Noise and vibration due to rotor eccentricity in a HDD spindle system

Transcription

1 DOI /s Technical Paper Noise and vibration due to rotor eccentricity in a HDD spindle system Sangjin Sung Gunhee Jang Kyungjin Kang Received: 7 October 2013 / Accepted: 8 March 2014 / Published online: 1 April 2014 Springer-Verlag Berlin Heidelberg 2014 Abstract This paper numerically and experimentally investigates the characteristics of torque ripple and unbalanced magnetic force (UMF) due to rotor eccentricity and their effects on noise and vibration in a hard disk drive (HDD) spindle motor with 12 poles and 9 slots. The major excitation frequencies of a non-operating HDD spindle system with rotor eccentricity are the least common multiples (LCM) of pole and slot numbers of the cogging torque and the harmonics of slot number ±1 of the UMF. An experimental setup is developed to measure the UMF generated by rotor eccentricity and to verify the simulated UMF. In the operating HDD spindle motor, the harmonics of the commutation frequency of torque ripple (multiplication of pole and phase) are increased by the interaction of the driving current and rotor eccentricity, and they are the same as the LCM of pole and slot numbers for a HDD spindle motor with 12 poles and 9 slots. The major excitation frequencies of the UMF while operating condition are also the harmonics of slot number ±1 and the harmonics of commutation frequency ±1. We verify that the source of the harmonics of slot number ±1 and the harmonics of commutation frequency ±1 in acoustic noise and vibration is rotor eccentricity of the UMF through experiments. 1 Introduction Torque ripple and unbalanced magnetic force (UMF) are major excitation sources of acoustic noise and vibration S. Sung G. Jang (*) K. Kang Department of Mechanical Engineering, Hanyang University, 17 Haengdang dong, Seongdong gu, Seoul , Republic of Korea ghjang@hanyang.ac.kr in hard disk drive (HDD) spindle motors. These are generally outer-rotor type motors with fluid dynamic bearings (FDBs). The FDBs constrain the rotating disk-spindle system to five degrees of freedom except for the direction of axial rotation. HDD spindle motors support rotating disks, which are larger and heavier than a permanent magnet (PM) and rotor back yoke. The rotating disk-spindle system is characterized by a whirling motion that is generated by the unbalanced mass of the HDD spindle system. Figure 1 shows the rotor eccentricity of a HDD spindle motor, which is equivalent to the radius of the whirling motion of the rotor. Rotor eccentricity can be generated not only by the unbalanced mass, but also by manufacturing errors. Such eccentricity results in non-uniform air gaps and changes the characteristics of torque ripple and UMF. The cogging torque of PM motors caused by interactions between the poles and slots, and commutation torque ripple due to interactions between the poles, slots, and driving current are major sources of torque ripple (Hanselman 2003; Hendershot and Miller 2010). The driving frequencies of cogging torque and commutation torque ripple are the least common multiples (LCM) of pole and slot numbers and the multiples of the multiplication of pole and phase numbers in ideal PM motors, respectively, (Jang and Lieu 1994). Additional harmonics are introduced by manufacturing errors, such as rotor and stator eccentricity, uneven magnetization of PMs, and uneven coil patterns (Hartman and Lorimer 2001; Sung et al. 2012). UMF is not generated in rotational symmetric motors with respect to pole, slot and winding configurations, such as PM motors with 12 poles, 9 slots and 3 phases (Jang et al. 1996). However, manufacturing errors may generate UMF even in rotational symmetric motors (Lee and Jang 2008b; Yoon 2005). Several groups have investigated the harmonic contents of torque ripple and UMF caused by rotor eccentricity. Kim

2 1462 Microsyst Technol (2014) 20: Table 1 Major specifications of the HDD spindle motor Design variables Value Reference speed (rpm) 5,400 Poles/slots 12/9 Torque constant (mnm/a) 6.06 Maximum residual flux density of PM (T) 0.70 Air gap length (mm) 0.25 Inner radius of PM (mm) 8.50 Outer radius of PM (mm) 10.0 Fig. 1 Rotor eccentricity of a HDD spindle motor and Lieu (2005) analytically demonstrated that rotor eccentricity generates slot harmonics in the torque ripple of a PM motor and the 1st and slot ±1 harmonics in the UMF. Lee and Jang (2008a) proposed an experimental device to measure the UMF of a PM motor and experimentally investigated the harmonics of UMF generated due to rotor eccentricity. However, they discussed the cogging torque and UMF of the PM motor only in the non-operating condition, and did not investigate the effects of torque ripple and UMF on acoustic noise and vibration in a HDD spindle system. In this study, we develop a finite element model of a 2.5 inch HDD spindle motor with 12 poles and 9 slots to investigate torque ripple and UMF caused by rotor eccentricity. The finite element model is verified by using the measured back electromotive force (EMF). The torque ripple and UMF are calculated by using the Maxwell stress tensor, and their characteristics are investigated by spectral analysis. We develop an experimental setup to measure UMF, and investigate the characteristics of UMF generated by rotor eccentricity. We also experimentally investigate the effects of torque ripple and UMF on acoustic noise and vibration in a HDD spindle system. 2 Finite element analysis A finite element model of a HDD spindle motor with 12 poles and 9 slots is developed in order to characterize torque ripple and UMF caused by rotor eccentricity, as shown in Fig. 2. The finite element model has approximately one million tetragon elements with four nodes. The PM of plastic-bonded neodymium has a maximum residual flux density of 0.7 T, and the PM is assumed to be magnetized in an ideal sinusoidal wave. Table 1 shows the major specifications of the HDD spindle motor. The driving current, which is measured while the HDD spindle system with two disks operates at 5,400 rpm by the six step commutation driving method, is applied to each phase, as shown in Fig. 3a. The effects of rotor eccentricity are included by calculating the magnetic field generated as the rotor rotates every 1 from 0 to 360 by changing the position of the rotor center along the whirl locus, as shown in Fig. 1. The magnetic field is investigated using FLUX2D software while considering the nonlinear B H characteristics of the stator core. Figure 3b shows the simulated and measured back EMF. The simulated back EMF agrees with the measured value. The normal and tangential magnetic force densities are calculated by the Maxwell stress tensor method as follows: Fig. 2 Magnetic finite element model of a HDD spindle motor

3 1463 Fig. 3 Measured a driving current and b back EMF of a HDD spindle motor operating at 5,400 rpm Fig. 4 Experimental setup to measure UMF of a HDD spindle motor caused by rotor eccentricity f n = 1 ( ) Bn 2 2µ B2 t 0 (1) 3 Experiment setup 3.1 experimental setup to measure UMF f t = 1 µ 0 (B n B t ) where f n, f t, μ o, B n, and B t are the normal and tangential magnetic force densities, the permeability of air, and the normal and tangential magnetic flux densities, respectively. The torque and the UMFs in the x and y directions are obtained by integrating the radial and tangential magnetic force densities as follows: T = L (r f n )dω (3) F x = L F y = L (f n cos λ f t sin λ)dω (f n sin λ + f t cos λ)dω where L, r, T, and F x and F y are the axial length of the motor, the radius of the integrating line, torque, and UMFs in the x and y directions, respectively. (2) (4) An experimental setup is developed to measure the UMF of HDD spindle motors and to verify the simulated characteristics of the UMF, as shown in Fig. 4. Since the UMF exerted on the rotor and stator moves the rotor to another equilibrium position by deforming the bearings, the UMF of the spindle motor cannot be measured in the assembled state. The rotor is separated from the stator in the experimental setup and a load cell is attached to the outside of the rotor. The disassembled stator of the spindle motor is fixed to an XY-table on the rotating shaft, and the disassembled rotor is fixed to an XYZ-table, so that the position of the rotor can be adjusted with respect to the center of the stator to change its eccentricity. The rotating shaft is connected to another driving motor through a belt. When the rotating shaft that is connected to the stator rotates at constant speed by the driving motor, an UMF is exerted on both the stator and rotor and is measured by the load cell on the stationary rotor. The load cell is a Honeywell model 31 with a measurement range between 250 and 250 g.

4 1464 Microsyst Technol (2014) 20: Fig. 5 Experimental setup to measure acoustic noise and vibration in a HDD spindle system Fig. 6 Experimental setup to measure rotor eccentricity in a HDD spindle system caused by unbalanced mass Fig. 7 Simulated a cogging torque and b frequency spectrum of an ideal HDD spindle motor in the non-operating condition 3.2 experimental setup to measure noise and vibration The vibration and acoustic noise of a HDD spindle system with two disks operating at 5,400 rpm are simultaneously measured in semi-anechoic chamber with background noise of 17.6 db-a, as shown in Fig. 5. The vibration is measured using an accelerometer attached to the top cover. The acoustic noise and overall sound pressure levels are measured by a microphone located 70 cm above the HDD cover. Rotor eccentricity is generated in the HDD spindle system by attaching an unbalanced mass to the disk, and is measured by a gap sensor when the HDD spindle motor operates at 5,400 rpm, as shown in Fig. 6.

5 1465 Fig. 8 Simulated a cogging torque and b frequency spectrum of a HDD spindle motor caused by a rotor eccentricity of 50 μm in the non-operating condition Fig. 9 Magnitudes of the 9th and 36th harmonics of the cogging torque according to rotor eccentricity in the non-operating condition 4 Results and discussion 4.1 cogging torque and UMF in the non operating condition In this study, we identify the frequency contents of the cogging torque and UMF of a HDD spindle motor with rotor eccentricity ranging from 0 to 50 μm in the non-operating condition. The 36th harmonic, which is the LCM harmonic of pole and slot numbers, is generated by the simulated cogging torque of the ideal HDD spindle motor with 12 poles and 9 slots in the non-operating condition, as shown in Fig. 7. However, the rotor eccentricity additionally generates the 9th harmonic, which is the slot harmonic, in the simulated cogging torque shown in Fig. 8. Figure 9 shows the magnitudes of the 9th and 36th harmonics of the simulated cogging torque according to increments of rotor eccentricity in the non-operating condition. The 36th harmonic of the torque ripple is barely affected by the rotor eccentricity, and the magnitude of the 9th harmonic increases as the rotor eccentricity increases. The magnitude of the 9th harmonic is very small in comparison with that of the 36th harmonic. Figures 10, 11 show the simulated and measured UMFs of the HDD spindle motor, and the frequency spectra of the x-directional UMF caused by a rotor eccentricity of 50 μm in the non-operating condition, respectively. UMF is not generated in an ideal HDD spindle motor due to the presence of rotational symmetry with respect to the pole, slot and winding configurations. However, the 1st, 9th ± 1 and 36th ± 1 harmonics of the UMF are generated by rotor eccentricity. The magnitudes of the 36th ± 1 harmonics are very small in comparison with those of the 9th ± 1 harmonics, and the 36th ± 1 harmonics cannot be observed in the measured UMF due to experimental noise. The magnitudes of the 9th ± 1 and 36th ± 1 harmonics increase as rotor eccentricity increases, as shown in Fig. 12. The magnitudes of the 9th ± 1 harmonics of the measured UMF are higher than those of the simulated UMF, because uneven Fig. 10 Simulated a UMFs and b frequency spectrum of x-directional UMF of a HDD spindle motor caused by a rotor eccentricity of 50 μm in the non-operating condition

6 1466 Microsyst Technol (2014) 20: Fig. 11 Measured a UMFs and b the frequency spectrum of x-directional UMF of a HDD spindle motor caused by a rotor eccentricity of 50 μm in the non-operating condition Fig. 12 Magnitudes of the a 9th ±1 and b 36th ±1 harmonics in simulated and measured x-directional UMF according to rotor eccentricity in the nonoperating condition Fig. 13 Simulated a torque ripple and b frequency spectrum of an ideal HDD spindle motor in the operating condition magnetization of PM may increase the 9th ± 1 harmonics of the UMF (Kang et al. 2013). However, the magnitudes of the 9th ± 1 harmonics vary with the increment of the rotor eccentricity and match well the simulated values. 4.2 Torque ripple and UMF in the operating condition The rotor eccentricity of the HDD spindle motor with two disks is approximately 8 μm at 5,400 rpm in the experimental setup shown in Fig. 6. In this study, we investigate the torque ripple and UMF caused by the rotor eccentricity of 8 μm in a HDD spindle motor with two disks operating at 5,400 rpm. Figure 13 shows the simulated torque ripple and the frequency spectrum of an ideal HDD spindle motor in the operating condition. The 36th harmonic of the torque ripple is generated by the interaction of poles and slots (LCM of pole and slot numbers) as well as by the commutation frequency of the driving current (multiplication of pole and phase number). However, the magnitude of the 36th harmonic is primarily affected by the driving current in the operating condition, as shown in Figs. 7, 13. The 36th harmonic of the torque ripple is barely affected by the rotor eccentricity, and the magnitude of the 9th harmonic is very small in comparison with that of the 36th harmonic when the rotor eccentricity is 8 μm, as shown in Fig. 14. Figure 15 shows the simulated UMF and the frequency spectrum of the x-directional UMF of the HDD spindle motor caused by a rotor eccentricity of 8 μm in the

