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| author | Prashant S | 2020-04-14 10:25:32 +0530 |
|---|---|---|
| committer | GitHub | 2020-04-14 10:25:32 +0530 |
| commit | 06b09e7d29d252fb2f5a056eeb8bd1264ff6a333 (patch) | |
| tree | 2b1df110e24ff0174830d7f825f43ff1c134d1af /Theory_Of_Machines_by_B_K_Sarkar | |
| parent | abb52650288b08a680335531742a7126ad0fb846 (diff) | |
| parent | 476705d693c7122d34f9b049fa79b935405c9b49 (diff) | |
| download | all-scilab-tbc-books-ipynb-master.tar.gz all-scilab-tbc-books-ipynb-master.tar.bz2 all-scilab-tbc-books-ipynb-master.zip | |
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diff --git a/Theory_Of_Machines_by_B_K_Sarkar/1-Basic_kinemtics.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/1-Basic_kinemtics.ipynb new file mode 100644 index 0000000..fa18783 --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/1-Basic_kinemtics.ipynb @@ -0,0 +1,568 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 1: Basic kinemtics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.10: angular_acceleration_of_connecting_rod_BA.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 10 PAGE NO 24\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.30(a),1.30(b),1.30(c)\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"Nao=300// speed of crank in rpm\n", +"AO=.15// length of crank in m\n", +"BA=.6// length of connecting rod in m\n", +"//===================\n", +"wAO=2*pi*Nao/60// angular velocity of link in rad/s\n", +"Vao=wAO*AO// linear velocity of A with respect to 'o'\n", +"ab=3.4// length of vector ab by measurement in m/s\n", +"Vba=ab\n", +"ob=4// length of vector ob by measurement in m/s\n", +"oc=4.1// length of vector oc by measurement in m/s\n", +"fRao=Vao^2/AO// radial component of acceleration of A with respect to O\n", +"fRba=Vba^2/BA// radial component of acceleration of B with respect to A\n", +"wBA=Vba/BA// angular velocity of connecting rod BA\n", +"fTba=103// by measurement in m/s^2\n", +"alphaBA=fTba/BA// angular acceleration of connecting rod BA\n", +"printf('linear velocity of A with respect to O= %.3f m/s\n radial component of acceleration of A with respect to O= %.3f m/s^2\n radial component of acceleration of B with respect to A= %.3f m/s^2\n angular velocity of connecting rod B= %.3f rad/s\n angular acceleration of connecting rod BA= %.3f rad/s^2',Vao,fRao,fRba,wBA,alphaBA)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.11: angular_acceleration_of_AB.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 11 PAGE NO 26\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.31(a),1.31(b),1.31(c)\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"wAP=10// angular velocity of crank in rad/s\n", +"P1A=30// length of link P1A in cm\n", +"P2B=36// length of link P2B in cm\n", +"AB=36// length of link AB in cm\n", +"P1P2=60// length of link P1P2 in cm\n", +"AP1P2=60// crank inclination in degrees \n", +"alphaP1A=30// angulare acceleration of crank P1A in rad/s^2\n", +"//=====================================\n", +"Vap1=wAP*P1A/100// linear velocity of A with respect to P1 in m/s\n", +"Vbp2=2.2// velocity of B with respect to P2 in m/s(measured from figure )\n", +"Vba=2.06// velocity of B with respect to A in m/s(measured from figure )\n", +"wBP2=Vbp2/(P2B*100)// angular velocity of P2B in rad/s\n", +"wAB=Vba/(AB*100)// angular velocity of AB in rad/s\n", +"fAB1=alphaP1A*P1A/100// tangential component of the acceleration of A with respect to P1 in m/s^2\n", +"frAB1=Vap1^2/(P1A/100)// radial component of the acceleration of A with respect to P1 in m/s^2\n", +"frBA=Vba^2/(AB/100)// radial component of the acceleration of B with respect to B in m/s^2\n", +"frBP2=Vbp2^2/(P2B/100)// radial component of the acceleration of B with respect to P2 in m/s^2\n", +"ftBA=13.62// tangential component of B with respect to A in m/s^2(measured from figure)\n", +"ftBP2=26.62// tangential component of B with respect to P2 in m/s^2(measured from figure)\n", +"alphaBP2=ftBP2/(P2B/100)// angular acceleration of P2B in m/s^2\n", +"alphaBA=ftBA/(AB/100)// angular acceleration of AB in m/s^2\n", +"//==========================\n", +"printf('Angular acceleration of P2B=%.3f rad/s^2\n angular acceleration of AB =%.3f rad/s^2',alphaBP2,alphaBA)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.12: Accelaration_of_the_slider.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 12 PAGE NO 28\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.32(a),1.32(b),1.32(c)\n", +"clc\n", +"clear\n", +"PI=3.141\n", +"AB=12// length of link AB in cm\n", +"BC=48// length of link BC in cm\n", +"CD=18// length of link CD in cm\n", +"DE=36// length of link DE in cm\n", +"EF=12// length of link EF in cm\n", +"FP=36// length of link FP in cm\n", +"Nba=200// roating speed of link BA IN rpm\n", +"wBA=2*PI*200/60// Angular velocity of BA in rad/s\n", +"Vba=wBA*AB/100// linear velocity of B with respect to A in m/s\n", +"Vc=2.428// velocity of c in m/s from diagram 1.32(b)\n", +"Vd=2.36// velocity of D in m/s from diagram 1.32(b)\n", +"Ve=1// velocity of e in m/s from diagram 1.32(b)\n", +"Vf=1.42// velocity of f in m/s from diagram 1.32(b)\n", +"Vcb=1.3// velocity of c with respect to b in m/s from figure\n", +"fBA=Vba^2*100/AB// radial component of acceleration of B with respect to A in m/s^2\n", +"fCB=Vcb^2*100/BC// radial component of acceleration of C with respect to B in m/s^2\n", +"fcb=3.52// radial component of acceleration of C with respect to B in m/s^2 from figure\n", +"fC=19// acceleration of slider in m/s^2 from figure\n", +"printf('velocity of c=%.3f m/s\n velocity of d=%.3f m/s\n velocity of e=%.3f m/s\n velocity of f=%.3f m/s\n Acceleration of slider=%f m/s^2',Vc,Vd,Ve,Vf,fC)\n", +"\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.13: angular_acceleration.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 13 PAGE NO 30\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.33(a),1.33(b),1.33(c)\n", +"clc\n", +"clear\n", +"PI=3.141\n", +"N=120// speed of the crank OC in rpm\n", +"OC=5// length of link OC in cm\n", +"cp=20// length of link CP in cm\n", +"qa=10// length of link QA in cm\n", +"pa=5// length of link PA in cm\n", +"CP=46.9// velocity of link CP in cm/s\n", +"QA=58.3// velocity of link QA in cm/s\n", +"Pa=18.3// velocity of link PA in cm/s\n", +"Vc=2*PI*N*OC/60// velocity of C in m/s\n", +"Cco=Vc^2/OC// centripetal acceleration of C relative to O in cm/s^2\n", +"Cpc=CP^2/cp// centripetal acceleration of P relative to C in cm/s^2\n", +"Caq=QA^2/qa// centripetal acceleration of A relative to Q in cm/s^2\n", +"Cap=Pa^2/pa// centripetal acceleration of A relative to P in cm/s^2\n", +"pp1=530\n", +"a1a=323\n", +"a2a=207.5\n", +"ACP=pp1/cp// angular acceleration of link CP in rad/s^2\n", +"APA=a1a/qa// angular acceleration of link PA in rad/s^2\n", +"AAQ=a2a/pa// angular acceleration of link AQ in rad/s^2\n", +"printf('angular acceleration of link CP =%.3f rad/s^2\n angular acceleration of link CP=%.3f rad/s^2\n angular acceleration of link CP=%.3f rad/s^2',ACP,APA,AAQ)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.1: Length_of_the_stroke.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 1 PAGE NO 15\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.14\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"AO=200// distance between fixed centres in mm\n", +"OB1=100// length of driving crank in mm\n", +"AP=400// length of slotter bar in mm\n", +"//====================================\n", +"OAB1=asind(OB1/AO)// inclination of slotted bar with vertical in degrees\n", +"beeta=(90-OAB1)*2// angle through which crank turns inreturn stroke in degrees\n", +"A=(360-beeta)/beeta// ratio of time of cutting stroke to the time of return stroke \n", +"L=2*AP*sind(90-(beeta)/2)// length of the stroke in mm\n", +"printf('Inclination of slotted bar with vertical= %.3f degrees\n Length of the stroke= %.3f mm',OAB1,L)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.2: Ratio_of_time_taken_on_the_cutting_to_the_return_stroke.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 2 PAGE NO 16\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.15\n", +"clc\n", +"clear\n", +"OA=300// distance between the fixed centres in mm\n", +"OB=150// length of driving crank in mm\n", +"//================================\n", +"OAB=asind(OB/OA)// inclination of slotted bar with vertical in degrees\n", +"beeta=(90-OAB)*2// angle through which crank turns inreturn stroke in degrees\n", +"A=(360-beeta)/beeta// ratio of time of cutting stroke to the time of return stroke \n", +"printf('Ratio of time taken on the cutting to the return stroke= %.0f',A)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.3: Ratio_of_time_taken_on_the_cutting_to_the_return_stroke.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 3 PAGE NO 16\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.16\n", +"clc\n", +"clear\n", +"OB=54.6// distance between the fixed centres in mm\n", +"OA=85// length of driving crank in mm\n", +"OA2=OA\n", +"CA=160// length of slotted lever in mm\n", +"CD=144// length of connectin rod in mm\n", +"//================================\n", +"beeta=2*(acosd(OB/OA2))// angle through which crank turns inreturn stroke in degrees\n", +"A=(360-beeta)/beeta// ratio of time of cutting stroke to the time of return stroke \n", +"printf('Ratio of time taken on the cutting to the return stroke= %.0f',A)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.4: Angular_velocity_of_connecting_rod.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 4 PAGE NO 17\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.18,1.19\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"Nao=180// speed of the crank in rpm\n", +"wAO=2*pi*Nao/60// angular speed of the crank in rad/s\n", +"AO=.5// crank length in m\n", +"AE=.5\n", +"Vao=wAO*AO// velocity of A in m/s\n", +"//================================\n", +"Vb1=8.15// velocity of piston B in m/s by measurment from figure 1.19\n", +"Vba=6.8// velocity of B with respect to A in m/s\n", +"AB=2// length of connecting rod in m\n", +"wBA=Vba/AB// angular velocity of the connecting rod BA in rad/s\n", +"ae=AE*Vba/AB// velocity of point e on the connecting rod\n", +"oe=8.5// by measurement velocity of point E\n", +"Do=.05// diameter of crank shaft in m\n", +"Da=.06// diameter of crank pin in m\n", +"Db=.03// diameter of cross head pin B m\n", +"V1=wAO*Do/2// velocity of rubbing at the pin of the crankshaft in m/s\n", +"V2=wBA*Da/2// velocity of rubbing at the pin of the crank in m/s\n", +"Vb=(wAO+wBA)*Db/2// velocity of rubbing at the pin of cross head in m/s\n", +"ag=5.1// by measurement\n", +"AG=AB*ag/Vba// position and linear velocity of point G on the connecting rod in m\n", +"//===============================\n", +"printf('Velocity of piston B= %.3f m/s\n Angular velocity of connecting rod= %.3f rad/s\n velocity of point E=%.1f m/s\n velocity of rubbing at the pin of the crankshaft=%.3f m/s\n velocity of rubbing at the pin of the crank =%.3f m/s\n velocity of rubbing at the pin of cross head =%.3f m/s\n position and linear velocity of point G on the connecting rod=%.3f m',Vb1,wBA,oe,V1,V2,Vb,AG)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.5: Linear_velocity_of_point_P.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 5 PAGE NO 19\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.20,1.21\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"N=120// speed of crank in rpm\n", +"OA=10// length of crank in cm\n", +"BP=48// from figure 1.20 in cm\n", +"BA=40// from figure 1.20 in cm\n", +"//==============\n", +"w=2*pi*N/60// angular velocity of the crank OA in rad/s\n", +"Vao=w*OA// velocity of ao in cm/s\n", +"ba=4.5// by measurement from 1.21 in cm\n", +"Bp=BP*ba/BA\n", +"op=6.8// by measurement in cm from figure 1.21\n", +"s=20// scale of velocity diagram 1cm=20cm/s\n", +"Vp=op*s// linear velocity of P in m/s\n", +"ob=5.1// by measurement in cm from figure 1.21\n", +"Vb=ob*s// linear velocity of slider B\n", +"printf('Linear velocity of slider B= %.2f cm/s\n Linear velocity of point P= %.2f cm/s',Vb,Vp)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.6: velocity_of_point_F.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"//CHAPTER 1 ILLUSRTATION 6 PAGE NO 20\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.22,1.23\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"AB=6.25// length of link AB in cm\n", +"BC=17.5// length of link BC in cm\n", +"CD=11.25// length of link CD in cm\n", +"DA=20// length of link DA in cm\n", +"CE=10\n", +"N=100// speed of crank in rpm\n", +"//========================\n", +"wAB=2*pi*N/60// angular velocity of AB in rad/s\n", +"Vb=wAB*AB// linear velocity of B with respect to A\n", +"s=15// scale for velocity diagram 1 cm= 15 cm/s\n", +"dc=3// by measurement in cm\n", +"Vcd=dc*s\n", +"wCD=Vcd/CD// angular velocity of link CD in rad/s\n", +"bc=2.5// by measurement in cm\n", +"Vbc=bc*s\n", +"wBC=Vbc/BC// angular velocity of link BC in rad/s\n", +"ce=bc*CE/BC\n", +"ae=3.66// by measurement in cm\n", +"Ve=ae*s// velocity of point E 10 from c on the link BC\n", +"af=2.94// by measurement in cm\n", +"Vf=af*s// velocity of point F\n", +"printf('The angular velocity of link CD= %.3f rad/s\n The angular velocity of link BC= %.3f rad/s\n velocity of point E 10 from c on the link BC= %.3f cm/s\n velocity of point F= %.3f cm/s',wCD,wBC,Ve,Vf)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.7: angular_velocity_of_link_BD.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 7 PAGE NO 21\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.24,1.25\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"Noa=600// speed of the crank in rpm\n", +"OA=2.8// length of link OA in cm\n", +"AB=4.4// length of link AB in cm\n", +"BC=4.9// length of link BC in cm\n", +"BD=4.6// length of link BD in cm\n", +"//=================\n", +"wOA=2*pi*Noa/60// angular velocity of crank in rad/s\n", +"Vao=wOA*OA// The linear velocity of point A with respect to oin m/s\n", +"s=50// scale of velocity diagram in cm\n", +"od=2.95// by measurement in cm from figure\n", +"Vd=od*s/100// linear velocity slider in m/s\n", +"bd=3.2// by measurement in cm from figure\n", +"Vbd=bd*s\n", +"wBD=Vbd/BD// angular velocity of link BD\n", +"printf('linear velocity slider D= %.3f m/s\n angular velocity of link BD= %.1f rad/s',Vd,wBD)\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.8: Angular_velocity_of_link_CD.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 8 PAGE NO 22\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.26,1.27\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"Noa=60// speed of crank in rpm\n", +"OA=30// length of link OA in cm\n", +"AB=100// length of link AB in cm\n", +"CD=80// length of link CD in cm\n", +"//AC=CB\n", +"//================\n", +"wOA=2*pi*Noa/60// angular velocity of crank in rad/s\n", +"Vao=wOA*OA/100// linear velocity of point A with respect to O\n", +"s=50// scale for velocity diagram 1 cm= 50 cm/s\n", +"ob=3.4// by measurement in cm from figure 1.27\n", +"od=.9// by measurement in cm from figure 1.27\n", +"Vcd=160// by measurement in cm/s from figure 1.27\n", +"wCD=Vcd/CD// angular velocity of link in rad/s\n", +"printf('Angular velocity of link CD= %d rad/s',wCD)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.9: velocity_of_sliding_of_the_block.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 1 ILLUSRTATION 9 PAGE NO 23\n", +"//TITLE:Basic kinematics\n", +"//Figure 1.28,1.29\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"Nao=120// speed of the crank in rpm\n", +"OQ=10// length of link OQ in cm\n", +"OA=20// length of link OA in cm\n", +"QC=15// length of link QC in cm\n", +"CD=50// length oflink CD in cm\n", +"//=============\n", +"wOA=2*pi*Nao/60// angular speed of crank in rad/s\n", +"Vad=wOA*OA/100// velocity of pin A in m/s\n", +"BQ=41// from figure 1.29 \n", +"BC=26// from firure 1.29 \n", +"bq=4.7// from figure 1.29\n", +"bc=bq*BC/BQ// from figure 1.29 in cm\n", +"s=50// scale for velocity diagram in cm/s\n", +"od=1.525// velocity vector od in cm from figure 1.29\n", +"Vd=od*s// velocity of ram D in cm/s\n", +"dc=1.925// velocity vector dc in cm from figure 1.29\n", +"Vdc=dc*s// velocity of link CD in cm/s\n", +"wCD=Vdc/CD// angular velocity of link CD in cm/s\n", +"ba=1.8// velocity vector of sliding of the block in cm\n", +"Vab=ba*s// velocity of sliding of the block in cm/s\n", +"printf('Velocity of RAM D= %.3f cm/s\n angular velocity of link CD= %.3f rad/s\n velocity of sliding of the block= %.3f cm/s',Vd,wCD,Vab)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Theory_Of_Machines_by_B_K_Sarkar/10-Brakes_and_Dynamometers.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/10-Brakes_and_Dynamometers.ipynb new file mode 100644 index 0000000..fc1cdbd --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/10-Brakes_and_Dynamometers.ipynb @@ -0,0 +1,435 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 10: Brakes and Dynamometers" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.10: Maximum_braking_torque.