Electrostatic Positioning of Diamagnetically Levitating Motion Stages

Abstract

Diamagnetism can be used for energy-less levitation, while allowing for friction-free movement of objects in vacuum conditions. A very suitable material can be found in Highly Oriented Pyrolytic Graphite(HOPG), which not only has relatively high diamagnetic properties, but also electrical properties which allow for contactless actuation through electrostatic forces. These properties open up the possibility for the design of a multiple degree-of-freedom(DOF) levitating precision motion stage. To this end a design was created consisting of a permanent magnet array, which is covered by a thin PCB, housing multiple electrodes. Above this PCB a square HOPG plate was made to levitate, which can be actuated in the vertical and lateral directions, as well as be rotated out-of-plane. Analytical models and FEM simulations were produced to find the dimensions of this design so that optimal performance could be achieved. An experimental setup was designed and manufactured to measure the performance of the design. It was shown that for voltages below Dutch main's voltage (230V), movements within the micrometer and millirad range could be achieved. Because of environmental disturbances, it was not possible to show movement at the nanometer scale, since these disturbances were in the submicron range. It can however be analytically calculated that for actuations of 1V, displacements of less than 1nm can be achieved. Another design challenge provided itself in the separation of the DOF's, since the electrostatic force always acts in the vertical direction, due to the attraction between the electrodes and the levitating plate. That's why the electrode set-up on the PCB was engineered in a way that rotations produced by lateral displacements could be cancelled by counter-actuation. This method was experimentally proven to work. It was then also shown that with this multiple electrode set-up, movement could be produced along a diagonal line, which shows that the plate could be made to move in multiple dimensions at once, as to be expected of a multiple DOF precision motion stage. This precision motion stage was manufactured at a fraction of the costs of comparable commercial multiple DOF precision motion stages that are currently available.