7 1467 Fig. 14 Simulated a torque ripple and b frequency spectrum of a HDD spindle motor caused by a rotor eccentricity of 8 μm in the operating condition Fig. 15 Simulated a UMFs and b the frequency spectrum of x-directional UMF of a HDD spindle motor caused by a rotor eccentricity of 8 μm in the operating condition The magnitudes of the 9th ± 1 harmonics are approximately proportional to the square of the rotor eccentricity, and the 36th ± 1 harmonics are linearly proportional to the rotor eccentricity. The 9th ± 1 harmonics and the 36th ± 1 harmonics of the UMF are significant in the operating condition. 4.3 noise and vibration Fig. 16 Magnitudes of the 9th ±1 and 36th ±1 harmonics in the simulated x-directional UMF according to rotor eccentricity in the operating condition operating condition. The driving current barely affects the 9th ± 1 harmonic of the UMF, but increases the magnitude of the 36th ± 1 harmonic of the UMF, as shown in Figs. 12, 15. Since the UMF is determined by tangential force density as well as radial force density, as shown in Eqs. (3), (4), the magnitudes of the 36th ± 1 harmonics of the UMF are affected by those of the 36th harmonic of the torque ripple, which in turn is significantly increased by the driving current. Figure 16 shows the magnitudes of the 9th ± 1 and 36th ± 1 harmonics in the simulated x-directional UMF according to rotor eccentricity in the operating condition. The torque ripple and UMF of the operating HDD spindle motor cannot be directly measured. Instead, we measure the acoustic noise and vibration, which are the responses of excitations of torque ripple and UMF. Figures 17, 18 show the measured acoustic noise and vibration of the HDD spindle system, respectively. The aerodynamic acoustic noise and vibration dominate the frequency range from 0 to 2 khz due to the rotating disks. The predominant discrete tone (PDT) noise is observed at the 36th and 72nd harmonics, which represent responses to torque ripple. The 9th ± 1 and 36th ± 1 harmonics are generated in acoustic noise and vibration due to a rotor eccentricity of 8 μm. The magnitudes of the 9th ± 1 and the 36th ± 1 harmonics of the acoustic noise and vibration increase with rotor eccentricity, as shown Fig. 19. These results agree with results for the UMF. We conclude that the sources of the 36th harmonics in acoustic noise and vibration are torque ripple, and that the sources of the 9th ± 1 and 36th ± 1 harmonics in

8 1468 Microsyst Technol (2014) 20: Fig. 17 Measured acoustic noise of a HDD spindle system with two disks operating at 5,400 rpm due to a rotor eccentricity of 2 μm and b rotor eccentricity of 8 μm Fig. 18 Measured vibration of a HDD spindle system with two disks operating at 5,400 rpm due to a rotor eccentricity of 2 μm and b rotor eccentricity of 8 μm Fig. 19 Magnitudes of the 9th ±1 and 36th ±1 harmonics in the measured a acoustic noise and b vibration of a HDD spindle system with two disks operating at 5,400 rpm according to rotor eccentricity acoustic noise and vibration are the UMF, caused by rotor eccentricity. 5 Conclusions In this study, we investigate torque ripple and UMF caused by rotor eccentricity in a HDD spindle motor and their effects on acoustic noise and vibration. The major excitation frequencies of a non-operating HDD spindle system with rotor eccentricity are the LCM of pole and slot numbers of the torque ripple and the harmonics of slot number ±1 of the UMF. In an operating HDD spindle motor, the harmonics of the commutation frequency of torque ripple (multiplication of pole and phase numbers) are increased considerably by interactions between the driving current and rotor eccentricity, and are the same as the LCM of pole and slot numbers for the HDD spindle motor with 12 poles and 9 slots. In addition, the major excitation frequencies of the UMF are the harmonics of slot number ±1 and the harmonics of commutation frequency ±1. We therefore experimentally verify that the sources of the harmonics of slot number ±1 and commutation frequency ±1 in acoustic noise and vibration are due to UMF caused by rotor eccentricity. The applications of this research include the reduction of noise and vibration in HDDs.

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