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Multidisciplinary Design of Electrical Drives

Frede BIaabjerg, Peter Omand Rasmussen, John K. Pedersen

Aalborg University, Institute of Energy Technology, Department of Electrical Energy Conversion Pontoppidanstraede 101, DK-9220 Aalborg East, Denmark w: w.iet.auc.dk

Phone +45 96359254 “ Fax +45 98151411 “ e-mail: [email protected]

Abstract - Traditionally, simulation tools for drives multidisciplinary issues and give some examples can simulate electrical parameters, torque and diffe- from a simulation tool which has more features rent loads. Those parameters are in many cases than a standard simulation tool for a drive. appropriate. However, power electronics in drives In order to simulate motor and partly the drive will also influence on torque ripple, temperature, [3]-[5] have in the mid 80’s adopted much initial vibration and acoustical noise from the motor and it is necessary to include those phenomena in the research on the SRM but also on other motors by next generation of simulation tools for electrical making computer-aided-design programs com- drives. This paper describes a new design program mercially available. Especially [4] is widely used where acoustic noise of electromagnetic origin can in industry today. With these programs it is not be simulated and even be heard by the motor and only possible to size/design motors but it is also drives designer. The design program is based on a possible to investigate different simple control simple vibrational/acoustic model where the strategies. However, those tools do not open the parameters can be calculated based on the possibility to evaluate acoustic noise and vibration geometry of the motor. Examples of vibrational acoustical modelling are included and verified in so it could be possible to compare the effect of both time and frequency domain. Special emphasis different design and control strategies to each is on the switched . other. Simulation of electrical circuits like power converter, and power devices for the motors and 1. INTRODUCTION the grid are also necessary. Here are important simulation tools SABER [6] and PSPICE [7]. Many During the last decades new motor-types have other circuit simulators exist on the market but in become alternatives to the de-motor and the general it is rather time-consuming to include . Of those most research efforts advanced motor-models both for the have been put into permanent motor and implementation of the models but also the the switched reluctance motor (SRM) in order to simulation time can be very long. In a long term it obtain a high eficiency and solve general problems can be expected that different simulation tools will with torque ripple, sensorless control, and opti- merge towards each other in order to give the mized control to obtain a low-cost drive. Most of the possibility to simulate multidisciplinary easily. problems are solved today and industrial drives This paper will first from an user-perspective in based on those motors exist now on the market. In drives discuss the demands to a multidisciplinary the last couple of years also publications dealing design tool for a drive. An advanced simulation with secondary problems like acoustic noise and tool for a switched reluctance drive will be vibration have appeared but those problems are presented which both can simulate power not solved yet. In [1] and [2], the problems are converters, a switched reluctance motor, including solved by control with very simple models without torque and electrical properties, but also special simulation tools and in some cases with vibrations and acoustic noise from the drive can moderate effect. The next step to improve the be simulated. The models which are used in the possibility to solve those problems is to develope programme are described and methods to simulation tools which beyond modelling electrical determine the parameters are also discussed. parameters and the developed torque, they should Finally, a few examples are shown which also simulate mechanical issues like acoustical demonstrate the multidisciplinary simulation tool. noise, vibration and temperature as well as simulating power converters and their influence on the utility grid. This paper will focus on those DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. Il. DEMANDS TO A MULTIDISCIPLINARY influence from a cable between the power SIMULATION TOOL converter and the motor. A combination of the developed models from the other levels with In order to simulate a complete drive it involves addition of vibration and acoustic models will give many different components and systems. Fig. 1 a multidisciplinary simulation approach. illustrates a complete drive system.

The drive consists of a power converter which TYPEOFMODELS Level TYPES DEMANDS is connected to the grid, a motor, a cable which High interfaces the motor and the power converter, a . Temperdwu ● HeatsInk ● Oiiburbn of controller for control of speed/torque and . Pawer n-rxbde Muffl tempeuture ● Motor OWpGrKxy . AcausWr@$e monitoring. The power converter has typically an . G&i . . ● rmves . T.aque AC/DC converter, a de-link filter and an DC/AC . Ektdcal @e converter. High frequency noise disturbances to I L-

