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diff --git a/Theory_Of_Machines_by__B._K._Sarkar/Chapter11.ipynb b/Theory_Of_Machines_by__B._K._Sarkar/Chapter11.ipynb new file mode 100755 index 00000000..ec8d5927 --- /dev/null +++ b/Theory_Of_Machines_by__B._K._Sarkar/Chapter11.ipynb @@ -0,0 +1,450 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:ebcd9b3d07a8d6768db168aed38e578ce5aca1ce1a2df85108f9e88506949f89"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter11-VIBRATIONS"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg290"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 11 ILLUSRTATION 1 PAGE NO 290\n",
+ "##TITLE:VIBRATIONS\n",
+ "import math\n",
+ "#calculate frequency of longitudinal vibration and transversve vibaration\n",
+ "##===========================================================================================\n",
+ "##INPUT DATA\n",
+ "PI=3.147\n",
+ "D=.1## DIAMETER OF SHAFT IN m\n",
+ "L=1.10## LENGTH OF SHAFT IN m\n",
+ "W=450## WEIGHT ON THE OTHER END OF SHAFT IN NEWTONS\n",
+ "E=200*10**9## YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n",
+ "## =========================================================================================\n",
+ "A=PI*D**2./4.## AREA OF SHAFT IN mm**2\n",
+ "I=PI*D**4./64.## MOMENT OF INERTIA \n",
+ "delta=W*L/(A*E)## STATIC DEFLECTION IN LONGITUDINAL VIBRATION OF SHAFT IN m\n",
+ "Fn=0.4985/(delta)**.5## FREQUENCY OF LONGITUDINAL VIBRATION IN Hz\n",
+ "delta1=W*L**3./(3.*E*I)## STATIC DEFLECTION IN TRANSVERSE VIBRATION IN m\n",
+ "Fn1=0.4985/(delta1)**.5## FREQUENCY OF TRANSVERSE VIBRATION IN Hz\n",
+ "##============================================================================================\n",
+ "##OUTPUT\n",
+ "print'%s %.2f %s %.2f %s '%('FREQUENCY OF LONGITUDINAL VIBRATION =',Fn,' Hz' 'FREQUENCY OF TRANSVERSE VIBRATION =',Fn1,'Hz')\n",
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "FREQUENCY OF LONGITUDINAL VIBRATION = 888.78 HzFREQUENCY OF TRANSVERSE VIBRATION = 34.99 Hz \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg290"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 11 ILLUSRTATION 2 PAGE NO 290\n",
+ "##TITLE:VIBRATIONS\n",
+ "##FIGURE 11.10\n",
+ "#calculate natural frequency of transverse vibration\n",
+ "#import math\n",
+ "##===========================================================================================\n",
+ "##INPUT DATA\n",
+ "PI=3.147\n",
+ "L=.9## LENGTH OF THE SHAFT IN m\n",
+ "m=100## MASS OF THE BODY IN Kg\n",
+ "L2=.3## LENGTH WHERE THE WEIGHT IS ACTING IN m\n",
+ "L1=L-L2## DISTANCE FROM THE OTHER END\n",
+ "D=.06## DIAMETER OF SHAFT IN m\n",
+ "W=9.81*m## WEGHT IN NEWTON\n",
+ "E=200.*10**9.## YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n",
+ "##==========================================================================================\n",
+ "##CALCULATION\n",
+ "I=PI*D**4./64.## MOMENT OF INERTIA IN m**4\n",
+ "delta=W*L1**2*L2**2./(3.*E*I*L)## STATIC DEFLECTION\n",
+ "Fn=.4985/(delta)**.5## NATURAL FREQUENCY OF TRANSVERSE VIBRATION\n",
+ "##=========================================================================================\n",
+ "##OUTPUT\n",
+ "print'%s %.1f %s'%('NATURAL FREQUENCY OF TRANSVERSE VIBRATION=',Fn,' Hz')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "NATURAL FREQUENCY OF TRANSVERSE VIBRATION= 51.9 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg291"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 11 ILLUSRTATION 3 PAGE NO 291 ##TITLE:VIBRATIONS\n",
