直流磁场控制电磁悬浮熔炼旋转稳定性的理论分析

Theory analysis of steady magnetic field on rotational stability of electromagnetic levitation melting

在没有直流磁场和存在直流磁场两种情况下 ,对悬浮于高频磁场的导电球在旋转扰动情况下的稳定性进行了理论分析 .悬浮感应器电流的无量纲角频率为ω-.在不存在直流稳定磁场的固态球悬浮情况下 ,存在一个临界无量纲角频率ω-c.当ω-<ω-c,球形悬浮试样对于旋转干扰是稳定的 ;当ω->ω-c,球形悬浮试样对于旋转干扰是不稳定的 .在直流稳定磁场的固态球悬浮情况下 ,存在一个无量纲角频率下限ω-c,1 和上限ω-c,2 .当ω-<ω-c ,1 或者ω->ω-c,2 ,球形悬浮试样对于旋转干扰是稳定的 ;当ω-c,1 <ω-<ω-c ,2 ,球形悬浮试样对于旋转干扰是不稳定的 .增大直流磁场可以增大ω-c ,1 ,减小ω-c ,2 ,即可以提高悬浮稳定性 .当直流磁场场强Bd达到某一临界值Bd ,c,球形悬浮试样在任意ω-情况下 ,总是稳定的 .相对于固态试样悬浮 ,液态试样悬浮稳定性要下降 .直流磁场可以减小熔体动力学失稳和熔体飞溅的趋势 。

The stability of an electrically conducting sphere levitated in a high frequency magnetic field with respect to rotational disturbances is analyzed theoretically with and without steady magnetic field respectively. The dimensionless angular frequency of inducer's current is (&omega;) over bar. Under the conditions of without steady magnetic field and the sphere is solid, there is exists a critical dimensionless angular frequency (&omega;) over bar (c). As (&omega;) over bar < (&omega;) over bar (c), the levitation of sphere sample is stable; as (&omega;) over bar > (&omega;) over bar (c), the levitation of sphere sample is unstable. Under the conditions of existing steady magnetic field and the sphere is solid, there are exist a lower limit dimensionless angular frequency (&omega;) over bar (c,1) and an upper limit dimensionless angular frequency (&omega;) over bar (c,2). As ($) over bar < (&omega;) over bar (c,1) or (&omega;) over bar > (&omega;) over bar (c,2), the levitation of sphere sample is stable; as (&omega;) over bar (c,1) < (&omega;) over bar < (&omega;) over bar (c,2) the levitation of sphere sample is unstable. The increasing of steady magnetic field can make (&omega;) over bar (c,1) increase and (&omega;) over bar (c,2) decrease. As the strength of steady magnetic field B-d reaches the critical value B-d,B-e, the levitation of sphere sample is always stable. Relative to that of solid sphere, the levitation stability of liquid sphere is decreasing. Steady magnetic field can reduce the hydrodynamic destabilization and melt splashing and improve the levitation stability of liquid sphere sample.