some design and prototyping issues on a 20000 rpm hdd spindle motor with a ferro-fluid bearing...

5
IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 2, MARCH 2001 805 Some Design and Prototyping Issues on a 20 000 rpm HDD Spindle Motor with a Ferro-Fluid Bearing System Shi Xin Chen, Qi De Zhang, How Ching Chong, Terutoshi Komatsu, and Cheng Hia Kang, Member, IEEE Abstract—A high-speed ferro-fluid bearing spindle motor for hard disk drive is introduced. Some design challenges and consid- erations on electrical motor, bearing system and spindle structure are addressed. The testing results of the prototypes are presented and discussed. The shown testing results of the prototypes indicate that the objective of developing a high-speed, high-performance, fluid-bearing spindle motor is fulfilled. It is a prospective spindle motor to be used in future hard disk drives. Index Terms—Design, ferro-fluid, fluid bearing, spindle motor. I. INTRODUCTION T HE DATA storage capacity of hard disk drives is increased in an amazing speed as a result of several key technology advancements in recording data on a disk with very high areal density. Recently, the areal density of hard disk drives has been increasing at a growth rate of 100%. The old estimated limit of areal density of 40 Gb/in has been broken. It is expected that the areal density will soon reach the level of 100 Gb/in . Therefore it is anticipated that the allowable nonrepeatable run out (NRRO) of spindle motors has to be suppressed to below 1 , which is required in a much increased track density recording. In addition to the demand for larger areal density and high storage capacity, the hard disk drives are also required to work faster, quieter and more reliable. All of these mentioned performances necessitate further improvements for spindle motor. Consequently, the requirements to the spindle motor used in hard disk drives become increasingly higher. It is known that the performance of a spindle motor largely de- pends on the performance of its bearings. Therefore, the bearing system becomes a key technology for the advancement of the spindle motor. To meet the ever-increasing demand for better spindle motors, development of a new type bearing system is a very important task for motor engineer. One of prospective al- ternatives to the conventional ball bearing is the fluid bearing [1], [2]. The spindle motor with hydrodynamic fluid bearing that pos- sesses the characteristics of lower nonrepeatable run out, lower acoustic noise, higher stiffness and higher damping coefficients is an ideal alternative to ball-bearing spindle motors. In recent Manuscript received July 17, 2000. S. X. Chen. Q. D. Zhang, and H. C. Chong are with Data Storage Institute, (NUS), Singapore 117608 (e-mail: [email protected]). T. Komatsu and C. H. Kang are with Ferrotec Corporation Singapore, BLK 21, Kallang Basin Industrial Estate, Singapore 339412 (e-mail: ftsgko- [email protected]). Publisher Item Identifier S 0018-9464(01)02522-5. years, many fluid-bearing spindle motors have been developed. However, there still exist some problems to be solved before a large-scale application of fluid bearing spindle in hard disk drives. The lubricant leakage is one of the major problems for the implementation of fluid bearing spindle motor in hard disk drives. This paper reports the development of a high-speed spindle motor that employs ferro-fluid as bearing lubricant and a com- pound seal consisting of magnetic seal and viscous pumping in its leakage-free high-speed bearings. The intention is to take the advantages of hydrodynamic oil-film bearings with higher load capacity, higher stiffness and higher damping coefficients and in the meantime, tackle the lubricant leakage problem by use of the compound seal. In this paper, some design considerations and challenges in regard to a high-speed, ferro-fluid bearing spindle motor are discussed. The prototypes are fabricated. The testing results are presented. After continuously running at 20 000 rpm for more than two months, the prototypes did not confess any lubricant leakage. The prototypes have very low nonrepeatable run out and lower acoustic noise. Therefore the developed ferro- fluid bearing spindle motor is a promising alternative to conven- tional ball bearing spindle motors. II. SPECIFICATIONS Following are the major specifications of the spindle motor developed by Data Storage Institute (Singapore) and Ferrotec corporation (Singapore). Disk drive format: 2.5 inch Height: 22 mm Disks to be carried: 5 disks Operating speed 20 000 rpm Motor topology: 3 phase (BLDC) Supply voltage 12 V 5% Back emf (line) 7.6 V max. Starting current 2.0 A Starting Torque 6.2 mNm at Is 1.7 A Run-up time 15 sec. Non Repeatable Run-out 1 inch (radial) Acoustic noise 30 dB(A) (1 meter) Operating temperature 0 C–70 C max. Projected MTBF 100 000 hrs III. MOTOR DESIGN The specified speed of the motor is 20 000 rpm. High speed motor means higher power dissipation as windage loss increases 0018–9464/01$10.00 © 2001 IEEE

Upload: vutu

Post on 09-Mar-2017

212 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Some design and prototyping issues on a 20000 rpm HDD spindle motor with a ferro-fluid bearing system

IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 2, MARCH 2001 805

Some Design and Prototyping Issues on a 20 000rpm HDD Spindle Motor with a Ferro-Fluid Bearing

SystemShi Xin Chen, Qi De Zhang, How Ching Chong, Terutoshi Komatsu, and Cheng Hia Kang, Member, IEEE

Abstract—A high-speed ferro-fluid bearing spindle motor forhard disk drive is introduced. Some design challenges and consid-erations on electrical motor, bearing system and spindle structureare addressed. The testing results of the prototypes are presentedand discussed. The shown testing results of the prototypes indicatethat the objective of developing a high-speed, high-performance,fluid-bearing spindle motor is fulfilled. It is a prospective spindlemotor to be used in future hard disk drives.

Index Terms—Design, ferro-fluid, fluid bearing, spindle motor.

I. INTRODUCTION

T HE DATA storage capacity of hard disk drives is increasedin an amazing speed as a result of several key technology

advancements in recording data on a disk with very high arealdensity. Recently, the areal density of hard disk drives has beenincreasing at a growth rate of 100%. The old estimated limitof areal density of 40 Gb/inhas been broken. It is expectedthat the areal density will soon reach the level of 100 Gb/in.Therefore it is anticipated that the allowable nonrepeatable runout (NRRO) of spindle motors has to be suppressed to below1 ″, which is required in a much increased track densityrecording. In addition to the demand for larger areal density andhigh storage capacity, the hard disk drives are also required towork faster, quieter and more reliable. All of these mentionedperformances necessitate further improvements for spindlemotor. Consequently, the requirements to the spindle motorused in hard disk drives become increasingly higher.

It is known that the performance of a spindle motor largely de-pends on the performance of its bearings. Therefore, the bearingsystem becomes a key technology for the advancement of thespindle motor. To meet the ever-increasing demand for betterspindle motors, development of a new type bearing system is avery important task for motor engineer. One of prospective al-ternatives to the conventional ball bearing is the fluid bearing[1], [2].

The spindle motor with hydrodynamic fluid bearing that pos-sesses the characteristics of lower nonrepeatable run out, loweracoustic noise, higher stiffness and higher damping coefficientsis an ideal alternative to ball-bearing spindle motors. In recent

Manuscript received July 17, 2000.S. X. Chen. Q. D. Zhang, and H. C. Chong are with Data Storage Institute,

(NUS), Singapore 117608 (e-mail: [email protected]).T. Komatsu and C. H. Kang are with Ferrotec Corporation Singapore,

BLK 21, Kallang Basin Industrial Estate, Singapore 339412 (e-mail: [email protected]).

Publisher Item Identifier S 0018-9464(01)02522-5.

years, many fluid-bearing spindle motors have been developed.However, there still exist some problems to be solved beforea large-scale application of fluid bearing spindle in hard diskdrives. The lubricant leakage is one of the major problems forthe implementation of fluid bearing spindle motor in hard diskdrives.

This paper reports the development of a high-speed spindlemotor that employs ferro-fluid as bearing lubricant and a com-pound seal consisting of magnetic seal and viscous pumping inits leakage-free high-speed bearings. The intention is to take theadvantages of hydrodynamic oil-film bearings with higher loadcapacity, higher stiffness and higher damping coefficients and inthe meantime, tackle the lubricant leakage problem by use of thecompound seal. In this paper, some design considerations andchallenges in regard to a high-speed, ferro-fluid bearing spindlemotor are discussed. The prototypes are fabricated. The testingresults are presented. After continuously running at 20 000 rpmfor more than two months, the prototypes did not confess anylubricant leakage. The prototypes have very low nonrepeatablerun out and lower acoustic noise. Therefore the developed ferro-fluid bearing spindle motor is a promising alternative to conven-tional ball bearing spindle motors.

II. SPECIFICATIONS

Following are the major specifications of the spindle motordeveloped by Data Storage Institute (Singapore) and Ferroteccorporation (Singapore).

Disk drive format: 2.5 inchHeight: 22 mmDisks to be carried: 5 disksOperating speed 20 000 rpmMotor topology: 3 phase (BLDC)Supply voltage 12 V 5%Back emf (line) 7.6 V max.Starting current 2.0 AStarting Torque 6.2 mNm at Is 1.7 ARun-up time 15 sec.Non Repeatable Run-out 1 inch (radial)Acoustic noise 30 dB(A) (1 meter)Operating temperature 0C–70 C max.Projected MTBF 100 000 hrs

III. M OTOR DESIGN

The specified speed of the motor is 20 000 rpm. High speedmotor means higher power dissipation as windage loss increases

0018–9464/01$10.00 © 2001 IEEE

Page 2: Some design and prototyping issues on a 20000 rpm HDD spindle motor with a ferro-fluid bearing system

806 IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 2, MARCH 2001

Fig. 1. The motor cogging torque after optimization (under-slung design).

at a rate of at least the second power of the disk rotation speed,dependent on disk spacing. Iron loss of the spindle motor run-ning at this speed will be dominant and much increased. Thespindle motor should be so designed within limited space asto produce enough torque to drive all these loads without gen-erating excess heat. In order to reduce acoustic noise, speedfluctuation and high frequency RRO, the spindle motor shouldhave low cogging torque and low unbalanced radial force. Twotypes of motor with different configurations were designed andcompared for the 2.5″ format, 20 000 rpm spindle with a ferro-fluid bearing system. One configuration was of motor-in-huband the another one was of motor-under-slung. However, be-cause of the space limitation, it was difficult for the configura-tion of motor-in-hub to generate enough working torque. For afixed voltage supply and spindle speed, torque constant of thespindle motor is almost fixed and the same for these two con-figurations. Thicker conductor is needed to carry higher cur-rent to produce high torque, without generating excess heat.Therefore, the motor-under-slung configuration was adopted formeeting the load requirement of 5 disks and a better powermanagement. To avoid high frequency RRO and PES causedby the unbalanced radial magnetic force arising primarily fromthe interaction between unsymmetrical stator magnetic struc-ture and magnet poles [3], the spindle motor should be devisedfrom one of the balanced configurations, such as 4-pole/6-slot,6-pole/9-slot, 8- pole/12-slot, and 12-pole/9-slot, etc. Spindlemotor iron loss is primarily dependent on the square of the mul-tiplication of the spindle motor speed (in revolution per second)and the number of magnet pole pairs in the motor. Iron loss com-pared to copper loss is dominant in high speed spindle motors.A spindle motor with fewer pole pairs has less iron loss [3].However magnetic flux per pole will be higher for the motorwith fewer pole pairs. Thicker back iron ring has to be used.As a result, effective diameter of the motor will decreaseand so will the motor torque which is proportional to the squareof . Therefore a brushless DC motor with a balanced con-figuration of 6 poles and 9 slots was adopted for the 20 000rpm ferro-fluid bearing spindle motor. The balanced configura-tion of 6-pole/9-slot is associated with high cogging toque. Forminimizing the cogging torque, a special magnetization tech-nique and the teeth shape optimization were used to reduce thecogging torque. Magnetization wires of the magnetization fix-ture were arranged such that about 70% of every magnet seg-ment (the ring magnet has 6 segments) was magnetized. Re-shaping the top surfaces of stator teeth with an optimal curvaturewas performed according to Taguchi’s robust design method[4], [5]. Figs. 1 and 2 show the cogging torque and workingtorque of the motor after optimization. The motor current used

Fig. 2. Motor running torque after optimization (under-slung design).

in the modeling and simulation was 0.8 Amperes. Before theoptimization, the peak to peak value of the cogging torque ofthe motor is 5.80 milli-Nm, the average working torque was3.96 milli-Nm. The torque ripple ratio, (Trmax–Trmin)/Trava, isaround 140%, where Trmax, Trmin and Trava are the maximumrunning torque, the minimum running torque, and the averagerunning torque respectively. Contribution of cogging torque tothe torque ripple was dominant before optimization. After op-timization, the peak to peak value of the cogging torque wasreduced to 0.492 milli-Nm. The average working torque was3.87 milli-Nm and the ratio of (Trmax–Trmin)/Trava was re-duced to 14.2%. Contribution of cogging torque to the torquebecame minor compared to the commutation torque ripple.

IV. BEARING DESIGN

A good spindle motor should possess the characteristics oflower nonrepeatable run out, lower acoustic noise, lower powerconsumption and higher shock-resistance capability. However,some of these requirements are contradicted, especially for afluid bearing spindle motor. For example, higher stiffness ofthe bearing system results in lower non- repeatable run-out butcauses higher power loss. Higher viscosity of lubricant enableshigher load capacity and stiffness of bearing system but makesthe performance of bearing system vulnerable to the changes ofworking temperature. Besides the considerations of bearing dy-namic characteristics, the difficulty and the cost of bearing partsmachining should also be considered carefully. Tighter toler-ance specifications for parts machining necessitate high preci-sion machining and, of course, ensure the required performanceof the assembled spindle motor. But it inevitably cause highercost for the final products. All of these contradictory require-ments have to be carefully considered and balanced.

The performance of the fluid bearing is affected by many pa-rameters. Generally, it can be expressed as following function:

(1)

whereand are diameter and length of journal

bearing, respectively.is radial clearance when the eccen-tricity of bearing is zero.is the viscosity of lubricant.is rotating speed of spindle motor.

, , , and are parameters related to the groovepattern of journal/thrust bearing.

Among these parameters, the effect of the individual param-eter to the bearing performance is different. With the help of

Page 3: Some design and prototyping issues on a 20000 rpm HDD spindle motor with a ferro-fluid bearing system

CHEN et al.: SOME DESIGN AND PROTOTYPING ISSUES ON A 20 000 rpm HDD SPINDLE MOTOR 807

TABLE ITHE VALUES OF DESIGN PARAMETERS OFD, L, C , �, G AND �

AT DIFFERENTLEVELS

TABLE IITHE NOISELEVEL OF DESIGNPARAMETERSD, L,C , �,G , AND �

Taguchi’s Method [4], numerical experiments were designed.The effects of different design parameters on the performanceof the bearing as well as the sensitivities of these parameters tothe parts machining deviations were investigated. To avoid toomuch computing time, we first chose four parameters,, ,and as the control factors and investigated their effect on thebearing performance. Then another set of parameters, ,

and was investigated. Each control factor was consideredhaving three level settings and the noise level for each controlfactor was also considered having three level settings. Table Ishows the concrete value of each parameter at different settings.Table II gives out the noise level setting for each control param-eter. The standard orthogonal array was used to determinethe combinations of the parameter values as well as their noiselevels in each numerical test. Two rounds of the numerical testswere carried out. In the first round of numerical experiments,only parameters , , , and , were changed. Other designparameters were kept constant with following values:

rotational speed 20 000 rpm;groove pattern: herringbone groove;groove number ;groove angle ;groove depth C;groove width ;groove region ratio .

For the second round of numerical experiments, the param-eters , , , and were variable while the other parame-ters were kept the same value as in the first round experiments.The diameter and the length of the journal bearing were fixedto mm in the second round of experiments.Solving the Reynolds equation, we obtained the pressure dis-tribution and other dynamic characteristics of the bearing.

The numerical experiments showed that the diameter of shaft,the clearance of bearing and the viscosity of lubricant havemore influence on the performance of the fluid bearing thanother parameters. The parameters associated with the bearinggroove pattern have relatively smaller effect on the bearing

(a)

(b)

(c)

Fig. 3. (a) The radial stiffness of bearing system at different eccentricity ratio.(b) The radial load capacity of bearing system at different eccentricity ratio.(c) The total power loss of bearing system at different eccentricity ratio.

performance. Among the design parameters, the bearingclearance is the most sensitive factor to the parts machiningdeviations. Based on the results of numerical experiments, a setof optimum parameters was chosen in terms of highest ratio ofstiffness to power consumption of the bearing system. It enablesus to obtain a high load capacity and high stiffness spindlemotor with a reasonable level of power consumption. The finalparameters for the journal bearing are: mm;

m; Pa*s at 20C, C and.

Fig. 3(a)–(c) show the stiffness, the load capacity and thepower consumption versus different eccentricity ratios of thebearing system with above design parameters at rotating speedof 20 000 rpm at an environment temperature of 20C. FromFig. 3(a) and (c), it is observed that when the eccentricity ratio

changes from 0 to 0.3, the variation of the radial stiffnessand the total power consumption of the bearing system is quitesmall, the curves are almost flat. That is, for a small range ofchange in radial load of the spindle motor, the performance ofthe spindle motor is quite stable. In the meantime, a low viscousferro-fluid was selected as the lubricant of the bearing system toachieve a better bearing stability and robustness toward temper-ature changes. To prevent lubricant leakage, a compound sealing

Page 4: Some design and prototyping issues on a 20000 rpm HDD spindle motor with a ferro-fluid bearing system

808 IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 2, MARCH 2001

Fig. 4. The schematic of motor bracket.

TABLE IIITHE RELATIONSHIP BETWEEN THEWALL THICKNESS OF THEBRACKET AND

THE FIRST MODE FREQUENCY

was designed for the bearing system. The compound seal con-sists of a magnetic seal and a viscous pumping seal. The viscouspumping seal prevents lubricant from leakage when motor is ro-tating, The magnetic seal keeps lubricant remained in bearingwhen motor is at rest. A reservoir was also added to the sealingsystem to accommodate the extra volume of the lubricant due tothe temperature rising and keep it remaining in the bearings.

V. SPINDLE STRUCTUREDESIGN

The total outer dimensions of the spindle motor are limitedby the format of 2.5″ hard disk drive. As mentioned previously,there are two configurations of spindle motor for hard diskdrive. One is the motor-in-hub configuration and other one isthe motor-under-slung configuration. We selected the design ofmotor-under-slung configuration because it could provide morespace to accommodate the electrical motor. However, even withthe motor-under-slung configuration, the space is still verytight for the lamination of electrical motor and the spindle basebracket. Referring to Fig. 4, it is obvious that if the outer dimen-sion or the height of lamination stator is increased, the thicknessof the bracket walls has to be reduced, vices versa. A thickerlamination stator is of course, helpful to increase workingtorque of the motor. However, it results in a thinner wall of thespindle bracket and lower resonance frequency of the spindlemotor. Therefore, to improve the dynamic characteristics of thespindle motor, we have to sacrifice some working torque ofthe spindle motor to increase the wall thickness of the bracket.Table III shows the natural frequencies of the first mode of thebracket at different wall thickness. It is observed that at 0.5 mmwall thickness, the frequency of the first mode of the bracket isonly 4476 Hz, as increase in the wall thickness, the frequencyof the first mode becomes higher and higher, reaching 9388 Hzat the wall thickness of 1.26 mm. After that wall thickness, thegain of the frequency due to the increase of the bracket wall

Fig. 5. Spindle motor prototype.

thickness is not significant. Therefore, the wall thickness of1.26 mm was chosen and it is a reasonable choice to trade-offthe requirements from spindle motor dynamic considerationand the demands for a greater working torque.

VI. PROTOTYPETESTING

The prototypes of the spindle motor mentioned above werefabricated (Fig. 5). Testing on the motor level (without disksmounted on the spindle motor) has been carried out. Mechanicalbalancing for the prototyped motors was not carried out beforetesting. Fig. 6(a) shows the measurement results of the radial andthe axial repeatable runout (RRO) of the prototypes at differentspeeds. It is found that the radial repeatable runout increaseswith the increase of the rotating speed of the spindle motor whilethe axial repeatable runout first decreases with the increase ofthe speed. After 15 000 rpm, it also increases with the speed.This result is understandable. Because the motor is not balanced,with the increase of rotating speed, the radial unbalance forceis also increased, therefore, results in greater vibration ampli-tude. In other hand, the effect of vibration caused by the unbal-ance force is relatively smaller in axial direction. At first, theincrease of the axial stiffness due to speed increase successfullysuppresses the axial vibration amplitude. However, with the fur-ther increase of the motor speed, the increase of stiffness cannotfurther suppress the amplitude of vibration. Consequently, theaxial repeatable runout becomes higher with the increase of themotor speed. As regard to RRO measurement accuracy, the max-imum value is 0.0559 m for the radial repeatable runout and0.0643 m for the axial repeatable runout respectively, for allrotating speeds. At the speed of 20 000 rpm, the radial and axialRRO are 6.01 m and 2.24 m, respectively. The radial non-repeatable runout (NRRO) and axial NRRO at different speedsare shown in Fig. 6(b) and (c), respectively. The values offorradial and axial NRRO are 0.0195m and 0.0099 m, respec-tively. It is observed that at 5000 rpm, the radial NRRO regis-ters the highest value of 0.0309m, then it gradually reduces to0.0168 m at 10 000 rpm. With the further increase of the speed,the radial NRRO increases again. At 20 000 rpm, the radialNRRO is 0.0281 m (1.1 in). The axial NRRO also shows sim-ilar trend except that its minimum value locates at 15 000 rpm.At 20 000 rpm, the axial NRRO is 0.0356m (1.4 in), slightlyhigher than that of radial nonrepeatable runout. The reason forthe appearance of the valley point in both radial and axial NRRO

Page 5: Some design and prototyping issues on a 20000 rpm HDD spindle motor with a ferro-fluid bearing system

CHEN et al.: SOME DESIGN AND PROTOTYPING ISSUES ON A 20 000 rpm HDD SPINDLE MOTOR 809

(a)

(b)

(c)

Fig. 6. (a) The radial and axial repeatable runout versus the spindle speed.(b) The radial nonrepeatable runout versus the spindle speed. (c) The axialnonrepeatable runout versus the spindle speed.

measurements is to be identified. The starting time of the spindlemotor at 20 000 rpm is around 3 seconds in unloaded condition(without disks mounted on the spindle motor). Fig. 7(a) showsthe working current versus the rotating speed. The working cur-rent of the spindle motor at 20 000 rpm is around 0.6 (A) asshown in Fig. 7(b). The power consumption of the spindle motorat 20 000 rpm is around 7.2 Watt. The estimated windage loss,the iron loss and the copper loss together are around 1.6 Wattat 20 000 rpm. Deducting the above power loss from the totalpower consumption of the spindle motor, the net power loss ofthe bearing system is about 5.6 Watt, almost 25% higher thanthat of the predicted power loss of 4.5 Watt. The electrical mea-surement also shows that the back-EMF calculated from the de-signed magnetic structure and the number of coil turns agreedvery well with the measured one. After continuously runningthe spindle motor for more than two months, careful observationunder a microscope did not reveal any oil traces on both end ofthe spindle motor. It means that the compound seal consistingof magnetic seal and viscous pumping seal succeeded to preventlubricant leakage out of the spindle motor. Fig. 8 shows the dis-tribution of 1/3 octave spectrum and noise level of the prototypespindle motor at 20 000 rpm. The acoustic noise at 20 000 rpmis less than 34 dB(A), measured with the microphone of a pre-cision sound pressure level meter hung right above the spindle

(a)

(b)

Fig. 7. (a) The working current of the prototype versus speed. (b) The workingcurrent of the prototype at 20 000 rpm. (The total time shown is 48 ms).

Fig. 8. Measurement result of acoustic noise at rotating speed 20 000 rpmAcoustic Level, A:33.9 dB(A)/20.0 u Pa;L:60.3 dB(A)/20.0 u Pa.

motor at a distance of 30 cm. The background noise level of theanechoic chamber is around 24 dB (A).

VII. CONCLUSION

A high-speed ferro-fluid bearing spindle motor is intro-duced. Some design challenges and considerations of motorand bearing system are discussed. The testing results of theprototypes are presented. The results shown indicate that theobjective of developing a high-speed, high performance fluidbearing spindle motor with lower nonrepeatable run out andzero lubricant leakage is fulfilled.

REFERENCES

[1] K. A. Liebler, “Future trends in spindle bearings for disk drives,”DataStorage, pp. 37–40, Nov./Dec. 1995.

[2] Q. D. Zhang, S. X. Chen, and Z. J. Liu, “Design of a hybrid fluidbearing system for HDD spindles,”IEEE Trans. Magn., vol. 35, no. 2,pp. 2638–2640, 1999.

[3] S. X. Chen, Z. J. Liu, T. S. Low, and Q. D. Zhang, “Future high speedspindle and components for hard disk drives,”INSIGHT, IDEAMAJournal, pp. 26–28, Jan./Feb. 1999.

[4] T. P. Bagchi,Taguchi Method Explained: Practical Steps to Robust De-sign, India: Prentice-Hall, 1993.

[5] S. X. Chen and T. S. Low, “The robust design approach for reducingtorque in permanent magnet motors,”IEEE Trans. Magn., vol. 34, no.4, pp. 2135–2137, 1998.