Numerical Modeling and Structure Optimization for Magnetic Levitation Planar Machine Using PCB Coils
Abstract
:1. Introduction
2. Numerical Model Design and Computation
2.1. Working Principle of ML System
2.2. Construction of Numerical Model
2.2.1. Magnetic Nodes
2.2.2. Coordinate Transformation
2.2.3. Computation of Magnetic Force
2.2.4. Gaussian Quadrature
2.3. Heat Transfer Equation for PCB
2.4. Power Loss Caused by Resistance and Voltage Drop
3. Optimal Design for the ML System
3.1. Optimization of Variables and Objective Functions
3.2. Optimization Algorithms and Constraints
4. Validation and Verification of Magnetic Model and Optimization Process
4.1. Feasibility of the Modified Magnetic Node Model
4.2. Optimization Process and Results
4.3. Effectiveness and Versatility of the Proposed Optimization
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value |
---|---|
Heat transfer coefficient () | 15 W/m2k |
Inner length of the coil (L) | 60 mm |
Inner width of the coil (W) | 10 mm |
Distance from the inner to the outer coil (D) | 10 mm |
Thickness of copper (h) | 0.2 mm |
Distance between each wire (d) | 0.1 mm |
Resistivity () | mm |
Air gap (g) | 1.5 mm |
Length of the magnet () | 40 mm |
Width of the magnet () | 10 mm |
Remanence () | 1.2 T |
The relative permeability of magnet () | 1.1 |
Density of the magnet () | |
Height of the magnets () | 8 mm |
Constant weight of the stator () | 20 N |
Room temperature | 25 °C |
Type | Size | Results | ||
---|---|---|---|---|
Turns (turns) | Thickness (mm) | in MATLAB (N/A) | in Radia (N/A) | |
Figure 4 | 3 | 3.84 | 0.599 | 0.605 |
3 | 4.48 | 0.666 | 0.675 | |
3 | 5.76 | 0.782 | 0.796 | |
3 | 7.68 | 0.917 | 0.936 | |
7 | 8.32 | 1.905 | 1.950 | |
10 | 8.32 | 2.858 | 2.737 | |
13 | 8.32 | 3.810 | 3.647 |
Basic Parameter | Values for 1D ML System | Values for 2D ML System |
---|---|---|
Length of the magnets () | 40 mm | 16 mm |
Width of the magnets () | 10 mm | 8 mm |
Height of the magnets () | 12 mm | 11 mm |
Constant weight of the stator () | 23 N | 10 N |
Thickness of the PCB coil () | 9.2 mm | 8.32 mm |
Total width of one PCB coil () | 30 mm | 48 mm |
Total length of one PCB coil () | 80 mm | 48 mm |
Total turns of one PCB coil () | 180 turns | 171 turns |
Number of layer of PCB | 20 layers | 19 layers |
Thickness of the copper (h) | 0.2 mm | 0.2 mm |
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Zhang, H.; He, J.; Xu, X.; Wang, R.; Xu, M.; Xu, F. Numerical Modeling and Structure Optimization for Magnetic Levitation Planar Machine Using PCB Coils. Actuators 2025, 14, 33. https://doi.org/10.3390/act14010033
Zhang H, He J, Xu X, Wang R, Xu M, Xu F. Numerical Modeling and Structure Optimization for Magnetic Levitation Planar Machine Using PCB Coils. Actuators. 2025; 14(1):33. https://doi.org/10.3390/act14010033
Chicago/Turabian StyleZhang, Han, Jiawen He, Xianze Xu, Rui Wang, Manman Xu, and Fengqiu Xu. 2025. "Numerical Modeling and Structure Optimization for Magnetic Levitation Planar Machine Using PCB Coils" Actuators 14, no. 1: 33. https://doi.org/10.3390/act14010033
APA StyleZhang, H., He, J., Xu, X., Wang, R., Xu, M., & Xu, F. (2025). Numerical Modeling and Structure Optimization for Magnetic Levitation Planar Machine Using PCB Coils. Actuators, 14(1), 33. https://doi.org/10.3390/act14010033