Abstract：Permanent magnet linear motors (PMLMs) are widely applied in precision machining and high-accuracy positioning systems due to their high stiffness, fast dynamic response, and direct-drive characteristics. However, vibrations induced by normal electromagnetic force waves can significantly degrade machining accuracy and operational stability. Conventional vibration analysis relies heavily on finite element methods (FEM), which, although accurate, are computationally intensive and inefficient for iterative design optimization. This study develops a fast and accurate analytical vibration model for PMLMs based on the Euler-Bernoulli beam theory to elucidate the quantitative relationships among electromagnetic forces, structural parameters, and vibration responses. The equivalent elastically supported beam model is established, incorporating the effects of support stiffness and normal electromagnetic forces. The normal electromagnetic forces are obtained using the Maxwell stress tensor method, which accounts for longitudinal end effects. As a result, the model improves the accuracy of excitation prediction. The natural frequencies of the mover are analytically derived for both pitching and bending modes. The analytical results are validated by FEM simulations and modal tapping experiments. For the first two modes, the analytical predictions deviate from experimental results by less than 10%. Based on the forced-vibration equation of the equivalent beam, a vibration transfer function is derived, and the vibration responses are obtained using the modal superposition method. The resulting displacement spectra show that the largest response appears at twice the supply frequency, with additional peaks occurring at higher even multiples and near the natural frequencies. The influence of structural parameters on vibration response is analyzed. (1) Reducing slider spacing decreases the second bending mode response. (2) Increasing the mover yoke thickness reduces both pitching and bending responses. (3) Increasing slider support stiffness effectively suppresses pitching vibration. A dedicated vibration test platform is constructed. The experimental displacement spectra agree with analytical results in both dominant frequency components and relative response trends, with amplitude errors within 50% for the 2 times frequency component. The feasibility of the proposed model for early-stage vibration prediction and structural optimization is verified. In summary, this paper proposes an analytical model for PMLM vibration analysis that quantitatively links structural parameters to vibration responses, enabling targeted design strategies for low-vibration PMLMs. The method offers a practical theoretical tool for rapid vibration evaluation and suppression during the initial design phase.
富仁杰, 董婷, 张博, 冯威, 赵桂林. 基于欧拉梁理论的永磁直线电机振动解析计算与分析[J]. 电工技术学报, 2026, 41(14): 4706-4717.
Fu Renjie, Dong Ting, Zhang Bo, Feng Wei, Zhao Guilin. Vibration Analytical Calculation and Analysis of Permanent Magnet Linear Motor Based on Euler Beam Theory. Transactions of China Electrotechnical Society, 2026, 41(14): 4706-4717.
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2026, Vol. 41 