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 10 ILLUSRTATION 10 PAGE NO 275\n", +"//TITLE:Brakes and Dynamometers\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"n=12;// Number of blocks\n", +"q=16;//Angle subtended in degrees\n", +"d=0.9;//Effective diameter in m\n", +"m=2000;//Mass in kg\n", +"k=0.5;//Radius of gyration in m\n", +"b1=0.7;//Distance in m\n", +"b2=0.03;//Distance in m\n", +"a=0.1;//Distance in m\n", +"P=180;//Force in N\n", +"N=360;//Speed in r.p.m\n", +"U=0.25;//Coefficient of friction\n", +"\n", +"Tr=((1+(U*tand(q/2)))/(1-(U*tand(q/2))))^n;//Tensions ratio\n", +"T2=(P*b1)/(a-(b2*Tr));//Tension in N\n", +"T1=(Tr*T2);//Tension in N\n", +"TB=(T1-T2)*(d/2);//Torque in N.m\n", +"aa=(TB/(m*k^2));//Angular acceleration in rad/s^2\n", +"t=((2*3.14*N)/60)/aa;//Time in seconds\n", +"\n", +"printf('(i) Maximum braking torque is %3.4f Nm \n(ii) Angular retardation of the drum is %3.4f rad/s^2 \n(iii) Time taken by the system to come to rest is %3.1f s',TB,aa,t)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.1: Torque_transmitted_by_the_block_brake.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 10 ILLUSRTATION 1 PAGE NO 268\n", +"//TITLE:Brakes and Dynamometers\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"d=0.32;//Diameter of the drum in m\n", +"qq=90;//Angle of contact in degree\n", +"P=820;//Force applied in N\n", +"U=0.35;//Coefficient of friction\n", +"\n", +"\n", +"U1=((4*U*sind(qq/2))/((qq*(3.14/180))+sind(qq)));//Equivalent coefficient of friction\n", +"F=((P*0.66)/((0.3/U1)-0.06));//Force value in N taking moments\n", +"TB=(F*(d/2));//Torque transmitted in N.m\n", +"\n", +"printf('Torque transmitted by the block brake is %3.4f N.m',TB)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.2: DISTANCE_TRAVELLED_BY_CYCLE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 10 ILLUSRTATION 2 PAGE NO 269\n", +"//TITLE:Brakes and Dynamometers\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"m=120;//Mass of rider in kg\n", +"v=16.2;//Speed of rider in km/hr\n", +"d=0.9;//Diameter of the wheel in m\n", +"P=120;//Pressure applied on the brake in N\n", +"U=0.06;//Coefficient of friction\n", +"\n", +"F=(U*P);//Frictional force in N\n", +"KE=((m*(v*(5/18))^2)/2);//Kinematic Energy in N.m\n", +"S=(KE/F);//Distance travelled by the bicycle before it comes to rest in m\n", +"N=(S/(d*3.14));//Required number of revolutions\n", +"\n", +"printf('The bicycle travels a distance of %3.2f m and makes %3.2f turns before it comes to rest',S,N)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.3: Maximum_torque_absorbed.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 10 ILLUSRTATION 3 PAGE NO 270\n", +"//TITLE:Brakes and Dynamometers\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"S=3500;//Force on each arm in N\n", +"d=0.36;//Diamter of the wheel in m\n", +"U=0.4;//Coefficient of friction \n", +"qq=100;//Contact angle in degree\n", +"\n", +"qqr=(qq*(3.14/180));//Contact angle in radians\n", +"UU=((4*U*sind(qq/2))/(qqr+(sind(qq))));//Equivalent coefficient of friction\n", +"F1=(S*0.45)/((0.2/UU)+((d/2)-0.04));//Force on fulcrum in N\n", +"F2=(S*0.45)/((0.2/UU)-((d/2)-0.04));//Force on fulcrum in N\n", +"TB=(F1+F2)*(d/2);//Maximum torque absorbed in N.m\n", +"\n", +"printf('Maximum torque absorbed is %3.2f N.m',TB)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.4: The_maximum_braking_torque_on_the_drum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 10 ILLUSRTATION 4 PAGE NO 271\n", +"//TITLE:Brakes and Dynamometers\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"a=0.5;//Length of lever in m\n", +"d=0.5;//Diameter of brake drum in m\n", +"q=(5/8)*(2*3.14);//Angle made in radians\n", +"b=0.1;//Distance between pin and fulcrum in m\n", +"P=2000;//Effort applied in N\n", +"U=0.25;//Coefficient of friction\n", +"\n", +"T=exp(U*q);//Ratios of tension\n", +"T2=((P*a)/b);//Tension in N\n", +"T1=(T*T2);//Tension in N\n", +"TB=((T1-T2)*(d/2))/1000;//Maximum braking torque in kNm\n", +"\n", +"printf('The maximum braking torque on the drum is %3.3f kNm',TB)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.5: Tensions_in_the_side.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 10 ILLUSRTATION 5 PAGE NO 271\n", +"//TITLE:Brakes and Dynamometers\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"q=220;//Angle of contact in degree\n", +"T=340;//Torque in Nm\n", +"d=0.32;//Diameter of drum in m\n", +"U=0.3;//Coefficient of friction\n", +"\n", +"Td=(T/(d/2));//Difference in tensions in N\n", +"Tr=exp(U*(q*(3.14/180)));//Ratio of tensions\n", +"T2=(Td/(Tr-1));//Tension in N\n", +"T1=(Tr*T2);//Tension in N\n", +"P=((T2*(d/2))-(T1*0.04))/0.5;//Force applied in N\n", +"b=(T1/T2)*4;//Value of b in cm when the brake is self-locking\n", +"\n", +"printf('The value of b is %3.2f cm when the brake is self-locking \n Tensions in the sides are %3.3f N and %3.3f N',b,T1,T2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.6: Torque_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 10 ILLUSRTATION 6 PAGE NO 272\n", +"//TITLE:Brakes and Dynamometers\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"d=0.5;//Drum diamter in m\n", +"U=0.3;//Coefficient of friction\n", +"q=250;//Angle of contact in degree\n", +"P=750;//Force in N\n", +"a=0.1;//Band width in m\n", +"b=0.8;//Distance in m\n", +"ft=(70*10^6);//Tensile stress in Pa\n", +"f=(60*10^6);//Stress in Pa\n", +"b1=0.1;//Distance in m\n", +"\n", +"T=exp(U*(q*(3.14/180)));//Tensions ratio\n", +"T2=(P*b*10)/(T+1);//Tension in N\n", +"T1=(T*T2);//Tension in N\n", +"TB=(T1-T2)*(d/2);//Torque in N.m\n", +"t=(max(T1,T2)/(ft*a))*1000;//Thickness in mm\n", +"M=(P*b);//bending moment at fulcrum in Nm\n", +"X=(M/((1/6)*f));//Value of th^2\n", +"//t varies from 10mm to 15 mm. Taking t=15mm,\n", +"h=sqrt(X/(0.015))*1000;//Section of the lever in m\n", +"\n", +"printf('Torque required is %3.2f N.m \nThickness necessary to limit the tensile stress to 70 MPa is %3.3f mm \n Section of the lever taking stress to 60 MPa is %3.1f mm',TB,t,h)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.7: Power_TO_BD_ratio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 10 ILLUSRTATION 7 PAGE NO 273\n", +"//TITLE:Brakes and Dynamometers\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"P1=30;//Power in kW\n", +"N=1250;//Speed in r.p.m\n", +"P=60;//Applied force in N\n", +"d=0.8;//Drum diameter in m\n", +"q=310;//Contact angle in degree\n", +"a=0.03;//Length of a in m\n", +"b=0.12;//Length of b in m\n", +"U=0.2;//Coefficient of friction\n", +"B=10;//Band width in cm\n", +"D=80;//Diameter in cm\n", +"\n", +"T=(P1*60000)/(2*3.14*N);//Torque in N.m\n", +"Td=(T/(d/2));//Tension difference in N\n", +"Tr=exp(U*(q*(3.14/180)));//Tensions ratio\n", +"T2=(Td/(Tr-1));//Tension in N\n", +"T1=(Tr*T2);//Tension in N\n", +"x=((T2*b)-(T1*a))/P;//Distance in m;\n", +"X=(P1/(B*D));//Ratio\n", +"\n", +"printf('Value of x is %3.4f m \n Value of (Power/bD) ratio is %3.4f',x,X)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.8: Time_required_to_bring_the_shaft_to_the_rest_from_its_running_condition.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 10 ILLUSRTATION 8 PAGE NO 274\n", +"//TITLE:Brakes and Dynamometers\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"m=80;//Mass of flywheel in kg\n", +"k=0.5;//Radius of gyration in m\n", +"N=250;//Speed in r.p.m\n", +"d=0.32;//Diamter of the drum in m\n", +"b=0.05;//Distance of pin in m\n", +"q=260;//Angle of contact in degree\n", +"U=0.23;//Coefficient of friction\n", +"P=20;//Force in N\n", +"a=0.35;//Distance at which force is applied in m\n", +"\n", +"Tr=exp(U*q*(3.14/180));//Tensions ratio\n", +"T2=(P*a)/b;//Tension in N\n", +"T1=(Tr*T2);//Tension in N\n", +"TB=(T1-T2)*(d/2);//Torque in N.m\n", +"KE=((1/2)*(m*k^2)*((2*3.14*N)/60)^2);//Kinematic energy of the rotating drum in Nm\n", +"N1=(KE/(TB*2*3.14));//Speed in rpm\n", +"aa=((2*3.14*N)/60)^2/(4*3.14*N1);//Angular acceleration in rad/s^2\n", +"t=((2*3.14*N)/60)/aa;//Time in seconds\n", +"\n", +"printf('Time required to bring the shaft to the rest from its running condition is %3.1f seconds',t)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.9: Minimum_force_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 10 ILLUSRTATION 9 PAGE NO 275\n", +"//TITLE:Brakes and Dynamometers\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"n=12;//Number of blocks\n", +"q=15;//Angle subtended in degree\n", +"P=185;//Power in kW\n", +"N=300;//Speed in r.p.m\n", +"U=0.25;//Coefficient of friction\n", +"d=1.25;//Diamter in m\n", +"b1=0.04;//Distance in m\n", +"b2=0.14;//Distance in m\n", +"a=1;//Diatance in m\n", +"m=2400;//Mass of rotor in kg\n", +"k=0.5;//Radius of gyration in m\n", +"\n", +"Td=(P*60000)/(2*3.14*N*(d/2));//Tension difference in N\n", +"T=Td*(d/2);//Torque in Nm\n", +"Tr=((1+(U*tand(q/2)))/(1-(U*tand(q/2))))^n;//Tension ratio\n", +"To=(Td/(Tr-1));//Tension in N\n", +"Tn=(Tr*To);//Tension in N\n", +"P=((To*b2)-(Tn*b1))/a;//Force in N\n", +"aa=(T/(m*k^2));//Angular acceleration in rad/s^2\n", +"t=((2*3.14*N)/60)/aa;//Time in seconds\n", +"\n", +"printf('Minimum force required is %3.0f N \nTime taken to bring to rest is %3.1f seconds',P,t)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Theory_Of_Machines_by_B_K_Sarkar/11-VIBRATIONS.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/11-VIBRATIONS.ipynb new file mode 100644 index 0000000..96b2550 --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/11-VIBRATIONS.ipynb @@ -0,0 +1,395 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 11: VIBRATIONS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.10: FREQUENCY_OF_TRANSVERSE_VIBRATION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 11 ILLUSRTATION 10 PAGE NO 296\n", +"//TITLE:VIBRATIONS\n", +"//FIGURE 11.18\n", +"clc\n", +"clear\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", +"printf('FREQUENCY OF TRANSVERSE VIBRATION = %.3f Hz',Fn)\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.11: CRITICAL_SPEED_OF_SHAFT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 11 ILLUSRTATION 11 PAGE NO 297\n", +"//TITLE:VIBRATIONS\n", +"//FIGURE 11.19\n", +"clc\n", +"clear\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", +"printf('CRITICAL SPEED OF SHAFT = %.3f rpm',Nc)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.12: FREQUENCY_OF_FREE_TORSIONAL_VIBRATION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 11 ILLUSRTATION 12 PAGE NO 298\n", +"//TITLE:VIBRATIONS\n", +"//FIGURE 11.20\n", +"clc\n", +"clear\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", +"printf('FREQUENCY OF FREE TORSIONAL VIBRATION = %.2f Hz',Fn)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.13: THE_RANGE_OF_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 11 ILLUSRTATION 13 PAGE NO 300\n", +"//TITLE:VIBRATIONS\n", +"//FIGURE 11.21\n", +"clc\n", +"clear\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", +"printf('CRITICAL SPEED OF SHAFT = %.3f rpm\n THE RANGE OF SPEED IS FROM %.3f rpm TO %.3f rpm',Nc,N1,N2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.1: FREQUENCY_OF_TRANSVERSE_VIBRATION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 11 ILLUSRTATION 1 PAGE NO 290\n", +"//TITLE:VIBRATIONS\n", +"clc\n", +"clear\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", +"printf('FREQUENCY OF LONGITUDINAL VIBRATION =%.3f Hz\n FREQUENCY OF TRANSVERSE VIBRATION =%.3f Hz',Fn,Fn1)\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.2: NATURAL_FREQUENCY_OF_TRANSVERSE_VIBRATION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 11 ILLUSRTATION 2 PAGE NO 290\n", +"//TITLE:VIBRATIONS\n", +"//FIGURE 11.10\n", +"clc\n", +"clear\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", +"printf('NATURAL FREQUENCY OF TRANSVERSE VIBRATION=%.3f Hz',Fn)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.3: FREQUENCY_OF_TORSIONAL_VIBRATION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 11 ILLUSRTATION 3 PAGE NO 291\n", +"//TITLE:VIBRATIONS\n", +"//FIGURE 11.11\n", +"clc\n", +"clear\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", +"printf('FREQUENCY OF LONGITUDINAL VIBRATION = %.3f Hz\n FREQUENCY OF TRANSVERSE VIBRATION = %.3f Hz\n FREQUENCY OF TORSIONAL VIBRATION = %.3f Hz',Fn,Fn1,Fn2)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.6: FREQUENCY_OF_TRANSVERSE_VIBRATION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 11 ILLUSRTATION 6 PAGE NO 294\n", +"//TITLE:VIBRATIONS\n", +"//FIGURE 11.14\n", +"clc\n", +"clear\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", +"printf('FREQUENCY OF TRANSVERSE VIBRATION = %.3f Hz',Fn)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Theory_Of_Machines_by_B_K_Sarkar/12-balancing_of_reciprocating_masses.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/12-balancing_of_reciprocating_masses.ipynb new file mode 100644 index 0000000..65d6778 --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/12-balancing_of_reciprocating_masses.ipynb @@ -0,0 +1,321 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 12: balancing of reciprocating masses" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.1: Magnitude_of_balance_mass_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 12 ILLUSRTATION 1 PAGE NO 310\n", +"//TITLE:Balancing of reciprocating of masses\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"N=250// speed of the reciprocating engine in rpm\n", +"s=18// length of stroke in mm\n", +"mR=120// mass of reciprocating parts in kg\n", +"m=70// mass of revolving parts in kg\n", +"r=.09// radius of revolution of revolving parts in m\n", +"b=.15// distance at which balancing mass located in m\n", +"c=2/3// portion of reciprocating mass balanced \n", +"teeta=30// crank angle from inner dead centre in degrees\n", +"//===============================\n", +"B=r*(m+c*mR)/b// balance mass required in kg\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"F=mR*w^2*r*(((1-c)^2*(cosd(teeta))^2)+(c^2*(sind(teeta))^2))^.5// residual unbalanced forces in N\n", +"printf('Magnitude of balance mass required= %.0f kg\n Residual unbalanced forces= %.3f N',B,F)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.2: swaying_couple.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 12 ILLUSRTATION 2 PAGE NO 310\n", +"//TITLE:Balancing of reciprocating of masses\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"g=10// acceleration due to gravity approximately in m/s^2\n", +"mR=240// mass of reciprocating parts per cylinder in kg\n", +"m=300// mass of rotating parts per cylinder in kg\n", +"a=1.8//distance between cylinder centres in m\n", +"c=.67// portion of reciprocating mass to be balanced\n", +"b=.60// radius of balance masses in m\n", +"r=24// crank radius in cm\n", +"R=.8//radius of thread of wheels in m\n", +"M=40\n", +"//=======================================\n", +"Ma=m+c*mR// total mass to be balanced in kg\n", +"mD=211.9// mass of wheel D from figure in kg\n", +"mC=211.9//..... mass of wheel C from figure in kg\n", +"theta=171// angular position of balancing mass C in degrees\n", +"Br=c*mR/Ma*mC// balancing mass for reciprocating parts in kg\n", +"w=(M*g^3/Br/b)^.5// angular speed in rad/s\n", +"v=w*R*3600/1000// speed in km/h\n", +"S=a*(1-c)*mR*w^2*r/2^.5/100/1000// swaying couple in kNm\n", +"printf('speed=%.3f kmph\n swaying couple=%.3f kNm',v,S)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.3: swaying_couple.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 12 ILLUSRTATION 3 PAGE NO 313\n", +"//TITLE:Balancing of reciprocating of masses\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"g=10// acceleration due to gravity approximately in m/s^2\n", +"a=.70//distance between cylinder centres in m\n", +"r=60// crank radius in cm\n", +"m=130//mass of rotating parts per cylinder in kg\n", +"mR=210// mass of reciprocating parts per cylinder in kg\n", +"c=.67// portion of reciprocating mass to be balanced\n", +"N=300//e2engine speed in rpm\n", +"b=.64// radius of balance masses in m\n", +"//============================\n", +"Ma=m+c*mR// total mass to be balanced in kg\n", +"mA=100.44// mass of wheel A from figure in kg\n", +"Br=c*mR/Ma*mA// balancing mass for reciprocating parts in kg\n", +"H=Br*(2*pi*N/60)^2*b// hammer blow in N\n", +"w=(2*pi*N/60)// angular speed\n", +"T=2^.5*(1-c)*mR*w^2*r/2/100//tractive effort in N\n", +"S=a*(1-c)*mR*w^2*r/2/2^.5/100// swaying couple in Nm\n", +"\n", +"printf('Hammer blow=%.3f in N\n tractive effort= %.3f in N\n swaying couple= %.3f in Nm',H,T,S)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.4: unbalanced_primary_couple.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 12 ILLUSRTATION 4 PAGE NO 314\n", +"//TITLE:Balancing of reciprocating of masses\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"mR=900// mass of reciprocating parts in kg\n", +"N=90// speed of the engine in rpm\n", +"r=.45//crank radius in m\n", +"cP=.9*mR*(2*pi*N/60)^2*r*2^.5/1000// maximum unbalanced primary couple in kNm\n", +"printf('maximum unbalanced primary couple=%.3f k Nm',cP)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.5: maximum_unbalanced_secondary_force.