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| Improved Impedance Modeling of Self-Inductive Displacement Sensor Based on the Modulus and Angle of the Coil Impedance |
| Chen Xinwei1, Li Hongwei1, Ren Zongqiang2, Yu Wentao1, Ding Yinshu3 |
1. School of Electrical Engineering Shandong University Jinan 250061 China;
2. School of Electrical Engineering Xi'an Jiaotong University Xi'an 710049 China;
3. Shandong Tomorrow Machinery Group Co. Ltd Jinan 250200 China |
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Abstract At present, active magnetic bearing (AMB) is widely used in various industries. The rotor displacement sensor detects the rotor vibration displacement in real-time to provide a control basis for the AMB controller. Therefore, it is a vital component that affects the control performance of AMB. The self-inductive displacement sensor is increasingly widely used in AMBs for its many advantages. Since the iron core reluctance and the leakage flux in the air-gap magnetic circuit are not considered, the traditional ideal model of the self-inductive displacement sensor fails to predict the performance of the sensor accurately. Therefore, this paper proposes an improved impedance model of the self-inductive displacement sensor based on the modulus and angle of the coil impedance.
Firstly, according to the working principle, a sensor equivalent magnetic circuit model is established for the differential self-inductive displacement sensor. The influence of eddy current and hysteresis effects on the reluctance of iron cores is considered by introducing the complex permeability, and the leakage flux and edge effect on the reluctance of the air gap is considered by introducing the air-gap stray coefficient. Then, an improved impedance model of sensor coils is established. By the improved impedance model, the output voltage and sensitivity of the sensor are predicted.
Secondly, under different excitation frequencies and rotor displacements, the resistance and inductance of iron coils of a designed sensor are measured based on a designed coil impedance test rig, and the output voltage of the designed sensor is measured based on a designed sensor static performance test rig. According to the experimental results, the parameters of the improved impedance model are obtained. Then, the output voltage and sensitivity of the sensor are predicted under different excitation frequencies. Finally, the results show that the prediction absolute error of the output voltage is less than 0.05 V, and the relative error of the sensitivity prediction is less than 1%, which verifies the accuracy of the impedance improvement model.
The following conclusions can be drawn. (1) The improved impedance model can accurately account for the effects of eddy currents and hysteresis loss in iron cores at high frequencies by introducing complex magnetic permeability. (2) The improved impedance model can accurately account for the impact of flux leakage and edge effects in air-gap by introducing the air-gap reluctance stray coefficient. (3) Variations in model parameters with rotor displacement and excitation frequency are obtained through experiments, and an accurate improved impedance model of the sensor is established and verified.
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Received: 07 December 2023
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2025, Vol. 40 
