A Study On The Static Characteristics Of High-temperature Superconducting Levitation Body When Lateral Traversing

The interaction between a permanent magnet (PM) and a high temperaturesuperconductor (HTS) has drawn researchers' attention for the last nearly twentyyears because of the possible applications of HTSs, such as flywheel energystorage systems and magnetic bearing systems. Now, in the study of the verticaland lateral forces, the experimental researches are more than the theoretical ones,and also the researches on levitation force are more than these on lateral force. Inthis paper, for a typical superconducting levitation system composed of a HTS anda PM, the vertical and lateral forces are considered, and then the some very usefulresults are obtained from modification of the frozen-image method and simulationof the vertical and lateral forces.The frozen-image method is modified. The exact solutions are obtained forthe point magnetic dipole over a flat nonideal type-â…¡superconductor using of thevertical and horizontal movement images. Comparing with the frozen-imagemethod, our method can give the lateral force in zero field cooling and thehysteresis in the vertical and lateral forces. The two characteristics can not beobtained by the frozen-image method. In this case, the vertical stiffness duringvertical traverses and the lateral and cross stiffnesses during lateral traverses areobtained by the analytic expressions of vertical and lateral forces. The vertical andlateral forces are obtained by the modified frozen-image method when the PMmoves arbitrarily. The levitation force during vertical traverses and the lateral andvertical forces during lateral traverses are recalculated by the modifiedfrozen-image method and the equivalent current loops for all images.The vertical and lateral forces are simulated. A set of analytic expressions ofmagnetic field distribution are derived, not only for one rectangular PM bulk, butalso for n rectangular PM bulks arranged by alternating north pole and southpole of the magnet. The major characteristics of magnetic filed produced by one,two or three PM bulks are analyzed. The finite element method and the currentvector potential are adopted in the simulations. The numerical methods which canbe used to deal with the electromagnetic field of HTS, static levitationcharacteristics are established. By comparing the numerical results with experimental data, the numerical methods are validated. The vertical and lateralforces, static magnetic stiffnesses are simulated. The calculations show that thoseforces and stiffnesses are significantly influenced by the movement history. In thiscase, the relationship between lateral force and initial cooling condition isinvestigated. A concept of transition cooling height (z_c0) is given. The levitatingbody is laterally stable when the initial CH is less than z_c0, whereas, when CH ismore than z_c0, the levitating body is possibly laterally unstable. The effects of thephysical parameters, the levitating height during lateral traverses and thedimensions of the system on the transition cooling height and the vertical andlateral forces are presented.