+ "##FIGURE 11.11\n",
+ "import math\n",
+ "#calculate frequency of longitudnial vibration and frequency of transverse vibration and torisional vibration\n",
+ "##===========================================================================================\n",
+ "##INPUT DATA\n",
+ "PI=3.147\n",
+ "g=9.81## ACCELERATION DUE TO GRAVITY IN N /m**2\n",
+ "D=.050## DIAMETER OF SHAFT IN m\n",
+ "m=450## WEIGHT OF FLY WHEEL IN IN Kg\n",
+ "K=.5## RADIUS OF GYRATION IN m\n",
+ "L2=.6## FROM FIGURE IN m\n",
+ "L1=.9## FROM FIGURE IN m\n",
+ "L=L1+L2\n",
+ "E=200.*10**9## YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n",
+ "C=84.*10**9## MODUKUS OF RIDITY OF SHAFT MATERIAL IN Pascals\n",
+ "##=========================================================================================\n",
+ "A=PI*D**2./4.## AREA OF SHAFT IN mm**2\n",
+ "I=PI*D**4./64.## \n",
+ "m1=m*L2/(L1+L2)## MASS OF THE FLYWHEEL CARRIED BY THE LENGTH L1 IN Kg\n",
+ "DELTA=m1*g*L1/(A*E)## EXTENSION OF LENGTH L1 IN m\n",
+ "Fn=0.4985/(DELTA)**.5## FREQUENCY OF LONGITUDINAL VIBRATION IN Hz\n",
+ "DELTA1=(m*g*L1**3*L2**3)/(3*E*I*L**3)## STATIC DEFLECTION IN TRANSVERSE VIBRATION IN m\n",
+ "Fn1=0.4985/(DELTA1)**.5## FREQUENCY OF TRANSVERSE VIBRATION IN Hz\n",
+ "J=PI*D**4./32.## POLAR MOMENT OF INERTIA IN m**4\n",
+ "Q1=C*J/L1## TORSIONAL STIFFNESS OF SHAFT DUE TO L1 IN N-m\n",
+ "Q2=C*J/L2## TORSIONAL STIFFNESS OF SHAFT DUE TO L2 IN N-m\n",
+ "Q=Q1+Q2## TORSIONAL STIFFNESS OF SHAFT IN Nm\n",
+ "Fn2=(Q/(m*K**2))**.5/(2.*PI)## FREQUENCY OF TORSIONAL VIBRATION IN Hz\n",
+ "##=======================================================================================\n",
+ "print'%s %.3f %s %.3f %s %.3f %s '%('FREQUENCY OF LONGITUDINAL VIBRATION = ',Fn,' Hz''FREQUENCY OF TRANSVERSE VIBRATION = ',Fn1,' Hz'' FREQUENCY OF TORSIONAL VIBRATION = ',Fn2,' Hz')\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "FREQUENCY OF LONGITUDINAL VIBRATION = 248.014 HzFREQUENCY OF TRANSVERSE VIBRATION = 14.916 Hz FREQUENCY OF TORSIONAL VIBRATION = 5.673 Hz \n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex6-pg294"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 11 ILLUSRTATION 6 PAGE NO 294\n",
+ "##TITLE:VIBRATIONS\n",
+ "##FIGURE 11.14\n",
+ "import math\n",
+ "#calculate frequency of transverse vibration\n",
+ "##===========================================================================================\n",
+ "##INPUT DATA\n",
+ "PI=3.147\n",
+ "g=9.81## ACCELERATION DUE TO GRAVITY IN N /m**2\n",
+ "D=.06## DIAMETER OF SHAFT IN m\n",
+ "L=3.## LENGTH OF SHAFT IN m\n",
+ "W1=1500.## WEIGHT ACTING AT C IN N\n",
+ "W2=2000.## WEIGHT ACTING AT D IN N\n",
+ "W3=1000.## WEIGHT ACTING AT E IN N\n",
+ "L1=1.## LENGTH FROM A TO C IN m\n",
+ "L2=2.## LENGTH FROM A TO D IN m\n",
+ "L3=2.5## LENGTH FROM A TO E IN m\n",
+ "I=PI*D**4./64.\n",
+ "E=200.*10**9.## YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n",
+ "##===========================================================================================\n",
+ "DELTA1=W1*L1**2.*(L-L1)**2./(3.*E*I*L)## STATIC DEFLECTION DUE TO W1\n",
+ "DELTA2=W2*L2**2.*(L-L2)**2./(3.*E*I*L)## STATIC DEFLECTION DUE TO W2\n",
+ "DELTA3=W2*L3**2.*(L-L3)**2./(3.*E*I*L)## STATIC DEFLECTION DUE TO W2\n",
+ "Fn=.4985/(DELTA1+DELTA2+DELTA3)**.5## FREQUENCY OF TRANSVERSE VIBRATION IN Hz\n",
