1. 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

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

3. 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

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

5. 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)])

6. 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)

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

8. 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

9. 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

10. 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

11. 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

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

13. Electrical power losses
Armature copper loss
Pcu=R ia2

14. 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]]

15. 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)

16. 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.

17. Angular velocity with deterministic and no deterministic disturbances

18. Friction power losses in the slip bearings

19. Brush friction power loss

20. Ventilation power loss

21. Eddy current power loss

22. Electrical power loss

23. Temperature fluctuation

24. Armature resistance fluctuation

25. Torque vs angular speed

26. Torque vs electric current

27. Angular speed vs electric current

28. 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

29. 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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