中文摘要：

永磁涡流联轴器能够在无机械接触和磨损的情况下实现转矩的传输，因此广泛适用于许多工业应用场合。该文推导了运动导体涡流问题分别在固定坐标系和运动坐标系下的尤拉表述和拉格朗日表述，证明了两种表述的统一性；基于子域分析方法，提出了一种包含永磁体阵列、气隙、导体和导体背铁四个区域在内的永磁涡流联轴器场域解析模型，对该多层场域边值问题进行了求解，并推导出一种非常简洁的傅里叶级数形式的转矩表达式；为了确保在达到转矩设计要求前提下尽可能节约永磁体材料使用量，基于所建立的永磁涡流联轴器解析模型，提出一种永磁阵列优化方法。通过算例分析，并比较三维有限元分析和实验结果，验证了文中所提出的解析模型及永磁阵列优化方案的有效性。

英文摘要：

Permanent magnet eddy current transmission devices can transfer torque without any mechanical contact and wear and thus they are widely applicable to many industrial applications. The Eulerian formulation and the Lagrangian formulation respectively corresponding to the moving conductor eddy current problem described in moving coordinates and that in fixed coordinates were derived, and the two formulations proved to be equivalent to each other. Based on the subdomain method, a four-layered analytical model of permanent magnet eddy current couplings where the permanent magnet array, the air gap, the conductor and its back iron were taken into account was presented, the multi-layer boundary value problem was solved, and a very simple torque expression represented by the Fourier series was derived. To economize the amount of permanent magnet material as much as possible, an optimization method for exploiting the permanent magnet array was proposed by using the developed analytical model of permanent magnet eddy current couplings. By analyzing the examples and comparing the results obtained by the three-dimensional finite element analysis and the experiments, the effectiveness of the analytical model and the optimization scheme proposed in this paper was verified.