3228 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011

Minimization of Outlet Edge Force Using Stair Shape Auxiliary Teeth in aStationary Discontinuous Armature Linear Permanent Magnet Motor

Yong-Jae Kim and Sang-Yong Jung

Department of Electrical Engineering, Chosun University, Gwangju 501-759, KoreaSchool of Information and Communication Engineering, Sungkyunkwan University, Suwon 440-746, Korea

The stationary discontinuous armatures that are used in permanent magnet linear synchronous motors (PM-LSMs) have been pro-posed as a driving source for transportation systems. However, the stationary discontinuous armature PM-LSM contains the outlet edgeswhich always exist as a result of the discontinuous arrangement of the armature. For this reason, the high alteration of the outlet edgecogging force produced between the armature’s core and the mover’s permanent magnet when a mover passes the boundary betweenthe armature’s installation part and non-installation part has been indicated as a problem. Therefore, we have examined the outlet edgecogging force by installing the stair-shaped auxiliary teeth at the armature’s outlet edge in order to minimize the outlet edge coggingforce generated when the armature is arranged discontinuously. This paper presents the results of 2-D numerical analysis by FEM ofthe cogging force exerted by the outlet edge.

Index Terms—Discontinuous arrangement, linear synchronous motor, outlet edge cogging force, stair-shaped auxiliary teeth, 2-D nu-merical analysis.

I. INTRODUCTION

L INEAR motors have become popular in the field of fac-tory automation where there is great demand for high-

speed, low noise, simplification of driving apparatus and main-tenance-free transportation [1]–[4]. Usually, in a transportationsystem using linear motors, a full-length (continuous) arma-ture-side-on-ground design is employed. This design is very re-liable although it is costly in long-distance transportation sys-tems. Therefore, in order to resolve the problem of higher costs,the authors’ laboratory has proposed a stationary discontinuousarmature PM-LSM in which the armature is engaged only whenaccelerated and decelerated operation is necessary when thePM-LSM is used with long-distance transportation systems infactories.Fig. 1 shows speed profiles of PM-LSM horizontal trans-

portation systems. The mover is accelerated by the short arma-ture unit (accelerator) and is then driven by its own inertia. Sincethe velocity of the mover decreases, the mover enters the nextarmature unit which is installed in order to make it re-accelerateand decelerate, and there it is re-accelerated and decelerated.However, the stationary discontinuous armature PM-LSM

contains outlet edges, which always exist as a result of thediscontinuous arrangement of the armature. For this reason,the outlet edge cogging force generated between the entranceend (entry interval) and the exit end (ejection interval) hasbecome a problem. The problem is that the cogging force thatoperates at each outlet edge affects the mover’s drive, so thereis a possibility that hunting occurs during acceleration and de-celeration when freewheeling changes over to re-accelerationand deceleration [5]. Particularly, hunting acts as the majorfactor of vibration and noise and, in the worst case, causesstep out due to load disturbance. Therefore, a reduction of

Manuscript received February 21, 2011; accepted April 07, 2011. Date ofcurrent version September 23, 2011. Corresponding author: S.-Y. Jung (e-mail:syjung@ece.skku.ac.kr).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMAG.2011.2144962

Fig. 1. Speed profiles of PM-LSM horizontal transportation systems.

cogging force at each outlet edge is highly desirable in order toprevent the possibility of hunting occurring at re-accelerationand deceleration and this allows stable drive of the stationarydiscontinuous armature PM-LSM.Recently, researchers have proposed some methods for re-

ducing cogging force with regular periodicity which affects ma-chine output or driving characteristics [6]–[11]. One of themprovides skew for permanent magnets or cores, and anotherchanges the magnetic end arrangement. However, cogging forcegenerated at the outlet edge of the stationary discontinuous ar-mature PM-LSM does not possess regular periodicity and itpulls the mover into the armature area at the entry interval, andpulls it back to the armature side at the ejection interval. Weconsidered applying the auxiliary teeth with stair shape at theoutlet edge of the armature in order to reduce the cogging forceof the outlet edge.This paper presents the results of two-dimensional (2-D) nu-

merical analysis with a finite element method (FEM) of the cog-ging force exerted by the outlet edge as a result of altering theshape of auxiliary teeth into a stair shape. Moreover, we ob-tained the calculation by comparing the cogging force of theoutlet edge of both the basic and the proposed models by ana-lyzing the stair-shaped auxiliary teeth in which the outlet edgecogging force is minimized the most.

II. FORCE GENERATED AT THE OUTLET EDGE

Fig. 2 shows forces exerted in the mover at the outlet edge.In Fig. 2, we can see that the force generated at the outlet

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KIM AND JUNG: MINIMIZATION OF OUTLET EDGE FORCE USING STAIR SHAPE AUXILIARY TEETH 3229

Fig. 2. Forces exerted in the mover at the outlet edge. (a) Entry interval (en-trance end) and (b) ejection interval (exit end).

edge has an effect on the mover. If the mover goes through theboundary between the installation part and the non-installationpart of the armature of a stationary discontinuous armaturePM-LSM, the attractive force produced between the armature’score and mover’s permanent magnet fluctuates highly. Theattractive force produced at the entry interval operates in thesame direction as the mover. That is, the mover is acceleratedby a force, which pulls the mover into the armature area. Onthe other hand, the attractive force generated at the ejectioninterval operates in a direction opposite that of the mover.In other words, the mover becomes decelerated by the force,which pulls the mover back to the armature area.

III. 2-D NUMERICAL ANALYSIS OF THE OUTLET EDGECOGGING FORCE

A. Basic Model

To examine the cogging force generated at each outlet edge,we used 2-D numerical analysis with a FEM. The general-pur-pose electromagnetic field analysis software (JMAG-Studio)was used for 2-D numerical analysis. The basic model is shownin Fig. 3. The armature used for measurement has 17 slots and4-pole permanent magnets which are arranged in the mover.The pole pitch is 30 mm and the pitch of the armature’s slotis 10 mm. The number of elements is 61,200, and the numberof nodes is 31,314. The method of analysis is as follows:after setting an air-gap of 5 mm between the armature and themover, the mover enters the armature area at the moment whenthere is incomplete alignment between them and the movermove at intervals of 0.5 mm to the section that is completelybeyond the armature area. The 2-D numerical analysis result ofcogging force at the outlet edge is shown in Fig. 4. As indicatedby Fig. 4, the outlet edge cogging force at the entry intervalincreases as the mover moves into the armature area due tothe change in the number of magnetic poles which are alignedwith the armature. However, the cogging force decreases at thecomplete alignment of the mover with the armature interval.Moreover, we found that outlet edge cogging force at the ejec-tion interval increases as the mover passes through the armaturearea due to the change in the number of magnetic poles whichare aligned with the armature. When the air-gap is 5 mm, amaximum outlet edge cogging force of 13.4 N is generated atthe entry and ejection intervals. On the other hand, a coggingforce of 0.6 N is generated at the same time as the moverbecomes completely aligned with the armature. Therefore, wefound that the cogging force in this situation is much less thanthe cogging force at each outlet edge.

Fig. 3. Basic model. (a) Side view of the armature. (b) 2-D numerical analysisbasic model.

Fig. 4. Cogging force waveform of basic model.

B. Proposed Model for Reduction the Outlet Edge CoggingForce

We tried to reduce the cogging force generated at the outletedge by installing the auxiliary teeth at the outlet edge of thearmature. As a result, we found that if we install the auxiliaryteeth as the outlet edge cogging force reduction method, the ap-propriate pitch of the auxiliary teeth was 2.5 mm, height 22 mm,and width 7.5 mm. We discovered that a 28.4% reduction of theoutlet edge cogging force was possible when using proposedmodel with auxiliary teeth, compared with the basic model [12].However, more reduction of cogging force at each outlet edge

which affects the output of the instrument or driving character-istics is highly necessary because cogging force generated atthe outlet edge is still large. Therefore, we altered the shape ofthe auxiliary teeth which is installed at the end edge of the ar-mature into a stair shape. Also, we analyzed the cogging forcegenerated at the outlet edge using 2-D numerical analysis witha FEM. The scale of analysis is from the armature area withthe complete alignment of the mover to the end of the armaturewhere the mover has completely exit. Fig. 5 shows the proposedmodel with auxiliary teeth of original shape and the proposedmodel with stair-shaped auxiliary teeth. In case the auxiliaryteeth are altered into a stair shape, the length of Z which rep-resents the distance between the stair steps and the number ofstair-step must be decided.First, the Z-length which is the interval between the stair steps

must be analyzed. Fig. 6 shows the auxiliary teeth with stairshape adjusted by the Z-length. Fig. 6(a) shows the stair-shapedauxiliary teeth with the Z-length of 1.5 mm, (b) 3 mm, and (c)

3230 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011

Fig. 5. Proposed model. (a) Proposed model with auxiliary teeth of originalshape. (b) Proposed model with stair-shaped auxiliary teeth. (c) 2-D numericalanalysis proposed model.

Fig. 6. Proposed model with stair-shaped auxiliary teeth. (a) Proposed model#1 with the Z-length of 1.5 mm. (b) Proposed model #2 with the Z-length of3 mm. (c) Proposed model #3 with the Z-length of 4.5 mm.

4.5 mm. Please note that the number of stair steps was calcu-lated as three for all the lengths in this figure. Fig. 7 shows the

Fig. 7. Outlet edge’s cogging force waveform of each model.

Fig. 8. Harmonic analysis of each model.

waveform of the outlet edge’s cogging force of each model.As indicated by Fig. 7, the basic model generated the max-imum cogging force of 13.4 N while the proposed model withauxiliary teeth showed its maximum cogging force of 9.6 N.Also, when the stair-shaped auxiliary teeth was installed, cog-ging force generated at the outlet edge was more reduced thanthe other models. Among the proposedmodels with stair-shapedauxiliary teeth, proposed model #2 with the Z-length of 3 mmshowed the least cogging force of outlet edge with themaximumcogging force of 6.1 N. By comparing the basic model and theproposed model with auxiliary teeth, we found that the reduc-tion of maximum outlet edge cogging force by 7.3 N and 3.5 Nwas possible by using the proposed model #2 with Z-length of3 mm of auxiliary teeth with stair shape. Fig. 8 shows the har-monic analysis of the basis model, proposed model with aux-iliary teeth, and the proposed model #2 of auxiliary teeth withstair shape. In Fig. 8, we can observe that almost all the har-monic components of the proposed model #2 with stair-shapedauxiliary teeth are smaller than the harmonic constituents of thebasic model and proposed model with original auxiliary teeth.Particularly, the components of both the 5th and 6th harmonicswere drastically reduced. As a result, the maximum coggingforce of the proposed model #2 with stair-shaped auxiliary teethshowed reduction as well.Next, the change of the maximum cogging force was mea-

sured when the numbers of the stair step of the stair-shaped aux-iliary teeth were adjusted. Fig. 9 show the proposed model withstair shape when the numbers of stair-steps were adjusted. Fig. 9shows the shape of the auxiliary teeth (a) when the stair stepswere adjusted into 2 steps, and (b) when the stair steps were 4.

KIM AND JUNG: MINIMIZATION OF OUTLET EDGE FORCE USING STAIR SHAPE AUXILIARY TEETH 3231

Fig. 9. Proposed model with stair-shaped auxiliary teeth. (a) Proposed model#4 when the stair steps were adjusted into 2 steps. (b) Proposed model #5 whenthe stair steps were adjusted into 4 steps.

Fig. 10. Outlet edge’s cogging force waveform by the numbers of stair stepsof stair-shaped auxiliary teeth.

Fig. 10 shows the waveform of the cogging force by the num-bers of stair steps of stair-shaped auxiliary teeth. As indicatedby Fig. 10, the maximum cogging force generated at the outletedge when the stair-shaped auxiliary teeth was adjusted into 2stair steps was 8 N, and when the stair steps were adjusted into 4,the maximum cogging force was 6.4 N. When the stair steps ofauxiliary teeth were adjusted into 2 steps, the cogging force gen-erated at the outlet edge was increased compared to the proposedmodels with 3 or 4 stair steps. Moreover, the proposed modelwhich was adjusted with 4 stair steps showed increase of cog-ging force by 0.3 N compared to the proposed model with 3 stairsteps. However, the difference of cogging force generated at theoutlet edge was extremely small, thus insignificant. Therefore,considering the total length of the stair-shaped auxiliary teeth,the appropriate number of the stair steps for the stair-shapedauxiliary teeth was 3.

IV. CONCLUSION

In this paper, the auxiliary teeth with a stair shape have beenproposed in order to reduce the cogging force of the outlet edge

in the stationary discontinuous armature PM-LSM which fea-tures discontinuous arrangement of the LSM’s armature. Fromthe results of a 2-D numerical analysis with a FEM, we foundthat the maximum cogging force generated at the outlet edge ofthe basic model was 13.4 N, while the maximum cogging forceof the proposed model with auxiliary teeth was 9.6 N. How-ever, in case the proposed model #2 with stair-shaped auxiliaryteeth was used, the maximum cogging force generated at theoutlet edge was only 6.1 N which is 54.5% less than the basicmodel and 36.5% less than the proposed model with the auxil-iary teeth. From the above results, we confirmed that in case thestair shape is used as a reduction method of the cogging force,the appropriate pitch of the auxiliary teeth is 2.5 mm, height22 mm, width 7.5 mm, number of stair-steps 3 with the intervalof 3 mm between the stair steps.

ACKNOWLEDGMENT

This study was supported by research funds from ChosunUniversity, 2009.

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