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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Ch:21 V belt drive"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 21-1 - Page 579"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import sqrt, pi, asin, degrees, exp\n",
"P1=12*10**3#\n",
"d=0.3#\n",
"D=0.9#\n",
"C=0.9#\n",
"A=230*10**-6#\n",
"#density is rho\n",
"rho=1100#\n",
"N=1500#\n",
"#Maximum stress is sig\n",
"sig=2.1*10**6#\n",
"#semi groove angle is b\n",
"b=20*pi/180#\n",
"u=0.22#\n",
"m=rho*A#\n",
"v=2*pi*N*d/(60*2)#\n",
"Tc=m*v**2#\n",
"T1=A*sig#\n",
"#wrap angle is thetaA\n",
"ang=(D-d)/(2*C)#\n",
"thetaA=pi/180*(180-(2*degrees(asin(ang))))\n",
"thetaB=((2*pi)-thetaA)#\n",
"x=u*thetaB#\n",
"T2=Tc+((T1-Tc)/exp(x))#\n",
"P2=(T1-T2)*v#\n",
"n=P1/P2#\n",
"n=3# #(rounding off to nearest whole number)\n",
"print \"Tc is %0.1f N \"%(Tc)#\n",
"print \"\\nT1 is %0.0f N \"%(T1)#\n",
"print \"\\nT2 is %0.1f N \"%(T2)#\n",
"print \"\\nP2 is %0.0f W \"%(P2)#\n",
"print \"\\nn is %0.0f \"%(n)#\n",
" \n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Tc is 140.5 N \n",
"\n",
"T1 is 483 N \n",
"\n",
"T2 is 288.2 N \n",
"\n",
"P2 is 4589 W \n",
"\n",
"n is 3 \n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 21-2 - Page 579"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sin\n",
"D=0.6#\n",
"d=0.3#\n",
"C=0.9#\n",
"m=0.193#\n",
"n=2#\n",
"N=1500#\n",
"u=0.3#\n",
"v=2*pi*N/60*d/2#\n",
"P=150*10**3#\n",
"Tc=m*v**2#\n",
"#let T1-T2=T\n",
"T=P/(n*v)#\n",
"thetaA=pi/180*(180-(2*degrees(asin((D-d)/(2*C)))))#\n",
"thetaB=((2*pi)-thetaA)#\n",
"#Groove angle=b\n",
"b=17.5*pi/180#\n",
"x=u*thetaA/sin(b)#\n",
"y=exp(x)#\n",
"c=(Tc*(1-y))#\n",
"T2=(T+(Tc*(1-y)))/(y-1)#\n",
"#T2=(T-y)/Tc#\n",
"T1=T+Tc#\n",
"Lp=2*sqrt((C**2)-((D-d)/2)**2)+(thetaA*d/2)+(thetaB*D/2)#\n",
"v=sqrt(T/(3*m))#\n",
"print \"Tc is %0.2f N \"%(Tc)#\n",
"print \"\\nT1 is %0.0f N \"%(T1)#\n",
"print \"\\nT2 is %0.2f N \"%(T2)#\n",
"print \"\\nLp is %0.3f m \"%(Lp)#\n",
"print \"\\nv is %0.2f m/s \"%(v)#\n",
"print \"\\nThe designation of the belt is B-3251-45 \"#\n",
"#The difference in values of T1 and T2 is due to rounding-off of values."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Tc is 107.15 N \n",
"\n",
"T1 is 3290 N \n",
"\n",
"T2 is 98.93 N \n",
"\n",
"Lp is 3.239 m \n",
"\n",
"v is 74.15 m/s \n",
"\n",
"The designation of the belt is B-3251-45 \n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 21-3 - Page 580"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import tan\n",
"C=1#\n",
"m=0.35#\n",
"d=0.25#\n",
"P=22*10**3#\n",
"#Let the smaller pulley dia be n\n",
"#Let the larger pulley dia be N\n",
"n=1000#\n",
"N=400#\n",
"D=d*n/N#\n",
"v=2*pi*n*d/(60*2)#\n",
"Tc=m*v**2#\n",
