{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 4:Selection of Motor Power Rating"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.1,Page no:49"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from scipy.optimize import fsolve\n",
"#Variable declaration\n",
"P=30.0 #[Power KW\n",
"theta1=30.0 #Temperature degree C\n",
"t1=40.0 # time in min\n",
"theta2=45.0 #Final temperature in degree C\n",
"\n",
"#Calculation\n",
"t2=80.0 #min(t2=2*t1)\n",
"#theta=theta_f*(1-exp(-t/T))\"\n",
"def f(T):\n",
" return((1-math.exp(-80.0/T))/(1-math.exp(-40/T))-(theta2/theta1))\n",
"T=fsolve(f,1)\n",
"theta_f=theta1/(1.0-math.exp(-t1/T)) #degreeC\n",
"#Result\n",
"print\"(a).Thermal time constant: \",round(T[0],2),\"minutes\"\n",
"print\"(b).Final temperature rise: \",theta_f,\"degrees\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" (a).Thermal time constant: 57.71 minutes\n",
"(b).Final temperature rise: 60.0 degrees\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.2,Page no:50"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Variable declaration\n",
"P=30.0 #Power in KW\n",
"theta1=20.0 #Temerature degree C\n",
"t1=30.0 #Time in min\n",
"theta2=30.0 #Temperature in degree C\n",
"t2=60.0 #Final time innmin(t2=2*t1)\n",
"\n",
"#Calculation\n",
"#Let exp(-t1/T)=x then exp(-t2/T)=x**2\n",
"#theta1/theta2=(1-x)/(1-x**2)\n",
"#x**2*theta1-x*theta2+theta2-theta1=0\n",
"def f(T):\n",
" return(((1-math.exp(-t2/T))/(1-math.exp(-t1/T)))-theta2/theta1)\n",
"T=fsolve(f,1)\n",
"theta_f=theta1/(1-math.exp(-t1/T)) #degreeC\n",
"\n",
"#Result\n",
"print\"Thermal time constant : \",round(T[0],2),\"minutes\"\n",
"print\"Final temperature rise : \",theta_f,\"C\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Thermal time constant : 43.28 minutes\n",
"Final temperature rise : 40.0 C\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.3,Page no:51"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Variable declaration\n",
"T_ambient=30 #Ambient tmeperature in dgree C\n",
"P=30.0 #Power in KW\n",
"theta1=54.0-T_ambient #Temperature durin g full load operation degree C\n",
"t1=1.0 #Time in hour\n",
"theta2=67.0-T_ambient #Temperature in degree C\n",
"t2=2.0 #Time in hour(t2=2*t1)\n",
"\n",
"#Calculation\n",
"def f(T):\n",
" return(((1-math.exp(-2/T))/(1-math.exp(-1/T)))-theta2/theta1)\n",
"T=fsolve(f,1)\n",
"theta_f=theta1/(1-math.exp(-t1/T)) #degreeC\n",
"theta_steady=theta_f+30 #degreeC\n",
"\n",
"#Result\n",
"print\"(a) Final steady state temperature : \",round(theta_steady,2),\"C\"\n",
"print\"(b) Heating time constant :\",round(T[0],2),\"hour\"\n",
"theta2=theta_f #degree C\n",
"t=2.7 #hour\n",
"theta=40-30 #degree C\n",
"Tdash=-t/math.log(theta/theta2) #hour\n",
"print\"(c) Cooling time constant: \",round(Tdash,2),\"hour\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" (a) Final steady state temperature : 82.36 C\n",
"(b) Heating time constant : 1.63 hour\n",
"(c) Cooling time constant: 1.63 hour\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.4,Page no:52"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Variable declaration\n",
"T=110.0 #Time in min\n",
"Tdash=150.0 #Final time in min\n",
"t=30.0 #Run time of motor min\n",
"tdash=45.0 #Switch off time in min\n",
"theta_f=50.0 #final temperature rise in degree C\n",
"\n",
"#Calculation\n",
"#theta=theta_f-(theta_f-theta1)*exp(-t/T)\n",
"#theta1=theta*exp(-tdash/Tdash) \n",
"theta=(theta_f-theta_f*math.exp(-t/T))/(1-math.exp(-tdash/Tdash)*math.exp(-t/T)) #degreeC\n",
"\n",
"#Result\n",
"print\"Maximum temperature rise of the motor: \",round(theta,2),\"C\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum temperature rise of the motor: 27.37 C\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.5,Page no:52"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Variable declaration\n",
"theta1=20.0 #Initial temperature in degreeC\n",
"theta2=28.0 #Final temperature in degreeC\n",
"dthetaBYdt1=0.08 #Rate of temp rise in degreeC/min\n",
"dthetaBYdt2=0.06 #Rate of temp rise in degreeC/min\n",
"\n",
"#Calculation\n",
"#theta=theta_f-(theta_f-theta1)*exp(-t/T)\n",
"#dtheta/dt=(theta_f-theta)/T\n",
"#dthetaBYdt1/dthetaBYdt2=(theta_f-theta1)/(theta_f-theta2)\n",
"theta_f=(theta2*dthetaBYdt1-theta1*dthetaBYdt2)/(dthetaBYdt1-dthetaBYdt2)\n",
"T=(theta_f-theta1)/dthetaBYdt1 #min\n",
"\n",
"#Result\n",
"print\"Final temperature rise,theta_f= : \",theta_f,\"C\"\n",
"print\"Heating time constant: \",T,\"minutes\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Final temperature rise,theta_f= : 52.0 C\n",
"Heating time constant: 400.0 minutes\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.6,Page no:59"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Variable declaration\n",
"cycle1=50.0 #Duty cycle hp\n",
"t1=20.0 #Time in sec\n",
"cycle2=100.0 #Duty cycle in hp\n",
"t2=20.0 #Time in sec\n",
"cycle3=150.0 #3rd duty cycle in hp\n",
"t3=10.0 #time sec\n",
"cycle4=120.0 #4th duty cyclein hp\n",
"t4=20.0 #time sec\n",
"cycle5=0.0 #th duty cycle in hp\n",
"t5=15.0 #sec\n",
"\n",
"#Calculation\n",
"hp_rms=math.sqrt((cycle1**2*t1+cycle2**2*t2+cycle3**2*t3+cycle4**2*t4+cycle5**2*t5)/(t1+t2+t3+t4+t5)) #hp\n",
"\n",
"#Result\n",
"print\"hp(rms) for the motor : \",round(hp_rms,2),\"hp\"\n",
"print\"We should choose 100hp motor.\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"hp(rms) for the motor : 94.74 hp\n",
"We should choose 100hp motor.\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.7,Page no:61"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Variable declaration\n",
"t_on=15.0 #Time for full load [min]\n",
"t_off=25.0 #time for off load in [min]\n",
"T=100.0 #Heating time constant in [min]\n",
"Tdash=140.0 #Cooling time constant in [min]\n",
"theta_f=55.0 #Continuous full load operation time in [degree C]\n",
"\n",
"#Calculation\n",
"#theta=theta_f-(theta_f-theta1)*exp(-t/T)\n",
"#theta1=theta*exp(-tdash/Tdash) \n",
"theta_max=theta_f*(1-math.exp(-t_on/T))/(1-math.exp(-(t_off/Tdash+t_on/T))) #degreeC\n",
"\n",
"#Result\n",
"print\"Maximum temperature rise: \",round(theta_max,2),\"C\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum temperature rise: 27.36 C\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.8,Page no:62"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"\n",
"#Variable declaration\n",
"Rating=100.0 #Rating in KW\n",
"alfa=0.9 #Ratio rating unitless\n",
"ts=20.0 #Running time in min\n",
"T=100.0 #Heating time constant in min\n",
"\n",
"#Calculation\n",
"S=math.sqrt((1.0+alfa)/(1.0-math.exp(-ts/T))) \n",
"ShortTimeRating=S*Rating #KW\n",
"\n",
"#Result\n",
"print\"Short time rating: \",round(ShortTimeRating,1),\"kW\"\n",
"print\"NOTE:Answer is wrong in the textbook.\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Short time rating: 323.8 kW\n",
"NOTE:Answer is wrong in the textbook.\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.9,Page no:62"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Variable declaration\n",
"T=80.0 #Heating time constant in min\n",
"Tdash=110.0 #cooling time constant in min\n",
"Rating=50.0 #Full load rating in [KW]\n",
"ts=15.0 #Runt time in [min]\n",
"\n",
"#Calculation\n",
"S=math.sqrt(1.0/(1.0-math.exp(-ts/T))) \n",
"ShortTimeRating=S*Rating #KW\n",
"t_off=20.0 #min\n",
"S=math.sqrt((1.0-math.exp(-(ts/T+t_off/Tdash)))/(1.0-math.exp(-(ts/T))))\n",
"DutyRating=S*Rating #KW\n",
"\n",
"#Result\n",
"print\"(a) Short time rating of motor: \",round(ShortTimeRating,1),\"kW\"\n",
"print\"(b) Intermittent periodic duty rating: \",round(DutyRating,2),\"kW\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Short time rating of motor: 120.9 kW\n",
"(b) Intermittent periodic duty rating: 67.2 kW\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.10,Page no:63"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Variable declaration\n",
"T=90.0 #Heating time constant in [min]\n",
"t=25.0 #time in min \n",
"ShortTimeRating=50.0 #Short time rating in KW\n",
"Eff=80/100.0 #Efficiency\n",
"\n",
"#Calculation\n",
"#Let full load rating is P KW and Losses=Pc\n",
"#CuLoss=(P/(P*Eff))**2 & alfa=Pc/CuLoss\n",
"alfa=(Eff)**2 #unitless\n",
"S=math.sqrt(((1.0+alfa)/(1.0-math.exp(-t/T))-alfa)) \n",
"ContinuousRating_fl=ShortTimeRating/S #KW\n",
"\n",
"#Result\n",
"print\"Full load continuous rating: \",round(ContinuousRating_fl,1),\"kW\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Full load continuous rating: 20.2 kW\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.11,Page no:63"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Variable declaration\n",
"Rating=25.0 #Rating in [KW]\n",
"T=90.0 #Heating time constant in min\n",
"ts=30.0 #time in min\n",
"\n",
"#Calculation\n",
"S=math.sqrt(1.0/(1.0-math.exp(-ts/T))) \n",
"HalfHourRating=S*Rating #KW\n",
"\n",
"#Result\n",
"print\"Half hour rating of motor: \",round(HalfHourRating,2),\"kW\"\n",
"print\"Answer wrong in textbook.\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Half hour rating of motor: 46.96 kW\n",
"Answer wrong in textbook.\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.12,Page no:63"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration:\n",
"ts=20 #rating itme in [min]\n",
"W=300 #rating in [W]\n",
"T=60 #time constant in [minutes]\n",
"max_eff_load=0.8 #Maximum effeciency of motor at load\n",
"\n",
"#Calculations\n",
"import sympy\n",
"P=sympy.Symbol('P')\n",
"pc=sympy.Symbol('pc')\n",
"Full_load_CL=(P/(0.8*P))**2*pc\n",
"alpha=pc/Full_load_CL\n",
"S=math.sqrt((1.0+alpha)/(1-math.exp(-ts/64.0))-alpha)\n",
"Cont_rating=W/round(S,1)\n",
"\n",
"#Result\n",
"print\"Continuous rating of motor is :\",round(Cont_rating,1),\"W\"\n",
"print\"NOTE:There is a slight error in book in calculation of S,approximate value is taken\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Continuous rating of motor is : 130.4 W\n",
"NOTE:There is a slight error in book in calculation of S,approximate value is taken\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Continuous rating of motor is : 130.4 W\n",
"NOTE:There is a slight error in book in calculation of S,approximate value is taken\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.13,Page no:67"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"#Variable declaration\n",
"P=6.0 #poles\n",
"f=50.0 #Frequency in [Hz]\n",
"MoI=9.5 #Moment of inertia in [Kg-m**2]\n",
"Tr=550.0 #Torque in [N-m]\n",
"S=5.0/100.0 #Slip\n",
"Tmax=720.0 #MAximum torque in [N-m]\n",
"T_LH=1020.0 #Torque requirement in [N-m]\n",
"th=12.0 #Time in [sec]\n",
"Tmin=220.0 #Light torque req in [N-m]\n",
"Snl=3.0/100.0 #No load slip\n",
"Ns=120.0*f/P #Speed in rpm\n",
"\n",
"#Calculation\n",
"Nnl=Ns-Ns*Snl #rpm\n",
"Nrated=Ns-Ns*S #rpm\n",
"omega_mo=Nnl*2.0*math.pi/60.0 #rad/s\n",
"omega_mr=Nrated*2.0*math.pi/60.0 #rad/s\n",
"J=(Tr/(omega_mo-omega_mr))*(th/math.log((T_LH-Tmin)/(T_LH-Tmax))) #Kg-m**2\n",
"MoI_flywheel=J-MoI #Kg-m**2\n",
"\n",
"#Result\n",
"print\"Moment of inertia of flywheel : \",MoI_flywheel,\"kg-m^2\"\n",
"print\"NOTE:Answer in the book is wrong.\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Moment of inertia of flywheel : 3203.36081501 kg-m^2\n",
"NOTE:Answer in the book is wrong.\n"
]
}
],
"prompt_number": 26
}
],
"metadata": {}
}
]
}