{
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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Ch:25 Gears"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 25-1 - Page 669"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"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)#"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"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"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 25-2 - Page 669"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"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",
"from sympy import symbols, solve\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"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"dp is 77 mm \n",
"\n",
"dg is 309 mm \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 25-3 - Page 670"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"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."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Sb is 16110 N \n",
"\n",
"Sw is 25200 N \n",
"\n",
"P is 11.657 kW \n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 25-4 - Page 670"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"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)#"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"BHN is 333 \n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 25-5 - Page 671"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"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)#"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Ps is 2166.67 N \n",
"\n",
"Pd is 1358.6 N \n",
"\n",
"BHN is 282 \n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 25-4 - Page 672"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"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",
" \n",
" #The difference in the values is due to rounding-off of the values."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"m is 6 mm \n",
"\n",
"Pd is 434.590 N \n",
"\n",
"Sw is 13244 N \n"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}