3664 Chen

3664 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 9, SEPTEMBER 2010

Design and Operation of Interior Permanent-Magnet Motors With TwoAxial Segments and High Rotor SaliencyHang-Sheng Chen, David G. Dorrell, and Mi-Ching Tsai

Electric Motor Technology Research Center, National Cheng Kung University, Tainan 701, TaiwanSchool of Electrical, Mechanical and Mechatronic Systems, University of Technology Sydney, Sydney, NSW 2007, Australia

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan

Skewing the magnets in a brushless interior permanent-magnet motor can be difficult. One method to overcome this problem is to useaxial segments that are rotated (twisted) with respect to each other. Compared to other methods of rotor skewing, this method mayreduce manufacturing cost and the complexity of the rotor. This paper addresses the use of two axial segments and the associated effectson the back-electromotive force (EMF) waveform and motor performance. The back-EMF waveforms of an interior permanent-magnetmotor are deeply influenced by the tooth-slot and winding harmonics. They should be sinusoidal to reduce torque ripple for ac motorservo drives and other applications where smooth operation is required. In the paper, we present the two-segment rotor structure to-gether with a simple technique for reducing high-order back-EMF harmonics, and we derive the optimal twisted angle of the proposedtwo-segment rotor. This minimizes the total harmonic distortion of the back-EMF waveform due to tooth-slot effects. We examine cog-ging torque and the reduction in cogging torque. We apply the twisted angle rotor to two different compressor motors. In addition tothe back-EMF, we address the torque ripple under load and the effect of twist on back-EMF constant. We examine the results usingfinite-element analysis and validate them by experimental measurement.

Index TermsBack-EMF, IPM, I-Psi loop, permanent-magnet motor, skew, torque.

I. INTRODUCTION

R ECENTLY, interior permanent-magnet (IPM) motorshave become important due to their perceived superiorperformance over conventional induction motors and otherdrive machines. A unique characteristic of the IPMs is that the-axis inductance is greater than the -axis inductance because

the permanent magnets are embedded in the rotors so that -axissaliency is produced. As a result, a reluctance torque can begenerated which can enhance the efficiency [1][3] and allowenhanced field weakening. Therefore, this type of motor can beused in several applications, such as air conditioners, electricscooters, and servo drives, to achieve the required performance.

In addition to high efficiency and field weakening operation,many IPM motor applications, such as air conditioners andservos, require the motor be able to produce smooth torque tominimize vibration and noise. Brushless permanent-magnetAC motor drives [4] are often chosen for these applications (theIPM motor is included in this category of machine); they havevarious attractive features, such as low torque ripple and lowacoustic noise, and their topology in terms of stator layout androtor arrangement can be varied. For this sort of motor drive,the back-EMF should be sinusoidal to reduce torque ripple [5].However, the back-EMF waveforms often contain high-orderharmonics due to tooth-slot effects and lower order harmonicsbecause of phase-belt winding harmonics. Hence IPM motorswhich exhibit a smooth sinusoidal back-EMF waveform canproduce lower vibration and noise. There are many new control

Manuscript received November 19, 2009; revised March 16, 2010; acceptedMarch 25, 2010. Date of publication April 19, 2010; date of current version Au-gust 20, 2010. Corresponding author: M.-C. Tsai (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2010.2048037

methods [6][8] which can reduce torque ripple with non-ideal(or sinusoidal) back-EMF waveforms. However, the back-EMFwaveform profile is still the most basic property that can beaddressed in order to reduce torque ripple and smooth theoperation. Various techniques can be utilized to improve thisand two are investigated in this paper.

The back-EMF waveform is a function of several motorparameters. The main parameters are stator winding layout,slot and pole number [9], [10], stator tooth width [11], magnetmagnetization [12][14], and skew. Various techniques havebeen developed for reducing the high-order harmonics in theback-EMF waveform. These include: double-layer windingarrangements [15]; rotor structure [16]; pole-arc to pole-pitchratio and saliency [17]; fractional slotting; and rotor magneticshape design [18][21]. These are all well-known methodswhich can be employed to produce sinusoidal back-EMFwaveforms. Fractional slot and skewed rotor arrangementsare very common. However, the first technique cannot reducethe influence of the tooth-slot effect completely while the lastmethod may increase the manufacturing cost.

