Create Presentation
Download Presentation

Download Presentation
## 微機電分析 MEMS Actuator Cantilever Beam

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**1-Dimensional Model**• Pull-in voltage**The system will be unstable when a moving plate is displaced**g0/3**2-Dimensional Model**• Bernoulli-Euler beam bending theory (1)small deflection for which the radius of curvature equals the inverse of the second-derivative of deflection (2)no shear deformation from the transverse loading (3)no in-plane curvature adjustment due to transverse extension or compression of the thickness**(4)the supports are ideally fixed**(5)membrane effects from stress-stiffening are negligible (6)anticlastic curvature along a beam’s width w is geometrically insignificant • The coupled electromechanical equation where the fringing-field correction ff = 0.65g/w for cantilevers (stress-free) for beams**Algebra equation**B : bending parameter S : stress parameter • Simulation methods (1)finite-difference MATLAB scripts (2)Rayleigh-Ritz energy methods**Table 1. Closed-form M-TEST models for ideal test**structures**3-Dimensional Model**• The effects which should be considered id 3D model (1)Plate Effect (2)Support Compliance (3)Stress-Gradients Through Film Thickness • Plate effect (2D Bernoulli-Euler mechanics)**Support Compliance**• Built-in support found in conformal deposition processes of MEMS fabrication • Built-in residual stress (1)Increase structure compliance (2)Increase rotate in the presence of external moments**Stress-Gradients Through Film Thickness**• Nonuniform stresses in the film thickness create built-in moments, which is released cantilevers cause them to curl out of plane.**Because the stress-gradients is assumed to be uniform**in-plane • Due to linearity for small deflections • Modified coefficient for VPI**Modeling Using the Graphical User Interface**2D Version**Model Navigator**• 2D Multiphysics： • MEMS Module>Structural Mechanics>Plane Strain • COMSOL Multiphysics>Deformed Mesh>Moving Mesh (ALE) • Frame (ale) MEMS Module>Electrostatics> Electrostatics**Geometry Modeling**• Options>Axes/Grid Settings Clear Axis equal check box • Draw Rectangle/Square(holding shift and click)**Physics Settings for Electrostatics**• Multiphysics>Electrostatics (emes) • Subdomain Settings Physics>Subdomain Settings (1)Subdomains 1, 3, and 4 default settings εr = 1(for air) (2)Subdomain 2 εr = 4.5(for polysilicon) Force tab>enter variable Fes**Boundary Conditions**Physics>Boundary Settings (1)select the Interior boundaries check box (2)enter boundary conditions in the table below**Physics Settings for Moving Mesh**• Multiphysics>Moving Mesh (ale) • Subdomain Settings (1)Subdomains 1, 3, and 4 Keep the default Free displacement setting (2)Subdomain 2 use Physics induced displacement enter variable dx=u, dy=v**Boundary Conditions**(1)Enter themesh displacements, dx and dy (2)Do not assign any settings for interior boundaries, which appear dimmed**Physics Settings for Plane Strain**• Multiphysics>Plane Strain (smpn) • Physics>Properties Large deformation select On • Subdomain Settings (1)Subdomain 2enter the following settings pull-in voltageuse nonlinear parametric solver (2)Subdomains 1, 3, and 4clear the Active in this domain check box**Boundary Conditions**(1)verifythe Interior boundaries check box is cleared (2)Constraint tab Boundary 3Constraint conditionFixed (3)Load tab Boundary 3,6,8Value/expression FX=0, FY=0 (4) Boundary 4Value/expression FX=Fes_nTx_emes , FY=Fes_nTy_emes**Mesh Generation**• Mesh>Mapped Mesh Parameters • Boundary tab Select boundaries and click Constrained edge element distribution check box • Enter the value of Number of edge elements (1)Boundaries 1, 3, and 5 5 (2)Boundary 660 (3)Boundary 104 • Click Remesh and then OK**Computing the Solution**• Solver>Solver Parameters • Solver list>Parametric>General tab (1)Name of parameterenter Vin (2)List of parameter valuesenter 1:6, 6.1:0.1:6.3 • Click OK and then click Solve on the Main toolbar**Postprocessing and Visualization**• Postprocessing>Plot Parameters • To see deformations inside the cantilever beam： • General tabselect the Surface check box and clear other check boxes of plot types • Surface tabPredefined quantities listselect Plane Strain (smps)>Total displacement**To visualize the deformed mesh in the air domain**• General tab (1)clear the Element refinement: Auto check box and type 1 in the associated edit field (2)Only the Surface and Geometry edges check boxes are selected (3)Frame listselect Frame (ale) • Surface tab (1)Predefined quantities listselect Electrostatics (emes)>Electric potential (2)Fill style listselect Wireframe**To find the displacement of the cantilever beam’s tip over**voltage • Postprocessing>Domain Plot Parameters • Point tab (1)Point selection listselect Point 5 (2)Predefined quantities listselect Plane Strain (smpn)>Y-displacement (smps)