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Software Design tool for Optimum Axial FluxBLDC Motors

J.W.K.K. Jayasundara∗, Rohan Munasinghe†∗Department of Electronic and Telecommunication

University of Moratuwa, Katubedda, MoratuwaEmail: kosala@ent.mrt.ac.lk

†Department of Electronic and Telecommunication,University of Moratuwa,Email: rohan@ent.mrt.ac.lk

Abstract— The Axial Flux BLDC motors are relatively new,specially at higher power ratings over 10kW. Therefore thedesigners face a lot of difficulties in designing and optimizingthe motor for a given application. This paper presents a newmethod to optimize the performance in speed, torque, torquestability, power output, power density and motor dimensions inview of the cost and reliability for a given motor; specially to beused for traction purposes. By this method, the motor designerscan easily choose the exact parameters of the motor to match therequirement and make sure of the optimization of the design. Asoftware interface and simulation results are presented to checkthe level of optimization achievable with the system. This paperdiscusses a three phase axial flux outer rotor BLDC motor, butthe core equations can be easily changed to simulate for any kindof motor with the same software and simulation interface.

I. INTRODUCTION

BLDC motor design and simulation has been one of themain research fields in the electric drives design. There are alot of designs in the axial flux motors for traction purposes.

The BLDC motor simulation is mainly done for a narrowconsideration. In Ref. [10], a Matlab / Simulink model wasdesigned for a comprehensive analysis of a given motor interms of BLDC motor drive characteristics and a GraphicalUser Interface. In Ref. [12], the motor optimization is sim-ulated for the standard and straight tooth shapes in terms ofefficiency for a high efficient solar powered aircraft. In Ref.[11], a BLDC model is simulated for a very precise torquecalculation by calculating the real back EMF and the deviationof the back EMF with the different magnet type selection.Also a few commercial software are available for a completesimulation of a given BLDC motor and show the motor outputparameters including finite element analysis.

There are a few other papers that discuss different aspects ofthe motor simulation, but all these papers including the threepapers discussed above are concerned only on a very narrowarea of the motor design. It’s hard to find any simulationthat takes into consideration the variation of many designparameters such as the magnet size, air gap, number of torqueetc.. and the variation of motor output parameters (torque,power output, efficiency, cost) with them. Also the variationof the motor manufacturing cost with these design parametersare not found. Further, the simulations are for a single type ofmotor design or an optimization with a single parameter. There

is no discussion on the overall optimization with differentweights on the motor output parameters.

Very comprehensive BLDC motor designs can be found inRef. [3],[8] and a lot of other papers. This paper is based on aprevious design [1] for an axial flux double outer rotor BLDCmotor with a broader and more general design range.

This paper discusses on a simulation and optimization soft-ware on a general BLDC motor to optimize the performanceaccording to a given set of requirements. Therefore the samesimulation can be used to optimize a full range of BLDCmotors. Also the consideration of all the key design and outputparameters makes the simulation a complete motor design toolwithout having a very deep analysis on individual parameters,which would make the simulation too much complex andtake the simulation out of the scope of this research. Theoptimization value and the variation plots of the motor outputparameters against the design parameters allow the user tochoose the most optimized and best motor for his requirementwithout much effort.

The scope of the paper limits to three phase axial flux BLDCmotors which is the most common type of BLDC motor usedin traction purposes, but the same procedure can be used forany kind of a motor with a little modification to the equationset.

II. ARCHITECTURE OF THE DESIGN TOOL

A. Functional Block Diagram

This software design tool is using a mathematical equationset as the model of the motor [1],[3]. Out of them, only theimportant equations are presented here. The required motoroutput parameters such as peak and average power, peak andaverage torque, torque speed curve and number of poles aresupplied to the simulator. The simulator then calculates thephysical motor parameters such as the number of windings,efficiency, rated current etc. Also the variation of the userparameters (motor output parameters) are plotted against thecalculated physical motor parameters. This helps a lot inchanging these physical parameters to optimize the motorwhile keeping the motor requirements intact. A basic blockdiagram of the simulator is shown in the Fig. 1.

