{
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Ch:26 Helical gears"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 26-1 - Page 698"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"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)#"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"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"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 26-2 - Page 698"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"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)#"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pt is 747.78 N \n",
"\n",
"Pa is 272.2 N \n",
"\n",
"Pr is 289.64 N \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 26-3 - Page 699"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"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."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"P is 22.936 kW \n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 26-4 - Page 700"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"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"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"mn is 2.5 mm \n",
"\n",
"TC is 1965 N \n",
"\n",
"Sb is 5790.8 N \n"
]
}
],
"prompt_number": 4
}
],
"metadata": {}
}
]
}