A MEMS Reynolds Equation Squeeze Film Damping Model With Border Effect

Micro-resonators are widely used nowadays,so their sensitivity is required to be higher.However,due to the scale effect,the gas damping produced in the working process has a great influence on the sensitivity of the device,in which squeeze film damping is a common kind of gas damping.Therefore,establishing a squeeze film damping model with higher accuracy has become a research focus.Through the research and development of the past 20 years,now there are many squeeze film damping models.However,after study,it is found that these models are basically derived from the boundary conditions of constant pressure around the plate,the accuracy is low.In order to solve this problem,it is necessary to fully consider the border effect of squeeze film damping,establish the modified model,and verify the accuracy of the modified model by using finite element method.The research object of non-perforated plate is the squeeze structure of circular plate.Based on the existing non-perforated plate squeeze film damping model,a modified model was established by using the effective length theory,and the model was verified by changing the radius and gap height of the circular plate structure.By comparing the unmodified model,the modified model and the simulation model,it is found that the border effect has a greater influence on the squeeze film damping when the gap height is larger and the plate size is smaller,and the accuracy of the modified model is about 5%higher than that of the unmodified model.Perforated plates are studied in two steps.First,take the ring structure as the research object,the effective length theory is also used to modify the original model,by changing the perforation ratio and the gap height compared three kinds of model results to verify the accuracy of the modified model,found that the accuracy of modified model remain below 3%,and draw the conclusion:when the perforation ratio and gap height are larger,the effect of border effect on the film damping increases.Then,on the basis of the research of the ring structure,the general form of the rectangular perforated plate is studied.From the perspective of small hole elements,establish and modify a constant-pressure boundary theoretical model that are easy to calculate and the influence of perforation ratio and gap height on border effect is analyzed.It is found that the border effect of rectangular perforated plate will cause large error even in the case of small perforation ratio and small clearance height,and compared with the non-perforated plate,the border effect of the perforated plate is significantly enhanced,and the accuracy of the modified model is higher.Then the modified model is compared with the Bao model,and the accuracy of the modified model is about 20%higher than that of the Bao model when the extrusion characteristic is strong.When the extrusion characteristic is weak,the accuracy is still higher than that of Bao model when calculating the large perforation ratio.Finally,the feasibility of the modified model is verified from the perspective of pressure and analyze the problems that need to be paid attention to when using this model.