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.

     

Improved modified Reynolds equation for thin-film gas lubrication from an extended slip velocity boundary condition

An extended slip velocity boundary condition is derived from the regularized 13 moment equations firstly. Different from the existing slip velocity boundary condition, the slip coefficients of the extended one are not fixed, which will change with the wall accommodation coefficient and the Knudsen number of the gas flow. Using the extended slip velocity condition, an improved modified Reynolds equation for thin-film gas lubrication is established. From solving the improved modified Reynolds equation, the pressure distribution of the slider gas bearing is obtained and has a better agreement with that from the direct simulation Monte Carlo method under different pitch angles and wall velocities. It is found that the improved modified Reynolds equation can predict a more accurate pressure distribution of the slider gas bearing than the Fukui and Kaneko’s lubrication model from the linearized Boltzmann equation in the near transition regime.     

Effects of interface curvature on Poiseuille flow through microchannels and microtubes containing superhydrophobic surfaces with transverse grooves and ribs

This paper presents numerical results pertaining to the effects of interface curvature on the effective slip behavior of Poiseuille flow through microchannels and microtubes containing superhydrophobic surfaces with transverse ribs and grooves. The effects of interface curvature are systematically investigated for different normalized channel heights or tube diameters, shear-free fractions, and flow Reynolds numbers. The numerical results show that in the low Reynolds number Stokes flow regime, when the channel height or tube diameter (normalized using the groove–rib spacing) is sufficiently large, the critical interface protrusion angle at which the effective slip length becomes zero is θ _c ≈ 62°–65°, which is independent of the shear-free fraction, flow geometry (channel and tube), and flow driving mechanism. As the normalized channel height or tube diameter is reduced, for a given shear-free fraction, the critical interface protrusion angle θ _c decreases. As inertial effects become increasingly dominant corresponding to an increase in Reynolds number, the effective slip length decreases, with the tube flow exhibiting a more pronounced reduction than the channel flow. In addition, for the same corresponding values of shear-free fraction, normalized groove–rib spacing, and interface protrusion angle, longitudinal grooves are found to be consistently superior to transverse grooves in terms of effective slip performance.     

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.     

Investigations on characteristics of micro/meso scale gas foil journal bearings for 100–200 W class micro power systems using first order slip velocity boundary conditions and the effective viscosity model

In this paper, a modified compressible Reynolds equation for micro/meso scale gas foil journal bearings considering first order slip and effective viscosity under rarefied flow conditions is presented. The influence of rarefaction effect on the load carrying capacity, attitude angle, speed and frequency dependent stiffness and damping coefficients, modal impedance, natural frequencies and unbalance response is studied. From numerical analysis, it has been found that there is significant change in all the static and dynamic characteristics predicted by the no-slip model and model with effective viscosity. There is also a considerable difference between the values predicted by a model with effective viscosity and a model without effective viscosity. For a given eccentricity ratio, the influence of effective viscosity on load carrying capacity and attitude angle is more significant for the typical operating speed range of micro/meso scale gas turbines. The influence of effective viscosity decreases with increase in compliance of bearing structure. Similarly, the influence of effective viscosity on frequency dependent stiffness and damping coefficients increases with excitation frequency ratio. Significant change in natural frequency, modal impedance and unbalance response for model with no slip and slip with effective viscosity is observed. The influence of effective viscosity is found to be significant with increase in Knudsen number.     

Air bearing dynamic stability on bit patterned media disks

Bit Patterned media (BPM) recording is one of the potential technologies to be used in future disk drives in order to increase the areal density to 5 Tbit/in². But one of the main obstacles for BPM is to achieve dynamic stability of the air bearing slider at the head-disk interface (HDI). In this paper we first use a direct simulation method to check the accuracy of our previously developed Homogenization Reynolds equation solution. After confirming the accuracy it is then implemented to study the slider’s flying attitude on BPM disks. Then we investigate the system’s parameters using a system identification method by simultaneously solving the equations of motion of the slider and the Homogenization Reynolds equation. We observe that the first pitch mode frequency of the air bearing increases with increase of pattern groove area ratio and pattern height. And the stiffness decreases when the pattern groove area ratio or pattern height increases. We conclude that a partially planarized BPM is preferred in order to maintain the dynamic stability of the HDI.     

