MEMS Squeeze-Film Damping General Energy Transfer Model

With the rapid development of MEMS,it is important to improve the MEMS design level.Squeeze-film air damping plays a significant role in the design of MEMS.Recently,it has been extensively studied for the prediction of squeeze-film air damping,and many squeeze-film damping models have been proposed.Based on these models,this paper has made some improvements and innovations.For squeeze-film damping in rarefied air,this paper has given the molecular weighted averaged traveling distance.By combing the improvement of ETM and Sumali's empirical formula,the general energy transfer model?Gen-ETM?has been proposed.By using Gen-ETM,the effect of plate size ratio on the squeeze-film air damping has been discussed,plate size ratio is defined as the ratio of plate length to plate width.The results show that,for a fixed area plate,the quality factor increases as the plate size ratio increases.Besides,the expression of Gen-ETM for circular plate has been given.For Gen-ETM,the quality factor of circular plate is 0.99 times that of the square plate with the same area.For squeeze-film damping of perforated plate in rarefied air,based on the previous energy transfer model for perforated plate?P-ETM?,this paper has given the analytical expression of the probability of gas molecules entering the gap,by studying the molecular movement in the holes.Combing the improvement of P-ETM and Sumali's empirical formula,this paper has proposed the squeeze-film damping model for perforated plate?P-Gen?.The effect of gap distance on quality factor is discussed.The results show that,as the gap distance increases,the gas squeezing effect is weakened and the squeeze-film damping decreases.The effect of gap distance on squeeze-film air damping becomes small as the hole size increases.For squeeze-film air damping in the transition regime,this paper has used the TRT-LBM for the first time.By the comparison of squeeze-film damping in the transition regime,TRT-LBM shows better accuracy than previous Reynolds'equation model and MC model.Besides,according to Veijola's effective size theory,this paper studies the application of the effective size in the transition regime.The results verify that,Veijola's effective size is valid only for Kn<0.1.a?1+bKn?h₀ form of effective size is invalid in the transition regime.For squeeze-film air damping of perforated plate,by considering the velocity of hole wall,this paper has improved the perforated-circular-plate Reynolds'equation damping model.On the other hand,by considering the edge effect on the damping of hole cell,this paper has improved the simulation radius of hole cell using Veijola's effective size.With these two improvements,the modified perforated-circular-plate Reynolds'equation damping model is proposed.Compared with FEM results,for small perforation ratio,the deviation between the modified model and the previous model is small.However,for large perforation ratio,the results of the modified model matches with FEM better than the previous model.At last,an efficient numerical damping model?MC-S?is proposed based on ETM and MC model.The experimental results show that,the MC-S model has higher computational efficiency than MC model,and has high accuracy than ETM.In addition,using MC-S model to replace MC model,the feasibility of Sumali's empirical formula for plates of various sizes has been discussed.