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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 22: FRICTION CLUTCHES"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 22.10: FC2210.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// 22-10\n",
+"clc;\n",
+"clear;\n",
+"w2=2*%pi*1400/60;\n",
+"w1=0.8*w2;\n",
+"P=40*10^3;\n",
+"T=P/w2;\n",
+"n=4;\n",
+"T1=T/4;\n",
+"R=0.16;//Inner radius of drum\n",
+"r=0.13;//radial distance of each shoe from axis of rotation\n",
+"u=0.22;//coefficient of friction\n",
+"x=u*r*R*((w2^2)-(w1^2))\n",
+"m =T1/x;\n",
+"l=R*%pi/3;\n",
+"N=T1/(R*u);\n",
+"p=1*10^5;\n",
+"b=N/(p*l)*10^3;\n",
+"\n",
+" // printing data in scilab o/p window\n",
+"printf('\nThe full speed is %0.1f rad/sec',w2);\n",
+"printf('\nThe engagement speed is %0.2f rad/sec',w1);\n",
+"printf('\nThe number of shoes is %0.0f ',n);\n",
+"printf('\nThe Torque is %0.1f Nm',T);\n",
+"printf('\nThe Torque per shoe is %0.1f Nm',T1);\n",
+"printf('\nThe mass per shoe is %0.2f kg',m);\n",
+"printf('\nThe length of friction lining is %0.5f m',l);\n",
+"printf('\nThe width is %0.1f mm',b);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 22.1: FC221.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// 22-1\n",
+"clc;\n",
+"clear;\n",
+"u=0.28 //(coefficient of friction)\n",
+"N=300 //(Engine rpm)\n",
+"I=7.2 \n",
+"Pmax= 0.1; \n",
+"R1=70;\n",
+"R2=110;\n",
+"n=2; //(Both sides of the plate are effective)\n",
+"//Using Uniform Wear Theory\n",
+"//Axial Force W\n",
+"W=n*%pi*Pmax*R1*(R2-R1);\n",
+"//Frictional Torque Tf\n",
+"Tf=u*W*(R1+R2)/2*(10^-3);\n",
+"w=2*%pi*N/60;\n",
+"//Power P\n",
+"P=Tf*w;\n",
+"//Torque = Mass moment of inertia*angular acceleration\n",
+"a=Tf/I;\n",
+"t=w/a; \n",
+"//Angle turned by driving shaft theta1 through which slipping takes place\n",
+"theta1=w*t;\n",
+"//angle turned by driven shaft theta2\n",
+"theta2=a*(t^2)/2;\n",
+"E=Tf*(theta1-theta2);\n",
+"\n",
+" // printing data in scilab o/p window\n",
+"printf('\nThe force is %0.1f N',W);\n",
+"printf('\nThe Torque is %0.2f Nm',Tf);\n",
+"printf('\nThe Power is %0.0f W',P);\n",
+"printf('\nThe angular acceleration is %0.2f rad/sec^2',a);\n",
+"printf('\nThe time taken is %0.1f sec',t);\n",
+"printf('\nThe energy is %0.2f Nm',E);\n",
+"\n",
+"//The difference in the answer of energy 'E' is due to rounding-off of values.\n",
+"\n",
+"\n",
+"\n",
+"\n",
+"\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 22.2: FC222.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// 22-2\n",
+"clc;\n",
+"clear;\n",
+"//Power P\n",
+"P=80*10^3; //(Watt)\n",
+"N=3000; //(Engine rpm)\n",
+"w=2*%pi*3*10^3/60\n",
+"Tf=8*10^4/w;\n",
+"Rm=100;//(mm)\n",
+"p=0.2 //N/mm^2\n",
+"u=0.22 \n",
+"// let width b= (R1-R2). \n",
+"//Axial force W=2*pi*Rm*b*p\n",
+"//Torque T=u*W*Rm\n",
+"b=Tf/(u*2*%pi*(Rm^2)*p);\n",
+"b=50; \n",
+"R2=Rm+b;\n",
+"R1=Rm-b;\n",
+"Di=2*R1; //inner diameter\n",
+"W=2*%pi*Rm*b*p;\n",
+"n=8; //n is number of springs\n",
+"//Axial force per spring W1\n",
+"W1=W/n;\n",
+"W1=W1+15;\n",
+"//axial deflection del\n",
+"del=10; \n",
+"//stiffness k\n",
+"k=W1/del;\n",
+"// Spring index C\n",
+"C=6;\n",
+"//number of coils n1\n",
+"n1=6; //Assumption\n",
+"d=k*n*n1*(C^3)/(80*10^3);\n",
+"d=11; // Rounding off to nearest standard value\n",
+"D=C*d;\n",
+"clearance=2;\n",
+"FL=((n1+2)*d)+(2*del)+clearance; // two end coils, therefore (2*del)\n",
+"\n",
+" // printing data in scilab o/p window\n",
+"\n",
+"printf('\nThe Torque is %0.2f Nm',Tf);\n",
+"printf('\nThe width is %0.0f mm',b);\n",
+"printf('\nThe force is %0.0f N',W);\n",
+"printf('\nThe Axial force per spring is %0.0f N',W1);\n",
+"printf('\nThe Spring stiffness is %0.0f N/mm',k);\n",
+"printf('\nThe Spring wire diameter is %0.0f mm',d);\n",
+"printf('\nThe Mean coil diameter is %0.0f mm',D);\n",
+"printf('\nThe Free length is %0.0f mm',FL);\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 22.3: FC223.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// 22-3\n",
+"clc;\n",
+"clear;\n",
+"//Power P\n",
+"P=40*10^3 //Watt\n",
+"n1=100; //rpm\n",
+"n2=400; //rpm\n",
+"//Speed factor Ks\n",
+"Ks=0.9+0.001*n2;\n",
+"//Clutch power Pc\n",
+"Pc=P*n2/(n1*Ks)*10^-3;\n",
+"\n",
+" // printing data in scilab o/p window\n",
+"printf('\nThe Speed factor is %0.1f ',Ks);\n",
+"printf('\nThe clutch poweris %0.0f KW',Pc);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 22.4: FC224.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//22-4\n",
+"clc;\n",
+"clear;\n",
+"// plot Torque vs Ro/Ri\n",
+"//x=Ro/Ri\n",
+"//According to Uniform Wear theory\n",
+"x=[0 0.2 0.4 0.577 0.6 0.8 1.0];\n",
+"n=length(x);\n",
+"for i=1:n\n",
+" Tf(i)=(x(i)-(x(i)^3));\n",
+"end\n",
+"plot (x,Tf);\n",
+"xtitle('','Ro/Ri');\n",
+"ylabel('Tf');\n",
+"xgrid(2);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 22.5: FC225.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// 22-5\n",
+"clc;\n",
+"clear;\n",
+"n1=4;\n",
+"n2=3;\n",
+"n=(n1+n2-1);\n",
+"R2=80;\n",
+"R1=50;\n",
+"//According to Uniform Pressure Theory\n",
+"//W=p*pi*((R2^2)-(R1^2)) T=n*2*u*W*((R2^3)-(R1^3))/(((R2^2)-(R1^2))*3)\n",
+"P=15*10^3;\n",
+"N=1400;\n",
+"u=0.25;\n",
+"w=2*%pi*N/60;\n",
+"T=P/w;\n",
+"W=T*3*((R2^2)-(R1^2))/(n*2*u*((R2^3)-(R1^3)))*10^3;\n",
+"p=W/(%pi*((R2^2)-(R1^2)));\n",
+"\n",
+" // printing data in scilab o/p window\n",
+"printf('\nThe angular speed is %0.2f rad/sec',w);\n",
+"printf('\nThe Torque is %0.3f Nm',T);\n",
+"printf('\nThe uniform pressure is %0.3f N/mm^2',p);\n",
+"printf('\nThe Force is %0.1f N',W);\n",
+"\n",
+"\n",
+"\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 22.6: FC226.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//FRICTION CLUTCHES\n",
+"// PAGE 584, 22-6\n",
+"clc;\n",
+"P=5*10^3;\n",
+"N=1000;\n",
+"w=2*%pi*N/60;\n",
+"Rm=50;\n",
+"pm=0.3;\n",
+"Tf=P/w;\n",
+"u=0.1;\n",
+"R2=50*2/(0.6+1);\n",
+"R1=0.6*R2;\n",
+"//According to uniform Wear theory\n",