Double-disk rotating viscous micro-pump with slip flow

In this paper numerical solution was provided for the 2D, axisymmetric Navier-Stokes equations coupled with energy equation for gaseous slip flow between two micro rotating disks pump. A first-order slip boundary condition was applied to all internal solid walls. The objective is to study the effect of Knudsen number, rotational Reynolds number and gap height on pump head, flow rate, coefficient of moments and overall micro-pump efficiency. Pump head, flow rate, coefficient of moments and pump efficiency were calculated for various pump operating conditions when the mass flow rate is applied at the pump inlet port. Detailed investigations were performed for rotational Reynolds number equals to 10. Effect of gap height between the two disks was studied. Effect of rotational Reynolds number on maximum flow rate and maximum pressure rise was simulated. The present numerical results for no-slip were compared with previously published experimental and theoretical data and found to be in a very good agreement. Knudsen number Kn values were found to be major parameters that affect the performance of pump. Pump performance decreases with increasing Kn. Optimal pump performance occurs around middle point of pump operating range. Pump operating range decreases with increasing Kn numbers. Pump performance is found to experience a steep degradation for Kn approaching 0.1. Maximum flow rate increases with rotational speed almost linearly. Maximum pressure rise also increases with rotational speed. Reducing gap height results in increasing maximum pressure rise, while increasing gap height results in larger maximum flow rate.     

Dynamic characteristics of a coupled journal and thrust hydrodynamic bearing in a HDD spindle system due to its groove location

 This research numerically analyzes the dynamic characteristics of a coupled journal and thrust hydrodynamic bearing due to its groove location which has the static load due to the weight of a rotor in the axial direction and the dynamic load due to its mass unbalance in the radial direction. The Reynolds equation is transformed to solve a plain member rotating type of journal bearing (PMRJ), a grooved member rotating type of journal bearing (GMRJ), a plain member rotating type of thrust bearing (PMRT), and a grooved member rotating type of thrust bearing (GMRT). FEM is used to solve the Reynolds equations in order to calculate the pressure distribution in a fluid film. Reaction forces and friction torque are obtained by integrating the pressure and shear stress along the fluid film, respectively. Dynamic behaviors, such as whirl radius or axial displacement of a rotor, are determined by solving its nonlinear equations of motion with the Runge–Kutta method. This research shows that the groove location affects the pressure distribution in the fluid film and consequently the dynamic performance of a HDD spindle system. Received: 5 July 2001/Accepted: 17 October 2001     

Numerical simulation of slider air bearings based on a mesh-free method for HDD applications

This paper focuses on the development of a computational method to be used as a tool for air bearing simulation and design in modern hard disk drive. A data density of 100 Gb/in.² has already been achieved in today’s production. The hard disk drive industry’s next goal is to increase the data density to 1 Tb/in.² . New features in air bearing designs include shaped rails, multiple etching depths and negative pressure pockets. Thus, mesh generation is a difficult task in the air bearing simulation. This, in turn, demands the development of an accurate and easy-to-use computational method to solve Reynolds equations based on various flow models. Least square finite difference scheme, one of mesh-less methods, is presented to solve the slider air bearing problems of hard disk drives. For each specified attitude, the air bearing pressure is obtained by solving the Reynolds equation using the mesh-free method. The discretized nonlinear systems of equations are solved by successive over-relaxation (SOR) implementation, and the results of the numerical solutions are compared with other numerical and experimental data.     

Friction and wear of spindle motor hydrodynamic bearings for information storage systems during startup and shutdown

This paper investigates the friction and wear characteristics of two typical hydrodynamic bearings for hard disk drive (HDD) spindle motors (SPM), i.e., the herringbone groove and multi-taper bearings, during start-up and shut-down transient operation. The friction characteristics are calculated by a lubricated friction model which is an extension of Kogut and Etsion’s dry friction model (a modified version of the CEB model), while the wear characteristics are qualitatively evaluated in non-dimensional form by the semi-analytical wear model proposed by Holm–Archard. The average flow Reynolds equation and the pressure-compliance relationship of elastic–plastic roughness contact are used together to consider the combined effects of partial lubrication and asperity contact occurring during start-up and shut-down. Then, the friction and wear characteristics of the herringbone groove and multi-taper bearings are calculated and compared under the condition of HDD application.     

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.     

Scale effect on filling stage in micro-injection molding for thin slit cavities

Micro-injection molding is the main method molding complex micro plastic parts accurately at one process. It is more complex than traditional injection molding because of the micro-scale effect. The polymeric flow in micro channels differs from those in macro ones significantly, and the molding theories of traditional injection molding can not be used in micro-injection molding. In this study, the effects of micro-scale, such as micro-viscosity and wall slip, were considered based on the flow characteristics of micro-injection molding, and the mathematical model and the numerical model were built. The simulation of filling stage in micro-injection molding was implemented by hybrid finite element/finite difference/control volume method accordingly. The influence of micro-viscosity and wall slip on filling stage was investigated by numerical analysis. The results indicated that the micro-scale effects have important influence on the filling stage of micro-injection molding, and the micro-scale effects become more and more significant as the gap thickness drops.     

