Investigation of the Dynamics of a 2-DoF Actuation Unit Cell for a Cooperative Electrostatic Actuation System
Abstract
:1. Introduction
2. System Concept, Materials, and Methods
2.1. The Cooperative Concept and Actuation Unit Cell
2.2. The Analytical Model of the AUC
2.3. FE Modeling and Simulation
2.3.1. Static Analysis
2.3.2. Transient Analysis
2.4. Solving the Analytical (Lumped-Parameter) Model by MATLAB/Simulink
3. Results
3.1. Pull-In Voltage
3.2. Pull-In Time
3.3. Pull-Out Time
4. Discussion
4.1. Dynamic Behavior
4.2. Output Force
4.3. Fabrication Feasibility Analysis
4.4. Error Estimation for the Used SQFD Modeling Approach in COMSOL
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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Description | Symbol | Value | Unit |
---|---|---|---|
Height of unit cell | h | 50 | µm |
Width of cell wall | ww | 15 | µm |
Size of cell wall along x-axis (inner dimension) | cx | 500 | µm |
Size of cell wall along y-axis (inner dimension) | cy | 500 | µm |
Size of anchor (x-axis) | ax | 100 | µm |
Size of anchor (y-axis) | ay | 100 | µm |
Width of x-axis spring (flexure width) | wx | 2 | µm |
Width of y-axis spring (flexure width) | wy | 2 | µm |
Length of connector beams of x-axis spring | lc,x | 50 | µm |
Length of span beam of x-axis spring | ls,x | 200 | µm |
Length of extension beams of x-axis spring | le,x | 53 | µm |
Length of connector beams of y-axis spring | lc,y | 50 | µm |
Length of span beam of y-axis spring | ls,y | 200 | µm |
Length of extension beams of y-axis spring | le,y | 53 | µm |
Length of stationary electrodes | le | 460 | µm |
Width of stopper (length of contact area) | ws | 25 | µm |
Nominal air gap between electrodes | d | 5 | µm |
Stroke (distance between mov. electrode at rest and stopper) | s | 4 | µm |
Young’s modulus | E | 170 | GPa |
Poisson’s ratio | ν | 0.28 | - |
Density (c-Si) | ρ | 2329 | kg/m3 |
Air viscosity | µ | 1.845 × 10−5 | Pa.s |
Actuation Voltage | Vo | variable | V |
Description | Symbol | Device 1 | Device 2 | Unit |
---|---|---|---|---|
Height of unit cell | h | 50 | 100 | µm |
Width of cell wall | ww | 25 | 35 | µm |
Size of cell wall (inner) | cx and cy | 500 | 600 | µm |
Size of anchor | ax and ay | 100 | 100 | µm |
Width of spring (flexure width) | wx and wy | 2.5 | 5 | µm |
Length of connector beams | lc,x and lc,y | 50 | 50 | µm |
Length of span beams | ls,x and ls,y | 200 | 300 | µm |
Length of extension beams | le,x and le,y | 53 | 82.5 | µm |
Length of stationary electrodes | le | 480 | 600 | µm |
Width of stopper | ws | 25 | 25 | µm |
Nominal air gap between electrodes | d | 5 | 4 | µm |
Stroke | s | 4 | 3 | µm |
Equivalent mass (assuming r = 0.5) | meq | 6.46 | 22.65 | µg |
Equivalent spring constant 1 | keq | 40.4 | 304.8 | N/m |
Pull-in voltage 1 | Vpull-in | 83.9 | 104.3 | V |
Collapse voltage (2nd pull-in) 1 | Vcollapse | 152.0 | 165.9 | V |
Actuation voltage | Vo | 110 | 130 | V |
Pull-in time (corresponding to Vo) 2 | tpull-in | 32.2 | 24.9 | µs |
Net force of AUC (at 1µm) 2,3 | F | 0.04 | 0.19 | mN |
Net force of AUC (at 2µm) 2,3 | F | 0.06 | 0.51 | mN |
Realignment margin | δ | ±2 | ±1 | µm |
Pull-out time (corresponding to δ) 2 | tpull-out | 283 | 91 | µs |
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Albukhari, A.; Mescheder, U. Investigation of the Dynamics of a 2-DoF Actuation Unit Cell for a Cooperative Electrostatic Actuation System. Actuators 2021, 10, 276. https://doi.org/10.3390/act10100276
Albukhari A, Mescheder U. Investigation of the Dynamics of a 2-DoF Actuation Unit Cell for a Cooperative Electrostatic Actuation System. Actuators. 2021; 10(10):276. https://doi.org/10.3390/act10100276
Chicago/Turabian StyleAlbukhari, Almothana, and Ulrich Mescheder. 2021. "Investigation of the Dynamics of a 2-DoF Actuation Unit Cell for a Cooperative Electrostatic Actuation System" Actuators 10, no. 10: 276. https://doi.org/10.3390/act10100276