Cross stiffness is usually defined as a change in the vertical force when the levitating body moves a small lateral displacement in a high-temperature superconductor (HTS) magnetic levitation system. In most of the existing research reports, the improvement of the levitation stiffness is usually focused on the radial (lateral) and axial (vertical) stiffnesses. The cross stiffness should be studied carefully because it can be used to analyze the stability and dynamical properties of the HTS levitations. In this paper, the quantitative properties of the cross stiffness have been investigated by a numerical method. The variations of the cross stiffness at different lateral positions are analyzed for some physical and geometrical parameters, cooling conditions and movement history of a levitated permanent magnet. The reasons for the characteristics of the cross stiffness can be obtained by the vertical force–lateral displacement curves with some minor loops under different parameters and cooling conditions.

交叉刚度通常定义为当悬浮体在高温超导体（HTS）磁悬浮系统中移动较小的横向位移时垂直力的变化。在大多数现有研究报告中，悬浮刚度的改善通常集中在径向（横向）和轴向（垂直）刚度上。交叉刚度应仔细研究，因为它可用于分析HTS悬浮的稳定性和动力特性。本文通过数值方法研究了交叉刚度的定量特性。针对不同的横向和横向刚度变化，分析了悬浮磁石的一些物理和几何参数，冷却条件和运动历史。