Quadratic Approximation Method for the Limit Value of Magnetic Stiffness in a High Temperature Superconducting Levitation System

A quadratic approximation method for the limit value of magnetic stiffness in a high temperature superconducting levitation system is presented. The levitation configuration discussed is that of a cylindrical permanent magnet (PM) placed above a coaxial high temperature superconductor (HTS). The magnetic levitation force between the PM and the HTS is gained based on Kim's critical model and Ampère circulation theorem. The central issue of magnetic stiffness associated with the hysteresis of levitation force is discussed. Firstly, To a given levitation gap between the PM and the HTS, the approximate values of magnetic stiffness is obtained corresponding to different displacement increments from 0.05 mm to 3 mm. In the first approximation the least square method is used for curve fitting force-displacement table. Secondly, the limit value of magnetic stiffness is gained at the zero displacement increment in the polynomial fitting curve of the first approximate values. The results show that the limit value of magnetic stiffness is dependent on the large levitation gap and the movement direction of the levitation object. The given displacement increments, such as 0.5 mm or 1 mm, are more suitable in superconducting levitation experiments. The difference between experiment data of magnetic stiffness and the limit ones is investigated.