PZT微驱动器磁头的动特性研究

采用摄动法对描述超薄气体润滑理论的修正雷诺方程进行处理,建立了气体润滑的静动态方程,求解得到磁头气膜的无量纲刚度系数和阻尼系数,并讨论了磁头线速度对空气膜刚度系数和阻尼系数的影响.采用的磁头模型是一种PZT微驱动器磁头,其主体部分飞高为20 nm,读写头处飞高可达5 nm.模拟结果表明,磁头末端下降15 nm后,其动态特性和稳定性明显提高;磁头线速度在8.0 m/s～11.2 m/s变化时,气膜刚度系数线性增加,阻尼系数却线性减小.     

Analytical solution of gas lubricated slider microbearing

The analytical solution of a two-dimensional, isothermal, compressible gas flow in a slider microbearing is presented. A higher order accuracy of the solution is achieved by applying the boundary condition of Kn ² order for the velocity slip on the wall, together with the momentum equation of the same order (known as the Burnett equation). The analytical solution is obtained by the perturbation analysis. The order of all terms in continuum and momentum equations and in boundary conditions is evaluated by incorporating the exact relation between the Mach, Reynolds and Knudsen numbers in the modelling procedure. Low Mach number flows in microbearing with slowly varying cross-sections are considered, and it is shown that under these conditions the Burnett equation has the same form as the Navier–Stokes equation. Obtained analytical results for pressure distribution, load capacity and velocity field are compared with numerical solutions of the Boltzmann equation and some semi-analytical results, and excellent agreement is achieved. The model presented in this paper is a useful tool for the prediction of flow conditions in the microbearings. Also, its results are the benchmark test for the verifications of various numerical procedures.     

磁头润滑面形状对气动力特性的影响

本文采用微分离散差分方法求解滑流条件下的修正Reynolds方程．对于一阶导数间断的物理量——气膜厚度采用高精度保凸性磨光法进行处理．给出了气膜压强分布立体图以及几种因加工误差造成磁头滑块润滑面变形的误差型面的飞升曲线、中心线上压强分布、压力中心和负载随加工误差大小的变化情况，指出了磁头滑块润滑面加工时宁凸勿凹的倾向性意见．     

Slip model for the ultra-thin gas-lubricated slider bearings of an electrostatic micromotor in MEMS

A new slip model derived by molecular dynamics has been used to investigate the ultra-thin gas-lubricated slider bearings beneath the three bushings of an electrostatic micromotor in micro-electro-mechanical systems (MEMS). Modified Reynolds equation is proposed based on the modified slip model. Analytical solutions for flow rate, pressure distribution, load carrying capacity and streamwise location using the modified Reynolds equation are obtained and compared with the results gained from those in the literature. It demonstrates that the new second-order slip model is of greater accuracy than that predicted by the first-order, second-order slip models and MMGL model and produces a good approximation to variable hard sphere (VHS) and variable soft sphere (VSS) models, which agree well with the solution obtained from the linearized Boltzmann equation. It is indicated that the slip effect reduces the pressure distribution and load carrying capacity, and shifts the streamwise location of the load carrying capacity, which should not be ignored to study the step-shaped slider bearings in micromotors for MEMS devices.     

Six-DOF vibrations of partial contact sliders in hard disk drives

A six-degree-of-freedom slider dynamic simulator is developed to analyze the slider’s motion in the vertical, pitch, roll, yaw, length and width directions. The modified time-dependent Reynolds equation is used to model the air bearing and a new second order slip model is used for a bounded contact air bearing pressure. The simulator considers the air bearing shear acting on the air bearing surface and the slider–disk contact and adhesion. Simulation results are analyzed for the effects of the disk surface micro-waviness and roughness, skew angle, slider–disk friction and micro-trailing pad width on the vertical bouncing, down-track and off-track vibrations of a micro-trailing pad partial contact slider.     

Effects of disk surface roughness on static flying characteristics of air bearing slider by using a combined method of Reynolds equation and rough disk surface

Reynolds equation was modified with adding the surface roughness parameters to analyze the effects of disk surface roughness on the static flying characteristic of an air bearing slider. However, the modification demands the complicated mathematical expressions and related knowledge of physics and mathematics. In this paper, a combined method of Reynolds equation without introducing the roughness parameters and rough disk surface is proposed to investigate the effects of disk surface roughness on the static flying characteristics of an air bearing slider, it is different from those models of modified Reynolds equation introducing the disk surface roughness used by many researchers. More importantly, this method avoids the complicated numerical calculation resulted from the mathematical expressions including the Peklenik parameter \(\gamma\) and roughness R_a. By using an Ω air bearing slider, we investigated the effects of disk surface roughness on the static flying characteristics of this slider, the results show that the Peklenik parameter \(\gamma\) and roughness R_a have a significant influence on the pressure distribution, the load carrying capacity and the location of the pressure centre.     

