2008 International ANSYS Conference

Transcription

1 2008 International ANSYS Conference Nonlinear Piezoelectric Analysis with ANSYS-MATLAB/Simulink coupling Masahiro Matsumoto Cybernet Systems Co., Ltd 2008 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary

2 Agenda Introduction Overview of Analysis Modal Analysis with ANSYS Experiment result A nonlinear vibration phenomenon Examination of new analytical technique Consideration of large-deflection effect ANSYS-MATLAB/Simulink coupling Other cases (hysteresis model) Conclusion 2008 ANSYS, Inc. All rights reserved. 2 ANSYS, Inc. Proprietary

3 Introduction (Japanese market) Piezoelectric devices are widely used in electronics, automotive, and many other industries in Japan, such as: Power devices (electro mechanical) piezo actuator ultrasonic motor,etc. Sensors (mechanical electro) acceleration sensor, gyro sensor,etc. Circuits (resonance) ceramic resonator, SAW Filter,etc ANSYS, Inc. All rights reserved. 3 ANSYS, Inc. Proprietary

4 Introduction (sales promotion) We propose a piezoelectric analysis to a wide customer in Japan by customizing Workbench. CAD Interface Auto Mesh Optimized approach (DesignXplorer) 2008 ANSYS, Inc. All rights reserved. 4 ANSYS, Inc. Proprietary

5 Introduction (Today s problem) Under increasingly harsh operation environments of piezoelectric devices, The following nonlinear effects are becoming vital factors in piezoelectric analysis. Large deflection effects Material nonlinearity Temperature dependence This paper discusses the techniques to achieve efficient nonlinear piezoelectric analysis using ANSYS- MATLAB/Simulink coupling ANSYS, Inc. All rights reserved. 5 ANSYS, Inc. Proprietary

6 Overview of Analysis Spectacle-type Wearable Retinal Imaging Display (RID) RID consists of three modules: a light source module, an optical scanning module, and an eyepiece module. This optical scanning module uses an optical micro electro mechanical system (Piezoelectric mirror). Piezoelectric mirror 2008 ANSYS, Inc. All rights reserved. 6 ANSYS, Inc. Proprietary

7 Overview of Analysis (cont.) Model 1 Model 2 Mirror & beam (Si) Piezoelectric Upper electrode Under electrode The difference between Model1 and Model2 is only the intervals of the beams ANSYS, Inc. All rights reserved. 7 ANSYS, Inc. Proprietary

8 Modal Analysis (Model1) Mode Frequency [Hz] Mode Shape 1 14,701 anti plane Mode3 : Torsion mode 2 29,340 in plane 3 32,868 torsion Frequency of focus Because torsion vibration is the key operation movement, Mode3 is important ANSYS, Inc. All rights reserved. 8 ANSYS, Inc. Proprietary

9 Modal Analysis (Model2) Mode Frequency [Hz] Mode Shape 1 9,086 antiplane Mode4 : Torsion mode 2 29,068 inplane 3 31,045 Bending 4 31,142 Torsion Because torsion vibration is the key operation movement, Mode4 is important. Frequency of focus 2008 ANSYS, Inc. All rights reserved. 9 ANSYS, Inc. Proprietary

10 Experiment result of torsion mode Model 1 Model 2 freq. rises freq. falls freq. rises freq. falls Amplitude drops The resonance frequency of torsion mode is roughly corresponding. The resonance frequency of Model2 is different from Model1 when the frequency rises and falls. Moreover the Model2 amplitude drops when the frequency rises. Why? 2008 ANSYS, Inc. All rights reserved. 10 ANSYS, Inc. Proprietary

11 A nonlinear vibration phenomenon When the deflection increase, a nonlinear effect becomes important. It is known that the reaction force works by the third power of the deflection, (The Duffing equation). m x 1 DOF Mass-Damper system F kx+βx 3 kx 0 x One of the vibration characteristic is that the reaction force(= Stiffness) increases as the amplitude grows, and the resonance frequency changes depending on the amplitude. it is necessary to consider this nonlinear effect in piezoelectric devices (piezo mirror, ultrasonic motor,etc) with small damping. Amplitude freq. rises Voltage increase freq. falls 0 Frequency 2008 ANSYS, Inc. All rights reserved. 11 ANSYS, Inc. Proprietary

