J.M.M. Rovers

Analysis Method of the Dynamic Force and Torque Distribution in the Magnet Array of a Commutated Magnetically Levitated Planar Actuator

This paper concerns the analysis of the dynamic forces and torques acting on the magnets in a Halbach permanent magnet array of a magnetically levitated moving-magnet planar actuator. A new analysis tool is presented which predicts the dynamic force and torque distribution on the magnet array. This design tool uses lookup table data, which are generated by numerically solving the Lorentz force and torque integral, to describe the force and torque between each magnet and coil in the topology. It offers a fast and accurate solution for the analysis of magnetically levitated planar actuators. The results for two different commutation methods are presented.

Overview of Analytical Models for the Design of Linear and Planar Motors

In this paper, an overview of analytical techniques for the modeling of linear and planar permanent-magnet motors is given. These models can be used complementary to finite element analysis for fast evaluations of topologies, but they are indispensable for the design of magnetically levitated planar motors and other coreless multi-degrees of freedom motors, which are applied in (ultra) high-precision applications. The analytical methods describe the magnetic fields based on magnetic surface charges and Fourier series in 2-D and 3-D.

Analytical Calculation of the Force Between a Rectangular Coil and a Cuboidal Permanent Magnet

This paper concerns the analysis of the force between a rectangular coil and a cuboidal permanent magnet. The magnetic flux density distribution due to the permanent magnet is determined using the surface charge method, and an analytical equation is obtained for the Lorentz force on a cuboidal current carrying volume. These analytical results are used to calculate the Lorentz force on a rectangular coil modeled using four current carrying volumes. The calculations are verified both by measurements and numerical integration. These results can be used in the design and real-time control of planar actuators for industrial levitation/positioning platforms or other (ironless) actuators.

Multiphysical analysis of moving-magnet planar motor topologies

Moving-magnet magnetically levitated planar motors are considered for use as a wafer stage in the semiconductor lithographic industry. This puts high requirements on the accuracy and the dissipated power and cooling performance of such motors. The goal of this paper is to analyze the multi-physical behavior of three moving-magnet planar topologies using an electromagnetic model, a mechanical model, and a thermal model. This behavior is evaluated using a trajectory and performance criteria which are representative for the application. The static and dynamic behavior are evaluated.

Calculation of the Static Forces Among the Permanent Magnets in a Halbach Array

This paper concerns the analysis of the interaction force among the permanent magnets (PM) in a Halbach array as used in a moving-magnet planar actuator. The goal is to analyze the magnitude of these forces and to what extent the mechanical construction of an aluminium plate, on which the permanent magnets are mounted, is deformed by the interaction force among the permanent magnets. The interaction forces are obtained from analytical models which have been verified with an electromagnetic Finite Element Method (FEM) simulation. These results are used in a mechanical FEM simulation to determine the deformation of the magnet assembly.

Modeling of Relative Permeability of Permanent Magnet Material Using Magnetic Surface Charges

For high-accuracy applications, accurate electromagnetic modeling tools are required. One commonly used technique to model the magnetic field of permanent magnets is the magnetic surface charge method. In principle, this method assumes a volume without boundaries, i.e., a relative permeability equal to unity everywhere in the volume. In previous publications, material with a relative permeability unequal to unity in the vicinity of the permanent magnet was modeled using the method of images, however, commonly, the relative permeability of the permanent magnet material itself was neglected. This paper presents a method to take the permeability of the magnetic material into account.

Force and Torque Errors Due to Manufacturing Tolerances in Planar Actuators

This paper discusses the force and torque errors in moving-magnet planar actuators due to manufacturing tolerances. Two different planar actuator topologies are under consideration, and errors due to variations in the magnetization vector, the magnet positions, and the coil positions are evaluated by Monte-Carlo simulations. The effect of these force and torque errors on the positioning accuracy of the planar actuators are estimated from the process sensitivity transfer of a suitable controller.

Effects of eddy currents due to a vacuum chamber wall in the airgap of a moving-magnet linear actuator

This paper discusses the effects of eddy currents induced in an electrically conducting plate which is placed in the airgap of a linear synchronous actuator with moving permanent magnets. The eddy currents induced in this plate, which is part of a controlled atmosphere chamber, cause not only damping but also deteriorate the actuator performance by disturbing the position measurement with Hall sensors. Furthermore, feed-forward controllers are less effective due to the suppression of high frequent armature fields. These effects are analyzed with an analytical model and verified with finite element simulations and measurements.

Design and measurements of the Double Layer Planar Motor

Moving-magnet magnetically levitated planar motors are considered for use as a wafer stage in the semiconductor lithographic industry. This puts high requirements on the accuracy and the dissipated power and cooling performance of such motors. A novel planar motor topology is developed, which consists of a double layered coil structure and is therefore referred to as Double Layer Planar Motor. This planar motor is analyzed using an electromagnetic model, a mechanical model, and a thermal model. This behavior is evaluated using a trajectory and performance criteria which are representative for the application. Both the static and the dynamic behavior is evaluated. Measurements on a prototype are presented.

Disturbance Effects of Electrically Conductive Material in the Air Gap of a Linear Permanent Magnet Synchronous Motor

This paper discusses the disturbance of the electromagnetic performance of coreless linear synchronous permanent magnet actuators due to an electrically conductive material in the air gap which is part of the cooling system. Time-varying magnetic fields in the air gap give rise to induced eddy currents in the conductive material. These induced currents disturb the magnetic fields of the current-carrying coils and the magnet array. Different measurements are presented differentiating between the disturbance of the coil field and the magnet field. The effects of these disturbances on the motor performance are discussed. Suggestions are given to make changes to the shape of the conductive material to minimize these disturbances.