Theoretical analysis of the slip flow effect on gas-lubricated micro spherical spiral groove bearings for machinery gyroscope

The performance of a gas-lubricated micro spherical spiral groove bearing (MSSGB) with slip flow effect is investigated. A modified Reynolds equation incorporated with Barber’s first-order slip flow model is proposed to investigate the flow characteristics of gas in MSSGBs. Parameter transformation and oblique coordinate transformation are applied to eliminate the curve effect on the calculation domain. An improved finite difference method (FDM) based on Green’s formula is used to solve the Reynolds equation. The perturbation method is adopted to determine the dynamic coefficients. The effects of slip flow and bearing parameters, including the groove depths, rotor speeds, and eccentricity ratios, on the bearing characteristics are investigated and discussed. Prediction results show that the slip flow effect on MSSGB performance is significant. Moreover, the groove depth at micro clearance has a crucial influence on bearing performance.     

An improved Reynolds-equation model for gas damping of microbeam motion

An improved gas-damping model for the out-of-plane motion of a near-substrate microbeam is developed based on the Reynolds equation (RE). A boundary condition for the RE is developed that relates the pressure at the beam edge to the beam motion. The coefficients in this boundary condition are determined from Navier-Stokes slip-jump (NSSJ) simulations for small slip lengths (relative to the gap height) and from direct simulation Monte Carlo (DSMC) molecular gas dynamics simulations for larger slip lengths. This boundary condition significantly improves the accuracy of the RE when the microbeam width is only slightly greater than the gap height between the microbeam and the substrate. The improved RE model is applied to microbeams fabricated using the SUMMiT V process.     

Thermohydrodynamic analysis of micro spherical spiral groove gas bearings under slip flow and surface roughness coupling effect

The effects of gas rarefaction and surface roughness are temperature-related and always neglected in macroscale. These effects were considered in the analysis of the thermohydrodynamic performance of micro spherical spiral groove bearings. The Reynolds equation and the energy equation incorporated with Wu’s slip model and the Weierstrass–Mandelbrot function to analysis the coupling effect of slip flow and surface roughness. The effects of spherical grooves on computational accuracy were reduced through parameter transformation and oblique coordinates. To describe the temperature boundary condition at the grooved region, a simple gas-mixing model was presented for the grooves. Prediction results showed that temperature reduced bearing forces and friction torque through the slip flow effect. Surface roughness increased not only temperature significantly but also bearing forces and friction torque through a high eccentricity ratio and a low bearing clearance.

     

Lattice Boltzmann modeling of microchannel flows in the transition flow regime

Owing to its kinetic nature and distinctive computational features, the lattice Boltzmann method for simulating rarefied gas flows has attracted significant research interest in recent years. In this article, a lattice Boltzmann (LB) model is presented to study microchannel flows in the transition flow regime, which have gained much attention because of fundamental scientific issues and technological applications in various micro-electro-mechanical system (MEMS) devices. In the model, a Bosanquet-type effective viscosity is used to account for the rarefaction effect on gas viscosity. To match the introduced effective viscosity and to gain an accurate simulation, a modified second-order slip boundary condition with a new set of slip coefficients is proposed. Numerical investigations demonstrate that the results, including the velocity profile, the non-linear pressure distribution along the channel, and the mass flow rate, are in good agreement with the solution of the linearized Boltzmann equation, the direct simulation Monte Carlo (DSMC) results, and the experimental results over a broad range of Knudsen numbers. It is shown that taking the rarefaction effect on gas viscosity into consideration and employing an appropriate slip boundary condition can lead to a significant improvement in the modeling of rarefied gas flows with moderate Knudsen numbers in the transition flow regime.     

