Finite element modal analysis of an HDD considering the flexibility of spinning disk–spindle, head–suspension–actuator and supporting structure

This paper presents a finite element method to analyze the free vibration of a flexible HDD (hard disk drive) composed of the spinning disk–spindle system with fluid dynamic bearings (FDBs), the head–suspension–actuator with pivot bearings, and the base plate with complicated geometry. Finite element equations of each component of an HDD are consistently derived with the satisfaction of the geometric compatibility in the internal boundary between each component. The spinning disk, hub and FDBs are modeled by annular sector elements, beam elements and stiffness and damping elements, respectively. It develops a 2-D quadrilateral 4-node shell element with rotational degrees of freedom to model the thin suspension efficiently as well as to satisfy the geometric compatibility between the 3-D tetrahedral element and the 2-D shell element. Base plate, arm, E-block and fantail are modeled by tetrahedral elements. Pivot bearing of an actuator and air bearing between spinning disk and head are modeled by stiffness elements. The restarted Arnoldi iteration method is applied to solve the large asymmetric eigenvalue problem to determine the natural frequencies and mode shapes of the finite element model. Experimental modal testing shows that the proposed method well predicts the vibration characteristics of an HDD. This research also shows that even the vibration motion of the spinning disk corresponding to half-speed whirl and the pure disk mode are transferred to a head–suspension–actuator and base plate through the air bearing and the pivot bearing consecutively. The proposed method can be effectively extended to investigate the forced vibration of an HDD and to design a robust HDD against shock.     

Magnetically induced vibration of a flexible rotating disk-spindle system due to the internal magnetic force arising from the spindle motor of a HDD

This paper investigates the magnetically induced vibration of a flexible rotating disk-spindle system and stationary stator-base due to the internal excitation of the local magnetic force arising from the spindle motor of a HDD. A three-dimensional magnetic finite element model of the spindle motor is developed, and the Maxwell stress tensor method is applied to calculate the local magnetic force acting on the stationary teeth and rotating permanent magnet of the spindle motor. Also, a three-dimensional structural finite element model is developed and local magnetic force is applied to teeth and permanent magnet. The simulated forced vibration of the base plate matched well with the measured one. The dominant frequency component of local magnetic force is the 12th harmonic corresponding to the number of poles, but the dominant frequency component of vibration is the 36th harmonic corresponding to the least common multiple of the number of poles and slots because the 12 and 24th harmonics in local force are canceled out when they are summed up along the air gap. The 12th, 24th and 36th harmonics of the axial vibration are mostly affected by the axial magnetic force, and the amplitudes of those harmonics are increased with the increase of stator eccentricity.     

Robust optimal design of a magnetizer to reduce the harmonic components of cogging torque in a HDD spindle motor

This research proposes a robust optimal design methodology to reduce the cogging torque of a hard disk drive (HDD) spindle motor due to the coil-positioning error of the magnetizer. The design optimization problem of the magnetizer is formulated with an objective function of the cogging torque and the constraints of the torque constant. The coil-positioning errors measured by computerized tomography are considered as the random variables of the robust optimal design problem. Additional design variables of the magnetizer are chosen in the optimization problem, such as back-yoke thickness, notch depth, etc. Magnetic finite element analysis of the HDD spindle motor is also performed to calculate the cogging torque and torque constant. The cogging torque and torque constant of the optimal design are compared with those of the conventional design, demonstrating that the proposed method effectively reduces the cogging toque of the HDD spindle motor.     

Finite element modal analysis of a rotating disk–spindle system in a HDD with hydrodynamic bearings considering the flexibility of a complicated supporting structure

This paper presents a method to analyze the free vibration of a rotating disk–spindle system in a HDD with hydrodynamic bearings (HDBs) considering the flexibility of a complicated base structure by using finite element method. Finite element equations of each component of a HDD spindle system from the spinning flexible disk to the flexible base plate are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between the sleeve and hydrodynamic bearings to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. The validity of the proposed method is verified by comparing the calculated damped natural frequencies and modes with the experimental results. This research also shows that the supporting structure which includes the stator, housing and base plate plays an important role in determining the natural frequencies and mode shapes of a HDD spindle system     

Analysis of dynamic characteristics of a HDD spindle system supported by ball bearing due to temperature variation

 This paper presents a method to investigate the characteristics of a ball bearing and the dynamics of a HDD spindle system due to temperature variation. Finite element model is developed for the rotating and stationary parts of a HDD spindle system separately to determine their thermal deformations by using ANSYS, a finite element program. Then, the relative position of the rotating part with respect to the stationary part is determined by solving the equilibrium equation of the contact force between upper and lower ball bearings. The validity of the proposed method is verified by comparing the theoretical natural frequencies of a HDD spindle system with the experimental ones before and after temperature variation. The proposed method makes it possible to predict the characteristics of a ball bearing and the dynamics of a HDD spindle system due to temperature variation. It shows that the elevated temperature results in the increase of contact angle and the decrease of bearing deformation, contact force and bearing stiffness, which result in the decrease of the natural frequencies of a HDD spindle system. Received: 20 June 2002 / Accepted: 28 August 2002     

Whirling, tilting and axial motions of a HDD spindle system due to the manufacturing errors of FDBs

This paper investigates the whirling, tilting and axial motions of a hard disk drive (HDD) spindle system due to manufacturing errors of fluid dynamic bearings (FDBs). HDD spindle whirls around the sleeve with tilting angle due to the centrifugal force of unbalanced mass and the gyroscopic moment of rotating spindle in addition to axial motion. The whirling, tilting and axial motions may be increased by the manufacturing errors of FDBs such as imperfect cylindricity of sleeve bore, or imperfect perpendicularity between shaft and thrust plate. They increase the disk run-out to limit memory capacity and they may result in the instability of the HDD spindle system. This paper proposes the modified Reynolds equations for the coupled journal and thrust FDBs to include the variable film thickness due to the cylindricity of sleeve bore and the perpendicularity between shaft and thrust plate. Finite element method is used to solve the modified Reynolds equation to calculate the pressure distribution. Reaction forces and friction torque are obtained by integrating the pressure and shear stress, respectively. The whirling, tilting and axial motions of the HDD spindle system are determined by solving the equations of a motion of a HDD spindle system in six degrees of freedom with the Runge-Kutta method. It shows that the imperfect cylindricity and perpendicularity increase the whirl radius, axial runout and tilting angle of the HDD spindle system. However, the degradation of dynamic performance due to the imperfect perpendicularity between shaft and thrust plate can be improved by allowing the other manufacturing error of the cylindricity of sleeve bore in such a way to compensate the bad effect of the imperfect perpendicularity.     

Multi-body structural effects on the head-disk interface during operational shocks in hard disk drives

Over the past decades, there has been an increase in the demand for hard disk drives (HDDs) used in mobile computing devices. The work performance of a HDD mainly depends on its ability to withstand external disturbances in such applications. Studies of the HDD’s responses and failures during external shocks can be very beneficial for improving the HDD’s designs. Multi-body operational shock (op-shock) models are developed to study the HDDs’ responses during external shocks. Four models which include different components (a disk, a spindle motor, a base plate, a pivot and a head actuator assembly) are introduced in this study to investigate the effects of various components on the drives’ operating performance. It is found that the models must include certain critical components in order to give results for performance reliability when subjected to operational shocks.     

Development and optimal design of a HDD spindle motor with pulling magnet to reduce electrical loss

A conventional hard disk drive (HDD) spindle motor has a pulling plate to generate the axial magnetic force. However, the pulling plate consumes significant amount of iron loss due to the alternating magnetic field on the pulling plate. We propose the new design of a HDD spindle motor with pulling magnet to generate the pre-load as well as to eliminate the iron loss of the pulling plate. We also develop an optimal design methodology to minimize iron and copper losses from the spindle motor of a computer HDD while maintaining the same level of torque ripple and pulling force. The new design is optimized by the developed optimal design methodology. A metamodel is constructed from the three-dimensional finite element analysis of the magnetic field and the meta-modeling techniques, and the accuracies of the metamodels are discussed. The proposed optimal design problem is solved by the progressive quadratic approximation method. The proposed design reduces the electrical loss of the HDD spindle motor by 30.42?% while maintaining the same level of torque ripple and pulling force.     

Development of a new spindle motor for a hard disk drive

A new spindle motor is developed with a sloped permanent magnet (PM) for a hard disk drive (HDD). In a conventional spindle motor, a pulling plate is installed at the stationary part under the rotating PM to pull down rotating bodies. This axial force is required for stable operation of the spindle motor using a hydrodynamic bearing. However, the pulling plate has considerable iron loss and a negative torque opposing the direction of rotation due to the induced eddy currents. Our proposed model has a sloped PM surface to generate the required axial force as well as torque without the pulling plate. Optimal design is carried out by a response surface methodology, and the new spindle motors are prototyped. The resulting electrical and mechanical performance of the prototyped motors is compared with that of conventional models, showing the possibility of adapting the proposed model for an HDD spindle motor.     

Analysis of contact phenomena between a head stack assembly and disk during operational shock

A hard disk drive (HDD) is very sensitive to shock. Increasing portability demands have led to increased HDD exposure to unexpected shocks. Therefore, the dynamic characteristics of an HDD were utilized to investigate the relative behavior of the disk and head stack assembly (HSA) during operational shock. A finite element model of HDD was constructed to simulate operational shock. This model included the spindle system, base, HSA, and disk. The relative behavior of the disk and HSA was analyzed using different bases with different stiffness. A drop test was performed to verify the simulation results. A modified base design was then proposed to protect against contact between the disk and HSA in HDD.     

Robust design of a HDD spindle system supported by fluid dynamic bearings utilizing the stability analysis of five degrees of freedom of a general rotor-bearing system

This paper proposes a method to improve the robustness of a hard disk drive (HDD) spindle supported by fluid dynamic bearings (FDBs) by utilizing the stability analysis of the five degrees of freedom of a general rotor-bearing system. The Reynolds equations and the perturbed equations of the coupled journal and thrust bearings were solved by FEM to calculate the dynamic coefficients. The paper introduces the radius of gyration to the equations of motion in order to consistently define the stability problem with respect to a single variable, i.e., the mass. The critical mass, which is the threshold between the stability and instability of the HDD spindle, is determined by solving the linear equations of motion. The proposed method was applied to improve the robustness of a HDD spindle supported by FDBs by varying the groove parameters. It shows that the optimized groove design obtained using the proposed method increases both the stability and the modal damping ratio of the half-speed whirl mode. This research also determines the motions of the rotating disk-spindle system by solving its nonlinear equations of motion with the Runge?CKutta method. It shows that the groove design optimized using the proposed method has a small whirl radius in the steady state. It also shows that it has very little displacement due to the shock excitation, and that it quickly recovers to the equilibrium state.     

Finite element modal analysis of a spinning flexible disk-spindle system in a HDD considering the flexibility of complicated supporting structure

The free vibration of a spinning flexible disk-spindle system in a HDD considering the flexibility of complicated supporting structure is analyzed by FEM and substructure synthesis. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The stationary shaft is also modeled by Timoshenko beam. The flexible supporting structure with a complex shape which includes the stator core, housing and base plate is modeled by using a four-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility at the interface node between the one-dimensional (1-D) beam element and the 3-D solid element. Rigid link constraint is imposed at the interface area between shaft and housing to describe the physical motion at this interface. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies and mode shapes with the experimental ones. This research shows that the flexible supporting structure as well as the rigid link constraint between shaft and housing play an important role in accurately predicting the natural frequencies.     

Improvement of dynamic characteristics of a HDD spindle system supported by ball bearing at elevated temperature

This research investigates how the design variables of ball bearing affect the bearing stiffness and the natural frequencies of a hard disk drive (HDD) spindle system at elevated temperature. It shows that any design change that increases the contact angle of ball bearing reduces the variation in the bearing stiffness and the natural frequencies at elevated temperature. This research also proposes a robust HDD spindle motor in which a wave spring maintains a constant preload minimizing the effect of temperature variation. Experimental modal testing shows that the reduction of the natural frequencies at elevated temperature is much less in the proposed HDD spindle system than in the conventional spindle system. The proposed HDD spindle motor can improve the dynamic reliability of a HDD spindle system, which contributes to the high track density of a HDD.     

Linear actuator for precise track following

A new air bearing linear actuator with a Voice Coil Motor (VCM) was investigated for a precise head track following in an Hard Disk Drive (HDD) magnetic recording tester system. The actuator has a servo bandwidth of two times as wide as that of a conventional HDD, due to a high stiffness without any friction. A low-pass filter was introduced to precisely monitor the step response behavior by reducing the relatively large noise of the used optical fiber sensor. The effect of the low-pass filter was investigated comparing with the other method. Track following accuracy was also tested by using a conventional 2.5-inch hard disk drive. The head installed on the actuator could follow on a track by using Position Error Signal (PES) from the servo pattern. When a Double Metal In Gap (D-MIG) head of 4 μm track-width was loaded on a disk rotating at 4200rpm, the tracking error could be compressed down to one-twentieth of the track-width. The tested system did not show any azimuth error of head-tracking due to the linear motion. In conclusion, the air-bearing linear actuator is suitable for a precise track following mechanism of a spin-stand tester for an HDD system.     

