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"name": ""
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 17: FRACTIONAL HORSE POWER MOTORS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.1,Page number: 570\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the slip and efficiency of induction motor.\"\"\"\n",
"\n",
"#Variable Declaration:\n",
"f=50 #Frequency rating of the induction motor(in Hertz) \n",
"P=4 #Number of poles in the induction motor \n",
"N=1410 #Speed of the motor(in rpm)\n",
"Po=375 #Output Power(in Watts)\n",
"V=230 #Voltage rating of the induction motor(in Volts) \n",
"I=2.9 #Input current(in Amperes)\n",
"pf=0.71 #Power factor(lagging) \n",
"\n",
"\n",
"#Calculations:\n",
"Ns=(120.0*f)/P\n",
"slip=(Ns-N)/Ns\n",
"\n",
"\n",
"#Result:\n",
"print \"Slip is %.2f percent.\" %(slip*100)\n",
"Pin=V*I*pf\n",
"efficiency=Po/Pin\n",
"print \"The efficiency is %.2f percent.\" %(efficiency*100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Slip is 6.00 percent.\n",
"The efficiency is 79.19 percent.\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.2,Page number: 570\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\n",
"\"\"\"Finding the currents and the power factor in the induction motor.\"\"\"\n",
"\n",
"from cmath import phase,rect,polar\n",
"from math import radians,degrees,cos\n",
"\n",
"#Variable Declartion:\n",
"V=rect(230,0) #Voltage rating of the split-phase induction motor(in Volts) \n",
"Z_M=5+ 12*1j #Impedance of the main winding(in Ohms)\n",
"Z_A=12+ 5*1j #Start-winding impedance(in Ohms)\n",
"\n",
"\n",
"#Calculations:\n",
"mod_Z_M=abs(Z_M)\n",
"mod_Z_A=abs(Z_A)\n",
"phi_M=phase(Z_M)\n",
"phi_A=phase(Z_A)\n",
"I_M=V/Z_M\n",
"mod_I_M=abs(I_M)\n",
"phi_I_M=degrees(phase(I_M))\n",
"I_A=V/Z_A\n",
"mod_I_A=abs(I_A)\n",
"phi_I_A=degrees(phase(I_A))\n",
"I_L=I_M+I_A\n",
"mod_I_L=abs(I_L)\n",
"phi_I_L=degrees(phase(I_L))\n",
"phi=phi_I_A-phi_I_M\n",
"pf=cos(radians(phi_I_L))\n",
"\n",
"\n",
"#Result:\n",
"print \"(a)The current in the main winding is %.2f A at a phase angle of %.2f degrees.\" %(mod_I_M,phi_I_M)\n",
"print \"(b)The current in the starting winding is %.2f A at a phase angle of %.2f degrees.\" %(mod_I_A,phi_I_A)\n",
"print \"(c)The line current is %.2f A at a phase angle of %.2f degrees.\" %(mod_I_L,phi_I_L)\n",
"print \"(d)The phase displacement between the two winding currents is %.2f degrees.\" %(phi)\n",
"print \"(e)The power factor is %.4f lagging.\" %(pf) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The current in the main winding is 17.69 A at a phase angle of -67.38 degrees.\n",
"(b)The current in the starting winding is 17.69 A at a phase angle of -22.62 degrees.\n",
"(c)The line current is 32.72 A at a phase angle of -45.00 degrees.\n",
"(d)The phase displacement between the two winding currents is 44.76 degrees.\n",
"(e)The power factor is 0.7071 lagging.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.3,Page number: 571\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the capacitance in series with the auxiliary winding to maximize starting torque.\"\"\"\n",
"\n",
"from math import radians,degrees,atan,pi,tan\n",
"\n",
"#Variable Declaration:\n",
"X_M=20 #Inductive reactance of the main winding(in Ohm)\n",
"R_M=2 #Resistance of the main winding(in Ohm)\n",
"X_A=5 #Inductive reactance of the auxiliary winding(in Ohm)\n",
"R_A=25 #Resistance of the auxiliary winding(in Ohm)\n",
"f=50 #Frequency rating of the split-phase induction motor(in Hertz) \n",
"\n",
"\n",
"#Calculations:\n",
"angle_M=atan(X_M/R_M)\n",
"angle_A=degrees(angle_M)-90\n",
"Xc=X_A-(R_A*tan(radians(angle_A)))\n",
"\n",
"\n",
"#Result:\n",
"C=1/(2*pi*f*Xc)\n",
"print \"The value of capacitance connected in series with the auxiliary winding to obtain maximum starting torque is %e F.\" %(C)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The value of capacitance connected in series with the auxiliary winding to obtain maximum starting torque is 4.244132e-04 F.\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.4,Page number: 576\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the resolution and shaft speed of a stepper motor.\"\"\"\n",
"\n",
"#Variable Declaration:\n",
"beta=2.5 #Step-angle of a stepper motor(in degrees)\n",
"step_freq=3600 #Stepping frequency(in pps)\n",
"\n",
"\n",
"#Calculations:\n",
"res=360/beta\n",
"number_steps=res*25\n",
"shaft_speed=(beta*step_freq)/360\n",
"\n",
"\n",
"#Result:\n",
"print \"(a)The resolution is %d steps per revolution.\" %(res)\n",
"print \"(b)The number of steps required for the shaft to make 25 revolutions=%d.\" %(number_steps)\n",
"print \"(c)The shaft speed is %.2f rps.\" %(shaft_speed)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The resolution is 144 steps per revolution.\n",
"(b)The number of steps required for the shaft to make 25 revolutions=3600.\n",
"(c)The shaft speed is 25.00 rps.\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.5,Page number:577\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the number of stator and rotor poles in a VR motor.\"\"\"\n",
"\n",
"#Variable Declaration:\n",
"m=3 #Number of phases\n",
"beta=15 #Step angle(in degrees)\n",
"\n",
"\n",
"#Calculations:\n",
"Nr=360/(m*beta)\n",
"Ns1=(Nr*360)/(360-(beta*Nr))\n",
"Ns2=(Nr*360)/(360+(beta*Nr))\n",
"\n",
"\n",
"#Result:\n",
"print \"(a) The number of rotor poles is %d.\" %(Nr)\n",
"print \"(b)\"\n",
"print \" Case 1: Ns>Nr\"\n",
"print \" The number of stator poles is %d. \\n\" %(Ns1)\n",
"print \" Case 2: Ns<Nr\"\n",
"print \" The number of stator poles is %d.\" %(Ns2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The number of rotor poles is 8.\n",
"(b)\n",
" Case 1: Ns>Nr\n",
" The number of stator poles is 12. \n",
"\n",
" Case 2: Ns<Nr\n",
" The number of stator poles is 6.\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17.6,Page number: 579\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the number of rotor and stator teeth in VR stepper motor.\"\"\"\n",
"\n",
"#Variable Declaration:\n",
"m=4 #Number of stacks\n",
"beta=1.8 #Step angle(in degrees)\n",
"\n",
"\n",
"#Calculations:\n",
"Nr=360/(m*beta)\n",
"Ns=Nr\n",
"\n",
"\n",
"#Result:\n",
"print \"The number of rotor teeth is %d.\" %(Nr)\n",
"print \"The number of stator teeth is %d.\" %(Ns)\n",
"print \"\\nNOTE: In a multistack stepper motor the number of stator teeth is same as that of the rotor teeth.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The number of rotor teeth is 50.\n",
"The number of stator teeth is 50.\n",
"\n",
"NOTE: In a multistack stepper motor the number of stator teeth is same as that of the rotor teeth.\n"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}