Vibration Of Disk Research Articles

1102 円筒容器内回転積層円盤間乱流における圧力変動とディスク振動の同時計測(OS11-1 流体関連振動・騒音,OS11 流体関連振動・騒音)

The complex flow features inside hard disk drive models are investigated experimentally in an axially symmetric shroud configurations. The experiment focuses on both pressure fluctuation and disk vibration. we observed pressure fluctuation excites the natural frequency of disk. The correlation of them in the turbulent flow between disks is evident.

IL09 JWSF BETWEEN ROTATING DISKS

Many researchers have studied the flow around single/plural rotating disks with infinite/finite radii. These flow problems can be found out in various industrial applications such as axial compressors, vaneless diffusers, multiple-disk pumps, disk/dram-brake systems. In general, these types of flow are likely to entail non-axisymmetric secondary flows, which occasionally cause disk vibrations and noises. In the present study, the author especially deal with the flow between co-rotating disks, namely, the disks which rotate co-axially in the same direction at the same angular velocity, with a narrow gap enclosed by a stationary shroud at their circumferences. This flow is modeled on that inside the random-access disk storage devices of computers. The author experimentally and numerically shows that this flow is very complicated with three-dimensionality and turbulence, despite the simplicity in its imposed boundary conditions of geometry.

두꺼운 디스크의 면외 진동 해석을 위한 준-해석적 환상 민드린 평판 요소

이 논문은 두꺼운 디스크의 면외 고유 진동을 유한 요소법을 사용하여 회전 관성 및 횡 전단 변형의 효과를 포함하면서 단순하고 효율적으로 정밀하게 해석할 수 있는 새로운 준-해석적 환상 민드린 평판 요소를 제시한다. 환상 민드린 평판의 평형 방정식의 정확한 해인 정적 변형 모드를 사용하여 요소의 보간 함수, 강성 및 질량 행렬은 절 직경 수에 대하여 유도되며, 이와 같은 요소는 면외 강체 운동을 정확하게 표현할 수 있고 전단 잠김이 없다. 제시된 요소를 적용하여 동심 링으로 지지되거나 지지되지 않은 균일 디스크 및 다단 디스크의 고유진동수를 해석하고, 그 결과를 선행 연구의 이론적 결과 또는 2차원 쉘 요소를 사용하여 얻어진 유한요소 해석 결과와 비교하여 제시된 요소의 수렴성 및 정확성을 조사하였다. This paper presents a new semi-analytical annular Mindlin plate element with which out-of-plane natural vibration of thick disks can be analyzed simply, efficiently, and accurately through FEM by including effects of rotary inertia and transverse shear deformation. Using static deformation modes which are exact solutions of equilibrium equations of annular Mindlin plate, the element interpolation functions, stiffness and mass matrices corresponding to each number of nodal diameters are derived. The element is capable of representing out-of-plane rigid-body motions exactly and free from shear locking. Natural frequencies of uniform and multi-step disks with or without concentric ring support are analyzed by applying the presented element. Such results are compared with theoretical predictions of previous works or FEA results obtained by using two-dimensional shell element to investigate the convergence and accuracy of the presented element.

Design of a Kind of Drilling Machine for Semicircle Shaft

The central shaft of floor strainer are composed of two semicircle shafts, which is made manually now. An automatic drilling machine is researched in this paper, which can sequence and feed workpiece, positioning automatically and feed automatically when drilling. The sequencing and feeding are implemented by vibration disk. The automatic positioning is implemented by Index Man and positioning disc. The feeding mechanism is executed by pneumatic device and its control system.

Interaction of rocking vibration of a buried rigid circular disc and a two-layer transversely isotropic half-space

A linear elastic layer of finite thickness bonded on a half-space each containing a transversely isotropic material is considered. A rigid circular disc attached to the interface of these two domains is considered to be affected by a rocking vibration of constant amplitude. With the aid of a scalar potential function, the equations of motion in each domain are solved using Fourier series and Hankel integral transforms. Because of the involved integral transforms, the mixed boundary value problem is changed to dual integral equations; which are reduced to Fredholm integral equations. Because of the complex integrand function existing in the dynamic case, analytical solution cannot be given in general. However, a closed-form solution is introduced for the static case, which itself degenerates to the solution for an isotropic case existing in the literature. The contact stress in between the rigid disc and the surrounding media, and the related impedance function are analytically determined in the static case. With the help of contour integration, the governing Fredholm integral equations are numerically evaluated in the dynamic case. The dynamic contact pressure and the impedance function are numerically evaluated in a general dynamic case. The shape induced singularity in the contact pressure is investigated in detail. Some numerical evaluations are given for different transversely isotropic materials to show the effect of anisotropy.

