Comb-drive devises have been widely applied in many fields. However, the application of high frequency sensor, such as rocket chamber, still remains problems. In this work, a finite element code was used for the design, optimization and visualization of a comb drive accelerator. In the simulation results, the post-optimization design has high performance in high frequency oscillation operating environment. The optimization is based on the ideal eigenfrequency and Nelder-Mead method. The 3-D working conditions are realized by testing and comparing the time and frequency domain of pre-optimized and optimized design wh ose frequency ranges from 2000 Hz to 5000 Hz. Finally, the electric potential and capacitance in comb drive are visualized, which shows the better electric signals and displacements.
In contemporary society, the Micro-Electro-Mechanical System (MEMS) devices play a significant role in many fields, e.g. accelerator, fluid control, micro-power system, MEMS fuse system and internet of things (IOT) [
However, the design and optimization of comb drive sensor become a challenge for the society since the geometry of the devices is complex. Xie et al. has already designed and fabricated the out of plane comb drives which can achieve the aim of realizing [
In this work, I used the powerful simulation software―COMSOL to make the model more vivid and visual. The study of the vertical comb-finger actuation for CMOS MEMS is also been realized, simulated and tested. In addition, behavioral simulation using the 3-D NODAS library matched the experimental results within 7% for frequency response. Comparing with this work, the frequency domain study was conducted to optimize the model which nobody has involved in this filed. I also parameterized the geometry of the comb drive structure, e.g. fingers and stators. As a result, I can easily change the structure for optimization in the model. In this way, the model can solve the problems that have mentioned above.
The schematic of the comb drive used in this work is shown in
length, and g for gaps between two fingers. In order to stimulate the real working circumstance of comb drives,
Before the optimization, each parameter is set up the proper number, as 200 µm for l f , w f 20 µm, l s t 100 µm, g f 20 µm, l s p 400 µm, w s p 20 µm, and w s t expresses as:
w s t = 6 w f + 5 ( g f + w f ) (1)
which can derive that w s t is 380 µm. On the other hand, the thickness is 5 µm, and the size of air box is large enough to cover the whole model.
After fixing the right stator, I apply an oscillating voltage with 1 V amplitude to the left comb. The relation between the displacement, u, and the time domain, t, which is the first 1 ms, can be easily obtained by solving the equation below:
ρ u ¨ = ∇ ⋅ s + F V (2)
where ρ is the density, s is the stress tensor and FV is the external force density.
Then we simulate the deformation of the moving comb in the frequency domain. The frequency ranges from 2000 Hz to 5000 Hz, which is the average frequency of the rocket, is used to calculate the displacement, u. The inertia force applied on the moving comb is set to be constant. We expect the larger displacement with the same inertia force amplitude since the larger displacement can induce more significant electric signal change. Thus, we can optimize the structure in order to obtain the maximum displacement in the frequency where
the rocket chamber operates. In the end, we compare this pre-optimized design (PD) to with the optimized design (OD) to show the improvement of the device.
Different displacement fields with different frequencies (freq) are shown in Figures 3(a)-(d). The volume color represents the displacement field for each part.
First, the eigen modes of the mechanics are evaluated. As widely known, the rocket chamber operating frequency has a range from 5000 - 10,000 Hz, which is our objective frequency. The eigenfrequency should be as close as the objective to output the maximum displacement. For the physical material, the specific frequency which reachs the maximum amplitude is called Eigenfrequency. Before the optimization, the eigen frequencies of the pre-optimized design’s (PD) are far away from 5000 Hz which is the operation frequency of the rocket chamber. As a result of the frequency mismatch, the performance of the PD is not considered appropriate for the rocket chamber application.
To compare these two different modes, the second eigen mode (
The optimization used Nelder-Mead method to obtain a better performance of the comb drive accelerator. The variable in the optimization is the length of
the suspension spring. The constraint boundary of the optimization is set up to vary from 180 µm to 200 µm, while varying from 80 µm to 120 µm. The goal of the optimization is to get the frequency of the translational mode to as close as 10,000 Hz. Therefore, the objective of the optimization is the square of the difference between the translational mode frequency and the designated 10,000 Hz. The math is to minimize this objective while using different geometries of the comb drive. Represented results of the optimization are shown in
It can be found that, when equals to 2 µm with 1.2 µm, the eigenfrequency is closest to the 10,000 Hz where our design goal is achieved.
