b.vignesh edited by sarath s nair technologyfuturae

Series Wound DC Motor Modeling andSimulation, Considering Magnetic, Mechanicaland Electric Power Losses

B.VIGNESHEdited By

Sarath S Nairwww.technologyfuturae.com

1www.technologyfuturae.com

Contents

Introduction DC Series motor ideal model Series wound DC motor losses Mechnical losses Magnetic losses Electrical losses Additional losses Conclusion References


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


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


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)])


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)


Power loss Pp(τ)=Pe(τ)-Pm(τ) Efficiency η (τ)=Pm(τ)/Pe(τ)


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


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


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


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


Magnetic power loss

Eddy current losses Pf(t)=w2[ea]2/(12ρ (NA)2 )


Electrical power losses

Armature copper loss Pcu=R ia2


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]]


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)


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.


Angular velocity with deterministic and no deterministic disturbances


Friction power losses in the slip bearings18www.technologyfuturae.com

Brush friction power loss19www.technologyfuturae.com

Ventilation power loss 20www.technologyfuturae.com

Eddy current power loss21www.technologyfuturae.com

Electrical power loss22www.technologyfuturae.com

Temperature fluctuation23www.technologyfuturae.com

Armature resistance fluctuation24www.technologyfuturae.com

Torque vs angular speed25www.technologyfuturae.com

Torque vs electric current26www.technologyfuturae.com

Angular speed vs electric current27www.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


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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