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.     

适应连续外扰的时滞加速度反馈控制器

在采用加速度传感器的振动主动控制平台中,为了有效抑制外力可用微分方程描述的含输入时滞受迫振动响应,基于积分变换和状态导数极点配置法,提出了一种适应连续外扰的时滞加速度反馈控制器设计方法.以粘贴有压电陶瓷和加速度传感器的受正弦激励的智能梁为仿真控制对象,仿真结果表明,此控制器能在任意输入时滞下有效抑制智能梁的持续受迫振动响应.与不考虑时滞的同类控制器相比,该控制器有较好的稳定性及控制效果.     

A design based on final-state control for residual vibrationless seeking in hard disk drives

A new design method - based on a final-state control (FSC) - for short-span seeking in a hard-disk drive (HDD) has been developed. The short-span seeking is performed by two-degree-of-freedom (2-DOF) control, which uses a feedforward (FF) control input along with a reference trajectory. The design method can directly generate the FF control input, whose derivative at a specified order is minimized and whose power spectrum amplitude is reduced at a specified frequency. The residual vibration caused by mechanical resonance can therefore be reduced by the generated FF control input. Test with a 2.5-in form-factor HDD experimentally confirmed that the developed seeking control significantly reduces the residual vibration in a HDD.     

Vibration Control of a Planar Parallel Manipulator Using Piezoelectric Actuators

This paper presents an active damping control approach applied to piezoelectric actuators attached to flexible linkages of a planar parallel manipulator for the purpose of attenuation of unwanted mechanical vibrations. Lightweight linkages of parallel manipulators deform under high acceleration and deceleration, inducing unwanted vibration of linkages. Such vibration must be damped quickly to reduce settling time of the manipulator platform position and orientation. An integrated control system for a parallel manipulator is proposed to achieve precise path tracking of the platform while damping the undesirable manipulator linkage vibration. The proposed control system consists of a PD feedback control scheme for rigid body motion of the platform, and a linear velocity feedback control scheme applied to piezoelectric actuators to damp unwanted linkage vibrations. In this paper, we apply the proposed vibration suppression algorithm to two different types of piezoelectric actuators and evaluate their respective performances. The two piezoelectric actuators are (i) a PVDF layer applied to the flexible linkage and (ii) PZT actuator segments also applied to the linkage. Simulation results show that both piezoelectric actuators achieve good performance in vibration attenuation of the planar parallel manipulator. The dynamics of the planar parallel platform are selected such that the linkages have considerable flexibility, to better exhibit the effects of the vibration damping control system proposed.     

Track-following control with active vibration damping and compensation of a dual-stage servo system

This paper proposes a vibration control scheme for an actuated-slider dual-stage servo system. The control scheme consists of three components: a basic track-following servo loop, a feedback vibration damping loop around the main actuator, the voice coil motor (VCM), and a feedforward vibration compensation loop around the secondary microactuator (MA). A strain gauge sensor fabricated on the surface of the suspension detects airflow-excited structural vibrations and its output is fed to the feedback damping and feedforward compensation loops simultaneously. A higher sampling rate can be utilized for both the feedback damping and feedforward compensation controllers to achieve better performance. Simulation results show that the track-misregistration (TMR) resulting from the airflow-excited structural vibrations can be greatly attenuated, achieving a total reduction in TMR by 27% over the conventional dual-stage actuation without dedicated vibration control. Based on this control scheme and simulation results, projection of the system performance to the target of 500k tracks per inch (TPI) is performed, yielding some guidelines on how to improve disk drives operational conditions and control effect in order to approach the targeted areal density, 3 TMR budget of 5 nm.