Radially sandwiched cylindrical piezoelectric transducer

A new type of radially sandwiched piezoelectric short cylindrical transducer is developed and its radial vibration is studied. The transducer is composed of a solid metal disk, a radially polarized piezoelectric ceramic short tube and a metal tube. The radial vibrations of the solid metal disk, the radially polarized piezoelectric tube and the metal tube are analyzed and their electromechanical equivalent circuits are introduced. Based on the mechanical boundary conditions among the metal disk, the piezoelectric tube and the metal tube, a three-port electromechanical equivalent circuit for the radially sandwiched transducer is obtained and the frequency equation is given. The theoretical relationship of the resonance and anti-resonance frequencies and the effective electromechanical coupling coefficient with the geometrical dimensions is analyzed. The radial vibration of the sandwiched transducer is simulated by using two different numerical methods. It is shown that the analytical resonance and anti-resonance frequencies are in good agreement with the numerically simulated results. The transducer is expected to be used in piezoelectric resonators, actuators and ultrasonic radiators in ultrasonic and underwater sound applications.

In-Plane and Transverse Eigenmodes of High-Speed Rotating Composite Disks

We apply Hamilton's principle and model the coupled in-plane and transverse vibrations of high-speed spinning disks, which are fiber-reinforced circumferentially. We search for eigenmodes in the linear regime using a collocation scheme, and compare the mode shapes of composite and isotropic disks. As the azimuthal wavenumber varies, the radial nodes of in-plane waves are remarkably displaced in isotropic disks while they resist such displacements in composite disks. The reverse of this phenomenon happens for transversal waves and the radial nodes move toward the outer disk edge as the azimuthal wavenumber is increased in composite disks. This result is in accordance with the predictions of Nowinski's theory, and therefore, it is independent of the magnitude of the spinning velocity and the mode frequency. Although there are notable differences between the form of governing equations derived from Hamilton's principle and Nowinski's theory, transverse eigenmodes differ a little in the two approaches. We argue that the application of orthotropic composites as the core material of the next generation of hard disk drives, together with an angular velocity controller, can enhance the data access rate.

Model Predict Vibration and Noise of Disc Brake

The problem brake squeal is one of the important areas of application in the automotive industry. Most brake squeal is produced by vibration (resonance instability) of the brake components, especially the pads and discs are known as force-coupled excitation. Until now have many research about predict vibration and noise of disc brake but unfortunate the results is not satisfied. This paper presents model for prediction stability of disc brake for a model four degrees of freedom. The result shows stability of system and when occurrence brake squeal.

Vertical vibration of a rigid disc embedded in a poroelastic half-space in contact with a fluid half-space

This paper considers the problem of the vertical vibration of a rigid disc embedded in a poroelastic half-space in contact with a fluid half-space. A time-harmonic Green’s function for a vertical point force in a poroelastic half-space in contact with a fluid half-space is first derived. The fundamental solution is obtained using the boundary conditions at the plane passing through the point force and the boundary conditions at the poroelastic medium-fluid interface. The solution of the disc vibration problem is obtained by integrating the point force Green’s function over the contact area with unknown tractions, which are determined from the boundary conditions. The solution is expressed in terms of dual integral equations that are converted into a Fredholm integral equation of the second kind and are solved numerically. Selected numerical results for the vertical dynamic compliance coefficient are examined based on different poroelastic materials, embedment depth and frequency of excitation; moreover, the results are analyzed for two different cases, namely, with or without fluid overlying the poroelastic medium to demonstrate the effect of fluid. These results are helpful in understanding the dynamic response of foundations embedded in the seabed under seawater.

Analytical solution of transient in-plane vibration of a thin viscoelastic disc and its multi-precision evaluation

The analytical solution of transient in-plane vibration of a thin viscoelastic disc caused by a radial pressure load is presented. Using the multi-precision implementation of FFT based algorithm, the inverse Laplace transform is carried out and the spatio-temporal distributions of displacement components are obtained. The efficiency and the accuracy of the process of analytical solution evaluation are discussed in detail and the consequences in context of the application of results are mentioned. Finally, the results of numerical simulation are presented. They are used for the verification of the correctness of the derived analytical formulae and their evaluation and for the determination of numerical model capabilities.

