| In recent years,with the wide application of high-temperature superconductors in magnetic levitation bearings and energy storage of flywheels,related research on the experimental and theoretical calculations of the interaction between permanent magnets and high-temperature superconductors has gradually increased.However,in the study of the static characteristics of permanent magnets and superconductors,theoretically systematically discussing the influence of the relative azimuth between permanent magnets and superconductors on the forces and moments on the suspension has not been reported.The calculation method and results in this paper have certain theoretical significance for the design of superconducting magnetic bearing.In this paper,based on the modified frozen-image method,a high-temperature superconducting magnetic levitation model is established when the magnetization direction of the permanent magnet and the c-axis of the superconducting block are at any angle ?.At the same time,the model is used to derive the permanent magnet in the superconductor Analytical expressions of lateral force,vertical force,and moment received at any position above and at any angle.The qualitative comparison with the existing experimental and theoretical results verifies the correctness and reliability of the calculation model in this paper.In this paper,the above force and moment analytical expressions are used to study the vertical force,lateral force and moment of the permanent magnet under different cooling conditions at any position above the superconductor and at any angle of the magnetization direction.It was found under both zero field cooling and field cooling:(1)The magnetization direction angle has a significant effect on the force and moment received by the permanent magnets in vertical cyclic movement and in-plane cyclic movement.(2)The force and moment of the permanent magnet at each selected fixed position are periodically changed with the change of the magnetization direction angle.(3)When the position of the permanent magnet and the direction of magnetization change at the same time,the effect on the force and moment of the permanent magnet is more significant.(4)When the magnetization direction angle is 0°?90°?180°?270°?360°,the permanent magnet is only affected by the vertical force when it moves vertically and cyclically,not by the lateral force and moment.However,comparing the zero-field cooling with the field cooling,it is found that the influence of the magnetization direction angle on the force and moment of the permanent magnet is different except for the similarities in the above four aspects.Mainly reflected in the impact on the change rate of force and moment,hysteresis characteristics,the maximum value,the position of the permanent magnet corresponding to the maximum value,etc.are very different. |
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