Analytical Modeling of Multi-DOF Permanent Magnet Linear Braking via Equivalent Circuit Method

The permanent magnet linear braking (PMLB) has garnered significant attention for its contactless operation and high force density. However, conventional analytical models often exhibit limited accuracy due to oversimplified geometric assumptions and the inability to accommodate the multi degree-of-freedom (DOF) attitude variations of the mover. To address these limitations, this paper presents a novel three-dimensional analytical model based on an equivalent circuit method. Specifically, the permanent magnet (PM) is equivalently represented as a rectangular current carrying coil using the surface current method. The mutual inductance between this equivalent PM coil and the brake coil is calculated via the discrete Neumann formula. A dynamic equivalent circuit is then constructed to determine the induced currents in the brake coil, and the resulting braking force is evaluated using both the energy method and the method of images. The proposed model is thoroughly validated through finite element method (FEM) simulations. Additionally, the impact of various attitude conditions on braking performance is systematically analyzed. Finally, experimental results obtained from a full-scale prototype and measurement system show excellent agreement with the theoretical predictions, thereby confirming the model’s accuracy and practical applicability.