Boundary conditions for shear flow past a permeable interface modeled as an array of cylinders

The boundary condition relating the macroscopic jump in the tangential velocity across a permeable interface consisting of a particulate lattice to the shear rate prevailing on either side of the interface is discussed. The computation of the velocity jump hinges on the realization that shear flow on one side of the interface induces a slip velocity on that side and a streaming drift velocity on the other side. The direction and magnitude of the slip and drift velocities depend on the interface constitution, solid fraction, and Reynolds number. Numerical computations are performed for a model two-dimensional interface consisting of a periodic array of cylinders. In the case of longitudinal unidirectional flow, the boundary conditions are defined in terms of previously computed drift and slip velocity coefficients for any ratio of the shear rates above and below the interface and any Reynolds number. To study the behavior in the complementary case of transverse flow, the Navier-Stokes equation is solved numerically using a finite-difference method on an orthogonal grid generated by conformal mapping, using the stream function/vorticity formulation. The results reveal that inertial effects promote the magnitude of the slip and drift velocity, and illustrate the streamline pattern near the interface.     

Simplified molecular gas film lubrication equation and accommodation coefficient effects

As the spacing between the flying head/slider and the rotating disk in hard disk drives (HDDs) continues to decrease, the interaction between the molecular gas and the surfaces of the disk and the head/slider becomes significant. The influence of surface accommodation coefficient (AC) is an important factor to govern the static characteristics of the head/slider. Starting from the polynomial logarithm fitting equations of Poisueille flow rate and Couette flow rate, a new simplified molecular gas film lubrication (MGL) equation is proposed to simulate the ultra-thin air bearing film in HDDs. The new MGL equation is simpler than that of the polynomial logarithm form of MGL equation. The new approach produces very good approximations for both Poisueille flow rate and Couette flow rate with very little differences to those based on the original MGL equation. The new simplified MGL equation is solved by using a meshless method, called least square finite difference (LSFD) method. Effects of ACs on the static characteristics of air bearing films in HDDs with ultra-low flying heights are investigated. Numerical results show that effects of ACs on the static characteristics are significant for the case of symmetric molecular interaction. On the other hand, effects of ACs at the disk surface on the static characteristics are significant for the case of non-symmetric molecular interaction, while effects of ACs at the slider surface on the static characteristics are weak.     

Molecular dynamics-based prediction of boundary slip of fluids in nanochannels

Computational modeling and simulation can provide an effective predictive capability for flow properties of the confined fluids in micro/nanoscales. In this paper, considering the boundary slip at the fluid–solid interface, the motion property of fluids confined in parallel-plate nanochannels are investigated to couple the atomistic regime to continuum. The corrected second-order slip boundary condition is used to solve the Navier–Stokes equations for confined fluids. Molecular dynamics simulations for Poiseuille flows are performed to study the influences of the strength of the solid–fluid coupling, the fluid temperature, and the density of the solid wall on the velocity slip at the fluid boundary. For weak solid–fluid coupling strength, high temperature of the confined fluid and high density of the solid wall, the large velocity slip at the fluid boundary can be obviously observed. The effectiveness of the corrected second-order slip boundary condition is demonstrated by comparing the velocity profiles of Poiseuille flows from MD simulations with that from continuum.     

Dynamic response of 1-in. form factor disk drives to external shock and vibration loads

The dynamic response of the head disk interface is investigated numerically for two different designs of 1-in. hard disk drive enclosures, the so-called “thin” enclosure and the “thick” enclosure. First, the in-plane and out-of-plane vibration response is determined. Then, the effects of linear shock and head slap are studied. Simulation results show that the thinner enclosure has better performance with respect to forced vibrations in terms of reduced amplitude of slider vibrations. In addition, the effect of operational shock on the dynamic characteristics of textured and untextured sliders is studied. A finite element formulation of the time-dependent Reynolds equation (with Boltzmann slip flow correction) was used to obtain the air bearing response. The results show that the dynamic flying characteristics of textured sliders are improved compared to that of untextured sliders.     

Thermo-molecular gas-film lubrication (t-MGL) analysis for heat-assisted magnetic recording head sliders

In the present paper the static lubrication characteristics of a slider flying over a running boundary wall with arbitrary local temperature distributions are analyzed using the thermomolecular gas-film lubrication (t-MGL) equation. We obtain two approximate solutions: (a) a linearized solution when the temperature deviation is small ( \( \tau_{W} \ll 1 \) ) and arbitrarily distributed, and (b) a solution for the case with a very large bearing number \( (\varLambda \to \infty ) \) . We herein numerically calculate the static lubrication characteristics and verify the validities of these two approximate solutions. Moreover, we calculate the characteristics for various temperature distributions produced by laser heating.     

