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+{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 10: Toothed Gearing"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 1, Page 320"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "Teeth=48\n",
+ "pitch=.75 #in\n",
+ "\n",
+ "#Calculations\n",
+ "D=Teeth*pitch/math.pi\n",
+ "\n",
+ "#Result\n",
+ "print \"The pitch diameter is %.3f in\"%D"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The pitch diameter is 11.459 in\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 2, Page 320"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=48#teeth\n",
+ "pd=4#diametral pitch\n",
+ "\n",
+ "#Calculations\n",
+ "D=T/pd#pitch diameter\n",
+ "p=math.pi/pd#the circular pitch\n",
+ "\n",
+ "#Results\n",
+ "print \"The pitch diameter = %.f in\\nThe circular pitch = %.4f in\"%(D,p)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The pitch diameter = 12 in\n",
+ "The circular pitch = 0.7854 in\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3, Page 321"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "T=48\n",
+ "m=6#mm ; module\n",
+ "\n",
+ "#Calculations\n",
+ "D=m*T\n",
+ "p=math.pi*m\n",
+ "dia=D/10#cm\n",
+ "P=p*0.0393700787#inches\n",
+ "\n",
+ "#Results\n",
+ "print \"Pitch diameter = %.1f cm\\nCircular pitch = %.4f in\"%(dia,P)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Pitch diameter = 28.0 cm\n",
+ "Circular pitch = 0.7421 in\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4, Page 334"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "phi=20*math.pi/180\n",
+ "\n",
+ "#Calculations\n",
+ "#Solution a)\n",
+ "ar=1\n",
+ "t1=2*ar/math.sin(phi)**2#from equation 10.7\n",
+ "T1=math.ceil(t1)\n",
+ "#Solution b)\n",
+ "aw=1.\n",
+ "t2=2*aw/((1+3*math.sin(phi)**2)**(1./2)-1)#from euation 10.6\n",
+ "T2=math.ceil(t2)\n",
+ "#solution c)\n",
+ "t=1.\n",
+ "T=3.\n",
+ "A=(t/T)*(t/T+2)\n",
+ "t3=2*aw*(t/T)/((1+A*math.sin(phi)**2)**(1./2)-1)#from 10.5\n",
+ "T3=math.ceil(t3)\n",
+ "\n",
+ "#Results\n",
+ "print \"Smallest number of teeth theoretically required in order to avoid interference on a pinion which is to gear with\"\\\n",
+ " \"\\na) A rack , t= %.f\\nb) An equal pinion , t= %.f\\nc) A wheel to give a ratio of 3 to 1 , t= %.f\"%(T1,T2,T3)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Smallest number of teeth theoretically required in order to avoid interference on a pinion which is to gear with\n",
+ "a) A rack , t= 18\n",
+ "b) An equal pinion , t= 13\n",
+ "c) A wheel to give a ratio of 3 to 1 , t= 15\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 5, Page 338"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "t=25\n",
+ "phi=20*math.pi/180\n",
+ "\n",
+ "#Calculations\n",
+ "#let pitch be 1 \n",
+ "R=t/(2*math.pi)#R=t*p/(2*math.pi)\n",
+ "Larc=1.6#1.6*p\n",
+ "#AB=Larc*math.cos(phi)\n",
+ "AB=Larc*math.cos(phi)\n",
+ "Ra=(4.47+13.97)**(1./2)#by simplifying AB+2{(Ra^2-R^2*cos(phi)^2)-R*sin(phi)} and using p =1\n",
+ "Addendum=Ra-R\n",
+ "#writing p in place of p=1\n",
+ "\n",
+ "#Result\n",
+ "print \"Addendum required = %.2fp\"%Addendum"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Addendum required = 0.32p\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 6, Page 338"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "#let module be 1\n",
+ "m=1\n",
+ "t1=28\n",
+ "t2=45\n",
+ "\n",
+ "#Calculations\n",
+ "r=t1*m/2\n",
+ "R=t2*m/2\n",
+ "ra=r+m\n",
+ "Ra=R+m\n",
+ "phi1=14.5*math.pi/180\n",
+ "#10.8 => AB =(ra^2-r^2*cos(phi)^2)^(1/2)+(Ra^2-R^2*cos(phi)^2)^(1/2)-(r+R)*sin(phi)\n",
+ "#AB=A+B-C\n",
+ "A=m*(ra**2-r**2*math.cos(phi1)**2)**(1./2)\n",
+ "B=m*(Ra**2-R**2*math.cos(phi1)**2)**(1./2)\n",
+ "C=m*(r+R)*math.sin(phi1)\n",
+ "AB=A+B-C\n",
+ "p=math.pi*m\n",
+ "ABp=AB/math.pi\n",
+ "arc1=ABp/math.cos(phi1)#length of arc of contact\n",
+ "phi2=20*math.pi/180\n",
+ "#10.8 => AB =(ra^2-r^2*cos(phi)^2)^(1/2)+(Ra^2-R^2*cos(phi)^2)^(1/2)-(r+R)*sin(phi)\n",
+ "a=m*(ra**2-r**2*math.cos(phi2)**2)**(1./2)\n",
+ "b=m*(Ra**2-R**2*math.cos(phi2)**2)**(1./2)\n",
+ "c=m*(r+R)*math.sin(phi2)\n",
+ "ab=a+b-c\n",
+ "abp=ab/math.pi\n",
+ "arc2=abp/math.cos(phi2)#length of arc of contact\n",
+ "\n",
+ "#Results\n",
+ "print \"Length of path of contact\\nWhen phi = 14.5 degrees = %.3fm\\nWhen phi = 20 degrees = %.2fm\"\\\n",
+ " \"\\n\\nLength of arc of contact\\nWhen phi = 14.5 degrees = %.2fp\\nWhen phi = 20 degrees = %.3fp\"%(AB,ab,arc1,arc2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Length of path of contact\n",
+ "When phi = 14.5 degrees = 6.092m\n",
+ "When phi = 20 degrees = 4.97m\n",
+ "\n",
+ "Length of arc of contact\n",
+ "When phi = 14.5 degrees = 2.00p\n",
+ "When phi = 20 degrees = 1.685p\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 22:21:54 +0000