Multiple-relaxation-time Lattice Boltzmann Model For Squeeze Film Air Damping Of Large Knudsen Number In Mems

MEMS resonators are widely used as oscillators in oscillating circuits and resonant micro-sensors.The squeeze-film air damping is an essential factor determining its performance.However,there are many limitations in the study of squeeze-film damping with the macro-continuous media model or the micro-molecular dynamic theory model under the large Knudsen number.Based on the multiple-relaxation-time lattice Boltzmann method(MRT-LBM),this paper investigates the squeeze-film damping under large Knudsen number,verifies its accuracy in different flow regimes and different structures,and discusses the factors influencing the squeeze-film damping.First,the mechanism of squeeze-film damping is introduced.Compared with the air damping of a single vibrating plate,the gas is squeezed repeatedly in the gap when another fixed plate exists,forming the squeeze-film damping,which greatly increases the damping factor.Besides,the flow characteristics and applicable theories in different flow regime are analyzed.Secondly,four typical models of squeeze-film damping,including Reynolds equation model,modified Reynolds equation model,energy transfer model(ETM)and molecular dynamic(MD)simulation model,are introduced.Reynolds equation model and modified Reynolds equation model are based on macro-continuous fluid medium theory,while ETM model and MD simulation model are derived from molecular dynamics theory.Thirdly,the basic principle and program structure of lattice Boltzmann method are described.The MRT-LBM model used in this paper is D2Q9 model and d3q19 model.The gas wall boundary adopts the mixed boundary condition of Succi,while the open boundary adopts the convective boundary condition.The effective relaxation time and generalized second-order slip boundary conditions of Guo are used to solve the micro scale flow problem,and verified by the micro channel flow.After that,based on the experimental data,the comparative studies on the squeeze-film damping of long rectangular plate and approximate square plate are carried out,and the influences of various parameters on the squeeze-film damping is investigated.It is found that the quality factor of squeeze-film damping system increases with the increase of thickness of the plate and gap height,and decreases with the increase of the width and length of the plate.The results of MRT-LBM in slip and continuous regime,transition regime and low-vacuum free molecule regime agree well with the experimental data.The modified Reynolds equation model has larger deviation after entering in the transition regime.The ETM model and MD simulation model are only suitable for transition regime and free molecular regime,and the calculation of long rectangular plate is more accurate,while the calculation error of square-like plate is larger.Finally,this paper firstly uses the two-dimensional MRT-LBM to study the squeeze film damping of circular plates,and the results are compared with FEM analysis and modified Reynolds equation model to verify its accuracy.It is found that the results of FEM simulation and the modified Reynolds equation almost coincide,which is also very consistent with the results of MRT-LBM.At the same time,It can be seen that the quality factor of the squeeze-film damping system decreases with the increase of radius and increases with the increase of gap height,and for square-like plates and round plates with the same area,the round plates lead to larger squeeze film damping.