B.VIGNESH Edited By Sarath S Nair technologyfuturae
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Series Wound DC Motor Modeling andSimulation, Considering Magnetic, Mechanicaland Electric Power Losses
B.VIGNESHEdited By
Sarath S Nairwww.technologyfuturae.com
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Contents
Introduction DC Series motor ideal model Series wound DC motor losses Mechnical losses Magnetic losses Electrical losses Additional losses Conclusion References
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Introduction
There are three types of DC motors: shunt wound DC motor, series wound DC motors, compound wound DC motor.
Has relatively high starting torques Has good accelerating torque Have low speed at high loads and high speed at low
loads Under same load conditions rating of series motor
will be less than for a shunt motor
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Diagram of DC series motor (dotted line showing electrical, mechanical and magnetic component)
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SERIES WOUND DC MOTOR IDEAL MODEL here there are no disturbances of any kind are
examined the power losses through the input and output power.
Hence we obtain the following equation Angular velocity ω(τ)= (ξ .k.i(τ).ea+RJ ω(τ - ξ))/ (RJ+ ξ [Rb+k2i2(τ)])
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Armature current ia(τ)=ea/(R+kω(τ)) Torque T(τ)=kia2(τ) Mechanical power Pm(τ)= ω ( τ)*T(τ) Electrical power Pe(τ)=ea*ia(τ)
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Power loss Pp(τ)=Pe(τ)-Pm(τ) Efficiency η (τ)=Pm(τ)/Pe(τ)
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SERIES WOUND DC MOTOR LOSSES
Within the DC motor components energy is exchanged between different sections in these exchange, there are power losses.
Mechanical losses Magnetic losses Electrical losses
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Mechanical losses the mechanical losses are found in surfaces in contact and
constant friction 1.Friction losses in the slip bearings These losses are due to continuous friction PRC=0.52dglg√(Vg
3 ) Diameter dg=2.84√(Pm/n) Length lg=2.5dg Peripheral speed Vg=(∏.n.dg)/6000
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If the machine has rolling bearings PRC =150(dg)3n 10-6 the result is multiplied by the number of bearings PRC= nc.PRC Brush friction power losses PRE PRE=9.81µePSeVcol
Peripheral speed Vcol=(∏.Dcol.n)/6000 Brushes surface friction Se=∑Brushes surface
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Ventilation Losses Pv=1.1 V VV
2
Cooling of motor is determined by V=∑losses transformed into heat/1000te The fan speed given by Vv=(∏.Dv.n)/6000 Mechanical losses of the machine PMR=PRC+PRE+PV
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Magnetic power loss
Eddy current losses Pf(t)=w2[ea]2/(12ρ (NA)2 )
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Electrical power losses
Armature copper loss Pcu=R ia2
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Additional losses In an electric machine there are areas in continuous
friction that can contribute to heat emission either by exposing to a long working time and / or by excessive load
The wire conductor resistance R= ρL/A The resistivity is given by ρ= ρα20˚C[1+ α [T-20˚C]] Therefore R(τ)= ρ L/A =L/A ρα20˚C[1+ α [T-20˚C]]
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In developing the mathematical model, there are equations where the resistance and resistivity of the material occurs. Then the following equations are rewritten:
ω(t)= (ξ .k.i(t).ea+R(τ)J ω(τ - ξ))/(R(τ)J+ ξ [R(τ)b+k2i2(t)]) Electrical current ia(τ)=ea/(R(τ)+kω(t)) Power losses Pf(t)= w2[e(f)]2 /(12 ρα20˚C[1+ α [T-20˚C]] (NA)2 ) Copper losses Pcu=R(τ) ia2(τ)
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GENERALIZATION OF A SERIES WOUND DC MOTOR In this section there is a more complete analysis, and
random noises are added aside from considering to the model, considering also the internal losses.
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Angular velocity with deterministic and no deterministic disturbances
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Friction power losses in the slip bearings18www.technologyfuturae.com
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Brush friction power loss19www.technologyfuturae.com
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Ventilation power loss 20www.technologyfuturae.com
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Eddy current power loss21www.technologyfuturae.com
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Electrical power loss22www.technologyfuturae.com
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Temperature fluctuation23www.technologyfuturae.com
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Armature resistance fluctuation24www.technologyfuturae.com
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Torque vs angular speed25www.technologyfuturae.com
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Torque vs electric current26www.technologyfuturae.com
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Angular speed vs electric current27www.technologyfuturae.com
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Conclusion
By including the powers losses in the series wound DC motor simulation in addition to the disturbances a series of graphs were obtained which give broader information of the possible behaviour of the system
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References
J. S. Valdez Martínez, P. Guevara López, J. J. Medel Juárez. Series Wound DC Motor Modeling and Simulation, Considering Magnetic, Mechanical and Electric Power Losses. Sept.09
B.L.Theraja.A.K.Theraja.A Textbook Electrical Technology.S.Chand and Company ltd.
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