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**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

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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√(Vg3 ) 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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**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

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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 bearings**

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**Brush friction power loss**

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**Ventilation power loss**

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**Eddy current power loss**

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Electrical power loss

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**Temperature fluctuation**

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**Armature resistance fluctuation**

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**Torque vs angular speed**

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**Torque vs electric current**

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**Angular speed vs electric current**

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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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