A Magnetic and Mechanical Force Model for the Design of an Archimedean Spiral Flexure Bearing for a Linear Direct-Drive Electromagnetic Actuator

This paper deals with the presentation of a theoretical model developed to help the design of a suspension guiding element of a linear direct-drive magnetic actuator using Archimedean spiral flexure bearings. While most of current approaches only focus on the linear force of this actuator, this paper aims to emphasis the radial force evolution with off-centering of the moving part, eventually allowing a precise dimensioning of the guiding element. The first part of the paper is dedicated to the theoretical calculation of both the magnetic axial force and the magnetic radial force acting between the magnetized moving part and the stator part of the actuator. This calculation is led with a three-dimensional (3-D) to 2-D magnetic permeance network. In the second part of the paper, another theoretical model is led to calculate both the axial and radial mechanical behavior of the flexure bearings also used as springs. The stiffness of the spring is calculated taking into account its parameters versatility, namely in terms of geometry variation and relative to the number of spiral arms. A comparison between the models, the finite element method and the measurements on a prototype are also proposed to validate both models that eventually give acceptable results. The combination of both models-the magnetic one and the mechanical one-enables a fast and accurate evaluation of the viability of the actuator design for the engineer.