Modelling of squeeze film between parallel rectangular plates of finite length considering inertia effects

Abstract

Squeeze film of finite length rectangular plate is widely used in MEMS devices, immersion lithography machines and other engineering fields. The damping force of squeeze film of finite length rectangular plates can be obtained by multiplying the solution of infinite length rectangular plates with a correction factor depending on the aspect ratio. Whether the correction factor is the same for the inertia force is attractive to be studied. The distributions of velocity and pressure are obtained by solving the 3D Navier-Stokes(NS) equations with free and half sealed outlets, which shows the leakage of flow in the length direction causes the drop of maximum pressure comparing with the infinite case, which is about 56.6% for square plates. The squeeze film force ratios for 3D to 2D models with different aspect ratios have been obtained under the conditions of different film thickness, viscosity and rectangular width. It is concluded that the correction factor of damping force can be used to modify the inertia force. The damping and inertia coefficients can be easily extracted from the modified analytical solution of parallel rectangular squeeze film with finite length, which can be applied to the modelling of system dynamics.