,d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6.3 Pg 171"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " shaft diameter = 14.1 mm. Use 15 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi, ceil\n",
+ "# Given Data\n",
+ "P=5## kW\n",
+ "N=1000## rpm\n",
+ "Syt=300## N/mm.sq.\n",
+ "n=2## factor of safety\n",
+ "v=0.25## Poisson's ratio\n",
+ "\n",
+ "#P=2*pi*N*T/(60*1000)\n",
+ "T=P/(2*pi*N/(60*1000))## N.m\n",
+ "#tau = 16*T/pi/d**3 # shear stress & sigma1 = tau#sigma2=0#sigma3=-tau\n",
+ "# max. shear strain energy theory, sigma1**2+sigma3**2+(sigma3-sigma1)**2=2*(Syt/n)**2 \n",
+ "d=(16*T*1000/pi/sqrt(2/6*(Syt/n)**2))**(1/3)## mm (putting values of tau)\n",
+ "print ' shaft diameter = %.1f mm. Use %.f mm.'%(d,ceil(d))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6.4 Pg 171"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " shaft diameter(using ASME Code) = 46.7 mm. Use diameter = 47 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,tan\n",
+ "# Given Data\n",
+ "Sut=700## MPa\n",
+ "Syt=460## Mpa\n",
+ "F1BYF2=3## ratio of tensions\n",
+ "dg=300## mm\n",
+ "dp=400## mm\n",
+ "P=25## kW\n",
+ "N=600## rpm\n",
+ "alfa=20## degree\n",
+ "Km=1.5## fatigue factor\n",
+ "Kt=1.5## shock factor\n",
+ "\n",
+ "tau_d1=0.30*Syt## MPa\n",
+ "tau_d2=0.18*Sut## MPa\n",
+ "tau_d=min(tau_d1, tau_d2)## MPa (taking minimum value)\n",
+ "tau_d=0.75*tau_d##MPa (Accounting keyway effect)\n",
+ "\n",
+ "# Pulley D\n",
+ "# P= 2*pi*N*T/60\n",
+ "T=P/(2*pi*N/(60*1000))## N.m\n",
+ "# (F1-F2)*dp/2=T\n",
+ "SUB_F1F2 = T*2/dp## N (where SUB_F1F2 = F1-F2)\n",
+ "F2 = SUB_F1F2/(F1BYF2-1) ## N (putting value of ratio)\n",
+ "F1=F1BYF2*F2## N\n",
+ "F=F1+F2## N \n",
+ "# Gear B\n",
+ "Ft=T*2/dg## N\n",
+ "Fr=Ft*tan(alfa*pi/180)## N\n",
+ "\n",
+ "# Bearing Reactions\n",
+ "\n",
+ "#Vertical forces\n",
+ "#RA*2*dg+Fr*dg=F*dg#\n",
+ "RA=(F*dg-Fr*dg)/(2*dg)## N (downwards)\n",
+ "RC=RA+Fr+F## N (upwards)\n",
+ "MA=0;MB_v=-RA*dg## N.mm\n",
+ "MC=-F*dg## N.mm\n",
+ "#Horizontal forces\n",
+ "MB_h=Ft*2*dg/4## N.mm\n",
+ "#Resultant B.M at B\n",
+ "MB=sqrt(MB_v**2+MB_h**2)## N.mm\n",
+ "Mmax=MC##N.mm\n",
+ "T=T*1000## N.mm\n",
+ "# d**3=16/pi/tau_d*sqrt((Km*M)**2+(Kt*T)**2)\n",
+ "d=(16/pi/tau_d*sqrt((Km*Mmax*1000)**2+(Kt*T)**2))**(1/3)\n",
+ "print ' shaft diameter(using ASME Code) = %.1f mm. Use diameter = %.f mm.'%(d,d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6.5 Pg 174"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " shaft diameter(using ASME Code) = 51.0 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,tan\n",
+ "# Given Data\n",
+ "L=1000## mm\n",
+ "alfa=20## degree\n",
+ "dg=500## mm\n",
+ "L1=250## mm\n",
+ "L2=300## mm\n",
+ "dp=600## mm\n",
+ "Wp=2000## N\n",
+ "F1=2.5*1000## N\n",
+ "F1BYF2=3## ratio of tensions\n",
+ "tau_d=42## MPa\n",
+ "\n",
+ "F2=F1/F1BYF2## N\n",
+ "T=(F1-F2)*dp/2## N.mm\n",
+ "Ftg=2*T/dg## N\n",
+ "Frg=Ftg*tan(alfa*pi/180)## N\n",
+ "F=F1+F2## N\n",
+ "\n",
+ "# Vertical Loads\n",
+ "RAV=(Ftg*(L1+dg)+Wp*L2)/L## N\n",
+ "RBV=Ftg+Wp-RAV## N\n",
+ "MCV=RAV*L1##N.mm\n",
+ "MDV=RBV*L2## N.mm\n",
+ "# Horizontal Loads\n",
+ "RAH=(Frg*(L1+dg)+F*L2)/L##N\n",
+ "RBH=Frg+F-RAH## N\n",
+ "MCH=RAH*L1## N.mm\n",
+ "MDH=RBH*L2## N.mm\n",
+ "MD=sqrt(MDV**2+MDH**2)## N.mm\n",
+ "Mmax=MD##N.mm\n",
+ "Te=MCV+MDV;# N.mm\n",
+ "# d**3 = 16*Te/%pi/tau_d\n",
+ "d = (16*Te/pi/tau_d)**(1/3);# mm\n",
+ "\n",
+ "print ' shaft diameter(using ASME Code) = %.1f mm.'%(d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6.6 Pg 176"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " shaft diameter = 34 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "Tmax=400## N.mm\n",
+ "Tmin=200## N.mm\n",
+ "Mmax=500## N.mm\n",
+ "Mmin=250## N.mm\n",
+ "Sut=540## MPa\n",
+ "Syt=420## MPa\n",
+ "n=2## factor of safety\n",
+ "\n",
+ "Se=0.35*Sut## MPa\n",
+ "\n",
+ "Mm=(Mmax+Mmin)/2## N.m\n",
+ "Ma=(Mmax-Mmin)/2## N.m\n",
+ "Tm=(Tmax+Tmin)/2## N.m\n",
+ "Ta=(Tmax-Tmin)/2## N.m\n",
+ "Sys=0.5*Syt# MPa\n",
+ "Ses=0.5*Se## MPa\n",
+ "# Max. Distortion energy theory - Syt/n = 32/pi/d**3*sqrt((Mm+Ma*(Syt/Se)**2)+0.75*(Tm+Ta*(Sys/Ses))**2)\n",
+ "d = (32/pi*sqrt((Mm+Ma*(Syt/Se))**2+0.75*(Tm+Ta*(Sys/Ses))**2)*1000/(Syt/n))**(1/3) # # mm\n",
+ "print ' shaft diameter = %.f mm.'%(d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6.7 Pg 177"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " shaft diameter = 57 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "Wmax=40## kN\n",
+ "Wmin=20## kN\n",
+ "L=500## mm\n",
+ "Se_dash=350## MPa\n",
+ "Sut=650## MPa\n",
+ "Syt=500## MPa\n",
+ "n=1.5## factor of safety\n",
+ "ka=0.9# # surface finish factor\n",
+ "kb=0.85## size factor\n",
+ "ke=1## load factor\n",
+ "Kf=1## fatigue strength factor\n",
+ "\n",
+ "Wm=1/2*(Wmax+Wmin)## N\n",
+ "Wa=1/2*(Wmax-Wmin)## N\n",
+ "Se=ka*kb*ke*Se_dash##MPa\n",
+ "Mm=Wm*L/1000/4## kN.m\n",
+ "Ma=Wa*L/1000/4## kN.m\n",
+ "#sigma_m=32*Mm/pi/d**3# & sigma_a=32*Ma/pi/d**3\n",
+ "#soderburg failure criteria - 1/n=sigma_m/Syt+Kf*sigma_a/Se\n",
+ "#d=((32/pi*n/1000)*(Mm/Syt+Kf*Ma/Se))*(1/3)\n",
+ "d=((32/pi/1000)*(Mm/Syt+Kf*Ma/Se)*n)**(1/3)*1000## mm\n",
+ "print ' shaft diameter = %.f mm.'%(d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6.8 Pg 178"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " shaft diameter = 40.31 mm.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "Tmax=300## N.mm\n",
+ "Tmin=-100## N.mm\n",
+ "Mmax=400## N.mm\n",
+ "Mmin=-200## N.mm\n",
+ "n=1.5## factor of safety\n",
+ "Sut=500## MPa\n",
+ "Syt=420## MPa\n",
+ "sigma_d=280## MPa\n",
+ "ka=0.62# # surface finish factor\n",
+ "kb=0.85## size factor\n",
+ "keb=1## load factor for bending\n",
+ "kes=0.58## load factor for torsion\n",
+ "Kfb=1## fatigue strength factor for bending \n",
+ "Kfs=1## fatigue strength factor for torsion\n",
+ "\n",
+ "Se_dash=0.5*Sut## MPa\n",
+ "Se=ka*kb*keb*Se_dash## MPa\n",
+ "Ses_dash=0.5*Se_dash## MPa\n",
+ "Ses=ka*kb*kes*Ses_dash## MPa\n",
+ "Sys=0.5*Syt## MPa\n",
+ "Mm=(Mmax+Mmin)/2## N.m\n",
+ "Ma=(Mmax-Mmin)/2## N.m\n",
+ "Tm=(Tmax+Tmin)/2## N.m\n",
+ "Ta=(Tmax-Tmin)/2## N.m\n",
+ "\n",
+ "# tau_d/n = (16/pi/d**3)*sqrt((Mm+Ma*(Syt/Se)**2)+(Tm+Ta*(Sys/Ses))**2)\n",
