A parametric study on rocking vibration of rotating disk/spindle systems with hydrodynamic bearings: rotating-shaft design

 The system studied in this paper is a rotating disk/spindle assembly supported by hydrodynamic bearings with a rotating shaft design. Based on an experimentally verified mathematical model [1, 2], this paper presents how various spindle parameters affect critical vibration modes of the system, such as half-speed whirls and (0, 1) unbalanced modes (i.e., rocking modes). The parameters studied include number of disks, hub/shaft interface stiffness, shaft rigidity, thrust bearing location, radial bearing stiffness, radial bearing damping, and radial bearing locations. To simulate operational tests, the numerical study focuses on frequency response functions (FRF) of rotating disk/spindle systems subjected to linear base excitations. Simulation results show that 1-disk configuration has smaller FRF amplitude than the 4-disk configuration. In addition, the amplitude of half-speed whirl is primarily controlled by the radial bearing stiffness. In contrast, the amplitude of (0, 1) unbalanced modes is dominated by hub/shaft interface stiffness. Finally, radial bearing locations significantly affect the amplitude of half-speed whirls and (0, 1) unbalanced modes simultaneously. Received: 16 October 2001/Accepted: 31 December 2001     

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.     

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.     

A parametric study on rocking vibration of hard disk drive spindle motors with fluid-dynamic bearings and rotating-shaft design

This paper presents a thorough parametric study to identify critical parameters controlling rocking vibration of hard disk drive (HDD) spindle motors. The spindle motors studied are of rotating-shaft design with fluid-dynamic bearings (FDB). The rocking vibration of interest results primarily from first three pairs of (0,1) unbalanced modes (also known as rocking modes, pitch modes, or gyro modes) and half-speed whirls. The parametric study shows that the transverse mass moment of inertia of the rotating part is the most critical parameter affecting the rocking amplitude. Also, FDB in-line stiffness dominates the amplitude of the half-speed whirls. Surprisingly, FDB in-line damping coefficient can considerably affect the amplitude of the second (0,1) unbalanced mode. Finally, bearing locations are very critical parameters for rocking amplitude of FDB spindles. Unfortunately, there is not a set of optimal bearing positions that will minimize vibration for all (0,1) unbalanced modes.The work was completed when the first author was a graduate student at the University of Washington, Seattle, Washington, USA.

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Hinge pivot for disk drive

This paper discusses the findings of a hinge pivot for use in hard disk drives (HDD). The actuator assembly in a HDD is supported by a pivot cartridge and controlled by a servo system to perform seek and track following operations for data recording. The cartridge is composed of a pair of pre-loaded ball bearings. Due to the demand for thin hard disk drives and hence, the need to reduce the height of the actuator assembly, a hinge pivot is proposed to replace the set of bearings. The shaft of the pivot is connected to the sleeve with thin hinges made of ultra-high heat-resistant polyamide film, such as Upilex. Measurement showed that the hinge pivot did not exhibit the nonlinear effects during low frequency actuation, such was inherent for ball bearing pivots. Experiment also showed that at least a million life cycles can be achieved without any performance degradation.     

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     

基于子结构的风力发电高塔系统的动力特性分析

采用子结构模态综合(Component Mode Synthesis,CMS)法和频响综合(Frequency response function-Based Substructure,FBS)法分析大型高耸装配结构风力发电高塔系统动力特性.通过子结构模态或频率响应函数(Frequency Response Function,FRF)信息综合成整体的模态或FRF信息,在保证整体分析精度的条件下提高计算效率,同时解决风电塔系统模态和FRF信息不易获得的问题.建立风电塔系统各个子结构的有限元模型和整体模型,分别使用MSC Nastran和LMS Virtual.Lab对各个子结构进行模态综合和频响综合分析,并将综合的结果与整体建模计算的结果进行对比,验证采用子结构CMS法和FBS法分析风力发电高塔系统的可行性和正确性.     

