Vibration Of Disk Research Articles

The measurement of the absolute displacement of a noisy disc brake

The investigation of in-plane vibration of a noisy disc brake is problematic because it is difficult both to measure and to verify. Because of the disc structure and the inability to visualize disc in-plane vibration, there has been reluctance by researchers to accept the contribution of a displacement parallel to the surface of the object, or in-plane displacement, to noise generation. In addition to measuring absolute displacement, it has been difficult to isolate the in-plane and out-of-plane components of displacement using either non-contact or conventional displacement measurement techniques. This paper investigates absolute displacement of a brake disc during noise generation. Double-pulsed holographic interferometry is used to record a series of time-related images of the brake head from three different angles of observation. Because each image views the brake head from a different perspective, each of them records a different degree of in-plane and out-of-plane displacement. By careful analysis of the three images, it is possible to isolate the in-plane displacement from the out-of-plane displacement. The time-related series allows the displacement to be investigated over a full cycle of excitation and so create an animation of the mode of vibration. It is seen that the in-plane displacement is complex and that its amplitude may be about twice that of the out-of-plane displacement.

A Sensitivity-Based Method for Direct Stochastic Analysis of Nonlinear Forced Response for Bladed Disks With Friction Interfaces

An efficient method is developed to calculate stochastic and uncertainty characteristics of forced response for nonlinear vibrations of bladed disks with friction and gap contact interfaces. Uncertainty ranges, statistical characteristics, and probability density functions for forced response levels are determined directly without any sampling procedure. The method uses approximations of the forced response level based on derived analytically and calculated extremely fast and accurately sensitivity coefficients of forced response with respect to friction contact interface parameters. The method effectiveness allows analysis of strongly nonlinear vibration of bladed disks using realistic large-scale finite element models. The method is implemented in a program code developed at Imperial College and numerical examples of application of the method for stochastic analysis of a realistic blisc with underplatform dampers are provided.

공기 유동 효과를 고려한 회전 디스크의 진동 특성 (II) - 실험적 검증 -

Experimental studies on the aerodynamic coupling effect on natural frequencies, critical speed and flutter instability of rotating disks are investigated in this paper. The theoretical analysis uses a fluid-structure model where the aerodynamic effects are represented in terms of elastic, lift and damping and stiffness components. The experiments performed using a vacuum chamber and ASMO/DVD disks rotating in vacuum, open and enclosure in several gaps with stationary wall give three main results. One is that the aerodynamic effect by the surrounding air reduces the natural frequencies and critical speeds of the vibration modes. The second is that natural frequency of disks rotating in open air is larger than that in enclosure. Finally, it is shown that the disk vibration is reduced as the gap between the disk and the rigid wall decreases.

612 SPR法を用いた動的平面シェル方程式の数値解析(G01-1 計算力学(1)有限要素法・メッシュフリー法他,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

The SPR (Superconvergent Patch Recovery) method proposed by Zienkiewicz and Zhu (1992) is incorporated in the time integration process of the dynamic plane shell equation. The SPR method is employed to compute the second-order spatial differentiations such as Laplacian of displacement, and to evaluate the restoration force due to flexural rigidity. The defects of rank deficiency of an SPR matrix and hourglass mode instability are overcome by remedies proposed by Yue and Robbins Jr. (2007), and Flanagan and Belytschko (1981), respectively. The proposed numerical method is validated with comparison of the theoretical and numerical results of a free vibration of a circular disk.

Investigation of vertical vibrations of rigid disk on saturated poroelastic stratum under high-frequency excitation

The forced high-frequency vertical vibrations of a rigid circular disk on a saturated poroelastic stratum supported by a rigid rock foundation are studied. An exact formulation is developed for the dual integral equations governing the mixed boundary-value problem of the vertical vibration. By finding an approximate solution to the exact governing dual integral equations, an evaluation of the amplitude response of the rigid disk is presented for the case of a frictionless contact both between the disk and the stratum and between the stratum and the foundation. The influences of parameters regarding the disk and the elastic stratum on the amplitude response of the disk are discussed. It is concluded that the amplitude response of the disk is dependent on the exciting frequency, the depth of the stratum, the Poison’s ratio of the solid skeleton, the porosity of the medium and the radius and mass of the disk.

