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Performance analysis of high-speed spindle aerostatic bearings

Aerostatic bearings design and analysis with the application to precision engineering: State-of-the-art and future perspectives

Recent success of microelectromechanical systems (MEMS) in projection displays have raised similar expectation for an efficient, low power, affordable, full-page and pneumatic tactile display. Such design has not been achieved by the conventional technology but could bring significant improvement to current refreshable Braille displays. This paper demonstrates a novel bulk-micromachined electrostatic microvalve suitable for a pneumatic tactile display. The microvalve, a silicon perforated diaphragm juxtaposed to a silicon inlet orifice, requires relatively low closing voltage against a large supply differential pressure and flow rate, i.e., 72.9 V-rms for 19.3 kPa and 85 mi/min. Such an attractive characteristic is due to its unique curved-compliant structure that has, unlike other electrostatic microvalves, no tolerance for any initial air gap between its electrodes. As a design tool, a mechanical model of the microvalve is introduced based on the lubrication theory and large plate deflection theory. The model is established on a steady-state coupled field problem of fluid-solid mechanics. Reynolds and von-Karman equations were simultaneously solved for the microvalve geometry by finite difference approximation and double Fourier series expansion. The results of the model and experiments are compared and found to be in good agreement with a relative error less than 10%.

A novel bulk micromachined electrostatic microvalve with a curved-compliant structure applicable for a pneumatic tactile display

A novel bulk-micromachined electrostatic microvalve with a curved-compliant structure applicable for a pneumatic tactile display

A Finite Element model for the noncontacting gas face seal is developed based on the modified Reynolds Equation developed by Fukui and Kaneko (4), (5) that considers the slip flow effects. Numerical studies of a representative spiral groove seal at the slow speed (≤, 500 rpm) and the low pressure (≤ .303 MPa) conditions showed that slip flow can significantly affect the seal performances such as the lift-off speed, leakage rate, load carrying capacities. Without the consideration of the slip flow effect, the lift-off speed and the corresponding leakage rate would be greatly underestimated, especially at near ambient pressure condition. By examining the F-h characteristic curves, it was found that under the parameters presented in the present study the slip flow could be significant for Knudsen number, Kn as small as .05, and the slip flow in effect reduces the viscous pumping resulting in a loss of load carrying capacities. Presented at the 55th Annual Meeting Nashville, Tennessee May 7–11, 2000

Finite Element Analysis of the Spiral Groove Gas Face Seal at the Slow Speed and the Low Pressure Conditions — Slip Flow Consideration

A comparative study is made of various finite difference and finite element solutions of the Reynolds equation for the steady, isoviscous, incompressible hydrodynamic lubrication problem. Numerical solutions are obtained for both one- and two-dimensional slider bearings, and the predicted load capacity is evaluated against that of the corresponding exact analytical solution. Two finite difference schemes of nominal second-and fourth-order accuracy are employed. Linear, quadratic, and cubic elements are used in the finite element solutions. The different solution methods are evaluated in terms of accuracy, computational complexities and cost. Presented at the 40th Annual Meeting in Las Vegas, Nevada May 6–9, 1985

An Evaluation of Finite Difference and Finite Element Methods for the Solution of the Reynolds Equation

A finite element procedure is presented for the solution of fluid film lubrication problem that allows for a temperature dependent viscosity. The major concern is with the solution of the three dimensional fluid film and pad energy equations. A major advantage of the method developed here over previous finite element schemes is that the system of equations for the temperature field may be solved by iterative methods. This is because the discrete equations are formulated using either the parabolic form of the energy equation along with appropriate backwards differencing, or using upwinding with the elliptic form of the energy equation. The method is powerful in that it can treat bearing film with reverse flow. A convenience of the method is that the film and pad are treated as a single continuum and their temperature fields solved for simultaneously. Presented at the 42nd Annual Meeting in Anaheim, California May 11–14, 1987

L. R. Gero

Papers

An Evaluation of Finite Difference and Finite Element Methods for the Solution of the Reynolds Equation

A Three Dimensional Thermohydrodynamic Finite Element Scheme for Fluid Film Bearings