"topwidth=22#\n",
"h=14#\n",
"bottomwidth=topwidth-(2*h*tan(20*pi/180))#\n",
"A=(topwidth+bottomwidth)/2*h#\n",
"#let allowable tension be Ta\n",
"Ta=2.2#\n",
"T1=A*Ta#\n",
"u=0.28#\n",
"thetaA=pi/180*(180-(2*degrees(asin((D-d)/(2*C)))))\n",
"thetaB=((2*pi)-thetaA)#\n",
"#Groove angle=b=19\n",
"b=19*pi/180#\n",
"x=u*thetaA/sin(b)#\n",
"T2=Tc+((T1-Tc)/exp(x))#\n",
"n=P/((T1-T2)*v)#\n",
"Lp=2*sqrt((C**2)-((D-d)/2)**2)+(thetaA*d/2)+(thetaB*D/2)#\n",
"print \"Tc is %0.2f N \"%(Tc)#\n",
"print \"\\nT1 is %0.1f N \"%(T1)#\n",
"print \"\\nT2 is %0.1f N \"%(T2)#\n",
"print \"\\nn is %0.1f \"%(n)#\n",
"print \"\\nLp is %0.3f m \"%(Lp)#\n",
"print \"\\nThe designation of the belt is C-3414-47 \"#\n",
" \n",
" # difference in value of Lp is due to rounding-off the values of thetaA and thetaB."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Tc is 59.97 N \n",
"\n",
"T1 is 520.7 N \n",
"\n",
"T2 is 102.7 N \n",
"\n",
"n is 4.0 \n",
"\n",
"Lp is 3.410 m \n",
"\n",
"The designation of the belt is C-3414-47 \n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 21-4 - Page 580"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"P=12*10**3#\n",
"Ks=1.1#\n",
"Pd=12*10**3*Ks#\n",
"N=1440#\n",
"B=17#\n",
"t=11#\n",
"d=200#\n",
"i=3#\n",
"D=i*d#\n",
"C=1000#\n",
"# since angle of contact theta is very small\n",
"theta=(D-d)/C#\n",
"theta=theta*180/pi#\n",
"Kc=0.8#\n",
"Lp=(2*C)+(pi/2*(D+d))+(((D-d)**2)/(4*C))#\n",
"Li=Lp-45#\n",
"Ki=1.1#\n",
"#let number of v-belts required = n\n",
"#let the KW rating be KWR\n",
"KWR=5.23#\n",
"n=(P*Ks)/(KWR*Ks*Ki*10**3)#\n",
"n=3#\n",
"print \"D is %0.1f mm \"%(D)#\n",
"print \"\\nC is %0.1f mm \"%(C)#\n",
"print \"\\nn is %0.3f \"%(n)#\n",
"print \"\\nLi is %0.0f mm \"%(Li)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"D is 600.0 mm \n",
"\n",
"C is 1000.0 mm \n",
"\n",
"n is 3.000 \n",
"\n",
"Li is 3252 mm \n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"exa 21-5 - Page 581"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"N=800;\n",
"P=20;\n",
"i=2.5;\n",
"Ks=1.5; #(from table for 3-5 hrs/day)\n",
"Pd=P*Ks;\n",
"d=250;\n",
"D=i*d;\n",
"C=1.6*D;\n",
"Lp=(2*C)+(pi*(D+d)/2)+((D-d)**2)/(4*C);\n",
"Li=Lp+74;\n",
"Listd=3454;\n",
"Lp=Listd+74;\n",
"p=[1, -1.0768, 0.0175];\n",
"from sympy import symbols, solve\n",
"P = symbols('P')\n",
"expr = P**2*p[0]+P*p[1]+p[2]\n",
"z = solve(expr, P)[1]\n",
"KW=9.4;\n",
"Kc=0.795;\n",
"K1=1;\n",
"n=Pd/(KW*Kc*K1);\n",
"print \" C is %0.4f m \"%(z);\n",
"print \"\\n Pd is %0.0f KW \"%(Pd);\n",
"print \"\\n n is %0.2f KW \"%(n);\n",
" \n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" C is 1.0603 m \n",
"\n",
" Pd is 30 KW \n",
"\n",
" n is 4.01 KW \n"
]
}
],
"prompt_number": 17
}
],
"metadata": {}
}
]
}