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 12 ILLUSRTATION 5 PAGE NO 315\n", +"//TITLE:Balancing of reciprocating of masses\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"mRA=160// mass of reciprocating cylinder A in kg\n", +"mRD=160// mass of reciprocating cylinder D in kg\n", +"r=.05// stroke lenght in m\n", +"l=.2// connecting rod length in m\n", +"N=450// engine speed in rpm\n", +"//===========================\n", +"theta2=78.69// crank angle between A & B cylinders in degrees\n", +"mRB=576.88// mass of cylinder B in kg\n", +"n=l/r// ratio between connecting rod length and stroke length\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"F=mRB*2*w^2*r*cosd(2*theta2)/n\n", +"printf('Maximum unbalanced secondary force=%.3f N in anticlockwise direction thats why - sign',F)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.6: hammer_blow.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 12 ILLUSRTATION 6 PAGE NO 316\n", +"//TITLE:Balancing of reciprocating of masses\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"rA=.25// stroke length of A piston in m\n", +"rB=.25// stroke length of B piston in m\n", +"rC=.25// stroke length C piston in m\n", +"N=300// engine speed in rpm\n", +"mRL=280// mass of reciprocating parts in inside cylinder kg\n", +"mRO=240// mass of reciprocating parts in outside cylinder kg\n", +"c=.5// portion ofreciprocating masses to be balanced \n", +"b1=.5// radius at which masses to be balanced in m\n", +"//======================\n", +"mA=c*mRO// mass of the reciprocating parts to be balanced foreach outside cylinder in kg\n", +"mB=c*mRL// mass of the reciprocating parts to be balanced foreach inside cylinder in kg\n", +"B1=79.4// balancing mass for reciprocating parts in kg\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"H=B1*w^2*b1// hammer blow per wheel in N\n", +"printf('Hammer blow per wheel= %.3f N',H)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.7: swaying_couple.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 12 ILLUSRTATION 7 PAGE NO 318\n", +"//TITLE:Balancing of reciprocating of masses\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"mR=300// reciprocating mass per cylinder in kg\n", +"r=.3// crank radius in m\n", +"D=1.7// driving wheel diameter in m\n", +"a=.7// distance between cylinder centre lines in m\n", +"H=40// hammer blow in kN\n", +"v=90// speed in kmph\n", +"//=======================================\n", +"R=D/2// radius of driving wheel in m\n", +"w=90*1000/3600/R// angular velocity in rad/s\n", +"//Br*b=69.625*c by mearument from diagram\n", +"c=H*1000/(w^2)/69.625// portion of reciprocating mass to be balanced\n", +"T=2^.5*(1-c)*mR*w^2*r// variation in tractive effort in N\n", +"M=a*(1-c)*mR*w^2*r/2^.5// maximum swaying couple in N-m\n", +"printf('portion of reciprocating mass to be balanced=%.3f\n variation in tractive effort=%.3f N\n maximum swaying couple=%.3f N-m',c,T,M)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.8: unbalanced_secondary_couple.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 12 ILLUSRTATION 8 PAGE NO 320\n", +"//TITLE:Balancing of reciprocating of masses\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"N=1800// speed of the engine in rpm\n", +"r=6// length of crank in cm\n", +"l=24// length of connecting rod in cm\n", +"m=1.5// mass of reciprocating cylinder in kg\n", +"//====================\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"UPC=.019*w^2// unbalanced primary couple in N-m\n", +"n=l/r// ratio of length of crank to the connecting rod \n", +"USC=.054*w^2/n// unbalanced secondary couple in N-m\n", +"printf('unbalanced primary couple= %.3f N-m\n unbalanced secondary couple=%.3f N-m',UPC,USC)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Theory_Of_Machines_by_B_K_Sarkar/2-TRANSMISSION_OF_MOTION_AND_POWER_BY_BELTS_AND_PULLEYS.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/2-TRANSMISSION_OF_MOTION_AND_POWER_BY_BELTS_AND_PULLEYS.ipynb new file mode 100644 index 0000000..10abacc --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/2-TRANSMISSION_OF_MOTION_AND_POWER_BY_BELTS_AND_PULLEYS.ipynb @@ -0,0 +1,715 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2: TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.10: stress_developed_on_tight_side_of_belt.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2,ILLUSTRATION 10 PAGE 64\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//INPUT\n", +"t=5//THICKNESS OF BELT IN m\n", +"PI=3.141\n", +"U=.3\n", +"e=2.71\n", +"THETA=155*PI/180//ANGLE OF CONTACT IN radians\n", +"V=30//VELOCITY IN m/s\n", +"density=1//in m/cm^3\n", +"L=1//LENGTH\n", +"\n", +"//calculation\n", +"Xb=80// (T1-T2)=80b;so let (T1-T2)/b=Xb\n", +"Y=e^(U*THETA)// LET Y=T1/T2\n", +"Zb=80*Y/(Y-1)// LET T1/b=Zb;BY SOLVING THE ABOVE 2 EQUATIONS WE WILL GET THIS EXPRESSION\n", +"Mb=t*L*density*10^-2// m/b in N\n", +"Tcb=Mb*V^2// centrifugal tension/b\n", +"Tmaxb=Zb+Tcb// MAX TENSION/b\n", +"Fb=Tmaxb/t//STRESS INDUCED IN TIGHT BELT\n", +"\n", +"//OUTPUT\n", +"printf('THE STRESS DEVELOPED ON THE TIGHT SIDE OF BELT=%f N/cm^2',Fb)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.11: speed_of_the_pulley.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2,ILLUSTRATION 11 PAGE 65\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//INPUT\n", +"C=4.5// CENTRE DISTANCE IN metres\n", +"D1=1.35// DIAMETER OF LARGER PULLEY IN metres\n", +"D2=.9// DIAMETER OF SMALLER PULLEY IN metres\n", +"To=2100// INITIAL TENSION IN newtons\n", +"b=12// WIDTH OF BELT IN cm\n", +"t=12// THICKNESS OF BELT IN mm\n", +"d=1// DENSITY IN gm/cm^3\n", +"U=.3// COEFFICIENT OF FRICTION\n", +"L=1// length in metres\n", +"PI=3.141\n", +"e=2.71\n", +"\n", +"//CALCULATION\n", +"M=b*t*d*L*10^-2// mass of belt per metre length in KG\n", +"V=(To/3/M)^.5// VELOCITY OF FOR MAX POWER TO BE TRANSMITTED IN m/s\n", +"Tc=M*V^2// CENTRIFUGAL TENSION IN newtons\n", +"// LET (T1+T2)=X\n", +"X=2*To-2*Tc // THE VALUE OF (T1+T2)\n", +"F=(D1-D2)/(2*C)\n", +"ALPHA=asind(F)\n", +"THETA=(180-(2*ALPHA))*PI/180// ANGLE OF CONTACT IN radians\n", +"// LET T1/T2=Y\n", +"Y=e^(U*THETA)// THE VALUE OF T1/T2\n", +"T1=X*Y/(Y+1)// BY SOLVING X AND Y WE WILL GET THIS EQN\n", +"T2=X-T1\n", +"P=(T1-T2)*V/1000// MAX POWER TRANSMITTED IN kilowatts\n", +"N1=V*60/(PI*D1)// SPEED OF LARGER PULLEY IN rpm\n", +"N2=V*60/(PI*D2)// SPEED OF SMALLER PULLEY IN rpm\n", +"//OUTPUT\n", +"printf('\n MAX POWER TO BE TRANSMITTED =%f KW',P)\n", +"printf('\n SPEED OF THE LARGER PULLEY =%f rpm',N1)\n", +"printf('\n SPEED OF THE SMALLER PULLEY =%f rpm',N2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.12: efficiency_of_drive.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2,ILLUSTRATION 12 PAGE 66\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//============================================================================================================================\n", +"//INPUT\n", +"PI=3.141\n", +"e=2.71\n", +"D1=1.20// DIAMETER OF DRIVING SHAFT IN m\n", +"D2=.50// DIAMETER OF DRIVEN SHAFT IN m\n", +"C=4// CENTRE DISTANCE BETWEEN THE SHAFTS IN m\n", +"M=.9// MASS OF BELT PER METRE LENGTH IN kg\n", +"Tmax=2000// MAX TENSION IN N\n", +"U=.3// COEFFICIENT OF FRICTION\n", +"N1=200// SPEED OF DRIVING SHAFT IN rpm\n", +"N2=450// SPEED OF DRIVEN SHAFT IN rpm\n", +"//==============================================================================================================================\n", +"//CALCULATION\n", +"V=PI*D1*N1/60// VELOCITY OF BELT IN m/s\n", +"Tc=M*V^2// CENTRIFUGAL TENSION IN N\n", +"T1=Tmax-Tc// TENSION ON TIGHTSIDE IN N\n", +"F=(D1-D2)/(2*C)\n", +"ALPHA=asind(F)\n", +"THETA=(180-(2*ALPHA))*PI/180// ANGLE OF CONTACT IN radians\n", +"T2=T1/(e^(U*THETA))// TENSION ON SLACK SIDE IN N\n", +"TL=(T1-T2)*D1/2// TORQUE ON THE SHAFT OF LARGER PULLEY IN N-m\n", +"TS=(T1-T2)*D2/2// TORQUE ON THE SHAFT OF SMALLER PULLEY IN N-m\n", +"P=(T1-T2)*V/1000// POWER TRANSMITTED IN kW\n", +"Pi=2*PI*N1*TL/60000// INPUT POWER\n", +"Po=2*PI*N2*TS/60000// OUTPUT POWER\n", +"Pl=Pi-Po// POWER LOST DUE TO FRICTION IN kW\n", +"n=Po/Pi*100// EFFICIENCY OF DRIVE IN %\n", +"//==================================================================================================================================\n", +"//OUTPUT\n", +"printf('\nTORQUE ON LARGER SHAFT =%f N-m',TL)\n", +"printf('\nTORQUE ON SMALLER SHAFT =%f N-m',TS)\n", +"printf('\nPOWER TRANSMITTED =%f kW',P)\n", +"printf('\nPOWER LOST DUE TO FRICTION =%f kW',Pl)\n", +"printf('\nEFFICIENCY OF DRINE =%f percentage',n)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.13: no_of_belts_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2,ILLUSTRATION 13 PAGE 67\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//============================================================================================================================\n", +"//INPUT\n", +"PI=3.141\n", +"e=2.71\n", +"P=90// POWER OF A COMPRESSOR IN kW\n", +"N2=250// SPEED OF DRIVEN SHAFT IN rpm\n", +"N1=750// SPEED OF DRIVER SHAFT IN rpm\n", +"D2=1// DIAMETER OF DRIVEN SHAFT IN m\n", +"C=1.75// CENTRE DISTANCE IN m\n", +"V=1600/60// VELOCITY IN m/s\n", +"a=375// CROSECTIONAL AREA IN mm^2\n", +"density=1000// BELT DENSITY IN kg/m^3\n", +"L=1// length to be considered\n", +"Fb=2.5// STRESSS INDUCED IN MPa\n", +"beeta=35/2// THE GROOVE ANGLE OF PULLEY\n", +"U=.25// COEFFICIENT OF FRICTION\n", +"//=================================================================================================================================\n", +"//CALCULATION\n", +"D1=N2*D2/N1// DIAMETER OF DRIVING SHAFT IN m\n", +"m=a*density*10^-6*L// MASS OF THE BELT IN kg\n", +"Tmax=a*Fb// MAX TENSION IN N\n", +"Tc=m*V^2// CENTRIFUGAL TENSION IN N\n", +"T1=Tmax-Tc// TENSION ON TIGHTSIDE OF BELT IN N\n", +"F=(D2-D1)/(2*C)\n", +"ALPHA=asind(F)\n", +"THETA=(180-(2*ALPHA))*PI/180// ANGLE OF CONTACT IN radians\n", +"T2=T1/(e^(U*THETA/sind(beeta)))//TENSION ON SLACKSIDE IN N\n", +"P2=(T1-T2)*V/1000// POWER TRANSMITTED PER BELT kW\n", +"N=P/P2// NO OF V-BELTS\n", +"N3=N+1\n", +"//======================================================================================================================================\n", +"//OUTPUT\n", +"printf('NO OF BELTS REQUIRED TO TRANSMIT POWER=%f APPROXIMATELY=%d\n',N,N3)\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.14: initial_rope_tension.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2,ILLUSTRATION 14 PAGE 68\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"\n", +"clc\n", +"clear\n", +"//============================================================================================================================\n", +"//INPUT\n", +"PI=3.141\n", +"e=2.71\n", +"P=75// POWER IN kW\n", +"D=1.5// DIAMETER OF PULLEY IN m\n", +"U=.3// COEFFICIENT OF FRICTION\n", +"beeta=45/2// GROOVE ANGLE\n", +"THETA=160*PI/180// ANGLE OF CONTACT IN radians\n", +"m=.6// MASS OF BELT IN kg/m\n", +"Tmax=800// MAX TENSION IN N\n", +"N=200// SPEED OF SHAFT IN rpm\n", +"//=============================================================================================================================\n", +"//calculation\n", +"V=PI*D*N/60// VELOCITY OF ROPE IN m/s\n", +"Tc=m*V^2// CENTRIFUGAL TENSION IN N\n", +"T1=Tmax-Tc// TENSION ON TIGHT SIDE IN N\n", +"T2=T1/(e^(U*THETA/sind(beeta)))//TENSION ON SLACKSIDE IN N\n", +"P2=(T1-T2)*V/1000// POWER TRANSMITTED PER BELT kW\n", +"No=P/P2// NO OF V-BELTS\n", +"N3=No+1// ROUNDING OFF\n", +"To=(T1+T2+Tc*2)/2// INITIAL TENSION\n", +"//================================================================================================================================\n", +"//OUTPUT\n", +"printf('NO OF BELTS REQUIRED TO TRANSMIT POWER=%f APPROXIMATELY=%d\n',No,N3)\n", +"printf('INITIAL ROPE TENSION=%f N',To)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1: finding_the_diameter_of_the_belt.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2 ILLUSRTATION 1 PAGE NO 57\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"Na=300;//driving shaft running speed in rpm\n", +"Nb=400;//driven shaft running speed in rpm\n", +"Da=60;//diameter of driving shaft in mm\n", +"t=.8;//belt thickness in mm\n", +"s=.05;//slip in percentage(5%)\n", +"//==========================================================================================\n", +"//calculation\n", +"Db=(Da*Na)/Nb;//finding out the diameter of driven shaft without considering the thickness of belt\n", +"Db1=(((Da+t)*Na)/Nb)-t///considering the thickness\n", +"Db2=(1-s)*(Da+t)*(Na/Nb)-t//considering slip also\n", +"//=========================================================================================\n", +"//output\n", +"printf('the value of Db is %3.0f cm',Db)\n", +"printf('\nthe value of Db1 is %f cm',Db1)\n", +"printf('\nthe value of Db2 is %f cm',Db2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2: speed_of_shafts.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2,ILLUSRTATION 2 PAGE NO 57\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//====================================================================================\n", +"//input\n", +"n1=1200//rpm of motor shaft\n", +"d1=40//diameter of motor pulley in cm\n", +"d2=70//diameter of 1st pulley on the shaft in cm\n", +"s=.03//percentage slip(3%)\n", +"d3=45//diameter of 2nd pulley\n", +"d4=65//diameter of the pulley on the counnter shaft\n", +"//=========================================================================================\n", +"//calculation\n", +"n2=n1*d1*(1-s)/d2//rpm of driven shaft\n", +"n3=n2//both the pulleys are mounted on the same shaft\n", +"n4=n3*(1-s)*d3/d4//rpm of counter shaft\n", +"\n", +"//output\n", +"printf('the speed of driven shaft is %f rpm\nthe speed of counter shaft is %f rpm',n2,n4)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3: length_of_belt.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2 ILLUSTRATION 3 PAGE NO:58\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//==============================================================================\n", +"//input\n", +"d1=30//diameter of 1st shaft in cm\n", +"d2=50//diameter 2nd shaft in cm\n", +"pi=3.141\n", +"c=500//centre distance between the shafts in cm\n", +"//==============================================================================\n", +"//calculation\n", +"L1=((d1+d2)*pi/2)+(2*c)+((d1+d2)^2)/(4*c)//lenth of cross belt\n", +"L2=((d1+d2)*pi/2)+(2*c)+((d1-d2)^2)/(4*c)//lenth of open belt\n", +"r=L1-L2//remedy\n", +"//==============================================================================\n", +"//OUTPUT\n", +"printf('length of cross belt is %3.3fcm \n length of open belt is %3.3f cm \n the length of the belt to be shortened is %3.0f cm',L1,L2,r)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4: power_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2,ILLUSTRATION 4 PAGE 59\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//====================================================================================\n", +"//INPUT\n", +"D1=.5// DIAMETER OF 1ST SHAFT IN m\n", +"D2=.25// DIAMETER OF 2nd SHAFT IN m\n", +"C=2// CENTRE DISTANCE IN m\n", +"N1=220// SPEED OF 1st SHAFT\n", +"T1=1250// TENSION ON TIGHT SIDE IN N\n", +"U=.25// COEFFICIENT OF FRICTION\n", +"PI=3.141\n", +"e=2.71\n", +"//====================================================================================\n", +"//CALCULATION\n", +"L=(D1+D2)*PI/2+((D1+D2)^2/(4*C))+2*C\n", +"F=(D1+D2)/(2*C)\n", +"ALPHA=asind(F)\n", +"THETA=(180+(2*ALPHA))*PI/180// ANGLE OF CONTACT IN radians\n", +"T2=T1/(e^(U*THETA))// TENSION ON SLACK SIDE IN N\n", +"V=PI*D1*N1/60// VELOCITY IN m/s\n", +"P=(T1-T2)*V/1000// POWER IN kW\n", +"//====================================================================================\n", +"//OUTPUT\n", +"printf('\nLENGTH OF BELT REQUIRED =%f m',L)\n", +"printf('\nANGLE OF CONTACT =%f radians',THETA)\n", +"printf('\nPOWER CAN BE TRANSMITTED=%f kW',P)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5: tension_in_belt.