9 ● :q7k&ency up the grid are normally reduced by an EM1-filter. The ● Cabb drive can be controlled without or with sensors for ● Matw . Tmmient ● filten phenomeca ● ** Ii-4%$lcv.flectica!nobe current and speed. In some cases the phase . converter ● . Comnwn made GM Ciffemntial mode are also measured. In order to simulate t 1 such a complete drive system it is important to I i-----J 0 ● Lasses define what the goals are for the simulation and . Power devices . Lass ddibufian ● Motor ● EhwerKy then use the appropriate models and simulation ● Cobb . Tfwn7Ul ●Gird Avemge ● stms / C@!4-lg . COnvertef tools. Fig. 2 shows different modelling levels which ● control ● Canfm!er pwfcmimce ●Laad have to be covered in order to solve the simulation am.e.1 problem completely. l----J~I . Turn-on The simulation of the drive can be done at least . LMve cimiis ● Tunwff ● Power csevice$ . On-store, Off-date at four different levels as illustrated in Fig. 2. The . Mofu ● High accwocy . Campownts . mol lowest level is at component level where very [w- ● stress ● Magnetic detailed models of the components are used. The owributbn ●T ue simulation time is traditionally long. Next level is 1 E LOW average models where simplified expressions are used for the components. The simulation time will be much shorter. Here it is also possible to simulate the performance of the controller. The Fig. 2. Modelling levels for simulation third level is high-frequency models where special of a complete drive. models are used to model the inductive and capacitive parts of the systems in order to simulate Fig. 2 shows also which type of devices should be covered as well as different demands to the e.g. EM1/EMC of the drive. There may also be models are given. In order to operate with such a

EMC/EMl Powerconverter ,------f --- Acoustics ;Grid AC/DC DC-Filter DC/AC ; Motor)’ EMI Y~– Cable Low/high& Filter frequency; electrical’: - _ @ “ ‘: E“ :$ i- noise I Temperature ------UK ------_-l

Observers - I Monitoring k- 6)

Fig. 1. A complete drive including power converter, controller, cable and motor.

— simulation tool, it is also important to have access detailed report file where all the specified and to methods where the parameters for the models calculated data are available. Time-domain simu- can be determined easily, which includes lations are of course also available. The time do- parameter extraction procedures and a measure- main solutions can continuously be seen on the ment setup. In some cases model-parameters may screen during simulation. A couple of postproces- be determined by results from Finite Element sing tools are included to calculate e.g. sound- Method (FEM) software for magnetics and mecha- spectra and efficiency. Finally, the multidiscipli- nical structure. nary output like acoustic noise, vibration and cal- A simulation tool which covers all the levels in culation of resonance frequencies are also Fig. 2 do not exist today and especially the multi- available. in some cases during a design proces disciplinary disciplines are difficult to find. In the a prototype has been build and a more accurate following a simulation tool which can simulate simulation model is interesting. To obtain this the power converter (grid and motor), electrical motor can be characterized on an automatic properties in the motor, mechanical load, acoustic characterization system for switched reluctance noise and vibrations will be presented. drives and the data will then be used in the simulation tool as shown in Fig. 3. Ill. MULTIDISCIPLINARY SIMULATION TOOL INPUT SIMULATIONTOOL OUTPUT A multidisciplinary simulation tool has been Motor data Report Switched Reluctance Design developed especially for simulation of switched . Geome~ . Geometry and Simulation reluctance drives. The basic model for the electro- ● Materki ● Weight ● Bearing SRDaS ● Flux- ● Permanen cuwes magnetic behaviour is based on the ideas in [4] ------magnek . E~clency and many extra facilities are added. The simulator 1 l-lI n is geometry based and it is entitled SRDaS Power canverfer llme-domain I I I (Switched Reluctance Design and Simulation). An . Rectir%r ● ● Electromagnetic model ● Current ● Inverter ● Recfrfcal model ● input-output description of the simulation package . Active Flux rectifier ● vibrational model ● speed is shown in Fig. 3. The simulation tool uses models ● Acoustic model . Taque which are describing the electromagnetic, electri- ● finite Element Methad H ● Load model Canlroller Multidisciplinary cal, mechanical, acoustic and load. To determine ● Past-processing took I*PI I I the parameters for the simulation a combination of !-----l ● Acoustic noise FEM, magnetic equivalent circuit modelling and ● Vibrations empirical methods are included and thereby it is * Resanarsce possible to simulate a new designed switched Edl---- a reluctance motor without any real prototypes Motor-porumeters (virtuel prototyping). Automatic characterkstion system As input are motor data, type of power conver- frx ~“tched reluctance drives ters used, the structure and type of controller for current and speed control. As output are a very Fig. 3. Input-output description of the multidisciplinary simulation tool.

Whration~noise model

Fig. 4. Complete dynamical simulation model for a three phase 6/4 SRM including vibration and acoustical model. All models are implemented in a CAD package developed in Borland Delphi where the whole SR- is dynamical simulated. In Fig. 4 is a block diagram of the complete simulation model for a 6/4 SRM shown. An input block, a motor and a converter model block, a load model block and a vibratiordacoustic model block are used. In order to show some of the facilities in the multidisciplinary program, different screen dumps are made from the new simulation tool. In Fig. 5 is the geometry based editor for the motor shown where a number of data can be specified. Fig. 6 shows the calculated vibration modes and Fig. 7 shows a plot of the used grid-structure when FEM is used in the unaligned position. The output from the measure- Fig. 6. Calculation of stator-vibration mode ment system are shown in Fig. 8 [13]. The results in SRDaS on a 6/4 SRM. are obtained from the motor specified in Fig. 5. When a sound output is needed, the speed is fixed. It is assumed that the sound pressure is repetitive each stroke which means the total A-weighted sound pressure level only is calculated from the sound pressure over one stroke. As an option the sound pressure waveform can be transformed into a Windows WAV-file. This means it is possible to hear the acoustic noise from a given motor design and control strategy and then compare it with other design and control strategies. This is quite powerful because sound has to be heard and judged by the designer. In Fig. 9 is the dynamical simulation unit shown. If the button “FF~ of sound pressure” is pushed two charts will appear together with the total sound pressure level, see Fig. 10. The first chart contains the time domain signal of the sound pressure and the other chart contains the spectrum Fig. 7. FEM-calculation in SRDaS on a 6/4 SRM. of the sound pressure and the A-weighted sound pressure level. Many other waveforms and results can be obtained in the simulation package.

Fig. 8. Imported parameters from Fig. 5. Geometry-based editor for SRDaS. the measurement system used in SRDaS on a 6/4 SRM. consider the yoke of the SRM and describe it as a thin cylinder. The first six resonance frequencies are shown in Fig. 11, where sinusoidal deformations around the stator periphery are assumed.

M-niiO Mode 1

o Mode 5 ~oMock 3

(~ .~ Fig. 9. Dynamical simulation in SRDaS on a 6/4 SRM.

Fig. 11 .Vibration modes for a thin cylinder (SRM stator yoke).

If the normal forces are considered for a classical 3 phase 6/4 motor, they would primary try to trig Mode 2 and a 3 phase 12/8 motor would primary try to trig Mode 4. It could actually be quite interesting to compare a 6/4 with a 12/8 not only from an electromagnetic point of view, which already is done in [9], but also from an acoustic noise point of view. This is because of the different primary resonance frequencies and also the different Fig. 10. Calculation of sound in time and frequency domain. main excitation frequencies for the same speed. The sound pressure level value in the upper line is the total sound pressure level at the stator periphery over one stator pole. The upper chart is the sound pressure waveform, during Calculation of resonance frequencies one stroke and the lower chart is spectrum of the sound In order to calculate the resonance pressure and the A-weighted sound pressure level. frequencies Rayleigh’s equation from 1888 can be used [10]. IV. MECHANICAL AND ACOUSTICAL MODELLING

