Abstract-This paper identifies an abstraction that is found in the equations that describe the 3D interaction between cuboidal permanent magnets and applies this to the magnetic design of a gravity compensator. It shows how the force between magnets and its position-sensitivity, important design parameters for magnetically levitated 6-DoF gravity compensators, may be translated into the magnetic domain and verifies this with 3D analytical models. With this information, a number of basic gravity compensator topologies is derived. These topologies are subsequently investigated in more detail, with specific focus on combining a high force with low position sensitivity.

The development of sophisticated advanced vibration isolation is important because even the minutest vibrations have disastrous effects on the performance of static and moving parts in high-precision machines. This paper concerns with the isolation of these vibrations for a large static body in an advanced micro-lithographic system, where a passive/active electromagnetic solution is presented. In these configurations passive permanent magnets (PM) provide the gravity compensation and active electromagnets the accurate positioning. This paper only considers the applicability of a passive magnetic solution for this high force gravity compensation application, or, more specifically, the influence of various PM array topologies on the force density. Further, fast-solving analytical models are presented and consequently are used to illustrate the feasibility of using passive permanent magnets for gravity compensation in this demanding high precision industrial application.

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Purpose -The purpose of this paper is to present novel analytical expressions which describe the 3D magnetic field of arbitrarily magnetized triangular-shaped charged surfaces. These versatile expressions model that the field of triangular-shaped permanent magnets (PMs) are very suitable to model skewed slotless machines. Design/methodology/approach -The analytical 3D surface charge method is normally used to provide field expressions for PMs in free space. In this paper, the analytical surface charge integrals are analytically solved for charged right-triangular surfaces. The resulting field is compared with that obtained by finite element modeling (FEM) and subsequently applied in two examples. Findings -The comparison with FEM shows that the 3D analytical expressions are very accurate and exhibit very low-numerical noise. These fast-solving versatile expressions are therefore considered suitable to model triangular-shaped or polyhedral-shaped PMs.Research limitations/implications -The surface charge method assumes that the relative permeability is equal to 1 and therefore soft-magnetic materials need to be modeled using the method of images. The PMs are assumed to be ideal in terms of homogeneity, magnetization vector, permeability, demagnetization, and geometrical tolerances. Practical implications -Many applications, such as the subclass of slotless synchronous linear actuators with a skewed PM structure and planar magnetic bearings, are very suitable to incorporate this modeling technique, since it enables the analysis of a variety of performance data. Originality/value -As an addition to the common 3D analytical field expressions for cuboidal or cylindrical PMs, this paper presents novel expressions for magnets having triangular surfaces.