design and modelling of bldc motor for automotive applications42-48).pdf · design and modelling of...

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Int. J. Elec&Electr.Eng&Telecoms. 2015 E Elakkia et al., 2015

DESIGN AND MODELLING OF BLDC MOTOR FORAUTOMOTIVE APPLICATIONS

E Elakkia1*, S Anita1, R Girish Ganesan1 and S Saikiran2

*Corresponding Author: E Elakkia,[email protected]

This paper presents design, simulation and analysis of three phase BLDC motor for automotiveapplications. Finite Element Analysis (FEA) of the BLDC motor is done to confirm the flux linkagecharacteristics of the design. The proposed BLDC motor is designed and simulated using FEAbased design software tool MotorSolve. Simulation results from the design software tool focuseson the torque and magnetic flux density distribution. The BLDC motor is modelled using MATLAB/SIMULINK and the dynamic characteristics of PMBLDC motor are monitored.

Keywords: Finite Element Analysis (FEA), BLDC motor, Electronic commutation

INTRODUCTIONThe BLDC motor is the most preferredmachine for automotive application, as it hashigh reliability and efficiency. It has thecapability to provide large volume of torquefor wide speed ranges. Electroniccommutation technique and permanentmagnet rotor cause BLDC to have immediateadvantages over brushed DC motor andinduction motor in electric vehicle application[6], [15], [17].

The BLDC motor construction is similar tothe ac permanent magnet synchronous motorwith permanent magnets on the rotor andwindings on the stator [12]. The energized

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1 RMK Engineering College, Kavaraipettai.2 BOSCH Electrical Drives India Pvt. Ltd., Bangalore, India.

stator windings create electromagnet polesand permanent magnets create the rotor flux.A rotating field is created on the stator andmaintained, by using the appropriatesequence to supply the stator phases. Theenergized stator phase attracts the rotor. Thisaction of rotor chasing after the electromagnetpoles on the stator is the fundamental actionused in brushless permanent magnet motors.The BLDC motor operates based on the rotorposition information. According to the rotorposition, the phase windings are switched ina sequence to obtain the rotation [14] [16]. Thetorque developed in BLDCM is affected by thewaveform of back-Emf. Usually the BLDCmotor has trapezoidal back-Emf waveform

Research Paper

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and stator is fed by rectangular stator currentand theoretically it gives a constant torque butthe torque ripple exists due to current ripple,emf waveform imperfection and phase currentcommutation [13].

Electronic commutation of BLDC Motorcontrol algorithm is more complex comparedto other motor types. Therefore accurate modelof motor is required to have complete andprecise control scheme of BLDC. A motormodel providing torque for related values ofcurrent and back emf is required to design thedrive system [15].

On obtaining the analytical designparameters the electromagnetic analysis isgenerally done using finite element methodwhich provides solutions based on numericalmethods. The method basically involves thediscretization of the motor cross-section intosmaller areas called finite elements. By usingFEM, it is possible to make the accurate fieldcalculations in the electrical machines [7].

ANALYTICAL DESIGNThe analytical designing available in MotorSolve provides an initial design of a motormodel. It gives a complete design includingdimensions, winding layout, phase coil detailsand end turn electrical parameters.

In order to determine the size of a radial fluxmotor that will produce a required torque, thefollowing scaling law can be used [9].

2 (1)r

T KD L

where k is a constant, Dr is the rotor outerdiameter and L is the stack length.

where,

(2)sL rD

(3)rs

DD

f

where Ds is the stator outer diameter, r is motoraspect ratio and f is rotor-stator ratio, (1) canbe expressed as:

3 (4)r

rT K D

f

Approximate expressions for stator androtor dimensions can be obtained relating thedimensions of the ferromagnetic portions ofthe motor to the number of magnet poles, thenumber of slots and the rotor outside radius

Tooth width, (5)r gtb

s st t

D Bw

N K B

Back iron Depth, (6)2

r gsy

m st t

D Bw

N K B

Core thickness, (7)2

r gry

m st ry

D Bw

N K B

where, Ns is No. of slots, Nm is No. of poles,Kst is Stacking factor. Bt, Bsy, Bry are fixedmaximum flux density specified in the statorteeth, the back iron depth and rotor core andBg, Flux density in the air gap.

Power balance between the input power Pi,the mechanical power Pm and the windingslosses Pl is expressed as:

(8)i m lP P P

Input power is given by,

cos (9)i ph rms rmsP N V I

where, 1 (10 )

2 2 3

peak lin er m s

V VV

the mechanical power is given by

2 (11)

60m r pmP T V T

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and the losses (include the Ohmic loss in thecoil sides only, the losses in the end turns aswell as the core losses are not taken intoaccount) are given by

2 ( 12)l s s rm sP N R I

where, (13)s l

LR NN

A

where, Nph is No. of phases, Ns is No. of slots,Irms is Rated current, Vline is supply voltage, is coil material conductivity, Nl is No. of layers,N is No.of turns and Aw is conductor area [4]and [8].