+ "tau_d=sigma_d/2## MPa\n",
+ "d = ((16/pi)*sqrt((Mm+Ma*(Syt/Se)**2)+(Tm+Ta*(Sys/Ses))**2)/(tau_d*10**6/n))**(1/3)*1000## mm\n",
+ "print ' shaft diameter = %.2f mm.'%(d)\n",
+ "# Note - answer in the from math import sqrt,pi textbook is not accurate."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Machine_Design-I_by_Dr._Sadhu_Singh/chapter7.ipynb b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter7.ipynb
new file mode 100644
index 00000000..9d58d669
--- /dev/null
+++ b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter7.ipynb
@@ -0,0 +1,929 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 7 - Keys & Couplings"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 7.1 Pg 195"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " shaft diameter = 48.29 mm. Use d = 50 mm.\n",
+ " \n",
+ " thickness of hub = 25 mm\n",
+ " \n",
+ " diameter of recess in flanges = 75 mm\n",
+ " \n",
+ " outside diameter of protecting flange = 200 mm\n",
+ " \n",
+ " width of key = 12.5 mm. Use b = 15 mm\n",
+ " \n",
+ " length of key = 75 mm.\n",
+ " \n",
+ " thickness for square key = 15 mm\n",
+ " \n",
+ " Hub length = 75 mm\n",
+ " \n",
+ " Number of bolts = 4\n",
+ " \n",
+ " Bolt diameter = 11.86 mm. Use db=12 mm\n",
+ " \n",
+ " Bolt diameter (based on Tensile load) = 21.9 mm. Use db=15 mm\n",
+ " \n",
+ " Flange thickness = 18.5 mm. Use t=20 mm\n",
+ " \n",
+ " permissible bearing stress in flange = 2.76 MPa < 30 MPa\n",
+ " \n",
+ " shearing of the flange at the junction with hub = 3.17 MPa < 15 MPa.\n",
+ " Values are acceptable.\n",
+ " \n",
+ " permissible crushing strength of bolts = 14.0 MPa < 60 MPa.\n",
+ " Hence design is safe.\n",
+ " \n",
+ " Thickness of protecting flange = 10 mm\n",
+ " \n",
+ " Hub overlap = 3 mm (min)\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,floor\n",
+ "from numpy import roots\n",
+ "# Given Data\n",
+ "P=20## kW\n",
+ "N=240## rpm\n",
+ "tau_s=45## MPa\n",
+ "tau_b=30## MPa\n",
+ "sigma_b=60## MPa\n",
+ "sigma_cs=2*tau_s## MPa\n",
+ "tau_ci=15## MPa\n",
+ "#Tmax=1.25*Tm\n",
+ "mu=0.15## coefficient of friction\n",
+ "\n",
+ "#SHAFT DIAMETER\n",
+ "# P= 2*pi*N*Tm/60/1000 \n",
+ "Tm=P/(2*pi*N/60/1000)## N.m\n",
+ "Tmax=1.25*Tm## N.m\n",
+ "# pi*d**3*tau_s/16= Tmax\n",
+ "d=(Tmax/(pi*tau_s/16)*1000)**(1/3)## mm\n",
+ "print ' shaft diameter = %.2f mm. Use d = 50 mm.'%(d)\n",
+ "d=50## mm\n",
+ "\n",
+ "# HUB DIAMETER\n",
+ "# Tmax=pi/16*((d1**4-d**4)/d1)*tau_h\n",
+ "tau_h=tau_ci## MPa\n",
+ "#d1*(Tmax/(pi/16)/tau_h)-d1**4=d**4 -- eqn(1)\n",
+ "Tmax=Tmax*1000## N.mm\n",
+ "p=[1, 0 ,0 ,-Tmax/(pi*tau_h/16), -d**4] ## polynomial coefficients from eqn(1)\n",
+ "d1=roots(p)## roots of poly \n",
+ "d1=d1[0]## mm (taking +ve value)\n",
+ "d1=100## mm (empirically adopted) \n",
+ "t1=(d1-d)/2## mm (thickness of hub)\n",
+ "print ' \\n thickness of hub = %.f mm'%(t1)\n",
+ "d4=d+t1## mm (diameter of recess in flanges)\n",
+ "print ' \\n diameter of recess in flanges = %.f mm'%(d4)\n",
+ "d3=4*d## mm (outside diameter of protecting flange)\n",
+ "print ' \\n outside diameter of protecting flange = %.f mm'%(d3)\n",
+ "\n",
+ "# Hub length\n",
+ "b=d/4## mm (width of key)\n",
+ "l=1.5*d## mm (length of key)\n",
+ "print ' \\n width of key = %.1f mm. Use b = 15 mm'%(b)\n",
+ "b=15## mm\n",
+ "print ' \\n length of key = %.f mm.'%(l) \n",
+ "t=b## mm (thickness for square key)\n",
+ "print ' \\n thickness for square key = %.f mm'%(t)\n",
+ "print ' \\n Hub length = %.f mm'%(l)\n",
+ "\n",
+ "#Number of bolts\n",
+ "n=floor(4*d/150+3)## no. of bolts\n",
+ "print ' \\n Number of bolts = %.f'%(n)\n",
+ "\n",
+ "# Bolt diameter\n",
+ "r2=1.5*d## mm\n",
+ "F=Tmax/r2/n## N\n",
+ "#pi/4*db**2*tau_b=F\n",
+ "db=sqrt(F/(pi/4*tau_b))## mm\n",
+ "print ' \\n Bolt diameter = %.2f mm. Use db=12 mm'%(db)\n",
+ "bolt_dia=db##mm\n",
+ "\n",
+ "# Bolt diameter based on Tensile load\n",
+ "r3=d3/2## mm\n",
+ "r4=d4/2## mm\n",
+ "rf=2/3*((r3**3-r4**3)/(r3**2-r4**2))## mm\n",
+ "#Tmax=n*mu*Pi*rf## N\n",
+ "Pi=Tmax/(n*mu*rf)## N\n",
+ "# Pi=pi/4*db**2*sigma_t\n",
+ "sigma_t=sigma_b## MPa\n",
+ "db=sqrt(Pi/(pi/4*sigma_t))## mm \n",
+ "print ' \\n Bolt diameter (based on Tensile load) = %.1f mm. Use db=15 mm'%(db)\n",
+ "db=15## mm (adopted)\n",
+ "\n",
+ "# Flange thickness\n",
+ "t2=0.5*t1+6## mm (empirically)\n",
+ "print ' \\n Flange thickness = %.1f mm. Use t=20 mm'%(t2)\n",
+ "t2=20## mm (adopted)\n",
+ "#F=n*db*t2*sigma_c\n",
+ "sigma_ci=F/n/db/t2## MPa\n",
+ "#2*pi*d1**2*tau*t2/4=Tmax\n",
+ "tau=Tmax/(2*pi*d1**2*t2/4)## MPa\n",
+ "print ' \\n permissible bearing stress in flange = %.2f MPa < 30 MPa'%(sigma_ci)\n",
+ "print ' \\n shearing of the flange at the junction with hub = %.2f MPa < 15 MPa.'%(tau)\n",
+ "print ' Values are acceptable.'\n",
+ "\n",
+ "# Check for crushing of bolt\n",
+ "#n*db*t2*sigma_cb*d2/2=Tmax\n",
+ "d2=d1+d## mm\n",
+ "db=bolt_dia##mm\n",
+ "sigma_cb=Tmax/(n*db*t2*d2/2)## MPa\n",
+ "print ' \\n permissible crushing strength of bolts = %.1f MPa < 60 MPa.'%(sigma_cb)\n",
+ "print ' Hence design is safe.'\n",
+ "\n",
+ "# Thickness of protecting flange\n",
+ "t3=0.5*t2## mm\n",
+ "print ' \\n Thickness of protecting flange = %.f mm'%( t3)\n",
+ "# Hub overlap \n",
+ "ho=3## mm (min)\n",
+ "print ' \\n Hub overlap = %.f mm (min)'%(ho)\n",
+ "#Note - Answer for **Bolt diameter based on Tensile load** is calculated wrong in the textbook(error in Pi calculation)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 7.2 Pg 200"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " shaft diameter = 40.55 mm. Use d = 42 mm.\n",
+ " \n",
+ " thickness of hub = 21 mm\n",
+ " \n",
+ " outside diameter of protecting flange = 168 mm. Use 170 mm\n",
+ " \n",
+ " width of key = 10.5 mm. Use b = 12 mm\n",
+ " \n",
+ " length of key = 63 mm.\n",
+ " \n",
+ " thickness for square key = 12 mm\n",
+ " \n",
+ " Hub length = 63 mm\n",
+ " \n",
+ " Number of bolts = 4.68. Use n=6\n",
+ " \n",
+ " Bolt diameter = 8.57 mm. Use db=20 mm for design purpose\n",
+ " \n",
+ " pitch circle diameter of bolts = 136 mm \n",
+ " \n",
+ " Permissible shear stress in bolts = 3.58 MPa < 35 MPa. Hence design is safe.\n",
+ " \n",
+ " length of bush = 35 mm\n",
+ " \n",
+ " Bending stress in pin = 28.7 MPa\n",