Separated pivot-shaft actuator for small skew angle in hard disk drives

A large skew angle in a hard disk drive (HDD) adversely affects the flying stability of the head sliders and the off-track capability of the read/write head. A novel actuator in the form of a separated pivot-shaft actuator (SPA) with a small skew angle is proposed in this paper. The SPA was particularly designed for a four-disk 3.5-in. HDD and has a skew angle of ±1.6°, which is approximately one-tenth of that of a conventional voice coil motor. The SPA was numerically analyzed by a finite element method, and its mechanical characteristics were compared with those of a long-arm actuator (LAA) (which is a strong candidate for a small-skew-angle actuator) with respect to the seek performance and frequency response. It was found that the SPA had a higher resonant frequency, which enabled the achievement of a wider servo-bandwidth compared to the LAA, and that the average seek time of the SPA was significantly shorter than that of the LAA.     

Transient dynamic analysis of ferro-fluid bearing spindle motor

 With areal recording density of hard disk drives (HDD) historically growing at an average of 60% per year and fast spindle speed to continue to reduce access time, it is becoming increasingly more difficult to maintain the precise positioning required of the GMR heads to read and write data. Any unexpected vibration will cause the data written to a wrong data track. Consequently, the dynamic behaviors of HDD spindle systems and their potential influences on track misregistration are key issues in disk drive design. With rapid advances in the emerging consumer device market, the fluid bearing spindle motors, which have low NRRO, low acoustic noise and high damping, are being developed as next generation spindles. This paper is to study transient dynamic performance of HDD ferro-fluid bearing spindle systems. The FEA based component mode synthesis method is used to reduce the overall spindle system dimensions. The effect of the unbalanced magnetic pulls (UMP) due to two different types of motor configurations (balanced and unbalanced configurations) on the dynamic behaviors of spindle system was investigated. The simulated results show that the motor with balanced configuration provides better spindle dynamic performance due to absence of UMP. The UMP derived from the unbalanced configuration can result in some frequency resonance interactions and adversely affect the HDD servo-tracking system. Received: 5 July 2001/Accepted: 17 October 2001     

Dynamics simulation of MEMS device embedded hard disk drive systems

Currently, hard disk drives (HDD) use rotating disks to store digital data and magnetic recording heads are flying on the disk to read/write data. The recording heads are mounted on a slider–suspension assembly, which makes heads move from one track to another on the disk. The heads movement is controlled by close-loop feedback servo systems. It is well known that dynamic behaviors of head–slider–suspension-assembly (HSA) systems are of great influence on the track per inch capacity of HDD [1, 2]. As the problem is structurally complex, it is usually investigated using experimental methods or finite element simulation models [3]. Furthermore, the dual-stage servo system has been commonly considered as one promising solution to increase the servo bandwidth of the recording positioning system for high TPI HDDS. In particular, MEMS device embedded systems are superior to others in batch-fabrication. However, this dual-stage system has also resulted in more difficulties in predicting HDD dynamic performance. This paper presents the study of the problem using the macromodeling simulation approach. It applies efficient FEM based sub-structuring syntheses (SSS) [4] and fast boundary element method (BEM) approaches incorporated with system dynamics technology to investigate the dynamic characteristics of MEMS actuator embedded HSA systems for HDD.This research is funded by the Agency for Science, Technology and Research of Singapore, Strategic Research Program. Also, the authors would like to thanks Miss Jia Wenhui, who is a Research Student with ECE Department at National University of Singapore, Mr. Lim Boon Buan, the former research engineer with Data Storage Institute, for the MEMS actuator modeling and analytical work.     

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

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.     

Experimental and numerical investigation of shock response in 3.5 and 2.5 in. form factor hard disk drives

The shock performance of the head/disk interface (HDI) of 3.5 and 2.5 in. hard disk drives (HDDs) is investigated. The displacement of the actuator arm, the suspension, and the disk due to linear shock loads is studied experimentally for both non-operating and operating states of the disk drive. A finite element model of the disk drive was developed to simulate the shock response. Numerical simulation results and experimental results are compared and presented.