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On active acceleration control of vibration isolation systems

Active vibration isolation systems (VIS) have been widely used from the space shuttle applications to the ground vehicle suspensions. The main control objective is to achieve the minimum vibrations at the flotor for given vibrations at the stator. With respect to a fundamental limitation of using the PD type flotor acceleration controller, an I (integral) and II (double integral) type flotor acceleration controller is proposed in this paper. By incorporating the feedforward compensation of the umbilical dynamics, the proposed acceleration controller is able to experimentally push down the lowest isolation frequency from 1.4 Hz (when PID control is used) to 0.03 Hz with a sufficiently improved vibration isolation performance up to 10 Hz, with respect to a MIM (Microgravity Vibration Isolation Mount) system tested on the ground. A unique frequency selective filter (FSF) is also proposed, which experimentally suppresses a fixed-frequency umbilical resonant mode at 22.2 Hz with an attenuation of 20 dB.     

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.     

Statistical energy analysis on vibrational energy transmission in hard disk drive components

One of the problems found in the 2.5 in. hard disk drives (HDDs) in operation is the vibration of the HDD case. Aiming to find crucial information to reduce the vibration transmitted to the outer shell of HDD, the parameters involving vibrational energy transmission through the main components of HDD are identified by the test-based statistical energy analysis (SEA). First, the vibration tests of HDD in the idle mode are performed in order to identify the contribution of the main components; the top cover, the platters, and the actuator arm to the overall vibration of HDD. The SEA parameters including the dissipation loss factors of the individual components and coupling loss factors of the pairs of the components are then experimentally determined in order to calculate the vibration transmission power among the components. The determined parameters, hence, provide some vibrational energy transmission characteristics to facilitate the design of the HDD components to generate less vibration. With some further studies using this concept, the vibration due to shock exerted to the shell of HDD that is transmitted to main components inside the HDD can also be reduced.     

Piezoelectric film attached suspension for detecting disk flutter and reducing track misregistration

To increase the recording density of hard disk drives, high accuracy of head positioning is required. But disk flutter, which is airflow induced vibration, is a major contributor to head positioning error. For detecting disk flutter, we proposed a suspension to which a PVDF film sensor was attached, and built the suspension into an actual HDD. Comparing the power spectrum of disk vertical vibration with that of the PVDF film sensor output, disk flutter was well detected. We also implemented a feedforward controller and confirmed that the influence of disk flutter on position error signal is considerably suppressed.     

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.     

Settling control with reference redesign for dual actuator hard disk drive systems

This paper considers settling control of a recording head for a dual actuator system for hard disk drives consisting of a coarse actuator (voice coil motor, VCM) and a fine actuator (peizoelectric transducer, PZT). The design method proposed in this paper is called the dual actuator reference trajectory re-design (RTRD). In this method, the design is divided into three steps. In the first step, the coarse actuator loop is designed to achieve stability and basic performance. In the second step, the fine actuator path is designed by loop shaping for superior performance of the overall system. Finally, the reference signals are generated for both the coarse and fine actuators by minimizing the square integral of jerk during the transition. The reference signals are updated or redesigned in real time as the recording head approaches the target track for smooth landing and minimal residual vibration. The “soft switching” technique is applied for gradually introducing the fine actuator (PZT actuator), which may shorten the settling time and achieve a smooth settling response. The effectiveness of the proposed approach is evaluated by simulations.     

多元多项式函数的三层前向神经网络逼近方法

该文首先用构造性方法证明:对任意r阶多元多项式,存在确定权值和确定隐元个数的三层前向神经网络.它能以任意精度逼近该多项式.其中权值由所给多元多项式的系数和激活函数确定,而隐元个数由r与输入变量维数确定.作者给出算法和算例,说明基于文中所构造的神经网络可非常高效地逼近多元多项式函数.具体化到一元多项式的情形,文中结果比曹飞龙等所提出的网络和算法更为简单、高效;所获结果对前向神经网络逼近多元多项式函数类的网络构造以及逼近等具有重要的理论与应用意义,为神经网络逼近任意函数的网络构造的理论与方法提供了一条途径.     

挠性飞行器时间燃料优化姿态机动控制的振动抑制

研究了使用反作用推力作为执行机械的姿态控制系统,针对挠性飞行器姿态机动控制,给出了命令整形时间燃料优化设计方法,在机动过程中,挠性振动对机动时间、燃料消耗和机动精度具有很大的影响,文中给出了挠性振动抑制手段,使机动完成的同时,振动得到有效抑制,由于振动频率和振动阻尼不易精确参数化,所以考虑挠性振动掏设计方法对振动频率和振动阻尼的鲁棒性设计问题,最后通过仿真验证了方法的可行性和有效性。     

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.     

MEMS-based accelerometers use in Hard Disk Drives

 We describe the use of micro electro-mechanical systems (MEMS)-based accelerometers for the compensation of vibrations in commercial hard disk drives (HDDs). Using formal analysis of the HDD mechanics, effects of generic roto-translation on the head position are evaluated. It is shown that such effects can be compensated using feed forward compensation from a weighted sum of the signal provided by two linear and one rotational accelerometer, mounted on the HDD. Rotational acceleration has been obtained using a recently developed MEMS-based, low cost rotational accelerometer. Experimental results presented here show 20 dB disturbance reduction, achieved with a simple, variable gain feed-forward compensator. Received: 5 July 2001/Accepted: 17 October 2001     

A note on Routh-Hurwitz determinants and integral square errors

Let p(s) be a polynomial, all of whose roots lie in the left half plane. The purpose of this note is to show that when the transfer function p(0)/p(s) tracks unit step input, the integral square error (ISE) of the response has a simple expression in terms of the Routh—Hurwitz determinants for p. This enables us to generalize a result of Hall : he pointed out that for a quadratic polynomial with fixed natural frequency, the minimum ISE is attained for a damping factor of ½. We find the corresponding result for polynomials of any degree.     

A novel feedforward control technique for a flexible dual manipulator

This paper proposes a feedforward control technique for two flexible links attached to one motor to suppress residual vibrations in a point-to-point motion. In the proposed method, we attempt to express the trajectory of the joint angle using a combination of cycloidal and polynomial functions, which enables the easy generation of a smooth motion. The generated trajectory depends on the coefficients of the polynomial function. To minimize the residual vibrations of the two flexible links, the coefficients are tuned using a particle swarm optimization algorithm, which is a type of a metaheuristic algorithm. The optimal trajectory obtained by this approach can suppress residual vibrations; i.e., multimode vibration control can be realized. Simulations and experiments are performed to evaluate the applicability and effectiveness of the proposed method.     

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     

Evolutionary design and implementation of a hard disk drive servo control system

The ever increasing demand for higher storage capacity and smaller magnetic hard disk drives have driven the need of developing a high performance head positioning servo control system. To meet the challenge, this paper presents the design and real-time implementation of a robust two-degree-of-freedom servo system for physical 3.5-in. hard disk drive with single voice-coil-motor actuator using a multi-objective evolutionary algorithm toolbox. Besides the simplicity in controller structure, such an evolutionary servo control system is capable of meeting various performance specifications of hard disk drives in both the time and frequency domains. It is shown that the servo system optimally moves the magnetic head onto the desired track with minimal control effort, and keeps it on the track robustly against plant uncertainties or runout disturbances. Validation results of the evolutionary servo control system are compared with classical PID and RPT controllers, which show excellent closed-loop response and robustness in the face of practical perturbations in HDD.     

Efficient simulation of hard disk drive operational shock response using model order reduction

The complex structure, coupled mechanical and fluidic energy domains, and inherent nonlinearity of air bearing between slider and disk involved in the hard disk drive (HDD) are normally presented as a large scale problem which will result in very heavy computational costs in terms of intensive computation and time consuming for HDD research communities and industries to carry out the transient dynamic simulation for HDD design verification, performance analysis, and optimization by using the traditional full-order models, such as finite element model (FEM). This paper presents a method of application of model order reduction (MOR) technique to dramatically reduce the computation time for HDD transient shock performance analysis while capturing the behaviors of original problem faithfully. The reduced models are obtained by performing MOR directly to the FEMs through Krylov subspace and Arnoldi algorithm. The transient operational shock response results of the reduced models of a head suspension assembly (HSA) subjected to half-sine shock pulse demonstrate that the reduced models can dramatically reduce total computation by at least three orders and have very good agreement with those simulated from the original large problem by full-order FEM.