Robust shaft design to compensate deformation in the hub press-fitting and disk clamping process of 2.5″ HDDs

We investigated deformation of the outer diameter of a shaft due to the hub press-fitting and disk clamping processes associated with a 2.5″ hard disk drive. We propose a new robust shaft design to minimize the effect of deformation on the outer diameter of the shaft. We numerically show the effect of deformation on the shaft due to the pressure, stiffness, and damping coefficients of fluid dynamic bearings (FDBs), and the critical mass and excitation response of the rotor-bearing system. We also experimentally measured the axial non-repeatable runout and the amplitude at the half speed whirl frequency of FDBs with both conventional and proposed designs. Through these tests we confirm that the proposed design improves the static and dynamic performance of the FDBs and rotor-bearing system.     

Effects of stray magnetic forces on position error signals during a long seeking-and-settling process

This paper is to study how stray magnetic forces encountered in a long seeking process affect position errors of a hard disk drive after it finishes the seek and settles. The study consists of three parts: analysis of stray magnetic forces, numerical modeling, and analysis of numerical results. In the analysis of stray magnetic forces, we lump the stray magnetic forces into three components D1, D2 and D4. Specifically, D1 is a pair of stray magnetic forces in the plane of the voice coil. The two forces act on the two equal legs of the voice coil. In addition, the two forces point to and away from the pivot center, respectively. D2 is a pair of stray magnetic forces out of the plane of the voice coil. The two forces are equal in magnitudes but opposite in directions. The two force components also act on the two equal legs of the voice coil. D4 is identical to D2, except that the two force components in D4 act in the same direction. In the numerical study, we adopt a numerical model that includes a spinning spindle motor, a spinning disk pack with multiple disks, a stationary base plate with a top cover, and a slewing head-stack assembly. Moreover, multiple bearings are present in the model to connect the multiple components. In particular, fluid-dynamic bearings connect the rotating spindle and disk pack with the base plate, pivot bearings connect the base plate with the head-stack assembly, and air bearings connect the spinning disk pack with head sliders located at the tip of the slewing head-stack assembly. Also, the numerical model assumes that the head-stack assembly seeks according to a user-specified seeking profile. Numerical simulations show two major conclusions. First, stray magnetic force component D1 does not lead to significant position errors when the head-stack assembly settles. Stray magnetic force components D2 and D4, however, can affect the position errors by significantly exciting torsion and bending modes of the head-stack assembly. Second, a flex cable can significantly increase position errors below 1 kHz during settling.     

Stability analysis of a disk-spindle supported by a plain journal bearing and pivot bearing

A hydrodynamic bearing is widely used for hard disk drives, and it is better than a ball bearing in terms of vibration suppression, noise reduction and shock resistance. However, its cost to performance ratio should be further improved. In this study we analyzed the stability of a disk-spindle assembly supported by a hydrodynamic plain journal bearing and a pivot bearing at the bottom of the shaft. As a result, we found that a half-frequency whirl of a vertical spindle caused by the plain journal bearing becomes stable if the gyro factor of the rotor is larger than 0.5. We examined the effects of the bearing design parameters on the stability of the disk-spindle assembly, including the flexibility of the shaft. We also compared the stability of a disk-spindle assembly supported by two plain journal bearings and found that the vertical spindle is always unstable. Thus, the bottom end of the shaft should be supported as a fulcrum.     

On investigation of vibro-acoustics of FDB spindle motors for hard disk drives

The present work investigates vibro-acoustic behaviors of the fluid dynamic bearing (FDB) spindle motors for hard disk drives (HDD) through the sound spectra and the frequency response functions (FRF) of the motor structure. The quantitative evidence on the significance of the acoustic noise originated from the electromagnetic source is deduced from the sound spectra that were measured in two distinct cases of the spinning motor: in the normal operation and at the moment immediately after the power supply was disconnected. It is found that the effect of electromagnetic noise source is more dominant than the combined effect of the mechanical and aerodynamic sources. In addition, it is identified that, within the audible range of frequency, the frequency range of 13.4–20 kHz deems important to the noise problem as it is the main contributor to the acoustic noise for the FDB spindle motors. Moreover, the structural resonances that can be identified via the FRF are found to play an important role in the noise emitted by the motors. The concurrence of resonance and excitation frequencies clearly intensifies the sound spectrum, resulting in high discrete peaks, hence higher decibel level.     

