{
"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 sympy import Symbol\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",
"n = Symbol('n') #number of locomotive required\n",
"W=100 #weight of each locomotive\n",
"\n",
"#calculation\n",
"Md=W*n\n",
"Fm=9810*u*Md\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)\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 \n",
"Fm=9810*0.3*Md\n",
"if (Fm>Ft) :\n",
" print\"\\nThe train can be accelarated with \",n,\"locomotives\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Fm= 245250.0*n\n",
"\n",
"Fb= 10715.0*n + 535750.0\n",
"\n",
"equating Fb and Fm we get\n",
"\n",
"The number of locomotives is n: 3\n",
"\n",
"The train can be accelarated with 3 locomotives\n"
]
}
],
"prompt_number": 18
}
],
"metadata": {}
}
]
}