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2,ILLUSTRATION 5 PAGE 5\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//=====================================================================================================\n", +"//input\n", +"n1=100// of driving shaft\n", +"n2=240//speed of driven shaft\n", +"p=11000//power to be transmitted in watts\n", +"c=250//centre distance in cm\n", +"d2=60//diameter in cm\n", +"b=11.5*10^-2//width of belt in metres\n", +"t=1.2*10^-2//thickness in metres\n", +"u=.25//co-efficient of friction \n", +"pi=3.141\n", +"e=2.71\n", +"//===================================================================================================\n", +"//calculation for open bely drive\n", +"d1=n2*d2/n1\n", +"f=(d1-d2)/(2*c)//sin(alpha) for open bely drive\n", +"//angle of arc of contact for open belt drive is,theta=180-2*alpha\n", +"alpha=asind(f)\n", +"teta=(180-(2*alpha))*3.147/180//pi/180 is used to convert into radians\n", +"x=(e^(u*teta))//finding out the value of t1/t2\n", +"v=pi*d2*10*n2/60//finding out the value of t1-t2\n", +"y=p*1000/(v)\n", +"t1=(y*x)/(x-1)\n", +"Fb=t1/(t*b)/1000\n", +"//=======================================================================================================\n", +"//calculation for cross belt drive bely drive\n", +"F=(d1+d2)/(2*c)//for cross belt drive bely drive\n", +"ALPHA=asind(F)\n", +"THETA=(180+(2*ALPHA))*pi/180//pi/180 is used to convert into radians\n", +"X=(e^(u*THETA))//finding out the value of t1/t2\n", +"V=pi*d2*10*n2/60//finding out the value of t1-t2\n", +"Y=p*1000/(V)\n", +"T1=(Y*X)/(X-1)\n", +"Fb2=T1/(t*b)/1000\n", +"//========================================================================================================\n", +"//output\n", +"printf('for a open belt drive:\n')\n", +"printf('the tension in belt is %.3f N\nstress induced is %.3f kN/m^2\n',t1,Fb)\n", +"printf('for a cross belt drive:\n')\n", +"printf('the tension in belt is %.3f N\nstress induced is %.3f kN/m^2\n',T1,Fb2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.6: width_of_belt_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2,ILLUSTRATION 6 PAGE 61\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//========================================================================================\n", +"//INPUT\n", +"D1=80//DIAMETER OF SHAFT IN cm\n", +"N1=160//SPEED OF 1ST SHAFT IN rpm\n", +"N2=320//SPEED OF 2ND SHAFT IN rpm\n", +"C=250//CENTRE DISTANCE IN CM\n", +"U=.3//COEFFICIENT OF FRICTION\n", +"P=4//POWER IN KILO WATTS\n", +"e=2.71\n", +"PI=3.141\n", +"f=110//STRESS PER cm WIDTH OF BELT\n", +"//========================================================================================\n", +"//CALCULATION\n", +"V=PI*D1*10^-2*N1/60//VELOCITY IN m/s\n", +"Y=P*1000/V//Y=T1-T2\n", +"D2=D1*N1/N2//DIAMETER OF DRIVEN SHAFT\n", +"F=(D1-D2)/(2*C)\n", +"ALPHA=asind(F)\n", +"THETA=(180-(2*ALPHA))*PI/180//ANGLE OF CONTACT IN radians\n", +"X=e^(U*THETA)//VALUE OF T1/T2\n", +"T1=X*Y/(X-1)\n", +"b=T1/f//WIDTH OF THE BELT REQUIRED \n", +"//=======================================================================================\n", +"//OUTPUT\n", +"printf('THE WIDTH OF THE BELT IS %f cm',b)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.7: power_supplied_by_drum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2 ILLUSRTATION 7 PAGE NO 62\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"m=1000// MASS OF THE CASTING IN kg\n", +"PI=3.141\n", +"THETA=2.75*2*PI// ANGLE OF CONTACT IN radians\n", +"D=.26// DIAMETER OF DRUM IN m\n", +"N=24// SPEED OF THE DRUM IN rpm\n", +"U=.25// COEFFICIENT OF FRICTION\n", +"e=2.71\n", +"T1=9810// TENSION ON TIGHTSIDE IN N\n", +"//=============================================================================================\n", +"//CALCULATION\n", +"T2=T1/(e^(U*THETA))// tension on slack side of belt in N\n", +"W=m*9.81// WEIGHT OF CASTING IN N\n", +"R=D/2// RADIUS OF DRUM IN m\n", +"P=2*PI*N*W*R/60000// POWER REQUIRED IN kW\n", +"P2=(T1-T2)*PI*D*N/60000// POWER SUPPLIED BY DRUM IN kW\n", +"//============================================================================================\n", +"//OUTPUT\n", +"printf('FORCE REQUIRED BY MAN=%f N\n POWER REQUIRED TO RAISE CASTING=%f kW\n POWER SUPPLIED BY DRUM=%f kW\n',T2,P,P2)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.8: power_capacity_of_belt.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2,ILLUSTRATION 8 PAGE 62\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//INPUT\n", +"t=9//THICKNESS IN mm\n", +"b=250//WIDTH IN mm\n", +"D=90//DIAMETER OF PULLEY IN cm\n", +"N=336//SPEED IN rpm\n", +"PI=3.141\n", +"U=.35//COEFFICIENT FRICTION\n", +"e=2.71\n", +"THETA=120*PI/180\n", +"Fb=2//STRESS IN MPa\n", +"d=1000//DENSITY IN KG/M^3\n", +"\n", +"//CALCULATION\n", +"M=b*10^-3*t*10^-3*d//MASS IN KG\n", +"V=PI*D*10^-2*N/60//VELOCITY IN m/s\n", +"Tc=M*V^2//CENTRIFUGAL TENSION\n", +"Tmax=b*t*Fb//MAX TENSION IN N\n", +"T1=Tmax-Tc\n", +"T2=T1/(e^(U*THETA))\n", +"P=(T1-T2)*V/1000\n", +"\n", +"//OUTPUT\n", +"printf('THE TENSION ON TIGHT SIDE OF THE BELT IS %f N\n',T1)\n", +"printf('THE TENSION ON SLACK SIDE OF THE BELT IS %f N\n',T2)\n", +"printf('CENTRIFUGAL TENSION =%f N\n',Tc)\n", +"printf('THE POWER CAPACITY OF BELT IS %f KW\n',P)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.9: thickness_of_belt.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 2,ILLUSTRATION 9 PAGE 63\n", +"//TITLE:TRANSMISSION OF MOTION AND POWER BY BELTS AND PULLEYS\n", +"clc\n", +"clear\n", +"//INPUT\n", +"P=35000//POWER TO BE TRANSMITTED IN WATTS\n", +"D=1.5//EFFECTIVE DIAMETER OF PULLEY IN METRES\n", +"N=300//SPEED IN rpm\n", +"e=2.71\n", +"U=.3//COEFFICIENT OF FRICTION\n", +"PI=3.141\n", +"THETA=(11/24)*360*PI/180//ANGLE OF CONTACT\n", +"density=1.1//density of belt material in Mg/m^3\n", +"L=1//in metre\n", +"t=9.5//THICKNESS OF BELT IN mm\n", +"Fb=2.5//PERMISSIBLE WORK STRESS IN N/mm^2\n", +"\n", +"//CALCULATION\n", +"V=PI*D*N/60//VELOCITY IN m/s\n", +"X=P/V//X=T1-T2\n", +"Y=e^(U*THETA)//Y=T1/T2\n", +"T1=X*Y/(Y-1)\n", +"Mb=t*density*L/10^3//value of m/b\n", +"Tc=Mb*V^2//centrifugal tension/b\n", +"Tmaxb=t*Fb//max tension/b\n", +"b=T1/(Tmaxb-Tc)//thickness in mm\n", +"//output\n", +"printf('\nTENSION IN TIGHT SIDE OF THE BELT =%f N',T1)\n", +"printf('\nTHICKNESS OF THE BELT IS =%f mm',b)\n", +"\n", +"" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Theory_Of_Machines_by_B_K_Sarkar/3-FRICTION.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/3-FRICTION.ipynb new file mode 100644 index 0000000..edbdd36 --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/3-FRICTION.ipynb @@ -0,0 +1,684 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3: FRICTION" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.10: FORCE_REQUIRED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 10 PAGE NO 108\n", +"//TITLE:FRICTION\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"PI=3.147\n", +"d=2.5// MEAN DIA OF BOLT IN cm\n", +"p=.6// PITCH IN cm\n", +"beeta=55/2// VEE ANGLE\n", +"dc=4// DIA OF COLLAR IN cm\n", +"U=.1// COEFFICIENT OF FRICTION OF BOLT\n", +"Uc=.18// COEFFICIENT OF FRICTION OF COLLAR\n", +"W=6500// LOAD ON BOLT IN NEWTONS\n", +"L=38// LENGTH OF SPANNER\n", +"//=============================================================================================\n", +"//CALCULATION\n", +"//LET X=tan(py)/tan(beeta)\n", +"//y=tan(ALPHA)*X\n", +"PY=atand(U)\n", +"ALPHA=atand(p/(PI*d))\n", +"X=tand(PY)/cosd(beeta)\n", +"Y=tand(ALPHA)\n", +"T1=W*d/2*10^-2*(X+Y)/(1-(X*Y))// TORQUE IN SCREW IN N-m\n", +"Tc=Uc*W*dc/2*10^-2// TORQUE ON BEARING SERVICES IN N-m\n", +"T=T1+Tc// TOTAL TORQUE \n", +"P1=T/L*100// FORCE REQUIRED BY @ THE END OF SPANNER\n", +"//=============================================================================================\n", +"//OUTPUT\n", +"printf('FORCE REQUIRED @ THE END OF SPANNER=%3.3f N',P1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.11: POWER_LOST_IN_FRICTION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 11 PAGE NO 109\n", +"//TITLE:FRICTION\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"d1=15// DIAMETER OF VERTICAL SHAFT IN cm\n", +"N=100// SPEED OF THE MOTOR rpm\n", +"W=20000// LOAD AVILABLE IN N\n", +"U=.05// COEFFICIENT OF FRICTION\n", +"PI=3.147\n", +"//==================================================================================\n", +"T=2/3*U*W*d1/2// FRICTIONAL TORQUE IN N-m\n", +"PL=2*PI*N*T/100/60// POWER LOST IN FRICTION IN WATTS\n", +"//==================================================================================\n", +"//OUTPUT\n", +"printf('POWER LOST IN FRICTION=%3.3f watts',PL)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.12: NO_OF_COLLARS_REQUIRED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 12 PAGE NO 109\n", +"//TITLE:FRICTION\n", +"clc\n", +"clear\n", +"//===================================================================================\n", +"//INPUT DATA\n", +"PI=3.147\n", +"d2=.30// DIAMETER OF SHAFT IN m \n", +"W=200000// LOAD AVAILABLE IN NEWTONS\n", +"N=75// SPEED IN rpm\n", +"U=.05// COEFFICIENT OF FRICTION\n", +"p=300000// PRESSURE AVAILABLE IN N/m^2\n", +"P=16200// POWER LOST DUE TO FRICTION IN WATTS\n", +"//====================================================================================\n", +"//CaLCULATION\n", +"T=P*60/2/PI/N// TORQUE INDUCED IN THE SHFT IN N-m\n", +"//LET X=(r1^3-r2^3)/(r1^2-r2^2)\n", +"X=(3/2*T/U/W)\n", +"r2=.15// SINCE d2=.30 m\n", +"c=r2^2-(X*r2)\n", +"b= r2-X\n", +"a= 1\n", +"r1=( -b+ sqrt (b^2 -4*a*c ))/(2* a);// VALUE OF r1 IN m\n", +"d1=2*r1*100// d1 IN cm\n", +"n=W/(PI*p*(r1^2-r2^2))\n", +"//================================================================================\n", +"//OUTPUT\n", +"printf('\nEXTERNAL DIAMETER OF SHAFT =%3.3f cm\nNO OF COLLARS REQUIRED =%.3f or %.0f',d1,n,n+1)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.13: POWER_ABSORBED_IN_FRICTION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 13 PAGE NO 111\n", +"//TITLE:FRICTION\n", +"clc\n", +"clear\n", +"//===================================================================================\n", +"//INPUT DATA\n", +"PI=3.147\n", +"W=20000// LOAD IN NEWTONS\n", +"ALPHA=120/2// CONE ANGLE IN DEGREES\n", +"p=350000// INTENSITY OF PRESSURE\n", +"U=.06\n", +"N=120// SPEED OF THE SHAFT IN rpm\n", +"//d1=3d2\n", +"//r1=3r2\n", +"//===================================================================================\n", +"//CALCULATION\n", +"//LET K=d1/d2\n", +"k=3\n", +"Z=W/((k^2-1)*PI*p)\n", +"r2=Z^.5// INTERNAL RADIUS IN m\n", +"r1=3*r2\n", +"T=2*U*W*(r1^3-r2^3)/(3*sind(60)*(r1^2-r2^2))// total frictional torque in N\n", +"P=2*PI*N*T/60000// power absorbed in friction in kW\n", +"//================================================================================\n", +"printf('\nTHE INTERNAL DIAMETER OF SHAFT =%3.3f cm\nTHE EXTERNAL DIAMETER OF SHAFT =%3.3f cm\nPOWER ABSORBED IN FRICTION =%.3f kW',r2*100,r1*100,P)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.14: FINDING_Radii.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 14 PAGE NO 111\n", +"//TITLE:FRICTION\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"PI=3.147\n", +"P=10000// POWER TRRANSMITTED BY CLUTCH IN WATTS\n", +"N=3000// SPEED IN rpm\n", +"p=.09// AXIAL PRESSURE IN N/mm^2\n", +"//d1=1.4d2 RELATION BETWEEN DIAMETERS \n", +"K=1.4// D1/D2\n", +"n=2\n", +"U=.3// COEFFICIENT OF FRICTION\n", +"//==========================================================================================\n", +"T=P*60000/1000/(2*PI*N)// ASSUMING UNIFORM WEAR TORQUE IN N-m\n", +"r2=(T*2/(n*U*2*PI*p*10^6*(K-1)*(K+1)))^(1/3)// INTERNAL RADIUS\n", +"\n", +"//===========================================================================================\n", +"printf('THE INTERNAL RADIUS =%f cm\n THE EXTERNAL RADIUS =%f cm',r2*100,K*r2*100)\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.15: MAX_AXIAL_INTENSITY_OF_PRESSURE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 14 PAGE NO 111\n", +"//TITLE:FRICTION\n", +"clc\n", +"//βμαφɳρΠπ\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"PI=3.147\n", +"n1=3// NO OF DICS ON DRIVING SHAFTS\n", +"n2=2// NO OF DICS ON DRIVEN SHAFTS\n", +"d1=30// DIAMETER OF DRIVING SHAFT IN cm\n", +"d2=15// DIAMETER OF DRIVEN SHAFT IN cm\n", +"r1=d1/2\n", +"r2=d2/2\n", +"U=.3// COEFFICIENT FRICTION\n", +"P=30000// TANSMITTING POWER IN WATTS\n", +"N=1800// SPEED IN rpm\n", +"//===========================================================================================\n", +"//CALCULATION\n", +"n=n1+n2-1// NO OF PAIRS OF CONTACT SURFACES\n", +"T=P*60000/(2*PI*N)// TORQUE IN N-m\n", +"W=2*T/(n*U*(r1+r2)*10)// LOAD IN N\n", +"k=W/(2*PI*(r1-r2))\n", +"p=k/r2/100// MAX AXIAL INTENSITY OF PRESSURE IN N/mm^2\n", +"//===========================================================================================\n", +"// OUTPUT\n", +"printf('MAX AXIAL INTENSITY OF PRESSURE =%f N/mm^2',p)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.1: finding_out_the_coefficient_of_friction.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 1 PAGE NO 102\n", +"//TITLE:FRICTION\n", +"//FIRURE 3.16(a),3.16(b)\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"P1=180// PULL APPLIED TO THE BODY IN NEWTONS\n", +"theta=30// ANGLE AT WHICH P IS ACTING IN DEGREES\n", +"P2=220// PUSH APPLIED TO THE BODY IN NEWTONS\n", +"//Rn= NORMAL REACTION\n", +"//F= FORCE OF FRICTION IN NEWTONS\n", +"//U= COEFFICIENT OF FRICTION\n", +"//W= WEIGHT OF THE BODY IN NEWTON\n", +"//==========================================================================================\n", +"//CALCULATION\n", +"F1=P1*cosd(theta)// RESOLVING FORCES HORIZONTALLY FROM 3.16(a)\n", +"F2=P2*cosd(theta)// RESOLVING FORCES HORIZONTALLY FROM 3.16(b)\n", +"// RESOLVING FORCES VERTICALLY Rn1=W-P1*sind(theta) from 3.16(a)\n", +"// RESOLVING FORCES VERTICALLY Rn2=W+P1*sind(theta) from 3.16(b)\n", +"// USING THE RELATION F1=U*Rn1 & F2=U*Rn2 AND SOLVING FOR W BY DIVIDING THESE TWO EQUATIONS\n", +"X=F1/F2// THIS IS THE VALUE OF Rn1/Rn2\n", +"Y1=P1*sind(theta)\n", +"Y2=P2*sind(theta)\n", +"W=(Y2*X+Y1)/(1-X)// BY SOLVING ABOVE 3 EQUATIONS\n", +"U=F1/(W-P1*sind(theta))// COEFFICIENT OF FRICTION\n", +"//=============================================================================================\n", +"//OUTPUT\n", +"printf('WEIGHT OF THE BODY =%.3fN\nTHE COEFFICIENT OF FRICTION =%.3f',W,U)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.2: DISTANCE_ALONG_THE_INCLINED_PLANE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 2 PAGE NO 103\n", +"//TITLE:FRICTION\n", +"//FIRURE 3.17\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"THETA=45// ANGLE OF INCLINATION IN DEGREES\n", +"g=9.81// ACCELERATION DUE TO GRAVITY IN N/mm^2\n", +"U=.1// COEFFICIENT FRICTION\n", +"//Rn=NORMAL REACTION\n", +"//M=MASS IN NEWTONS\n", +"//f=ACCELERATION OF THE BODY\n", +"u=0// INITIAL VELOCITY\n", +"V=10// FINAL VELOCITY IN m/s^2\n", +"//===========================================================================================\n", +"//CALCULATION\n", +"//CONSIDER THE EQUILIBRIUM OF FORCES PERPENDICULAR TO THE PLANE\n", +"//Rn=Mgcos(THETA)\n", +"//CONSIDER THE EQUILIBRIUM OF FORCES ALONG THE PLANE\n", +"//Mgsin(THETA)-U*Rn=M*f.............BY SOLVING THESE 2 EQUATIONS \n", +"f=g*sind(THETA)-U*g*cosd(THETA)\n", +"s=(V^2-u^2)/(2*f)// DISTANCE ALONG THE PLANE IN metres\n", +"//==============================================================================================\n", +"//OUTPUT\n", +"printf('DISTANCE ALONG THE INCLINED PLANE=%3.3f m',s)\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.3: workdone.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 3 PAGE NO 104\n", +"//TITLE:FRICTION\n", +"//FIRURE 3.18\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"W=500// WEGHT IN NEWTONS\n", +"THETA=30// ANGLE OF INCLINATION IN DEGRESS\n", +"U=0.2// COEFFICIENT FRICTION\n", +"S=15// DISTANCE IN metres\n", +"//============================================================================================\n", +"Rn=W*cosd(THETA)// NORMAL REACTION IN NEWTONS\n", +"P=W*sind(THETA)+U*Rn// PUSHING FORCE ALONG THE DIRECTION OF MOTION\n", +"w=P*S\n", +"//============================================================================================\n", +"//OUTPUT\n", +"printf('WORK DONE BY THE FORCE=%3.3f N-m',w)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.4: FINDING_OUT_COEFFICIENT_OF_FRICTION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 4 PAGE NO 104\n", +"//TITLE:FRICTION\n", +"//FIRURE 3.19(a) & 3.19(b)\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"P1=2000// FORCE ACTING UPWARDS WHEN ANGLE=15 degrees IN NEWTONS\n", +"P2=2300// FORCE ACTING UPWARDS WHEN ANGLE=20 degrees IN NEWTONS\n", +"THETA1=15// ANGLE OF INCLINATION IN 3.19(a)\n", +"THETA2=20// ANGLE OF INCLINATION IN 3.19(b)\n", +"//F1= FORCE OF FRICTION IN 3.19(a)\n", +"//Rn1= NORMAL REACTION IN 3.19(a)\n", +"//F2= FORCE OF FRICTION IN 3.19(b)\n", +"//Rn2= NORMAL REACTION IN 3.19(b)\n", +"//U= COEFFICIENT OF FRICTION\n", +"//===========================================================================================\n", +"//CALCULATION\n", +"//P1=F1+Rn1 RESOLVING THE FORCES ALONG THE PLANE\n", +"//Rn1=W*cosd(THETA1)....NORMAL REACTION IN 3.19(a)\n", +"//F1=U*Rn1\n", +"//BY SOLVING ABOVE EQUATIONS P1=W(U*cosd(THETA1)+sind(THETA1))---------------------1\n", +"//P2=F2+Rn2 RESOLVING THE FORCES PERPENDICULAR TO THE PLANE\n", +"//Rn2=W*cosd(THETA2)....NORMAL REACTION IN 3.19(b)\n", +"//F2=U*Rn2\n", +"//BY SOLVING ABOVE EQUATIONS P2=W(U*cosd(THETA2)+sind(THETA2))----------------------2\n", +"//BY SOLVING EQUATIONS 1 AND 2\n", +"X=P2/P1\n", +"U=(sind(THETA2)-(X*sind(THETA1)))/((X*cosd(THETA1)-cosd(THETA2)))// COEFFICIENT OF FRICTION\n", +"W=P1/(U*cosd(THETA1)+sind(THETA1))\n", +"//=============================================================================================\n", +"//OUTPUT\n", +"//printf('%f',X)\n", +"printf('COEFFICIENT OF FRICTION=%3.3f\n WEIGHT OF THE BODY=%3.3f N',U,W)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.5: EFFORT_NEED_TO_APPLIED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 5 PAGE NO 105\n", +"//TITLE:FRICTION\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"d=5// DIAMETER OF SCREW JACK IN cm\n", +"p=1.25// PITCH IN cm\n", +"l=50// LENGTH IN cm\n", +"U=.1// COEFFICIENT OF FRICTION\n", +"W=20000// LOAD IN