Effects of thrust hydrodynamic bearing stiffness and damping on disk-spindle axial vibration in hard disk drives

This paper aims at investigating the effects of variations in thrust hydrodynamic bearing (HDB) parameters such as axial stiffness and damping coefficients on the axial vibration of disk-spindle systems in hard disk drives. For a parametric study, a closed-form axial frequency response function (FRF) of HDB spindle systems is derived as a function of the axial stiffness and damping coefficients of thrust HDBs. It is known that the axial vibration of the disk-spindle system is composed of two main parts: the vibration of the rigid hub in the axial direction and the disk deflection in the transverse direction. The results from this research clearly show that the vibration amplitudes at low frequency range is dominated by the axial vibration of the hub, and the amplitude of the unbalanced (0,0) mode is dominated by the disk deflection. The parametric study reveals that at low frequency range an increase in the bearing stiffness significantly reduces the hub axial vibration, and hence the axial vibration of the disk-spindle system. Surprisingly, a too much increase in the damping results in a higher amplitude of the unbalanced (0,0) mode. This is because a heavy damping constrains the hub vibration to nearly no motion, resulting in a direct transmission of vibration from the base to disk. To confirm the parametric study, a vibration test was performed on two HDB spindle motors with identical design but different fluid viscosity. The higher viscosity represents the higher axial stiffness and damping in the thrust bearing. The test result indicates that the spindle motor with higher viscosity has a larger unbalanced (0,0) mode amplitude when subjected to an axial base excitation.     

Validation,performance, convergence and application of free interface component mode synthesis

During the past three decades the component mode synthesis methods were extensively presented in the literature. Unfortunately, it seems that no convergence criterion was clearly defined in the literature. A free interface method is presented in this paper and six test cases are used to evaluate the number of retained substructure modes necessary to ensure convergence. The approach is validated numerically and experimentally. Also, an application of the proposed free interface method to optimization design is presented.     

An approach to predict lower-order dynamic behaviors of a 5-DOF hybrid robot using a minimum set of generalized coordinates

This paper presents an effective semi-analytical approach for predicting lower-order dynamics of a five degrees-of-freedom (DOF) hybrid robot named TriMule, which is composed of a 3-DOF parallel mechanism plus a 2-DOF A/C wrist. In this method, the governing equations of motion of limbs within the parallel mechanism are first formulated by finite element analysis (FEA) and then reduced to super-element models. This is followed by exploiting a general stiffness model of multiple DOF joints connecting the super-elements. These two threads lead to the reduced dynamic model of the parallel mechanism while keeping the full set of lower-order modes retained. Finally, the dynamic model of entire system is established by merging the models of parallel mechanism and wrist. The computational results show that the lower-order natural frequencies, mode shapes of the entire system, and the frequency response functions (FRFs) of the robot tool center point (TCP) estimated by the proposed approach have very good agreement with those obtained by a full order FE model and experimental modal tests. The merits of this approach lie in that the established model allows the full set of lower-order dynamics of the entire system to be predicted effectively and accurately by only using fourteen generalized coordinates.     

Optimal design of fluid dynamic bearings to develop a robust disk-spindle system in a hard disk drive utilizing modal analysis

This research proposes an optimal design methodology for fluid dynamic bearings (FDBs) in a hard disk drive to improve the dynamic performance of the disk-spindle system. We solved equations of motion for the rigid rotor supported by FDBs with five degrees of freedom. Five modal damping ratios were selected as multi-objective functions. The constraint equations were the friction torque of the FDBs and the stiffness and damping coefficients related to under-damped vibration modes. Ten major design variables of the FDBs were chosen for this optimization problem. The steady-state whirl radius and the shock response at half-speed whirl of the rotating rigid spindle-bearing system were evaluated as RRO and NRRO, respectively. The RRO and NRRO of the optimal design were compared with those of the conventional design. Our results show that the proposed method effectively reduces RRO and NRRO.     

A study of non-operational dynamic responses of disk in 3.5 in. hard disk drive to impact load

Hard disk drives have to be designed to sustain operational and non-operational shock. There are many analytical models and numerical schemes proposed and many experiments conducted for analyzing the transient impact responses of hard disk drives. The existing researches have been focused on the slider-suspension responses at the head-disk interface in which the linear models have been used and the effects of spindle motor have been ignored. In this study, the complex vibrations of disk of 3.5 in. hard disk drive (HDD) under shock are experimentally investigated. The hammer impact test and linear drop test are conducted for the HDD to study the effect of shock on the disk responses. The results show that the nonlinear rock modes substantially contribute to the vibrations of disk when HDD is under shock impact. The nonlinear properties of the disk responses and the mode damping ratio are evaluated by using empirical mode decomposition approach.     

