IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011 4171 Design and Realization of a Linear Magnetic Gear Robert C. Holehouse, Kais Atallah, and Jiabin Wang Department of Electronic and Electrical Engineering, The University of Sheffield, Sheffield S1 3JD, U.K. This paper describes a 3.25:1 linear magnetic gear which has been designed and prototyped to meet the performance requirements of an aerospace application. It has been shown that the force capability of the linear magnetic gear is very sensitive to the spacing between the pole-piece rings and that a 5% reduction in the distance between pole pieces may result in a 30% decrease in force transmission capability. It has also been shown that for a given output stroke requirement, in order to maximize volumetric force density, magnetic designs with large airgap diameters and shorter high-speed armature axial lengths would be preferred. Index Terms—Linear machine, linear magnetic gear, permanent magnets. I. INTRODUCTION T HE increasing demand for high force density linear ac- tuators is currently being met almost exclusively by em- ploying a hydraulic actuator or an electromechanical actuator with a lead/ball/rollerscrew and nut to transform rotary motion to linear motion. However, in addition to the poor hydraulic power transmission density, the reliability and maintenance re- quirements of both actuation systems as well the higher risk of jamming of electromechanical actuators can be significant issues. Therefore, despite their relatively poor thrust force density, linear electromagnetic actuators are increasingly being consid- ered for applications spanning from industrial automation to au- tomotive active suspension [1], [2]. An alternative approach to increase the force transmission capability of electromagnetic ac- tuators is to employ a linear magnetic gear with a linear brush- less permanent-magnet machine [3], [4]. Further, since a linear magnetic gear exhibits inherent over- load protection, viz. when the output armature is subjected to a load force which is larger than the pull-out force, it will slip harmlessly, thereby preventing physical damage to the magnetic gear and the systems connected to it. This feature is very impor- tant for aerospace applications. The paper describes a 3.25:1 linear magnetic gear which has been designed and prototyped to meet the performance require- ments of an aerospace application. It has been shown that manu- facturing tolerances can have a significant effect on transmitted force capability. II. FORCE DENSITY The linear magnetic gear considered in this paper has the same principle of operation as the rotary magnetic gear de- scribed in [5]–[8]. It consists of three tubular armatures with the outer and inner carrying arrays of permanent magnets having different numbers of poles and the intermediate having a set of Manuscript received February 21, 2011; accepted May 07, 2011. Date of cur- rent version September 23, 2011. Corresponding author: K. Atallah (e-mail: k.atallah@sheffield.ac.uk). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2011.2157101 annular ferromagnetic pole pieces (Fig. 1), which modulate the magnetic fields produced by the magnet arrays. It may be shown [3] that when the outer permanent-magnet armature is kept stationary, the gear ratio between high-speed armature (inner permanent magnet armature) and pole-piece ar- mature is given by (1) where is the number of active ferromagnetic pole pieces and is the number of pole pairs on the high-speed armature. In [3], it was shown that an active force density of 2 MN/m could be achieved. However, unlike rotary magnetic gears, not all magnetic components are simultaneously contributing to force transmission, therefore, the magnetic volumetric force density, where the volume encompassing all of the magnetic components is considered, depends on the stroke and gear ratio. If is the active force density, where only the volume of the magnetic components active at any instant of time is con- sidered, the transmitted force is given by (2) For a gear ratio , an output stroke and a high-speed ar- mature of active length , the total length of the gear will be (3) and (4) resulting in a volumetric force density (5) Fig. 2 shows the variation of the gear force density with the gear ratio. It can be seen that the highest force density is achieved when the output stroke is significantly shorter than the length of the high-speed armature. It can also be seen that the force density decreases with an increasing gear ratio. For many applications, with a specified output stroke and force requirement, it is the overall system force density that is of most interest (i.e., the combined density of the gear and the high-speed low-force machine driving it). If a machine of force 0018-9464/$26.00 © 2011 IEEE