Behavior of fluid lubricant and air–oil interface of operating FDBs due to operating condition and seal design

This paper investigated the behavior of fluid lubricant and air–oil interface of operating fluid dynamic bearings (FDBs) by using two-phase flow analysis of air and oil to describe the oil sealing mechanism of operating FDBs. The two-phase flow of fluid lubricant and air was analyzed by using the Navier–Stokes equation and the volume of fluid method of a multi-phase flow. The proposed numerical method was verified by the numerical result of the Reynolds equation and the experimental result of the prior researcher. This research also discussed the effect on the oil leakage of the operating FDBs due to the existence of inward pumping groove, tapering angle and initial position of fluid.     

The holy grail of microfluidics: sub-laminar drag by layout of periodically embedded microgrooves

The sub-laminar drag effect of microgroove surfaces was studied numerically in a steady two-dimensional channel flow at subcritical Reynolds numbers. Considerations are restricted to grooves of a few viscous length scales in depth, which are assumed not to promote the laminar to turbulent transition process. It was found that the drag reduction effect is due to the layout of grooves with respect to the flow direction and contour geometry. Results of computations show that for grooves of curved contour placed normal to the flow direction, drag arising from viscous and pressure forces is modulated due to the functional dependence of forces on the surface area projected in the flow direction. Such a groove layout leads to a large skin-friction reduction, but a comparable increase in pressure drag results in sub-laminar drag if drag over flat surface is considered as a reference. For a curved groove contour, the drag reduction increases with increasing Reynolds number and reaches about 5 % at Reynolds numbers approaching critical.     

Computations of gas microflows using pressure correction method with Langmuir slip model

A Langmuir slip model combined with continuum-based compressible Navier-Stokes equations is proposed and implemented for the purpose of analyzing complex microscale gas flows. For our model, an efficient compressible pressure correction algorithm based on an unstructured grid is developed and modified to be applicable to low Reynolds number slip flows in microgeometries. Gaseous slip flows in a uniform microchannel and compressible flow at backward-facing step are computed for the assessment of the adequacy of the method. Separated flow in a T-shaped micro-manifold is also simulated for the Reynolds number ranging from 10 to 60. In the uniform microchannel flow, the pressure increases nonlinearly in Langmuir slip model as the Knudsen number increases, while it drops nonlinearly in Maxwell slip model. The results from Langmuir slip model have been found to be more compatible with physics. From all the simulation cases, nonlinear behavior owing to both compressibility and rarefaction clearly appears in terms of streamwise velocity, pressure profiles and even reattachment length in the separation-associated flows. These results show that the suggested pressure correction method along with the Langmuir slip model may effectively simulate complex microscale gas flows, thereby offering a sound theoretical and numerical basis and an inexpensive computation procedure.     

带有均压槽的气体静压推力轴承设计

针对空间机器人地面微重力模拟实验中存在侧向干扰力/力矩,工作台面不平整等特殊情况,设计了具有周向和径向均压槽的高承载力、高刚度圆盘气体静压推力轴承,并采用变形雷诺方程对轴承的承载特性进行了建模和数值分析.为了验证理论计算结果的正确性,使用Fluent对轴承的承载力特性进行仿真分析,并且分析了高压气体产生的冲击力对承载性能的影响.最后,在标准测试平台上对该轴承的承载力特性进行了实验,并与不带有均压槽的轴承进行对比分析,证明了结构设计和理论分析的正确性.     

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.     

Studies on a micro turbine device with both journal- and thrust-air bearings

This paper presents design, fabrication, analysis and test of a silicon-based micro turbine device that is driven by compressed air. To improve the motion stability at high rotational speed, the turbine device employs an enhanced micro air bearing system that includes both journal air bearing and thrust air bearings. The double-sides dynamic thrust air bearings are designed to support the rotor from both its top and bottom sides. The top thrust air bearing employs pump-in spiral groove configuration, and the bottom bearing uses pump-out spiral groove configuration. The dynamic journal air bearing is formed by a plain circular trench with a short journal length (L) and a narrow radial clearance (C). The critical aspect ratio (L/C) over 20:1 is realized through an optimized fabrication process. The micro turbine device has been fabricated, integrated and tested. During the test, the turbine device demonstrated stable operations at a rotational speed of 14,700 rpm.     

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.     

Dynamic characteristics of micro air bearings for microsystems

This paper reports on the dynamic characteristics of micro air bearings that include thrust and journal air bearings for microsystems. The dynamic thrust air bearing employs a spiral groove configuration. Analysis shows that the motion stability and load capacity of a thrust air bearing imposes a contradictive requirement on the groove pattern of the air bearing. The dynamic journal air bearing is realized by using a plain circular trench with a narrow radial clearance of C, and a very small aspect ratio of bearing length versus diameter (L/D). Analysis on the shock tolerance of the journal air bearing shows that the shock tolerance increases with the bearing number, the bearing aspect ratio of L/D and its initial equilibrium eccentricity ratio ε ₀. The optimum values of the bearing parameters are explored and recommended. A prototype of turbine device has been designed based on the recommended bearing configurations and realized via microfabrication.