A predictive technique for evaluating structural vibration gain of damped suspensions in hard disk drives

The problem of resonant vibration of suspensions used in hard disk drives has been the subject of ongoing research. This study focuses on implementation of a finite element modeling methodology to predict the response for a suspension that includes an added damping component, either as a traditional constraint layer damper or as a design tool. High gains in suspensions result in off-track of the slider, which is the mechanism for reading and writing data. Analytical methodology uses the concept of modal strain energy to predict the modal damping of the structure at each resonant mode. Loss factors and strain energies of each material used in the structure quantify the amount of modal damping at a particular mode. Development of the methodology allows optimization studies of standard damping applications, such as a constraint layer damper. In addition, the methodology enables FEA as a design tool to develop innovative solutions for improved efficiency and higher performance.     

Modelling of Torsion Beam Rear Suspension by Using Multibody Method

The multibody systems analysis has become one of the main simulation techniques to calculate the elasto-kinematics characteristics of a car suspension under wheel loads or to realize complex full vehicle models in order to predict the handling performances or the NVH quality. The modelling of torsion beam rear suspensions—widely adopted in cars belonging to B or C class—presents some problems arising from the structural behaviour of this component. A linear method based on component mode synthesis was used to represent the flexible torsion beam within the multibody model. This kind of approach was compared with a non-linear FE analysis. The elasto-kinematics analysis of the suspension was performed by using SIMPACK multibody code. The main suspension parameters (toe angle, camber angle, wheelbase and track variation) were calculated by changing wheel travel and loads. Static analyses, involving great displacements, were performed and a different number of modes were considered in the modal condensation of the torsion beam. The results of multibody simulations were compared with those obtained from a non-linear FE model. Different stiffness values of the bushings that connect the torsion beam to the vehicle chassis were taken into account.     

Prediction of in-process frequency response function and chatter stability considering pose and feedrate in robotic milling

Chatter occurs easily during robotic milling owing to the low structural stiffness of industrial robots and can degrade the machining quality or even cause robot failure. The accurate frequency response function (FRF) of the robot is essential for predicting chatter stability and selecting the appropriate process parameters. However, the FRF of a robot is affected by multiple factors, such as pose, operating state, and external excitation. In this study, an in-process FRF prediction method considering robot pose and feedrate was developed and used to predict chatter stability. Firstly, the static FRFs were obtained from the experimental modal analysis for different robot poses and used to train a Gaussian process regression (GPR) model. Subsequently, the static FRF predicted using GPR and the modal parameters identified by operational modal analysis (OMA) were used to calculate the in-process FRFs of the robot in the operation state. After removing the harmonic components of the vibration signals using a matrix notch filter, OMA was conducted using the least-squares complex frequency. Furthermore, the FRF of the robot was transformed from the robot flange coordinate system into the engagement coordinate system using the kinematics model and the tool path. The dynamic milling model, considering tool and robot modes was used for predicting stability. Finally, the proposed method was demonstrated by time-domain simulation of the robot-tool system and milling tests, and the effects of the running state and feed direction on chatter stability considering robot mode were analyzed.     

Lubricant evaluation method for FDBs using TOF-SIMS

 With the increase in recording density and data transfer rate of hard disk drive (HDD), fluid dynamic bearing (FDB) motors have been introduced due to their silence and high rotation accuracy. Although lubricant plays a major role in the development of FDB motors, it is extremely difficult to perform thorough evaluation because the quantity of lubricant used in the motor is as small as several micro liters. This paper describes a lubricant evaluation method for FDBs using the time of flight secondary ion mass spectrometry (TOF-SIMS), which enables simultaneous analyses of elements and organic molecules at PPM levels in an extremely small quantity of sample. By using this method, we found that worn metal elements generated both from spindle and bearings have substantial influences on lubricant degradation. Received: 5 July 2001/Accepted: 1 November 2001