IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 2, MARCH 2002 1157

Detent Force Minimization Techniques in PermanentMagnet Linear Synchronous Motors

Ki-Chae Lim, Joon-Keun Woo, Gyu-Hong Kang, Jung-Pyo Hong, and Gyu-Tak Kim

Abstract—Detent force produced in permanent magnet linearmachines generally causes an undesired vibration and noise. Thispaper analyzes detent force and thrust in permanent magnet linearsynchronous motor by using various detent force minimizationtechniques.

A two-dimensional finite-element analysis is used to predict de-tent force and thrust due to structural factors and nonlinearity.Moreover, moving node techniques for the drawing models is usedto reduce modeling time and efforts.

Index Terms—Detent force minimization techniques, finite-element analysis, moving node technique for the drawing model,permanent magnet linear synchronous motor.

I. INTRODUCTION

PERMANENT magnet (PM) motors have been used in awide variety of industrial applications such as robotics,

power string and high-precision position control [1]. They arecurrently being developed in order to implement better servo-performance. For the embodiment of high-performance PM mo-tors, the cogging torque reduction, vibration, and noise is a vitaldesign consideration [1], [2].

In the linear PM motor, especially permanent magnet linearsynchronous motor (PMLSM), there are two additional forcecomponents, which affect their performance, except the electro-magnetic (EM) force. The first component, commutation rippleforce, is due to the harmonic content of the current and voltagewaveforms. The second component, detent force analogous tocogging torque of rotary PM motors, is produced by the phys-ical structure of PM motors [1]–[6].

Detent force is developed from the magnetic attraction be-tween the permanent magnets mounted on the rotor and thestator teeth [2]. It is the attractive force component that attemptsto maintain the alignment between the stator teeth and the per-manent magnets on the rotor [1]–[6]. And detent force makestorque ripple producing both vibration and noise of motors anddeteriorating the control characteristics of speed control at lowspeed as well as of position control. Therefore, detent force re-duction is an essential requirement in PMLSM.

Manuscript received July 5, 2001. This work was supported by the Korea Sci-ence and Engineering Foundation (KOSEF) through the Machine Tool ResearchCenter at Changwon National University.

K.-C. Lim is with Dong-Sung Electric Machine Co. Ltd., Kimhae,Kyungnam, Korea (e-mail: kclim@cosmos.changwon.ac.kr).

J.-K. Woo is with LG Innotek Co. Ltd., Gumi, Gyeongbuk, Korea (e-mail:jkwoo@lycos.co.kr).

G.-H. Kang, J.-P. Hong, and G.-T. Kim are with the Electrical EngineeringDepartment, Changwon National University, Changwon, Kyungnam, Korea(e-mail: kgh1004@cosmos.changwon.ac.kr; jphong@sarim.changwon.ac.kr;gtkim@sarim.changwon.ac.kr).

Publisher Item Identifier S 0018-9464(02)02053-8.

There are several detent force minimization techniques inPMLSM: permanent magnet width adjustment; asymmetricpermanent magnet arrangement; and using semi-closed slot ofstator core. When these techniques are applied to PMLSM, thechanges of characteristics should be sufficiently considered.Therefore, this paper analyses the variations of detent forceand EM force according to several detent force minimizationtechniques.

Most of the recent studies on detent force calculation makeuse of some form of analytical method or finite-element anal-ysis (FEA) [2]–[6]. They are specific to a particular techniqueof reducing detent force, which results from difficulty of gener-alization of analytical methods and excessive demand for mod-eling and computational time of FEA even if it provides moreaccurate analysis results and accounts for the nonlinear charac-teristics and the complex geometry.

This paper uses moving model node technique, which re-moves the demand for remodeling of FEA model according tothe simple geometric variations, to calculate detent force, elec-tromagnetic force and thrust.

Moving model node technique generates the preprocess dataautomatically according to the variation of each geometric de-sign variable through mesh generation after changing the ini-tial modeling data (node, line, region, etc.) of analysis model. Itcan reduce the efforts of both remodeling and preprocess withrespect to geometric design variables and the analysis time byapplying batch process including the input of moving objectinformation, mesh generation, and characteristic analysis (postprocess).