Velocity inversion of micro cylindrical Couette flow: A lattice Boltzmann study

In this work the micro gas flow between two concentric cylinders is investigated by a lattice Boltzmann equation (LBE) model with multiple relaxation times. A local kinetic boundary condition is proposed for the LBE to model the gas–wall interaction. Numerical simulations are conducted to examine the tangential velocity distribution under different flow conditions. It is shown that the proposed LBE can capture the velocity inversion phenomenon successfully. Comparisons with the Navier–Stokes solutions and DSMC results are also made and it is shown that the LBE yields better predictions.     

Nonlocal vibration and instability analysis of carbon nanotubes conveying fluid considering the influences of nanoflow and non-uniform velocity profile

In this article, the influences of non-uniform velocity profile attributable to slip boundary condition and viscosity of fluid on the dynamic instability of carbon nanotubes (CNTs) conveying fluid are investigated. The nonlocal elasticity theory and the Euler–Bernoulli beam theory are employed to derive partial differential equation of nanotubes conveying fluid. Furthermore, a dimensionless momentum correction factor (MCF) is obtained as a function of Knudsen number (Kn) so as to insert the effects of non-uniform velocity profile into the equation of motion. In continuation, complex eigen-frequencies of the system are attained with respect to different boundary conditions, the momentum correction factor, slip boundary condition and nonlocal parameter. The results delineate that considering the effects of non-uniform velocity profile could diminish predicted critical velocity of flow. Therefore, the divergence instability occurs in the lower values of flow velocity. In addition, the MCF decreases through enhancement of Kn; hence, the effects of non-uniform velocity profile are more noticeable for liquid fluid than gas fluid.     

Magnetohydrodynamic three-dimensional flow of nanofluids with slip and thermal radiation over a nonlinear stretching sheet: a numerical study

A numerical simulation for mixed convective three-dimensional slip flow of water-based nanofluids with temperature jump boundary condition is presented. The flow is caused by nonlinear stretching surface. Conservation of energy equation involves the radiation heat flux term. Applied transverse magnetic effect of variable kind is also incorporated. Suitable nonlinear similarity transformations are used to reduce the governing equations into a set of self-similar equations. The subsequent equations are solved numerically by using shooting method. The solutions for the velocity and temperature distributions are computed for several values of flow pertinent parameters. Further, the numerical values for skin-friction coefficients and Nusselt number in respect of different nanoparticles are tabulated. A comparison between our numerical and already existing results has also been made. It is found that the velocity and thermal slip boundary condition showed a significant effect on momentum and thermal boundary layer thickness at the wall. The presence of nanoparticles stabilizes the thermal boundary layer growth.

     

A multiplicative decomposition of Poiseuille number on rarefaction and roughness by lattice Boltzmann simulation

Poiseuille number of rarefied gas flow in channels with designed roughness is studied and a multiplicative decomposition of Poiseuille number on the effects of rarefaction and roughness is proposed. The numerical methodology is based on the mesoscopic lattice Boltzmann method. In order to eliminate the effect of compressibility, the incompressible lattice Boltzmann model is used and the periodic boundary is imposed on the inlet and outlet of the channel. The combined bounced condition is applied to simulate the velocity slip on the wall boundary. Numerical results reveal the two opposite effects that velocity gradient and friction factor near the wall increase as roughness effect increases; meanwhile, the increments of the rarefaction effect and velocity slip lead to a corresponding decrement of friction factor. An empirical relation of Poiseuille number which contains the two opposite effects and has a better physical meaning is proposed in the form of multiplicative decomposition, and then is validated by available experimental and numerical results.     

Examination of flying height of magnetic head slider in simulations and measurements at nanometer-order spacing

This paper describes a comparison with the experimental flying heights and the simulated flying heights, which were calculated by using the linearized Boltzmann equation and the conventional modified Reynolds equations. The experiments were measured under the ambient pressure from atmospheric pressure to 6.7 × 10^?3 MPa. The calculated results of the linearized Boltzmann equation were almost the same as the experimental results from the high spacing range to the low spacing range of 10 nm. At the slider spacing of 10 nm, it was confirmed that the difference between the experimentally measured results and the calculated results of the linearized Boltzmann equation was less than 5%, and the differences in the conventional slip flow approximation equations were over 30%.