Abstract
The effect of minor loop size on the magnetic stiffness has not been paid attention to by most researchers in experimental and theoretical studies about the high temperature superconductor (HTS) magnetic levitation system. In this work, we numerically investigate the average magnetic stiffness obtained by the minor loop traverses Δz (or Δx) varying from 0.1 mm to 2 mm in zero field cooling and field cooling regimes, respectively. The approximate values of the magnetic stiffness with zero traverse are obtained using the method of linear extrapolation. Compared with the average magnetic stiffness gained by any minor loop traverse, these approximate values are Not always close to the average magnetic stiffness produced by the smallest size of minor loops. The relative deviation ranges of average magnetic stiffness gained by the usually minor loop traverse (1 or 2 mm) are presented by the ratios of approximate values to average stiffness for different moving processes and two typical cooling conditions. The results show that most of average magnetic stiffness are remarkably influenced by the sizes of minor loop, which indicates that the magnetic stiffness obtained by a single minor loop traverse Δz or Δx, for example, 1 or 2 mm, can be generally caused a large deviation.
Highlights
Magnetic stiffness between high temperature superconductor (HTS) bulks and magnetic source is one of the important parameters in the bulk applications, such as magnetic bearing in flywheel system[1] and magnetic levitating transporter.[2]
When the permanent magnet (PM) moves vertically or laterally relative to the HTS, the average magnetic stiffness is obtained by the minor loop traverses ∆z varying from 0.1 mm to 2 mm is respectively addressed in zero field cooling (ZFC) and field cooling (FC)
As the PM passes through some specially positions, the approximate values are not close to the average magnetic stiffness produced by the smallest minor loop traverses in FC
Summary
Magnetic stiffness between high temperature superconductor (HTS) bulks and magnetic source (for example, permanent magnets) is one of the important parameters in the bulk applications, such as magnetic bearing in flywheel system[1] and magnetic levitating transporter.[2]. Cross stiffness kzx means that a horizontal displacement results in a change in the vertical force. It is obvious that the magnetic stiffness kzz, kxx and kzx can gain exact values when the minor loop size ∆z or ∆x approaches to zero. Because of the irreversible nature of flux penetration, the minor loop size effects on its slope, i.e., the magnetic stiffness. Some researchers measured the magnetic stiffness by a very small reverse displacement of 20 μm in order to reduce the experimental errors.[6] So small minor loop was usually hard to realize in the experiments of HTS magnetic levitation system. The size of minor loop was 1 or 2 mm in the most measurements of the magnetic stiffness.[7,8,9,10] In these measurement, the average
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