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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Ch:25 Gears"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 25-1 - Page 669"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dp is 125 mm \n",
+ "\n",
+ "dg is 300 mm \n",
+ "\n",
+ "CD is 212.5 mm \n",
+ "\n",
+ "ha is 5 mm \n",
+ "\n",
+ "hf is 6.25 mm \n",
+ "\n",
+ "c is 1.25 mm \n",
+ "\n",
+ "r is 2 mm \n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt, pi\n",
+ "Zp=25#\n",
+ "Zg=60#\n",
+ "m=5#\n",
+ "dp=m*Zp#\n",
+ "dg=m*Zg#\n",
+ "CD=(dp+dg)/2#\n",
+ "ha=m#\n",
+ "hf=1.25*m#\n",
+ "c=hf-ha#\n",
+ "r=0.4*m#\n",
+ "print \"dp is %0.0f mm \"%(dp)#\n",
+ "print \"\\ndg is %0.0f mm \"%(dg)#\n",
+ "print \"\\nCD is %0.1f mm \"%(CD)#\n",
+ "print \"\\nha is %0.0f mm \"%(ha)#\n",
+ "print \"\\nhf is %0.2f mm \"%(hf)#\n",
+ "print \"\\nc is %0.2f mm \"%(c)#\n",
+ "print \"\\nr is %0.0f mm \"%(r)#"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 25-2 - Page 669"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dp is 77 mm \n",
+ "\n",
+ "dg is 309 mm \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi\n",
+ "from sympy import symbols, solve\n",
+ "N=800#\n",
+ "P=6000#\n",
+ "n=200#\n",
+ "Cs=1.4#\n",
+ "sigb=150#\n",
+ "FOS=2#\n",
+ "Zp=18#\n",
+ "Zg=Zp*N/n#\n",
+ "Y=pi*(0.154-(0.912/Zp))#\n",
+ "p=[1 ,0 ,-9.5846, -38.135]#\n",
+ "P = symbols('P')\n",
+ "expr = P**3*p[0]+P**2*p[1]+P*p[2]+p[3]\n",
+ "m=solve(expr, P)[0]#\n",
+ "dp=m*Zp#\n",
+ "dg=m*Zg#\n",
+ "# printing data in scilab o/p window\n",
+ "print \"dp is %0.0f mm \"%(dp)#\n",
+ "print \"\\ndg is %0.0f mm \"%(dg)#\n",
+ "# Answer is given wrong in the textbook"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 25-3 - Page 670"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Sb is 16110 N \n",
+ "\n",
+ "Sw is 25200 N \n",
+ "\n",
+ "P is 11.657 kW \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi\n",
+ "Zp=30#\n",
+ "N=1000#\n",
+ "Zg=75#\n",
+ "m=5#\n",
+ "b=60#\n",
+ "sigut=450#\n",
+ "BHN=350#\n",
+ "Cs=1.5#\n",
+ "FOS=2#\n",
+ "dp=m*Zp#\n",
+ "dg=m*Zg#\n",
+ "v=2*pi*N*dp/(60*1000*2)#\n",
+ "Cv=3/(3+v)#\n",
+ "sigb=450/3#\n",
+ "Y=0.358#\n",
+ "Sb=m*b*sigb*Y#\n",
+ "Q=(2*Zg)/(Zp+Zg)#\n",
+ "K=0.16*(BHN/100)**2#\n",
+ "Sw=b*dp*Q*K#\n",
+ "Pt=Sb*Cv/(Cs*FOS)#\n",
+ "P=Pt*v#\n",
+ "P=P*10**-3#\n",
+ "print \"Sb is %0.0f N \"%(Sb)#\n",
+ "print \"\\nSw is %0.0f N \"%(Sw)#\n",
+ "print \"\\nP is %0.3f kW \"%(P)#\n",
+ "\n",
+ "#The difference in the value of Sw is due to rounding-off of the value of Q."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 25-4 - Page 670"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "BHN is 333 \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi\n",
+ "n=240#\n",
+ "P=8000#\n",
+ "N=1200#\n",
+ "CD=300#\n",
+ "Cs=1.5#\n",
+ "alpha=20*pi/180#\n",