After adapting all the parameters from the optimization, we built the optimized design (OD) and tested the new design to compare its performance with our original design. Comparison of the displacement is shown in
| The optimization results | lfinger (m) | lstator (m) | Objective |
|---|---|---|---|
| 2.00 × 10−4 | 1.00 × 10−4 | 1.2869 × 107 | |
| 1.98 × 10−4 | 1.00 × 10−4 | 1.3063 × 107 | |
| 2.00 × 10−4 | 1.02 × 10−4 | 1.2370 × 107 | |
| 1.96 × 10−4 | 1.00 × 10−4 | 1.3250 × 107 | |
| 2.00 × 10−4 | 9.80 × 10−5 | 1.3389 × 107 | |
| 2.00 × 10−4 | 1.20 × 10−4 | 8.5970 × 106 |
| The relation between frequency and displacement of PD and OD | Frequency (Hz) | PD Displacement (m) | OD Displacement (m) |
|---|---|---|---|
| 2000 | 4.3095 × 10−6 | 4.3171 × 10−6 | |
| 2250 | 4.3350 × 10−6 | 4.3453 × 10−6 | |
| 2500 | 4.3638 × 10−6 | 4.3773 × 10−6 | |
| 2750 | 4.3961 × 10−6 | 4.4133 × 10−6 | |
| 3000 | 4.4321 × 10−6 | 4.4533 × 10−6 | |
| 3250 | 4.4718 × 10−6 | 4.4977 × 10−6 | |
| 3500 | 4.5156 × 10−6 | 4.5467 × 10−6 | |
| 3750 | 4.5635 × 10−6 | 4.6004 × 10−6 | |
| 4000 | 4.6159 × 10−6 | 4.6593 × 10−6 | |
| 4250 | 4.6730 × 10−6 | 4.7237 × 10−6 | |
| 4500 | 4.7351 × 10−6 | 4.7939 × 10−6 | |
| 4750 | 4.8027 × 10−6 | 4.8705 × 10−6 | |
| 5000 | 4.8759 × 10−6 | 4.9539 × 10−6 |
Next, we simulated the relation between the applied forces and displacements. The results of frequency dependent displacement are presented in
In the static electric domain, the electric field E satisfies the following relation
E = − ∇ V (5)
∇ ⋅ ε 0 ε r E = ρ v (6)
where V is the electric potential, ε is the permittivity and ρ v is the electric charge density. The capacitance of the device can be calculated as C = Q / V = 3.2581 × 10 − 14 F , if the device is in static.
C = ε S d (7)
| The difference between the displacement before and after the optimization. | Applied force | Displacement field PD | Displacement field OD | Difference |
|---|---|---|---|---|
| 0 | 0 | 0 | ||
| 1.00 | 0.04216233 | 0.042133753 | 285,769 | |
| 2.00 | 0.08432466 | 0.084267506 | 571,538 | |
| 3.00 | 0.12648699 | 0.126401259 | 857,307 | |
| 4.00 | 0.16864932 | 0.168535012 | 11,430.8 | |
| 5.00 | 0.21081165 | 0.210668766 | 14,288.5 | |
| 6.00 | 0.25297398 | 0.252802519 | 17,146.1 | |
| 7.00 | 0.29513631 | 0.294936272 | 20,003.8 | |
| 8.00 | 0.33729864 | 0.337070025 | 22,861.5 | |
| 9.00 | 0.37946097 | 0.379203778 | 25,719.2 | |
| 10.00 | 0.42162330 | 0.421337531 | 28,576.9 |
where S is the effective area, and d is the effective distance between two capacitor plates.
field and the color represents the electric potential. As the movement of the device is to the right, the displacement field is positive. This figure is clear to show the distribution of the electric field in the comb drive device.
In this work, comb drive devices in rocket camber were designed, optimized, simulated and tested with a fully coupled FEA model. The model realized the visualization to help the design and optimization. The OD performed order of magnitude higher sensitive in the frequency range of the working rocket chamber. The parameterization helped to change the variables quickly in this model and made it convenient for the optimization. After the optimization, the electric filed response had been tested by comparing with the PD model and OD model. The PD had larger electric signal in response to the mechanical vibration.
Zhang, Z.C. (2018) Design and Optimization of Comb Drive Accelerator for High Frequency Oscillation. Modern Mechanical Engineering, 8, 1-10. https://doi.org/10.4236/mme.2018.81001