{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Ch:8 Springs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exa 8-1 - Page 224" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Ks is 1.0000 \n", "\n", " Kw is 1.1025 \n", "\n", " Kc is 1.103 \n", "\n", " The Spring Stiffness is 16.0 N/mm\n", "\n", " The Axial deflection is 18.000 mm\n" ] } ], "source": [ "d=5#\n", "D=30#\n", "G=84*(10**3)#\n", "Na=15#\n", "#Axial Load W\n", "W=300#\n", "#Spring index C\n", "C=30/5#\n", "#Shear stress Augmentation factor Ks\n", "Ks=((2*C)+1)/(2*C)#\n", "#Wahl's factor Kw\n", "Kw=(((4*C)-1)/((4*C)-4))+(0.615/C)#\n", "#Curvature correction factor Kc\n", "Kc=Kw/Ks#\n", "#Spring stiffness k\n", "k=(G*(d**4))/(8*(D**3)*Na)#\n", "#Axial deflection delta\n", "delta=W/k#\n", "print \" Ks is %0.4f \"%(Ks)#\n", "print \"\\n Kw is %0.4f \"%(Kw)#\n", "print \"\\n Kc is %0.3f \"%(Kc)#\n", "print \"\\n The Spring Stiffness is %0.1f N/mm\"%(k)#\n", "print \"\\n The Axial deflection is %0.3f mm\"%(delta)#" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exa 8-2 - Page 224" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " wire diameter is 2.314 mm \n", "\n", " mean diameter is 18.516 mm \n", "\n", " Number of acting coils are 11.117 \n" ] } ], "source": [ "from math import pi\n", "W=196.2#\n", "lenthofscale=50#\n", "k=196.2/50#\n", "C=8#\n", "Ks=(1+(0.5/C))#\n", "\n", "# Let us choose oil tempered wire 0.6-0.7 %C. Refer to Table 8-4 for constants A and m, relating strength wire \n", "#diameter.\n", "G=77.2*(10**3)#\n", "A=1855#\n", "m=0.187#\n", "# equating Tmax=0.5*sig(ut).\n", "# Ks*(8*W*D/(pi*(d**3)))=0.5*A/(d**2)\n", "d1=(Ks*(8*W*C/(pi*A*0.5)))#\n", "d=d1**(1/1.813)#\n", "D=C*d#\n", "Na=G*(d**4)/(8*(D**3)*k)#\n", "#Solid length = SL\n", "SL=(Na-1)*d\n", "\n", "print \" wire diameter is %0.3f mm \"%(d)#\n", "print \"\\n mean diameter is %0.3f mm \"%(D)#\n", "print \"\\n Number of acting coils are %0.3f \"%(Na)#\n", "\n", "#The difference in the values of d,D and Na is due to rounding-off the digits." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exa 8-3 - Page 225" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Ultimate tensile Strength is 2060.5 MPa \n", "\n", " Force at which the spring hook fails is 211.3 N \n" ] } ], "source": [ "from math import pi\n", "d=1.626#\n", "A=2211#\n", "m=0.145#\n", "rm=3#\n", "ri=(rm-(d/2))#\n", "sigma=A/(d**m)#\n", "W=(sigma*pi*(d**3)*ri)/(32*(rm**2))#\n", "print \" Ultimate tensile Strength is %0.1f MPa \"%(sigma)#\n", "print \"\\n Force at which the spring hook fails is %0.1f N \"%(W)#\n", "\n", "#The difference in the values of sigma and W is due to rounding-off the digits." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exa 8-4 - Page 226" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " d is 2.337mm \n", "\n", " D is 22.20 mm\n", "\n", " Ls is 26.18 mm\n", "\n", " Lo is 83.68 mm\n", "\n", "The diameter is within space constraints\n" ] } ], "source": [ "from math import pi\n", "Do=25#\n", "# mean coil diameter D=25-d\n", "W=150#\n", "T=800#\n", "G=81000#\n", "# Substituting values in equation T=8*W*D/(pi*(d**3))\n", "# therefore, the equation becomes d**3 + 0.477*d = 11.936\n", "#consider d=2.2mm, (d can be taken between 2.2-2.3mm)\n", "d=2.337# #(nearest available wire gauge)\n", "C=9.5#\n", "D=22.2# \n", "Do=D+d#\n", "Ks=1+(0.5/C)#\n", "Tmax=Ks*8*W*D/(pi*(d**3))#\n", "# check for safety- Tmax=5.26):\n", " print 'The spring will fail under buckling'\n", "\n", "\n", "#Values after the decimal point has not been considered for answer of Torsional yeild strength in the book, whereas answers for deflection and free-length is different as entire value of variables is taken for calculation in the code." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exa 8-8 - Page 229" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k is 3.000 N/mm \n", "\n", " W is 77.5 N \n", "\n", " Lo is 49.720 mm \n", "\n", " p is 5.302 mm \n", "The spring will fail under buckling\n" ] } ], "source": [ "from math import pi\n", "d=2#\n", "Do=20#\n", "D=Do-d#\n", "C=D/d#\n", "Na=9#\n", "#Material hard drawn spring steel\n", "A=1783#\n", "m=0.19#\n", "G=81000#\n", "sig=A/(d**m)#\n", "Tys=0.45*sig\n", "Kf=1.5#\n", "Ta=Tys/Kf#\n", "Ks=1+(0.5/C)#\n", "W=(Ta*pi*(d**3))/(8*D*Ks)#\n", "k=(G*(d**4))/(8*(D**3)*Na)#\n", "Del=W/k#\n", "Lo=((Na+1)*d)+(1.15*Del)#\n", "p=(Lo-d)/Na#\n", "print \"k is %0.3f N/mm \"%(k)#\n", "print \"\\n W is %0.1f N \"%(W)#\n", "print \"\\n Lo is %0.3f mm \"%(Lo)#\n", "print \"\\n p is %0.3f mm \"%(p)\n", " \n", " \n", "if ((Lo)>=47.34):\n", " print 'The spring will fail under buckling'\n", "\n", "#The answer for value of spring rate 'k' is misprinted in the book. Due to this all subsequent values of del,Lo,p is calucated incorrectly in the book." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exa 8-9 - Page 230" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Maximum Torque is 497.25 Nmm \n", "\n", " theta3 is 0.327 turns \n", "\n", " Ne is 0.293 turns \n", "\n", " ke is 22089.3 N/mm \n", "\n", " theta1+theta2 is 0.0225 turns \n", "\n", " D1 is 13.46 mm \n", "\n", " IRC is 0.75 mm \n", "\n", " FRC is 0.23 mm \n" ] } ], "source": [ "from math import pi\n", "# for music wire\n", "d1=11.5#\n", "A=2211#\n", "d=1.5#\n", "m=0.145#\n", "sigut=A/(d**m)#\n", "sigy=0.78*sigut#\n", "Do=16#\n", "E=2*(10**5)#\n", "Nb=4.25#\n", "D=Do-d#\n", "C=D/d#\n", "Ki=((4*(C**2))-C-1)/(4*C*(C-1))#\n", "Mmax=(sigy*pi*(d**3))/(32*Ki)#\n", "kc=((d**4)*E)/(10.8*D*Nb)#\n", "theta3=Mmax/kc#\n", "l1=20#\n", "l2=20#\n", "Ne=(l1+l2)/(3*pi*D)#\n", "Na=Nb+Ne#\n", "k=((d**4)*E)/(10.8*Na*D)#\n", "thetat=Mmax/k#\n", "ke=(3*pi*(d**4)*E)/(10.8*(l1+l2))#\n", "# angdisp=theta1+theta2=Mmax/ke#\n", "angdisp=Mmax/ke#\n", "#D1 is final coil diameter\n", "D1=(Nb*D)/(Nb+theta3)#\n", "#IRC=Initial radial clearance\n", "IRC=((D-d)-d1)/2#\n", "#FRC=Final radial clearance\n", "FRC=((D1-d)-d1)/2#\n", "\n", "\n", "\n", "print \" Maximum Torque is %0.2f Nmm \"%(Mmax)#\n", "print \"\\n theta3 is %0.3f turns \"%(theta3)#\n", "print \"\\n Ne is %0.3f turns \"%(Ne)#\n", "print \"\\n ke is %0.1f N/mm \"%(ke)#\n", "print \"\\n theta1+theta2 is %0.4f turns \"%(angdisp)#\n", "print \"\\n D1 is %0.2f mm \"%(D1)#\n", "print \"\\n IRC is %0.2f mm \"%(IRC)#\n", "print \"\\n FRC is %0.2f mm \"%(FRC)#" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exa 8-10 - Page 231" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " d is 2.0 mm \n", "\n", " D is 15.0 mm \n", "\n", " Na is 11.00 mm \n" ] } ], "source": [ "from math import pi\n", "A=1783#\n", "m=0.190#\n", "d=1.5#\n", "D=15#\n", "M=300#\n", "E=20800#\n", "k=30#\n", "#sigult= ultimate strength of the material\n", "# sigy= yield strength of the material\n", "sigult=A/(d**m)#\n", "sigy=0.7*sigult#\n", "#siga= allowable yield strength of the material\n", "siga=sigy/2#\n", "C=D/d#\n", "Ki=(4*(C**2)-C-1)/(4*C*(C-1))#\n", "Z=pi*(d**3)/32#\n", "#sigb=bending strength of the material#\n", "sigb=Ki*M/Z#\n", "while (sigb>=siga) :\n", " d=d+0.15#\n", " D=15#\n", " C=D/d#\n", " sigult=A/(d**m)#\n", " sigy=0.7*sigult#\n", " siga=sigy/2#\n", " Ki=(4*(C**2)-C-1)/(4*C*(C-1))#\n", " Z=pi*(d**3)/32#\n", " sigb=Ki*M/Z#\n", "\n", "d=2## rounding off the value of the diameter.\n", "Na=(d**4)*E/(64*D*k)#\n", "print \" d is %0.1f mm \"%(d)#\n", "print \"\\n D is %0.1f mm \"%(D)#\n", "print \"\\n Na is %0.2f mm \"%(Na)#" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exa 8-11 - Page 231" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t is 14 mm \n", "\n", " Wf is 10909 N \n", "\n", " I is 34300 mm**4 \n", "\n", " del is 52.0 mm \n" ] } ], "source": [ "from math import pi\n", "L=1180#\n", "W=40*(10**3)#\n", "Nf=2#\n", "Ng=8#\n", "E=207*(10**3)#\n", "#sigut is ultimate strength\n", "sigut=1400#\n", "FOS=2#\n", "#siga= allowable yield strength of the material\n", "siga=1400/2#\n", "#sigbf=bending strength in full length\n", "sigbf=700#\n", "b=75#\n", "t=((4.5*W*L)/(((3*Nf)+(2*Ng))*sigbf))**(0.5)#\n", "t=14#\n", "I=(Nf*b*(t**3))/12#\n", "Wf=(3*Nf*W)/((3*Nf)+(2*Ng))#\n", "Del=(Wf*(L**3))/(48*E*I)#\n", "print \" t is %0.0f mm \"%(t)#\n", "print \"\\n Wf is %0.0f N \"%(Wf)#\n", "print \"\\n I is %0.0f mm**4 \"%(I)#\n", "print \"\\n del is %0.1f mm \"%(Del)#" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exa 8-12A - Page 232" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t is 15.0 mm \n", "\n", " deli is 16.0 mm \n", "\n", " Wi is 6366 N \n" ] } ], "source": [ "W=80000#\n", "sigbfr=500#\n", "L=1100#\n", "Nf=3#\n", "Ng=10#\n", "N=Nf+Ng#\n", "t=((1.5*W*L)/(N*6*sigbfr))**(1/3)#\n", "t=15#\n", "b=6*t#\n", "E=207*10**3#\n", "deli=(W*(L**3))/(8*E*N*b*(t**3))#\n", "Wi=(W*Nf*Ng)/(N*((3*Nf)+(2*Ng)))#\n", "print \" t is %0.1f mm \"%(t)#\n", "print \"\\n deli is %0.1f mm \"%(deli)#\n", "print \"\\n Wi is %0.0f N \"%(Wi)#" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exa 8-13 - Page 233" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Tm is 169.77 MPa \n", "\n", " Ta is 86.2 MPa \n", "\n", " FOS is 1.548 \n" ] } ], "source": [ "from math import pi\n", "#ultimate strength=sigut\n", "sigut=1500#\n", "C=7#\n", "d=3#\n", "D=C*d#\n", "Ks=1+(0.5/C)#\n", "Kw=(((4*C)-1)/((4*C)-4))+(0.615/C)#\n", "Pmax=120#\n", "Pmin=40#\n", "Pm=80#\n", "Tm=(Ks*8*Pm*D)/(pi*(d**3))#\n", "Ta=(Kw*8*Pmin*D)/(pi*(d**3))#\n", "Tse=0.22*sigut#\n", "Tys=0.45*sigut#\n", "x=(Tys-(0.5*Tse))/(0.5*Tse)#\n", "y=((x)*Ta)+Tm#\n", "FOS=(Tys/y)#\n", "print \" Tm is %0.2f MPa \"%(Tm)#\n", "print \"\\n Ta is %0.1f MPa \"%(Ta)#\n", "print \"\\n FOS is %0.3f \"%(FOS)#" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## exa 8-14 - Page 234" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Tm is 186.64 MPa \n", "\n", " Ta is 126.337 MPa \n", "\n", " FOS is 1.26 \n" ] } ], "source": [ "from math import pi\n", "Tse=360#\n", "Tys=660#\n", "d=25#\n", "P=0.03#\n", "m=40#\n", "Pmin=((pi*(d**2)*P)/4)+(m*9.81/1000)#\n", "k=6#\n", "#Additional load= Padd=k*further compression in spring\n", "Padd=k*10#\n", "Pmax=Padd+Pmin#\n", "Pm=(Pmax+Pmin)/2#\n", "Pa=(Pmax-Pmin)/2#\n", "d=2#\n", "D=12#\n", "C=6#\n", "Ks=1+(0.5/C)#\n", "Ks=1.083#\n", "Kw=(((4*C)-1)/((4*C)-4))+(0.615/C)#\n", "Ta=(Kw*8*Pa*D)/(pi*(d**3))#\n", "Tm=(Ks*8*Pm*D)/(pi*(d**3))#\n", "x=(Tys-(0.5*Tse))/(0.5*Tse)#\n", "y=((x)*Ta)+Tm#\n", "FOS=(Tys/y)#\n", "print \" Tm is %0.2f MPa \"%(Tm)#\n", "print \"\\n Ta is %0.3f MPa \"%(Ta)#\n", "print \"\\n FOS is %0.2f \"%(FOS)#" ] } ], "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 }