+ " \n",
+ " Maximum shear stress in pin = 14.78 MPa < 35 MPa. Hence design is safe.\n",
+ " \n",
+ " Flange thickness = 16.5 mm. Use t=18 mm\n",
+ " \n",
+ " shearing of the flange at the junction with hub = 2.30 MPa < 15 MPa.\n",
+ " Values are acceptable.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from numpy import roots,pi,sqrt\n",
+ "# Given Data\n",
+ "P=30## kW\n",
+ "N=750## rpm\n",
+ "#Tmax=1.2*Tm## MPa\n",
+ "tau_s=35## MPa\n",
+ "tau_b=35## MPa\n",
+ "tau_k=35## MPa\n",
+ "sigma_cs=70## MPa\n",
+ "sigma_ck=70## MPa\n",
+ "sigma_cb=70## MPa\n",
+ "tau_ci=15## MPa\n",
+ "pb=0.8## MPa\n",
+ "\n",
+ "#sigma_cs=2*tau_s## MPa\n",
+ "\n",
+ "#Tmax=1.5*Tm\n",
+ "mu=0.15## coefficient of friction\n",
+ "\n",
+ "#SHAFT DIAMETER\n",
+ "# P= 2*pi*N*Tm/60/1000 \n",
+ "Tm=P/(2*pi*N/60/1000)## N.m\n",
+ "Tmax=1.2*Tm## N.m\n",
+ "# pi*d**3*tau_s/16= Tmax\n",
+ "d=(Tmax/(pi*tau_s/16)*1000)**(1/3)## mm\n",
+ "print ' shaft diameter = %.2f mm. Use d = 42 mm.'%(d)\n",
+ "d=42## mm\n",
+ "\n",
+ "# HUB DIAMETER\n",
+ "# Tmax=pi/16*((d1**4-d**4)/d1)*tau_h\n",
+ "tau_h=tau_ci## MPa\n",
+ "#d1*(Tmax/(pi/16)/tau_h)-d1**4=d**4 -- eqn(1)\n",
+ "Tmax=Tmax*1000## N.mm\n",
+ "p=[1, 0 ,0 ,-Tmax/(pi*tau_h/16) ,-d**4] ## polynomial coefficients from eqn(1)\n",
+ "d1=roots(p)## roots of poly \n",
+ "d1=d1[0]## mm (taking +ve value)\n",
+ "d1=2*d## mm (empirically adopted) \n",
+ "t1=(d1-d)/2## mm (thickness of hub)\n",
+ "print ' \\n thickness of hub = %.f mm'%(t1)\n",
+ "#d4=d+t1## mm (diameter of recess in flanges)\n",
+ "#print ' \\n diameter of recess in flanges = %.f mm'%(d4)\n",
+ "d3=4*d## mm (outside diameter of protecting flange)\n",
+ "print ' \\n outside diameter of protecting flange = %.f mm. Use 170 mm'%(d3)\n",
+ "d3=170## mm (adopted)\n",
+ "\n",
+ "#Key size & Hub length\n",
+ "b=d/4## mm (width of key)\n",
+ "l=1.5*d## mm (length of key)\n",
+ "print ' \\n width of key = %.1f mm. Use b = 12 mm'%(b)\n",
+ "b=12## mm\n",
+ "print ' \\n length of key = %.f mm.'%(l) \n",
+ "t=b## mm (thickness for square key)\n",
+ "print ' \\n thickness for square key = %.f mm'%(t)\n",
+ "print ' \\n Hub length = %.f mm'%(l)\n",
+ "\n",
+ "#Number of bolts\n",
+ "n=(0.04*d+3)## no. of bolts\n",
+ "print ' \\n Number of bolts = %.2f. Use n=6'%(n)\n",
+ "n=6## adopted\n",
+ "\n",
+ "# Bolt diameter\n",
+ "db=0.5*d/sqrt(n)## mm\n",
+ "print ' \\n Bolt diameter = %.2f mm. Use db=20 mm for design purpose'%(db)\n",
+ "db=20##mm (adopted)\n",
+ "bolt_dia=db##mm\n",
+ "dsb=24## mm(shank diameter of bolt for design)\n",
+ "\n",
+ "# Outer diameter of rubber bush\n",
+ "trb=2## mm (thickness of rubber bush)\n",
+ "tbb=6## mm (thickness of brass bush)\n",
+ "d3=dsb+2*trb+2*tbb## mm \n",
+ "d2=d1+d3+2*tbb## mm (pitch circle diameter of bolts)\n",
+ "print ' \\n pitch circle diameter of bolts = %.f mm '%(d2)\n",
+ "\n",
+ "# Check of shear in bolt\n",
+ "F=2*Tmax/n/d2## N\n",
+ "#pi/4*db*2*tau=F\n",
+ "tau=F/(pi/4*db**2)##MPa\n",
+ "print ' \\n Permissible shear stress in bolts = %.2f MPa < 35 MPa. Hence design is safe.'%( tau)\n",
+ "\n",
+ "# Length of brush\n",
+ "pb=0.8## MPa(bearing pressure of brush)\n",
+ "#F=l2*d3*pb#\n",
+ "l2=F/d3/pb## mm\n",
+ "print ' \\n length of bush = %.f mm'%(l2)\n",
+ "\n",
+ "# Check for pin in bending\n",
+ "c=5## mm (clearance between two flanges)\n",
+ "l3=(l2-c)/2+c##mm\n",
+ "#M=pi/32*db**3*sigma_b & M=F*l3\n",
+ "sigma_b = F*l3/(pi/32*db**3)## MPa\n",
+ "print ' \\n Bending stress in pin = %.1f MPa'%(sigma_b)\n",
+ "\n",
+ "# Maximum shear stress in pin\n",
+ "tau_max=sqrt((sigma_b/2)**2+tau**2)##MPa\n",
+ "print ' \\n Maximum shear stress in pin = %.2f MPa < 35 MPa. Hence design is safe.'%(tau_max)\n",
+ "\n",
+ "# Flange thickness\n",
+ "t2=0.5*t1+6## mm (empirically)\n",
+ "print ' \\n Flange thickness = %.1f mm. Use t=18 mm'%(t2)\n",
+ "t2=18## mm (adopted)\n",
+ "tau=Tmax/(2*pi*d1**2*t2/4)## MPa\n",
+ "print ' \\n shearing of the flange at the junction with hub = %.2f MPa < 15 MPa.'%(tau)\n",
+ "print ' Values are acceptable.'\n",
+ "\n",
+ "#Note - Answer in llast part is calculated wrong in the textbook(error in calculation)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 7.3 Pg 204"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " length of hub = 111 mm\n",
+ " \n",
+ " Force required to shift the connection = 1278.9 N\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "n=8## no. of spline\n",
+ "d=52## mm\n",
+ "D=60## mm\n",
+ "pm=6## MPa\n",
+ "mu=0.06## coefficient of friction\n",
+ "N=320## rpm\n",
+ "P=20## kW\n",
+ "\n",
+ "T=60*10**3*P/2/pi/N## N.m\n",
+ "l=8*T*10**3/pm/n/(D**2-d**2)## mm\n",
+ "print ' length of hub = %.f mm'%(l)\n",
+ "Rm=(D+d)/4## mm\n",
+ "F=T*10**3/Rm## N\n",
+ "Ff=mu*F##N (Force of friction)\n",
+ "print ' \\n Force required to shift the connection = %.1f N'%(Ff)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 7.4 Pg 204"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " for key to be equally strong in shear & crushing - \n",
+ "\n",
+ " b= 18.75 mm. Use b=20 mm.\n",
+ " \n",
+ " t=26.67 mm. Use t=27 mm\n",
+ " for key to be equally strong in shear as shaft - \n",
+ "\n",
+ " l=110.4 mm. Use l=115 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi\n",
+ "# Given Data\n",
+ "d=75## mm\n",
+ "tau=50## MPa\n",
+ "sigma_c=75## MPa\n",
+ "print ' for key to be equally strong in shear & crushing - \\n'\n",
+ "b=d/4## mm\n",
+ "print ' b= %.2f mm. Use b=20 mm.'%(b)\n",
+ "b=20##mm\n",
+ "#2*b/t=sigma_c/tau for key to be equally strong in shear & crushing\n",
+ "t=2*b/(sigma_c/tau)## mm\n",
+ "print ' \\n t=%.2f mm. Use t=27 mm'%(t)\n",
+ "l= pi*d**2/8/b## mm (for key to be equally strong in shear as shaft)\n",
+ "print ' for key to be equally strong in shear as shaft - \\n'\n",
+ "print ' l=%.1f mm. Use l=115 mm'%(l)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 7.6 Pg 205"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " shaft diameter = 100.00 mm.\n",
+ " \n",
+ " thickness of hub = 50 mm\n",
+ " \n",
+ " diameter of recess in flanges = 150 mm\n",
+ " \n",
+ " outside diameter of protecting flange = 400 mm.\n",
+ " \n",
+ " width of key = 25.0 mm.\n",
+ " \n",
+ " length of key = 150 mm.\n",
