{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 10:Traction Drives" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No:10.1,Page No:320" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#variable declaration\n", "Ma=480 #mass of each motor armature in kg 0.48tonne=480kg\n", "Da=0.5 #average diameter of each motor in m\n", "m=450 #mass of each wheel in kg\n", "R=0.54 #radius of each wheel tread in m\n", "M=40 #combine wight of one motor and one trailer coach in ton\n", "alpha=5 #accelaration\n", "N=4 #number of DC motors \n", "a=0.4 #gear ratio\n", "r=20 #train resistance\n", "\n", "#calculation\n", "Jw=1/2*m*R**2 #inertia of the each wheel\n", "nw=2*(N*2) #total number of wheels\n", "J1=nw*Jw #total inertia of all the wheels\n", "\n", "Jm=N*(1/2*Ma*(Da/2)**2) #approximate inertia of all the motors\n", "J2=Jm/a**2 #approximate innertia of the motor referred to the wheels\n", "\n", "Fa2=(J1+J2)*alpha*1000/3600/R #Tractive efforts for driving rorating parts\n", "Fa1=277.8*M*alpha #tractive efforts to accelerate the train mass horizontally\n", "Fr=r*M #Tractive efforts required to overcome train resistance\n", "Ft=Fa1+Fa2+Fr #Tractive efforts required to move the train\n", "Tm=a*R*Ft/N #torque per motor\n", "\n", "#results\n", "print\"\\nTorque per motor:Tm=\",round(Tm,1),\"N-m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Torque per motor:Tm= 3241.3 N-m\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No:10.2,Page No:321" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#variable declaration\n", "M=100 #mass of each motor armature in tonne\n", "Me=100\n", "Tm=5000 #torque of each motor in N-m\n", "Da=0.5 #average diameter of each motor in m\n", "m=450 #mass of each wheel in kg\n", "R=0.54 #radius of each wheel tread in m\n", "N=4 #number of DC motors \n", "r=25 #train resistance N/tonne\n", "a=0.25 #gear ratio \n", "nt=0.98 #gear transmission efficiency\n", "G=50 #up gradient\n", "Vm=100 #speed in kmph\n", "\n", "#calculation \n", "Ft=nt*Tm*N/a/R #Tractive efforts required to move the train\n", "alpha=(Ft-(9.81*M*G+M*r))/(277.8*1.1*Me) #accelaration\n", "t=Vm/alpha #time taken to attain speed of Vm\n", "\n", "#results\n", "print\"\\n time taken to reach a speed of 100kmph is :t=\",round(t,1),\"sec\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", " time taken to reach a speed of 100kmph is :t= 32.6 sec\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No:10.3,Page No:321" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#variable declaration\n", "G=8 #up gradient\n", "r=25 #train resistance N/tonne\n", "M=500 #mass of the electric train in tonne\n", "n=0.8 #combine effiency of transmission and motor\n", "#speed time curve characteristics\n", "t1=60 #characteristic for uniform accelaration at v1 in sec\n", "alpha=2.5 #given accelaration in km/hr/sec at t1\n", "t2=5*60 #characteristic for constant speed in sec \n", "t3=3*60 #characteristic for coasting in sec\n", "B=3 #dynamic braking deceleration in km/hr/sec\n", "\n", "#calculation\n", "Vm=alpha*t1 #peak voltage\n", "Fg=9.81*M*G #tractive effort required to overcome the force of gravity\n", "Fr=M*r #tractive effort required to overcome the train resistance\n", "F_bc=Fg+Fr #retarding force during coasting\n", "\n", "Me=1.1*M\n", "B_c=F_bc/(277.8*Me) #deceleration during coasting\n", "V=Vm-B_c*t3 #speed after coasting\n", "t4=V/B #characteristic for a dynamic braking of 3km/hr/sec\n", "\n", "d1=1/2*Vm*t1/3600 #distance covered during accelaration \n", "d2=Vm*t2/3600 #distance covered during constant speed\n", "d3=1/2*(Vm+V)*t3/3600 #distance covered coasting\n", "d4=1/2*V*t4/3600 #distance covered during braking\n", "D=d1+d2+d3+d4 #distance during stops\n", "D1=d1+d2\n", "x=D1/D\n", "y=1-x\n", "E=(0.01072*Vm**2/D)*(Me/M)+2.725*G*x+0.2778*r*x #specific energy output\n", "Eo=E/n #specific energy consumption\n", "\n", "#results\n", "print\"\\n Specific energy consumption is :Eo=\",round(Eo,1),\"Whptpkm\" " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", " Specific