Optimization Design of Linear Variable Reluctance Resolver Structure Based on Kriging Surrogate Model

Abstract

With the rapid development of high-end CNC machine tools and gravity energy storage technologies, long-stroke linear motion systems impose higher requirements on the measurement accuracy, reliability, and environmental adaptability of position sensors. Traditional optical and magnetic grating sensors are susceptible to interference in harsh conditions such as oil contamination and suffer from high costs and difficult maintenance. The Linear Variable Reluctance Resolver (LVRR) has become a potential ideal alternative due to its robust structure, strong anti-interference ability, and low cost. However, the "longitudinal end effect" and air-gap magnetic field distortion caused by extending the rotary structure to a linear one severely deteriorate the sinusoidal quality of the output signal, making it difficult for position resolution accuracy to meet high-precision control demands. To address this, this paper proposes an efficient structural optimization method combining Finite Element Analysis (FEA), the Kriging surrogate model, and the Expected Improvement (EI) criterion. By constructing a global Kriging surrogate model with mover end-tooth thickness, air-gap length, and slot depth as design variables and minimizing the Total Harmonic Distortion (THD) as the objective, the method employs a sequential iterative strategy to dynamically balance local exploitation and global exploration in the design space. Simulation results show that this method effectively suppresses end leakage flux and high-order harmonics. After optimization, the THD of the sensor's output voltage is reduced from 5.32% to 2.14%, and the peak electrical angle error converges to within $\pm0.9^\circ$, significantly improving the system's linearity and detection accuracy.