Performing a detailed, accurate finite element analysis of MEMS device can prove time consuming when you are trying to fully characterize a device over its entire operating range in order to understand how it responds/interacts with its drive/senses circuitry. ANSYS Multiphysics provides the user with a semiautomatic way to perform this characterization, and represent the results in a reduced order model (The reduced order model is a mathematical representation of the coupled electrostatic structural system derived from a full FEA model) that accommodates effects such as:
That is, an approach that retains the accuracy (high fidelity) of a full finite element model. The approach we use makes the basic assumption that the dynamic behavior of any flexible structure is accurately described by a superposition of its dominant mode shapes. MEMS devices can typically be characterized by only a few modes, and hence the entire system can be reduced down to handful of unknowns (model amplitudes and electrode voltages)DOFs) and thus solved very efficiently. The reduced equation set with these DOF is used by our new elements ROM144.
The ROM144 element is a 2-D or 3-D reduced order model of a coupled electrostatic-structural system. The element fully couples the electromechanical domains and represents a reduced order model suitable for use in finite element analysis as well as electromechanical circuit simulations. The element has ten modal degrees of freedom relating modal forces and modal displacements (EMF), ten voltage degrees of freedom relating electrical current and potential (VOLT) and, optionally, ten master nodes relating nodal forces to nodal displacements (UX).
The element is suitable for simulating the electromechanical response of Microelectromechanical devices (MEMS) such as clamped beams, micromirror actuators, and RF switches. The element is derived from a series of uncoupled structural and electrostatic domain simulations. The ROM144 element represents a complicated flexible structure whose nodes move mainly in one direction either X, Y or Z referred to the global Cartesian axes. For instance, torsional systems with angles less than ten degree or flexible bending of cantilevers or membranes obey those restrictions (pressure sensors, cantilever for AF microscopy, RF filter). Geometrical nonlinearities caused by stress stiffening or initial prestress are considered as well as multiple conductor systems.
There are four key steps required in creating and using ROM144 model of your device as follows:
1. Model Preparation: Creates the necessary finite element model for the generation pass.
2. Generation Pass: Executes a modal analysis of the structure. It also executes an optional static analysis to determine the deformation state of the structure under operating conditions. Using this information, the generation pass then selects the modes and performs computations to create a reduced order model. Also at this stage a VHDL-A/MS mathematical model of the ROM structure is created and may be exported for use in electrical design automation (EDA) system simulators.
3. Use Pass: Uses the reduced order model in an analysis. The reduced order model is stored in a ROM database and a polynomial coefficients file, and utilized by the ROM144 element. The Use Pass allows any type of analyses (transient, harmonic, static etc) with various load situations. The ROM144 element can be coupled to ANSYS Multiphysics circuit elements (CIRC124, CIRC125) at the voltage ports, plus mechanical DOF ports can be coupled to lumped spring, mass, damper and gap elements to enable relatively complex system level simulation.
4. Expansion Pass: Extracts the full DOF set solution and computes stresses on the original structure created in the model preparation phase. This allows detailed review of the stress and displacements in original FEA model used in the preparation phase. Animations can also be created to visulaize the dynamic response of the structure.
The following diagram explains the generation pass process. A test load is applied to the model to simulate the primary motion of the device. A modal analysis is then performed to compute the mode shapes. The test load deflection is then compared with these mode shapes and the mode shape order and contribution determined. The user can then select which modes will be used to build the device response surface through linear combination (permutations) of these selected modes. The device response surface and database for the reduced order model (ROM144) are constructed automatically.
The ROM144 element can be accessed via the ANSYS APDL command language or via the GUI. The following screen shot shows the ROM144 main GUI menu:
Analyzing the electrostatic-structural response of a typical MEMS device can prove to be quite time consuming using the traditional finite element approach. The ROM144 approach automates much of the process such as balding the response surface for the device. As an example of analysis times, consider the following device, a torsional micromirror:
The model consists of 19136 elements, 29346 nodes. Three conductors with three capacitance functions are involved.
Generation Pass:
6 sampling points for the first dominant mode, 5 for the second dominant mode.
Total of 30 sampling points.
Total time on a 750 MHz. PC was 14 minutes to create the ROM.Use Pass:
DC voltage sweep (160 substeps) 15 - 20 sec. on a PC
Harmonic response analysis (100 substeps) 10 - 15 sec. on a PC
ANSYS ROM144 transient analysis (1570 substeps) 20 - 30 sec. on a PC
VHDL simulation tool transient analysis (1570 substeps) 25 - 35 sec. on a PC
Graph illustrating the accuracy of the ROM144 results compared to experimental data for a torsional mirror device:
Related Technical References: