{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ch:21 V belt drive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 21-1 - Page 579"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "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"
     ]
    }
   ],
   "source": [
    "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",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 21-2 - Page 579"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "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"
     ]
    }
   ],
   "source": [
    "from math import sqrt, pi, asin, degrees, exp,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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 21-3 - Page 580"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "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"
     ]
    }
   ],
   "source": [
    "from math import sqrt, pi, asin, degrees, exp,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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 21-4 - Page 580"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "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"
     ]
    }
   ],
   "source": [
    "from math import sqrt, pi\n",
    "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 21-5 - Page 581"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " C is 1.0603 m \n",
      "\n",
      " Pd is 30 KW \n",
      "\n",
      " n is 4.01 KW \n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, solve\n",
    "from math import pi\n",
    "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",
    "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)"
   ]
  }
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