In this paper, two artificial magnetic particles (1#, 2#) with known magnetic parameters were taken as the objects, a finite element model based on Gauss’s law was established for the calculation of the transient Maxwell magnetic stress tensor on the surfaces of particles and kinetic study, a high-speed camera was used to obtain the motion behaviors of magnetic particles in comparison with the simulation. According to the results of multiple simulation-experiment comparisons, the motion behaviors of magnetic particles in the finite element simulation were consistent with experimental phenomena under the identical conditions, indicated that the accuracy of the model is reliable. In the comparison of two kinds of magnetic force calculations, the magnetic force FM based on the Gaussian formula had a similar tendency to FD based on the kinetic calculations, and since the FM was obtained by converting the surface tension of particles, it more accurately reflected the overall magnetic force and magnetic torque acting on the particles. Kinetic analysis showed that the magnetic force acting on a particle was strictly dependent on its magnetization, dynamic and non-uniform magnetization caused the magnetic particle to be subjected to magnetic force and magnetic torque in the non-uniform magnetic field, resulting in displacements and flips. In addition, compared to the particle release attitude, the influence of the distribution of magnetic substance and the particle’s release position on the displacement was particularly significant. The 3D finite element model established for dry magnetic separation can be further used for the study of dynamic, non-uniform magnetization and the force of magnetic particle or grain groups, which is of certain significance for the kinetic study of magnetic separation and improving research of magnetic separation equipment.

中文翻译：

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基于高斯-麦克斯韦磁应力张量的干磁分离动力学研究：一种三维有限元法 （FEM）


本文以两个已知磁参数的人工磁粒子（1#、2#）为对象，建立了基于高斯定律的有限元模型，计算了粒子表面的瞬态麦克斯韦磁应力张量和动力学研究，利用高速相机获得了磁粒子的运动行为与仿真结果的对比。根据多次仿真-实验对比的结果，有限元仿真中磁粒子的运动行为与相同条件下的实验现象一致，表明模型的准确性是可靠的。在两种磁力计算的比较中，基于高斯公式的磁力 FM 与基于动力学计算的磁力 FM 具有相似的趋势，并且由于 FM 是通过转换粒子的表面张力获得的，因此它更准确地反映了作用在粒子上的整体磁力和磁力矩。动力学分析表明，作用在粒子上的磁力严格取决于其磁化强度，动态和非均匀磁化强度导致磁粒子在不均匀磁场中受到磁力和磁矩，从而导致位移和翻转。此外，与粒子释放姿态相比，磁性物质的分布和粒子的释放位置对位移的影响尤为显著。 为干磁分离建立的三维有限元模型可以进一步用于动态、非均匀磁化强度和磁粒或晶团力的研究，对磁分离的动力学研究和提高磁分离设备的研究具有一定的意义。