Journal of Computational Acoustics, Vol. 12, No. 1 (2004) 85–97c© IMACS

A FEM-BASED QUASI-STATIC NEURO-MODEL FOR ACOUSTICNOISE IN SWITCH RELUCTANCE MOTORS

C. LUCAS

Center of Excellence for Control and Intelligent Processing,Dept. of Electrical and Computer Eng., University of Tehran,

and School of Intelligent Systems, IPM, P.O.Box 19395-5746, Tehran, IranLucas@ipm.ir

D. SHAHMIRZADI∗ and M. NIKKHAH BAHRAMI†

Dept. of Mechanical Eng., University of Tehran, Tehran, Iran∗danial shahmirzadi@me.ut.ac.ir

†mbahrami@ut.ac.ir

H. GHAFOORIFARD

Dept. of Electrical Eng., Amirkabir University of Technology,and School of Intelligent Systems, IPM, Tehran, Iran

h ghafoorifard@hotmail.com

Received 1 June 2002Revised 1 April 2003

Elimination of stator oscillations in electromotors is among the least studied, but important prob-lems that can influence the electric performance, mechanical wear and tear and acoustical noise.In this paper, we focus on a switch reluctance motor (SRM) designed and prototyped for eventualproduction in Iran. The stator oscillation problems due to radial forces in SRMs have been reportedas more acute as compared to similar motors. Due to the complicated mechanical and electricalstructure of SRMs, obtaining any analytical model for its acoustical noise is quite impossible. Thisnecessitates using numerical and experimental methods for obtaining an approximating model foracoustical noise. Since, off line simulation can be carried out, finite element (FE) analysis can beutilized so as to generate enough data for identifying a valid model. In this paper, we introduce aneuro-model with excitation current (amp) and position of stator (degree) as inputs and acousticalnoise (db) as output. We performed two subsequent FE analysis using ANSYS package. Our firstmagnetic analysis is aimed at getting magnetic forces on the body of the stator and rotor, by ex-erting excitation current. In the second acoustical analysis, we give the magnetic forces, resultingfrom previous corresponding analysis, to the model and get the acoustical noise. We consider theacoustical behavior of the motor, in its inside and outside spaces, separately. Our approach is quasi-static, since we performed some FEM static analyses for approximating the dynamic behavior ofthe motor. Some simulation results of a acoustic noise in a designed SR motor, using our proposedmodel, is also given.

Keywords: Switch reluctance motor, electromotors, acoustical noise, neuro-model, finite elementmethod, quasi-static approach.

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1. Introduction

The switched reluctance technology, despite its rather long history, has attracted much at-tention in recent years and has become a serious contender for existing technologies forelectromotor production. Its importance is much more pronounced in Iran, since its pro-duction is more feasible than other new approaches, like permanent magnet technology. SRmotors have several advantages like lower cost and more ease of manufacturing, but alsosuffer from some drawbacks, the most important of which are torque ripple and acousti-cal noise.1–5,10 The elimination of torque ripple has been the subject of many importantstudies.11,12 The possibility of its manipulation via intelligent feedback control has been amain factor in reviving industrial interest in its design and manufacturing.9 However, sev-eral studies have shown that stator vibrations due to radial forces are as important, if notmore so, in the production of acoustic noise and deterioration of the performance of thedrive3,5 and some methods to reduce the oscillation of the stator are given.6 Rotor vibra-tion and modal deflection is considered to be negligible,3 so we assume a perfect geometricalmodel for rotor and stator, in our analysis. The analysis presented in this paper, has beencarried out, in conjunction with a comprehensive design effort, in order to deal with thescientifically less studied aspects of vibration and noise, alongside the better understoodand already known procedures to reduce the torque ripple. Since, achieving an analyticalmodel for the noise of SR motors is very cumbersome, using any numerical or experimentalmethod in developing the model can be so appropriate, and some FE based analysis areperformed to do this.7 Here, we focused our analysis on the mechanical vibrations of aspecific 6/4 SR motor whose design procedure as well as intelligent torque ripple controlprocedures and implementation, has been reported elsewhere.8–10,13–14,16

2. Model Development

As mentioned, we aim to obtain a model for acoustic noise of SRMs. Since, due to intricatenature of acoustic noise as well as complicate structure of SRMs, developing any analyticalmodel for SRMs’ acoustic noise is impossible. An efficient alternative for this purpose isusing any numerical or experimental method. In this paper, we used finite element method(FEM) as a powerful tool in numerical analyses in order to generate ample data and thentrain a neural network for learning their behavior. Our procedure of proposing the modelis elaborated in the subsequent sections.

