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

Contents Introduction DC Series motor ideal model Series wound DC motor losses Mechnical losses Magnetic losses Electrical losses Additional losses Conclusion References www.technologyfuturae.com

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 www.technologyfuturae.com

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

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)]) www.technologyfuturae.com

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) www.technologyfuturae.com

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

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 www.technologyfuturae.com

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√(Vg3 ) Diameter dg=2.84√(Pm/n) Length lg=2.5dg Peripheral speed Vg=(∏.n.dg)/6000 www.technologyfuturae.com

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 www.technologyfuturae.com

Cooling of motor is determined by Ventilation Losses Pv=1.1 V VV2 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 www.technologyfuturae.com

Magnetic power loss Eddy current losses Pf(t)=w2[ea]2/(12ρ (NA)2 ) www.technologyfuturae.com

Electrical power losses Armature copper loss Pcu=R ia2 www.technologyfuturae.com

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]] www.technologyfuturae.com

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) www.technologyfuturae.com

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. www.technologyfuturae.com

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

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

Brush friction power loss www.technologyfuturae.com

Ventilation power loss www.technologyfuturae.com

Eddy current power loss www.technologyfuturae.com

Electrical power loss www.technologyfuturae.com

Temperature fluctuation www.technologyfuturae.com

Armature resistance fluctuation www.technologyfuturae.com

Torque vs angular speed www.technologyfuturae.com

Torque vs electric current www.technologyfuturae.com

Angular speed vs electric current www.technologyfuturae.com

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 www.technologyfuturae.com

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. www.technologyfuturae.com

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