Horizontal vibration of a rigid disk buried in a poroelastic half-space in contact with a fluid half-space

This paper addresses the horizontal vibration of a rigid disk embedded in a poroelastic half-space in contact with a fluid half-space using the poroelastic theory of potentials. The solution of this problem is expressed in terms of dual integral equations that are converted into Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the horizontal dynamic impedance coefficient are examined based on different poroelastic materials, embedment depths, and excitation frequencies; furthermore, the results are analyzed for the cases in which there is and is no fluid overlying the poroelastic medium to examine the effect of fluid. The results of this study are helpful for designing a foundation embedded in the seabed due to dynamic horizontal forces.

Vibration Characteristics of Guided Circular Saws: Experimental and Numerical Analyses

Studying the vibrational characteristics of guided circular saws is of particular interest in the current study. Guided circular saws are free in both the inner and outer rim. They are restrained from having axial motion by using two space-fixed guide pads in either side of the blade. Because of the small clearance between the guide pads and the saw blade, the blade is capable of having rigid body tilting and a translational degree of freedom. At first, we attempted to develop an understanding regarding the vibrational characteristics of such disks through experimental investigations. An electromagnet was used to generate random white noise for the purpose of exciting the bending waves. Using inductance displacement probes, the frequencies and amplitudes of the disk vibrations were measured and the mean deflections were plotted. In the next step, a space-fixed external force (air jet) was used to excite the disks in the lateral direction. The experimental results indicate that the blade frequencies show a significant change as a result of the initial lateral displacement imposed by the external force. It was also seen that due to the presence of the external force, a stationary wave develops and collapses at a higher speed. For the numerical simulations, the nonlinear governing equations based on Von Kármán plate theory were used. The effect of rigid body degrees of freedom was taken into account. As an approximation, the guide pads were modeled with four space-fixed springs. Using Galerkin’s method, the governing equations were discretized and their equilibrium solutions were found. After linearizing the governing equations around the equilibrium solution, the effect of nonlinearity on the amplitude and frequency response of the guided blade was investigated. It was seen that the numerical results were in close agreement with the experimental results.

A coupled fluid layer–rigid disk–poroelastic half-space vibration problem

This paper proposes a coupled fluid layer–foundation–poroelastic half-space vibration model to study how still water affects foundations operating underwater. As an example, we consider the problem of the vertical vibration of a rigid disk on a poroelastic half-space covered by a fluid layer having a finite depth. The solution of the disk vibration problem is obtained using the boundary conditions at the free surface of the fluid layer and the boundary conditions at the fluid layer–poroelastic medium interface. The solution is expressed in terms of dual integral equations that are converted into Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the vertical dynamic impedance coefficient are examined based on different water depths, poroelastic materials, disk permeabilities and frequencies of excitation. Based on the numerical results, it is proposed that the hydrodynamic pressure caused by the foundation vibration is the intrinsic reason that the existence of a fluid layer has such a great effect on the dynamic characteristics of the foundation. In many cases, the hydrodynamic pressure caused by the foundation vibration cannot be ignored when designing dynamic underwater foundations. These results are helpful in understanding the dynamic response of foundations under still water without water waves, such as foundations in pools, lakes and reservoirs.

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.

Sound radiation from in-plane vibration of thick annular discs with a narrow radial slot

The vibro-acoustic characteristics of in-plane vibration in a thick annular disc containing a narrow radial slot are investigated with a hybrid approach combining numerical or experimental results with pre-developed analytical calculations. Structural eigenfunctions for in-plane vibrations of the disc are approximated as linear combinations of eigenfunctions for a uniform disc that has same material properties and geometric dimensions except for the slot. Acoustic radiations from the normal modes of the disc are calculated using a theoretical solution introduced in previous work for the uniform disc along with the results from the approximations of structural eigenfunctions. Vibration and sound radiation from the disc due to a harmonic force fixed to the disc outer surface are investigated using the mode expansion method. The effects of the circumferential distance between the radial excitation and slot on the vibro-acoustic responses are investigated using the same method. Finally, contributions of sound radiations from two split vibration modes to the overall sound radiation from the sample disc are also investigated. Based on these results, it can be concluded that the procedure suggested in this study has good accuracy in calculating the in-plane vibro-acoustic properties of a thick annular disc with a radial slot.

An adaptive control strategy based on passive piezoelectric shunt techniques applied to mistuned bladed disks

This paper mainly presents an adaptive control strategy based on passive piezoelectric shunt techniques for mistuned bladed disks. Resonant shunted piezoelectric patches are attached onto the disk between adjacent blades to reduce the blade vibration through blade–disk coupling. This piezoelectric network is of engineering interest since piezoelectric transducers are placed out of the main stream in turbomachinery. Piezoelectric damping and piezoelectric mistuning are exploited to minimize blade mistuning effects in this study. Initially an optimal piezoelectric mistuning obtained by genetic algorithm optimization is introduced into a given blade-mistuned disk to achieve a further blade vibration mitigation. In reality the blade mistuning pattern is not constant in the long run. Benefiting from the manageability and controllability of piezoelectric shunt circuits, this adaptive control strategy is to adjust the “optimal” piezoelectric mistuning pattern according to the slowly varying blade mistuning pattern. Numerical simulation reveals that a good performance is achieved with respect to reducing the vibration of time-variant mistuned bladed disks.

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.

Nonlinear interactions as trigger for chaotic vibrations in a simplified brake system

In automotive disc-brake squeal, much of the focus in the past two decades has been directed to the analysis of a brake system's vibration response in the frequency domain using the complex eigenvalue analysis (CEA) to predict the number of unstable vibration modes. Unfortunately, it is well known that not all predicted unstable vibration modes will lead to squeal and the magnitude of negative damping does not always indicate squeal propensity. In the complex eigenvalue approach, only linearised equilibrium is analysed and non-linear behaviour of the brake system is not taken into account. On the other hand, non-linear (transient) time-domain analysis simulates the dynamic behaviour closer to a real brake system, but is rarely applied as it is computationally expensive and frequency domain analyses are very popular in industry practice. In this paper, a simplified brake system in the form of an isotropic pad-on-disc system is considered. Specifically, the pad motion and a related instability are investigated using a nonlinear finite element time-domain analysis (ABAQUS 6.8-4). The complex eigenvalue method fails to detect in-plane acting pad-mode instabilities which initiate in-plane intermittent out-of-plane impulsive excitation. This excitation leads to intermittent chaotic behaviour of the pad and quasi-periodic out-of-plane disc vibration. If the pad behaves in a turbulent fashion, the disc's out-of-plane motion shows toroidal chaos. This chaotic disc vibration could be the cause of the instantaneous brake squeal described in the literature.

A Minimum Parameter Adaptive Approach for Rejecting Multiple Narrow-Band Disturbances With Application to Hard Disk Drives

Many servo systems are subjected to narrow-band disturbances that generate vibrations at multiple frequencies. One example is the track-following control in a hard disk drive (HDD) system, where the airflow-excited disk and actuator vibrations introduce strong and uncertain spectral peaks to the position error signal. Such narrow-band vibrations differ in each product and can appear at frequencies above the bandwidth of the control system. We present a feedback control scheme that adaptively enhances the servo performance at multiple unknown frequencies, while maintaining the baseline servo loop shape. A minimum parameter model of the disturbance is first introduced, followed by the construction of a novel adaptive multiple narrow-band disturbance observer for selective disturbance cancellation. Evaluation of the proposed algorithm is performed on a simulated HDD benchmark problem.

Time harmonic point load and dynamic contact problem of contacting fluid and poroelastic half-spaces

The dynamic response of contacting fluid and fluid-saturated poroelastic half- spaces to a time-harmonic vertical point force or a point pore pressure is investigated. The solutions are formulated using the boundary conditions at the fluid-porous medium interface. The point load solutions are then used to solve the dynamic problem of the vertical vibration of a rigid disc (both permeable and impermeable discs are included) on the surface of the poroelastic half-space. The contact problems are solved by integrating the point force and point pore pressure solutions over the contact area with unknown discontinuous force and pore pressure distributions, which are determined from the boundary conditions. The solutions are expressed in terms of dual integral equations, which are converted to Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the vertical dynamic compliance coefficient for the cases with or without fluid overlying the poroelastic half-space are presented to show the effects of the fluid. The influence of the permeability condition of the disc on the compliance of the poroelastic half-space is investigated. The displacement, vertical stress, pore pressure in the poroelastic half-space and water pressure in the fluid half-space are also examined for different poroelastic materials and frequencies of excitation. The present results are helpful in the study of the dynamic response of foundations on the seabed under seawater.