Fig. 1. Motor magnetic model.

A Fem-Based Quasi-Static Neuro-Model for Acoustic Noise 87

2.1. Magnetic FEM analyses

The first part of our data generation procedure is concerned with magnetic finite elementanalyses. The general structure of SR motor magnetic model, we consider, is given in Fig. 1.

As observed in the Fig. 1, in magnetic analyses, we assumed two inputs and one out-put parameter. As reported in some studies, one of the main sources of acoustic noise isradial forces on the body of the stator and rotor.3,5 Generally, In the unloaded operatingcondition of a SR motor, the main forces exerted on the body of the rotor and stator, aremagnetic forces, resulting from magnetic fields between rotor and stator. These magneticfields, themselves, are generated due to the excitation current, applied on the stator poles.These are the main reasons, why we choose excitation current as one of the model inputsand magnetic forces on the body of the stator and rotor, as the model output. Since, weaim to model the dynamic behavior of the motor, the rotor angular position is also aninput parameter for the model. For generality of our analyses, we attempt to cover a widerange of motor working conditions, so we varied the values of excitation current, from 2to 30 amperes, by increments of 2 amperes. We varied, the values of rotor position from0◦ to 45◦, by increments of 3◦. The results can determine the full 0◦–360◦ range for rotorpositions via the geometric symmetries. Eventually, we will obtain results of 240 (15*16)distinct conditions of the motor. We have used ANSYS model, in our magnetic analyses, asgiven in Fig. 2. In our magnetic analyses, we ignore the coupling effects, means that at thetime of exciting one pair of poles, the other poles are assumed to be unexcited. This is notthe case in real applications, but simplifies the computational space of analyses noticeably,since it is shown that making this assumption, does not lead to any significant inaccuracy.So, we apply the excitation current to just one pair of poles. In ANSYS software package,for calculating the magnetic force, in a body, the body must be completely surrounded by amargin, and defined as a component. Defining the whole rotor and stator as two componentsand getting forces on them, is not so accurate for consequent procedures, since we aim toexert the values of these forces as inputs to the acoustic analyses. For obtaining, more real-istic results, we partition the rotor and stator to some components, as each pole along side

Fig. 2. ANSYS magnetic model for the SR motor alongside its meshes.

88 C. Lucas et al.

Fig. 3. The directions and locations of magnetic forces.

Fig. 4. Motor acoustic model.

regions in its vicinity, is defined as a component. Thus, we have 10 components in the wholemodel, to calculate magnetic forces in them. The results of magnetic forces are provided inthe form of sum of forces in X direction and Y direction, separately. At the end of this unit,it is worth to mention that in this section, we have 16 magnetic analysis (correspond toeach value of rotor position), in each of them, there are 15 distinct set of results. Each set ofresults of these very time- consuming analyses, is a 20-valued force vector (10 component*2direction). Due to large space it takes, we ignore to give the results of magnetic force valuesin this paper. However, a descriptive configuration showing the locations and directions ofthe magnetic forces has been provided in Fig. 3.

2.2. Acoustic FEM analyses

We apply the magnetic forces, obtained from previous magnetic analyses, to acoustic model,so that it leads us to values of acoustic noise (in db). The general structure of acoustic model,we consider, is given in Fig. 4 and the model, used in ANSYS package, is given in Fig. 5.

The model, given in Fig. 5, represents the solid motor and the fluid in its internal andexternal, environments, alongside the meshes applied to it. Although, we considered, fromthe fluid elements provided by ANSYS package, only circles of radius 1 meter, around themotor, the results are correct in the presence of infinite environment. The direct result ofacoustic analyses in the ANSYS is pressure gradients in the environment fluid, which by

A Fem-Based Quasi-Static Neuro-Model for Acoustic Noise 89

Fig. 5. ANSYS acoustic model for the SR motor alongside its meshes.

0 5 10 15 20 25 30120

130

140

150

160

170

180

190

200

210

i(amp)

soun

d pr

essu

re le

vel (

db)

inside acoustical noise of SRM00 03 06 09 12 15 18 21 24 27 30 33 36 39 42 45 Theta

Fig. 6. Inside acoustic noise as a function of excitation current (sorted in terms of rotor position).

assuming a reference fluid pressure, it can be mapped to the acoustical noise (in db), bythe formula given in the (4.1).

Lsp = 20.log(

Pref + ΔP

|Pref |)

. (2.1)

We consider the maximum value of acoustic noise in the internal and external envi-ronments of the motor. The noise level inside the motor can be important when there areconnections (e.g. heat transfer holes) between the two environments. The results of insideand outside acoustic noise in our motor are shown in Figs. 6 and 7, respectively. As observedin the figures above, there are some unexpected behaviors in the acoustic noises in the SR

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0 5 10 15 20 25 30-120

-100

-80

-60

-40

-20

0

20

40

i(amp)

soun

d pr

essu

re le

vel (

db)

outside acoustical noise of SRM 00 03 06 09 12 15 18 21 24 27 30 33 36 39 42 45 Theta

Fig. 7. Outside acoustic noise as a function of excitation current (sorted in terms of rotor position).

Fig. 8. Situation for rotor position of 21◦. The switching between poles is easily identifiable.

motors, that happen simultaneously in its inside and outside spaces. One of the worst casesoccurs in the behaviors of noise of the motor, corresponding to rotor position of 21◦. Theabrupt transition in this rotor position can happen due to switching between the rotor andstator poles, as can be seen, in the Fig. 8, which corresponds to rotor position of 21◦. Theresults of finite elements analyses, in some cases, may become inaccurate due to any sin-gularity, stiffness, etc. The peak in the inside noise for rotor position of 21◦ is extremelydubious. For confirming this abrupt increase in mentioned plot, we generated two pointsin the vicinity of 12 amperes that the peak occurs in. We obtained the results of inside

A Fem-Based Quasi-Static Neuro-Model for Acoustic Noise 91

0 5 10 15 20 25 30140

150

160

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200

210

i(amp)

soun

d pr

essu

re le

vel (

db)

inside acoustical noise of SRM (For Theta=21)

12

11.5 12.5

Fig. 9. Two modifier points around the peak in the inside noise for rotor position of 21◦, corresponds toi = 12 amp.

0 5 10 15 20 25 30 35 40 45120

130

140

150

160

170

180

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200

210

Theta(Degree)

soun

d pr

essu

re le

vel (

db)

inside acoustical noise of SRM020406081012141618202224262803i

Fig. 10. Inside acoustic noise as a function of rotor position (sorted in terms of excitation current).

acoustic noise, in the excitation current values of 11.5 and 12.5 amperes. As illustrated inFig. 9, these results are in complete agreement to availability of peak in the 12 amperes.

The plots of Figs. 6 and 7 are the presentation of the results sorted in terms of θ. Themore applicable plots, can be obtained by rearranging the data of plots 5 and 6, to achieve

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0 5 10 15 20 25 30 35 40 45-120

-100

-80

-60

-40

-20

0

20

40

Theta(Degree)

soun

d pr

essu

re le

vel (

db)

outside acoustical noise of SRM

020406081012141618202224262830i

Fig. 11. Outside acoustic noise as a function of rotor position (sorted in terms of excitation current).

Fig. 12. Overall structure for acoustic system of SR motor.

the inside and outside noise behaviors, sorted in terms of i, that are given in Figs. 10and 11.

These plots can be assumed as acoustic noise of motor while being in rotation, under fixedexcitation current. Up to this point, we have generated 242 results of different conditionsfor motor operation.

2.3. Neural network training

Having carried out the time-consuming finite element analysis for both force values andnoise levels, we now have data sorted as i(amp), θ(degree) and SPL(db), the first twoconstituting the inputs and the last constituting the output of the model we seek to identify.The structure of overall acoustic system for SR motor is illustrated in Fig. 12.

In this stage, we aim to train a neural network to obtain a satisfactory neuro-model foroverall acoustical noise, illustrated in Fig. 12. The procedure for training the neural networkis given in Ref. 15. The structure of the selected neural network topology is depicted inFig. 13. The results of outputs of the trained neural network in comparison to real FE data,is shown in Figs. 14 and 15, for inside and outside acoustic noise, respectively.

A Fem-Based Quasi-Static Neuro-Model for Acoustic Noise 93

Fig. 13. Topology of designed neural network for modeling the acoustic noise of SR motor.

Fig. 14. Real FE data in comparison with neural network outputs, for INSIDE acoustic noise.

So, at this stage, we are able to obtain the inside and outside acoustic noise levels of ourSR motor, by giving the neural network, the rotor position and excitation current.

3. Noise Variation In A Complete Rotation Cycle

The ultimate purpose of this study is getting the acoustic noise in a specific switch reluctancedrive whose design procedure is reported elsewhere.8–10,13,14,16 The current waveform hasbeen determined by the adopted control strategy so as to track the desired speed, whilemaximizing the efficiency and minimizing the torque ripple. These profiles and waveforms

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Fig. 15. Real FE data in comparison with neural network outputs, for OUTSIDE acoustic noise.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

100

200

300

omeg

a(rp

m)

a

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5000

10000

15000

b

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

5

10

15

20

time(s)

curr

ent(

i)

c

Fig. 16. (a) Speed variation, (b) position variation and (c) current waveform.

are illustrated in Fig. 16. Our designed SR motor is operating in the nominal speed of3000 rpm and from Fig. 16(a), we recognize that the settling time of the motor is verysmall, about 0.35 s, that allows us to ignore the transient behavior of the motor. So wefocus on achieving the acoustic noise of our motor, in the steady state condition, for onecycle. Since by having the values of excitation current and rotor position of the motor, we

A Fem-Based Quasi-Static Neuro-Model for Acoustic Noise 95

0.9176 0.9196 0.9216 0.9236 0.9256 0.9276 0.9296 0.9316 0.9336 0.9356 0.9376-226

10141822

curr

ent(

i)

0.9176 0.9196 0.9216 0.9236 0.9256 0.9276 0.9296 0.9316 0.9336 0.9356 0.93761.44

1.4461.4521.4581.4641.47

1.476x 10

4

thet

a(de

gree

)

A Whole Cycle Rotation In Steady State Condition

0.9176 0.9196 0.9216 0.9236 0.9256 0.9276 0.9296 0.9316 0.9336 0.9356 0.9376120

160

200

insi

de n

oise

(db)

0.9176 0.9196 0.9216 0.9236 0.9256 0.9276 0.9296 0.9316 0.9336 0.9356 0.9376-100

-60

-20

20

time(s)outs

ide

nois

e(db

)

a

b

c

d

Fig. 17. (a) Theta variation, (b) current waveform, (c) inside acoustic noise and (d) outside acoustic noise.All for a complete cycle of the motor in steady state condition.

can obtain the corresponding values of inside and outside acoustic noise, the results of thisprocedure is given in Fig. 17, for a one whole rotation cycle.

4. Concluding Remarks

This paper, mainly concerned with the acoustic sound of switch reluctance motors, sincehigh acoustic noise level of SRMs is reported as main factor in hindering its broad applica-tions. Achieving an analytical model for the noise of SR motors is very cumbersome, andany numerical or experimental method in developing the model must be utilized. In thisstudy, we applied finite element method as a powerful numerical analysis. We generatedsome off-line data by magnetic and acoustic FE analyses using ANSYS package, and usedthem for training a neural network to obtain a model for acoustic noise of a specific SRM.We considered the noise for inside and outside spaces of the motor, separately. Our neuro-model was capable of getting excitation current and angular position of the rotor as inputsand resulting in acoustic noise. In other word, we approximated the dynamic behavior of themotor with numbers of quasi-static behaviors. Some simulation results, about the acousticnoise level of a specific motor, are given at the end of the paper. A major contributionof this work is to pave the way for direct analysis and optimization of the acoustic noiseperformance of electromotors. At present, the designers only try to shift the natural fre-quencies away from the audible range. Any attempt to control the noise level itself is onlyindirectly or not at all. Although there can be no general purpose lumped model for thegeneration of acoustic noise in all electromotors or at least all configurations of SR-motors,

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the proposed method is general enough to be applicable to any production line of a motorwith a particular configuration or any other device for that purpose.

Acknowledgment

We greatly appreciate helps and opportunities provided by industrial switch reluctancemotor group, in the project of “Design, Construction and Intelligent Control of SR motors”.

