The effective length and width are computed by comparing the analytical results based on the Reynolds equation to the numerical results obtained by 3-D FEM. In this section, for the torsion plate, the squeeze-film thickness can be expressed as:. In fact, many micro-resonators have a simple structure and simple boundary conditions. Convergence analysis of the series for the pressures in the air gap. I have given all the conditions as is in video. On comparing the present model with the FEM results and experimental results available in the literature, the following conclusions can be drawn.
The assumption limits the operating frequency range. Transient Response Analysis Overview. Comparison of the spring constant of the type II devices obtained by the FEM model and the present model. The damping force caused by the mechanical resistance of the channel is not zero in the case of large perforation ratios. The aim of this paper is to provide an analytical model for estimating the squeeze-film damping in a perforated torsion microplate. Only the damping force acting on the lower surface of the perforated plate is considered in the second approach.
Convergence analysis of the series for the pressures in the air gap. Here, N x is the number of holes along xamping -direction and N y is the squesze of holes along y -directions. The microplate is operated in normal direction to the substrate.
Displacement and pressure results at the bottom of the top plate on the circumference of the hole are shown in Figure 1.
In the dual axis resonator, there are two types of motion, one about the inner torsional axis and the second about the outer torsional axis. Any help will be beneficial for me.
We can identify two groups in this respect. The Reynolds squeeze film approach assumes a continuous fluid flow regime. Table 3 Dimensions and parameters for the type I microplate.
Thanks a lot Peteroznewman. The damping obtained by the experimental results including the two damping can be expressed by: An analytical formula and Dampin simulations for the viscous damping of a periodic perforated MEMS microstructure outside the lubrication approximation.
A previous modal analysis indicated that the pertinent eigenfrequency was kHz. The perforation effect is model by calculating the equivalent electrical impedance for squeeze film damping, the flow resistance of the holes, end effect of the holes and the compressibility effect.
Harmonic analysis is a linear analysis. FLUID supports 4-node and 8-node options, along with degenerative triangles. The second reason for the discrepancy is the intrinsic damping of the material.
Vishesh has been awarded the Your Question Solved badge. The dimensions and parameters of the microplates used in simulations are listed in Table 3. Published online Mar The rilm of the analysis is to compute the equivalent squeeze stiffness and damping coefficient for an assumed uniform plate velocity.
Hot Topics 1 RGP table for supercritical, gas and liquid phase 2 problem with units not matching with initialized data? Accurate system-level damping model for highly perforated micromechanical devices. Recent Activity knv is a new member in the nasys. In the first approach, the fluid in air zqueeze is modeled by the Navier-Stokes equation, which is solved by using 3-D elements in FEM.
Analytical expressions for the squeeze-film damping and spring constants have been found. The effective length and width are computed by comparing the analytical results based on the Reynolds equation to the numerical results obtained by 3-D FEM. For continuum theory to be sqeueze, the Knudsen number should be less than 0.
The following squeeze film analysis topics are available: Are you on a Student license or a Research license? For the present model, we varied perforation ratios from 0.
squeeze film analysis
A static analysis is used to determine the damping effects at low frequencies. To check the validity of the present model at different values of frequency, we also compare the damping torques and the spring torques obtained by dampnig present model and the FEM model in camping range from 1 kHz to MHz.
Chapter 3: Squeeze Film Analysis
The second group [ 891011121314151617181920 ] is devoted to presenting an easy-to-use analytical model for calculating the squeeze-film damping. The pressure in the air gap is obtained using the double sine series. Current structures in torsion micro-resonators can be classified into two main types. InHomentcovschi et al. Squesze Squeeze-film damping is one of the most dominant factors that limits the performance of high-Q dampinb.
F Re is the real component of the pressure force. A static analysis is used to determine the damping effects at low frequencies.
Open in a separate window. The total damping squeeae calculated by multiplying the damping due to the single cell by the total number of cells. The torsion plate is symmetric with respect to the rotation axis.
An Analytical Model for Squeeze-Film Damping of Perforated Torsional Microplates Resonators
At low frequencies, the fluid can escape before it compresses. See Applying Body Loads for details on applying body loads. A similar analysis as the one given for the squeeze-film damping in the type Ahsys device can be given for the type II device.
Above the maximum frequency, the inertia terms cannot be neglected. Since the analysis is linear, the magnitude of the velocity can be arbitrary for computing the coefficients. I am having a research license.