Study on lateral stability of levitation modules for low- and medium-speed maglev trains

In order to study the lateral dynamics stability of the levitation module of low- and medium-speed maglev train, the motion equation is simplified by reasonable assumptions, and the simplest lateral dynamics model is established under the premise of retaining the lateral dynamic characteristics of the levitation module. The model can be characterized by a non-autonomous differential equation with periodic coefficients, which can be transformed into a damped Mathieu equation under certain conditions, with its stability equivalent to that of its Poincaré mapping. The stability of the system can be determined by whether the largest modulus of the eigenvalues of the mapped coefficient matrix is > 1. Then, the sensitivity frequency of the vertical electromagnetic force is obtained by calculating the stability domain of the equation in the parameter space. When the variation frequency of the vertical electromagnetic force is approximately equivalent to the sensitivity frequency, the lateral dynamics model is more likely to be unstable. Besides, the variation amplitude and variation frequency of the vertical electromagnetic force, and other factors such as vehicle load and system damping will also change the stability of the lateral dynamics model. However, due to the uncontrollability of these factors, it is necessary to install a lateral damper for the levitation module to improve the lateral stability.