IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011 4219 Design and Analysis of Linear Stator Permanent Magnet Vernier Machines Yi Du , K. T. Chau , Ming Cheng , Ying Fan , Yubin Wang , Wei Hua , and Zheng Wang School of Electrical Engineering, Southeast University, Nanjing 210096, China School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong This paper presents a new class of linear permanent magnet (PM) vernier machines which is suitable for low speed and high thrust force applications. The machine is composed of a tubular stator and a tubular translator. The stator consists of an iron core with salient teeth wound with 3-phase armature windings and PMs mounted on the surface of stator teeth. The translator is designed as a simple tubular iron core with salient teeth so that it is very robust to transmit high thrust force. By using the finite element method, the char- acteristics and performances of the proposed machine are analyzed and verified. Index Terms—High thrust force, linear machine, low speed, stator permanent magnet (PM) machine, vernier machine. I. INTRODUCTION L OW speed high thrust force linear machines are more and more attractive for direct-drive applications such as railway traction and wave energy conversion. Compared with the conventional rotary drive system, the linear drive system possesses the merit to eliminate the costly and bulky rotary-to-linear mechanism and the number of energy trans- formation steps can be reduced. Consequently, the system efficiency can be improved and the system size can be minified. In general, the linear machine in the direct-drive system has a bulky size and a large number of poles because of the low-speed operation. Although the use of high energy rare-earth perma- nent magnets (PMs) has significantly improved the force den- sity of linear machines, a conventional linear PM synchronous machine can only offer about 20–30 [1] which is not enough for those low speed, high thrust force applications. Con- sequently, some special machines have been proposed. In [2], a magnetic gear is artfully integrated with a PM brushless ma- chine to achieve low speed motion and high speed machine de- sign simultaneously. However, it involves three airgaps and two moving parts, thus suffering from the difficulty of manufacture. In [3], the PM vernier machine is developed which employs the magnetic gearing effect. However, it suffers from the problems of mechanical integrity and thermal instability since the PMs are located in the rotor. In [4], the vernier hybrid (VH) machine is proposed which can offer the shear stress of 200–250 in theory. In this machine, the PMs are mounted on surface of the stator teeth so that the problems of the mechanical integrity and thermal instability can be avoided. However, the cogging force of this machine is quite large. The purpose of this paper is to design and analyze a new class of linear stator PM vernier (LSPMV) machines which can pro- duce high thrust force, low speed motion, while exhibiting low cogging force. It should noted that the LSPMV machine pro- posed in the paper is a kind of variable reluctance PM machines. Manuscript received February 20, 2011; accepted May 09, 2011. Date of cur- rent version September 23, 2011. Corresponding author: K. T. Chau (e-mail: ktchau@eee.hku.hk). 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.2011.2156392 Its translator has salient teeth only without any PMs or windings, and is similar to that of the PM flux switching, switched reluc- tance and synchronous reluctance machines. However, its stator is fundamentally different from the others, since it incorporates PMs mounted on the stator tooth surfaces. Most importantly, the LSPMV machine makes use of the magnetic gearing principle, based on the relationship between the number of PM poles, the number of armature winding poles and the number of translator teeth, which can significantly reduce the output speed while in- crease the output force, hence improving the force density. In Section II, the configuration of the proposed machine will be described. In Section III, the machine design will be discussed. In Section IV, the characteristics of the proposed machine will be analyzed by using the finite element method (FEM). Finally, conclusion will be drawn in Section V. II. MACHINE CONFIGURATION Fig. 1 shows the configuration of the proposed machine which is composed of a tubular stator and a tubular translator. The stator consists of an iron core with salient teeth wound with 3-phase armature windings and PMs inset on the surface of the stator teeth. The magnetization directions of these PMs are ad- jacent alternant. Thus the magnet flux in the airgap is almost sinusoidal. The translator is designed as a simple tubular iron core with salient teeth so that it is very robust to transmit high thrust force. The proposed LSPMV machine operates similarly as the con- ventional PM vernier machine. The key difference is that the PMs are located in the stator (not in the translator), and the translator teeth function to modulate the magnetic fields pro- duced by the PMs. In order to facilitate the insertion of arma- ture winding, the stator adopts the open slot structure and there is no PM mounted between the adjacent stator teeth. Since this opening does not involve iron core, it will not significantly af- fect the machine performance. Then each of the stator teeth can be considered as a single vernier construction and the phase of the flux linkage in each of them can be modulated through ad- justing the distance between the adjacent stator teeth. Compared with the existing linear VH (LVH) machine, the number of PMs on each stator tooth of the proposed LSPMV machine is not limited to be an even number. Table I shows a comparison between the existing LVH machine and the pro- posed LSPMV machine, where is the pole-pair number of 0018-9464/$26.00 © 2011 IEEE