Design and Analysis of a Permanent Magnet Synchronous Motor Considering Axial Asymmetric Position of Rotor to Stator

: This paper presents the design and analysis of a permanent magnet synchronous motor (PMSM)consideringtheaxialasymmetricPMoverhangforasmartactuator(SA)applicationsuchas an isokinetic exercise machine. This structure helps take advantage of the motor space effectively and makes the system small in size and light in weight. However, two drawbacks related to the performance of motoroccur when the axial asym metricPMoverhangisused:(1)anaxialattractive force (AAF) is created, which can produce motor noise and vibration; (2) the torque of motor is reduced compared with the symmetric PM overhang model. We used five steps to solve these problems. Firstly, the AAF according to the variation in axial position of the rotor to the stator was calculated and analyzed. Secondly, the torque was calculated under the same conditions to confirm thatthesystemrequirementsweresatisfied.Thethree-dimensionalfiniteelementanalysiswasused to determine the AAF and torque. Thirdly, the appropriate axial position of the rotor to the stator was suggested considering the analysis results and space inside the housing. Next, the commercial bearingty pewaschosenso that the totalforceactingonthebearingwasbelowthebearingloadlimit to ensure motor stability. Finally, a prototype model was made and tested to confirm the accuracy of the analytical results. Through this study, by using the axial asymmetric PM overhang, the total length of SA was reduced by 5mm and the performance of motor wasguaranteed.


I. INTRODUCTION
Smart actuators (SAs) composed of modules integrating an electric motor, gear reducer, andcontroller,whicharewidelydevelopedasdrivingmodulesforrobots,areusedinmanyapplications to make the compact system. In this study, we examined when SAs are used as an electrical load on anisokineticexercisemachine(IEM),anddescribedthedesignandanalysisoftheelectricmotorthat constitutes theSA. IEM is a machine that controls the speed of contraction within the range of motion. It is widely used in rehabilitative activities or sports rehabilitation [1]. The main components of an IEM system areshowninFigure1a.Theelectricloadmainlyconsistsofacontroller,electricmotor,andreduction gear. Conventionally,thethreemaincomponentsoftheelectricloadareplacedseparately,creatingthe conventional electric load, as shown in Figure1b. However, since the space for the system islimited, using a SA type electric load is useful, as shown in Figure2. The SA module may help simplify the systemstructure,improvereliability,andcreateacompactsystem [2].Researchersareinterestedinthe permanentmagnetsynchronousmotor(PMSM)designforSAmoduletoachievehighefficiencyand high power density, which can be designed using optimal design techniques or the PM overhang to generate more magnetic flux in the air-gap [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Most PMSMs use a PM overhang structure in the rotortooperatetheHalleffectsensorforcost-savingandasimplifiedmotorstructure [4].  Kang et al. [5] investigated the asymmetric PM overhang effect from the view point of Z-axis thrust, vibration, and noise. Chun et al. [6] analyzed the effect of symmetric and asymmetric PM overhang on the linkage fluxes of the stator and axial magnetic forces. In this study, we investigated the axial asymmetric position of the rotor with PM overhang to stator with the aim of providing more space inside the motor. Figure3a depicts the half cross-section view of symmetric brushless PMSM. As shown in Figure3b, the space (I) at the rear of the motor is only used for containing end-winding, coilconnections, and theHalleffectsensorboard,sothemechanicalandcontrollerparts must be placed in the other areas. If the axial asymmetry of the PM overhang is used, the area (II) is freed up and can be used for bearings and supporting parts. This study was developed from Luu et al. [17], providing a moredetailed and clearexplanationofthetheoryandanalyticalresultsalongwith additional experimentalresults. The use of PM overhang has a positive effect on the performance of the motor; however, theasymmetricPMoverhangbreakstheaxialmagneticsymmetryofmotorandreducesthemagnetic torque. This generates an axial attractive force (AAF). AAF can damage the bearing and create noise and vibration [5]. Therefore, we investigated the value of AAF according to the axial position of the rotortothestator.ThetorquevalueisalsoaffectedbytheasymmetricPMoverhang,sowecalculatedthetorquetoensuretha tthesystemrequirementwassatisfied.BothAAFandtorqueweredetermined using three-dimensional finite element analysis (3-D FEA). Afterward, the commercial bearing was selected to ensure the stability of the motor. Considering the analysis results together with the actual dimension of the motor, the appropriateaxialposition oftherotortothestatorwasdetermined.Finally, the analysis results were validated by theexperiment.

III. AAF ANALYSIS DUE TO ASYMMETRIC PMOVERHANG
Due to the asymmetric configuration, the 3-D FEA was used to calculate the AAF values. The magnetic field can be solved using commercial software (3D Maxwell, ANSYS, Inc., USA). The virtual workmethodisusedtodeterminetheaxialattractiveforceandmagnetictorque [18].
whereW mag isthetotalstoredmagneticenergy,Bisthemagneticfluxdensity,Histhemagneticfield,zistheaxialdisplaceme nt,F θ istheforceintheθ-direction,andR rotor istheradiusoftheouterrotor. Figure5showstheperiodical3-DanalysismodelsofthePMmotor.Sincethemodelhasafractional slot per pole configuration, which is 20-pole and 24-slot, a 1/4 periodic of the machine was modeled in 3-D FEA. The Neumann boundary condition was applied to reduce the analysis time. The model withsymmetricalPMoverhanghasa5mmonbothsides.Theair-gapfluxdensitydistributionin both symmetric and asymmetric models is shown in Figure6. In the case of the symmetric model, theairgapfluxdensityisdistributedsymmetricallyonbothsidesoftheoverhangregion.Incontrast, the asymmetric model generates asymmetrical flux, which produces AAF and motorvibration.