energy consumption is :Eo= 41.1 Whptpkm\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No:10.4,Page No:323" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#variable declaration\n", "G=20 #up gradient\n", "r=25 #train resistance N/tonne\n", "M=500 #mass of the electric train in tonne\n", "n=0.8 #combine effiency of transmission and motor\n", "#speed time curve characteristics\n", "t1=50 #characteristic for uniform accelaration at v1 in sec\n", "alpha=3 #given accelaration in km/hr/sec at t1\n", "t2=10*60 #characteristic for constant speed in sec \n", "B=2.5 #uniform braking deceleration in kmphs to rest\n", "\n", "\n", "#calculation \n", "Vm=alpha*t1 #peak voltage\n", "t3=Vm/B #characteristic for a uniform braking of B=2.5 kmphs\n", "\n", "#(i)during accelaration total tractive effort \n", "Me=1.1*M\n", "Fta=277.8*Me*alpha-9.81*M*G+M*r #total tractive effort during accelaration\n", "Da=1/2*Vm*t1/3600 #distance covered during accelaration ,and t1 is in seconds\n", "Ea=Fta*Da*1000/3600 #energy output during accleration in Wh\n", "\n", "#(ii)during uniform speed net tractive effort\n", "Ftu=-9.81*M*G+M*r #total tractive effort during uniform speed\n", "#the answer for Ftu in the book is -105220 N which is wrong which leads to the other incorrect answers in the book\n", "\n", "Du=Vm*t2/3600 #distance traveled,and t2 is in seconds\n", "Eu=Ftu*Du*1000/3600 #energy output in Wh\n", "\n", "#(iii)during braking net tractive effort\n", "Ftb=-277.8*Me*B-9.81*M*G+M*r #total tractive effort for the net braking\n", "Db=1/2*Vm*t3/3600 #distance covered during braking\n", "Eb=Ftb*Db*1000/3600 #energy output during braking in Wh\n", "\n", "E=Ea/n+n*(Eu+Eb) #net energy consumption\n", "D=Da+Du+Db #total distance traveled\n", "Eo=E/(M*D) #specific energy consumption\n", "\n", "#results \n", "print\"(i)Energy consumption during accelaration is :Ea :\",round(Ea),\"Wh\"\n", "print\" There is a slight difference in the answer due to the number of decimal place\"\n", "print\"\\n(ii)Energy consumption during uniform speed is :Eu :\",round(Eu),\"Wh\" \n", "print\"\\n(iii)Energy consumption during braking is :Eb :\",round(Eb,1),\"Wh\" \n", "print\"\\n Net Energy consumption is E :\",round(E,1),\"Wh\" \n", "print\"\\n Total Distance traveled is D :\",round(D,4),\"km\"\n", "print\"\\n Specific Energy consumption is Eo :\",round(Eo,2),\"Whptpkm\"\n", "#answers in the book are incorrect\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(i)Energy consumption during accelaration is :Ea : 107862.0 Wh\n", " There is a slight difference in the answer due to the number of decimal place\n", "\n", "(ii)Energy consumption during uniform speed is :Eu : -594444.0 Wh\n", "\n", "(iii)Energy consumption during braking is :Eb : -162352.4 Wh\n", "\n", " Net Energy consumption is E : -470610.4 Wh\n", "\n", " Total Distance traveled is D : 27.2917 km\n", "\n", " Specific Energy consumption is Eo : -34.49 Whptpkm\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No:10.5,Page No:325" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#variable declaration\n", "Mm=40 #weight of the motor coach in tonne\n", "Mt=35 #weight of the trailer in tonne\n", "u=0.2 #co-efficient of adhesion\n", "r=30 #train resistance N/tonne\n", "\n", "#calculation\n", "#(a)when the motor to trailer ratio is 1:2\n", "M=Mm+2*Mt #weight of one unit\n", "Me=1.1*M\n", "Md=40 #weight on the driving wheels\n", "Fm=9810*u*Md #total tractive effort without the wheel\n", "Ft=Fm #at maximum accelaration \n", "alpha=(Ft-M*r)/(277.8*Me) #required accelaration since Ft=277.8*u*alpha*M*r\n", "\n", "#(b)when the motor to trailer ratio is 1:1\n", "M=Mm+Mt #weight of one unit\n", "Me=1.1*M\n", "Md=40 #weight on the driving wheels\n", "Fm=9810*u*Md #total tractive effort wihout the wheel\n", "Ft=Fm #at maximum accelaration \n", "alpha1=(Ft-M*r)/(277.8*Me) #required accelaration since Ft=277.8*u*alpha*M*r\n", "\n", "\n", "#results\n", "print\"(a)maximum accelaration on a level track is alpha :\",round(alpha,4),\"kmphps\"\n", "print\"\\n(b)maximum accelaration when motor to trailer coaches ratio is 1:1 is alpha :\",round(alpha1,3),\"kmphps\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)maximum accelaration on a level track is alpha : 2.2366 kmphps\n", "\n", "(b)maximum accelaration when motor to trailer coaches ratio is 1:1 is alpha : 3.326 kmphps\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No:10.6,Page No:326" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#variable declaration\n", "G=10 #up gradient of the locomotive\n", "Ml=110 #weight of the locomotive coach in tonne\n", "Mt=500 #weight of the train in tonne\n", "r=35 #train resistance N/tonne\n", "n=0.8 #80% of the locomotive weight is carried by the driving wheels\n", "alpha=1 #acelaration in kmphps\n", "\n", "#calculation\n", "#when only the 110 tonne locomotive is present\n", "Md=Ml*n #weight of the motor\n", "M=Mt+Ml #total mass of the train\n", "Me=1.1*M\n", "Ft=277.8*Me*alpha+9.81*M*G+M*r #total tractive effort required to move the train\n", "Fm=Ft\n", "u=Fm/(9810*Md) #co-efficient of adhesion ,since Fm=9810*u*Md\n", "\n", "#when another locomotive of 70 is added together\n", "Md=Ml*n+70 # mass of the motor\n", "M_=Mt+Ml+70 # mass of the train\n", "Fm=9810*u*Md\n", "Ft=Fm\n", "M=Ft/(277.8*1.1*alpha+9.81*G+r) #total mass of the train, since Ft=277.8*Me*alpha+9.81*M*G+M*r\n", "W=M-M_ #weight of additional bogies to be attached\n", "\n", "\n", "#results\n", "print\"\\n Given co-efficient of adhesion is:\",round(u,2)\n", "print\"\\n Weight of additional bogies to be attached is:\",round(W,1),\"T\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", " Given co-efficient of adhesion is: 0.31\n", "\n", " Weight of additional bogies to be attached is: 415.2 T\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example No:10.7,Page No:327" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from __future__ import division\n", "\n", "#variable declaration\n", "Ml=1000 #weight of the empty train in tonne\n", "Mt=5000 #weight of the fully loaded train in tonne\n", "G=15 #gradient of the track\n", "V=30 #maximum speed of the train \n", "r=40 #train resistance in N/tonne\n", "u=0.25 #co-efficient of adhesion\n", "alpha=0.3 #acelaration in kmphps\n", "\n", "W=100 #weight of each locomotive\n", "\n", "#calculation\n", "Md=W*n\n", "Fm=9810*u*Md #total tractive without wheel\n", "Fb=9.81*(Mt+W*n)*G-(Mt+W*n)*r \n", "print\"\\nFm=\",Fm\n", "print\"\\nFb=\",Fb\n", "print\"\\nequating Fb and Fm we get\"\n", "n=535750/(245250-10715) #number of locomotive required\n", "\n", "#results\n", "if (n>2) : \n", " n=3\n", "print\"\\nThe number of locomotives is n:\",n \n", "Md=W*n\n", "M=Ml+W*n\n", "Ft=277.8*1.1*M*alpha+9.81*M*G+M*r #tractive effore required to move the train\n", "Fm=9810*0.3*Md\n", "if (Fm>Ft) :\n", " print\"\\nThe train can be accelarated with \",n,\"locomotives\"" ], "language": "python", "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'n' is not defined", "output_type": "pyerr", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0;31m#calculation\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m \u001b[0mMd\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mW\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 17\u001b[0m \u001b[0mFm\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m9810\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mu\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mMd\u001b[0m \u001b[0;31m#total tractive without wheel\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0mFb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m9.81\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mMt\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mW\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mG\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mMt\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mW\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'n' is not defined" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }