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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Ch:26 Helical gears"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 26-1 - Page 698"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "m is 4.14 mm \n",
+ "\n",
+ "alpha is 20.647 deg \n",
+ "\n",
+ "Pa is 90.8 mm \n",
+ "\n",
+ "Pd is 72.8 mm \n",
+ "\n",
+ "Ga is 215 mm \n",
+ "\n",
+ "Gd is 197 mm \n",
+ "\n",
+ "b is 48.55 mm \n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt, pi, sin, cos, tan, atan\n",
+ "Zp=20#\n",
+ "Zg=50#\n",
+ "alphan=20*pi/180#\n",
+ "phi=15*pi/180#\n",
+ "mn=4#\n",
+ "m=mn/cos(phi)#\n",
+ "alpha=180/pi*atan(tan(alphan)/(cos(phi)))#\n",
+ "dp=Zp*m#\n",
+ "dg=Zg*m#\n",
+ "ha=4#\n",
+ "hd=1.25*mn#\n",
+ "#Let addendum circle dia of pinion be Pa\n",
+ "Pa=dp+(2*mn)#\n",
+ "#Let dedendum circle dia of pinion be Pd\n",
+ "Pd=dp-(2.5*mn)#\n",
+ "#Let addendum circle dia of gear be Ga\n",
+ "Ga=dg+(2*mn)#\n",
+ "#Let dedendum circle dia of gear be Gd\n",
+ "Gd=dg-(2.5*mn)#\n",
+ "b=pi*mn/sin(phi)#\n",
+ "print \"m is %0.2f mm \"%(m)#\n",
+ "print \"\\nalpha is %0.3f deg \"%(alpha)#\n",
+ "print \"\\nPa is %0.1f mm \"%(Pa)#\n",
+ "print \"\\nPd is %0.1f mm \"%(Pd)#\n",
+ "print \"\\nGa is %0.0f mm \"%(Ga)#\n",
+ "print \"\\nGd is %0.0f mm \"%(Gd)#\n",
+ "print \"\\nb is %0.2f mm \"%(b)#"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 26-2 - Page 698"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Pt is 747.78 N \n",
+ "\n",
+ "Pa is 272.2 N \n",
+ "\n",
+ "Pr is 289.64 N \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import pi, sin, cos, tan\n",
+ "P=5000#\n",
+ "Zp=25#\n",
+ "Zg=50#\n",
+ "mn=4#\n",
+ "alphan=20*pi/180#\n",
+ "phi=20*pi/180#\n",
+ "N=1200#\n",
+ "m=mn/cos(phi)#\n",
+ "dp=Zp*m#\n",
+ "dg=Zg*m#\n",
+ "v=2*pi*N*dp/(60*2*1000)#\n",
+ "Pt=P/v#\n",
+ "Pa=Pt*tan(phi)#\n",
+ "Pr=Pt*tan(alphan)/cos(phi)#\n",
+ "print \"Pt is %0.2f N \"%(Pt)#\n",
+ "print \"\\nPa is %0.1f N \"%(Pa)#\n",
+ "print \"\\nPr is %0.2f N \"%(Pr)#"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 26-3 - Page 699"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "P is 22.936 kW \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi, sin, cos, tan\n",
+ "Zp=24#\n",
+ "Zg=72#\n",
+ "alphan=20*pi/180#\n",
+ "phi=24*pi/180#\n",
+ "N=720#\n",
+ "mn=5#\n",
+ "b=50#\n",
+ "sigut=600#\n",
+ "BHN=360#\n",
+ "Cs=1.4#\n",
+ "FOS=2#\n",
+ "sigb=sigut/3#\n",
+ "dp=mn*Zp/cos(phi)#\n",
+ "Zp=Zp/(cos(phi))**3#\n",
+ "Zg=Zg/(cos(phi))**3#\n",
+ "Y=0.358+((0.364-0.358)*1.48/2)#\n",
+ "Sb=b*mn*sigb*Y#\n",
+ "Q=(2*Zg)/(Zp+Zg)#\n",
+ "K=0.16*(BHN/100)**2#\n",
+ "Sw=b*dp*Q*K/(cos(phi)**2)#\n",
+ "v=2*pi*N*dp/(60*2*1000)#\n",
+ "Cv=5.6/(5.6+sqrt(v))#\n",
+ "Peff=Sb/FOS#\n",
+ "Pt=Peff*Cv/Cs#\n",
+ "P=Pt*v#\n",
+ "P=P*10**-3#\n",
+ "print \"P is %0.3f kW \"%(P)#\n",
+ "#The difference in the value is due to rounding-off of the values."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 26-4 - Page 700"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "mn is 2.5 mm \n",
+ "\n",
+ "TC is 1965 N \n",
+ "\n",
+ "Sb is 5790.8 N \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi, sin, cos, tan, atan\n",
+ "Zp=25#\n",
+ "Zg=100#\n",
+ "P=5000#\n",
+ "N=2000#\n",
+ "alphan=20*pi/180#\n",
+ "phi=15*pi/180#\n",
+ "sigut=660#\n",
+ "Cs=1.5#\n",
+ "FOS=1.8#\n",
+ "v=10#\n",
+ "Zp1=Zp/(cos(phi))**3#\n",
+ "Zg1=Zg/(cos(phi))**3#\n",
+ "Y=0.348+(0.74*0.004)#\n",
+ "sigb=sigut/3#\n",
+ "Cv=5.6/(5.6+sqrt(v))#\n",
+ "#Sb=FOS*Peff\n",
+ "mn=FOS*P*Cs*60*1000*2*cos(phi)/(2*pi*N*Cv*Zp*12*sigb*Y)#\n",
+ "mn=mn**(1/3)#\n",
+ "mn=2.5#\n",
+ "dp=mn*Zp/cos(phi)#\n",
+ "Q=(2*Zg)/(Zp+Zg)#\n",
+ "b=12*mn#\n",
+ "Sb=12*sigb*Y#\n",
+ "K=Sb*(cos(phi)**2)/(dp*Q*b)#\n",
+ "BHN=sqrt(K/0.16)*100#\n",
+ "dg=mn*Zg/cos(phi)#\n",
+ "phip=mn+(0.25*sqrt(dp))#\n",
+ "ep=16+(1.25*phip)#\n",
+ "phig=mn+(0.25*sqrt(dg))#\n",
+ "eg=16+(1.25*phig)#\n",
+ "e=ep+eg#\n",
+ "e=e*10**-3#\n",
+ "r1=dp/2#\n",
+ "r2=dg/2#\n",
+ "Pd=e*N*Zp1*b*r1*r2/(2530*sqrt(r1**2+r2**2))#\n",
+ "v=2*pi*N*dp/(60*2*1000)#\n",
+ "#Let tangential component be TC\n",
+ "TC=(Cs*1845/mn)+(Pd*cos(alphan)*cos(phi))#\n",
+ "\n",
+ "Sb=b*mn*sigb*Y#\n",
+ "print \"mn is %0.1f mm \"%(mn)#\n",
+ "print \"\\nTC is %0.0f N \"%(TC)#\n",
+ "print \"\\nSb is %0.1f N \"%(Sb)#\n",
+ "#The difference in the value of Sb is due to rounding-off of t"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
generated by cgit (git 2.34.1) at 2024-12-21 07:09:09 +0000