Appendix A

In this section, we give some of ANSYS modeling specifications we used in our acousticanalyses.

Element size

The length of the elements we used in meshing the model is 0.3 cm. The diameter of thestructural model itself is 1.8 m and the region we considered the noise contours is a circlewith radial 1 m around the structural model.

Element Types

Type number 82 (for the structural parts of the model), Type number 29 (for the environ-mental fluids with two different options, one for the fluids in contacting with the structuralparts and one for the fluids without any contact with solid materials), Type 129 (for simu-lating the infinite environment around the model).

Material P roperties

E=2e 11 & ρ = 7000 & ν = 0.3 (the mechanical properties of the structural parts of themodel), ρ = 1030 & SONC=1460 (the acoustical properties of the environmental fluid).

References

1. C. Neagoe, A. Foggia and R. Krishnan, Impact of pole tapering on the electromagnetic torqueof the switched reluctance motor, Electric Machines and Drives Conference Record, 1997. IEEEInternational, pp. WIA/2.1–2.3.

2. M. Gabsi, F. Camus, T. Loyau and J. L. Barbry, Noise reduction of switched reluctance machine,Electric Machines and Drives, 1999. International Conference IEMD’99, pp. 263–265.

3. R. S. Colby, F. Mottier and T. J. E. Miller, Vibration modes and acoustic noise in a 4-phaseswitched reluctance motor, Industry Applications Conference, 1995. 30th IAS Annual Meeting,IAS ’95, Conference Record of the 1995 IEEE 1, pp. 441–447,.

4. D. W. J. Pulle, J. C. S. Lai, J. F. Milthorpe and N. Huynh, Quantification and analysis ofacoustic noise in switched reluctance drives, Power Electronics and Applications, 1993, 5thEuropean Conference 6, pp. 65–70.

5. M. N. Anwar and I. Husain, Radial force calculation and acoustic noise prediction in switchedreluctance machines, Industry Applications Conference, 1999, 34th IAS Annual Meeting Con-ference Record of the 1999 IEEE 4, pp. 2242–2249.

6. C. Lucas, D. Shahmirzadi and H. Ghafoorifard, Eliminating stator oscillation through FINplacement, Int. J. Engineering Simulation 3(1) (2002) 3.

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7. B. Fahimi and M. Ehsani, Spatial distribution of acoustic noise caused by radial vibration inswitched reluctance motors: Application to design and control, IEEE Conf. (2000) 114.

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9. R. C. Becerra, M. Ehsani and T. J. E. Miller, Commutation of SR motors, Power Electronics,IEEE 8 (1993) 257.

10. M. Shorakaa and C. Lucas, Noise and vibration control in SRMs from multiple sources, M.SThesis University of Tehran, IRAN, Oct. 2000.

11. M. S. Islam and I. Husain, Torque ripple minimization with indirect position and speed sensingfor switched reluctance motors, Industrial electronics society, 1999. IECON’99 proceedings. The25th Annual Conference of the IEEE 3, pp. 1127–1132.

12. K. Russa, I. Husain and M. Elbuluk, Torque ripple minimization in switched reluctance machinesover a wide speed range, Industry Applications Conference, 1997. 32th IAS Annual Meeting.IAS’97 Conference Record of the 1997 IEEE, 1, pp. 668–675.

13. B. Mirzaeian, M. Moallem and C. Lucas, A Fuzzy expert system for predicting the performanceof switched reluctance motor, Int. J. Eng. 14(3) (2001) 229–237.

14. M. Moallem and G. E. Dawson, An improved magnetic equivalent circuit method for predictingthe characteristic of highly saturated electromagnet drives, IEEE Transaction on Magnetic 34(1998) 5.

15. D. Shahmirzadi, C. Lucas, M. Farshad and R. Pedrami, Training neural network for modellingthe acoustic behavior of switch reluctance motor, Neuroscience Events Int. Conference, Pro-ceeding of 4th Irano-Armenian Workshop on Neural Networks, May 20–22, 2002, School ofIntelligent Systems, Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran.

16. C. Lucas, M. Modir shanechi, P. Asadi and P. Mellati Rad, A robust speed controller for switchedreluctance motor with nonlinear QFT design approach, 2000 IEEE Industry Application Confer-ence/35th IAS and World Conference on Industry Applications of Electrical Energy, pp. 1573–1577.