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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:75a895f6b6e2b52911a88eac6dae9689200eafdf77449669257c302ec104ee3c"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Ch:23 Brakes"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 23-1 - Page 618"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "from math import asin, pi\n",
+ "W=20e3#\n",
+ "m=W/9.81#\n",
+ "#diameter of brake drum\n",
+ "Db=0.6#\n",
+ "p=1#\n",
+ "Vi=1#\n",
+ "Vf=0#\n",
+ "D=1#\n",
+ "R=0.5#\n",
+ "wi=Vi/R#\n",
+ "wf=0#\n",
+ "w=1#\n",
+ "Vav=0.5#\n",
+ "S=2#\n",
+ "t=S/Vav#\n",
+ "#angle turned by by hoist drum=theta\n",
+ "theta=0.5*wi*t#\n",
+ "K_E=0.5*m*Vi**2#\n",
+ "P_E=2*W#\n",
+ "T_E=K_E+P_E#\n",
+ "T=T_E/theta#\n",
+ "P=wi*T*10**-3#\n",
+ "Rb=Db/2#\n",
+ "Ft=0.5*T*p/Rb#\n",
+ "u=0.35#\n",
+ "N=Ft/u#\n",
+ "#contact area of brake lining=A\n",
+ "A=N/p#\n",
+ "b=0.3*Db#\n",
+ "L=A*10**-6/(b)#\n",
+ "#angle subtended at brake drum centre=theta2\n",
+ "theta2=2*(asin(L/Db))#\n",
+ "theta2=theta2*180/pi# # converting radian to degree\n",
+ "print \"T is %0.1f Nm \"%(T)#\n",
+ "print \"\\nP is %0.4f kW \"%(P)#\n",
+ "print \"\\nb is %0.2f m \"%(b)#\n",
+ "print \"\\nL is %0.3f m \"%(L)#\n",
+ "print \"\\ntheta2 is %0.0f deg \"%(theta2)#\n",
+ " "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "T is 10254.8 Nm \n",
+ "\n",
+ "P is 20.5097 kW \n",
+ "\n",
+ "b is 0.18 m \n",
+ "\n",
+ "L is 0.271 m \n",
+ "\n",
+ "theta2 is 54 deg \n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 23-2 - Page 618"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import exp\n",
+ "b=80#\n",
+ "t=2#\n",
+ "theta=225*pi/180#\n",
+ "u=0.22#\n",
+ "#F1/F2=e**(u*theta)\n",
+ "#let F1/F2=x#\n",
+ "x=exp(u*theta)#\n",
+ "#maximum tensile stress in steel tape is siga\n",
+ "siga=60#\n",
+ "A=b*t#\n",
+ "F1=siga*A#\n",
+ "F2=F1/x#\n",
+ "r=0.2#\n",
+ "T=(F1-F2)*r#\n",
+ "OA=30#\n",
+ "OB=100#\n",
+ "OC=350#\n",
+ "P=((F2*OB)+(F1*OA))/OC#\n",
+ "OA=F2*OB/F1#\n",
+ "print \"F1 is %0.0f N \"%(F1)#\n",
+ "print \"\\nF2 is %0.1f N \"%(F2)#\n",
+ "print \"\\nT is %0.2f Nm \"%(T)#\n",
+ "print \"\\nOA is %0.2f mm \"%(OA)#"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "F1 is 9600 N \n",
+ "\n",
+ "F2 is 4046.4 N \n",
+ "\n",
+ "T is 1110.72 Nm \n",
+ "\n",
+ "OA is 42.15 mm \n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 23-3 - Page 619"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import sin\n",
+ "theta=pi/3#\n",
+ "r=160#\n",
+ "u=0.3#\n",
+ "pmax=0.9#\n",
+ "b=40#\n",
+ "R=(4*r*sin(theta))/((2*theta)+sin(2*theta))#\n",
+ "#frictional torque is T\n",
+ "T=2*u*pmax*b*(r**2)*sin(theta)#\n",
+ "T=2*T*10**-3#\n",
+ "Rx=0.5*pmax*b*r*((2*theta)+(sin(2*theta)))*10**-3#\n",
+ "Ry=u*Rx#\n",
+ "print \"T is %0.2f Nmm \"%(T)#\n",
+ "print \"\\nR is %0.3f mm \"%(R)#\n",
+ "print \"\\nRx is %0.3f kN \"%(Rx)#\n",
+ "print \"\\nRy is %0.2f kN \"%(Ry)#"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "T is 957.75 Nmm \n",
+ "\n",
+ "R is 187.222 mm \n",
+ "\n",
+ "Rx is 8.526 kN \n",
+ "\n",
+ "Ry is 2.56 kN \n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 23-4 - Page 620"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import sin, cos, pi, sqrt\n",
+ "d=320#\n",
+ "r=d/2#\n",
+ "b=50#\n",
+ "u=0.3#\n",
+ "pmax=1#\n",
+ "c=115*2#\n",
+ "# From to fig. 23-9, distance OA=R is calculated.\n",
+ "R=sqrt(115**2+66.4**2)#\n",
+ "C=115*2#\n",
+ "theta1=0#\n",
+ "theta2=120*pi/180#\n",
+ "theta0=120*pi/180#\n",
+ "thetamax=pi/2#\n",
+ "Tr=u*pmax*b*r**2*(cos(theta1)-cos(theta2))/sin(thetamax)*10**-3#\n",
+ "#the notation 'r' is used for moments of right hand shoe, similarly 'l' for the left shoe.\n",