NEWTONS\n", +"PI=3.147\n", +"//=============================================================================================\n", +"//CALCULATION\n", +"ALPHA=atand(p/(PI*d))\n", +"PY=atand(U)\n", +"P=W*tand(ALPHA+PY)\n", +"P1=P*d/(2*l)\n", +"//=============================================================================================\n", +"//OUTPUT\n", +"printf('THE AMOUNT OF EFFORT NEED TO APPLY =%3.3f N',P1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.6: EFFICIENCY_OF_THE_MACHINE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 6 PAGE NO 106\n", +"//TITLE:FRICTION\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"d=50// DIAMETER OF SCREW IN mm\n", +"p=12.5// PITCH IN mm\n", +"U=0.13// COEFFICIENT OF FRICTION\n", +"W=25000// LOAD IN mm\n", +"PI=3.147\n", +"//===========================================================================================\n", +"//CALCULATION\n", +"ALPHA=atand(p/(PI*d))\n", +"PY=atand(U)\n", +"P=W*tand(ALPHA+PY)// FORCE REQUIRED TO RAISE THE LOAD IN N\n", +"T1=P*d/2// TORQUE REQUIRED IN Nm\n", +"P1=W*tand(PY-ALPHA)// FORCE REQUIRED TO LOWER THE SCREW IN N\n", +"T2=P1*d/2// TORQUE IN N\n", +"X=T1/T2// RATIOS REQUIRED\n", +"n=tand(ALPHA/(ALPHA+PY))// EFFICIENCY\n", +"//============================================================================================\n", +"printf('RATIO OF THE TORQUE REQUIRED TO RAISE THE LOAD,TO THE TORQUE REQUIRED TO LOWER THE LOAD =%.3f',X)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.7: EFFICIENCY_OF_MACHINE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 7 PAGE NO 107\n", +"//TITLE:FRICTION\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"d=39// DIAMETER OF THREAD IN mm\n", +"p=13// PITCH IN mm\n", +"U=0.1// COEFFICIENT OF FRICTION\n", +"W=2500// LOAD IN mm\n", +"PI=3.147\n", +"//===========================================================================================\n", +"//CALCULATION\n", +"ALPHA=atand(p/(PI*d))\n", +"PY=atand(U)\n", +"P=W*tand(ALPHA+PY)// FORCE IN N\n", +"T1=P*d/2// TORQUE REQUIRED IN Nm\n", +"T=2*T1// TORQUE REQUIRED ON THE COUPLING ROD IN Nm\n", +"K=2*p// DISTANCE TRAVELLED FOR ONE REVOLUTION\n", +"N=20.8/K// NO OF REVOLUTIONS REQUIRED\n", +"w=2*PI*N*T/100// WORKDONE BY TORQUE\n", +"w1=w*(7500-2500)/2500// WORKDONE TO INCREASE THE LOAD FROM 2500N TO 7500N\n", +"n=tand(ALPHA)/tand(ALPHA+PY)// EFFICIENCY\n", +"//============================================================================================\n", +"//OUTPUT\n", +"printf('workdone against a steady load of 2500N=%3.3f N\n workdone if the load is increased from 2500N to 7500N=%3.3f N\n efficiency=%.3f',w,w1,n)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.8: NO_OF_TEETH_ON_PINION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 8 PAGE NO 107\n", +"//TITLE:FRICTION\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"W=50000// WEIGHT OF THE SLUICE GATE IN NEWTON\n", +"P=40000// POWER IN WATTS\n", +"N=580// MAX MOTOR RUNNING SPEEED IN rpm\n", +"d=12.5// DIAMETER OF THE SCREW IN cm\n", +"p=2.5// PITCH IN cm\n", +"PI=3.147\n", +"U1=.08// COEFFICIENT OF FRICTION for SCREW\n", +"U2=.1// C.O.F BETWEEN GATES AND SCREW\n", +"Np=2000000// NORMAL PRESSURE IN NEWTON\n", +"Fl=.15// FRICTION LOSS\n", +"n=1-Fl// EFFICIENCY\n", +"ng=80// NO OF TEETH ON GEAR\n", +"//===========================================================================================\n", +"//CALCULATION\n", +"TV=W+U2*Np// TOTAL VERTICAL HEAD IN NEWTON\n", +"ALPHA=atand(p/(PI*d))// \n", +"PY=atand(U1)// \n", +"P1=TV*tand(ALPHA+PY)// FORCE IN N\n", +"T=P1*d/2/100// TORQUE IN N-m\n", +"Ng=60000*n*P*10^-3/(2*PI*T)// SPEED OF GEAR IN rpm\n", +"np=Ng*ng/N// NO OF TEETH ON PINION\n", +"//=========================================================================================\n", +"//OUTPUT\n", +"printf('NO OF TEETH ON PINION =%.2f say %d',np,np+1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.9: TO_FIND_THE_DIAMETER_OF_HAND_WHEEL.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 3 ILLUSRTATION 9 PAGE NO 108\n", +"//TITLE:FRICTION\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"d=5// MEAN DIAMETER OF SCREW IN cm\n", +"p=1.25// PITCH IN cm\n", +"W=10000// LOAD AVAILABLE IN NEWTONS\n", +"dc=6// MEAN DIAMETER OF COLLAR IN cm\n", +"U=.15// COEFFICIENT OF FRICTION OF SCREW\n", +"Uc=.18// COEFFICIENT OF FRICTION OF COLLAR\n", +"P1=100// TANGENTIAL FORCE APPLIED IN NEWTON\n", +"PI=3.147\n", +"//============================================================================================\n", +"//CALCULATION\n", +"ALPHA=atand(p/(PI*d))// \n", +"PY=atand(U)// \n", +"T1=W*d/2*tand(ALPHA+PY)/100// TORQUE ON SCREW IN NEWTON\n", +"Tc=Uc*W*dc/2/100// TORQUE ON COLLAR IN NEWTON\n", +"T=T1+Tc// TOTAL TORQUE\n", +"D=2*T/P1/2*100// DIAMETER OF HAND WHEEL IN cm\n", +"//============================================================================================\n", +"//OUTPUT\n", +"printf('SUITABLE DIAMETER OF HAND WHEEL =%3.3f cm',D)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Theory_Of_Machines_by_B_K_Sarkar/4-Gears_and_Gear_Drivers.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/4-Gears_and_Gear_Drivers.ipynb new file mode 100644 index 0000000..c7f8e77 --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/4-Gears_and_Gear_Drivers.ipynb @@ -0,0 +1,843 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4: Gears and Gear Drivers" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.10: Speed_of_wheels.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 10, Page 141\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//Input data\n", +"Ta=96;//Teeth of wheel A\n", +"Tc=48;//Teeth of wheel C\n", +"y=-20;//Speed of arm C in rpm in clockwise\n", +"\n", +"//Calculations\n", +"x=(y*Ta)/Tc\n", +"Tb=(Ta-Tc)/2;//Teeth of wheel B\n", +"Nb=(-Tc/Tb)*x+y;//Speed of wheel B in rpm\n", +"Nc=x+y;//Speed of wheel C in rpm\n", +"\n", +"//Output\n", +"mprintf('Speed of wheel B is %3.0f rpm \n Speed of wheel C is %3.0f rpm',Nb,Nc)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"//================================END OF PROGRAM=============================================" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.11: speed_of_the_arm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 11, Page 142\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"//Input data\n", +"Ta=40// no of teeth on gear A\n", +"Td=90// no of teeth on gear D\n", +"\n", +"//Calculations\n", +"Tb=(Td-Ta)/2// no of teeth on gear B\n", +"Tc=Tb// no of teeth on gear C\n", +"//\n", +"//x+y=-1\n", +"//-40x+90y=45\n", +"A=[1 1\n", +" -Ta Td]//Coefficient matrix\n", +"B=[-1\n", +" (Td/2)]//Constant matrix\n", +"X=inv(A)*B//Variable matrix\n", +"//\n", +"//x+y=-1\n", +"//-40x+90y=0\n", +"A1=[1 1\n", +" -Ta Td]//Coefficient matrix\n", +"B1=[-1\n", +" 0]//Constant matrix\n", +"X1=inv(A1)*B1//Variable matrix\n", +" \n", +"disp(X(2)) \n", +"printf('speed of the arm = %.3f revolution clockwise',X1(2))" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.12: Speed_of_wheel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 12, Page 144\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//Input data\n", +"Te=30;//Teeth of wheel E\n", +"Tb=24;//Teeth of wheel B\n", +"Tc=22;//Teeth of wheel C\n", +"Td=70;//Teeth of wheel D\n", +"Th=15;//Teeth of wheel H\n", +"Nv=100;//Speed of shaft V in rpm\n", +"Nx=300;//Speed of spindle X in rpm\n", +"\n", +"//Calculations\n", +"Nh=Nv;//Speed of wheel H in rpm\n", +"Ne=(-Th/Te)*Nv;//Speed of wheel E in rpm\n", +"Ta=(Tc+Td-Tb);//Teeth of wheel A\n", +"//x+y=-50\n", +"//y=300\n", +"x=(Ne-Nx)\n", +"Nz=(187/210)*x+Nx;//;//Speed of wheel Z in rpm\n", +"\n", +"//Output\n", +"mprintf('Speed of wheel Z is %3.3f rpm \n Direction of wheel Z is opposite to that of X',Nz)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.13: Speed_of_driven_shaft.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 13, Page 145\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//Input data\n", +"Tp=20;//Teeth of wheel P\n", +"Tq=30;//Teeth of wheel Q\n", +"Tr=10;//Teeth of wheel R\n", +"Nx=50;//Speed of shaft X in rpm\n", +"Na=100;//Speed of arm A in rpm\n", +"\n", +"//Calculations\n", +"//x+y=-50\n", +"//y=100\n", +"x=(-Nx-Na)\n", +"y=(-2*x+Na);//Speed of Y in rpm\n", +"\n", +"//Output\n", +"mprintf('Speed of driven shaft Y is %3.0f rpm \n Direction of driven shaft Y is anti-clockwise',y)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.14: pitch_circle_diameter.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 14, Page 146\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//Input data\n", +"d=216;//Ring diameter in mm\n", +"m=4;//Module in mm\n", +"\n", +"//Calculations\n", +"Td=(d/m);//Teeth of wheel D\n", +"Tb=Td/4;//Teeth of wheel B\n", +"Tb1=ceil(Tb);//Teeth of wheel B\n", +"Td1=4*Tb1;//Teeth of wheel D\n", +"Tc1=(Td1-Tb1)/2;//Teeth of wheel C\n", +"d1=m*Td1;//Pitch circle diameter in mm\n", +"\n", +"//Output\n", +"mprintf('Teeth of wheel B is %3.0f \n Teeth of wheel C is %3.0f \n Teeth of wheel D is %3.0f \n Exact pitch circle diameter is %3.0f mm',Tb1,Tc1,Td1,d1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.15: Revolution_of_gears.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 15, Page 147\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//Input data\n", +"Ta=100// no of teeth on gear A\n", +"Tc=101// no of teeth on gear C\n", +"Td=99// no of teeth on gear D\n", +"Tp=20// no of teeth on planet gear\n", +"y=1// from table 4.9(arm B makes one revolution)\n", +"x=-y// as gear is fixed\n", +"\n", +"//Calculations\n", +"Nc=(Ta*x)/Tc+y// Revolution of gear C \n", +"Nd=(Ta*x)/Td+y// Revolution of gear D\n", +"\n", +"//Output\n", +"printf('Revolution of gear C = %f\n Revolution of gear D = %f',Nc,Nd)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.16: speed_of_road_wheel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 16, Page 148\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//Input data\n", +"Ta=12// no of teeth on gear A\n", +"Tb=60// no of teeth on gear B\n", +"N=1000// speed of propeller shaft in rpm\n", +"Nc=210// speed of gear C in rpm\n", +"\n", +"//Calculations\n", +"Nb=(Ta*N)/Tb// speed of gear B in rpm\n", +"x=(Nb-Nc)\n", +"Nd=Nb+x// speed of road wheel driven by D\n", +"\n", +"//Output\n", +"printf('speed of road wheel driven by D= %d rpm',Nd)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.17: ratio_of_torques.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 17, Page 148\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"//Input data\n", +"Ta=20// no of teeth on pinion A\n", +"Tb=25// no of teeth on wheel B\n", +"Tc=50// no of teeth on gear C\n", +"Td=60// no of teeth on gear D\n", +"Te=60// no of teeth on gear E\n", +"Na=200// SPEED of the gear A\n", +"Nd=100// speed of the gear D\n", +"\n", +"//calculations\n", +"//(i)\n", +"//(5/6)x+y=0\n", +"//(5/4)x+y=200\n", +"A1=[(Tc/Td) 1\n", +" (Tb/Ta) 1]//Coefficient matrix\n", +"B1=[0\n", +" Na]//Constant matrix\n", +"X1=inv(A1)*B1//Variable matrix\n", +"Ne1=X1(2)-(Tc/Td)*X1(1)// \n", +"T1=(-Ne1/Na)// ratio of torques when D is fixed\n", +"//(ii)\n", +"//(5/4)x+y=200\n", +"//(5/6)x+y=100\n", +"A2=[(Tc/Td) 1\n", +" (Tb/Ta) 1]//Coefficient matrix\n", +"B2=[Nd\n", +" Na]//Constant matrix\n", +"X2=inv(A2)*B2//Variable matrix\n", +"Ne2=X2(2)-(Tc/Td)*X2(1)\n", +"T2=(-Ne2/Na)// ratio of torques when D ratates at 100 rpm\n", +"\n", +"//Output\n", +"printf('speed of E= %.2f rpm in clockwise direction\n speed of E in 2nd case(when D rotates at 100 rpm)= %d rpm in clockwise direction\n ratio of torques when D is fixed= %d \n ratio of torques when D ratates at 100 rpm= %d',Ne1,Ne2,T1,T2)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.1: Length_of_arc_of_contact.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 1, Page 133\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//INPUT DATA\n", +"TA=48;//Wheel A teeth\n", +"TB=30;//Wheel B teeth\n", +"m=5;//Module pitch in mm\n", +"phi=20;//Pressure angle in degrees\n", +"add=m;//Addendum in mm\n", +"\n", +"//CALCULATIONS\n", +"R=(m*TA)/2;//Pitch circle radius of wheel A in mm\n", +"RA=R+add;//Radius of addendum circle of wheel A in mm\n", +"r=(m*TB)/2;//Pitch circle radius of wheel B in mm\n", +"rA=r+add;//Radius of addendum circle of wheel B in mm\n", +"lp=(sqrt((RA^2)-((R^2)*(cosd(phi)^2))))+(sqrt((rA^2)-((r^2)*(cosd(phi)^2))))-((R+r)*sind(phi));//Length of path of contact in mm\n", +"la=lp/cosd(phi);//Length of arc of contact in mm\n", +"\n", +"//OUTPUT\n", +"mprintf('Length of arc of contact is %3.1f mm',la)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"//================================END OF PROGRAM=============================================" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.2: Addendum_of_wheel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 2, Page 133\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//INPUT DATA\n", +"TA=40;//Wheel A teeth\n", +"TB=TA;//Wheel B teeth\n", +"m=6;//Module pitch in mm\n", +"phi=20;//Pressure angle in degrees\n", +"pi=3.141\n", +"x=1.75;//Ratio of length of arc of contact to circular pitch\n", +"\n", +"//CALCULATIONS\n", +"Cp=m*pi;//Circular pitch in mm\n", +"R=(m*TA)/2;//Pitch circle radius of wheel A in mm\n", +"r=R;//Pitch circle radius of wheel B in mm\n", +"la=x*Cp;//Length of arc of contact in mm\n", +"lp=la*cosd(phi);//Length of path of contact in mm\n", +"RA=sqrt((((lp/2)+(R*sind(phi)))^2)+((R^2)*(cosd(phi))^2));//Radius of addendum circle of each wheel in mm\n", +"add=RA-R;//Addendum in mm\n", +"\n", +"//OUTPUT\n", +"mprintf('Addendum of wheel is %3.3f mm',add)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"//================================END OF PROGRAM=============================================" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.3: Length_of_arc_of_contact.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 3, Page 134\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//INPUT DATA\n", +"TA=48;//Gear teeth\n", +"TB=24;//Pinion teeth\n", +"m=6;//Module in mm\n", +"phi=20;//Pressure angle in degrees\n", +"\n", +"//CALCULATIONS\n", +"r=(m*TB)/2;//Pitch circle radius of pinion in mm\n", +"R=(m*TA)/2;//Pitch circle radius of gear in mm\n", +"RA=sqrt(((((r*sind(phi))/2)+(R*sind(phi)))^2)+((R^2)*(cosd(phi))^2));//Radius of addendum circle of gear in mm\n", +"rA=sqrt(((((R*sind(phi))/2)+(r*sind(phi)))^2)+((r^2)*(cosd(phi))^2));//Radius of addendum circle of pinion in mm\n", +"addp=rA-r;//Addendum for pinion in mm\n", +"addg=RA-R;//Addendum for gear in mm\n", +"lp=((R+r)*sind(phi))/2;//Length of path of contact in mm\n", +"la=lp/cosd(phi);//Length of arc of contact in mm\n", +"\n", +"//OUTPUT\n", +"mprintf('Addendum for pinion is %3.3f mm \n Addendum for gear is %3.2f mm \n Length of arc of contact is %3.3f mm',addp,addg,la)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"//================================END OF PROGRAM=============================================" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.4: Velocity_ratio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 4, Page 135\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//INPUT DATA\n", +"x=3.5;//Ratio of teeth of wheels\n", +"C=1.2;//Centre distance between axes in m\n", +"DP=4.4;//Diametrical pitch in cm\n", +"\n", +"//CALCULATIONS\n", +"D=2*C*100;//Sum of diameters of wheels in cm\n", +"T=D*DP;//Sum of teeth of wheels\n", +"TB1=T/(x+1);//Teeth of wheel B\n", +"TB=floor(TB1);//Teeth of whhel B\n", +"TA=x*TB;//Teeth of wheel A\n", +"DA=TA/DP;//Diametral pitch of gear A in cm\n", +"DB=TB/DP;//Diametral pitch of gear B in cm\n", +"Ce=(DA+DB)/2;//Exact centre distance between shafts in cm\n", +"TB2=ceil(TB1);//Teeth of wheel B\n", +"TA2=T-TB2;//Teeth of wheel A\n", +"VR=TA2/TB2;//Velocity ratio\n", +"\n", +"//OUTPUT\n", +"mprintf('Number of teeth on wheel A is %3.0f \n Number of teeth on wheel B is %3.0f \n Exact centre distance is %3.3f cm \n If centre distance is %3.1f m then \n Velocity ratio is %3.4f',TA,TB,Ce,C,VR)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"//================================END OF PROGRAM=============================================" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.5: Power_transmitted.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 5, Page 136\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//INPUT DATA\n", +"C=600;//Distance between shafts in mm\n", +"Cp=30;//Circular pitch in mm\n", +"NA=200;//Speed of wheel A in rpm\n", +"NB=600;//Speed of wheel B in rpm\n", +"F=18;//Tangential pressure in kN\n", +"pi=3.141\n", +"\n", +"//CALCULATIONS\n", +"a=Cp/(pi*10);//Ratio of pitch diameter of wheel A to teeth of wheel A in cm\n", +"b=Cp/(pi*10);//Ratio of pitch diameter of wheel B to teeth of wheel B in cm\n", +"T=(2*C)/(a*10);//Sum of teeth of wheels\n", +"r=NB/NA;//Ratio of teeth of wheels\n", +"TB=T/(r+1);//Teeth of wheel B\n", +"TB1=ceil(TB);//Teeth of wheel B\n", +"TA=TB1*r;//Teeth of wheel A\n", +"DA=a*TA;//Pitch diameter of wheel A in cm\n", +"DB=b*TB1;//Pitch diameter of wheel B in cm\n", +"CPA=(pi*DA)/TA;//Circular pitch of gear A in cm\n", +"CPB=(pi*DB)/TB1;//Circular pitch of gear B in cm\n", +"C1=(DA+DB)*10/2;//Exact centre distance in mm\n", +"P=(F*1000*pi*DA*NA)/(60*1000*100);//Power transmitted in kW\n", +"\n", +"//OUTPUT\n", +"mprintf('Number of teeth on wheel A is %3.0f \n Number of teeth on wheel B is %3.0f \n Pitch diameter of wheel A is %3.2f cm \n Pitch diameter of wheel B is %3.3f cm \n Circular pitch of wheel A is %3.4f cm \n Circular pitch of wheel B is %3.4f cm \n Exact centre distance between shafts is %3.2f mm \n Power transmitted is %3.3f kW',TA,TB1,DA,DB,CPA,CPB,C1,P)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"//================================END OF PROGRAM=============================================" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.6: Number_of_teeth_on_gear.