+ " \n",
+ " thickness for square key = 25 mm\n",
+ " \n",
+ " Hub length = 150 mm\n",
+ " \n",
+ " Number of bolts = 6.00.\n",
+ " \n",
+ " Bolt diameter = 18.38 mm. Use db=20 mm for design purpose\n",
+ " \n",
+ " Flange thickness = 31.0 mm. Use t=20 mm\n",
+ " \n",
+ " permissible bearing stress in flange = 3.21 MPa < 75 MPa\n",
+ " \n",
+ " shearing of the flange at the junction with hub = 5.52 MPa < 175 MPa.\n",
+ " Values are acceptable.\n",
+ " \n",
+ " permissible crushing strength of bolts = 19.25 MPa < 60 MPa.\n",
+ " Hence design is safe.\n",
+ " \n",
+ " Thickness of protecting flange = 16 mm\n",
+ " \n",
+ " Hub overlap = 3 mm (min)\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi,ceil,sqrt\n",
+ "from numpy import roots\n",
+ "# Given Data\n",
+ "P=135## kW\n",
+ "N=120## rpm\n",
+ "tau_s=55## MPa\n",
+ "tau_b=45## MPa\n",
+ "tau_ci=175## MPa\n",
+ "sigma_ci=75## MPa\n",
+ "\n",
+ "#sigma_cs=2*tau_s## MPa\n",
+ "\n",
+ "#Tmax=1.5*Tm\n",
+ "mu=0.15## coefficient of friction\n",
+ "\n",
+ "#SHAFT DIAMETER\n",
+ "# P= 2*pi*N*Tm/60/1000 \n",
+ "Tm=P/(2*pi*N/60/1000)## N.m\n",
+ "# pi*d**3*tau_s/16= Tm\n",
+ "d=(Tm/(pi*tau_s/16)*1000)**(1/3)## mm\n",
+ "d=ceil(d)\n",
+ "print ' shaft diameter = %.2f mm.'%(d)\n",
+ "Tmax=Tm## N.m\n",
+ "\n",
+ "# HUB DIAMETER\n",
+ "# Tmax=pi/16*((d1**4-d**4)/d1)*tau_h\n",
+ "tau_h=tau_ci## MPa\n",
+ "#d1*(Tmax/(pi/16)/tau_h)-d1**4=d**4 -- eqn(1)\n",
+ "Tmax=Tmax*1000## N.mm\n",
+ "p=[1, 0, 0, -Tmax/(pi*tau_h/16), -d**4] ## polynomial coefficients from eqn(1)\n",
+ "d1=roots(p)## roots of poly \n",
+ "d1=d1[0]## mm (taking +ve value)\n",
+ "d1=2*d## mm (empirically adopted) \n",
+ "t1=(d1-d)/2## mm (thickness of hub)\n",
+ "print ' \\n thickness of hub = %.f mm'%(t1)\n",
+ "d4=d+t1## mm (diameter of recess in flanges)\n",
+ "print ' \\n diameter of recess in flanges = %.f mm'%(d4)\n",
+ "d3=4*d## mm (outside diameter of protecting flange)\n",
+ "print ' \\n outside diameter of protecting flange = %.f mm.'%(d3)\n",
+ "\n",
+ "#Key size & Hub length\n",
+ "b=d/4## mm (width of key)\n",
+ "l=1.5*d## mm (length of key)\n",
+ "print ' \\n width of key = %.1f mm.'%(b)\n",
+ "print ' \\n length of key = %.f mm.'%(l) \n",
+ "t=b## mm (thickness for square key)\n",
+ "print ' \\n thickness for square key = %.f mm'%(t)\n",
+ "print ' \\n Hub length = %.f mm'%(l)\n",
+ "\n",
+ "#Number of bolts\n",
+ "n=ceil(4*d/150+3)## no. of bolts\n",
+ "print ' \\n Number of bolts = %.2f.'%(n)\n",
+ "\n",
+ "# Bolt diameter\n",
+ "r2=1.5*d## mm\n",
+ "F=Tm*1000/r2/n##N\n",
+ "#(pi/4)*db**2*tau_b=F\n",
+ "db=sqrt(F/((pi/4)*tau_b))## mm\n",
+ "print ' \\n Bolt diameter = %.2f mm. Use db=20 mm for design purpose'%(db)\n",
+ "db=20## mm (adopted for design)\n",
+ "bolt_dia=db##mm\n",
+ "\n",
+ "# Flange thickness\n",
+ "t2=0.5*t1+6## mm (empirically)\n",
+ "print ' \\n Flange thickness = %.1f mm. Use t=20 mm'%(t2)\n",
+ "#F=n*db*t2*sigma_c\n",
+ "sigma_ci=F/n/db/t2## MPa\n",
+ "#2*pi*d1**2*tau*t2/4=Tmax\n",
+ "tau=Tmax/(2*pi*d1**2*t2/4)## MPa\n",
+ "print ' \\n permissible bearing stress in flange = %.2f MPa < 75 MPa'%(sigma_ci)\n",
+ "print ' \\n shearing of the flange at the junction with hub = %.2f MPa < 175 MPa.'%(tau)\n",
+ "print ' Values are acceptable.'\n",
+ "\n",
+ "# Check for crushing of bolt\n",
+ "#n*db*t2*sigma_cb*d2/2=Tmax\n",
+ "d2=d1+d## mm\n",
+ "db=bolt_dia##mm\n",
+ "sigma_cb=Tmax/(n*db*t2*d2/2)## MPa\n",
+ "print ' \\n permissible crushing strength of bolts = %.2f MPa < 60 MPa.'%(sigma_cb)\n",
+ "print ' Hence design is safe.'\n",
+ "# Thickness of protecting flange\n",
+ "t3=0.5*t2## mm\n",
+ "print ' \\n Thickness of protecting flange = %.f mm'%( t3)\n",
+ "# Hub overlap \n",
+ "ho=3## mm (min)\n",
+ "print ' \\n Hub overlap = %.f mm (min)'%(ho)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 7.7 Pg 208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " for key to be equally strong in shear & crushing - \n",
+ "\n",
+ " b= 12.50 mm. Use b=15 mm.\n",
+ " \n",
+ " t=17.50 mm. Use t=20 mm\n",
+ " \n",
+ " for key to be equally strong in shear as shaft - \n",
+ "\n",
+ " l=65.45 mm. Use l=70 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "d=50## mm\n",
+ "tau=42## MPa\n",
+ "sigma_c=72## MPa\n",
+ "print ' for key to be equally strong in shear & crushing - \\n'\n",
+ "b=d/4## mm\n",
+ "print ' b= %.2f mm. Use b=15 mm.'%(b)\n",
+ "b=15##mm\n",
+ "#2*b/t=sigma_c/tau for key to be equally strong in shear & crushing\n",
+ "t=2*b/(sigma_c/tau)## mm\n",
+ "print ' \\n t=%.2f mm. Use t=20 mm'%(t)\n",
+ "l= pi*d**2/8/b## mm (for key to be equally strong in shear as shaft)\n",
+ "print ' \\n for key to be equally strong in shear as shaft - \\n'\n",
+ "print ' l=%.2f mm. Use l=70 mm'%(l)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 7.8 Pg 208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " design shear stress = 80 N/mm.sq.\n",
+ " \n",
+ " design crushing strength = 160 N/mm.sq.\n",
+ " \n",
+ " width of key = 6 mm. Use 7mm\n",
+ " \n",
+ " thickness of key = 7 mm.\n",
+ " \n",
+ " length of key based on shear failure = 29.76 mm or 30 mm\n",
+ " \n",
+ " length of key based on crushing failure = 29.76 mm or 30 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,ceil\n",
+ "\n",
+ "# Given Data\n",
+ "d=25## mm\n",
+ "N=550## rpm\n",
+ "P=12## kW\n",
+ "sigma_yt=400## N/mm.sq.\n",
+ "sigma_yc=400## N/mm.sq.\n",
+ "n=2.5## factor of safety\n",
+ "\n",
+ "# P= 2*pi*N*T/(60*10**3)\n",
+ "T=P/(2*pi*N/(60*10**3))## N.m\n",
+ "tau=0.5*sigma_yt## MPa\n",
+ "tau_d=tau/n## N/mm.sq.\n",
+ "print ' design shear stress = %.f N/mm.sq.'%(tau_d)\n",
+ "sigma_d=sigma_yc/n## N/mm.sq.\n",
+ "print ' \\n design crushing strength = %.f N/mm.sq.'%(sigma_d)\n",
+ "b=d/4##mm\n",
+ "print ' \\n width of key = %.f mm. Use 7mm'%(b)\n",
+ "b=ceil(d/4)## mm\n",
+ "t=b## mm\n",
+ "print ' \\n thickness of key = %.f mm.'%(t)\n",
+ "l_s=2*T*10**3/(d*b*tau_d)## mm (length of key based on shear failure)\n",
+ "print ' \\n length of key based on shear failure = %.2f mm or %.f mm'%(l_s, l_s)\n",
+ "l_c=4*T*10**3/(d*t*sigma_d)## mm (length of key based on crushing failure)\n",
+ "print ' \\n length of key based on crushing failure = %.2f mm or %.f mm'%(l_c, l_c)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 7.9 Pg 209"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Maximum transmitted torque = 248680 N.mm\n",
+ " \n",
+ " Hub diameter = 72 mm\n",
+ " \n",
+ " Thickness of hub = 18 mm\n",
+ " \n",
+ " Diameter of recess in flanges = 54 mm\n",
+ " \n",
+ " Outside diameter of protecting flange = 144 mm\n",
+ " \n",
+ " width of key = 9.0 mm.\n",
+ " \n",
+ " length of key = 54 mm.\n",
+ " \n",
+ " thickness for square key = 9 mm\n",
+ " \n",
+ " Hub length = 54 mm\n",
+ " \n",
+ " Number of bolts = 4.00.\n",
+ " \n",
+ " Bolt diameter = 5.57 mm. Use db=6 mm for design purpose\n",
+ " \n",
+ " Flange thickness = 15.0 mm. Use t=20 mm\n",
+ " \n",
+ " permissible bearing stress in flange = 3.20 MPa < 40 MPa\n",
+ " \n",
+ " shearing of the flange at the junction with hub = 2.04 MPa < 20 MPa.\n",
+ " Values are acceptable.\n",
+ " \n",
+ " permissible crushing strength of bolts = 12.79 MPa < 82 MPa.\n",
+ " Hence design is safe.\n",
+ " \n",
+ " Thickness of protecting flange = 8 mm\n",
+ " \n",
+ " Hub overlap = 3 mm (min)\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,ceil\n",
+ "# Given Data\n",
+ "d=36## mm\n",
+ "P=15## kW\n",
+ "N=720## rpm\n",
+ "#Tmax=1.25*Tm\n",
+ "sigma_yt=245## MPa (for C20 steel)\n",
+ "n=3## factor of safety\n",
+ "sigma=82## MPa (Design tensile stress)\n",
+ "\n",
+ "tau=0.577*sigma## MPa (shear stress)\n",
+ "sigma_u=200## MPa (for FG 200 cast Iron)\n",
+ "n2=5## factor of safety (for FG 200 cast Iron)\n",
+ "tau2=20## MPa shear stress (for FG 200 cast Iron)\n",
+ "\n",
+ "# Max. torque transmitted\n",
+ "#P=2*pi*N*Tm/(60*10**3)\n",
+ "Tm=P/(2*pi*N/(60*10**3))*1000## N.mm\n",
+ "Tmax=1.25*Tm## N.mm\n",
+ "print ' \\n Maximum transmitted torque = %.f N.mm'%(Tmax)\n",
+ "\n",
+ "# Hub diameter\n",
+ "tau_h=20## MPa (permissible shear stress in hub)\n",
+ "#Tmax=(pi/16)*(d1**4-d**4)/d1*tau_h ...eqn(1)\n",
+ "d1=2*d##mm (empirically)\n",
+ "tau_h=Tmax*1000/((pi/16)*(d1**4-d**4)/d1)## MPa\n",
+ "t1=(d1-d)/2## mm (thickness of hub)\n",
+ "print ' \\n Hub diameter = %.f mm'%(d1)\n",
+ "print ' \\n Thickness of hub = %.f mm'%(t1)\n",
+ "d4=d+t1## mm\n",
+ "print ' \\n Diameter of recess in flanges = %.f mm'%(d4)\n",
+ "d3=4*d##mm\n",
+ "print ' \\n Outside diameter of protecting flange = %.f mm'%(d3)\n",
+ "\n",
+ "#Hub length\n",
+ "b=d/4## mm (width of key)\n",
+ "l=1.5*d## mm (length of key)\n",
+ "print ' \\n width of key = %.1f mm.'%(b)\n",
+ "print ' \\n length of key = %.f mm.'%(l) \n",
+ "t=b## mm (thickness for square key)\n",
+ "print ' \\n thickness for square key = %.f mm'%(t)\n",
+ "print ' \\n Hub length = %.f mm'%(l)\n",
+ "\n",
+ "#Number of bolts\n",
+ "n=ceil(4*d/150+3)## no. of bolts\n",
+ "print ' \\n Number of bolts = %.2f.'%(n)\n",
+ "\n",
+ "# Bolt diameter\n",
+ "r2=1.5*d## mm\n",
+ "F=Tmax/r2/n##N\n",
+ "#(pi/4)*db**2*tau_b=F\n",
+ "db=sqrt(F/((pi/4)*tau))## mm\n",
+ "print ' \\n Bolt diameter = %.2f mm. Use db=6 mm for design purpose'%(db)\n",
+ "db=6## mm (adopted for design)\n",
+ "bolt_dia=db##mm\n",
+ "\n",
+ "# Flange thickness\n",
+ "t2=0.5*t1+6## mm (empirically)\n",
+ "print ' \\n Flange thickness = %.1f mm. Use t=20 mm'%(t2)\n",
+ "#F=n*db*t2*sigma_c\n",
+ "sigma_ci=F/n/db/t2## MPa\n",
+ "#2*pi*d1**2*tau*t2/4=Tmax\n",
+ "tau=Tmax/(2*pi*d1**2*t2/4)## MPa\n",
+ "print ' \\n permissible bearing stress in flange = %.2f MPa < 40 MPa'%(sigma_ci)\n",
+ "print ' \\n shearing of the flange at the junction with hub = %.2f MPa < 20 MPa.'%(tau)\n",
+ "print ' Values are acceptable.'\n",
+ "\n",
+ "# Check for crushing of bolt\n",
+ "#n*db*t2*sigma_cb*d2/2=Tmax\n",
+ "d2=d1+d## mm\n",
+ "db=bolt_dia##mm\n",
+ "sigma_cb=Tmax/(n*db*t2*d2/2)## MPa\n",
+ "print ' \\n permissible crushing strength of bolts = %.2f MPa < 82 MPa.'%(sigma_cb)\n",
+ "print ' Hence design is safe.'\n",
+ "# Thickness of protecting flange\n",
+ "t3=0.5*t2## mm\n",
+ "print ' \\n Thickness of protecting flange = %.f mm'%( t3)\n",
+ "# Hub overlap \n",
+ "ho=3## mm (min)\n",
+ "print ' \\n Hub overlap = %.f mm (min)'%(ho)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 7.10 Pg 212"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " (i) Diameter of bolts = 6.96 mm. Use 8 mm.\n",
+ " \n",
+ " (ii) Flange thickness = 10.4 mm. Use t2 = 12 mm\n",
+ " \n",
+ " (iii) Length of key = 100 mm\n",
+ "\t\td=35 mm\n",
+ "\t\tb=10 mm\n",
+ " \n",
+ " (iv) Hub length = 100 mm\n",
+ " \n",
+ " shear stress in hub = 12.67 N/mm.sq.\n",
+ " It is nearly equal to 10 N/mm.sq.\n",
+ " \n",
+ " hence design parameters are fine.\n",
+ " \n",
+ " (v) Power transmitted = 29.32 kW\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,ceil\n",
+ "# Given Data\n",
+ "d=35## mm\n",
+ "d2=125## mm\n",
+ "n=6## factor of safety\n",
+ "T=800## N.m\n",
+ "N=350## rpm\n",
+ "tau_s=63## MPa\n",
+ "tau_b=56## MPa\n",
+ "tau_CI=10## MPa\n",
+ "tau_k=46## MPa\n",
+ "\n",
+ "# Diameter of bolts:\n",
+ "F=2*T*10**3/d2/n## N\n",
+ "#pi/4*db**2*tau_b=F\n",
+ "db=sqrt(F/(pi/4*tau_b))## mm\n",
+ "print ' \\n (i) Diameter of bolts = %.2f mm. Use 8 mm.'%(db)\n",
+ "\n",
+ "# Flange thickness\n",
+ "d1=2*d## mm\n",
+ "#T=pi/2*d1**2*t2*tau_CI\n",
+ "t2=T*1000/(pi/2*d1**2*tau_CI)## mm\n",
+ "print ' \\n (ii) Flange thickness = %.1f mm. Use t2 = 12 mm'%(t2)\n",
+ "t2=12## mm\n",
+ "\n",
+ "#Key dimensions\n",
+ "b=10## mm (width of key)\n",
+ "t=7## mm (from tables)\n",
+ "#T=l*b*tau_k*d/2\n",
+ "l=T*10**3/(b*tau_k*d/2)## mm\n",
+ "l=ceil(l)## mm\n",
+ "print ' \\n (iii) Length of key = %.f mm\\n\\t\\td=%.f mm\\n\\t\\tb=%.f mm'%(l,d,b)\n",
+ "\n",
+ "# Hub length\n",
+ "lh=l## mm (length of hub)\n",
+ "print ' \\n (iv) Hub length = %.f mm'%(l)\n",
+ "tau_c=T*10**3/(pi/16*(d1**4-d**4)/d1)## N/mm.sq.\n",
+ "print ' \\n shear stress in hub = %.2f N/mm.sq.'%(tau_c)\n",
+ "print ' It is nearly equal to %.f N/mm.sq.'%(tau_CI)\n",
+ "print ' \\n hence design parameters are fine.'\n",
+ "\n",
+ "# Power transmitted\n",
+ "P=2*pi*N*T/60/10**3## kW\n",
+ "print ' \\n (v) Power transmitted = %.2f kW'%(P)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Machine_Design-I_by_Dr._Sadhu_Singh/chapter8.ipynb b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter8.ipynb