+ "Mfr=u*pmax*b*r*(4*r*(cos(theta1)-cos(theta2))+(R*(cos(2*theta1)-cos(2*theta2))))/(4*sin(thetamax))*10**-3#\n",
+ "Mpr=pmax*b*r*R*((2*theta0)-(sin(2*theta2)-(sin(theta1))))/(4*sin(thetamax))*10**-3#\n",
+ "F=(Mpr-Mfr)/c*10**3#\n",
+ "#Mpl+Mfl=F*c#\n",
+ "x=F*c*10**-3#\n",
+ "y=(Mpr/pmax)+(Mfr/pmax)#\n",
+ "pmax2=x/y#\n",
+ "Tl=pmax2*Tr#\n",
+ "Mpl=pmax2*Mpr#\n",
+ "Mfl=pmax2*Mfr#\n",
+ "T=Tl+Tr#\n",
+ "print \"Tr is %0.0f Nm \"%(Tr)#\n",
+ "print \"\\nMf is %0.2f Nm \"%(Mfr)#\n",
+ "print \"\\nMp is %0.2f Nm \"%(Mpr)#\n",
+ "print \"\\nTl is %0.1f Nm \"%(Tl)# \n",
+ "print \"\\nMfl is %0.2f Nm \"%(Mfl)#\n",
+ "print \"\\nMpl is %0.2f Nm \"%(Mpl)#\n",
+ "print \"\\nF is %0.1f N \"%(F)#\n",
+ "print \"\\nT is %0.1f Nm \"%(T)#\n",
+ " \n",
+ " #The difference in the answers are due to rounding-off of values.\n",
+ " "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tr is 576 Nm \n",
+ "\n",
+ "Mf is 695.51 Nm \n",
+ "\n",
+ "Mp is 1342.49 Nm \n",
+ "\n",
+ "Tl is 182.9 Nm \n",
+ "\n",
+ "Mfl is 220.79 Nm \n",
+ "\n",
+ "Mpl is 426.18 Nm \n",
+ "\n",
+ "F is 2812.9 N \n",
+ "\n",
+ "T is 758.9 Nm \n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 23-5 - Page 621"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "m=1100#\n",
+ "V=65*5/18#\n",
+ "t=4#\n",
+ "r=0.22#\n",
+ "mb=12#\n",
+ "C=460#\n",
+ "S=0.5*V*t#\n",
+ "#Total kinetic energy TE=K.E(vehicle)+K.E(rotating parts).\n",
+ "TE=((0.5*m*(V**2))+(0.1*0.5*m*(V**2)))#\n",
+ "E=TE/4#\n",
+ "w=V/r#\n",
+ "theta=S/r#\n",
+ "T=E/theta#\n",
+ "delT=E/(mb*C)#\n",
+ "print \"S is %0.2f m \"%(S)#\n",
+ "print \"\\nE is %0.2f Nm \"%(E)#\n",
+ "print \"\\nT is %0.2f Nm \"%(T)#\n",
+ "print \"\\ndelT is %0.2f \"%(delT)#\n",
+ " \n",
+ "#The difference in the answers are due to rounding-off of values."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "S is 36.11 m \n",
+ "\n",
+ "E is 49307.97 Nm \n",
+ "\n",
+ "T is 300.40 Nm \n",
+ "\n",
+ "delT is 8.93 \n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 23-6 - Page 621"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "T=35000#\n",
+ "u=0.4#\n",
+ "p=0.7#\n",
+ "r=200#\n",
+ "N=T/(u*r)\n",
+ "b=sqrt(N/p)#\n",
+ "l=b#\n",
+ "#2theta = theta2\n",
+ "theta2=2*asin(l/(2*r))#\n",
+ "F=u*N#\n",
+ "P=((250*N)-(u*N*80))/550#\n",
+ "Ry=N-P#\n",
+ "Rx=u*N#\n",
+ "R=sqrt(Rx**2+Ry**2)#\n",
+ "w=2*pi*100/60#\n",
+ "# Rate of heat generated is Q\n",
+ "Q=u*N*w*r/1000#\n",
+ "print \"N is %0.1f N \"%(N)#\n",
+ "print \"\\nb is %0.0f mm \"%(b)#\n",
+ "print \"\\nP is %0.1f N \"%(P)#\n",
+ "print \"\\nR is %0.2f N \"%(R)#\n",
+ "print \"\\nQ is %0.2f J/s \"%(Q)#\n",
+ "\n",
+ "#The answer to Rate of heat generated 'Q' is calculated incorrectly in the book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "N is 437.5 N \n",
+ "\n",
+ "b is 25 mm \n",
+ "\n",
+ "P is 173.4 N \n",
+ "\n",
+ "R is 316.81 N \n",
+ "\n",
+ "Q is 366.52 J/s \n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 23-7 - Page 622"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "Vi=20*5/18#\n",
+ "Vf=0#\n",
+ "m=80#\n",
+ "pmax=1#\n",
+ "u=0.1#\n",
+ "S=50#\n",
+ "KE=0.5*m*Vi**2#\n",
+ "N=KE/(u*S*2)#\n",
+ "t=sqrt(N/(pmax*3))#\n",
+ "b=3*t#\n",
+ "print \"KE is %0.1f Nm \"%(KE)#\n",
+ "print \"\\nN is %0.2f N \"%(N)#\n",
+ "print \"\\nt is %0.1f mm \"%(t)#\n",
+ "print \"\\nb is %0.1f mm \"%(b)#\n",
+ "\n",
+ "#The difference in the answers are due to rounding-off of values."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "KE is 1234.6 Nm \n",
+ "\n",
+ "N is 123.46 N \n",
+ "\n",
+ "t is 6.4 mm \n",
+ "\n",
+ "b is 19.2 mm \n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-19 22:40:51 +0000