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 6, Page 137\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//INPUT DATA\n", +"r=16;//Speed ratio\n", +"mA=4;//Module of gear A in mm\n", +"mB=mA;//Module of gear B in mm\n", +"mC=2.5;//Mosule of gear C in mm\n", +"mD=mC;//Module of gear D in mm\n", +"C=150;//Distance between shafts in mm\n", +"\n", +"//CALCULATIONS\n", +"t=sqrt(r);//Ratio of teeth\n", +"T1=(C*2)/mA;//Sum of teeth of wheels A and B\n", +"T2=(C*2)/mC;//Sum of teeth of wheels C and D\n", +"TA=T1/(t+1);//Teeth of gear A\n", +"TB=T1-TA;//Teeth of gear B\n", +"TC=T2/(t+1);//Teeth of gear C\n", +"TD=T2-TC;//Teeth of gear D\n", +"\n", +"//OUTPUT\n", +"mprintf('Number of teeth on gear A is %3.0f \n Number of teeth on gear B is %3.0f \n Number of teeth on gear C is %3.0f \n Number of teeth on gear D is %3.0f',TA,TB,TC,TD)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"//================================END OF PROGRAM=============================================" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.7: noof_teeth_on_gears.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 7, Page 138\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//INPUT DATA\n", +"N=4.5;//No. of turns\n", +"\n", +"//CALCULATIONS\n", +"Vh=N/2;//Velocity ratio of main spring spindle to hour hand spindle\n", +"Vm=12;//Velocity ratio of minute hand spindle to hour hand spindle\n", +"T1=8// assumed no of teeth on gear 1\n", +"T2=32// assumed no of teeth on gear 2\n", +"T3=(T1+T2)/4// no of teeth on gear 3\n", +"T4=(T1+T2)-T3// no of teeth on gear 4\n", +"printf('no of teeth on gear 1=%d\n no of teeth on gear 2=%d\n no of teeth on gear 3=%d\n no of teeth on gear 4=%d',T1,T2,T3,T4)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.8: Speed_of_wheel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 8, Page 139\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//Input data\n", +"Tb=70;//Teeth of wheel B\n", +"Tc=25;//Teeth of wheel C\n", +"Td=80;//Teeth of wheel D\n", +"Na=-100;//Speed of arm A in clockwise in rpm\n", +"y=-100//Arm A rotates at 100 rpm clockwise\n", +"\n", +"//Calculations\n", +"Te=(Tc+Td-Tb);//Teeth of wheel E\n", +"x=(y/0.5)\n", +"Nc=(y-(Td*x)/Tc);//Speed of wheel C in rpm\n", +"\n", +"//Output\n", +"mprintf('Speed of wheel C is %3.0f rpm \n Direction of wheel C is anti-clockwise',Nc)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"//================================END OF PROGRAM=============================================" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.9: Speed_of_wheels.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//Chapter-4, Illustration 9, Page 140\n", +"//Title: Gears and Gear Drivers\n", +"//=============================================================================\n", +"clc\n", +"clear\n", +"\n", +"//Input data\n", +"Tb=25;//Teeth of wheel B\n", +"Tc=40;//Teeth of wheel C\n", +"Td=10;//Teeth of wheel D\n", +"Te=25;//Teeth of wheel E\n", +"Tf=30;//Teeth of wheel F\n", +"y=-120;//Speed of arm A in clockwise in rpm\n", +"\n", +"//Calculations\n", +"x=(-y/4)\n", +"Nb=x+y;//Speed of wheel B in rpm\n", +"Nf=(-10/3)*x+y;//Speed of wheel F in rpm\n", +"\n", +"//Output\n", +"mprintf('Speed of wheel B is %3.0f rpm \n Direction of wheel B is clockwise \n Speed of wheel F is %3.0f rpm \n Direction of wheel F is clockwise',Nb,Nf)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"//================================END OF PROGRAM=============================================" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Theory_Of_Machines_by_B_K_Sarkar/5-Inertia_Force_Analysis_in_Machines.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/5-Inertia_Force_Analysis_in_Machines.ipynb new file mode 100644 index 0000000..a96d2fa --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/5-Inertia_Force_Analysis_in_Machines.ipynb @@ -0,0 +1,361 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5: Inertia Force Analysis in Machines" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1: Maximum_velocity_of_the_pisto.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 5 ILLUSRTATION 1 PAGE NO 160\n", +"//TITLE:Inertia Force Analysis in Machines\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"r=.3// radius of crank in m\n", +"l=1// length of connecting rod in m\n", +"N=200// speed of the engine in rpm\n", +"n=l/r\n", +"//===================\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"teeta=acosd((-n+((n^2)+4*2*1)^.5)/(2*2))// angle of inclination of crank in degrees\n", +"Vp=w*r*(sind(teeta)+(sind(2*teeta))/n)// maximum velocity of the piston in m/s\n", +"printf('Maximum velocity of the piston = %.3f m/s',Vp)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2: EX5_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 5 ILLUSRTATION 2 PAGE NO 161\n", +"//TITLE:Inertia Force Analysis in Machines\n", +"clc\n", +"clear\n", +"PI=3.141\n", +"r=.3// length of crank in metres\n", +"l=1.5// length of connecting rod in metres\n", +"N=180// speed of rotation in rpm\n", +"teeta=40// angle of inclination of crank in degrees\n", +"//============================\n", +"n=l/r\n", +"w=2*PI*N/60// angular speed in rad/s\n", +"Vp=w*r*(sind(teeta)+sind(2*teeta)/(2*n))// velocity of piston in m/s\n", +"fp=w^2*r*(cosd(teeta)+cosd(2*teeta)/(2*n))// acceleration of piston in m/s^2\n", +"costeeta1=(-n+(n^2+4*2*1)^.5)/(2*2)\n", +"teeta1=acosd(costeeta1)// position of crank from inner dead centre position for zero acceleration of piston\n", +"//===========================\n", +"printf('Velocity of Piston = %.3f m/s\n Acceleration of piston = %.3f m/s^2\n position of crank from inner dead centre position for zero acceleration of piston= %.3f degrees',Vp,fp,teeta1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3: Turning_moment_on_the_crank_shaft.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 5 ILLUSRTATION 3 PAGE NO 161\n", +"//TITLE:Inertia Force Analysis in Machines\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"D=.3// Diameter of steam engine in m\n", +"L=.5// length of stroke in m\n", +"r=L/2\n", +"mR=100// equivalent of mass of reciprocating parts in kg\n", +"N=200// speed of engine in rpm\n", +"teeta=45// angle of inclination of crank in degrees\n", +"p1=1*10^6// gas pressure in N/m^2\n", +"p2=35*10^3// back pressure in N/m^2\n", +"n=4// ratio of crank radius to the length of stroke\n", +"//=================================\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"Fl=pi/4*D^2*(p1-p2)// Net load on piston in N\n", +"Fi=mR*w^2*r*(cosd(teeta)+cosd(2*teeta)/(2*n))// inertia force due to reciprocating parts\n", +"Fp=Fl-Fi// Piston effort\n", +"T=Fp*r*(sind(teeta)+(sind(2*teeta))/(2*(n^2-(sind(teeta))^2)^.5))\n", +"printf('Piston effort = %.3f N\n Turning moment on the crank shaft = %.3f N-m',Fp,T)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4: net_force_on_piston.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 5 ILLUSRTATION 4 PAGE NO 162\n", +"//TITLE:Inertia Force Analysis in Machines\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"D=.10// Diameter of petrol engine in m\n", +"L=.12// Stroke length in m\n", +"l=.25// length of connecting in m\n", +"r=L/2\n", +"mR=1.2// mass of piston in kg\n", +"N=1800// speed in rpm\n", +"teeta=25// angle of inclination of crank in degrees\n", +"p=680*10^3// gas pressure in N/m^2\n", +"n=l/r\n", +"g=9.81// acceleration due to gravity\n", +"//=======================================\n", +"w=2*pi*N/60// angular speed in rpm\n", +"Fl=pi/4*D^2*p// force due to gas pressure in N\n", +"Fi=mR*w^2*r*(cosd(teeta)+cosd(2*teeta)/(n))// inertia force due to reciprocating parts in N\n", +"Fp=Fl-Fi+mR*g// net force on piston in N\n", +"Fq=n*Fp/((n^2-(sind(teeta))^2)^.5)// resultant load on gudgeon pin in N\n", +"Fn=Fp*sind(teeta)/((n^2-(sind(teeta))^2)^.5)// thrust on cylinder walls in N\n", +"fi=Fl+mR*g// inertia force of the reciprocating parts before the gudgeon pin load is reversed in N\n", +"w1=(fi/mR/r/(cosd(teeta)+cosd(2*teeta)/(n)))^.5\n", +"N1=60*w1/(2*pi)\n", +"printf('Net force on piston = %.3f N\n Resultant load on gudgeon pin = %.3f N\n Thrust on cylinder walls = %.3f N\n speed at which other things remining same,the gudgeon pin load would be reversed in directionm= %.3f rpm',Fp,Fq,Fn,N1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5: Net_load_on_the_gudgeon_pin.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 5 ILLUSRTATION 5 PAGE NO 163\n", +"//TITLE:Inertia Force Analysis in Machines\n", +"//Figure 5.3\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"N=1800// speed of the petrol engine in rpm\n", +"r=.06// radius of crank in m\n", +"l=.240// length of connecting rod in m\n", +"D=.1// diameter of the piston in m\n", +"mR=1// mass of piston in kg\n", +"p=.8*10^6// gas pressure in N/m^2\n", +"x=.012// distance moved by piston in m\n", +"//===============================================\n", +"w=2*pi*N/60// angular velocity of the engine in rad/s\n", +"n=l/r\n", +"Fl=pi/4*D^2*p// load on the piston in N\n", +"teeta=32// by mearument from the figure 5.3\n", +"Fi=mR*w^2*r*(cosd(teeta)+cosd(2*teeta)/(n))// inertia force due to reciprocating parts in N\n", +"Fp=Fl-Fi// net load on the gudgeon pin in N\n", +"Fq=n*Fp/((n^2-(sind(teeta))^2)^.5)// thrust in the connecting rod in N\n", +"Fn=Fp*sind(teeta)/((n^2-(sind(teeta))^2)^.5)// reaction between the piston and cylinder in N\n", +"w1=(Fl/mR/r/(cosd(teeta)+cosd(2*teeta)/(n)))^.5\n", +"N1=60*w1/(2*pi)// \n", +"printf('Net load on the gudgeon pin= %.3f N\n Thrust in the connecting rod= %.3f N\n Reaction between the cylinder and piston= %.3f N\n The engine speed at which the above values become zero= %.3f rpm',Fp,Fq,Fn,N1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6: Torque_exerted_on_the_crank_shaft.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 5 ILLUSRTATION 6 PAGE NO 165\n", +"//TITLE:Inertia Force Analysis in Machines\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"D=.25// diameter of horizontal steam engine in m\n", +"N=180// speed of the engine in rpm\n", +"d=.05// diameter of piston in m\n", +"P=36000// power of the engine in watts\n", +"n=3// ration of length of connecting rod to the crank radius\n", +"p1=5.8*10^5// pressure on cover end side in N/m^2\n", +"p2=0.5*10^5// pressure on crank end side in N/m^2\n", +"teeta=40// angle of inclination of crank in degrees\n", +"m=45// mass of flywheel in kg\n", +"k=.65// radius of gyration in m\n", +"//==============================\n", +"Fl=(pi/4*D^2*p1)-(pi/4*(D^2-d^2)*p2)// load on the piston in N\n", +"phi=asind(sind(teeta)/n)// angle of inclination of the connecting rod to the line of stroke in degrees\n", +"r=1.6*D/2\n", +"T=Fl*sind(teeta+phi)/cosd(phi)*r// torque exerted on crank shaft in N-m\n", +"Fb=Fl*cosd(teeta+phi)/cosd(phi)// thrust on the crank shaft bearing in N\n", +"TR=P*60/(2*pi*N)// steady resisting torque in N-m\n", +"Ts=T-TR// surplus torque available in N-m\n", +"a=Ts/(m*k^2)// acceleration of the flywheel in rad/s^2\n", +"printf('Torque exerted on the crank shaft= %.3f N-m\n Thrust on the crank shaft bearing= %.3f N\n Acceleration of the flywheel= %.3f rad/s^2',T,Fb,a)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.7: Effective_turning_moment_on_the_crank_shaft.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 5 ILLUSRTATION 7 PAGE NO 166\n", +"//TITLE:Inertia Force Analysis in Machines\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"D=.25// diameter of vertical cylinder of steam engine in m\n", +"L=.45// stroke length in m\n", +"r=L/2\n", +"n=4\n", +"N=360// speed of the engine in rpm\n", +"teeta=45// angle of inclination of crank in degrees\n", +"p=1050000// net pressure in N/m^2\n", +"mR=180// mass of reciprocating parts in kg\n", +"g=9.81// acceleration due to gravity\n", +"//========================\n", +"Fl=p*pi*D^2/4// force on piston due to steam pressure in N\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"Fi=mR*w^2*r*(cosd(teeta)+cosd(2*teeta)/(n))// inertia force due to reciprocating parts in N\n", +"Fp=Fl-Fi+mR*g// piston effort in N\n", +"phi=asind(sind(teeta)/n)// angle of inclination of the connecting rod to the line of stroke in degrees\n", +"T=Fp*sind(teeta+phi)/cosd(phi)*r// torque exerted on crank shaft in N-m\n", +"printf('Effective turning moment on the crank shaft= %.3f N-m',T)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.8: Effective_turning_moment_on_the_crank_shaft.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 5 ILLUSRTATION 8 PAGE NO 166\n", +"//TITLE:Inertia Force Analysis in Machines\n", +"//figure 5.4\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"D=.25// diameter of vertical cylinder of diesel engine in m\n", +"L=.40// stroke length in m\n", +"r=L/2\n", +"n=4\n", +"N=300// speed of the engine in rpm\n", +"teeta=60// angle of inclination of crank in degrees\n", +"mR=200// mass of reciprocating parts in kg\n", +"g=9.81// acceleration due to gravity\n", +"l=.8// length of connecting rod in m\n", +"c=14// compression ratio=v1/v2\n", +"p1=.1*10^6// suction pressure in n/m^2\n", +"i=1.35// index of the law of expansion and compression \n", +"//==============================================================\n", +"Vs=pi/4*D^2*L// swept volume in m^3\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"Vc=Vs/(c-1)\n", +"V3=Vc+Vs/10// volume at the end of injection of fuel in m^3\n", +"p2=p1*c^i// final pressure in N/m^2\n", +"p3=p2// from figure\n", +"x=r*((1-cosd(teeta)+(sind(teeta))^2/(2*n)))// the displacement of the piston when the crank makes an angle 60 degrees with T.D.C\n", +"Va=Vc+pi*D^2*x/4\n", +"pa=p3*(V3/Va)^i\n", +"p=pa-p1// difference of pressues on 2 sides of piston in N/m^2\n", +"Fl=p*pi*D^2/4// net load on piston in N\n", +"Fi=mR*w^2*r*(cosd(teeta)+cosd(2*teeta)/(n))// inertia force due to reciprocating parts in N\n", +"Fp=Fl-Fi+mR*g// piston effort in N\n", +"phi=asind(sind(teeta)/n)// angle of inclination of the connecting rod to the line of stroke in degrees\n", +"T=Fp*sind(teeta+phi)/cosd(phi)*r// torque exerted on crank shaft in N-m\n", +"printf('Effective turning moment on the crank shaft= %.3f N-m',T)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Theory_Of_Machines_by_B_K_Sarkar/6-Turning_Moment_Diagram_and_Flywheel.