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Series Wound DC Motor Modeling and Simulation, Considering Magnetic, Mechanical and Electric Power Losses B.VIGNESH Edited By Sarath S Nair www.technologyfuturae.com 1

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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 2www.technologyfuturae.com

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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 3www.technologyfuturae.com

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Diagram of DC series motor (dotted line showing electrical, mechanical and magnetic component) 4www.technologyfuturae.com

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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+k 2 i 2 ( τ )]) 5www.technologyfuturae.com

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Armature current ia(τ)=ea/(R+kω(τ)) Torque T(τ)=ki a 2 ( τ ) Mechanical power Pm(τ)= ω ( τ)*T(τ) Electrical power Pe(τ)=ea*ia(τ) 6www.technologyfuturae.com

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Power loss Pp(τ)=Pe(τ)-Pm(τ) Efficiency η (τ)=Pm(τ)/Pe(τ) 7www.technologyfuturae.com

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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 8www.technologyfuturae.com

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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 P RC =0.52d g l g √(V g 3 ) Diameter dg=2.84√(Pm/n) Length lg=2.5dg Peripheral speed Vg=(∏.n.dg)/6000 9www.technologyfuturae.com

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If the machine has rolling bearings P RC =150(d g ) 3 n 10 -6 the result is multiplied by the number of bearings P RC= n c.P RC Brush friction power losses PRE P RE =9.81µ e PS e V col Peripheral speed Vcol=(∏.Dcol.n)/6000 Brushes surface friction Se=∑Brushes surface 10www.technologyfuturae.com

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Ventilation Losses P v =1.1 V V V 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 P MR =P RC +P RE +P V 11www.technologyfuturae.com

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Magnetic power loss Eddy current losses P f (t)=w 2 [ea] 2 /(12ρ (NA) 2 ) 12www.technologyfuturae.com

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Electrical power losses Armature copper loss P cu =R i a 2 13www.technologyfuturae.com

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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= ρ α20˚C [1+ α [T-20˚C]] Therefore R( τ )= ρ L/A =L/A ρ α20˚C [1+ α [T-20˚C]] 14www.technologyfuturae.com

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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+k 2 i 2 (t)]) Electrical current ia(τ)=ea/(R(τ)+kω(t)) Power losses P f (t)= w 2 [e(f)] 2 /(12 ρ α20˚C [1+ α [T-20˚C]] (NA) 2 ) Copper losses P cu =R( τ ) i a 2 ( τ ) 15www.technologyfuturae.com

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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. 16www.technologyfuturae.com

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Angular velocity with deterministic and no deterministic disturbances 17www.technologyfuturae.com

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Friction power losses in the slip bearings 18www.technologyfuturae.com

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Brush friction power loss 19www.technologyfuturae.com

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Ventilation power loss 20www.technologyfuturae.com

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Eddy current power loss 21www.technologyfuturae.com

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Electrical power loss 22www.technologyfuturae.com

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Temperature fluctuation 23www.technologyfuturae.com

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Armature resistance fluctuation 24www.technologyfuturae.com

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Torque vs angular speed 25www.technologyfuturae.com

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Torque vs electric current 26www.technologyfuturae.com

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Angular speed vs electric current 27www.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 28www.technologyfuturae.com

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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. 29www.technologyfuturae.com

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Log On to www.technologyfuturae.com Technical Presentations, Research Reviews, New designs & Developments

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THANK YOU 31www.technologyfuturae.com

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