+ "##==========================================================================================\n",
+ "print'%s %.3f %s'%('FREQUENCY OF TRANSVERSE VIBRATION = ',Fn,' Hz')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "FREQUENCY OF TRANSVERSE VIBRATION = 4.080 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex10-pg296"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 11 ILLUSRTATION 10 PAGE NO 296\n",
+ "##TITLE:VIBRATIONS\n",
+ "##FIGURE 11.18\n",
+ "import math\n",
+ "#calculate FREQUENCY OF TRANSVERSE VIBRATION\n",
+ "##===========================================================================================\n",
+ "##INPUT DATA\n",
+ "PI=3.147\n",
+ "g=9.81## ACCELERATION DUE TO GRAVITY IN N /m**2\n",
+ "E=200.*10**9## YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n",
+ "D=.03## DIAMETER OF SHAFT IN m\n",
+ "L=.8## LENGTH OF SHAFT IN m\n",
+ "r=40000.## DENSITY OF SHAFT MATERIAL IN Kg/m**3\n",
+ "W=10.## WEIGHT ACTING AT CENTRE IN N\n",
+ "##===========================================================================================\n",
+ "I=PI*D**4./64.## MOMENT OF INERTIA OF SHAFT IN m**4\n",
+ "m=PI*D**2./4.*r## MASS PER UNIT LENGTH IN Kg/m\n",
+ "w=m*g\n",
+ "DELTA=W*L**3./(48.*E*I)## STATIC DEFLECTION DUE TO W\n",
+ "DELTA1=5.*w*L**4./(384.*E*I)## STATIC DEFLECTION DUE TO WEIGHT OF SHAFT \n",
+ "Fn=.4985/(DELTA+DELTA1/1.27)**.5\n",
+ "##==========================================================================================\n",
+ "print'%s %.3f %s'%('FREQUENCY OF TRANSVERSE VIBRATION = ',Fn,' Hz')\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "FREQUENCY OF TRANSVERSE VIBRATION = 39.426 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex11-pg297"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 11 ILLUSRTATION 11 PAGE NO 297\n",
+ "##TITLE:VIBRATIONS\n",
+ "##FIGURE 11.19\n",
+ "import math\n",
+ "#evaluvate CRITICAL SPEED OF SHAFT\n",
+ "##===========================================================================================\n",
+ "##INPUT DATA\n",
+ "PI=3.147\n",
+ "g=9.81## ACCELERATION DUE TO GRAVITY IN N /m**2\n",
+ "E=210.*10**9.## YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n",
+ "D=.18## DIAMETER OF SHAFT IN m\n",
+ "L=2.5## LENGTH OF SHAFT IN m\n",
+ "M1=25.## MASS ACTING AT E IN Kg\n",
+ "M2=50.## MASS ACTING AT D IN Kg\n",
+ "M3=20.## MASS ACTING AT C IN Kg\n",
+ "W1=M1*g\n",
+ "W2=M2*g\n",
+ "W3=M3*g\n",
+ "L1=.6## LENGTH FROM A TO E IN m\n",
+ "L2=1.5## LENGTH FROM A TO D IN m\n",
+ "L3=2.## LENGTH FROM A TO C IN m\n",
+ "w=1962.## SELF WEIGHT OF SHAFT IN N\n",
+ "##==========================================================================================\n",
+ "I=PI*D**4./64.## MOMENT OF INERTIA OF SHAFT IN m**4\n",
+ "DELTA1=W1*L1**2.*(L-L1)**2./(3.*E*I*L)## STATIC DEFLECTION DUE TO W1\n",
+ "DELTA2=W2*L2**2.*(L-L2)**2./(3.*E*I*L)## STATIC DEFLECTION DUE TO W2\n",
+ "DELTA3=W3*L3**2.*(L-L3)**2./(3.*E*I*L)## STATIC DEFLECTION DUE TO W3\n",
+ "DELTA4=5.*w*L**4./(384.*E*I)## STATIC DEFLECTION DUE TO w\n",
+ "Fn=.4985/(DELTA1+DELTA2+DELTA3+DELTA4/1.27)**.5\n",
+ "Nc=Fn*60## CRITICAL SPEED OF SHAFT IN rpm\n",
+ "##========================================================================================\n",
+ "print'%s %.3f %s'%('CRITICAL SPEED OF SHAFT = ',Nc,' rpm')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "CRITICAL SPEED OF SHAFT = 3111.629 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex12-pg298"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 11 ILLUSRTATION 12 PAGE NO 298\n",