+"W=pm*Rm*(R2-R1)*2*%pi;\n",
+"n=Tf*(10^3)/(u*W*Rm);\n",
+"pmax=pm*Rm/R1;\n",
+"\n",
+" // printing data in scilab o/p window\n",
+"printf('\nThe angular speed is %0.2f rad/sec',w);\n",
+"printf('\nThe Torque is %0.3f Nm',Tf);\n",
+"printf('\nThe Inner radius is %0.1f mm',R1);\n",
+"printf('\nThe Outer radius is %0.1f mm',R2);\n",
+"printf('\nThe number of contacting surfaces is %0.0f ',n);\n",
+"printf('\nThe max. pressure is %0.1f N/mm^2',pmax);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 22.7: FC227.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// 22-7\n",
+"clc;\n",
+"clear;\n",
+"P=12*10^3;\n",
+"N=750 //Speed=N\n",
+"w=2*%pi*N/60;\n",
+"Tf=P/w;\n",
+"p1=0.12;\n",
+"a=12.5;//Semi-cone angle\n",
+"u=0.3;\n",
+"k=u*0.18246*1.121/0.21644;\n",
+"R1=(Tf*(10^3)/k)^(1/3);\n",
+"R2=R1*1.242;\n",
+"Rm=1.121*R1;\n",
+"W=2*%pi*p1*R1*(R2-R1);\n",
+"\n",
+" // printing data in scilab o/p window\n",
+"printf('\nThe angular speed is %0.2f rad/sec',w);\n",
+"printf('\nThe Torque is %0.1f Nm',Tf);\n",
+"printf('\nThe Inner radius is %0.1f mm',R1);\n",
+"printf('\nThe Outer radius is %0.1f mm',R2);\n",
+"printf('\nThe mean radius is %0.2f mm',Rm);\n",
+"printf('\nThe axial force is %0.0f N',W);\n",
+"\n",
+"//The difference in the answer is due to rounding-off of values."
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 22.8: FC228.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//22-8\n",
+"clc;\n",
+"clear;\n",
+"//semi-cone angle is given as 15 degree\n",
+"k=sin(15*%pi/180);\n",
+"u=0.3;\n",
+"W=300;\n",
+"Rm=90/2;\n",
+"Tf=u*W*Rm/k;\n",
+"Tf=Tf*(10^-3);\n",
+"I=0.4;\n",
+"a=Tf/I;\n",
+"N=1440;\n",
+"w=2*%pi*N/60;\n",
+"t=w/a;\n",
+"//During Slipping\n",
+"theta1=w*t;\n",
+"theta2=theta1/2;\n",
+"U=Tf*(theta1-theta2);\n",
+"\n",
+" // printing data in scilab o/p window\n",
+"printf('\nThe Torque is %0.3f Nm',Tf);\n",
+"printf('\nThe angular acceleration is %0.3f rad/sec^2',a);\n",
+"printf('\nThe angular speed is %0.1f rad/sec',w);\n",
+"printf('\nThe time taken is %0.2f sec',t);\n",
+"printf('\nThe Energy lost in friction is %0.0f Nm',U);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 22.9: FC229.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// 22-9\n",
+"clc;\n",
+"clear;\n",
+"P=15*10^3;\n",
+"Ka=1.25;\n",
+"N=1500;\n",
+"w=2*%pi*N/60;\n",
+"Tf=P/w;\n",
+"d=(Tf*16/(50*%pi))^(1/3);\n",
+"d=25;\n",
+"Rm=5*d;\n",
+"Pav=0.12;\n",
+"u=0.22;\n",
+"b=Tf/(%pi*u*Pav*(Rm^2));\n",
+"b=40;\n",
+"R1=Rm-(b*sin(15*%pi/180)/2);\n",
+"R2=Rm+(b*sin(15*%pi/180)/2);\n",
+"\n",
+" // printing data in scilab o/p window\n",
+"printf('\nThe Torque is %0.2f Nm',Tf);\n",
+"printf('\nThe shaft diameter is %0.0f mm',d);\n",
+"printf('\nThe width is %0.0f mm',b);\n",
+"printf('\nThe Inner radius is %0.1f mm',R1);\n",
+"printf('\nThe Outer radius is %0.1f mm',R2);"
+ ]
+ }
+],
+"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
+}
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