IV. BEARING SELECTION CONSIDERING AXIAL ATTRACTIVEFORCE
To select the correct bearing for each application, several factors need to be considered, such as allowable space, bearing load (magnitude, direction), and rotational speed. For this studied motor, both axial and radial forces act upon the bearing. In the previous section, the axial force caused by axial asymmetry of the motor was determined, which is 99.27 N. We assumed that the motor is ideally symmetrical in the radial direction; thus the radial magnetic forces eliminate each other on the bearing. Therefore, the weight of the rotor and the rotational force (tangential component of the force) that generates the motor torque are considered radial loads. Since the maximum torque is less than twice the rated torque and the main operating point is the rated torque range, the rotational force was calculated based on the rated torque. To consider the maximum load on both bearings, we used the case where the direction of gravity to the rotor coincides with the direction of rotational force.Theradialloadwascalculatedbymultiplyingthesumofthesetwoloadsbyaloadfactorof1.2 (the value for the environment with little external impact on the shaft [19]). The load acting on each bearing was calculated using the moment equilibrium equation [19,20]. We chose deep groove ball bearings in this study because they can carry both axial and radial loads and have outstanding noise and vibration characteristics.Sincetheinnerringrotates,thevalueoftherotationalcoefficientVis1in Equation(4),sotheequationofequivalentloadontheballbearingisasexpressedinEquation (5). The dynamic equivalent radial load acting on the ball bearing is calculated by [20] Pr = X.V.Fr+Y.Fa (4) Pr = X.Fr + Y.Fa =0.496kN (5)  where Pr is the dynamic equivalent radial load N, Fr is the actual radial load N, Fa is the actual axial load N, X is the radial load factor, Y is the axial load factor, and V is the rotational factor.
The values for X and Y are listed in the bearing table provided by the manufacturer [20]. Consideringtheallowablespaceforthebearingandthebearingloadlimit,weusedthe6205-ZZ bearing (NTN Bearing Corporation, Japan) in thisstudy.

Resistance and Back Electromotive ForceComparison
Tocheckwhethertheprototypewasmanufacturedexactlyasthedesignedmodel,theresistanceandbackelectromotivefor ce(backEMF)weremeasuredusingadynamosystemasshowninFigure9. The data were acquired using the dynamo user interface and power analyzer. Table2presents the comparison of phase resistance and back EMF between the calculated values and experiment results for the symmetrical model. It was clearly observed that the error betweenthecalculatedandmeasured values was acceptable, at under5%.

Measurement of Axial AttractiveForce
Theforcemeasurementsystemwassetup,asillustratedinFigure10.Theloadcell(BDHS-1t)was used to measure the AAF value. A coupling is used to connect the motor shaft with the hand-wheel. Whenthehandwheelturnsintheclockwisedirection,therotormovesalongthe+z-direction,andvice versa. Each 180 • rotation of the hand-wheel, the rotor linearly moves 1.1 mm. Therefore, the AAF depending on the rotor position with respect to stator core wasmeasured.
ThecomparisonbetweenthecalculatedandexperimentalvaluesisshowninFigure11.TheAAFvalueincreases astheaxialpositionoftherotorcoretothestatorcoreincreases.Similartotheanalysis results, the measured value tended to be constant when Dx exceeded 9 mm. The experiment results are consistent with the analysisresults.

Isokinetic Exercise MachineTest
After the motor had been tested separately, it was assembled together with a controller and reduction gear to create the smart actuator type electric load as shown in Figure2. Both isotonic exercise mode and isokinetic exercise mode tests were implemented to check the performance ofthe system, as shown in Figure12a. In the isotonic mode, the same force is applied in the pedal and the value of force depends on selecting a resistance between 0 to 100%, while in the isokinetic mode, the constant speed is maintained regardless of the force exerted in the pedal. Both help to increase muscle endurance and muscle strength. In addition, training in the isokinetic mode also reduces the risk of injury. The torque value was measured in the two training modes and results are showninFigure12b,c.Theexperimentsshowthattheisokineticexercisemachineworkswellinboth training modes.

VI. CONCLUSIONS
Inthispaper,thedesignandanalysisofaPMSMwereproposedconsideringtheaxialasymmetric position of the rotor to the stator for efficient use of space inside the motor. Due to the axially asymmetrical motor, the Z-thrust force appeared, which may cause motor noise and vibration, and torque was reduced. To maintain the performance of motor, we numerically and experimentally investigated the axial force and torque according to the axial position of the rotor to the stator. Considering the available spaceforthebearing,andthesimulationresults,wefoundthat5mmisthe axial offset position of rotor core center to the stator core center, which means that the axial length of the motor can be decreased by up to 5mm. At a 5 mm of the axial offset position of the rotor to the stator, torque was reduced by 1.7% in comparison to the symmetric overhang PM model, which still met the system requirement. The process of how to choose a bearing to maintain the stability of the motor was alsopresented.