Design and measurement of a passive thrust magnetic bearing for a bearingless motor Eric Severson * , Astrid Røkke † , Robert Nilssen † , Tore Undeland † , and Ned Mohan * * Department of Electrical and Computer Engineering University of Minnesota, Minneapolis, Minnesota 55455 Email: sever212@umn.edu † Department of Electric Power Engineering Norwegian University of Science and Technology, Trondheim, Norway Email: Astrid.Roekke@ntnu.no Abstract—The design and construction of a permanent magnet thrust bearing for a bearingless motor is presented and a measurement technique is proposed to characterize the bearing. Optimal design of a bearingless motor requires the machine designer to be aware of the axial bearing’s performance under simultaneous axial and radial displacement. A simple, low-cost test setup which requires only two single-axis load cells is proposed and evaluated to make these measurements on the magnetic bearing stator. The measurement data are found to be in reasonable agreement with finite element calculations and to satisfy Earnshaw’s theorem, where the sum of stiffnesses in the three axes must be zero. The measurement technique displayed good test-retest reliability, with repeated radial force data having an average standard deviation of 2.1% for radial displacements greater than 0.5 mm and axial force data having a typical error of 0.9%. Index Terms—magnetic bearing, bearingless motor, force mea- surement, magnetic levitation. I. I NTRODUCTION Bearingless electric machines are able to utilize the same iron to act as both a motor/generator and a magnetic bearing. These machines have been of recent interest for applications that require either high rotational speed or a clean environment where the rotor must be located in a sealed chamber [1]–[3]. Typically, bearingless machines are able to provide magnetic bearing functionality in the radial and tilting directions but rely on a separate bearing for axial support. Such machines are most efficient when the motor has a vertical shaft and gravitational forces are counteracted by this bearing which, for the applications listed above, is typically a passive magnetic bearing. Unlike axial mechanical bearings, axial magnetic bearing designs have considerable unstable radial forces and variation in the axial stiffness when the rotor becomes eccen- tric. When bearingless machines are powered down, their rotor is allowed to eccentrically rest upon ”touchdown” or ”backup” bearings in a position where such undesirable effects in the axial magnetic bearing can be highly pronounced. For the bearingless machine designer, the force required to move the rotor from “rest” to a stable rotating position is a significant factor in determining the number of ampere-turns required for the suspension winding. Increasing the ampere- turns of the suspension winding decreases the space available for the torque winding and thus decreases the torque density of the machine. It is therefore desirable that the design of the external magnetic bearing minimize the unstabilizing radial forces and necessary that changes in the radial and axial stiffness as a function of radial and axial displacement be accurately measured. The design of an inexpensive, repulsive ring magnetic bearing utilizing neodymium magnets is considered for a bearingless ac homopolar machine. The radial unstabilizing force and changes in axial stiffness due to radial and axial displacement are explored through 3D finite element analysis, and a hardware prototype is constructed to validate the bearing performance with the proposed test method. The bearingless ac homopolar machine has been presented in [1], [4], [5] and is of interest to the authors as a vertical shaft machine for application in flywheel energy storage. Several different measurement techniques for radial and axial force and stiffness values are found in the literature [2], [3], [6]–[15]. The only approach capable of measuring forces as a function of both axial and radial displacement uses an expensive three-axis load cell and an automated x-y-z cross table [6]. This work proposes an alternative technique which requires only two inexpensive single-axis load cells and a manual x-y table. It is shown that this technique is able to measure the radial and axial forces of a magnetic thrust bearing over its entire range of operation. In this paper: conventional techniques to measure radial and axial force/stiffness are reviewed; the design of a passive magnetic bearing for a bearingless ac homopolar machine through finite element analysis is presented; the proposed mea- surement technique is described; finally, a hardware prototype is constructed and used to characterize the designed magnetic bearing. II. CONVENTIONAL MEASUREMENT TECHNIQUES A. Measurement goals Conventional approaches to radial and axial force and stiffness measurement are used in [2], [3], [6]–[15]. These measurements are made in test setups that include bearingless machines in [2], [3], [6]–[9]. In all of the aforementioned works, axial and radial force/stiffness are measured as a