II. A NALYSIS METHOD

A. Moving Model Node Technique

Accurate predictions to the performance of PM motors hasbeen a major concern for researchers and it has been improvedby using the numerical method to obtain more precise solutionsfor real problems. FEA has been one of the most powerful andwidely used techniques in electric machine design and analysis.However, it has the disadvantage over difficult modeling of geo-metric variations and excessive demands for computational timeand resources. To overcome these disadvantages, moving nodetechnique, which moves node data of triangulation mesh abovesliding line and modifies boundary condition, has been pro-posed [6]. It possibly makes deformation of triangulation datain case of coarse mesh and cannot consider geometric variationsof analysis model.

This paper proposes moving model node technique to initialpreprocess model.

0018-9464/02$17.00 © 2002 IEEE

1158 IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 2, MARCH 2002

Fig. 1. Flowchart of FEA with moving model node technique.

Fig. 2. Application of moving model node technique.

Fig. 1 presents the flowchart of FEA with moving model nodetechnique. Moving model node technique executes preprocessautomatically for the variations of geometric design variablesthrough the remesh after moving the initial modeling object,which represent nodes, lines or regions of analysis model and ofwhich a base unit is node. At first stage, analysis model for geo-metric variables requires the input of geometric model, drivingsource, and material properties. And then, the information ofthe moving objects should be determined and saved as a scriptformat file.

When the moving objects are selected and moved, the numberof segments used in mesh generation stage, among the movednodes is calculated based on initial segment data to avoid theunbalanced mesh data. After making the new moved model datathrough the transformation of the initial model data with movinginformation, modified model is automatically created by addingthe beforehand inputted driving source and material properties.The characteristic analysis of new model by moving model nodetechnique is executed after remesh and it is possible to producerepeatedly the analysis model with new dimension and figureby the transformation of moving information. Therefore, it canreduce the efforts of modeling, preprocess, and analysis time bybatch processing including the moving model node techniquewith moving information, mesh generation, and characteristicanalysis.

Fig. 2 shows the application of the proposed technique.Fig. 2(a) is moving node application to change slot shape with

Fig. 3. Structure and flux distribution of short secondary type PMLSM.

Fig. 4. Force analysis of short secondary type PMLSM.

TABLE ISPECIFICATION OFPROTOTYPICPMLSM

constant slot area and Fig. 2(b) shows moving line applicationto make various PM width analysis models.

After generating various dimension models, the moving nodetechnique is applicable to each model to reduce the analysis timeof computing of detent force distribution.

B. Analysis Model of Detent Force Reduction

To apply the detent force minimization techniques, the shortsecondary type PMLSM is considered in this paper. Fig. 3 showsits basic structure and flux distribution.

Fig. 4 shows analysis results of static force distribution withrespect to mover position. The resultant force described as thrusthas three component forces. One is an electromagnetic force.Another is an undesired detent force and the other is an end forceproduced by stator current without PM.

Since the end force is negligible in case of small current input,FEA model with periodic boundary condition is possibly takenfrom analysis region in Fig. 3.

Table I is the specification of prototypic PMLSM used in de-tent force analysis.

LIM et al.: DETENT FORCE MINIMIZATION TECHNIQUES 1159

Fig. 5. Detent/EM force according to PM width.

III. D ETENT FORCEMINIMIZATION TECHNIQUES

A. PM Width Adjustment

A fundamental harmonic component of detent force can beremoved by the adjustment of PM width toward constant slotpitch in stator. Fig. 5 shows the change of the maximum valueof detent/EM force according to both the number of slot per poleper phase, , and the adjustment of PM width.

PM width versus constant slot pitch to minimize detent forceis satisfied with equation ( 0.25) for an integer . Anal-ysis result is slightly different from value calculated by givenequation. This is due to the effect of saturation.