12 Examination of analytical technique Typical problem of piezoelectric device The damping is very small The Integration Time Step is very small. The transient analysis needs very long solution times. Breakthrough in the solution ( 0.05%) 1. Solution times is shortened by Reduction Model. 2. The nonlinear effect (large-deflection effect) is expressed with the feedback control. ANSYS-MATLAB/Simulink coupling 2008 ANSYS, Inc. All rights reserved. 12 ANSYS, Inc. Proprietary

13 ANSYS-MATLAB/Simulink coupling ANSYS data, which Structural Dynamics Toolbox (MATLAB 3 rd Party tool) degenerate, is built into MATLAB. Solution time has been greatly shortened by MATLAB. To consider the nonlinear model (torsion stiffness), the reaction force shown by the previous slides was added as a feedback control. This technique can adequately express the evaluated behavior. ANSYS database ANSYS Reduction Model Reduction model by SDT Excited by alternating voltage Nonlinear term Feedback control by reaction force 2008 ANSYS, Inc. All rights reserved. 13 ANSYS, Inc. Proprietary

14 Consideration of large-deflection effect twist R eaction Force (%) Model 1 y = -4E-06x x x Angle (deg) Predominant movement of the piezoelectric mirror is a torsion mode. Therefore, the nonlinear stiffness is calculated by the reaction force when the mirror is twisted. Model1 = 4e-6 Model2 = 5e-5 Because the interval of the beams which support the mirror is wide, Model2 s twist stiffness is high. The reaction force is used as the feedback control. Reaction Force (%) Model y = -5E-05x x x Angle(deg) 2008 ANSYS, Inc. All rights reserved. 14 ANSYS, Inc. Proprietary

15 ANSYS-MATLAB/Simulink coupling (Result) freq. rises freq. falls Model 1 Tyep freq. rises freq. falls Model 2 Tyep 2 Angle (deg) Angle (deg) x 10 4 Frequency (Hz) x 10 4 Frequency (Hz) Good Correlation!! 2008 ANSYS, Inc. All rights reserved. 15 ANSYS, Inc. Proprietary

16 Piezoelectric optimization analysis considering nonlinear material (hysteresis) 2008 ANSYS, Inc. All rights reserved. 16 ANSYS, Inc. Proprietary

17 Overview of Analysis (Cantilever) Purpose :To optimize the shape and the control system of vibration controller state feedback Objective variables : Minimization of Vibration/Control energy Design variables: Structure System : dimension Control System : weighting matrix F (control input) disturbance Reduction u u=-kx x x=ax+bu & y =Cx+Du Piezo film Reduction model Wp (Design parameter) L ( Design parameter ) Κ l = { k k L k } k k k u = Kx 1 2 n u 2008 ANSYS, Inc. All rights reserved. 17 ANSYS, Inc. Proprietary

18 hysteresis of piezoelectric actuator (Model) Mechanism of hysteresis (assumption ) A part of the inputs energy is accumulated internally as potential energy. The inputs are memorized. The energy isn t accumulated when new input is smaller than past input. The energy is accumulated when new input is larger than past input. The potential energy has retentivity. The energy is maintained without applying the opposite input. There is a limit in the energy accumulation, and the energy is saturated. Base Model y () t kx() t μ x( t) = dx Accumulation of energy 2008 ANSYS, Inc. All rights reserved. 18 ANSYS, Inc. Proprietary

19 hysteresis of piezoelectric actuator (Result) Input Output 2008 ANSYS, Inc. All rights reserved. 19 ANSYS, Inc. Proprietary

20 Search for multipurpose optimization hysteresis model ANSYS 4 x 10-3 W ithout control Vibration Cost Function2 Energy u'*u W idth = 0.1 W idth = 0.2 W idth = 0.3 saturation of quality C ost Function1 y'*y Control Energy Performance evaluation by Pareto-frontier Value Value Time (s) 4 x 10-3 W ith control LQ regulator NBI m ethod T im e (s) Comparison of the regulators 2008 ANSYS, Inc. All rights reserved. 20 ANSYS, Inc. Proprietary

21 Conclusion Japanese market and the marketing method of a piezoelectric device is introduced. The techniques to achieve efficient nonlinear piezoelectric analysis using ANSYS- MATLAB/Simulink coupling is proposed. ANSYS-MATLAB/Simulink coupling can efficiently optimize the controller design. This method enables us to built the material model of the research stage such as hysteresis into ANSYS!! 2008 ANSYS, Inc. All rights reserved. 21 ANSYS, Inc. Proprietary

22 Thank you 2008 ANSYS, Inc. All rights reserved. 22 ANSYS, Inc. Proprietary