Skewing is one of the most common methods to improve theback-EMF waveform [22][25]. This technique is used in mostsmaller permanent-magnet and induction motors, and has alsobeen applied in magnetic gearboxes to obtain improved trans-mission [26], [27]. However, skewing may cause various manu-facturing problems such as increased magnet cost due to theirshaping, and increased manufacturing costs through skewingthe stator or fitting magnets in skewed IPM rotor slots. In termsof numerical electromagnetic analysis, skewed rotor structuresrequire 3-D finite-element analysis (FEA) which necessitatestime-consuming simulations, or 2-D multi-slicing models withmany slices [28] which can also be time consuming. Analyticalmodels usually use a skew factor which does not account foraxial steel saturation effects.

In order to utilize skewing without substantially increasingthe costs through the reasons highlighted above, a skewed two-segment structure, as shown in Fig. 1, is investigated in this

0018-9464/$26.00 2010 IEEE

CHEN et al.: DESIGN AND OPERATION OF INTERIOR PERMANENT-MAGNET MOTORS WITH TWO AXIAL SEGMENTS 3665

Fig. 1. Proposed rotor with two-segment design with Rotor II rotated by anangle with respect to Rotor I.

Fig. 2. Winding layouts for one phase of (a) the 4-pole 36-slot motor and (b)the 4-pole 30-slot motor. There are two parallel paths in both windings witheach turn formed from three strands-in-hand of 0.85 mm diameter wire. For (a),the center coil-side of each three-coil-side belt has 17 turns, while the coil-sideseither side have 18 turns. The winding is single-layer concentric. The offsetbetween each phase is five slots. For (b), all the coils have 10 turns and thewinding is double-layer lap with an offset between phases of six slots.

paper. A similar rotor structure was adopted in [29][31] to re-duce cogging torque. By dividing the rotor into two axial sec-tions and shifting by an appropriate twisted angle , the influ-ence of slotting can be reduced; i.e., the high-order harmonics ofthe back-EMF waveform can be removed. This produces a moresinusoidal back-EMF waveform. In addition, cogging torqueand phase-belt harmonics can be reduced.

In the paper, two IPM motors are studied. The first has 4 polesand 36 stator slots while the second has 4 poles and 30 statorslots. The proposed two-section twisted-rotor design is inves-tigated using analytical analysis of the back-EMF waveforms,and further used in FEA simulations to validate the method andassess the motor characteristics. The winding layouts for the4-pole 36-slot and 4-pole 30-slot motors, which are single-lay-ered and double-layered respectively, are shown in Fig. 2 with afull description in the caption. Fig. 3 shows the rotor topologies(which are slightly different) and also illustrates the flux distri-butions on no-load. Table I gives full specifications for the twomotors. It is important to give this data to illustrate that they areproduction motors rather than experimental motors. The 36-slotmotor has a single-layer winding which is very typical for aconcentric-wound machine while the 30-slot motor is an ex-ample of a fractional-slot motor with lap windings and low cog-ging torque. The twisted angle design of the two-segment rotoraims to minimize the total harmonic distortion (THD) of theback-EMF and improve the cogging and load torque ripples. Inorder to support the validity of the twisted angle design, both

Fig. 3. Quarter cross sections (with finite-element solutions) for (a) the 4-pole36-slot motor with three 3 mm thick magnets per pole and (b) the 4-pole 30-slotmotor with four 3 mm thick magnets per pole. (a) 36 slot motor and illustrationof rotor bridge depth; (b) 30 slot motor.

simulated and measured results are presented, and the THD ofback-EMF waveforms for different twisted angles is analyzed.

The back-EMF and initial load results are obtained from 2-DFEA using Ansoft software. To investigate in detail the coggingtorque and also the torque under load, SPEED software fromthe University of Glasgow is utilized to assess the two-segmentrotor performance. This package has automated procedures tomake results straightforward to obtain. The results from this ad-ditional FEA study illustrate the instantaneous torque ripple andmean torque generation using current-flux-linkage curves (I-Psiloops).