+ "##TITLE:VIBRATIONS\n",
+ "##FIGURE 11.20\n",
+ "import math\n",
+ "#calculate FREQUENCY OF FREE TORSIONAL VIBRATION\n",
+ "##===========================================================================================\n",
+ "##INPUT DATA\n",
+ "PI=3.147\n",
+ "g=9.81## ACCELERATION DUE TO GRAVITY IN N /m**2\n",
+ "Na=1500.## SPEED OF SHAFT A IN rpm\n",
+ "Nb=500.## SPEED OF SHAFT B IN rpm\n",
+ "G=Na/Nb## GERA RATIO\n",
+ "L1=.18## LENGTH OF SHAFT 1 IN m\n",
+ "L2=.45## LENGTH OF SHAFT 2 IN m\n",
+ "D1=.045## DIAMETER OF SHAFT 1 IN m\n",
+ "D2=.09## DIAMETER OF SHAFT 2 IN m\n",
+ "C=84.*10**9## MODUKUS OF RIDITY OF SHAFT MATERIAL IN Pascals\n",
+ "Ib=1400.## MOMENT OF INERTIA OF PUMP IN Kg-m**2\n",
+ "Ia=400.## MOMENT OF INERTIA OF MOTOR IN Kg-m**2\n",
+ "\n",
+ "##======================================================================================\n",
+ "J=PI*D1**4./32.## POLAR MOMENT OF INERTIA IN m**4\n",
+ "Ib1=Ib/G**2.## MASS MOMENT OF INERTIA OF EQUIVALENT ROTOR IN m**2\n",
+ "L3=G**2.*L2*(D1/D2)**4.## ADDITIONAL LENGTH OF THE EQUIVALENT SHAFT\n",
+ "L=L1+L3## TOTAL LENGTH OF EQUIVALENT SHAFT\n",
+ "La=L*Ib1/(Ia+Ib1)\n",
+ "Fn=(C*J/(La*Ia))**.5/(2.*PI)## FREQUENCY OF FREE TORSIONAL VIBRATION IN Hz\n",
+ "##===================================================================================\n",
+ "print'%s %.2f %s'%('FREQUENCY OF FREE TORSIONAL VIBRATION = ',Fn,' Hz')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "FREQUENCY OF FREE TORSIONAL VIBRATION = 4.20 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex13-pg300"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "##CHAPTER 11 ILLUSRTATION 13 PAGE NO 300\n",
+ "##TITLE:VIBRATIONS\n",
+ "##FIGURE 11.21\n",
+ "import math\n",
+ "#calculate critical speed of shaft and the range of speed \n",
+ "##===========================================================================================\n",
+ "##INPUT DATA\n",
+ "PI=3.147\n",
+ "g=9.81## ACCELERATION DUE TO GRAVITY IN N /m**2\n",
+ "D=.015## DIAMETER OF SHAFT IN m\n",
+ "L=1.00## LENGTH OF SHAFT IN m\n",
+ "M=15.## MASS OF SHAFT IN Kg\n",
+ "W=M*g\n",
+ "e=.0003## ECCENTRICITY IN m\n",
+ "E=200.*10**9.## YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n",
+ "f=70.*10**6.## PERMISSIBLE STRESS IN N/m**2\n",
+ "##============================================================================================\n",
+ "I=PI*D**4./64.## MOMENT OF INERTIA OF SHAFT IN m**4\n",
+ "DELTA=W*L**3./(192.*E*I)## STATIC DEFLECTION IN m\n",
+ "Fn=.4985/(DELTA)**.5## NATURAL FREQUENCY OF TRANSVERSE VIBRATION\n",
+ "Nc=Fn*60.## CRITICAL SPEED OF SHAFT IN rpm\n",
+ "M1=16.*f*I/(D*g*L)\n",
+ "W1=M1*g## ADDITIONAL LOAD ACTING\n",
+ "y=W1/W*DELTA## ADDITIONAL DEFLECTION DUE TO W1\n",
+ "N1=Nc/(1.+e/y)**.5## MIN SPEED IN rpm\n",
+ "N2=Nc/(1.-e/y)**.5## MAX SPEED IN rpm\n",
+ "##===========================================================================================\n",
+ "print'%s %.3f %s %.3f %s %.3f %s '%('CRITICAL SPEED OF SHAFT = ',Nc,' rpm''THE RANGE OF SPEED IS FROM',N1,'rpm TO ',N2,' rpm')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "CRITICAL SPEED OF SHAFT = 762.330 rpmTHE RANGE OF SPEED IS FROM 709.555 rpm TO 828.955 rpm \n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |