Effect of magnet inclination angle on stability and vibration characteristics of permanent magnet inclined levitation systems

Permanent magnet levitation (PML) systems in maglev transportation and logistics generally exhibit transverse negative stiffness, insufficient self-stability, and poor oscillation self-attenuation. To tackle these issues, this study proposes a permanent magnet inclined levitation (PMIL) system, with the permanent magnet (PM) inclination angle as a key parameter. An analytical magnetic force model considering the PM inclination angle is developed, and the dynamic equations are derived. Through eigenvalue analysis, static characteristic analysis, and free/forced/random vibration simulations, the system’s dynamic response laws and nonlinear evolution mechanisms are revealed. Simulations compare dynamic responses of nonlinear and linearized models and evaluate anti-disturbance performance under random excitation. Results show that the inclination angle, levitation gap, and transverse offset jointly determine nonlinear force behaviors. Key parameters, such as system mass and equivalent stiffness coefficients, have critical thresholds that trigger stability transitions. Under small disturbances, the nonlinear model shows slower vibration decay and multi-frequency peaks than the linearized model. Frequency responses exhibit DOF-dependent characteristics: the levitation direction exhibits full-band amplitude variations, while lateral and roll directions only show local differences in the resonant band. Notably, increasing the PM inclination angle monotonically enhances system stability and vibration convergence, with anisotropic regulatory effects. However, the applicability of the linearized model declines significantly as the inclination angle rises, being only valid for small angles. This work establishes a theoretical framework for understanding the nonlinear dynamic behavior of PMIL systems, clarifying the regulatory mechanism of PM inclination angle for system stability and defining the applicable boundaries of the linearized model.