Squeeze-Film Air Damping of a Five-Axis Electrostatic Bearing for Rotary Micromotors

Abstract

Air-film damping, which dominates over other losses, plays a significant role in the dynamic response of many micro-fabricated devices with a movable mass suspended by various bearing mechanisms. Modeling the damping characteristics accurately will be greatly helpful to the bearing design, control, and test in various micromotor devices. This paper presents the simulated and experimental squeeze-film air damping results of an electrostatic bearing for use in a rotary high-speed micromotor. It is shown that the boundary condition to solve the three-dimensional Reynolds equation, which governs the squeeze-film damping in the air gap between the rotor and its surrounding stator sealed in a three-layer evacuated cavity, behaves with strong cross-axis coupling characteristics. To accurately characterize the damping effect, a set of multiphysics finite-element simulations are performed by computing both the rotor velocity and the distribution of the viscous damping force acting on the rotor. The damping characteristics varying with several key structure parameters are simulated and discussed to optimize the device structure for desirable rotor dynamics. An electrical measurement method is also proposed and applied to validate the numerical results of the damping coefficients experimentally. Given that the frequency response of the electric bearing is critically dependent on the damping coefficients at atmospheric pressure, a solution to the air-film damping measurement problem is presented by taking approximate curve fitting of multi-axis experimental frequency responses. The measured squeeze-film damping coefficients for the five-axis electric bearing agrees well with the numerical solutions. This indicates that numerical multiphysics simulation is an effective method to accurately examine the air-film damping effect for complex device geometry and arbitrary boundary condition. The accurate damping coefficients obtained by FEM simulation will greatly simplify the design of the five-axis bearing control system and facilitate the initial suspension test of the rotor for various micromotor devices.

Analysis and Compensation of Bias Drift for a Micromachined Spinning-Rotor Gyroscope with Electrostatic Suspension

“…The precession of the spinning rotor is governed by the equation: The MEMS device was fabricated using bulk microfabrication based on silicon on glass (SOG) technique, which includes several key processes, such as high-aspect-ratio dry etching, twice glass-silicon anodic bonding, aluminum sacrificial layer removal and vacuum packaging. The size of each fabricated die is 6.5 × 6.5 × 1.1 mm, as depicted in Figure 1b [27].…”

Vibration Control of an Unbalanced Single-Side Cantilevered Rotor System with a Novel Integral Squeeze Film Bearing Damper

“…A damping dissipation theoretical model diagram of the squeeze film area is shown in Figure 3. The squeeze film area of the integral squeeze film bearing damper can dampen vibration control and dissipate the energy of vibration [19,20].…”

Vortex-Induced Vibrations of an Elastic Micro-Beam with Gas Modeled by DSMC

“…On the other hand, air-film damping plays a significant role in the dynamic response of many micro-fabricated devices with a movable mass suspended by various bearing mechanisms. The problem has been considered by many authors [ 8 , 9 , 10 , 11 , 12 ]. Most studies have considered slow fluid velocity and used a continuum model based on Navier–Stokes equations.…”

“…Some authors have tried to present an easy-to-use analytical model [ 8 ], while others have used numerical methods to seek more accurate solutions. Seeking a more accurate numerical solution, Wang et al [ 9 ] and Wang et al [ 10 ] used finite element-based multiphysics simulation and the ALE DUGKS solution procedure, respectively. In the ALE-type DUGKS, the velocity of the mesh motion is introduced in the Boltzmann–BGK equation to modify the net flux of a cell interface (see [ 13 ]).…”