In Fig. 5, EM force with has maximum value aroundPM width of 51 mm because of the effect of the harmonic com-ponents of airgap flux density distribution, while detent forcehas minimum value.

B. Asymmetric Arrangement of PM

As detent force distribution in PMLSM has a period of slotpitch, it is written as following in equation from Fourier series.

(1)

where, is detent force of one pole andis the numberof poles.

In (1), the even harmonic term of detent force, especiallythe fundamental term, can be eliminated by disposing two PMsproperly being path of the same flux. This is explained as (2).

(2)

Fig. 6 shows detent force distribution by prototype and anal-ysis model using the asymmetric PM arrangement. The asym-metric PM arrangement makes detent force remarkably reducedin comparisons with that of prototype.

Fig. 7 is thrust distribution of prototype and asymmetric PMarrangement model. The experimental results are presented toshow the validity of the proposed method.

Fig. 8 shows results of detent force distribution whenis 1.Unlike results in Fig. 6, the decreasing quantity of detent forceby deposing PM asymmetrically is relatively small due to thedominant harmonic components of detent force distribution.

Fig. 6. Detent force reduction using asymmetric PM arrangement.

Fig. 7. Thrust characteristics of prototype model and asymmetric PMarrangement model.

Fig. 8. Detent force reduction using asymmetric PM arrangement (q = 1).

C. Semi-Closed Slot

Detent force depends on a slot aperture width in case of usingsemi-closed slot in stator core. This is due to the reducing influ-ence on the slot harmonic components of airgap flux densitydistribution according to the decrease of the slot aperture width.

Fig. 9 shows results of detent EM force with varying the slotaperture width and maintaining constant slot area by applyingthe proposed moving node technique. In Fig. 9, the decreasingslot aperture width makes detent force decreasing and EM force

1160 IEEE TRANSACTIONS ON MAGNETICS, VOL. 38, NO. 2, MARCH 2002

Fig. 9. Detent force reduction using semi-closed slot.

Fig. 10. Mixture of both PM width adjustment and asymmetric PMarrangement.

increasing, but the excessive decrease leads to the undesiredleakage flux.

D. Compound Application of Minimization Techniques

Detent force reduction can be archived by the mixture of morethan two minimization techniques with some attention.

Optimal PM widths in the case of 2 can be determinedas 48.87 and 60.37 mm shown in Fig. 5. For convenience ofmanufacture, the integer number is finally taken.

Detent force of analysis model using each PM width isrelatively smaller than that of prototype, however, it is stilllarge value. Therefore, the additional reduction is made fromarranging PM asymmetrically.

Fig. 10 shows results from the above mentioned procedure forPM width of 48 (mm). The final analysis results shows the out-standing reduction of detent force up to about 1.2% comparedwith that of prototype. In the case of PM width of 60 mm, the

Fig. 11. Mixture of minimization techniques with semi-closed slot.

reduction ratio of detent force is 7% and the effect of the asym-metric PM arrangement method is confined to some degree be-cause of the increasing flux linkage between two neighboringPMs.

The semi-closed slot with the asymmetric PM arrangementcan be applicable to detent force minimization. As shown inFig. 11, it also gives desired results.

IV. CONCLUSION

An analysis of various detent force minimization techniquesas applied to PMLSM has been performed. FEA is used to cal-culate detent force and thrust considering structural factors andnonlinearity. In addition, moving model node technique is pro-posed to increase the modeling efficiency of FEA with respectto various geometric changes.

The proposed minimization techniques have a significant ef-fect on detent force and their mixture is useful to minimize theresultant detent force to some extent.

REFERENCES

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[3] T. Li and G. Slemon, “Reduction of cogging torque in permanent magnetmotors,”IEEE Trans. Magn., vol. 24, pp. 2901–2903, 1988.

[4] T. Yoshimura, H. J. Kim, Watada, S. Torii, and D. Ebihara, “Analysis ofthe reduction of detent force in a permanent magnet linear synchronousmotor,” IEEE Trans. Magn., vol. 31, pp. 3737–3739, 1995.

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