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/6-Turning_Moment_Diagram_and_Flywheel.ipynb new file mode 100644 index 0000000..ecf3d87 --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/6-Turning_Moment_Diagram_and_Flywheel.ipynb @@ -0,0 +1,424 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6: Turning Moment Diagram and Flywheel" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.10: miminum_mass_moment_of_inertia_of_flywheel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"\n", +"//CHAPTER 6 ILLUSRTATION 10 PAGE NO 183\n", +"//TITLE:Turning Moment Diagram and Flywheel\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"Cs=.02// coefficient of fluctuation of speed \n", +"N=200// speed of the engine in rpm\n", +"//T2=15000-6000cosθ Torque required by the machine in Nm\n", +"//T1=15000+8000sin2θ Torque supplied by the engine in Nm\n", +"//T1-T2=8000sin2θ+6000cosθ Change in torque\n", +"theta1=acosd(0)\n", +"theta2=asind(-6000/16000)\n", +"theta2=180-theta2\n", +"//===============================================\n", +"//largest area,representing fluctuation of energy lies between theta1 and theta2\n", +"E=6000*sind(theta2)-8000/2*cosd(2*theta2)-(6000*sind(theta1)-8000/2*cosd(2*theta1))// total fluctuation of energy in Nm\n", +"Theta=180// angle with which cycle will be repeated in degrees\n", +"Theta1=0\n", +"Tmean=1/pi*((15000*pi+(-8000*cosd(2*Theta))/2)-((15000*Theta1+(-8000*cosd(2*Theta1))/2)))// mean torque of engine in Nm\n", +"P=2*pi*N*Tmean/60000// power of the engine in kw\n", +"w=2*pi*N/60// angular speed of the engine in rad/s\n", +"I=E/(w^2*Cs)// mass moment of inertia of flywheel in kg-m^2\n", +"printf('Power of the engine= %.3f kw\n minimum mass moment of inertia of flywheel= %.3f kg-m^2\n E value calculated in the textbook is wrong. Its value is -15,124. In textbook it is given as -1370.28',P,-I)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1: Kinetic_energy_of_flywheel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 6 ILLUSRTATION 1 PAGE NO 175\n", +"//TITLE:Turning Moment Diagram and Flywheel\n", +"clc\n", +"clear\n", +"k=1// radius of gyration of flywheel in m\n", +"m=2000// mass of the flywheel in kg\n", +"T=1000// torque of the engine in Nm\n", +"w1=0// speedin the begining\n", +"t=10// time duration\n", +"//==============================\n", +"I=m*k^2// mass moment of inertia in kg-m^2\n", +"a=T/I// angular acceleration of flywheel in rad/s^2\n", +"w2=w1+a*t// angular speed after time t in rad/s\n", +"K=I*w2^2/2// kinetic energy of flywheel in Nm\n", +"//==============================\n", +"printf('Angular acceleration of the flywheel= %.3f rad/s^2\n Kinetic energy of flywheel= %.3f N-m',a,K)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.2: Mass_of_the_flywheel_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 6 ILLUSRTATION 2 PAGE NO 176\n", +"//TITLE:Turning Moment Diagram and Flywheel\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"N1=225// maximum speed of flywheel in rpm\n", +"k=.5// radius of gyration of flywheel in m\n", +"n=720// no of holes punched per hour\n", +"E1=15000// energy required by flywheel in Nm\n", +"N2=200// mimimum speedof flywheel in rpm\n", +"t=2// time taking for punching a hole\n", +"//==========================\n", +"P=E1*n/3600// power required by motor per sec in watts\n", +"E2=P*t// energy supplied by motor to punch a hole in N-m\n", +"E=E1-E2// maximum fluctuation of energy in N-m\n", +"N=(N1+N2)/2// mean speed of the flywheel in rpm\n", +"m=E/(pi^2/900*k^2*N*(N1-N2))\n", +"printf('Power of the motor= %.3f watts\n Mass of the flywheel required= %.3f kg',P,m)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.3: Mass_of_the_flywheel_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 6 ILLUSRTATION 3 PAGE NO 176\n", +"//TITLE:Turning Moment Diagram and Flywheel\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"d=38// diameter of hole in cm\n", +"t=32// thickness of hole in cm\n", +"e1=7// energy required to punch one square mm\n", +"V=25// mean speed of the flywheel in m/s\n", +"S=100// stroke of the punch in cm\n", +"T=10// time required to punch a hole in s\n", +"Cs=.03// coefficient of fluctuation of speed\n", +"//===================\n", +"A=pi*d*t// sheared area in mm^2\n", +"E1=e1*A// energy required to punch entire area in Nm\n", +"P=E1/T// power of motor required in watts\n", +"T1=T/(2*S)*t// time required to punch a hole in 32 mm thick plate\n", +"E2=P*T1// energy supplied by motor in T1 seconds\n", +"E=E1-E2// maximum fluctuation of energy in Nm\n", +"m=E/(V^2*Cs)// mass of the flywheel required\n", +"printf('Mass of the flywheel required= %.0f kg',m)\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.4: Mass_of_the_flywheel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 6 ILLUSRTATION 4 PAGE NO 177\n", +"//TITLE:Turning Moment Diagram and Flywheel\n", +"//figure 6.4\n", +"clc\n", +"clear\n", +"//===================\n", +"pi=3.141\n", +"N=480// speed of the engine in rpm\n", +"k=.6// radius of gyration in m\n", +"Cs=.03// coefficient of fluctuaion of speed \n", +"Ts=6000// turning moment scale in Nm per one cm\n", +"C=30// crank angle scale in degrees per cm\n", +"a=[0.5,-1.22,.9,-1.38,.83,-.7,1.07]// areas between the output torque and mean resistance line in sq.cm\n", +"//======================\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"A=Ts*C*pi/180// 1 cm^2 of turning moment diagram in Nm\n", +"E1=a(1)// max energy at B refer figure\n", +"E2=a(1)+a(2)+a(3)+a(4)\n", +"E=(E1-E2)*A// fluctuation of energy in Nm\n", +"m=E/(k^2*w^2*Cs)// mass of the flywheel in kg\n", +"printf('Mass of the flywheel= %.3f kg',m)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.5: Mass_of_the_flywheel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 6 ILLUSRTATION 5 PAGE NO 178\n", +"//TITLE:Turning Moment Diagram and Flywheel\n", +"clc\n", +"clear\n", +"//==============\n", +"pi=3.141\n", +"P=500*10^3// power of the motor in N\n", +"k=.6// radius of gyration in m\n", +"Cs=.03// coefficient of fluctuation of spped \n", +"OA=750// REFER FIGURE\n", +"OF=6*pi// REFER FIGURE\n", +"AG=pi// REFER FIGURE\n", +"BG=3000-750// REFER FIGURE\n", +"GH=2*pi// REFER FIGURE\n", +"CH=3000-750// REFER FIGURE\n", +"HD=pi// REFER FIGURE\n", +"LM=2*pi// REFER FIGURE\n", +"T=OA*OF+1/2*AG*BG+BG*GH+1/2*CH*HD// Torque required for one complete cycle in Nm\n", +"Tmean=T/(6*pi)// mean torque in Nm\n", +"w=P/Tmean// angular velocity required in rad/s\n", +"BL=3000-1875// refer figure\n", +"KL=BL*AG/BG// From similar trangles\n", +"CM=3000-1875// refer figure\n", +"MN=CM*HD/CH//from similar triangles\n", +"E=1/2*KL*BL+BL*LM+1/2*CM*MN// Maximum fluctuaion of energy in Nm\n", +"m=E*100/(k^2*w^2*Cs)// mass of flywheel in kg\n", +"printf('Mass of the flywheel= %.3f kg',m)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.6: Angular_acceleration.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 6 ILLUSRTATION 6 PAGE NO 179\n", +"//TITLE:Turning Moment Diagram and Flywheel\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"PI=180//in degrees\n", +"theta1=0\n", +"theta2=PI\n", +"m=400// mass of the flywheel in kg\n", +"N=250// speed in rpm\n", +"k=.4// radius of gyration in m\n", +"n=2*250/60000// no of working strokes per minute\n", +"W=1000*pi-150*cosd(2*theta2)-250*sind(2*theta2)-(1000*theta1-150*cosd(2*theta1)-250*sind(2*theta1))// workdone per stroke in Nm\n", +"P=W*n// power in KW\n", +"Tmean=W/pi// mean torque in Nm\n", +"twotheta=atand(500/300)// angle at which T-Tmean becomes zero\n", +"THETA1=twotheta/2\n", +"THETA2=(180+twotheta)/2\n", +"E=-150*cosd(2*THETA2)-250*sind(2*THETA2)-(-150*cosd(2*THETA1)-250*sind(2*THETA1))// FLUCTUATION OF ENERGY IN Nm\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"Cs1=E*100/(k^2*w^2*m)// fluctuation range\n", +"Cs=Cs1/2// tatal percentage of fluctuation of speed\n", +"Theta=60\n", +"T1=300*sind(2*Theta)-500*cosd(2*Theta)// Accelerating torque in Nm(T-Tmean)\n", +"alpha=T1/(m*k^2)// angular acceleration in rad/s^2\n", +"printf('Power delivered=%.3f kw\nTotal percentage of fluctuation speed= %.3f\nAngular acceleration= %.3f rad/s^2',P,Cs,alpha)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.7: Energy_expended_in_performing_each_operation.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 6 ILLUSRTATION 7 PAGE NO 181\n", +"//TITLE:Turning Moment Diagram and Flywheel\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"m=200// mass of the flywheel in kg\n", +"k=.5// radius of gyration in m\n", +"N1=360// upper limit of speed in rpm\n", +"N2=240// lower limit of speed in rpm\n", +"//==========\n", +"I=m*k^2// mass moment of inertia in kg m^2\n", +"w1=2*pi*N1/60\n", +"w2=2*pi*N2/60\n", +"E=1/2*I*(w1^2-w2^2)// fluctuation of energy in Nm\n", +"Pmin=E/(4*1000)// power in kw\n", +"Eex=Pmin*12*1000// Energy expended in performing each operation in N-m\n", +"printf('Mimimum power required= %.3f kw\n Energy expended in performing each operation= %.3f N-m',Pmin,Eex)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.8: Amount_of_Torque_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 6 ILLUSRTATION 8 PAGE NO 182\n", +"//TITLE:Turning Moment Diagram and Flywheel\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"b=8// width of the strip in cm\n", +"t=2// thickness of the strip in cm\n", +"w=1.2*10^3// work required per square cm cut\n", +"N1=200// maximum speed of the flywheel in rpm\n", +"k=.80// radius of gyration in m\n", +"N2=(1-.15)*N1// minimum speed of the flywheel in rpm\n", +"T=3// time required to punch a hole\n", +"//=======================\n", +"A=b*t// area cut of each stroke in cm^2\n", +"W=w*A// work required to cut a strip in Nm\n", +"w1=2*pi*N1/60// speed before cut in rpm\n", +"w2=2*pi*N2/60// speed after cut in rpm\n", +"m=2*W/(k^2*(w1^2-w2^2))// mass of the flywheel required in kg\n", +"a=(w1-w2)/T// angular acceleration in rad/s^2\n", +"Ta=m*k^2*a// torque required in Nm\n", +"printf('Mass of the flywheel= %.3f kg\n Amount of Torque required= %.3f Nm',m,Ta)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.9: Reduction_in_speed_after_the_pressing_is_over.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 6 ILLUSRTATION 9 PAGE NO 182\n", +"//TITLE:Turning Moment Diagram and Flywheel\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"P=5*10^3// power delivered by motor in watts\n", +"N1=360// speed of the flywheel in rpm\n", +"I=60// mass moment of inertia in kg m^2\n", +"E1=7500// energy required by pressing machine for 1 second in Nm\n", +"//========================\n", +"Ehr=P*60*60// energy sipplied per hour in Nm\n", +"n=Ehr/E1\n", +"E=E1-P// total fluctuation of energy in Nm\n", +"w1=2*pi*N1/60// angular speed before pressing in rpm \n", +"w2=((2*pi*N1/60)^2-(2*E/I))^.5// angular speed after pressing in rpm \n", +"N2=w2*60/(2*pi)\n", +"R=N1-N2// reduction in speed in rpm\n", +"printf('No of pressings that can be made per hour= %.0f\n Reduction in speed after the pressing is over= %.2f rpm ',n,R)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Theory_Of_Machines_by_B_K_Sarkar/7-GOVERNORS.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/7-GOVERNORS.ipynb new file mode 100644 index 0000000..8f8e17e --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/7-GOVERNORS.ipynb @@ -0,0 +1,560 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7: GOVERNORS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.10: EQUILIBRIUM_SPEED_OF_GOVERNOR.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 10 PAGE NO 206\n", +"//TITLE:GOVERNORS\n", +"//FIGURE 7.10\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"PI=3.147\n", +"AE=.25// LENGTH OF UPPER ARM IN m\n", +"CE=.25// LENGTH OF LOWER ARM IN m\n", +"EH=.1// LENGTH OF EXTENDED ARM IN m\n", +"EF=.15// RADIUS OF BALL PATH IN m\n", +"m=5// MASS OF EACH BALL IN Kg\n", +"M=40// MASS OF EACH BALL IN Kg\n", +"//===================================================================\n", +"h=(AE^2-EF^2)^.5// HEIGHT OF THE GOVERNOR IN m\n", +"EM=h\n", +"HM=EH+EM// FROM FIGURE 7.10\n", +"N=((895/h)*(EM/HM)*((m+M)/m))^.5\n", +"printf('EQUILIBRIUM SPEED OF GOVERNOR = %.3f rpm',N)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.11: TENSION_IN_UPPER_ARM.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 11 PAGE NO 207\n", +"//TITLE:GOVERNORS\n", +"//FIGURE 7.11\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"PI=3.147\n", +"g=9.81// ACCELERATION DUE TO GRAVITY IN N/mm^2\n", +"AE=.25// LENGTH OF UPPER ARM IN m\n", +"CE=.25// LENGTH OF LOWER ARM IN m\n", +"ER=.175// FROM FIGURE 7.11\n", +"AP=.025// FROM FIGURE 7.11\n", +"FR=AP// FROM FIGURE 7.11\n", +"CQ=FR// FROM FIGURE 7.11\n", +"m=3.2// MASS OF BALL IN Kg\n", +"M=25// MASS OF SLEEVE IN Kg\n", +"h=.2// VERTICAL HEIGHT OF GOVERNOR IN m\n", +"EM=h// FROM FIGURE 7.11\n", +"AF=h// FROM FIGURE 7.11\n", +"N=160// SPEED OF THE GOVERNOR IN rpm\n", +"HM=(895*EM*(m+M)/(h*N^2*m))\n", +"x=HM-EM// LENGTH OF EXTENDED LINK IN m\n", +"T1=g*(m+M/2)*AE/AF// TENSION IN UPPER ARM IN N\n", +"printf('LENGTH OF EXTENDED LINK = %.3f m\n TENSION IN UPPER ARM =%.3f N',x,T1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.12: MAXIMUM_SPEED_OF_ROTATION.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 12 PAGE NO 208\n", +"//TITLE:GOVERNORS\n", +"//FIGURE 7.12,7.13\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"PI=3.147\n", +"EF=.20// MINIMUM RADIUS OF ROTATION IN m\n", +"AE=.30// LENGTH OF EACH ARM IN m\n", +"A1E1=AE// COMPARING FIRUES 7.12&7.13\n", +"EC=.30// LENGTH OF EACH ARM IN m\n", +"E1C1=EC// LENGTH OF EACH ARM IN m\n", +"ED=.165// FROM FIGURE 7.12 IN m\n", +"MC=ED// FROM FIGURE 7.12\n", +"EH=.10// FROM FIGURE 7.12 IN m\n", +"m=8// MASS OF BALL IN Kg \n", +"M=60// MASS OF SLEEVE IN Kg\n", +"DF=.035// SLEEVE DISTANCE FROM AXIS IN m\n", +"E1F1=.25// MAX RADIUS OF ROTATION IN m\n", +"g=9.81\n", +"//=========================================================\n", +"alpha=asind(EF/AE)// ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL IN DEGREES\n", +"beeta=asind(ED/EC)// ANGLE OF INCLINATION OF THE ARM TO THE HORIZONTAL IN DEGREES\n", +"k=tand(beeta)/tand(alpha)\n", +"h=(AE^2-EF^2)^.5// HEIGHT OF GOVERNOR IN m\n", +"EM=(EC^2-MC^2)^.5// FROM FIGURE 7.12 IN m\n", +"HM=EM+EH\n", +"N2=(895*EM*(m+(M/2*(1+k)))/(h*HM*m))^.5// EQUILIBRIUM SPEED AT MAX RADIUS\n", +"HC=(HM^2+MC^2)^.5// FROM FIGURE 7.13 IN m\n", +"H1C1=HC\n", +"gama=atand(MC/HM)\n", +"alpha1=asind(E1F1/A1E1)\n", +"E1D1=E1F1-DF// FROM FIGURE 7.13 IN m\n", +"beeta1=asind(E1D1/E1C1)\n", +"gama1=gama-beeta+beeta1\n", +"r=H1C1*sind(gama1)+DF// RADIUS OF ROTATION IN m\n", +"H1M1=H1C1*cosd(gama1)\n", +"I1C1=E1C1*cosd(beeta1)*(tand(alpha1)+tand(beeta1))// FROM FIGURE IN m\n", +"M1C1=H1C1*sind(gama1)\n", +"w1=(((m*g*(I1C1-M1C1))+(M*g*I1C1)/2)/(m*r*H1M1))^.5// ANGULAR SPEED IN rad/s\n", +"N1=w1*60/(2*PI)// //SPEED IN m/s\n", +"printf('MINIMUM SPEED OF ROTATION = %.3f rpm\n MAXIMUM SPEED OF ROTATION = %.3f rpm',N2,N1)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.1: PERCENTAGE_CHANGE_IN_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 1 PAGE NO 196\n", +"//TITLE:GOVERNORS\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"L=.4// LENGTH OF UPPER ARM IN m\n", +"THETA=30// INCLINATION TO THE VERTICAL IN degrees\n", +"K=.02// RISED LENGTH IN m\n", +"//============================================================================================\n", +"h2=L*cosd(THETA)// GOVERNOR HEIGHT IN m\n", +"N2=(895/h2)^.5// SPEED AT h2 IN rpm\n", +"h1=h2-K// LENGTH WHEN IT IS RAISED BY 2 cm\n", +"N1=(895/h1)^.5// SPEED AT h1 IN rpm\n", +"n=(N1-N2)/N2*100// PERCENTAGE CHANGE IN SPEED\n", +"//==========================================================================================\n", +"printf('PERCENTAGE CHANGE IN SPEED= %.f PERCENTAGE',n)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.2: RANGE_OF_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 2 PAGE NO 197\n", +"//TITLE:GOVERNORS\n", +"//FIGURE 7.5(A),7.5(B)\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"OA=.3// LENGTH OF UPPER ARM IN m\n", +"m=6// MASS OF EACH BALL IN Kg\n", +"M=18// MASS OF SLEEVE IN Kg\n", +"r2=.2// RADIUS OF ROTATION AT BEGINING IN m\n", +"r1=.25// RADIUS OF ROTATION AT MAX SPEED IN m\n", +"//===========================================================================================\n", +"h1=(OA^2-r1^2)^.5// HIEGHT OF GOVERNOR AT MAX SPEED IN m\n", +"N1=(895*(m+M)/(h1*m))^.5// MAX SPEED IN rpm\n", +"h2=(OA^2-r2^2)^.5// HEIGHT OF GONERNOR AT BEGINING IN m\n", +"N2=(895*(m+M)/(h2*m))^.5// MIN SPEED IN rpm\n", +"//===========================================================================================\n", +"printf('MAX SPEED = %.3f rpm\n MIN SPEED = %.3f rpm\n RANGE OF SPEED = %.3f rpm',N1,N2,N1-N2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.3: RANGE_OF_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 3 PAGE NO 197\n", +"//TITLE:GOVERNORS\n", +"//FIGURE 7.6\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"OA=.25// LENGHT OF UPPER ARM IN m\n", +"CD=.03// DISTANCE BETWEEN LEEVE AND LOWER ARM IN m\n", +"m=6// MASS OF BALL IN Kg\n", +"M=48// MASS OF SLEEVE IN Kg\n", +"AE=.17// FROM FIGURE 7.6\n", +"AE1=.12// FROM FIGURE 7.6\n", +"r1=.2// RADIUS OF ROTATION AT MAX SPEED IN m\n", +"r2=.15// RADIUS OF ROTATION AT MIN SPEED IN m\n", +"//============================================================================================\n", +"h1=(OA^2-r1^2)^.5// HIEGHT OF GOVERNOR AT MIN SPEED IN m\n", +"TANalpha=r1/h1\n", +"TANbeeta=AE/(OA^2-AE^2)^.5\n", +"k=TANbeeta/TANalpha\n", +"N1=(895*(m+(M*(1+k)/2))/(h1*m))^.5// MIN SPEED IN rpm\n", +"h2=(OA^2-r2^2)^.5// HIEGHT OF GOVERNOR AT MAX SPEED IN m\n", +"CE=(OA^2-AE1^2)^.5\n", +"TANalpha1=r2/h2\n", +"TANbeeta1=(r2-CD)/CE\n", +"k=TANbeeta1/TANalpha1\n", +"N2=(895*(m+(M*(1+k)/2))/(h2*m))^.5// MIN SPEED IN rpm\n", +"//========================================================================================================\n", +"printf('MAX SPEED = %.3f rpm\n MIN SPEED = %.3f rpm\n RANGE OF SPEED = %.3f rpm',N1,N2,N1-N2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.4: GOVERNOR_POWER.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 4 PAGE NO 199\n", +"//TITLE:GOVERNORS\n", +"//FIGURE 7.7\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"g=9.81// ACCELERATION DUE TO GRAVITY \n", +"OA=.20// LENGHT OF UPPER ARM IN m\n", +"AC=.20// LENGTH OF LOWER ARM IN m\n", +"CD=.025// DISTANCE BETWEEN AXIS AND LOWER ARM IN m\n", +"AB=.1// RADIUS OF ROTATION OF BALLS IN m\n", +"N2=250// SPEED OF THE GOVERNOR IN rpm\n", +"X=.05// SLEEVE LIFT IN m\n", +"m=5// MASS OF BALL IN Kg\n", +"M=20// MASS OF SLEEVE IN Kg\n", +"//===========================================================\n", +"h2=(OA^2-AB^2)^.5// OB DISTANCE IN m IN FIGURE\n", +"h21=(AC^2-(AB-CD)^2)^.5// BD DISTANCE IN m IN FIGURE\n", +"TANbeeta=(AB-CD)/h21// TAN OF ANGLE OF INCLINATION OF THE LINK TO THE VERTICAL\n", +"TANalpha=AB/h2// TAN OF ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL\n", +"k=TANbeeta/TANalpha\n", +"c=X/(2*(h2*(1+k)-X))// PERCENTAGE INCREASE IN SPEED \n", +"n=c*N2// INCREASE IN SPEED IN rpm\n", +"N1=N2+n// SPEED AFTER LIFT OF SLEEVE\n", +"E=c*g*((2*m/(1+k))+M)// GOVERNOR EFFORT IN N\n", +"P=E*X// GOVERNOR POWER IN N-m\n", +"\n", +"printf('SPEED OF THE GOVERNOR WHEN SLEEVE IS LIFT BY 5 cm = %.3f rpm\n GOVERNOR EFFORT = %.3f N\n GOVERNOR POWER = %.3f N-m',N1,E,P)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.5: RANGE_OF_SPEED_OF_GOVERNOR.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 5 PAGE NO 200\n", +"//TITLE:GOVERNORS\n", +"//FIGURE 7.8\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"g=9.81// ACCELERATION DUE TO GRAVITY \n", +"OA=.30// LENGHT OF UPPER ARM IN m\n", +"AC=.30// LENGTH OF LOWER ARM IN m\n", +"m=10// MASS OF BALL IN Kg\n", +"M=50// MASS OF SLEEVE IN Kg\n", +"r=.2// RADIUS OF ROTATION IN m\n", +"CD=.04// DISTANCE BETWEEN AXIS AND LOWER ARM IN m\n", +"F=15// FRICTIONAL LOAD ACTING IN N\n", +"//============================================================\n", +"h=(OA^2-r^2)^.5// HIEGTH OF THE GOVERNOR IN m\n", +"AE=r-CD// AE VALUE IN m\n", +"CE=(AC^2-AE^2)^.5// BD DISTANCE IN m\n", +"TANalpha=r/h// TAN OF ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL\n", +"TANbeeta=AE/CE// TAN OF ANGLE OF INCLINATION OF THE LINK TO THE VERTICAL\n", +"k=TANbeeta/TANalpha\n", +"N=((895/h)*(m+(M*(1+k)/2))/m)^.5// EQULIBRIUM SPEED IN rpm\n", +"N1=((895/h)*((m*g)+(M*g+F)/2)*(1+k)/(m*g))^.5// MAX SPEED IN rpm\n", +"N2=((895/h)*((m*g)+(M*g-F)/2)*(1+k)/(m*g))^.5// MIN SPEED IN rpm\n", +"R=N1-N2// RANGE OF SPEED\n", +"printf('EQUILIBRIUM SPEED OF GOVERNOR = %.3f rpm\n RANGE OF SPEED OF GOVERNOR= %.3f rpm',N,R)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.6: RANGE_OF_SPEED_OF_GOVERNOR.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 6 PAGE NO 202\n", +"//TITLE:GOVERNORS\n", +"//FIGURE 7.9\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"g=9.81// ACCELERATION DUE TO GRAVITY \n", +"OA=.30// LENGHT OF UPPER ARM IN m\n", +"AC=.30// LENGTH OF LOWER ARM IN m\n", +"m=5// MASS OF BALL IN Kg\n", +"M=25// MASS OF SLEEVE IN Kg\n", +"X=.05// LIFT OF THE SLEEVE\n", +"alpha=30// ANGLE OF INCLINATION OF THE ARM TO THE VERTICAL\n", +"//==============================================\n", +"h2=OA*cosd(alpha)// HEIGHT OF THE GOVERNOR AT LOWEST POSITION OF SLEEVE\n", +"h1=h2-X/2// HEIGHT OF THE GOVERNOR AT HEIGHT POSITION OF SLEEVE\n", +"F=((h2/h1)*(m*g+M*g)-(m*g+M*g))/(1+h2/h1)// FRICTION AT SLEEVE IN N\n", +"N1=((m*g+M*g+F)*895/(h1*m*g))^.5// MAX SPEEED OF THE GOVVERNOR IN rpm\n", +"N2=((m*g+M*g-F)*895/(h2*m*g))^.5// MIN SPEEED OF THE GOVVERNOR IN rpm\n", +"R=N1-N2// RANGE OF SPEED IN rpm\n", +"\n", +"printf('THE VALUE OF FRICTIONAL FORCE= %.3f F\n RANGE OF SPEED OF THE GOVERNOR = %.0f rpm',F,R)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.7: EQUILIBRIUM_SPEED_CORRESPONDING_TO_LIFT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 7 PAGE NO 203\n", +"//TITLE:GOVERNORS\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"PI=3.147\n", +"m=3// MASS OF EACH BALL IN Kg\n", +"a=.12// LENGTH OF VERTICAL ARM OF BELL CRANK LEVER IN m\n", +"b=.08// LENGTH OF HORIZONTAL ARM OF BELL CRANK LEVER IN m\n", +"r2=.12// RADIUS OF ROTATION OF THE BALL FOR LOWEST POSITION IN m\n", +"N2=320// SPEED OF GOVERNOR AT THE BEGINING IN rpm\n", +"S=20000// STIFFNESS OF THE SPRING IN N/m\n", +"h=.015// SLEEVE LIFT IN m\n", +"//==================================================\n", +"Fc2=m*(2*PI*N2/60)^2*r2// CENTRIFUGAL FORCE ACTING AT MIN SPEED OF ROTATION IN N\n", +"L=2*a*Fc2/b// INITIAL LOAD ON SPRING IN N\n", +"r1=a/b*h+r2// MAX RADIUS OF ROTATION IN m\n", +"Fc1=(S*(r1-r2)*(b/a)^2/2)+Fc2// CENTRIFUGAL FORCE ACTING AT MAX SPEED OF ROTATION IN N\n", +"N1=(Fc1/(m*r1)*(60/2/PI)^2)^.5\n", +"printf('INITIAL LOAD ON SPRING =%.3f N\n EQUILIBRIUM SPEED CORRESPONDING TO LIFT OF 15 cm =%.0f rpm',L,N1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.8: STIFFNESS_OF_THE_SPRING.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 8 PAGE NO 204\n", +"//TITLE:GOVERNORS\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"PI=3.147\n", +"m=3// MASS OF BALL IN Kg\n", +"r2=.2// INITIAL RADIUS OF ROTATION IN m\n", +"a=.11// LENGTH OF VERTICAL ARM OF BELL CRANK LEVER IN m\n", +"b=.15// LENGTH OF HORIZONTAL ARM OF BELL CRANK LEVER IN m\n", +"h=.004// SLEEVE LIFT IN m\n", +"N2=240// INITIAL SPEED IN rpm\n", +"n=7.5// FLUCTUATION OF SPEED IN %\n", +"//===================================\n", +"w2=2*PI*N2/60// INITIAL ANGULAR SPEED IN rad/s\n", +"w1=(100+n)*w2/100// FINAL ANGULAR SPEED IN rad/s\n", +"F=2*a/b*m*w2^2*r2// INITIAL COMPRESSIVE FORCE IN N\n", +"r1=r2+a/b*h// MAX RDIUS OF ROTATION IN m\n", +"S=2*((m*w1^2*r1)-(m*w2^2*r2))/(r1-r2)*(a/b)^2\n", +"printf('INITIAL COMPRESSIVE FPRCE = %.3f N\n STIFFNESS OF THE SPRING = %.3f N/m',F,S/1000)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.9: ALTERATION_IN_SPEED.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 7 ILLUSRTATION 9 PAGE NO 204\n", +"//TITLE:GOVERNORS\n", +"//FIGURE 7.3(C)\n", +"clc\n", +"clear\n", +"//===========================================================================================\n", +"//INPUT DATA\n", +"g=9.81// ACCELERATION DUE TO GRAVITY \n", +"PI=3.147\n", +"r=.14// DISTANCE BETWEEN THE CENTRE OF PIVOT OF BELL CRANK LEVER AND AXIS OF GOVERNOR SPINDLE IN m\n", +"r2=.11// INITIAL RADIUS OF ROTATION IN m\n", +"a=.12// LENGTH OF VERTICAL ARM OF BELL CRANK LEVER IN m\n", +"b=.10// LENGTH OF HORIZONTAL ARM OF BELL CRANK LEVER IN m\n", +"h=.05// SLEEVE LIFT IN m\n", +"N2=240// INITIAL SPEED IN rpm\n", +"F=30// FRICTIONAL FORCE ACTING IN N\n", +"m=5// MASS OF EACH BALL IN Kg\n", +"//==========================================\n", +"r1=r2+a/b*h// MAX RADIUS OF ROTATION IN m\n", +"N1=41*N2/39// MAX SPEED OF ROTATION IN rpm\n", +"N=(N1+N2)/2// MEAN SPEED IN rpm\n", +"Fc1=m*(2*PI*N1/60)^2*r1// CENTRIFUGAL FORCE ACTING AT MAX SPEED OF ROTATION IN N\n", +"Fc2=m*(2*PI*N2/60)^2*r2// CENTRIFUGAL FORCE ACTING AT MIN SPEED OF ROTATION IN N\n", +"c1=r1-r// FROM FIGURE 7.3(C) IN m\n", +"a1=(a^2-c1^2)^.5// FROM FIGURE 7.3(C) IN m\n", +"b1=(b^2-(h/2)^2)^.5// FROM FIGURE 7.3(C) IN m\n", +"c2=r-r2// FROM FIGURE 7.3(C) IN m\n", +"a2=a1// FROM FIGURE 7.3(C) IN m\n", +"b2=b1// FROM FIGURE 7.3(C) IN m\n", +"S1=2*((Fc1*a1)-(m*g*c1))/b1// SPRING FORCE EXERTED ON THE SLEEVE AT MAXIMUM SPEED IN NEWTONS\n", +"S2=2*((Fc2*a2)-(m*g*c2))/b2// SPRING FORCE EXERTED ON THE SLEEVE AT MAXIMUM SPEED IN NEWTONS\n", +"S=(S1-S2)/h// STIFFNESS OF THE SPRING IN N/m\n", +"Is=S2/S// INITIAL COMPRESSION OF SPRING IN m\n", +"P=S2+(h/2*S)// SPRING FORCE OF MID PORTION IN N\n", +"n1=N*((P+F)/P)^.5// SPEED,WHEN THE SLEEVE BEGINS TO MOVE UPWARDS FROM MID POSITION IN rpm\n", +"n2=N*((P-F)/P)^.5// SPEED,WHEN THE SLEEVE BEGINS TO MOVE DOWNWARDS FROM MID POSITION IN rpm\n", +"A=n1-n2// ALTERATION IN SPEED IN rpm\n", +"printf('INTIAL COMPRESSION OF SPRING= %.3f cm\n ALTERATION IN SPEED = %.3f rpm',Is*100,A)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Theory_Of_Machines_by_B_K_Sarkar/8-balancing_of_rotating_masses_.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/8-balancing_of_rotating_masses_.ipynb new file mode 100644 index 0000000..260e6d4 --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/8-balancing_of_rotating_masses_.ipynb @@ -0,0 +1,292 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8: balancing of rotating masses " + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1: magnitude_of_balancing_mass.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 8 ILLUSRTATION 1 PAGE NO 221\n", +"//TITLE:BALANCING OF ROTATING MASSES\n", +"pi=3.141\n", +"clc\n", +"clear\n", +"mA=12// mass of A in kg\n", +"mB=10// mass of B in kg\n", +"mC=18// mass of C in kg\n", +"mD=15// mass of D in kg\n", +"rA=40// radius of A in mm\n", +"rB=50// radius of B in mm\n", +"rC=60// radius of C in mm\n", +"rD=30// radius of D in mm\n", +"theta1=0// angle between A-A in degrees\n", +"theta2=60// angle between A-B in degrees\n", +"theta3=130// angle between A-C in degrees\n", +"theta4=270// angle between A-D in degrees\n", +"R=100// radius at which mass to be determined in mm\n", +"//====================================================\n", +"Fh=(mA*rA*cosd(theta1)+mB*rB*cosd(theta2)+mC*rC*cosd(theta3)+mD*rD*cosd(theta4))/10// vertical component value in kg cm\n", +"Fv=(mA*rA*sind(theta1)+mB*rB*sind(theta2)+mC*rC*sind(theta3)+mD*rD*sind(theta4))/10// horizontal component value in kg cm\n", +"mb=(Fh^2+Fv^2)^.5/R*10// unbalanced mass in kg\n", +"theta=atand(Fv/Fh)// position in degrees \n", +"THETA=180+theta// angle with mA\n", +"printf('magnitude of unbalaced mass=%.3f kg\n angle with mA= %.3f degrees',mb,THETA)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2: masses_of_D_and_E.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 8 ILLUSRTATION 2 PAGE NO 222\n", +"//TITLE:BALANCING OF ROTATING MASSES\n", +"pi=3.141\n", +"clc\n", +"clear\n", +"mA=5// mass of A in kg\n", +"mB=10// mass of B in kg\n", +"mC=8// mass of C in kg\n", +"rA=10// radius of A in cm\n", +"rB=15// radius of B in cm\n", +"rC=10// radius of C in cm\n", +"rD=10// radius of D in cm\n", +"rE=15// radius of E in cm\n", +"//============================\n", +"mD=182/rD// mass of D in kg by mearument\n", +"mE=80/rE// mass of E in kg by mearument\n", +"printf('mass of D= %.3f kg\nmass of E= %.3f kg',mD,mE)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.3: balancing_mass_and_angular_position.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 8 ILLUSRTATION 3 PAGE NO 223\n", +"//TITLE:BALANCING OF ROTATING MASSES\n", +"pi=3.141\n", +"clc\n", +"clear\n", +"mA=200// mass of A in kg\n", +"mB=300// mass of B in kg\n", +"mC=400// mass of C in kg\n", +"mD=200// mass of D in kg\n", +"rA=80// radius of A in mm\n", +"rB=70// radius of B in mm\n", +"rC=60// radius of C in mm\n", +"rD=80// radius of D in mm\n", +"rX=100// radius of X in mm\n", +"rY=100// radius of Y in mm\n", +"//=====================\n", +"mY=7.3/.04// mass of Y in kg by mearurement\n", +"mX=35/.1// mass of X in kg by mearurement\n", +"thetaX=146// in degrees by mesurement\n", +"printf('mass of X=%.3f kg\n mass of Y=%.3f kg\n angle with mA=%.0f degrees',mX,mY,thetaX)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4: balancing_mass_and_angular_position.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 8 ILLUSRTATION 4 PAGE NO 225\n", +"//TITLE:BALANCING OF ROTATING MASSES\n", +"pi=3.141\n", +"clc\n", +"clear\n", +"mB=30// mass of B in kg\n", +"mC=50// mass of C in kg\n", +"mD=40// mass of D in kg\n", +"rA=18// radius of A in cm\n", +"rB=24// radius of B in cm\n", +"rC=12// radius of C in cm\n", +"rD=15// radius of D in cm\n", +"//=============================\n", +"mA=3.6/.18// mass of A by measurement in kg\n", +"theta=124// angle with mass B in degrees by measurement in degrees\n", +"y=3.6/(.18*20)// position of A from B\n", +"printf('mass of A=%i kg\n angle with mass B=%i degrees\n position of A from B=%i m towards right of plane B',mA,theta,y)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.5: balancing_mass_and_angular_position.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 8 ILLUSRTATION 5 PAGE NO 226\n", +"//TITLE:BALANCING OF ROTATING MASSES\n", +"pi=3.141\n", +"clc\n", +"clear\n", +"mB=10// mass of B in kg\n", +"mC=5// mass of C in kg\n", +"mD=4// mass of D in kg\n", +"rA=10// radius of A in cm\n", +"rB=12.5// radius of B in cm\n", +"rC=20// radius of C in cm\n", +"rD=15// radius of D in cm\n", +"//=====================================\n", +"mA=7// mass of A in kg by mesurement\n", +"BC=118// angle between B and C in degrees by mesurement\n", +"BA=203.5// angle between B and A in degrees by mesurement\n", +"BD=260// angle between B and D in degrees by mesurement\n", +"printf('Mass of A=%i kg\n angle between B and C=%i degrees\nangle between B and A= %.1f degrees\n angle between B and D= %i degrees',mA,BC,BA,BD)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.6: mass_of_D.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 8 ILLUSRTATION 6 PAGE NO 228\n", +"//TITLE:BALANCING OF ROTATING MASSES\n", +"pi=3.141\n", +"clc\n", +"clear\n", +"mB=36// mass of B in kg\n", +"mC=25// mass of C in kg\n", +"rA=20// radius of A in cm\n", +"rB=15// radius of B in cm\n", +"rC=15// radius of C in cm\n", +"rD=20// radius of D in cm\n", +"//==================================\n", +"mA=3.9/.2// mass of A in kg by measurement\n", +"mD=16.5// mass of D in kg by measurement\n", +"theta=252// angular position of D from B by measurement in degrees\n", +"printf('Mass of A= %.1f kg\n Mass od D= %.1f kg\n Angular position of D from B= %i degrees',mA,mD,theta)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.7: load_on_each_bearing.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 8 ILLUSRTATION 7 PAGE NO 229\n", +"//TITLE:BALANCING OF ROTATING MASSES\n", +"\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"mA=48// mass of A in kg\n", +"mB=56// mass of B in kg\n", +"mC=20// mass of C in kg\n", +"rA=1.5// radius of A in cm\n", +"rB=1.5// radius of B in cm\n", +"rC=1.25// radius of C in cm\n", +"N=300// speed in rpm\n", +"d=1.8// distance between bearing in cm\n", +"//================================\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"BA=164// angle between pulleys B&A in degrees by measurement\n", +"BC=129// angle between pulleys B&C in degrees by measurement\n", +"AC=67// angle between pulleys A&C in degrees by measurement\n", +"C=.88*w^2// out of balance couple in N\n", +"L=C/d// load on each bearing in N\n", +"printf('angle between pulleys B&A=%i degrees\n angle between pulleys B&C= %i degrees\n angle between pulleys A&C= %i degrees\n out of balance couple= %.3f N\n load on each bearing= %.3f N',BA,BC,AC,C,L)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Theory_Of_Machines_by_B_K_Sarkar/9-cams_and_followers.ipynb b/Theory_Of_Machines_by_B_K_Sarkar/9-cams_and_followers.ipynb new file mode 100644 index 0000000..8630d7f --- /dev/null +++ b/Theory_Of_Machines_by_B_K_Sarkar/9-cams_and_followers.ipynb @@ -0,0 +1,138 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9: cams and followers" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2: maximum_velocity_and_acceleration.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 9 ILLUSRTATION 2 PAGE NO 247\n", +"//TITLE:CAMS AND FOLLOWERS\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"s=4// follower movement in cm\n", +"theta=60// cam rotation in degrees\n", +"THETA=60*pi/180// cam rotation in rad\n", +"thetaD=45// after outstroke in degrees\n", +"thetaR=90//....angle with which it reaches its original position in degrees\n", +"THETAR=90*pi/180// angle with which it reaches its original position in rad\n", +"THETAd=360-theta-thetaD-thetaR// angle after return stroke in degrees\n", +"N=300// speed in rpm\n", +"w=2*pi*N/60// speed in rad/s\n", +"Vo=pi*w*s/2/THETA// Maximum velocity of follower during outstroke in cm/s\n", +"Vr=pi*w*s/2/THETAR// Maximum velocity of follower during return stroke in cm/s\n", +"Fo=pi^2*w^2*s/2/THETA^2/100//Maximum acceleration of follower during outstroke in m/s^2\n", +"Fr=pi^2*w^2*s/2/THETAR^2/100//Maximum acceleration of follower during return stroke in m/s^2\n", +"printf('Maximum acceleration of follower during outstroke =%.3f m/s^2\nMaximum acceleration of follower during return stroke= %.3f m/s^2',Fo,Fr)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.3: maximum_velocity_and_acceleration.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 9 ILLUSRTATION 3 PAGE NO 249\n", +"//TITLE:CAMS AND FOLLOWERS\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"s=5// follower movement in cm\n", +"theta=120// cam rotation in degrees\n", +"THETA=theta*pi/180// cam rotation in rad\n", +"thetaD=30// after outstroke in degrees\n", +"thetaR=60//....angle with which it reaches its original position in degrees\n", +"THETAR=60*pi/180// angle with which it reaches its original position in rad\n", +"THETAd=360-theta-thetaD-thetaR// angle after return stroke in degrees\n", +"N=100// speed in rpm\n", +"w=2*pi*N/60// speed in rad/s\n", +"Vo=pi*w*s/2/THETA// Maximum velocity of follower during outstroke in cm/s\n", +"Vr=pi*w*s/2/THETAR// Maximum velocity of follower during return stroke in cm/s\n", +"Fo=pi^2*w^2*s/2/THETA^2/100//Maximum acceleration of follower during outstroke in m/s^2\n", +"Fr=pi^2*w^2*s/2/THETAR^2/100//Maximum acceleration of follower during return stroke in m/s^2\n", +"printf('Maximum acceleration of follower during outstroke =%.3f m/s^2\nMaximum acceleration of follower during return stroke= %.3f m/s^2',Fo,Fr)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.5: maximum_velocity_and_acceleration.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"//CHAPTER 9 ILLUSRTATION 5 PAGE NO 252\n", +"//TITLE:CAMS AND FOLLOWERS\n", +"clc\n", +"clear\n", +"pi=3.141\n", +"N=1000// speed of cam in rpm\n", +"w=2*pi*N/60// angular speed in rad/s\n", +"s=2.5// stroke of the follower in cm\n", +"THETA=120*pi/180// ANGULAR DISPLACEMENT OF CAM DURING OUTSTROKE IN RAD\n", +"THETAR=90*pi/180//ANGULAR DISPLACEMENT OF CAM DURING DWELL IN RAD\n", +"Vo=2*w*s/THETA// Maximum velocity of follower during outstroke in cm/s\n", +"Vr=2*w*s/THETAR//Maximum velocity of follower during return stroke in cm/s\n", +"Fo=4*w^2*s/THETA^2//Maximum acceleration of follower during outstroke in m/s^2\n", +"Fr=4*w^2*s/THETAR^2//Maximum acceleration of follower during return stroke in m/s^2\n", +"printf('Maximum acceleration of follower during outstroke =%.3f m/s^2\nMaximum acceleration of follower during return stroke= %.3f m/s^2',Fo,Fr)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |