Finite Element Analysis of Electro-Finite Element Analysis of Electro-thermalthermal Field in a Brushless DC MotorField in a Brushless DC Motor

2004/01/172004/01/17

Sangjin ParkSangjin Park

PREM, Hanyang UniversityPREM, Hanyang University

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MotivationMotivation Thermal Problem in a Brushless DC MotorThermal Problem in a Brushless DC Motor

– Increase of Power ConsumptionIncrease of Power Consumption• High Speed DriveHigh Speed Drive

• Hydrodynamic BearingHydrodynamic Bearing

– High Heat Generation in a Computer Hard Disk DriveHigh Heat Generation in a Computer Hard Disk Drive• Performance Variation due to Elevated TemperaturePerformance Variation due to Elevated Temperature

< Structure of HDB Spindle Motor >< Structure of HDB Spindle Motor >

Hub

Shaft

YorkPMStatorCoil

Thrust pad

Thrust Bearing

Journal Bearing

Sleeve

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Prior ResearchPrior Research– Liu Z.J., Howe D., Mellor P.H. and Jenkins M.K., "Coupled Liu Z.J., Howe D., Mellor P.H. and Jenkins M.K., "Coupled

thermal and electromagnetic analysis of a permanent magnet thermal and electromagnetic analysis of a permanent magnet brushless DC servo motor," Sixth International Conference on brushless DC servo motor," Sixth International Conference on Electrical Machines and Drives, 1993.Electrical Machines and Drives, 1993.

– Sebastian T., "Temperature effects on torque production and Sebastian T., "Temperature effects on torque production and efficiency of PM motors using NdFeB magnets," IEEE efficiency of PM motors using NdFeB magnets," IEEE Transactions on Industry Applications, 1995.Transactions on Industry Applications, 1995.

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Method of AnalysisMethod of Analysis Electro-thermal Field AnalysisElectro-thermal Field Analysis

– Electromagnetic FieldElectromagnetic Field• Time-stepping Finite Element MethodTime-stepping Finite Element Method

– Thermal FieldThermal Field• Finite Element Method of Heat Conduction EquationFinite Element Method of Heat Conduction Equation

Temperature Dependent ParametersTemperature Dependent Parameters– Electrical Parameters: Coil Resistance, PM CharacteristicsElectrical Parameters: Coil Resistance, PM Characteristics

– Mechanical Parameters: Viscosity of Fluid Lubricant Mechanical Parameters: Viscosity of Fluid Lubricant

- - 55 - -

Electromagnetic Field AnalysisElectromagnetic Field Analysis Maxwell Equation (2D)Maxwell Equation (2D)

FE Formulation by Galerkin MethodFE Formulation by Galerkin Method

y

M

x

MvJ

y

Av

yx

Av

xxyzz

PMofionmagnetizat:

potentialvectormagnetic:

densitycurrent:

materialofyreluctivit:

where,

M

A

J

v

z

ieei

ieieez

e

xyzz

NWANA

dW

y

M

x

MvJ

y

Av

yx

Av

x

,

0

0

3

1

)(

SS

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Voltage Equation of Inverter CircuitVoltage Equation of Inverter Circuit

Sjj

jjjii

iii Vtd

d

td

IdLIR

td

d

td

IdLIR

0 Djj

jjjii

iii Vtd

d

td

IdLIR

td

d

td

IdLIR

Scc

cccaa

aaa Vtd

d

td

IdLIR

td

d

td

IdLIR

0 Dbb

bbbaa

aaa Vtd

d

td

IdLIR

td

d

td

IdLIR

0 cba III

A

B

C

A B C

A B C

V12

< Commutation< Commutation > > < Duty On< Duty On > >

< Duty Off< Duty Off > >

Consider PWM switching Consider PWM switching action of inverter circuitaction of inverter circuit

Consider freewheeling Consider freewheeling current through diodecurrent through diode

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Time Dependency (Backward Difference Method)Time Dependency (Backward Difference Method)

Torque CalculationTorque Calculation– Maxwell Stress TensorMaxwell Stress Tensor

Equation of Motion of a RotorEquation of Motion of a Rotor

Moving Mesh AlgorithmMoving Mesh Algorithm

t

ii

dt

di

t

AA

dt

d tttttt

,A

dABBrT r 0

1

LoadTTJ

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Thermal Field AnalysisThermal Field Analysis Transient Heat Conduction Equation (Axisymmetric Case)Transient Heat Conduction Equation (Axisymmetric Case)

– Governing EquationGoverning Equation

– Boundary ConditionBoundary Condition

FE Formulation by Galerkin MethodFE Formulation by Galerkin Method– Similar Procedure as Electromagnetic FieldSimilar Procedure as Electromagnetic Field

– Time Differential Term : Backward Difference MethodTime Differential Term : Backward Difference Method

t

Tcq

z

Tk

zr

Trk

rr p

1

3

2

10

0

0

),,(

SonTThnz

TKn

r

TK

Sonqnz

TKn

r

TK

SonTtzrT

zzrr

zzrr

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Heat Source ModelHeat Source Model– Copper LossCopper Loss

•

– Iron LossIron Loss• Experimental DataExperimental Data

– Disk Windage LossDisk Windage Loss• Experimental DataExperimental Data

– HDB Friction LossHDB Friction Loss• Experimental DataExperimental Data

• Consider Viscosity VariationConsider Viscosity Variation

0 2000 4000 6000 8000 100000

1

2

3

4

5

6

7

8

Speed [rpm]

Po

we

r [W

]

Nidec 7.2K (Motor + Disk3.5 + Cover)

Other Loss Copper Loss FDB Friction LossDisk Windage Loss

< Power Consumption Test of Analysis Model< Power Consumption Test of Analysis Model > >

RIqCoil2

DiskDisk Tq

ViscosityHDBHDB FTq

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Boundary ModelBoundary Model– Natural Convection Boundary ConditionNatural Convection Boundary Condition

– Heat Transfer Coefficient (Simplified Form) Heat Transfer Coefficient (Simplified Form) • Upper Surface of HDD (SUpper Surface of HDD (S11))

• Lower Surface of HDD (SLower Surface of HDD (S22))

• Side Surface of HDD (SSide Surface of HDD (S33))

RadiusLeTemperaturAmbientSurfaceTwhere

CmWL

Th o

,)(,

/32.1 24/1

RadiusLCmWL

Th o

,/59.0 24/1

HeightLCmWL

Th o

,/42.1 24/1

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Coupled VariableCoupled Variable Temperature Dependent VariablesTemperature Dependent Variables

– Phase ResistancePhase Resistance

– Residual Flux Density of Permanent MagnetResidual Flux Density of Permanent Magnet

– Viscosity of Fluid LubricantViscosity of Fluid Lubricant

33.4,1 00 ewhereTTRR

30.1,1 00 ewhereTTBB rr

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Electro-thermal AnalysisElectro-thermal Analysis Analysis ProcedureAnalysis Procedure

Difference of Time ConstantDifference of Time Constant– Modified Time-Step in the Thermal Field Modified Time-Step in the Thermal Field

Magnetic Field Analysis considering Driving CircuitMagnetic Field Analysis considering Driving Circuit

PI ControllerPI Controller MaxwellEquation

+VoltageEquation

MaxwellEquation

+VoltageEquation

Mechanical Field AnalysisMechanical Field Analysis

TON TOFF

0

0

Carrier Wave

+-Ωref

InverterInverter

Ω

Heat Conduction Analysis(Temperature Determination)

Heat Conduction Analysis(Temperature Determination)

Equation of MotionEquation of MotionTorque

e u Speed

Heat Source CalculationHeat Source CalculationCurrent

Temperature Dependent Variables- Coil Resistance- Br of PM- Viscosity Factor

Temperature Dependent Variables- Coil Resistance- Br of PM- Viscosity Factor

Moving Mesh Algorithmby Angular Displacement

Moving Mesh Algorithmby Angular Displacement

ttt

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Analysis ModelAnalysis Model Specification of Analysis ModelSpecification of Analysis Model

– Hydrodynamic Bearing Brushless DC MotorHydrodynamic Bearing Brushless DC Motor

QuantityQuantity ValueValueInput VoltageInput Voltage 12 12 VV

PWM frequencyPWM frequency 40,000 40,000 HzHz

Rated speedRated speed 7,200 7,200 rpmrpm

Air gap lengthAir gap length 0.25 0.25 mmmm

Phase resistancePhase resistance 1.933 1.933 ΩΩ

Residual flux density of permanent magnetResidual flux density of permanent magnet 0.7 0.7 TT

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Magnetic FE ModelMagnetic FE Model Thermal FE ModelThermal FE Model

Disk

Base Plate

Cover

< 8,464 Triangular Elements< 8,464 Triangular Elements > > < 7,004 Triangular Elements< 7,004 Triangular Elements > >

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ResultResult Electromagnetic and Thermal FE Field at Steady StateElectromagnetic and Thermal FE Field at Steady State

– Initial Temperature : 25 ℃Initial Temperature : 25 ℃– Ambient Temperaure : 40 ℃Ambient Temperaure : 40 ℃

Max. 50.03℃, Min. 44.80℃ (RGB order)

< Equivalent Potential Line< Equivalent Potential Line > > < Temperature Distribution< Temperature Distribution > >

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Result Result Thermal ParametersThermal Parameters

Temperature ProfileTemperature Profile– Coil and Permanent MagnetCoil and Permanent Magnet

0 500 1000 1500 2000 2500 3000 3500 400025

30

35

40

45

50

Time [sec]

Tem

pera

ture

[de

gree

s]

Coil TemperaturePM Temperature

Temperature at the steady stateTemperature at the steady state

Phase Resistance : 9.53% increasePhase Resistance : 9.53% increase BBrr of PM : 2.35% decrease of PM : 2.35% decrease

TemperatureTemperature

CoilCoil 48.8 ℃48.8 ℃

PMPM 48.5 ℃48.5 ℃

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Temperature ProfileTemperature Profile– Bearing AreaBearing Area

0 500 1000 1500 2000 2500 3000 3500 400025

30

35

40

45

50

Time [sec]

Tem

pera

ture

[de

gree

s]

Upper JournalLower JournalUpper Thrust Lower Thrust

Temperature at the steady stateTemperature at the steady state

Friction Torque : 47.7% decreaseFriction Torque : 47.7% decrease

TemperatureTemperature

Upper JournalUpper Journal 49.4 ℃49.4 ℃

Lower JournalLower Journal 49.2 ℃49.2 ℃

Upper ThrustUpper Thrust 48.8 ℃48.8 ℃

Lower ThrustLower Thrust 48.3 ℃48.3 ℃

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Result Result Electrical ParametersElectrical Parameters

Phase Current ProfilePhase Current Profile

0.3 0.302 0.304 0.306 0.308 0.31-1

-0.5

0

0.5

1

Time [sec.]

Cur

rent

[A

]

Phase Current

Phase APhase BPhase C

0.3 0.302 0.304 0.306 0.308 0.31-1

-0.5

0

0.5

1

Time [sec.]

Cur

rent

[A

]

Phase Current

Phase APhase BPhase C

Electromagnetic AnalysisElectromagnetic Analysis Electro-thermal AnalysisElectro-thermal Analysis

PWM Duty RatioPWM Duty Ratio 82.8 %82.8 % 80.3 % (+ 2.5%)80.3 % (+ 2.5%)

Phase CurrentPhase Current 385 385 mAmA 320 320 mA (- 17%)mA (- 17%)

Copper LossCopper Loss 573 573 mWmW 434 434 mW (- 24%)mW (- 24%)

< Electromagnetic Analysis < Electromagnetic Analysis 25 ℃25 ℃ > > < Electro-thermal Analysis< Electro-thermal Analysis > >

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Torque ProfileTorque Profile

0.3 0.302 0.304 0.306 0.308 0.310

1

2

3

4

5

6

7x 10

-3

Time [sec.]

Tor

que

[N-m

]

Torque

0.3 0.302 0.304 0.306 0.308 0.310

1

2

3

4

5

6

7x 10

-3

Time [sec.]

Tor

que

[N*m

]

Torque

< Electromagnetic Analysis < Electromagnetic Analysis 25 ℃25 ℃ > > < Electro-thermal Analysis< Electro-thermal Analysis > >

Electromagnetic AnalysisElectromagnetic Analysis Electro-thermal AnalysisElectro-thermal Analysis

Average Load TorqueAverage Load Torque 4.25 4.25 mN-mmN-m 3.30 3.30 mN-m (- 22.4%)mN-m (- 22.4%)

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ConclusionConclusion This research proposes a transient finite element method This research proposes a transient finite element method

to analyze the electro-thermal field of a HDB brushless to analyze the electro-thermal field of a HDB brushless DC motor.DC motor.

The electro-thermal analysis may predict the motor The electro-thermal analysis may predict the motor performance of a HDD, effectively.performance of a HDD, effectively.

ProblemProblem– Non-axisymmetric modelNon-axisymmetric model

– Numerical heat source calculationNumerical heat source calculation

– Consideration of air flowConsideration of air flow

– Experimental ValidationExperimental Validation