An overall optimization value is calculated according to theuser requirement of the power, torque, efficiency and cost. This

Fourth International Conference on Industrial and Information Systems, ICIIS 2009, 28 - 31 December 2009, Sri Lanka

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Fig. 1. Motor Simulator Flow Chart

optimization value gives a direct idea of whether the designedmotor would match the user requirement. The motor designercan alter the design according to the output plots obtainedand the optimization value. Interpolations of the optimizationvalue can be achieved through the simulation software itself.

B. Motor Design EquationsThe equations are presented for the design of an axial

flux double outer stator three phase brushless DC motor. Theparameters in the equation are divided into motor designparameters and motor output parameters for the simulationpurposes. Only the core equations governing the simulationare given herewith and a more general set of equations for amulti phase PMSM can be found in reference [3],[1].

The motor (winding) flux linkage

Bm =Bmagnet

1 + µrm

2.Lm(4.Lg + 2.Ll

µl+ 4.Li

µi)

(1)

The flux linkage of a BLDC motor

λw = Tw/Iw (2)

The number of turns per winding

Nw = λw/[BmAshoe] (3)

The winding resistance needed

Rw = [Vw − Vbackemf ]/Iw (4)

Therefore the cable gauge can be calculated by

Acopper = NwLturnρcopper/Rw (5)

Stator Slot dimension can be calculated for the given wire sizeand packing factor

Lstator[Wshoe −Wwinding] = 2AcopperNwαpacking (6)

The number of windings per pole can be calculated as,

npole =λp

BmπApole(7)

where λp - the required flux linkage and the Apole - polelamination cross section area An additional amount of 5% willbe added to the total loss as a rule of thumb to represent theuncounted losses.

Ptotal = 1.05[Pcore + Pcopper + Peddi + Pbearing] (8)

III. DESIGN OPTIMIZATION

A. Optimization Procedure

The full set of equations including shown in Equ. 1 throughEqu. 8 can be arranged to a multi dimensional matrix withdifferent key design parameters being sweeped in an array ofpossible values. Hence the resultant matrix can be analyzedin terms of efficiency, power output and torque for extractingthe best possible combination of the input parameters.

The set of equations used to calculate the outputs in a singlepoint in the multi dimensional matrix can be represented as,

Pr1,r2..rm

ηr1,r2..rm

Cr1,r2..rm

Sr1,r2..rm

Or1,r2..rm

=

λ11 λ12 .... λ1n

λ21 λ22 .... λ2n

λ31 λ32 .... λ3n

λ41 λ42 .... λ4n

λ51 λ52 .... λ5n

.

V 1r1

V 2r2

....V nrm

Where P=power output, η=efficiency, C=cost, S=size of the

motor, O=grade of optimization V1,V2... Vn are the set of allinput parameters considered and hence the matrix becomes an’n’ dimension matrix. The r1,r2..rm location in the matrix isthe place where the output parameters are considered.

With each key variable being changed in the set of possiblevalues, the matrix can be extended to a multi dimensionalmatrix for analysis.

Due to the limitation of the graphs to three dimensional,only two input parameters (X and Y) can be varied for gettingthe output. Therefore the designer must fix the remaining inputparameters to obtain the plot.

As the optimization points of each of the output parameters(power output, efficiency, motor size and cost) are on differentlocations, a combination of the outputs is necessary for opti-mization. Therefore the outputs are weighted and added to getthe overall optimization value, which would get different typesof motors with different weights selected. For an example, theoptimization point of a high cost but very compact, higherefficient motor would vary greatly from a low cost motor ofthe same type. The optimization value is calculated as,

Optin = γp×Powern−γc×Costn+γη×ηn−γs×Sizen (9)

By getting the peaks of this Optimization plot, the optimummotors can easily be selected.

With the multi dimensional matrix, the full optimizationpoint can be selected for all the given variables by simplychoosing the highest value in the matrix. This point, whichcan’t be plotted with all the variables, can be calculatedand shown to the designer. This way, a direct set of inputparameters for the best optimization point would be obtained.

The multi dimensional matrix can be shrinked to a set of twodimensional graphs of each output variable by representing theinput parameters by different color curves. This way, a fulldetailed and flexible way is supplied to the designer to selectthe input parameters from any point of the graph according tohis requirement.

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Fig. 2. Motor torque - speed plot

B. User Interface

A number of input parameters must be entered for the simu-lations. They are basically taken as the required motor outputcharacteristics. Then the motor design parameters would becalculated accordingly. The most important input parametersare,

1. Torque-Speed curve: The main characteristic curve of anymotor is the Torque-Speed curve. The BLDC motors havea fixed type of characteristic plot as shown in the Fig. 2.Therefore the plot is a liner equation on which the designershould decide about the peak torque and peak RPM.

2. Dimensional Limitation: The designer should limit thedimensions of the motor such as the maximum radial diameter,minimum air gap, maximum magnet area, maximum axiallength etc. for the output parameter plots to be generatedwithin the limits given.

3. Performance Limitation: The minimum performance fac-tors such as efficiency, torque stability, maximum cost etcwould be set by the designer to limit the design within therange.

4. Cost limitation : The cost can be limited within thedesign, which can be used as a criteria for constraining thenumber of phases, size, magnet size etc within the design.

5. Optimization value : The individual preferences of themotor design in terms of cost, size, power, torque, efficiencycan be fed in to the system on which the current optimizationpercentage would be calculated. This will distinctively givea precise idea about how much effective the current motordesign is, and an easier way to obtain the best motor for agiven application.

Output parameters are of two types:1. Motor Design Parameters: The fixed motor design pa-

rameters such as the optimization value, number of windingsper pole, the magnet sizes, winding pole sizes, minimum shaftdiameters, bearing sizes etc. which are used to manufacture the

motor. These parameters can be fed back to change the inputparameters accordingly.

2. Motor Output Parameters: The parameters and plots suchas efficiency, torque, power output, speed, torque stability,motor dimensions, cost etc. which are the motor outputsneeded for the user. These parameters would be varied withthe appropriate input parameters for the designer to choose anoptimized value for the set of the collective values. Parameterplots would help to ease the decision and to get an idea ofthe direction and amplitude of interpolation for the motoroptimization.

The basic motor design requirements can be input tothe designed Matlab software and all the necessary designparameters can be obtained as in the Fig. 3. The MatlabGuide software was used to design the simulation to make itcomfortable for any vehicle designer without a sound Matlabknowledge to use the simulator. Also the optimization valuesand the characteristic curves will be displayed in a singlecommand.

IV. IMPLEMENTATION AND RESULTS

The simulator can be used for obtaining the motor charac-teristic curves and the torque, efficiency, cost and size againstdifferent types of motor design parameters such as the motordiameter, number of windings, air gap etc. as in the Fig. 4through Fig. 9. The total optimization value will be calculatedaccording to the designer requirement. By referring to thesecurves and the optimization values, the designer can easilychoose the optimum physical parameters of his design withoutgoing in to rigerrous calculations.

The Fig. 4 shows the average torque Vs. the rotor ring radiusfor a fixed radial length magnets and the optimum radial sizemagnets (in which the magnet radial length linearly increaseswith the rotor ring radius).It clearly shows the change of thetorque with the magnet size and the crossing point betweenthe variable magnet sizes and fixed magnet sizes (at mark A),after which the variable size magnets will be better.

Figure 5 shows the peak torque Vs. the rotor ring radius,which is almost the same as the Fig. 4. It is used when thepeak torque is considered. In each plot of the variation oftorque with some motor physical parameter, both the peakand average torques are considered. But only the averagetorque variation is shown in the graphs in this paper for otherparameter changes.

Figure 6 shows the change of the torque with the numberof windings per pole, while keeping all the other parametersconstant. But as the motor radius must be increased when thenumber of windings are to be increased, this curve would, inpractice, become a x3 curve. Therefore this linear plot is validonly for little changes in the number of windings for whichthe radius need not be changed.

Figure 7 shows the change of the torque with the air gap.The practical implementation of a very small air gap is achallenging task and highly costly. Therefore it is suggestedthat the knee point of this graps (at mark A) would be

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Fig. 3. The MATLAB GUI for motor simulation

selected as the motor air gap to compensate the torque andthe efficiency with the cost and simpler design.

Figure 8 show the change of the overall cost with the rotorradius (which can be considered as the actual size of themotor). While the cost depends on the number of windingsand other few factors, the main consideration is with the size.The calculation of the cost is highly variable with the time,availability of the resources and expertise; but the currentvalues were calculated from the practical expenses neededfor manufacturing the motor locally. Therefore the cost factorshould be changed according to the above parameters to suitethe designer’s own environment.

In the Fig. 9, the same calculation is done with the optimummagnet size. This magnet size also increases the torque in thesame way. But as can be seen from the curve, it also increasesthe overall cost at higher rate than the fixed magnet sizes.

V. CONCLUSION

With this system; the motor designs can be much optimizedin a very short time, less effort and knoledge requirement.

While the standard procedure is to use the years of experiencein motor design to optimize the results manually and checkfor the performance in each design, this system can automatethe process and make sure that the designer gets the mostoptimum design within the range.

The manual output graphs analysis still requires a goodexpertise due to the multi-dimensional nature. As a result,some of the variables must be fixed to analyze for a given setof three variables (in three dimensional space). Even thoughan automated process of motor design optimization can selectthe optimum set of parameters, it may not exactly match thedesigner requirement which is very hard to take into an equa-tion, (the definition of the optimization weights). Therefore itis recommended that this issue would be addressed in furtherto obtain a way to analyze the optimization weights from directuser requirements.

ACKNOWLEDGMENT

J. W. K. K. Jayasundara Author thanks the extensive con-tribution that Dr. late D.A.I. Munindradasa had rended for the

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Fig. 4. Motor Average Torque Vs. Rotor ring radius

Fig. 5. Motor Peak Torque Vs. Rotor ring radius

research.”

REFERENCES

[1] J.W.K.K. Jayasundara, D.A.I. Munindradasa Design of multi phase in-wheel axial flux permanent magnet motor for electric vehicles, ICIISconference 2006

[2] J.W.K.K. Jayasundara, D.A.I. Munindradasa Novel Sinusoidal PWMController strategy for axial flux permanent magnet motors, ICIISconference 2006

[3] F. Sahin, Design and Development of a high-speed Axial-flux permanent-magnet machine, Doctoral Thesis, ISBN 90-386-1380-1, Eidenhoven.

[4] A. Parviainen, Design of axial-flux permanent-magnet low-speed ma-chines and performance comparison between radial-flux and axial-fluxmachines, Doctoral Thesis, ISBN 952-214-029-5, Lappeenranta Univer-sity of Technology.

[5] A.J.A. Vandenput, A.M. Tuckey, F. Sahin, Design, development andtesting of a high-speed axial-fluxpermanent-magnet machine, IndustryApplications Conference, 2001

[6] V S Ramsden1, B C Mecrow2, H C Lovatt, DESIGN OF AN IN-WHEELMOTOR FOR A SOLAR-POWERED ELECTRIC VEHICLE, EighthInternational Conference on Electrical Machines and Drives, 1997

Fig. 6. Motor Peak Torque Vs. Number of windings per pole

Fig. 7. Motor Peak Torque Vs. air gap

[7] . Krvel, R. Nilssen, S. E. Skaar, E. Lvli, N. Sandy2, Design ofan Integrated 100kW Permanent Magnet Synchronous Machine in aPrototype Thruster for Ship Propulsion, ICEM2004, Cracow, Poland,5-8. Sept. 2004

[8] Metin Aydin, Surong Huang, Thomas A. Lipo, A New Axial Flux SurfaceMounted Permanent Magnet Machine Capable of Field Control, IndustryApplications Conference, 37th IAS Annual Meeting, 2002

[9] Duane Hanselman, Brushless Permanent Magnet Motor Design, SecondEdition, Published by: Writers’ Collective, 2003, ISBN: 9781932133639

[10] Wonbok Hong, Wootaik Lee, Byoung-Kuk Lee Dynamic Simulationof Brushless DC Motor Drives Considering Phase Commutation forAutomotive Applications, IEEE International Conference on ElectricMachines Drives, 2007.

[11] Jeon, Y.S. Mok, H.S. Choe, G.H. Kim, D.K. Ryu, J.S. A new simulationmodel of BLDC motor with real back EMF waveform, The 7th Workshopon Computers in Power Electronics, 2000.

[12] Perriard, Y. Ragot, P. Markovic, M. Brushless DC Motor OptimizationProcess - Choice between Standard or Straight Tooth Shape, IndustryApplications Conference, 2006. 41st IAS Annual Meeting.

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Fig. 8. Motor Cost Vs. motor radius

Fig. 9. Motor Cost Vs. Motor radius for square magnet size

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