II. METHOD OF REDUCING HIGH-ORDER HARMONICS OFBACK-EMF WAVEFORMS

A. Influence of SlottingThe air-gap reluctance in a slotted motor varies in circumfer-

ential direction because of the continuously changing perme-ability relationship of the slots and teeth due to rotation. Thisaffects the flux linkage and dictates the amplitude of the in-duced back-EMF. Hence, harmonics are superimposed on toback-EMF waveform due to the variation in air-gap reluctanceas the rotor rotates.


TABLE I4-POLE MOTOR PARAMETERS

Consider an unskewed motor structure, where the tooth fluxcan be denoted by a general Fourier series [11] where

(1)

For the tooth, the flux can be expressed as

(2)where is the rotor position, and are the number ofstator slots and rotor poles, and is the angular slot pitch de-fined by

(3)

Using Faradays law, the back-EMF is

(4)

where is the motor speed and is the turns of a coil linkingthe flux . Substituting (1) and (2) into (4) gives the back-EMFinduced into a coil around the th tooth:

(5)

Since the back-EMF of any coil can be found by summing theteeth enclosed by the coil, (5) can be rewritten:

(6)

From (6), the harmonics can be reduced by summing the toothback-EMFs. The voltage phases for successive teeth are offsetby a spatial harmonic where

(7)

so that the th harmonics cannot be eliminated due to the tooth-slot permeance effects. These result in a back-EMF ripple whichcan cause vibration and noise.

B. Calculation of the Twisted AngleIn order to counteract the tooth-slot effect and to lower man-

ufacturing cost, the two-segment rotor structure can be utilized.The required back-EMF waveform can be obtained using har-monic superposition and the waveform can be made more sinu-soidal by controlling the twist angle between the two axialrotor sections. The back-EMF can be obtained from

so that

(8)

where

In (8), and can be reduced using the summation of theback-EMF, while can be subtracted from when the twistedangle satisfies the equation:

(9)

where the denominator is the least common multiple (LCM) ofand ; i.e., the optimal twisted angle of the two-seg-

mented rotor structure can be calculated using (9) to minimizethe th harmonic(s). Hence, by twisting the rotor, tooth-slot


Fig. 4. Back-EMF THD of the 4-pole 36-slot IPM motor with nine differenttwisted angles.

effects can be limited using a technique which is more straight-forward in manufacturing terms than skewing the rotor or stator.Instead of using a full 3-D FEA to perform the motor analysis, a2-D FEA is applied to analyze the motor by simulating eachsegment. This method can be used to modify the back-EMFwaveform of any permanent-magnet motor with high tooth-sloteffects.

III. APPLICATION OF TWISTED ROTORS TO IPMMOTORSEFFECT ON BACK-EMF FROM ANALYTICAL STUDY

A. Harmonic Analysis of Back-EMF of Type M36 and M36-tSince the 4-pole 36-slot IPM motor has an integral-slot de-

sign, the least common multiple of and is 36. From(9) the optimal twisted angle is 5 deg, and this is used in theType M36-t motor. From Section II, the twisted angle designdecreases the high-order harmonics of the back-EMF and there-fore the THD should be lower for the Type M36-t motor. Fig. 4illustrates the back-EMF THD with nine different twisted an-gles. As expected, the lowest value of THD occurs at a twistedangle of 5 deg as suggested by (9). The THD increases eitherside of this twisted angle. Hence, 5 deg is the optimal twistedangle for the 4-pole 36-slot motor design. Fig. 5 shows the har-monic comparison of the back-EMF waveforms. Obviously, bytwisting the rotor, the low-order phase belt (5th, 7th, etc.) as wellas the high slotting order (17th and 19th) harmonics should bereduced. However, the amplitude of the fundamental back-EMFharmonic is not significantly affected. In Table II, the amplitudeof the main back-EMF waveform harmonics and the percentagedecreases with respect to 0 and 5 deg twist are given. The 17thand 19th order harmonics represent the tooth-slot permeanceharmonics, decrease by over 90%. However, the low-order (3rdto 9th) harmonics have much lower attenuation. If a particularwinding has a high 5th or 7th harmonic (for a star connectedmotor, as this sort of motor should be, 3rd harmonics are zero-order and can be ignored) then the twist angle can be further in-creased to attenuate those particular back-EMF harmonics.

B. Harmonic Analysis of Back-EMF of Type M30 and M30-tThe rotor twisted angle for the 4-pole 30-slot IPM motor

was found to be 3 deg by employing (9) .The back-EMF THD for this motor with six different twistedangles is shown in Fig. 6, which illustrates that 3 deg is the

Fig. 5. Back-EMF harmonics of Type M36 and M36-t at 5 deg.

TABLE IIHARMONIC AMPLITUDES OF TYPE M36 AND M36-T0 AND 5 deg TWIST

Fig. 6. Back-EMF THD of the 4-pole 30-slot IPM motor with nine differenttwisted angles.

optimal twisted angle. The harmonic analyses of the back-EMFwaveforms are compared in Fig. 7 at zero and this optimaltwisted angle. Table III gives the amplitudes of the back-EMFharmonics and the corresponding percentage reductions. The29th and 31st order harmonics are the second harmonics ofthe slotting and are reduced by over 90%; these are the mainharmonics attenuated by a 3 deg rotor twist. The 15th harmonicis a third and a zero order voltage so it can be ignored. Again,even though the high-order harmonics are substantially reducedby the optimal twisted angle of 3 deg, the fundamental voltageremains virtually constant. These simulations confirm thatthe proposed axial-section twisted-rotor design technique iseffective in reducing high-order harmonics.


Fig. 7. Back-EMF harmonics for M30 and M30-t at 3 deg.

TABLE IIIHARMONIC AMPLITUDES OF TYPE M30 AND M30-T0 AND 3 deg TWIST

IV. COGGING TORQUE OF THE TWO IPM MOTORS WITHTWISTED ANGLE USING FEA

Cogging torque is another important factor in the productionof torque ripple. It is generated on open-circuit by the interactionof the rotor magnets with the stator slotting reluctance. Sincethe twisted angle design of the two-segment rotor changes theair-gap reluctance, it reduces the cogging torque in IPM motors.A simulation was set up in SPEED and the cogging torque ob-tained over a 10 deg rotor movement, which is the period forcogging torque in the 36 slot motor. This can be a difficult sim-ulation to obtain. Care needs to be taken to set up the air-gaplayers correctly and move the rotor in small steps while keepingthe air-gap element shapes constant in their arrangement. Fig. 8compares the results of the cogging torque simulations for theM36 and M36-t motors, while Fig. 9 compares the coggingtorques for the M30 and M30-t motors. The axial lengths androtor radii should be considered herethe 36 slot motor is 70mm long while the 30 slot motor is 85 mm long. The rotor radiiare identical. Therefore, like-for-like comparisons should be inthe ratio of axial lengths so that the 36 slot motor will be only82% of the 30 slot motor for identical cogging force stress den-sities. The twisted angle essentially reduces the peak value ofcogging torque for both integral-slot and fractional-slot motordesigns.

For the 36 slot motor, the 5 deg twist means that when rotorsegment is aligned with the teeth (minimum reluctance) theother segments is aligned with the slot centers (maximumreluctance) so that the cogging torque in Fig. 8 halves in pitchand is significantly reduced. There is some slight variation inthe cogging torque on top of the main cogging oscillation andthis is due to some numerical drift.

Fig. 8. Comparison of cogging torque for M36 and M36-t (twisted rotor withreduced cogging torque and oscillation half period). The M36 motor has the cog-ging characteristic of either Segments 1 or 2; M36-t is the Net Cogging whichis the sum of Segments 1 and 2.

Fig. 9. Comparison of cogging torque for M30 and M30-t (twisted rotor withmuch reduced cogging torque and oscillation half period). The M30 motor hasthe cogging characteristic of either Segments 1 or 2; M30-t is the Net Coggingwhich is the sum of Segments 1 and 2.

For the 30 slot motor, the 3 deg twist leads to one segmentbeing aligned with the slots when one is aligned with the teeth.Again, the pitch of the cogging torque oscillation as the rotor isrotated halves and it is attenuated even further.

