Numerical Simulation Of Slide Film And Aqueeze Film Damping MRT-LBM Method For Micto-mechanical Resonance Devices

As the common basic component in MEMS,the micro-mechanical resonator is often close to micron or micro-nanoscale.Due to the influences of micro-scale effect,the gas damping plays an essential role in the properties of micro-mechanical resonators.Therefore,in the initial stage of the design,how to accurately simulate the gas damping effect of the device has become a research focus.In this paper,we analyze the previous gas damping models of the slide film and squeeze film,and find that for the damping problem of the slide film and squeeze film of MEMS resonators in the transition region,the Reynolds equation models based on the continuous medium are not suitable because of the gas rarefied effects.The modified models are mostly empirical model and lack theoretical basis.Molecular dynamics methods,such as the direct Monte Carlo method(DSMC),can effectively deal with damping problems of the rarefied gas,but they usually have a large amount of computation and some statistical noise.On this basis,this paper first proposes a more efficient and accurate multi-relaxation time lattice Boltzman model(MRT-LBM)to simulate the gas damping effect of MEMS resonators in the transition region.Through the Knudsen boundary layer model,the effects of wall and rarefaction are considered in the correction of relaxation time.Then the key parameters and boundary conditions of the two kinds of gas damping problems in MRT-LBM model are determined,and the corresponding simulation programs are written by the MATLB.The convergence of programs has been verified according to the lattice characteristics of the LBM method.In the slide film damping problems,the results of gas velocity distributions are compared among the MRT-LBM,DSMC and HLBM,and the coincidence degree of velocity distribution curve is compared with the different rebound combination coefficients between the MRT-LBM and HLBM.The validity of the slide film damping modified MRT-LBM is verified in the transition region,and the influences of the Knudsen number,Stokes number and inter-plate gap on the slide film damping are analyzed.In the squeeze film damping problems,two types of rectangular plate structures are researched through the modified MRT-LBM.The results of the quality factor are compared among the MRT-LBM,the modified Renault equation model of Veijola,the molecular dynamics model of Hutcherson and the experimental data,and the ability of MRT-LBM to deal with the plate squeeze film damping is verified.The results show that in the transition region,the MRT-LBM is more consistent with the experimental data,and the effects of the different states of the gas and plate structures on the damping are discussed.Finally,it is concluded that the MRT-LBM proposed in this paper has high validity and accuracy for the slide film and squeeze film damping in the transition region.