Characteristics of cross stiffness with different physical and geometrical parameters in a high-temperature superconductor levitation system

Highlights: • In both ZFC and FC, the absolute value of $k_{zx}$ at every $x_{wp}$ increases with $B_0$. • $k_{zx}$ cannot be significantly enhanced even decreases by improving $J_c$. • In ZFC, $k_{zx}$ is the largest at each $x_{wp}$ in the two passes of the PM as $\alpha =1.0$. • In FC, $k_{zx}$ has different characteristics with $\alpha$ at different $x_{wp}$. • $k_{zx}$ decrease with $\beta$ at every $x_{wp}$ under FC in the second pass of the PM. 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.