Table I shows that the 30 slot stator has a wider slot open-ings than the 36 slot stator and the cogging is higher. Compar-ison of the cogging torques in Figs. 8 and 9 illustrate that the30 slot motor has slightly lower unskewed coggingthis differ-ence would be even more marked if the axial lengths were thesame. In addition, the cogging in the 30 slot motor is far moreattenuated by the twisted rotor since it is more sinusoidal. Themechanisms involved in generating cogging are quite complex;however, it should be pointed out that the 36 slot stator has analignment with every pole (i.e., an integer number of slots perpole) in a 4-pole motor whereas the 30 slot motor has an align-ment with every pole-pair. The general perception is that thisshould lead to the 36 slot motor having higher cogging torquebut here the difference is not so pronounced. There will be 36oscillations of the cogging torque in the 36 slot motor and 60oscillations in the 30 slot motor. Another generalization is thatas the number of oscillations per revolution increases then theamplitude tends to decrease, especially if the number of polesaligning with an integral number of slots increases. These resultsshow that the cogging is very much a function of the rotor/statortopology. To illustrate this, Fig. 10 shows the cogging torque


Fig. 10. Comparison of cogging torque for M30 motor with successive rotor/stator changes: (i) the bridge in the rotor reduced from 2 mm (which it is in boththe 30 and 36 slot rotorsFig. 2) to 1 mm, (ii) the rotor of the M36 machinefitted (still with 1 mm bridge), (iii) the slot opening is reduced from 3.3 mm (30slot stator) to 2.32 mm (as it is in the 36 slot stator), and finally (iv) the air-gapis then increased from 0.65 mm to 1 mm.

Fig. 11. Comparison of cogging torque for M36 motor with reduction of thebridge from 2 mm to 1 mm.

with different arrangements. First, the rotor in the 30 slot motorhas the bridge decreased from 2 mm to 1 mm (defined in Fig. 3).This causes an increase in cogging from about 0.3 Nm peakup to just under 0.7 Nm peak. The rotor was replaced with therotor from the 36 slot motor (with the 1 mm bridge kept). Thecogging torque increases very slightly. The stator slot openingswere then reduced from 3.3 mm to 2.32 mm, this reduced thepeak cogging from 0.7 Nm to 0.5 Nm. The air-gap length wasthen increased from 0.65 mm to 1 mm. This further reduced thecogging. In comparison, the 36 slot motor had the bridge re-duced from 2 mm to 1 mm in a likewise fashion and Fig. 11illustrates that the cogging reduced from just over 0.3 Nm toabout 0.14 Nm peak, i.e., it reduced with a reduction in bridgewhich is the opposite to the 30 slot motor. Again, this illustratesthat the cogging torque is unpredictable and a function of sev-eral parameters.

If the cogging torque characteristics were sinusoidal, with 5deg twist in the 36 slot motor and 3 deg twist in the 30 slot motor,then the cogging would be eliminated since the cogging for eachsegment would be in complete anti-phase. However, they arenot sinusoidal in their shape so that the difference leads to thecogging characteristics for the M36-t and M30-t motors. Hence,the pitch of the cogging in the twisted rotor motors is much less.

When unskewed, the 36 slot rotor has a cogging torque which isabout 0.32 Nm peak-to-peak which is 3% of rated torque and thetwisted angle rotor reduces this to 0.13 Nm. The 30 slot motorhas a peak-to-peak cogging of about 0.26 Nm which is 2.6% ofthe rated torque. The use of fractional slot motors is popular andthe twisted angle rotor further reduces the cogging torque in the30 slot motor to about 0.011 Nm peak-to-peak which is 0.11%of rated torque and now much less than the 36 slot motor.

Other techniques often used in reducing torque is full skew(by one stator slot on either the stator or rotor), careful selectionof the magnet arc (in a surface magnet rotor) and careful designof the inter-pole axis of the rotor ( -axis).

Cogging torque will be carried through into the load torquewhen operating as well as affecting the starting torque. There-fore, in motors where load torque ripple is important, the cog-ging torque needs to be addressed in addition to ripple due toharmonic winding (or phase-belt) torque.

V. FEA SIMULATIONS AND EXPERIMENTALRESULTSOPEN-CIRCUIT BACK-EMF

AND LOAD TESTS

Experimental validation of the simulations were carried outvia an open-circuit back-EMF test and also a load test. The loadtest was carried out at phase advance and this is investigatedbelow. Obtaining valid instantaneous torque ripple character-istics were not possiblethe active load would produce smalltorque perturbations which would be in addition to those of themotor under test, hence invalidating the tests. However, meantorque measurements were possible.

In this section, the measured back-EMF waveforms of the twomotors are compared to the simulated waveforms obtained fromthe Ansoft models. This is then followed up by load test results.The performance of the motors was examined with torque anglevariation in order to assess the motor behavior with phase ad-vance. These motors have -axis saliency and are suitable forfield weakening control. In addition to the load simulation val-idation, the efficiency of M30 and M30-t motors was measuredto show the influence of the twisted angle.

For completeness, the load torque is assessed via SPEEDsimulations both in terms of instantaneous torque ripple andthe mean torque calculated from current-flux-linkage loops. Ex-tended twist angles are also assessed in order to change theshape of the load angle curve.

A. Back-EMF WaveformsFig. 12 shows the simulated and measured waveforms of the

three-phase back-EMFs for the unskewed 4-pole 36-slot IPMmotor with a single-layered winding. Note that the waveformsare uneven due to tooth-slot effects. With a rotor twisted angleof 5 deg for the 4-pole 36-slot motor, the voltage ripple reducessignificantly and the back-EMF waveforms become more sinu-soidal, as shown in Figs. 12 and 13.

The test was repeated for the double-layer 30 slot motor sothat the back-EMF waveforms of the Type M30 and M30-tmotors, as obtained from Ansoft FEA simulation and by mea-surement, are shown in Figs. 14 and 15. It is obvious that theback-EMF waveforms of Type M30-t with 3 deg twisted angleare improved.


Fig. 12. Three-phase back-EMF waveforms for 36 slot motor at 1800 rpm. (a)Simulated and (b) measured back-EMFs. Both traces have 50 V/division.

B. Torque From I-Psi LoopsA common assessment of the performance of an IPM motor

is to assess the variation of torque with torque anglethis is theangle of the current phasor with the -axis. For the 36 and 30slot motors, the torque calculations for the different simulationpackages is given in Table IV. The errors are less than 5% andthis is because there are some minor differences in the bridgearea of the Ansoft model (the true experimental motor topologyas used for the back-EMF simulation and measurement compar-isons) and SPEED model (a slightly modified bridge arrange-ment in order to fit a standard topology, but giving very similarresults). The twisted rotors are 5 deg for the 36 slot motor and 3deg for the 30 slot motor. It can be seen that there is little differ-ence in the torque when the rotor is twisted by a small degree.

It is now worth investigating the torque in more detail. Ex-perimental validation was obtained for the 30 slot motor sothis motor will be the focus of more detailed study; some fur-ther results for the 36 slot motor will included when necessary.The SPEED calculations in Table IV were obtained from cur-rent-flux-linkage loops (I-Psi loops) and Fig. 16 shows these

Fig. 13. Three-phase back-EMF waveforms for 36-t slot motor at 1800 rpm.(a) Simulated and (b) measured back-EMFs. Both with 50 V/division.

for the M30 and M30-t motors. These are for one phasetheloops for the other two loops are identical and the area enclosedin a loop represents the energy converted. From knowledge ofthe pole number and speed, the energy can be converted intothe mean torque. Since the torque is little changed from theunskewed to the twisted rotor case it can be seen that the loopsfor Segments 1 and 2 are very similar and their sum is very closeto the unskewed rotor loop. These results are for the currentphasor placed on the -axis.

C. Instantaneous Torque SimulationsWe can also address the instantaneous torque from these sim-

ulations. Fig. 17 gives the torque for the M30 and M30-t motors.There is some attenuation of the torque ripple when the rotor istwisted although it is not substantial. To further assess the af-fects of the twisted rotor then the exercise was repeated for the36 slot motor as illustrated in Fig. 18. This time the full-loadtorque ripple is attenuated.

The torque ripple under load is substantially higher thanthe cogging torque. Fig. 19 compares the torque when 10


Fig. 14. Three-phase back-EMF waveforms for 30 slot motor at 1800 rpm. (a)Simulated and (b) measured back-EMFs. Both with 50 V/division.

segments are used in the 30 slot motor with a front-to-backaxial skew of one stator slot (which gives a segment-to-segmenttwist of 1.2 deg). There is still torque ripple due to windingharmonicsthis can be the reduced by careful winding designand higher skewing. To illustrate the latter then the 30-slot10 segment rotor was twisted even further with 3 deg twistper segment (giving a stator skew front to back of 2.5 statorslotsthis would help damp the 5th and 7th winding harmonictorques). These results are given in Fig. 20. The torque rippleis now reduced to about 0.2 Nm peak-to-peak which is a 2.3%ripple (with the mean torque reduced to 8.96 Nm).D. 30 Slot Sine Wound Stator Simulations

With the two segment rotor the torque ripple is still 13.4%.As an exercise, the winding was graded (different number ofturns per coil) so that with winding is more sinusoidal. This isdone for the 30 slot motor and the results are shown in Fig. 21.The mean torque increases by over 1 Nm; however, the torqueripple only reduces by 1%. This winding in Fig. 2(b) has 5 coilsides per phase per belt with two slots gap on one side and threeon the other. From the two slot gap side the turns per coil for

Fig. 15. Three-phase back-EMF waveforms for 30-t slot motor at 1800 rpm.(a) Simulated and (b) measured back-EMFs. Both with 50 V/division.

TABLE IVTORQUE FOR DIFFERENT MOTORS FROM ANSOFT AND SPEED WHEN

CURRENT IS ON THE AXIS

successive coils in one phase belt are: 7, 11, 13, 12, and 7. Thisgives a total number of 50 turns per phase belt which is the sameas the lap-wound motor. Therefore further design modificationscan be implemented to reduce the torque ripple and as exam-ples of this then the slot openings are closed from 3.2 mm to1.5 mm. This reduced the ripple to 9% and in conjunction withthe two-segment rotor with 3 deg twist then the ripple is foundto be 6.2%. It should be borne in mind that reducing the slotopening may cause problems in winding the motor (automatedor manual) where the wire may no longer fit though the opening,


Fig. 16. Current-flux-linkage loops for the M30 and M30-t motors with fullload current on the -axis. The segment I-Psi loops are very close and the sumof the two loops is almost identical to the unskewed rotor I-Psi loop.

Fig. 17. Instantaneous torque for 30 slot motor with unskewed rotor and twistedrotor with full load current on -axis. The air-gap is split into four layers andMaxwell stresses are taken round the air-gap at the center of the two middleair-gap layers (Integration 1 and 2). (a) Unskewed rotor torque obtained fromtwo Maxwell stress integrals; (b) twisted rotor (Segment 1 and Segment 2 torquefrom mean of two Maxwell stresses).

so this may not necessarily be a satisfactory remedy. However,solutions such as the use of parallel strands-in-hand of thinnerwire can be used to overcome this issue.

A full comparison of the peak-to-peak load torque ripple forthe different 30 slot and 36 slot motors is given in Table V. Thisillustrates that several design changes have to be implementedto reduce the torque ripple, and that some changes are moreeffective than others.

Fig. 18. Instantaneous torque for 36 slot motor with unskewed rotor and twistedrotor showing torque ripple attenuation with full load current on -axis. Twosegment twisted rotor gives reasonable torque ripple attenuation.

Fig. 19. Variation of instantaneous torque at full load with increasing segmentnumber (current on -axis) showing influence of winding functions10 seg-ment twisted rotor (in 30 slot stator) which is twisted by 1.2 deg per segment.

Fig. 20. Variation of instantaneous torque at full load with increasing segmentnumber (current on -axis) showing influence of winding functions30 slotstator and 10 segment twisted rotor, which is twisted by 1.2 deg and 3 deg.

E. Variation in Torque With Torque Angle SimulationsIt is worth investigating the variation of torque with torque

angle to assess the performance of the motor under field weak-ening conditions. The motors were tested at 30 degree phaseadvance. Again, focusing on the 30 slot motor, the variations oftorque and rms line voltage are shown in Fig. 22. This figureillustrates that the motor exhibits good field weakening capa-bility. Many IPM motors do not work well with phase advanceup to 30 degrees. More detailed performance figures at 30 degadvance are given in the next section but one point to highlightis that the motor is running close to unity power factor at the 30deg phase advance with full load current, which leads to highefficiency operation.


TABLE VCOMPARISON OF MEAN TORQUE AND TORQUE RIPPLE WITH FULL LOAD CURRENT ON -AXIS

Fig. 21. Variation of instantaneous torque at full load with sine wound stator,narrow stator slot opening (1.5 mm) and two segment twist30 slot stator andfull load with current on -axis.

Fig. 22. Variation of torque and line voltage at full load current for 30 slotmachine (untwisted)M30-t results are very similar.

F. Experimental Load TestPerformance VerificationFrom the comparison of the M36 and M30 motors, the

back-EMF of the M30 motor appears to be more sinusoidal.Both motors are efficient; the efficiency of the 4-pole 30-slotIPM motor is examined here together with the mean torque.Fig. 23 shows the experimental setup used to test the motor.It was connected to a servo motor which acted as the load,and a torque transducer was used to measure the torque andspeed directly. The motor driver was programmed using theMicrochip MPLAB IDE, which is specific to sensorless drive

Fig. 23. Experimental set-up4-pole 30-slot motor under test for measure-ment of the efficiency.

control. The motor was driven at constant speed 3660 rpmand a load of about 10 Nm applied to the test motor. A phaseadvance of 30 deg was also used.

Table VI shows the measured motor output data of the 4-pole30-slot IPM motor at the rated speed of 3660 rpm, where theinput voltage and current are rms values. It is clear that theefficiency of M30 and M30-t motors are almost the same atrated speed with 30 degree phase advance. These are a littlehigh at around 95%the calculated efficiency is 91.8% andthis includes 247 W of copper loss (228 phase resistancemeasured with an RLC meter) and 91.7 W of iron loss (fromphase winding resistance measurement and SPEED calcula-tion). When the efficiency is over 90% small measurementsmall errors will cause the differences. The power was mea-sured using a three-phase power analyzer; with the power factorbeing very close to unity this measuring technique may wellproduce a 4.1% error in measurement, which is the difference inthe measured and calculated efficiencies. The optimal twistedangle can reduce back-EMF high-order harmonics; however,it does not significantly affect motor efficiency. The simulatedand measured torques appear to be the same at 9.96 Nm,showing excellent correlation at this particular load point.


TABLE VIMEASURED DATA OF 4-POLE 30-SLOT IPM MOTOR

VI. CONCLUSIONThis paper has presented a simple and effective method to

reduce high-order harmonics in the back-EMF waveform of anIPM using a two-segment rotor with a twisted angle betweenthe two axial segments. This modification can reduce the man-ufacturing cost when compared to full skewing. The proposedtwo-segment structure of the rotor reduces the cogging torquedue to the tooth-slot effect, and can suppress the high-orderback-EMF harmonics. The paper provides a formula to calculatethe optimal twisted angle of the rotor segments for production ofsinusoidal back-EMF waveforms. The optimal twisted angle de-sign was examined by analyzing the THD of these waveforms.

It was found that the cogging torque can also be reduced,while the motor efficiency remained almost constant when thetwisted rotor was used.

In addition to the back-EMF and cogging torque calculations,load torque was also investigated. Torque ripple due to windingMMF harmonics were apparent. While multi-stage segmentswere shown to reduce this, a reduction in mean torque is alsoassociated with this method since a high degree of skew is re-quired. This problem is better addressed using low-harmonicwindings with methods such as short pitching and graded coils(sinusoidal winding).

There are many recent papers which concentrate on partic-ular design aspects and techniques of permanent magnet mo-tors (for instance, [32][39], in addition to work already cited).This paper describes further design possibilities for brushlessPM motors and reflects the growing demand for new and in-novative design features in this type of motor for a broadeningbase of applications which are becoming more demanding intheir specification.

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