Optimization of the Wire Diameter Based on the Analytical Model of the Mean Magnetic Field for a Magnetically Driven Actuator
Abstract
:1. Introduction
2. Experimental Methods
2.1. Test Principle
2.2. Experiment Setup and Parameters
3. Data Processing and Analysis
3.1. Inherent Characteristic Parameters of Coils
3.1.1. Dimension Parameters
3.1.2. Static Resistance and Static Inductance
3.2. Sinusoidal Response
3.3. Square-Wave Response
3.3.1. Time-Domain Response
3.3.2. Steady-State Value and Response Time
4. Conclusions
- (1)
- The resistance and inductance are inversely proportional functions vs. the quartic of the enameled wire diameter. Under the sinusoidal voltage, a wider wire diameter is quite helpful for a higher magnetic field amplitude while it has little influence on the phase lag of the magnetic field. Under the square-wave voltage, the steady-state magnetic field was positively proportional to the square of the wire diameter, as a wider wire diameter is helpful for a higher steady-state magnetic field. Regarding the response speed, increasing the wire’s diameter is helpful for reducing the response time from 0 to the specified intensity, while it is helpless to improve the response speed from 0 to the steady-state or any other proportional value.
- (2)
- The proposed model was verified as the calculated results from the model were in good agreement with the experimental results. Specifically, the relative errors of the model in computing the resistance and the inductance were lower than 3.1% and 2.8%, respectively. For predicting the sinusoidal response, the errors were lower than 6.4% (lower than 2.0% under most conditions) in computing the amplitude and lower than 3.2% in computing the lagging phase. For predicting the square-wave response, the model calculated the amplitudes with errors lower than 1.2% and described the curve shape effectively.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Coil Label | External Diameter (Dwire) [mm] | Core Diameter (Dwire) [mm] | Number of Coil Turns (N) [Null] | Resistance (R) [Ω] | Inductance (L) [mH] |
---|---|---|---|---|---|
Coil 1 | 0.31 | 0.27 | 837 | 18.325 | 10.933 |
Coil 2 | 0.39 | 0.35 | 537 | 7.472 | 4.487 |
Coil 3 | 0.49 | 0.44 | 342 | 2.994 | 1.789 |
Coil 4 | 0.60 | 0.55 | 229 | 1.342 | 0.801 |
Coil 5 | 0.69 | 0.64 | 175 | 0.767 | 0.459 |
Coil 6 | 0.80 | 0.74 | 124 | 0.410 | 0.243 |
Parameter (Variable) [Unit] | Value |
---|---|
Coil length (La) [mm] | 16.5 |
Coil thickness (Lb) [mm] | 6.8 |
Diameter of skeleton shaft (Lf) [mm] | 18.2 |
Resistivity of copper (ρ) [Ω·m] | 1.71 × 10−8 |
Proportional coefficient (CHI) [null] | 0.8 |
Dwire | Tested Dcore | Dcore from 0.962 Dwire − 0.0277 | Relative Error of 0.962 Dwire − 0.0277 (%) | Dcore from 0.898 Dwire | Relative Error of 0.898 Dwire (%) |
---|---|---|---|---|---|
0.31 | 0.27 | 0.2705 | 0.1926 | 0.2784 | 3.1037 |
0.39 | 0.35 | 0.3475 | −0.7200 | 0.3502 | 0.0629 |
0.49 | 0.44 | 0.4437 | 0.8364 | 0.4400 | 0.0045 |
0.6 | 0.55 | 0.5495 | −0.0909 | 0.5388 | −2.0364 |
0.69 | 0.64 | 0.6361 | −0.6125 | 0.6196 | −3.1844 |
0.8 | 0.74 | 0.7419 | 0.2568 | 0.7184 | −2.9189 |
Coil Label | Coil Turns from Test | Coil Turns from Model 1 | Relative Error (%) |
---|---|---|---|
1 | 837 | 847.33 | 1.23 |
2 | 537 | 535.36 | −0.30 |
3 | 342 | 339.15 | −0.83 |
4 | 229 | 226.19 | −1.23 |
5 | 175 | 171.03 | −2.27 |
6 | 124 | 127.23 | 2.61 |
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Wu, Z.; Bai, H.; Xue, G.; Ren, Z. Optimization of the Wire Diameter Based on the Analytical Model of the Mean Magnetic Field for a Magnetically Driven Actuator. Aerospace 2023, 10, 270. https://doi.org/10.3390/aerospace10030270
Wu Z, Bai H, Xue G, Ren Z. Optimization of the Wire Diameter Based on the Analytical Model of the Mean Magnetic Field for a Magnetically Driven Actuator. Aerospace. 2023; 10(3):270. https://doi.org/10.3390/aerospace10030270
Chicago/Turabian StyleWu, Zhangbin, Hongbai Bai, Guangming Xue, and Zhiying Ren. 2023. "Optimization of the Wire Diameter Based on the Analytical Model of the Mean Magnetic Field for a Magnetically Driven Actuator" Aerospace 10, no. 3: 270. https://doi.org/10.3390/aerospace10030270