new file mode 100644
index 00000000..f1479e25
--- /dev/null
+++ b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter8.ipynb
@@ -0,0 +1,753 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 8 - Mechanical Springs"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 8.1 Pg 227"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Wahl's correction factor = 1.184 \n",
+ " \n",
+ " Wire diameter = 4.15 mm. Use 4.25 mm.\n",
+ " \n",
+ " Mean coil diameter = 34 mm.\n",
+ " \n",
+ " no. of active turns = 14\n",
+ " \n",
+ " total no. of turns for squared and ground ends = 16\n",
+ " \n",
+ " Free length of spring = 123.0 mm Use 124 mm\n",
+ " \n",
+ " Pitch of coils = 8.30 mm\n",
+ " \n",
+ " Check for buckling - \n",
+ " \n",
+ " ratio lf/Dm = 3.647 > 2.6. So, Providing guide is necessary.\n",
+ " \n",
+ " Critical load for buckling - \n",
+ " \n",
+ " Fcr = 170.5 N for hinged ends < Fmax\n",
+ " \n",
+ " Fcr = 480.5 N for fixed ends > Fmax\n",
+ " \n",
+ " From above two calculatio, it can be seen that spring is safe in buckling for fixed ends.\n",
+ " \n",
+ "\n",
+ " Lowest natural frequency for both ends fixed, fn = 3.079 Hz\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "Fmin=250## N\n",
+ "Fmax=300## N\n",
+ "Del=8## mm\n",
+ "C=8## spring index\n",
+ "tau_d=420## MPa\n",
+ "G=84## GPa\n",
+ "\n",
+ "# 1. Wahl's correction factor\n",
+ "Kw=(4*C-1)/(4*C-4)+0.615/C## Wahl's correction factor\n",
+ "print \"\\n Wahl's correction factor = %.3f \"%(Kw)\n",
+ "# 2. Wire diameter\n",
+ "# tau_d=Kw*8*Fmax*C/pi/d**2\n",
+ "d=sqrt(Kw*8*Fmax*C/pi/tau_d)## mm\n",
+ "print ' \\n Wire diameter = %.2f mm. Use 4.25 mm.'%(d)\n",
+ "d=4.25## mm\n",
+ "# 3. Mean coil diameter\n",
+ "Dm=8*d## mm\n",
+ "print ' \\n Mean coil diameter = %.f mm.'%(Dm)\n",
+ "# 4. Stiffness of spring\n",
+ "k=(Fmax-Fmin)/Del## N/mm\n",
+ "# 5. no. of active turns\n",
+ "n = G*10**3*d/8/C**3/k ## no. of active turns\n",
+ "print ' \\n no. of active turns = %.f'%(n)\n",
+ "# 6. total no. of turns for squared and ground ends\n",
+ "nt=n+2## total no. of turns for squared and ground ends\n",
+ "print ' \\n total no. of turns for squared and ground ends = %.f'%(nt)\n",
+ "# 7. Free length of spring\n",
+ "#lf=l_s+del_max+clashallowance(=0.15*del_max)\n",
+ "del_max=Del*Fmax/(Fmax-Fmin)##mm\n",
+ "l_s=nt*d## mm\n",
+ "lf=l_s+del_max+0.15*del_max## mm\n",
+ "print ' \\n Free length of spring = %.1f mm Use 124 mm'%(lf)\n",
+ "lf=124##mm\n",
+ "# 8. Pitch of coils\n",
+ "p=lf/(nt-1)##mm\n",
+ "print ' \\n Pitch of coils = %.2f mm'%(p)\n",
+ "# 9. Check for buckling\n",
+ "print ' \\n Check for buckling - '\n",
+ "m=lf/Dm## > 2.6 provided guide\n",
+ "print ' \\n ratio lf/Dm = %.3f > 2.6. So, Providing guide is necessary.'%(m)\n",
+ "kl_1=0.22## for hinged ends\n",
+ "kl_2=0.62## for fixed ends\n",
+ "Fcr_1=k*kl_1*lf##N (for hinged ends)\n",
+ "Fcr_2=k*kl_2*lf##N (for fixed ends)\n",
+ "print ' \\n Critical load for buckling - '\n",
+ "print ' \\n Fcr = %.1f N for hinged ends < Fmax'%(Fcr_1)\n",
+ "print ' \\n Fcr = %.1f N for fixed ends > Fmax'%(Fcr_2)\n",
+ "print ' \\n From above two calculatio, it can be seen that spring is safe in buckling for fixed ends.'\n",
+ "# 10. Lowest natural frequency for both ends fixed\n",
+ "rau=7800## N/mm.cube. (Density of spring material)\n",
+ "fn=d/(pi*n*Dm**2)*sqrt(G*10**3/8/(rau*10**-9))##\n",
+ "print ' \\n\\n Lowest natural frequency for both ends fixed, fn = %.3f Hz'%(fn)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 8.2 Pg 228"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " factor of safety = 1.44\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "Fmin=60## N\n",
+ "Fmax=140## N\n",
+ "d=3## mm\n",
+ "Dm=18## mm\n",
+ "Sut=1430## MPa\n",
+ "\n",
+ "C=Dm/d## spring index\n",
+ "Kw=(4*C-1)/(4*C-4)+0.615/C## Wahl's correction factor\n",
+ "Ks=1+0.5/C## Shear Stress factor\n",
+ "Fm=(Fmax+Fmin)/2## N\n",
+ "Fa=(Fmax-Fmin)/2## N\n",
+ "tau_m=Ks*(8*Fm*C)/(pi*d**2)## MPa\n",
+ "tau_a=Kw*(8*Fa*C)/(pi*d**2)## MPa\n",
+ "Ses_dash=0.22*Sut## MPa\n",
+ "Sys=0.45*Sut## MPa\n",
+ "#tau_m/Sys+tua_a/Ses_dash*(2-Ses_dash/Sys)=1/n\n",
+ "n=1/(tau_m/Sys+tau_a/Ses_dash*(2-Ses_dash/Sys))## factor of safety\n",
+ "print ' \\n factor of safety = %.2f'%(n)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 8.3 Pg 229"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Wahl's correction factor = 1.2525 \n",
+ " \n",
+ " Initial tortional shear stress = 85.05 MPa\n",
+ " \n",
+ " spring stiffness = 9.72 N/mm\n",
+ " \n",
+ " Spring load to cause yielding = 305.7 N\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "Fi=40## N\n",
+ "d=3## mm\n",
+ "C=6## spring index\n",
+ "n=15## factor of safety\n",
+ "tau=650## N/mm.sq.\n",
+ "G=84## kN/mm.sq.\n",
+ "\n",
+ "# Wahl's correction factor\n",
+ "Kw=(4*C-1)/(4*C-4)+0.615/C## Wahl's correction factor\n",
+ "print \"\\n Wahl's correction factor = %.4f \"%Kw\n",
+ "\n",
+ "# Initial tortional shear stress\n",
+ "tau_i=Kw*(8*Fi*C)/(pi*d**2)## MPa\n",
+ "print ' \\n Initial tortional shear stress = %.2f MPa'%(tau_i)\n",
+ "k=G*10**3*d/(8*C**3*n)## spring stiffness\n",
+ "print ' \\n spring stiffness = %.2f N/mm'%(k)\n",
+ "# Spring load to cause yielding\n",
+ "#tau=Kw*(8*Fi*C)/(pi*d**2)\n",
+ "F=tau/(Kw*(8*C)/(pi*d**2))\n",
+ "print ' \\n Spring load to cause yielding = %.1f N'%(F)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 8.4 Pg 230"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " diameter of spring wire = 8.48 mm or 9 mm\n",
+ " \n",
+ " Mean coil diameter = 54 mm\n",
+ " \n",
+ " no. of active coils = 9\n",
+ " \n",
+ " free length of spring = 127.75 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,ceil\n",
+ "# Given Data\n",
+ "Fmin=500## N\n",
+ "Fmax=1200## N\n",
+ "C=6## spring index\n",
+ "n=1.5## factor of safety\n",
+ "Sys=760## MPa\n",
+ "Ses_dash=350## MPa\n",
+ "Del=25## mm\n",
+ "G=82## kN/mm.sq.\n",
+ "\n",
+ "Kw=(4*C-1)/(4*C-4)+0.615/C## Wahl's correction factor\n",
+ "Ks=1+0.5/C## Shear stress factor\n",
+ "Fm=(Fmax+Fmin)/2## N\n",
+ "Fa=(Fmax-Fmin)/2## N\n",
+ "tau_m_into_d_sq=Ks*(8*Fm*C)/(pi)## where tau_m_into_d_sq = tau_m*d**2\n",
+ "tau_a_into_d_sq=Kw*(8*Fa*C)/(pi)## where tau_a_into_d_sq = tau_a*d**2\n",
+ "\n",
+ "#(tau_m-tau_a)/Sys+2*tua_a/Ses_dash=1/n\n",
+ "d=sqrt(n)*sqrt((tau_m_into_d_sq-tau_a_into_d_sq)/Sys+2*tau_a_into_d_sq/Ses_dash)## mm\n",
+ "print ' \\n diameter of spring wire = %.2f mm or %.f mm'%(d, ceil(d))\n",
+ "d=ceil(d)## mm\n",
+ "Dm=C*d## mm\n",
+ "print ' \\n Mean coil diameter = %.f mm'%( Dm)\n",
+ "#del=8*Fmax*Ci**3/(G*d)\n",
+ "i=(Del/(8*Fmax*C**3/(G*10**3*d)))## no. of active coils\n",
+ "i=ceil(i)## no. of active coils\n",
+ "print ' \\n no. of active coils = %.f'%(i)\n",
+ "nt=i+2## no. of active coils (for square & ground ends)\n",
+ "lf=nt*d+1.15*Del## mm\n",
+ "print ' \\n free length of spring = %.2f mm'%(lf)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 8.5 Pg 231"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Force on the valve = 3534.3 N\n",
+ " \n",
+ " Maximum deflection = 60 mm\n",
+ " \n",
+ " Maximum force = 5301.4 N\n",
+ " \n",
+ " Wahls correction factor = 1.2525 \n",
+ " \n",
+ " Diameter of spring wire = 13 mm\n",
+ " \n",
+ " Mean coil diameter = 78 mm\n",
+ " \n",
+ " number of turns = 8 \n",
+ " \n",
+ " Total number of turns for square & ground ends = 10 \n",
+ " \n",
+ " Free length = 199 mm. Use 200 mm\n",
+ " \n",
+ " Pitch of coil = 22.1 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,ceil\n",
+ "# Given Data\n",
+ "p=125## MPa\n",
+ "dv=60## mm\n",
+ "del1=40## mm\n",
+ "del2=20## mm\n",
+ "tau_max=600## MPa\n",
+ "G=85## kN/mm.sq.\n",
+ "C=6## spring index\n",
+ "\n",
+ "Fv=(pi/4)*dv**2*p/100## N (Force on the valve)\n",
+ "del_max=del1+del2## mm (Max. deflection)\n",
+ "Fmax=Fv*dv/del1## N (Max. force)\n",
+ "Kw=(4*C-1)/(4*C-4)+0.615/C## Wahl's correction factor\n",
+ "# tau = 8*Fmax*C*Kw/(pi*d**2)\n",
+ "d=sqrt((8*Fmax*C*Kw/(pi))/tau_max)## mm (Diameter of spring wire)\n",
+ "Dm=6*d## mm (Mean coil diameter)\n",
+ "n=G*10**3*d*del_max/(8*Fmax*C**3)## no. of turns\n",
+ "n = ceil(n)## no. of turns\n",
+ "nt=n+2## total no. of turns\n",
+ "lf=nt*d+1.15*del_max## mm (Free length)\n",
+ "p=lf/(nt-1)## mm (Pitch of coil)\n",
+ "print ' \\n Force on the valve = %.1f N'%(Fv)\n",
+ "print ' \\n Maximum deflection = %.f mm'%( del_max)\n",
+ "print ' \\n Maximum force = %.1f N'%( Fmax)\n",
+ "print ' \\n Wahl''s correction factor = %.4f '%(Kw)\n",
+ "print ' \\n Diameter of spring wire = %.f mm'%(d)\n",
+ "print ' \\n Mean coil diameter = %.f mm'%( Dm)\n",
+ "print ' \\n number of turns = %.f '%(n)\n",
+ "print ' \\n Total number of turns for square & ground ends = %.f '%(nt)\n",
+ "print ' \\n Free length = %.f mm. Use 200 mm'%(lf)\n",
+ "print ' \\n Pitch of coil = %.1f mm'%(p)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 8.7 Pg 232"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Spring force when valve is lifted = 1484.4 N\n",
+ " \n",
+ "\n",
+ " Design of spring - \n",
+ " \n",
+ " Spring stiffness = 61.85 N/mm\n",
+ " \n",
+ " Wahl's correction factor = 1.2525\n",
+ " \n",
+ " spring diameter = 7.54 mm or 8 mm\n",
+ " \n",
+ " no. of active coils = 6.29. Use n=7\n",
+ " \n",
+ " total no. of active coils = 8\n",
+ " \n",
+ " pitch of coils = 16.67 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,ceil\n",
+ "from numpy.linalg import solve\n",
+ "# Given Data\n",
+ "dv=30## mm\n",
+ "Wv=10## N\n",
+ "Wl=25## N\n",
+ "lf=100## mm\n",
+ "del1=20## mm\n",
+ "p=3.5## N/mm.sq.\n",
+ "valve_lift=2## mm\n",
+ "C=6## spring index\n",
+ "tau=500## N/mm.sq.\n",
+ "G=0.84*10**5## N/mm.sq.\n",
+ "\n",
+ "W=(pi/4)*dv**2*p## N (load on the valve at operating condition)\n",
+ "W1=W-Wv##N (Net load on the valve at operating condition)\n",
+ "#W1*100=Wl*150+S1*200+P*300 # taking momens about the fulcrum\n",
+ "#S1*200+P*300=W1*100-Wl*150 ...eqn(1)\n",
+ "valve_lift=20*100/200## mm #from figure (when spring is extended by 20 mm)\n",
+ "spring_extension=2*200/100## mm # from figure (when valve is lifted 2 mm)\n",
+ "valve_load=W*12/10## N # (when valve is lifted 2 mm)\n",
+ "W2=valve_load-Wv## N # (when valve is lifted 2 mm)\n",
+ "del2=del1+4## mm (when valve is lifted)\n",
+ "#S2=S1*del2/del1## spring force when valve is lifted\n",
+ "#S1*del2/del1-s2=0 ... eqn(1)\n",
+ "#W2*100=Wl*150+S2*200+P*300 # taking momens about the fulcrum\n",
+ "#S2*200+P*300 =W2*100-Wl*150 ... eqn(2)\n",
+ "#S1*200+P*300=W1*100-Wl*150 ...eqn(3)\n",
+ "# solving above 3 eqn. by matrix method\n",
+ "A=[[del2/del1, -1, 0],[200, 0, 300],[0, 200, 300]]\n",
+ "B=[[0],[W1*100-Wl*150],[W2*100-Wl*150]]\n",
+ "X=solve(A,B)## solution matrix\n",
+ "S1=X[0]## N\n",
+ "S2=X[1]## N\n",
+ "print ' \\n Spring force when valve is lifted = %.1f N'%(S2)\n",
+ "print ' \\n\\n Design of spring - '\n",
+ "k=(S2-S1)/(del2-del1)## N/mm (Spring stiffness)\n",
+ "print ' \\n Spring stiffness = %.2f N/mm'%(k)\n",
+ "Kw=(4*C-1)/(4*C-4)+0.615/C## Wahl's correction factor\n",
+ "print \" \\n Wahl's correction factor = %.4f\"%(Kw)\n",
+ "# tau=Kw*8*S2*C/pi/d**2 max. shear stress\n",
+ "d=sqrt(Kw*8*S2*C/pi/tau)## mm (spring diameter)\n",
+ "print ' \\n spring diameter = %.2f mm or %.f mm'%(d,d)\n",
+ "d=ceil(d)## mm\n",
+ "# k=G*d/(8*C**3*n) (Spring stiffness)\n",
+ "n=G*d/(8*C**3*k)## no. of active coils\n",
+ "print ' \\n no. of active coils = %.2f. Use n=7'%(n)\n",
+ "n=ceil(n)## rounding\n",
+ "nt=n+1## total no. of active coils\n",
+ "print ' \\n total no. of active coils = %.f'%(nt)\n",
+ "p=lf/(n-1)## mm (pitch of coils)\n",
+ "print ' \\n pitch of coils = %.2f mm'%(p)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 8.8 Pg 234"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " Spring stiffness = 12.5 N/mm\n",
+ " \n",
+ " By hit and trial method and using value of C**3/d -\n",
+ " \n",
+ " value of Spring Index, C = 4.8 \n",
+ " \n",
+ " value of wire diameter, d = 3.9 mm\n",
+ " \n",
+ " But we adopt d=4 mm.\n",
+ " Hence, Spring Index = 4.84 \n",
+ " \n",
+ " Mean coil diameter = 19.36 mm\n",
+ " \n",
+ " Outside coil diameter = 23.36 mm < 25 mm. Hence design is ok.\n",
+ " \n",
+ " Wahls correction factor = 1.322 \n",
+ " \n",
+ " Maximum shear stress = 1018.54 N/mm.sq.\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi\n",
+ "\n",
+ "# Given Data\n",
+ "Fmin=0## N\n",
+ "Fmax=1000## N\n",
+ "Del=80## mm\n",
+ "Do=25## mm\n",
+ "n=30## no. of turns\n",
