High-speed electrical machines (HSEMs) are becoming more popular in applications such as air handling devices. Using surface-mounted permanent magnet (PM) rotors manufactured from rare earth metals, they provide benefits over their mechanical transmission counterparts. However, these PMs have low tensile strength and are prone to failure under large centrifugal loads when rotating. Therefore, retaining sleeves are used to hold the PMs in compression to eliminate tensile stress and reduce failure risk. The magnets are also often held on a back iron or carrier, forming an assembly of three cylinders. The ability to predict these stresses is extremely important to rotor design. Current published work shows a lack of exploration of analytical methods of calculating these stresses for three-cylinder assemblies. This paper shows the development of plane stress, plane strain and generalised plane strain (GPS) theories for three cylinders. For a range of rotor designs, these theories are compared with finite element analysis (FEA). GPS is shown to be more accurate than plane stress or plane strain for the central region of long cylinders. For short cylinders and for the ends of cylinders, all three theories give poor results.

高速电机（HSEM）在诸如空气处理设备之类的应用中变得越来越流行。使用稀土金属制成的表面安装式永磁（PM）转子，它们比机械传动的同类产品更具优势。然而，这些PM的抗张强度低，并且在旋转时在大的离心载荷下易于失效。因此，使用固定套筒将PM保持在压缩状态，以消除拉伸应力并降低故障风险。磁体通常也被固定在护铁或载体上，形成三个圆柱体的组件。预测这些应力的能力对转子设计极为重要。当前发表的工作表明缺乏对计算三缸组件这些应力的分析方法的探索。本文展示了三个圆柱体的平面应力，平面应变和广义平面应变（GPS）理论的发展。对于一系列转子设计，将这些理论与有限元分析（FEA）进行了比较。对于长圆柱体的中心区域，GPS显示的精度比平面应力或平面应变的精度高。对于短圆柱体和圆柱体端部，这三个理论都给出了较差的结果。