+ "G=N/n#\n",
+ "dp=CD*2/6#\n",
+ "dg=5*dp#\n",
+ "v=2*pi*N*dp/(60*1000*2)#\n",
+ "Cv=3/(3+v)#\n",
+ "Pt=P/v#\n",
+ "Peff=Pt*Cs/Cv#\n",
+ "m=4#\n",
+ "b=10*m#\n",
+ "FOS=2#\n",
+ "Sb=Peff*FOS#\n",
+ "sigut=600#\n",
+ "sigb=sigut/3#\n",
+ "Zp=dp/m#\n",
+ "Zg=dg/m#\n",
+ "Q=(2*Zg)/(Zp+Zg)#\n",
+ "K=Sb/(b*dp*Q)#\n",
+ "BHN=sqrt(K/0.16)*100#\n",
+ "BHN=333#\n",
+ "print \"BHN is %0.0f \"%(BHN)#"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 25-5 - Page 671"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Ps is 2166.67 N \n",
+ "\n",
+ "Pd is 1358.6 N \n",
+ "\n",
+ "BHN is 282 \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi\n",
+ "alpha=20*pi/180#\n",
+ "N=800#\n",
+ "P=6000#\n",
+ "sigut=450#\n",
+ "i=5#\n",
+ "Cs=1.3#\n",
+ "v=3.6#\n",
+ "FOS=2#\n",
+ "Pt=P/v#\n",
+ "Cv=3/(3+v)#\n",
+ "sigb=sigut/3#\n",
+ "dp=3.6*1000*2*60/(2*pi*N)#\n",
+ "dp=86#\n",
+ "Sb=Pt*Cs/Cv*FOS#\n",
+ "#Let x be m**2*Y\n",
+ "x=Sb/(10*sigb)#\n",
+ "m=5#\n",
+ "Zp=18#\n",
+ "dp=m*Zp#\n",
+ "Zg=i*Zp#\n",
+ "dg=m*Zg#\n",
+ "b=10*m#\n",
+ "phip=m+(0.25*sqrt(dp))#\n",
+ "ep=32+(2.5*phip)#\n",
+ "phig=m+(0.25*sqrt(dg))#\n",
+ "eg=32+(2.5*phig)#\n",
+ "e=ep+eg#\n",
+ "e=e*10**-3#\n",
+ "Ps=Cs*Pt#\n",
+ "r1=dp/2#\n",
+ "r2=dg/2#\n",
+ "Pd=e*N*Zp*b*r1*r2/(2530*sqrt(r1**2+r2**2))#\n",
+ "Q=(2*Zg)/(Zp+Zg)#\n",
+ "K=Sb/(b*dp*Q)#\n",
+ "BHN=sqrt(K/0.16)*100#\n",
+ "print \"Ps is %0.2f N \"%(Ps)#\n",
+ "print \"\\nPd is %0.1f N \"%(Pd)#\n",
+ "print \"\\nBHN is %0.0f \"%(BHN)#"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 25-4 - Page 672"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "m is 6 mm \n",
+ "\n",
+ "Pd is 434.590 N \n",
+ "\n",
+ "Sw is 13244 N \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi\n",
+ "P=9000#\n",
+ "N=900#\n",
+ "n=150#\n",
+ "sigut=750#\n",
+ "BHN=300#\n",
+ "Cs=1.5#\n",
+ "FOS=2#\n",
+ "i=N/n#\n",
+ "x=sqrt(i)#\n",
+ "Zp=18#\n",
+ "Zg=x*Zp#\n",
+ "Zg=44#\n",
+ "#Let actual speed reduction be xa\n",
+ "xa=Zg/Zp#\n",
+ "n1=N/xa**2#\n",
+ "T1=P*60/(2*pi*N)#\n",
+ "i2=N/xa#\n",
+ "T2=N/i2*T1#\n",
+ "m=6#\n",
+ "dp=Zp*m#\n",
+ "dg=m*Zg#\n",
+ "phip=m+(0.25*sqrt(dp))#\n",
+ "ep=16+(1.25*phip)#\n",
+ "phig=m+(0.25*sqrt(dg))#\n",
+ "eg=16+(1.25*phig)#\n",
+ "e=ep+eg#\n",
+ "e=e*10**-3#\n",
+ "Pt=26000#\n",
+ "Ps=Cs*Pt#\n",
+ "r1=dp/2#\n",
+ "r2=dg/2#\n",
+ "b=10*m#\n",
+ "Pd=e*i2*Zp*b*r1*r2/(2530*sqrt(r1**2+r2**2))#\n",
+ "Q=(2*Zg)/(Zp+Zg)#\n",
+ "sigb=sigut/3#\n",
+ "Y=0.308#\n",
+ "\n",
+ "Sb=b*m*sigb*Y#\n",
+ "K=0.16*(BHN/100)**2#\n",
+ "Sw=b*dp*K*Q#\n",
+ "print \"m is %0.0f mm \"%(m)#\n",
+ "print \"\\nPd is %0.3f N \"%(Pd)#\n",
+ "print \"\\nSw is %0.0f N \"%(Sw) \n",
+ "#The difference in the values is due to rounding-off of the values."
+ ]
+ }
+ ],
+ "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
+}
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