높은 유연 모드 주파수를 갖는 가동 자석형 광 픽업 액추에이터 개발

Data transfer rate and storage capacity are main criteria of the performance of the optical disk drive. The highest data transfer rate and the largest storage capacity is most desirable. To increase these performances, the actuator of the optical disk drive should have a high servo bandwidth to compensate the vibration of an optical disk. The servo bandwidth is limited by some flexible modes of the actuator, thus it is essential to increase the natural frequencies of the flexible modes. In this paper, we suggested a moving magnet type actuator having high frequencies of the flexible modes. Generally, the moving magnet type actuator has an advantage to increase the natural frequencies of the flexible modes because the moving magnet type actuator has simple structure and the Young`s modulus of magnet is high. However, large moving mass and inefficiency of EM(electromagnetic) circuit cut down driving sensitivities of the actuator. To improve driving sensitivities, we designed the model with the closed electromagnetic circuit for tracking direction. In addition, driving sensitivities and the natural frequencies of the flexible modes were improved by using DOE(design of experiments) for electromagnetic circuit and modifying the lens holder.

Reducing position error signal (PES) due to disk vibration using an air shroud

The advances in magnetic recording technology demand higher magnetic head positioning accuracy and faster disk rotation speed. However, the higher rotational speed of disk generates the greater flow-induced vibration known as disk flutter, which causes the increase of the track misregistration (TMR). To overcome the issue, an air shroud is presented to reduce disk vibration and position error signal (PES) for magnetic recording. Computational fluid mechanics simulations are performed to study the flow pattern surrounding a disk with an air shroud for different openings. The air-bearing stiffness and damping effects of the disk spindle assembly with an air shroud are evaluated. Based on the computational fluid dynamics (CFD) simulation, the air shroud is prototyped and the disk vibrations with and without the air shroud at different disk rotation speeds are experimentally investigated using a laser Doppler vibrometer (LDV). Significant disk vibration reductions are attained while a shroud is installed onto a disk at certain disk rotation speeds. PESs are also measured for the cases with and without an air shroud during servo implementation. Reductions of PESs are observed when an air shroud is installed at some disk rotation speeds.

Computing the aeroelastic disk vibrations in a hard disk drive

Abstract The turbulent flow of air caused by the spinning of a single disk inside a typical hard disk drive casing is calculated using large eddy simulation (LES). The pressure acting on the disk is recorded as a function of time and is used to compute the vibrations of the spinning disk using a self-developed hybrid-spectral finite-difference code. This unidirectional fluid–structure interaction problem is computed for two commonly occurring cases: a disk actuated on one side only (Case 1) and a disk actuated on both sides (Case 2). The pressure loading on the disk is characterized in terms of its mean, root-mean-square (r.m.s.) and its spectral content. The mean pressure acting on the disk is asymmetrical in the case where the disk is actuated on one side only, leading to a mean deformation of the disk to one side. The r.m.s. vibrations of Case 2 are higher than those for Case 1 and their spectral distributions are almost identical. Large pressure fluctuations of the flow are found in the wake of the actuator arm and near the region where the shroud expands to accomodate the actuator. The spectral content of the excitation force due to the pressure is mainly in the low kHz frequency range, while higher frequencies are seen at the disk edge. This typically results in the excitation of the first 3–4 modes of the disk; however, (asymmetric) Case 1 displays the excitation of higher modes compared with (symmetric) Case 2.

Free vibration of polar orthotropic circular plates with elastic growth stresses and drying stresses

This study was performed to analyze effect of transverse growth stresses and drying stresses on natural frequencies of transverse free vibration of thin tree disk with free boundary condition. Using Rayleigh–Ritz method and finite element method, explicit closed form expression was derived for homogeneous orthotropic circular plates with internal stresses, which enables to predict both the effects of growth stresses, drying stresses, and combined growth and drying stresses on the natural frequency changes. This model can be used for predicting growth stresses from known natural frequencies. The same approach can also be undertaken to validate models visco-elastic drying stresses.

Experimental dynamic characterizations and modelling of disk vibrations for HDDs

Currently, the rotational speed of spindle motors in HDDs (Hard-Disk Drives) are increasing to improve high data throughput and decrease rotational latency for ultra-high data transfer rates. However, the disk platters are excited to vibrate at their natural frequencies due to higher air-flow excitation as well as eccentricities and imbalances in the disk-spindle assembly. These factors contribute directly to TMR (Track Mis-Registration) which limits achievable high recording density essential for future mobile HDDs. In this paper, the natural mode shapes of an annular disk mounted on a spindle motor used in current HDDs are characterized using FEM (Finite Element Methods) analysis and verified with SLDV (Scanning Laser Doppler Vibrometer) measurements. The identified vibration frequencies and amplitudes of the disk ODS (Operating Deflection Shapes) at corresponding disk mode shapes are modelled as repeatable disturbance components for servo compensation in HDDs. Our experimental results show that the SLDV measurements are accurate in capturing static disk mode shapes without the need for intricate air-flow aero-elastic models, and the proposed disk ODS vibration model correlates well with experimental measurements from a LDV.

Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration

New techniques are presented for generating reduced-order models of the vibration of mistuned bladed disks from parent finite element models. A novel component-based modeling framework is developed by partitioning the system into a tuned bladed disk component and virtual blade mistuning components. The mistuning components are defined by the differences between the mistuned and tuned blade mass and stiffness matrices. The mistuned-system model is assembled with a component mode synthesis technique, using a basis of tuned-system normal modes and attachment modes. The formulation developed is general and can be applied to any mistuned bladed disk, including those with large geometric mistuning (e.g., severe blade damage). In the case of small (i.e., blade frequency) mistuning, a compact reduced-order model is derived by neglecting the attachment modes. For this component mode mistuning model, the blade mistuning is projected first onto the component modes of a tuned, cantilevered blade, and then projected again onto the tuned-system normal modes via modal participation factors. In this manner, several natural frequencies of each mistuned blade can be used to capture systematically the effects of the complex physical sources of mistuning. A numerical validation of the developed methods is performed for both large and small mistuning cases using a finite element model of an industrial rotor.

Dual-Wavelength Membrane-Based Diffractive Optical Element with Extended Depth-of-Focus for Optical Pickup Head

An improved structure and optimization method for a high-numerical-aperture application for optical pickup heads that uses a low-stress silicon–nitride-membrane-based diffractive optical element to generate dual-wavelength pseudo-Bessel beams is described in this paper. The dual-wavelength membrane-type diffractive optical element with an extended focal depth for next-generation optical pickup applications has been demonstrated. The theoretical simulation and fabrication results detailing the resolution, longer depth-of-focus and diffractive efficiency are presented for the newly designed membrane diffractive optical element (DOE). This implies that the problems of disc vibration as well as the assembly and optical alignment of the many elements are solved.

Adaptive interferometry of protein on a BioCD

Adaptive spinning-disk interferometry is capable of measuring surface profiles of a thin biolayer with subnanometer longitudinal resolution. High-speed phase modulation in the signal beam arises from the moving surface height profile on the spinning disk and is detected as a homodyne signal via dynamic two-wave mixing. A photorefractive quantum-well device performs as an adaptive mixer that compensates disk wobble and vibration while it phase-locks the signal and reference waves in the phase quadrature condition (pi/2 relative phase between the signal and local oscillator). We performed biosensing of immobilized monolayers of antibodies on the disk in both transmission and reflection detection modes. Single- and dual-analyte adaptive spinning-disk immunoassays were demonstrated with good specificity and without observable cross-reactivity. Reflection-mode detection enhances the biosensing sensitivity to one-twentieth of a protein monolayer, creates a topographic map of the protein layer, and can differentiate monolayers of different species by their effective optical thicknesses.

환형 디스크 형상이 래디얼 진동에 의한 음향방사 특성에 미치는 영향

이 논문은 후판 환형 디스크의 기하학적인 형상이 래디얼 방향 진동에 의해 방사되는 소음에 미치는 영향을 연구하였다. 디스크의 내경을 고정한 상태에서 두께와 외경을 주어진 범위내에서 변경하면서 이론적인 해를 이용하여 래디얼 모드의 고유진동수와 진동모드의 변화를 검토하였다. 이 결과를 이용하여, 해당 형상을 가진 디스크의 래디얼 방향 고유진동에 의해 발생되는 원격음장, 음향파워 및 방사효율을 계산하였다. 이 결과로부터 고유진동에 의한 음향파워와 방사효율을 최소화할 수 있는 기하학적인 형상을 선택하였다. 마지막으로, 최적화된 디스크의 임의 위치에 단위 하모닉 가진을 가했을 경우에 발생되는 음향파워 및 방사효율 스펙트럼을 구하였으며, 전산해석을 통해 그 정확성을 검증하였다. 이 논문에 소개된 방법을 적용하면 주어진 제한 조건을 만족하면서 목표 주파수 범위내에서 래디얼 진동에 의해 발생되는 소음을 최소화할 수 있는 기하학적인 형상을 간편하고 논리적으로 구할 수 있다. This article investigates the effects of geometric configuration on the vibro-acoustic characteristics of in-plane vibration of a thick annular disc. Disc thickness and outer radius for a given inner radius are selected as independent variables having reasonable ranges. Variations in structural eigensolutions for radial modes are investigated using pre-developed analytical method. Based on these data, far-field sound pressure distributions due to the modal vibrations for a given geometry are also calculated using an analytical solution. Modal sound powers and radiation efficiencies are calculated from the far-field sound pressure distributions and vibratory velocity distributions on the radial surfaces. Based on the results explained above, the geometric configuration that minimizes modal sound radiations in a given frequency range is determined. Finally sound power and radiation efficiency spectra for a unit harmonic force from the selected geometric configuration are obtained from structural and acoustic modal data using the modal expansion technique. Multi-modal sound radiations of the optimized disc that are obtained using proposed analytical methods are confirmed with numerical results. Using the procedure introduced in this article, sound radiation due to in-plane modes within a specific frequency range can be minimized by the disc geometry modifications in a comprehensive and convenient manner.

27 kHz Ultrasonic Complex Vibration Source Using (1, 1) Mode Transverse Vibration Disk with Multiple Transducers of 40 mm Diameter

The configurations of a small-diameter 27 kHz ultrasonic complex vibration source using a (1,1)-mode transverse vibration disk with four bolt-clamped Langevin-type piezoelectric ceramic (PZT) transducers (BLTs) 40 mm in diameter is developed and studied. The vibration source is driven using two power amplifier systems and a circular vibration locus is obtained at a welding tip. A vibration amplitude of 8.5 µmp–0 (peak-to-zero value) is obtained at a driving voltage of 50 Vrms.

Dynamic stability of rotor-bearing systems subjected to random axial forces

This paper investigates the lateral vibration of a spinning disk–shaft system supported by a pair of ball bearings and subjected to a pair of random axial forces at both ends. The axial forces are assumed as the sum of a static force and a random process with a zero mean. Due to the random axial forces, the rotor-bearing system may experience parametric random instability under certain situations. In this work, the finite element method is applied to yield a set of discretized system equations first. The set of discretized system equations is partially uncoupled by the modal analysis procedure suitable for gyroscopic systems. The stochastic averaging method is then adopted to obtain Ito's equations for the response amplitudes of the system. Finally the first- and second-moment stability criteria are utilized to determine the stability boundaries of the system. Numerical results show that the rotor-bearing system is always stable in the sense of the first-moment stability, and the effects of the average axial compressive force and the disk mass, which will lower all frequencies of the system, tend to destabilize the second-moment stability of the system.

IMP를 이용한 근접장 기록 장치의 디스크 진동 및 편심 보상

Information storage devices using disks have a disk vibration at the frequency which is equivalent to the disk rotational speed. They also have a track vibration due to the disk eccentricity at the same frequency. In near field recording systems, the former affects the air-gap servo and the latter affects the tracking servo. In this paper, we introduce a novel control algorithm based on the internal model principle to both servos. A controller block designed by the principle is connected to the base lead-lag type compensator in parallel in order to cancel the repeatable run-out due to the disk vibration or eccentricity. Simulation and practical application of the algorithm on a near field recording system show good servo performance.

Wiggling Jump Strategy for Multiple-Beam Optical Disc System

As the traditional method for increasing the readout and write data rate in optical storage by increasing the disc rotational speed is at its upper bound, due to factors such as disc vibration, servo bandwidth, signal noise ratio, etc. multi-beam systems that enable higher data rates are emerging as an important option in the speed race. By using our new wiggling method for multi-beam optical storage, the extra link-overhead caused by traditional jumping is avoided. Using this method, a certain data rate can be achieved with one laser spot less than when using the traditional jump method. This means a considerable reduction in cost and power dissipation.

Piezoelectric Networks for Vibration Suppression of Mistuned Bladed Disks

Extensive investigations have been conducted to study the vibration localization phenomenon and the excessive forced response that can be caused by mistuning in bladed disks. Most previous researches have focused on analyzing∕predicting localization or attacking the mistuning issue via mechanical tailoring. Few have focused on developing effective vibration control methods for such systems. This study extends the piezoelectric network concept, which has been utilized for mode delocalization in periodic structures, to the control of mistuned bladed disks under engine order excitation. A piezoelectric network is synthesized and optimized to effectively suppress vibration in bladed disks. One of the merits of such an approach is that the optimum design is independent of the number of spatial harmonics, or engine orders. Local circuits are first formulated by connecting inductors and resistors with piezoelectric patches on the individual blades. Although these local circuits can function as conventional damped absorber when properly tuned, they do not perform well for bladed disks under all engine order excitations. To address this issue, capacitors are introduced to couple the individual local circuitries. Through such networking, an absorber system that is independent of the engine order can be achieved. Monte Carlo simulation is performed to investigate the effectiveness of the network for a bladed disk with a range of mistuning level of its mechanical properties. The robustness issue of the network in terms of detuning of the electric circuit parameters is also studied. Finally, negative capacitance is introduced and its effect on the performance and robustness of the network is investigated.

Vibration control of an HDD disk-spindle system utilizing piezoelectric bimorph shuntdamping: I. Dynamic analysis and modeling of the shunted drive

This work proposes a new piezoelectric shunt damping methodology to controlthe vibration of a computer hard disk drive (HDD) disk-spindle system. Thefirst part of this work (part I) deals with dynamic modeling of the piezoelectricshunted drive, while the second part of this work (part II) covers experimentalimplementation of the proposed shunt circuits. In the modeling, a target vibrationmode which significantly restricts the recording density increment of the drive isdetermined by analyzing the dynamic characteristics of the conventional drive. This isachieved by undertaking both modal testing and finite element (FE) analysis.In order to effectively suppress the unwanted vibration of the target mode, apiezoelectric bimorph is then designed and integrated to the drive by considering themode shapes of the target vibration mode. The mechanical impedance of theshunted bimorph is derived from lamination theory and piezoelectric constitutiveequations. In this derivation, the electromechanical coupling coefficient of theshunted drive is analytically incorporated with the mechanical impedance. Usingthe coupling coefficient, the shunt damping performance for the target vibrationmode is predicted and evaluated by presenting the displacement transmissibility.