+ "G=85## kN/mm.sq.\n",
+ "\n",
+ "k=(Fmax-Fmin)/Del## N/mm (Spring stiffness)\n",
+ "print ' \\n Spring stiffness = %.1f N/mm'%(k)\n",
+ "# k=G*d/(8*C**3*n) (Spring stiffness)\n",
+ "C_cube_BY_d=G*10**3/(k*8*n)## \n",
+ "\n",
+ "def hitntrial(c3d,Do):\n",
+ " from numpy import arange\n",
+ " for C in arange(5.0,4.5,-0.1):\n",
+ " d=C**3/(c3d)#\n",
+ " Doo=d*C+C#\n",
+ " if Doo<Do :\n",
+ " break\n",
+ " \n",
+ " return [C,d]\n",
+ "\n",
+ "[C,d]=hitntrial(C_cube_BY_d,Do)\n",
+ "print ' \\n By hit and trial method and using value of C**3/d -'\n",
+ "print ' \\n value of Spring Index, C = %.1f '%(C)\n",
+ "print ' \\n value of wire diameter, d = %.1f mm'%(d)\n",
+ "print ' \\n But we adopt d=4 mm.'\n",
+ "d=4## mm (adopted for design)\n",
+ "C=(C_cube_BY_d*d)**(1/3)## Spring index\n",
+ "print ' Hence, Spring Index = %.2f '%(C)\n",
+ "Dm=C*d## mm\n",
+ "print ' \\n Mean coil diameter = %.2f mm'%( Dm)\n",
+ "Do=Dm+d## mm\n",
+ "print ' \\n Outside coil diameter = %.2f mm < 25 mm. Hence design is ok.'%( Do)\n",
+ "Kw=(4*C-1)/(4*C-4)+0.615/C## Wahl's correction factor\n",
+ "print ' \\n Wahl''s correction factor = %.3f '%(Kw)\n",
+ "tau=8*Kw*C*Fmax/(pi*d**2)## N/mm.sq.\n",
+ "print ' \\n Maximum shear stress = %.2f N/mm.sq.'%(tau)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 8.10 Pg 235"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " wire diameter of spring = 7.28 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi\n",
+ "# Given Data\n",
+ "Fmin=600## N\n",
+ "Fmax=1000## N\n",
+ "C=6## spring index\n",
+ "n=1.5## factor of safety\n",
+ "Sys=700## N/mm.sq.\n",
+ "Ses_dash=350## N/mm.sq.\n",
+ "\n",
+ "Kw=(4*C-1)/(4*C-4)+0.615/C## Wahl's correction factor\n",
+ "Ks=1+0.5/C## Shear Stress factor\n",
+ "Fm=(Fmax+Fmin)/2## N\n",
+ "Fa=(Fmax-Fmin)/2## N\n",
+ "tau_m_into_d_sq=Ks*(8*Fm*C)/(pi)## where tau_m_into_d_sq = tau_m*d**2\n",
+ "tau_a_into_d_sq=Kw*(8*Fa*C)/(pi)## where tau_a_into_d_sq = tau_a*d**2\n",
+ "\n",
+ "#(tau_m-tau_a)/Sys+2*tua_a/Ses_dash=1/n\n",
+ "d=sqrt(n)*sqrt((tau_m_into_d_sq-tau_a_into_d_sq)/Sys+2*tau_a_into_d_sq/Ses_dash)## mm\n",
+ "print ' wire diameter of spring = %.2f mm'%(d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 8.11 Pg 236"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " initial tension in spring = 2500 N\n",
+ " \n",
+ " maximum tension in spring = 2688 N\n",
+ " \n",
+ " stiffness of spring = 31.25 N/mm\n",
+ " \n",
+ " diameter of spring = 17.19 mm. Use 18 mm.\n",
+ " \n",
+ " mean coil diameter = 99 mm\n",
+ " \n",
+ " outside coil diameter = 117 mm\n",
+ " \n",
+ " initial coil diameter = 81 mm\n",
+ " \n",
+ " no. of turns = 35\n",
+ " \n",
+ " total no. of turns(for extension spring) = 36\n",
+ " \n",
+ " free length of spring = 676 mm\n",
+ " \n",
+ " pitch of coils = 19.52 mm\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,ceil\n",
+ "# Given Data\n",
+ "dv=100##mm\n",
+ "C=5.5## spring index\n",
+ "pi=1## N/mm.sq.\n",
+ "p=1.075## N/mm.sq.\n",
+ "Del=6## mm\n",
+ "tau_max=400## N/mm.sq.\n",
+ "G=80## kN/mm.sq.\n",
+ "\n",
+ "Fi=(pi/4)*dv**2*pi## N (initial tension in spring)\n",
+ "print ' \\n initial tension in spring = %.f N'%( Fi)\n",
+ "F=(pi/4)*dv**2*p## N (maximum tension in spring)\n",
+ "print ' \\n maximum tension in spring = %.f N'%( F)\n",
+ "k=(F-Fi)/Del## N/mm (stiffness of spring)\n",
+ "print ' \\n stiffness of spring = %.2f N/mm'%(k)\n",
+ "#Tmax=F*Dm/2 where Dm=5.5*d\n",
+ "Tmax_BY_d=F*5.5/2## calculation\n",
+ "#Tmax=(pi/16)*d**3*tau_max\n",
+ "d=sqrt(Tmax_BY_d/((pi/16)*tau_max))## mm\n",
+ "print ' \\n diameter of spring = %.2f mm. Use 18 mm.'%(d)\n",
+ "d=ceil(d)## mm (rounding)\n",
+ "Dm=5.5*d##mm\n",
+ "print ' \\n mean coil diameter = %.f mm'%(Dm)\n",
+ "Do=Dm+d##mm\n",
+ "print ' \\n outside coil diameter = %.f mm'%(Do)\n",
+ "Di=Dm-d## mm\n",
+ "print ' \\n initial coil diameter = %.f mm'%(Di)\n",
+ "n=G*10**3*d*Del/8/(F-Fi)/C**3## no. of turns\n",
+ "print ' \\n no. of turns = %.f'%(n)\n",
+ "nt=n+1## total no. of turns\n",
+ "print ' \\n total no. of turns(for extension spring) = %.f'%(nt)\n",
+ "gi=1## mm (initial gap)\n",
+ "lf=nt*d+(nt-1)*gi## mm\n",
+ "print ' \\n free length of spring = %.f mm'%(lf)\n",
+ "p=lf/(nt-1)##mm\n",
+ "print ' \\n pitch of coils = %.2f mm'%(p)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 8.12 Pg 236"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " \n",
+ " (i) neglecting the effect of curvature\n",
+ " \n",
+ " Axial load = 412.3 N\n",
+ " \n",
+ " deflection per active turn = 9.954 mm/turn\n",
+ " \n",
+ "\n",
+ " (ii) considering the effect of curvature\n",
+ " \n",
+ " Axial load = 382.5 N\n",
+ " \n",
+ " deflection per active turn = 9.234 mm/turn\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,pi,ceil\n",
+ "# Given Data\n",
+ "d=6##mm\n",
+ "Do=75## mm\n",
+ "tau=350## N/mm.sq.\n",
+ "G=84## kN/mm.sq.\n",
+ "\n",
+ "print ' \\n (i) neglecting the effect of curvature'\n",
+ "dm=Do-d## mm\n",
+ "C=dm/d## spring index\n",
+ "Ks=1+0.5/C## shear stress factor\n",
+ "#tau=Ks*(8*Fmax*C)/(pi*d**2)\n",
+ "Fmax=tau/(Ks*(8*C)/(pi*d**2))## N\n",
+ "print ' \\n Axial load = %.1f N'%(Fmax)\n",
+ "delBYi=8*Fmax*C**3/(G*10**3*d)## mm/turn\n",
+ "print ' \\n deflection per active turn = %.3f mm/turn'%(delBYi)\n",
+ "print ' \\n\\n (ii) considering the effect of curvature'\n",
+ "Kw=(4*C-1)/(4*C-4)+0.615/C## Wahl's correction factor\n",
+ "#tau=Kw*(8*Fmax*C)/(G*d)\n",
+ "Fmax=tau/(Kw*8*C/(pi*d**2))#\n",
+ "print ' \\n Axial load = %.1f N'%(Fmax)\n",
+ "delBYn=8*Fmax*C**3/(G*10**3*d)## mm/turn\n",
+ "print ' \\n deflection per active turn = %.3f mm/turn'%(delBYn)\n",
+ "# Note - answer in the textbook is wrong for last part."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/Machine_Design-I_by_Dr._Sadhu_Singh/chapter9.ipynb b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter9.ipynb
new file mode 100644
index 00000000..e953fd83
--- /dev/null
+++ b/Machine_Design-I_by_Dr._Sadhu_Singh/chapter9.ipynb
@@ -0,0 +1,1257 @@
+{
+ "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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+}
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generated by cgit (git 2.34.1) at 2024-12-20 12:07:38 +0000