FINITE ELEMENT ANALYSISOF BLDC MOTOR USINGMOTORSOLVEThree phase, four pole BLDC is designedusing FEA based design software MotorSolveBLDC. Results obtained are analyzed.

Design Of BLDC Motor UsingMotorsolve BLDC SoftwareMotorSolve BLDC is electric motor designsoftware for brushless dc and permanentmagnet AC machines which provides easy-to-use templates and an automated-FEAsolver to calculate performance. Meeting thegrowing demand for higher efficiency andlower costs requires software that deliversreliable results and does not give falsepredictions for crucial performance factorsresulting in avoidable and costlycomplications. Modern electric motorsperformance cannot be predicted by generalapproximations and magnetic circuitcalculations. In FEA simulations:

• Performance is predictable duringsaturation.

• All sources of loss are accounted such aseddy current and hysteresis.

The geometrical dimensions of the machineare designed using MotorSolve software. Thespecification of the PMBLDC motor modelledfor this project, are given below in Table 1. Thecomputer-aided design is usually the first partsof the electric motor development. TheInfolytica MotorSolve is electric motor designsoftware for brushless DC motor. In this motordesign is obtained applying differenttemplates. The parameters of the electricmotor such as torque, losses, power and theothers are calculated by the help of anautomated-FEA (Finite Element Analysis)solver. The machine can be designed with thespecified parameters like the materials for theconstruction of stator, the material for the rotor,number of stator slots and number of rotorteeth. From this FEM we can calculate theperformance of the motor very accurately andprecisely. The output of the designed motor inthe FEM contains the output parameters likeback EMF, torque characteristics, etc. Thedisadvantage of the program is that the motor

Parameter Values

Number of phases 3

Number of armature slots 12

Number of poles 4

Outer radius of stator (mm) 45

Inner radius of stator (mm) 25

Outer radius of rotor (mm) 24.5

Inner radius of rotor (mm) 4

Magnet thickness (mm) 5

Magnet gap angle 0

Air gap thickness (mm) 0.5

Stack length (mm) 60

Table 1: BLDC Motor Specifications

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can be designed by using some definedtemplates only. The easy applicability is theadvantage of this program [5] and [9].

The cross section of Brushless DC motoris shown in Figure 1. The simulation resultsobtained from motorsolve software is shownin following figures. Distribution of flux densitywithin the motor is shown in Figure 2. Torquewaveform with oscillation and Back EMFwaveform is shown in Figures 3 and 4. Figure5 shows torque remains constant up to certainspeed and then it decreases as speedincreases.

Figure 1: Overall Model of BLDC UsingMotor Solve

Figure 2: Flux Density Distributionof BLDC Motor

Figure 3: Torque vs Source Phase AngleWaveform

Figure 4: Back EMF Waveformof BLDC Motor

Figure 5: Torque vs Rotor Speed

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MATHEMATICAL MODELLINGOF BLDC MOTORIn this paper a 3 phase, 4 pole, star connectedtrapezoidal back-EMF type BLDC is modelled.The back-emf is trapezoidal due to thetrapezoidal mutual inductance between statorand rotor.

Overall model is simplified using followingassumptions:

• Saturation in magnetic circuit is ignored.

• All phases have constant and equal statorresistance, self and mutual inductance.

• Losses such as Hysteresis and eddycurrent are eliminated.

• All semiconductor switches are ideal.

The dynamics of the machine are describedby a set of mathematical differential equations.The electrical and mechanical equations canbe obtained from the equivalent circuit shownin Figure 6.

( ) (16 )cc c c

diV Ri L M e

dt

where

R : Stator resistance per phase,

L : Stator inductance per phase,

M : Mutual inductance between phases.

ia, ib, ic : Stator current/phase.

Va, Vb, Vc : The respective phase voltage ofwinding.

The instantaneous back EMF in BLDC isexpressed as:

( ) (1 7 )a a ee f K

( ) ( 1 8 )b b ee f K

( ) (1 9 )c c ee f K

where, is the rotor mechanical speed, Ke isthe back EMF constant and is the rotorelectrical position.

The electric torque produced by each phaseis the product of the supply current I and themotor constant Kt and.

( ) (2 0 )a a t aT f K i

( ) (2 1 )b b t bT f K i

( ) ( 2 2 )c c t cT f K i

Thus the resultant electromagnetic torqueTe in N-M can be expressed as follows:

( 2 3 )e a b cT T T T

For simple system ,the equation of motionis,

(24 )e l

dJ B T T

dt

Figure 6: Equivalent Circuit of BLDC Motor

The modelled equations for armaturewinding of BLDC motor are as follows.

( ) (1 4)aa a a

diV R i L M e

dt

( ) ( 1 5 )bb b b

d iV R i L M e

d t

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where, Te is electromagnetic torque, Tl is theload torque, J is motor inertia, B is dampingconstant [1], [3] and [14].