The multidisciplinary part in the simulation package is the mechanical and acoustical (1) modelling. Therefore, those modelling methods are explained in details. ,. (% +%)3&u~ The calculation of the resonance modes for 12(1 -d) the stator is explained, where after a method to predict the different resonance frequencies is where f“ is the n-mode resonance frequency, E is presented. A new vibrational model which takes the modulus of elasticity, I is the moment of into account the couplings between the phases inertia, R~ is the outer radius of the stator yoke, R2 are also derived. is the inner radius of the stator yoke, L,t~ is the stack length, o~t~is the packing factor, p~tatotiron iS Resonance modes for the stator the mass density and v is Possion’s ratio. If the In order to predict the resonance frequencies equation is reduced, the stack length and in the SRM it is very advantageous only to packing factor will disappear which is obvious because the deflection is only considered in two where Xj is the total acceleration over pole j, xii is dimensions. the acceleration from the i’th pole only, N, is the Equation (1) is not necessarily completely number of stator poles and NPh.S~is the number of correct, but it is an important alternative to FEM phases. analysis because the results are achieved very For a 6/4 SRM, which is considered in this fast. Sinusoidal deformations are also assumed, paper the coupling matrix is then given by: which make the couplings between the phases easy to implement. In [11] is an equivalent equation derived, but unfortunately only Mode 2 can be calculated. Further, the deformation is (3) assumed to be ellipsoid, which is not attractive compared with a sinusoidal deformation. The Mode 2 in (1) has been tested for a 6/4 3 This matrix has the same structure like the phase SRM (see motor data in Appendix A). The inductance matrix for an induction motor, where measured frequency for Mode 2 was fz = 2740 an angle of 120° between the phases exist. [Hz] and the calculated frequency was fz = 2689 [Hz]. The tested SRM has hvo end-shields which V. PARAMETER EXTRACTION is fixed with three bolts which all touch the stator outer diameter. This arrangement increases the The acoustic noise model requires the normal stiffness, but on the other hand no consideration is force F“ and three parameters in the 2-order done to the extra vibration mass of the poles and vibrational system. Also in some cases it is windings. necessary to use model parameters from a real prototype and for that purpose a test system is Mass-spring-damper model with couplings build and can be used. between phases In order to show the modelling strategy for Normal force vibrations and noise the classical 3-phase 6/4 is The normal force which is applied on each used as an example and shown in Fig. 12. It is by spring-damper-system shown in Fig. 12 is a simplification assumed that the only mode, which calculated with Finite Element Methods on a 6/4 can be excited is Mode 2. SR-motor. The normal force is equal to the body / -0.5 force acting on the and is calculated by Maxwell’s stress tensor. In Fig. 13 the normal force is shown at 19 different rotor positions. Due to saturation in the SRM the normal force will also depend on the current. f- m J%- *W m m Fig. 12. Simple vibrational model for the SRM. U9 It is quite clear when forces are applied on a ring, m deflections will be seen all-around the ring. If two poles per phase motors are considered, which go * m Is ‘0 Cnwm#fAl ‘s means two opposite normal forces are acting on Fig. 13. Normal force as a f~;ction of current and the ring, the Mode 2 is of interest. The couplings of rotor position determined by FEM in SRDaS . the Mode 2 vibration-acceleration over each pole can then in general be described by : Spring-mass-damper constants If the stator of the SRM is assumed as a Np/tuo 4rr(i-i) cylindrical ring where two opposite forces are & ~ Xicos — (2) i=l ()N. acting, the spring constant K is then calculated [12] as K ., ZB (R3 - R2)3EL&o& (4) (0.5R3 +0.5R2)3

Due to the fact that both the Mode 2 resonance frequency, calculated by (1) and the spring constant is known the equivalent mass is easily calculated as

(5) ,Q.._\_;ll.f\)we’,#;%%: ~~ : : The damping constant C is complicated to q _...... +?lIi A T-- : calculate theoretically and therefore it is deter- -1oo !: : )’~;------:”------:------;-----:--”--- mined by measurement in this paper. It is clear 01234 678910 m5[r591 that more research or test is needed to establish either precise empirical expressions or to have Fig. 14. Experimental determination of damping theoretical damping models. The measurement to constant C in the mechanical model. extract the damping constant is a stand-still test where the rotor is parked. A square wave voltage The test system is fully computer controlled by waveform is applied and the current and a PC. The computer controls a stepper motor acceleration over the excited stator pole is which varies the rotor positions of the SRM. measured. The normal force is obtained by the Between the stepper motor and the SRM a gear force-current function in Fig. 13 and applied to a (Harmonic drive with no slip) and a torque second order spring-mass-damper system. The transducer (Strain gauge) is placed. A power unit unknown parameter C is adjusted until the impress currents/voltages dependent on the test deviation between the measured and the situation. The power unit can adjust the applied calculated acceleration is minimum. voltage and it can also be in current control mode. To measure the signals a high resolution Advanced test system for SRM oscilloscope (Nicolet PR042) is used which has An advanced and automatic test system is a horizontal resolution of 12 bit and all four developed to be used for more accurate channels are simultaneously sampled. Each simulation. Fig. 15 shows the hardware structure. channel can store 1 million samples.

Stepper motor Stepper Gear (128:l) Strain gauge Test motor pOWeI unit controller motor module (SRM) I I 1 LiHE

Fig. 15. Automatic test system for characterization of Switched Reluctance Motors and determination of parameters to SRDaS. +,

To obtain a complete characterization following around 39’0 of the airgap (250 pm), which slightly measurements may be done: would change the 3D normal force curves found 1) Static torque test (indirect method) by 2D FEM. 2) Flux-linkage test (direct method) In Fig. 18 and Fig. 19 are frequency spectra 3) Back-emf test shown of the sound pressure level. The measured spectra are averaged and measured for many The tests are done with the knowledge of the strokes which means smaller fluctuations in the rotor position. Test 3 is done if permanent speed give energy around the “correct” are inside the motor or the motor has a frequencies, but not exactly at the correct bias winding. Interesting parameters to be frequency. Therefore simulation and experiments measured are: are not fully comparable.

● Current The simulated and measured spectrum are

● Voltage much alike, especially at the Mode 2 resonance “ Torque frequency near 2.8 kHz, where all the dominating “ Rotor position noise exist. At frequencies above 8 kHz a deviation exist, mainly caused by background Reference [13] describes the system in more noise and higher order resonance frequencies. details. This deviation is not so important due to the fact that frequencies above 8 kHz have a small VI. MEASUREMENTS OF NOISE amplitude and therefore they will not give any AND VIBRATIONS significant content to the total sound pressure level. To demonstrate some of the capabilities in the In order to highlight the significance of the multidisciplinary simulation software tests are done program the total sound pressure level is on a 6/4 SRM, 0.55 kW. The parameters of the measured in 8 different working points, where motor are specified in Appendix A. two different simulation also are performed. The results are working points are selected (see Table l). shown in Table Il.

Table 1. Operating points for experiments Table Il. Simulated and measured sound and simulation of 6/4 SRM. aofi= 44.10. pressure level of 6/4 SRM . aof = 44.10.

Speed a.. Du& Measured Simulated [rpm] ~’”1 cycle Sound pressure Sound pressure [%] level [dBA] level [dBA]

510 40.5 100 84.3 88.3 2 520 38.4 50 80.2 I I I I I I 1020 37.0 100 87.6 91.0

1590 33.0 100 89.1 93.0 The 3D torque and 3D flux-linkage curves in the model are extracted from the static measuring I 2570 I 25.1 I 100 I 92.1 I 95.3 I system, while the vibrational parameters are 520 38.5 50 80.2 83.8 calculated by SRDaS using the motor geometry. 990 34.6 50 82.0 86.0 The 3D normal force curves are found by 2D 1 I 1 , FEM. The motor operates without load. 1460 I 33.0 I 70 85.7 I 89.3 [n Fig. 16 and Fig. 17 are the measured and I 2550 I 26.5 I 70 I 88.0 I 91.8 I simulated time domain results shown for two different operating points. If an offset of approximately 4 dBA By comparing the waveforms excellent (caused by the placement of the microphone, agrement are seen for the current, which also is which is placed about 1 cm away from the stator, expected due to the fact that the measured flux- while the simulation of the acoustics are done on Iinkage curves are used in the model. A smaller the stator) is neglected an excellent agreement difference is seen in the stator-acceleration and between the measured and simulated results are sound pressure. This is mainly caused by a higher seen. This means the program is powerful in the order stator resonance frequency, which is not design stage to understand the tendencies with included in the model. different motor design and control strategies. The deflection of the stator is relative small and at nominal speed and torque is the deflection simulated Measud:{: i- :., . :;.! :: [ :, :,, -100 !;013EiE!30 s 101s 20233035 ,, -4 ...... - ...... : . . . ..-. ~

2 ...... ~...... ! ::: :: ‘1”0- 0 (= 0 5 101520233035 g,~...... ~...... ~ ,W ...... ~...... II+ :

! ...... : IJ “w ~::: o 5 10 1s 25343s o 5 103s 20333035 I-lia- rA’? -5 :: :; :; E’ ?:::;;~ :,: :. :.. :. v, :.- ‘: 1! y [ ~.: ~.: o~ 0510,iti Jri3s Time [nii M ......

200 -.-...:. . ..+. ---...... -. -.. +...... :, :, i“-

2 ...... - . . ..L...... -- . . .. LJ-.-... -I ......

[:pj-2 ......

15, 233035 #“”o - [% Fig. 16. Simulated and measured time domain results in working point 1 for 6/4 SRM.

si32ulkd M- 100

0 ;0 -1oo 0246 0246 #mc[uL! u 14 ‘6 “ +=4 u ‘4 “ ‘8 4, 4 .,, ,,, ,. ::: ::: :: ~ ::: ::: :: 2 ...... ; ...... ::: ::: : ::: ;:: :: i21””””fl;””’””’””””;”-””’”””””’””~ :,, o 0 0246 03.46 33214361S 3%e[lkq u 14 16 1s ‘-’iirrz [:omg

,..

::: ::: :: Z ; ...... j ...... j ...... j . . . . .

~-z ...... { ...... !,- 12 14 16 Ig 03.46 lfke[trq n ‘4 ‘6 18

::: :: ::: ::

~“’46f~[~~’214161* Fig. 17. Simulated and measured time domain results in working point 2 for 6/4 SRM. w, prototype is build. The simulation tool is used on the classical 6/4 SRM where both vibration and acoustic noise measurements are performed. Excellent agreement between measurement and simulation are seen in both time domain and frequency domain. The future of a simulation tool like this is to extend it to other motor types and also to include the temperature effect.

REFERENCES

[1] Wu, Chi-Yao; Pollock, C., “Analysis and reduction of vibration and acoustic noise in the switched reluctance drive”, IEEE Transactions on lndusby Applications, VOL31, Fig. 18. Measured and simulated A-weighted sound no.1, pp. 91-98, Jan.-Feb. 1995. pressure spectrum in working point 1 for 6/4 SRM. [2] Pillay, P.; Samudio, R. M.; Ahmed, M.; Patel, R. T., “-controlled SRM drive for reduced acoustic noise and improved ride- through capability using supercapacitor- s“, IEEE Transactions on Industry Applications VOI31 no 5, pp. 1029-1038, Sep-Ott,1 995. [3] Krishnan, R.; Arumugam, R.; Lindsay J. F., “Design Procedure for Switched-Reluctance Motors”, IEEE Transactions on Industry Applications, Vol. 24 No. 3, pp. 456-461, 1988. [4] Miller, T. J. E.; McGilp M. l., “PC CAD for Switched Reluctance Drives”, Electric Machines and Drives Conference, IEE Publication, No. 282, pp. 360-366, December 1987. [5] Miller, T. J. E., “Switched reluctance motors and their control”, Magna Physics Pub. ; Clarendon Press, 1993, ISBN: 1881855023 (Magna Physics Pub.) 0198593872 (Clarendon Press) [6] SABER ver. 4.0. Analogy. Beaverton. -29 1 4 6 8 10 12 14 16 11 A ~] PSPICE ver. 8.0. Microsim. Fig. 19. Measured and s~a~d A-weighted sound [8] P. C. Kjaer, G. White, T.J.E. Miller, “Design of Switched pressure spectrum in working point 2 for 6/4 SRM. Reluctance Motor/Generator systems using the SABER Simulatofl. Proceed. of EPE 95, vol. 2, pp. 2.522-2.527, 1995. [9] Lovatt, H. C.; Stephenson, J. M., “Influence of number V1l. CONCLUSION of poles per phase in switched reluctance motors”, IEE Proceedings B (Electric Power Applications), VOI.I 39, no.4, In this paper are the demands to a pp. 307-314, .hIiy 1992. [10] Arnold, R. N.; Warburton G. B., “Flexural vibrations of multidisciplinary simulation tool for drives the walls of thin cylindrical shells having freely supported discussed and it is concluded none exist on the ends”, Proc. Roy. Sot. London Ser. A, 197, pp. 238-256 market today. However here is presented the (1949). foundation for a PC based design program 11] Colby, R. S.; Mottier, F; Miller, T. J. E., “Vibration Modes which cover multidisciplinary aspects like and Acoustic Noise in a 4-Phase Switched Reluctance Motor”, Proceed. of IAS ’95, pp. 441-447, 1995. acoustic noise and vibration of electro-magnetic [12] Timoshenko, D. P.; Gere, J. M., Theory of elastic origin for the Switched Reluctance Motor. The stability”, Mcgraw-Hill Book Company 1961. design program is based on a new developed [13] P.O. Rasmussen, G. Andersen, L. Helle, J.K. Pedersen, F. Blaabjerg, “Fully Auto-mated Characterization acoustic /vibrational model where the noise on a system for Switched Reluctance Motors”. Proceed. of ICEM single point on the stator periphery can be ’98, VOI. 3, pp. 1692-1698. investigated. Not only a single comparable value is the output but also the actual sound pressure, APPENDIX A which is generated with a PC-sound-card. The model is derived with simple equations based on Motor data for switched reluctance motor the geometry of the motor. This means that fast Phases :3 Power :0.55 kW calculations already can be done in the design Stator/rotor pole : 6/4 Torque :2.2 Nm state and many different design and control Current :21 ~M~ Efficiency :84.8 % Voltage : 80V~c Stack length :65 mm strategies can be investigated very fast and Speed :2455 RPM Outer diameter :110 mm compared to each other, even before a