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     

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.     

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     

Effect of an hourglass-shaped sleeve on the performance of the fluid dynamic bearings of a HDD spindle motor

This research investigated the characteristics of fluid dynamic bearings (FDBs) in a HDD spindle motor with an hourglass-shaped sleeve. We demonstrated experimentally that the hourglass-shaped sleeve generated through the ball-sizing process is a major source of large repeatable runout and non-repeatable runout in a HDD spindle system. We also numerically proved the effect of hourglass-shaped sleeves on pressure, friction torque, stiffness and damping coefficients, critical mass, and shock response. Finally, we proposed a robust design for FDBs with hourglass-shaped groove depths to compensate for the decrease in the static and dynamic performance of FDBs with hourglass-shaped sleeves. The proposed hourglass-shaped groove depth improves the performance of FDBs with both straight and hourglass-shaped sleeves.     

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.     

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     

Vibration predictions and verifications of disk drive spindle system with ball bearings

With areal recording density of hard disk drives (HDD) historically growing at an average of 60% per year, it is becoming increasingly more difficult to maintain the precise positioning required of the ever-smaller GMR heads to read and write data. Any unexpected vibration will cause the data written to a wrong data track, even the vibration amplitude is very small. Consequently, the dynamic behaviors of HDD spindle systems and their potential influence on track misregistration rate must be clearly understood. This paper is to apply an approach based on efficient component mode synthesis (CMS), incorporating multi-body system dynamics technology to predict dynamic characteristics of HDD ball-bearing spindle systems. First, the discrete governing equations of motion for HDD spindle systems, which consist of several flexible and rigid components, are derived through the use of Lagrangian equations. The elastic component modal frequencies and modal shape vectors are then obtained using a finite-element analysis. For ball bearing inherently defects, a mathematical model is used as a time-varying force, resulting in spindle vibrations. The time-varying force and component modal shape vectors are incorporated into the governing equations of the whole spindle systems. An implicit numerical integration method is used to obtain the forced vibration of the HDD spindle system. Finally, the dynamic responses of two typical HDD spindle systems are investigated numerically to predict the significant coupled vibration frequencies, mode shapes and resonance interactions. The results well agree with the solutions predicted by other analytical methods and the experimental results, respectively.     

Optimization of 3.5-in. HDD spindle motors for OP-vibration performance: theoretical prediction and experimental verification

The purpose of this paper is to optimize OP-vibration performance of 3.5-in. hard disk drive (HDD) spindle motors through theoretical prediction and experimental verification. OP-vibration performance of HDD is closely related to the first rocking vibration of spindle motors because excited frequencies of 3.5-in. HDD from the environment are mostly below 500 Hz and the first rocking vibration is the only resonance in the corresponding frequencies. Therefore, minimizing first rocking vibration leads to improve OP-vibration performance of the spindle motors. In order to minimize the first rocking vibration key parameters of FDB spindle motors were selected from a previous work done by Heo and Shen (Microsyst Technol 11:1204–1213, 2005). Then, the selected parameters have been optimized to minimize the first rocking vibration through a theoretical model developed at University of Washington. Then, experiments with ten prototype FDB spindle motors have been conducted to verify the theoretical results. Each prototype motor has different spindle parameter configurations including bearing coefficients, bearing locations, and center of gravity location, etc. Also, this paper demonstrated that radial measurements of spindle rocking vibration have better correlation with OP-vibration performance than axial measurements through PES measurements. Finally, the optimized design has been manufactured by a motor maker and has also successfully verified the theoretical prediction experimentally.     

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.     

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.     

Investigation of the electromechanical variables of the spindle motor and the actuator of a HDD due to positioning and free fall

This research investigates the electromechanical variables of a spindle motor and an actuator of an operating hard disk drive (HDD) due to the positioning and the free-fall of a HDD. Magnetic fields of a brushless DC motor and a voice coil motor are determined by the time-stepping finite element equation of the Maxwell equation and the driving circuit equation. The pressure of the fluid dynamic bearings (FDBs) is determined by solving the finite element equation of the Reynolds equation to calculate the reaction force and the friction torque. Dynamic equations of the rotating disk-spindle, actuator, and stationary bodies of a HDD are derived from the Newton–Euler’s equation. The speed control of the rotating disk-spindle and the servo control of the actuator are included to describe the head positioning between the rotating disk and the head. The simulation is performed to investigate the electromechanical variables of the spindle motor and the actuator due to the positioning and the free-fall of a HDD. This research shows that the positioning and the free-fall of a HDD change the electromechanical variables of the spindle motor and the actuator of an operating HDD, and that monitoring their electromechanical variables may identify the positioning and the free-fall of a HDD without using extra sensors.     

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.     

轴承预紧力对转子系统静动态特性的影响

轴承预紧力的大小直接影响到滚动轴承-转子系统的静动态特性. 综合考虑离心力和陀螺力矩效应,在Romax软件中建立了5自由度轴承-转子系统动力学模型,分析了预紧力对轴承刚度、工作接触角以及工作寿命的影响,并搭建了轴承 转子系统试验台做验证试验. 在不同轴承预紧力下,分别研究了轴承刚度、工作接触角、工作寿命、静载荷作用下轴承 转子系统的静变形以及动不平衡载荷作用下主轴系统的振动响应等,并在轴承-转子试验台上进行试验验证,得到了轴承预紧力与这些因素的关系曲线. 在此基础上,研究了预紧力对转子系统固有频率的影响,结果表明加大预紧力有助于提高系统的固有频率. 研究结果可为轴承-转子系统的设计与分析提供理论参考.     

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.     

不同载荷工况下机床主轴预紧力选取的数值分析方法

为研究预紧力对机床主轴的影响,提出在不同载荷工况下机床主轴预紧力选取的数值分析方法.计算得到预紧力与轴承刚度的关系,在轴系结构有限元模型中设置不同预紧力下的轴承刚度值,通过静力学分析求解轴系变形和刚度;计算得到预紧力与轴承发热量的关系,在轴系热分析有限元模型中设置轴承热源,通过传热分析求解主轴温升.计算结果表明,该方法...     

Improvement of slider off-track vibration through design parameter modifications of a compatible FDB spindle system

Recently, the hard disk drive (HDD) industry has tried to use a compatible spindle system regardless of the number of disks because of the resulting cost reduction and standardization of components. The center of gravity (CG) location predominantly affects the disk and slider off-track vibration, which is why the rocking mode of a spindle system is affected by the CG. Any changes to the CG affect the operational vibration of the spindle system. In a compatible fluid dynamic bearing (FDB) spindle system, changing the number of disks may alter the CG. Nevertheless, research into the compatibility of FDB designs has not been undertaken. In this study, FDB design parameters were selected to reduce the slider off-track vibration with variations in the CG considering a compatible spindle system. First, a verified finite element (FE) model of a spindle system was constructed. The amplitude and frequency of the rocking mode were compared between a one-disk spindle system and a two-disk spindle system using the FE model, considering the relationship between the CG location, which is changed by the number of disks, and the location of the upper and lower journal bearings. HDD prototypes were then manufactured using the improved design. Based on the manufactured spindle system, the variations in the rocking mode characteristics and slider off-track vibration were measured and operational vibration tests were performed to verify the effect of the number of disks on the slider off-track vibration. An improved FDB spindle design was developed with a reduced rocking mode, and a compatible spindle system was proposed.     

A bi-directional rotating fluid bearing system

 Most fluid bearing systems with grooves on the journal/thrust bearing surfaces were designed to rotate in a specified direction and cannot be reversed. This feature of such fluid bearings limits their application range and hence, a bi-directional rotating fluid bearing system is proposed. The results of numerical simulation on the dynamic characteristics of such bearing system are presented and compared with those of one-directional rotating fluid-bearing system. It shows that for the same load capacity and stiffness requirement, the bi-directional rotating fluid bearing system has a higher power consumption than that of the one-directional counterpart. However, the bi- directional rotating fluid bearing system provides the freedom of rotating spindle motor in either direction and widens the application range of fluid bearing spindle motors. Received: 5 July 2001/Accepted: 17 October 2001     

Analysis and design of hydrodynamic journal air bearings for high performance HDD spindle

In this paper, we proposed the design concept of NRRO-free non-contact bearings for a high performance hard disk drive (HDD) spindle. We numerically analyzed three types of hydrodynamic journal air bearings [gas dynamic bearing (GDB)], such as a partial herringbone groove, a sinusoidal wave, and a taper-flat type. And we compared their performances in terms of pressure distribution, load capacity, radial stiffness, unbalance response, and stability threshold. For the design examples, we examined the Case 1 with 2.0 m bearing clearance and 10000 rpm, and the Case 2 with 1.0 m clearance and 15000 rpm. As a result of numerical analysis, we found that the taper-flat type was the most promising for high performance HDD spindle compared with the other types. It can have the bearing stiffness of about 3.0 × 10⁶ N/m in Case 1 and of about 2.0 × 10⁷ N/m in Case 2. We also discussed the allowance of parameters for the optimal design of the taper-flat type journal bearing.     

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.