The PMBLDC motor is modelled inMATLAB/SIMULINK by using abovemathematical equations.

CONCLUSIONThe proposed BLDC motor is designedanalytically and analyzed using finite elementanalysis. The mathematical modeling is doneusing Matlab to verify the characteristics.

REFERENCES1. Abdolamir Nekoubin (2006), “Design a

Single-Phase BLDC Motor and Finite-Element Analysis of Stator Slots StructureEffects on the Efficiency”, WorldAcademy of Science, Engineering andTechnology, Vol. 5, No. 5.

2. Duane Hanselman (2006), BrushlessPermanent Magnet Motor Design, 2nd

Edition, Magna Physics Publishing.

3. Gencer C and Gedikpinar M (2006),“Modeling and Simulation of BLDCM

Motor Parameter Values

voltage 12 V

Rated speed 1000 rpm

Rated torque 1 Nm

Per phase resistance 0.1296

Per phase inductance 36.12 H

Back emf constant 4.775*10-2V/radS-1

Torque constant 0.04 Nm/A

No. of poles 4

Table 2: BLDC Motor Specification

Simulation ResultsThe simulation results of modelling ofpermanent magnet brushless DC motor areobtained by MATLAB/SIMULINK. The motorspecifications are given in the Table 2. Theback emf waveform for phase A, B and Cis shown in Figures 7, 8 and 9 respectively.Trapezoidal back emf is obtained by usingthe rotor position information. Three backe m f ea, eb, ec displaced from one anotherby 120°.

Figure 7: Backemf for Phase A

Figure 8: Backemf for Phase B

Figure 9: Backemf for Phase C

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Using MATLAB/SIMULINK”, Journal ofApplied Sciences, Vol. 6, No. 3, pp. 688-691, ISSN 1812-5654.

4. Hendershot J R and Miller T J E (1994),“Design of Brushless Permanent -Magnet Motor”, Magna PhysicsPublications.

5. Hong-Xing Wu, Shu-Kang Cheng andShu-Mei Cui (2005), “A Controller ofBrushless DC Motor for Electric Vehicle”,IEEE Trans. on Magnetics, Vol. 41,No. 1, pp. 509-513.

6. Jainesh M Patel, Hitesh V Hirvaniya andMulav Rathod (2014), “Simulation andAnalysis of Brushless DC Motor Basedon Sinusoidal PWM Control”, Vol. 2,No. 3, pp. 1236-1238.

7. James R Hendershot, “Brushless DCMotor Phase, Pole and SlotConfigurations”, Magna PhysicsCorporation, Hillsboro,Ohio.

8. Kovács G and Kuczmann M (2013),“Simulation of A PM Motor by the Help ofTwo Different Design Software Tools”,Bulletin of the Transilvania University ofBraov Series I: EngineeringSciences,Vol. 6, No. 55, No. 1.

9. Majid Pakdel (2009), “Analysis of theMagnetic Flux Density, the MagneticForce and the Torque in a 3D BrushlessDC Motor”, J. Electromagnetic Analysis& Applications, Vol. 1.

10. Nishtha Shrivastava and Anil Brahmin(2014), “Design of 3-Phase BLDC Motorfor Electric Vehicle Application by UsingFinite Element Simulation”, InternationalJournal of Emerging Technology andAdvanced Engineering, Vol. 4, No. 1.

11. Padmaraja Yedamale (2003), “BrushlessDC (BLDC) Motor Fundamentals”,AN885, Microchip Technology Inc.

12. Pramod Pal, Shubhum T M and Dr AmitOjha (2014), “Simulation of Brushless DCMotor for Performance Analysis UsingMATLAB/SIMULINK Environment”, Vol. 2,No. 6, pp. 1564-1567.

13. Purna Chandra Rao A, Obulesh Y P andCh Sai Babu (2012), “MathematicalModeling of BLDC Motor with ClosedLoop Speed Control Using PID ControllerUnder Various Loading Conditions”,ARPN Journal of Engineering andApplied Sciences, Vol. 7, No. 10, ISSN1819-6608.

14. Pushek Madaan (2013), “Brushless DCMotors – Part I: Construction andOperating Principles”, CypressSemiconductor.

15. Tashakori A, Ektesabi M andHosseinzadeh N (2010), “Characteristicof Suitable Drive Train for ElectricVehicle”, 3rd International Conference onPower Electronic and IntelligentTransportation System (PEITS),November 20-21.

16. Tashakori M Ektesabi and HosseinzedehN (2011), “Modeling of BLDC Motor withIdeal Back EMF for AutomotiveApplication”, World Congress onEngineering (WEC), Vol. II, pp. 978-988.

17. Tony Mathew and Caroline Ann Sam(2013), “Modeling and Closed LoopControl of BLDC Motor Using A SingleCurrent Sensor”, International Journal ofAdvanced Research in ElectricalElectronics and InstrumentationEngineering, Vol. 2, No. 6.

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