Fluid-structural damping effects dramatically slow and modify the structural response of MEMS device to their electrical actuation signals. For this reason many devices operate at a reduced pressure or in a high vacuum environment. At atmospheric pressure the fluid damping forces scale to be about 1000 larger the actuation force required in a vacuum! That's why electrostatic actuation is not commonly seen in macroscopic devices. Even at reduced pressures the damping effects need to be characterized in order to design the electronic drive algorithms that apply/measure the actuation forces. When a device moves relatively slowly, the fluid has enough time move out of the way, however at higher velocity the fluid doesn't have enough time to move and is simply compressed. The fluid damping changes drastically when the transition from compressible to incompressible flow occurs.
ANSYS Multiphysics can be used to compute squeeze film damping and fluid stiffness effects using either a Reynold squeeze film approximation or a Fluid Structural Interaction approach. Both are discussed in the following sections. The FSI approach is more complex, whereas the Reynolds squueze film is easier to implement and reasonably accurate and will suffice for most users.
2-D fluid damping elements are used to solve the Reynolds squeeze film equation on the face of the structure, plus oneleent type is aivalve ot simluated fluid flow throuh holes in the structure. Using a harmonic analysis the complex (real & imaginary) pressure distribution can be used to compute the frequency dependent damping and squeeze stiffness coefficients.
Applicable to: Rigid structures moving normal to a fixed wall (substrate or electrode). This approach is valid for small deflections of the structure. For large deflections, this method will break down because the assumption of rigid movement is invalid.
Pressure distribution over a flat plate at low-frequency (left image) and high-frequency (right image). At high frequency the fluid cannot escape from the region below the plate as easily and exerts a higher pressure more uniformly over the plate.
This approach was originally available to the ANSYS user as a heat transfer analogy where 2-D thermal elements are used to solve the Reynolds squeeze film equation on the face of the structure, by making use of appropriate substitution of material properties such as thermal conductivity, specific heat capacity and density. Using this approach the temperature DOF is analogous to Pressure. The approach was subsequently factored into the damping elements FLUID136, 138 & 139. Follow this link for the original technical paper covering the application of the heat transfer analogy approach.
Requires a user to set up a full fluid structural (FSI) analysis, impose a harmonic motion onto the structure, and compute the phase lag of the structures response. The phase lag is directly related to the fluid damping and stiffness coefficients, which are factored out of the devices equation of motion.
Applicable to: Rigid and flexible body systems, small and large deflections. Also handles mild fluid compressibility effects, important at higher frequencies. Also used when Reynolds equation breaks down.
Once the damping parameters (resistance and damping terms) have been computed they can be assigned to a reduced order macro model damper and spring element. These elements can be used in conjunction with the other ANSYS reduced order elements to efficiently simulate more complex MEMS systems, as shown below which is a reduced order model of a lateral comb drive, capturing electrostatic, fluid and structural physics in one simulation.
