Quantifying Discretization Errors in Electrophoretically-Guided Micro Additive Manufacturing
Abstract
:1. Introduction
1.1. Electrophoretically-Guided Micro Additive Manufacturing (EPµAM) Process
1.2. EPµAM Control Algorithm
1.3. Numerical Studies
2. Methods
2.1. Space Discretization Error Studies
2.2. Analysis of Time Discretization Errors
3. Results and Discussion
3.1. Space-Discretization Error Results
3.2. Comparative Evaluation Matrix
3.3. Parametric Sweeps of Pin and Parabolic Notch Electrode Geometries—Case Studies
3.4. Time-Discretization Error
3.5. Discussion
4. Conclusions and Future Work
- The space discretization study assessed the computed particle trajectories using the MSD technique. The obtained MSD curves allowed the selection of the top microelectrode geometry candidate for the EPμAM process. Partial geometric sweep FEM studies of the top two (out of six) electrode geometries demonstrated the nonlinear influence of the electrode geometry on particle mobilities.
- The time discretization study computed the time series of the electromechanical force (for three given actuating waveforms) acting on spherical particles in the middle of the EPμAM device’s workspace. The Pulse and PWM waveforms outperformed the Sinusoidal waveform with a 27% and 37% increase, respectively, in particle mobility.
Supplementary Files
Supplementary File 1Author Contributions
Funding
Conflicts of Interest
References
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Electrode Geometry | Width, w (µm) | Height, h (µm) |
---|---|---|
Step | 40 | 10 |
Channel | 40 | 10 |
Pin | 10 | 20 |
Notch | 10 | 20 |
Parabolic pin | 40 | 10 |
Parabolic notch | 40 | 10 |
Material domain | Ω1: Water (H2O) | Ω2: Alumina (Al2O3) |
---|---|---|
Relative permittivity (-/-) | 80.1 | 9.9 |
Electrical conductivity (S/m) | 2.5 × 10−2 | 1 × 10−13 |
Density (kg/m3) | 1000 | 2000 |
Dynamic viscosity (Pa·s) | 1 × 10−3 | Not Applicable |
Coefficient | Confidence Bounds (95%) | ||
---|---|---|---|
Name | Value | Lower | Upper |
DLL | 0.607 | 0.582 | 0.632 |
DLM | 0.159 | 0.152 | 0.165 |
DLR | 4.472 | 4.082 | 4.865 |
DQL | 0.436 | 0.365 | 0.507 |
DQM | 0.106 | 0.092 | 0.120 |
DQR | 0.806 | 0.666 | 0.946 |
vQL | 0.598 | 0.462 | 0.708 |
vQM | 0.332 | 0.287 | 0.371 |
vQR | 2.770 | 2.718 | 2.821 |
Electrode Shapes | Metric | Scores | ||||||
---|---|---|---|---|---|---|---|---|
Importance (1–4) 4—Highest 1—Lowest | MSD > MSDideal | dt > dtideal | Between Fits | Closest to Ideal | Subgroup Scores | Average Score | Weighted Average | |
Importance → | 3 | 4 | 2 | 1 | ||||
Step | L | 4 | 2 | 0 | 3 | 23 | 14.00 | 13.50 |
M | 1 | 0 | 2 | 5 | 12 | |||
R | 0 | 0 | 1 | 5 | 7 | |||
Channel | L | 3 | 2 | 0 | 4 | 21 | 14.67 | 14.50 |
M | 2 | 0 | 2 | 4 | 14 | |||
R | 0 | 0 | 2 | 5 | 9 | |||
Notch | L | 1 | 2 | 0 | 6 | 17 | 14.33 | 17.00 |
M | 6 | 1 | 1 | 1 | 25 | |||
R | 0 | 0 | 0 | 1 | 1 | |||
Pin | L | 6 | 2 | 0 | 1 | 27 | 26.67 | 26.75 |
M | 5 | 2 | 1 | 2 | 27 | |||
R | 6 | 1 | 1 | 2 | 26 | |||
Parabolic pin | L | 3 | 2 | 0 | 4 | 21 | 14.67 | 14.75 |
M | 2 | 1 | 1 | 3 | 15 | |||
R | 0 | 0 | 2 | 4 | 8 | |||
Parabolic notch | L | 5 | 2 | 0 | 2 | 25 | 19.00 | 18.00 |
M | 1 | 1 | 1 | 6 | 15 | |||
R | 3 | 0 | 1 | 6 | 17 |
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Pritchet, D.; Moser, N.; Ehmann, K.; Cao, J.; Huang, J. Quantifying Discretization Errors in Electrophoretically-Guided Micro Additive Manufacturing. Micromachines 2018, 9, 447. https://doi.org/10.3390/mi9090447
Pritchet D, Moser N, Ehmann K, Cao J, Huang J. Quantifying Discretization Errors in Electrophoretically-Guided Micro Additive Manufacturing. Micromachines. 2018; 9(9):447. https://doi.org/10.3390/mi9090447
Chicago/Turabian StylePritchet, David, Newell Moser, Kornel Ehmann, Jian Cao, and Jiaxing Huang. 2018. "Quantifying Discretization Errors in Electrophoretically-Guided Micro Additive Manufacturing" Micromachines 9, no. 9: 447. https://doi.org/10.3390/mi9090447