Reduced Order Modeling of the Squeeze Film Damping in MEMS

2006 ◽  
Author(s):  
Aurelio Soma` ◽  
Guido Spinola ◽  
Alberto Ballestra ◽  
Alessandro Pennetta
Keyword(s):  
Finite Element ◽  
Coupled Model ◽  
Reduced Order Modeling ◽  
Squeeze Film ◽  
Design Parameters ◽  
Reduced Order ◽  
Equivalent Damping ◽  
Squeeze Film Damping ◽  
Numerical Finite Element ◽  
Micro Systems

In this work the effect of the Squeeze Film Damping on MEMS structures is studied. When a device is being designed, it is very important to preview with good approximation its dynamic behavior. However, as the simulation of the micro-systems involves different physical domains, the analysis with numerical methods can turn out remarkably onerous. Moreover the Reduced Order Modeling is preferable when, due to technological reasons, the membrane is built with several holes and the geometrical FEM coupled model will be computational heavy. Therefore Reduced Order Models allow to integrate in a total mathematical model the main parameters, obtained by the numerical analysis, considering the behavior of the structure analyzed in different physical domains. In the present work the non-linear coefficients of equivalent damping and stiffness by finite element models are investigated to be exported in a reduced order model. By means of numerical finite element calculation is studied the sensitivity analysis related to design parameters such as dimension of the plate and the presence, or lack, of holes.

Deep Hole Honing Based on Squeeze Film Damping Technology

2009 ◽  
Vol 76-78 ◽  
pp. 252-257
Author(s):  
Tian Biao Yu ◽  
Ya Dong Gong ◽  
Wan Shan Wang
Keyword(s):  
Differential Equation ◽  
Experimental Result ◽  
Squeeze Film ◽  
Design Parameters ◽  
Improve Quality ◽  
Deep Hole ◽  
Squeeze Film Damper ◽  
Squeeze Film Damping ◽  
Hole Machining

In order to improve quality of deep hole machining, a new method of deep hole honing based on squeeze film damping technology is put forward. For analysis effect on damper parameters on honing quality, motion differential equation of honing spindle with a squeeze film damper (SFD) is established according to D' Alembert principle and according simulations are studied. Spindle of deep hole honing with a SFD is designed based on the result of simulations and experiments are carried on. Experimental result shows that SFD with reasonable design parameters has excellent damping function to honing spindle, and it can make the vibration of honing spindle reduced 20%～30% and the quality of deep hole machining improved 10%～20%.

Characterization of the Dynamical Response of a Micromachined G-Sensor to Mechanical Shock Loading

2007 ◽  
Author(s):  
Daniel E. Jordy ◽  
Mohammad I. Younis
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Squeeze Film ◽  
Dynamical Response ◽  
Mems Devices ◽  
Damping Coefficients ◽  
Squeeze Film Damping ◽  
Out Of Plane ◽  
Gap Width

Squeeze film damping has a significant effect on the dynamic response of MEMS devices that employ perforated microstructures with large planar areas and small gap widths separating them from the substrate. Perforations can alter the effect of squeeze film damping by allowing the gas underneath the device to easily escape, thereby lowering the damping. By decreasing the size of the holes, the damping increases and the squeeze film damping effect increases. This can be used to minimize the out-of-plane motion of the microstructures toward the substrate, thereby minimizing the possibility of contact and stiction. This paper aims to explore the use of the squeeze-film damping phenomenon as a way to mitigate shock and minimize the possibility of stiction and failure in this class of MEMS devices. As a case study, we consider a G-sensor, which is a sort of a threshold accelerometer, employed in an arming and fusing chip. We study the effect of changing the size of the perforation holes and the gap width separating the microstructure from the substrate. We use a multi-physics finite-element model built using the software ANSYS. First, a modal analysis is conducted to calculate the out-of-plane natural frequency of the G-sensor. Then, a squeeze-film damping finite-element model, for both the air underneath the structure and the flow of the air through the perforations, is developed and utilized to estimate the damping coefficients for several hole sizes. Results are shown for various models of squeeze-film damping assuming no holes, large holes, and assuming a finite pressure drop across the holes, which is the most accurate way of modeling. The extracted damping coefficients are then used in a transient structural-shock analysis. Finally, the transient shock analysis is used to determine the shock loads that induce contacts between the G-sensor and the underlying substrate. It is found that the threshold of shock to contact the substrate has increased significantly when decreasing the holes size or the gap width, which is very promising to help mitigate stiction in this class of devices, thereby improving their reliability.

A Component-Based Parametric Reduced-Order Modeling Technique and Its Application to Probabilistic Vibration Analysis and Design Optimization

2006 ◽  
Author(s):  
Keychun Park ◽  
Geng Zhang ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Design Optimization ◽  
Probabilistic Analysis ◽  
Structural Design ◽  
Vibration Analysis ◽  
Reduced Order Modeling ◽  
Design Parameters ◽  
Model Parameters ◽  
Reduced Order ◽  
Analysis And Design ◽  
Structural Design Optimization

In this paper, a component-based parametric reduced-order modeling (PROM) technique for vibration analysis of complex structures is presented, and applications to both structural design optimization and uncertainty analysis are shown. In structural design optimization, design parameters are allowed to vary in the feasible design space. In probabilistic analysis, selected model parameters are assumed to have predefined probability distributions. For both cases, each realization corresponding to a specific set of parameter values could be evaluated accurately based on the exact modes for the system with those parametric values. However, as the number of realizations increases, this approach becomes prohibitively expensive, especially for largescale finite element models. Recently, a PROM method that employs a fixed projection basis was introduced to avoid the eigenanalysis for each variation while retaining good accuracy. The fixed basis is comprised of a combination of selected mode sets of the full model calculated at only a few sampling points in the parameter space. However, the preparation for the basis may still be cumbersome, and the simulation cost and the model size increase rapidly as the number of parameters increases. In this work, a component-based approach is taken to improve the efficiency and effectiveness of the PROM technique. In particular, a component mode synthesis method is employed so that the parameter changes are captured at the substructure level and the analysis procedure is accelerated. Numerical results are presented for two example problems, a design optimization of a pickup truck and a probabilistic analysis of a simple L-shaped plate. It is shown that the new component-based approach significantly improves the efficiency of the PROM technique.

The Effect of Squeeze-Film Damping on Suppressing the Shock Response of MEMS

2009 ◽  
Author(s):  
Hadi Yagubizade ◽  
Mohammad I. Younis ◽  
Ghader Rezazadeh
Keyword(s):  
Reynolds Equation ◽  
Element Model ◽  
Squeeze Film ◽  
Beam Equation ◽  
Mechanical Shock ◽  
Shock Loads ◽  
Reduced Order ◽  
Squeeze Film Damping ◽  
Nonlinear Finite Element Model ◽  
Euler Bernoulli Beam

This paper presents an investigation into the response of a clamped-clamped microbeam to mechanical shock under the effect of squeeze-film damping (SQFD). In this work, we solve simultaneously the nonlinear Reynolds equation, to model squeeze-film damping, coupled with a nonlinear Euler-Bernoulli beam equation. A Galerkin-based reduced-order model and a finite-deference method (FDM) are utilized for the solid domain and for the fluid domain, respectively. Several results showing the effect of gas pressure on the response of the microbeams are shown. Comparison with the results of a multi-physics nonlinear finite-element model is presented. The results indicate that squeeze-film damping has more significant effect on the response of microstructures in the dynamic shock loads compared to the quasi-static shock loads.

scholarly journals Natural Frequncies of Coupled Blade-Bending and Shaft-Torsional Vibrations

2007 ◽  
Vol 14 (1) ◽  
pp. 65-80 ◽  
Author(s):  
B.O. Al-Bedoor
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Coupled Model ◽  
Small Deformation ◽  
Torsional Vibrations ◽  
Reduced Order ◽  
Rotating Speed ◽  
Coupled Equations ◽  
Stiffening Effect

In this study, the coupled shaft-torsional and blade-bending natural frequencies are investigated using a reduced order mathematical model. The system-coupled model is developed using the Lagrangian approach in conjunction with the assumed modes method to discretize the blade bending deflection. The model accounts for the blade stagger (setting) angle, the system rotating speed and its induced stiffening effect. The coupled equations of motion are linearized based on the small deformation theory for the blade bending and shaft torsional deformation to enable calculation of the system natural frequencies for various combinations of system parameters. The obtained coupled eignvalue system is ready for use as a reference for comparison for larger size finite element simulations and for the use as a fast check on natural frequencies for the coupled blade bending and shaft torsional vibrations in the design and diagnostics processes. Some results on the predicted natural frequencies are graphically presented and discussed pertinent to the coupling controlling factors and their effects. In addition, the predicted coupled natural frequencies are validated using the Finite Element Commercial Package (Pro-Mechanica) where good agreements are found.

Dynamics of Multilayer Microplates Considering Nonlinear Squeeze Film Damping

2006 ◽  
Author(s):  
M. T. Ahmadian ◽  
M. Moghimi Zand ◽  
H. Borhan
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Reynolds Equation ◽  
Finite Difference Methods ◽  
Shear Deformation Theory ◽  
Single Layer ◽  
Squeeze Film ◽  
First Order ◽  
Squeeze Film Damping ◽  
Good Agreement

This paper presents a model to analyze pull-in phenomenon and dynamics of multi layer microplates using coupled finite element and finite difference methods. First-order shear deformation theory is used to model dynamical system using finite element method, while Finite difference method is applied to solve the nonlinear Reynolds equation of squeeze film damping. Using this model, Pull-in analysis of single layer and multi layer microplates are studied. The results of pull-in analysis are in good agreement with literature. Validating our model by pull-in results, an algorithm is presented to study dynamics of microplates. These simulations have many applications in designing multi layer microplates.

scholarly journals Industrial Digital Twins based on the non-linear LATIN-PGD

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Philippe Barabinot ◽  
Ronan Scanff ◽  
Pierre Ladevèze ◽  
David Néron ◽  
Bruno Cauville
Keyword(s):  
Finite Element ◽  
High Performance ◽  
Reduced Order Modeling ◽  
Computational Time ◽  
Reduced Order ◽  
Finite Element Software ◽  
Digital Twins ◽  
Non Linear ◽  
Industrial Level ◽  
Early Design Phase

AbstractDigital Twins, which tend to intervene over the entire life cycle of products from early design phase to predictive maintenance through optimization processes, are increasingly emerging as an essential component in the future of industries. To reduce the computational time reduced-order modeling (ROM) methods can be useful. However, the spread of ROM methods at an industrial level is currently hampered by the difficulty of introducing them into commercial finite element software, due to the strong intrusiveness of the associated algorithms, preventing from getting robust and reliable tools all integrated in a certified product. This work tries to circumvent this issue by introducing a weakly-invasive reformulation of the LATIN-PGD method which is intended to be directly embedded into Simcenter Samcef$$^{\hbox {TM}}$$ TM finite element software. The originality of this approach lies in the remarkably general way of doing, allowing PGD method to deal with not only a particular application but with all facilities already included in such softwares—any non-linearities, any element types, any boundary conditions...—and thus providing a new high-performance all-inclusive non-linear solver.

scholarly journals Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part II: Application

2000 ◽  
Vol 123 (1) ◽  
pp. 100-108 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Theoretical Models ◽  
Companion Paper ◽  
Reduced Order Modeling ◽  
Bladed Disks ◽  
Reduced Order ◽  
Component Interface ◽  
Forced Responses

In this paper, the component-mode-based methods formulated in the companion paper (Part I: Theoretical Models) are applied to the dynamic analysis of two example finite element models of bladed disks. Free and forced responses for both tuned and mistuned rotors are considered. Comprehensive comparisons are made among the techniques using full system finite element solutions as a benchmark. The accurate capture of eigenfrequency veering regions is of critical importance for obtaining high-fidelity predictions of the rotor’s sensitivity to mistuning. Therefore, particular attention is devoted to this subject. It is shown that the Craig–Bampton component mode synthesis (CMS) technique is robust and yields highly reliable results. However, this is achieved at considerable computational cost due to the retained component interface degrees of freedom. It is demonstrated that this problem is alleviated by a secondary modal analysis reduction technique (SMART). In addition, a non-CMS mistuning projection method is considered. Although this method is elegant and accurate, it is seen that it lacks the versatility and efficiency of the CMS-based SMART. Overall, this work shows that significant improvements on the accuracy and efficiency of current reduced order modeling methods are possible.

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