Diamagnetic Levitating Rotor

This paper analyzes some basic design aspects for a three phase diamagnetic levitating rotor. A proposed design uses a triangular configuration of magnets for a levitating rotor. A formula for finding a the approximate levitation point of the rotor is given. The proposed system uses three phase alternating current and a nine coil configuration to drive the levitating rotor. For this configuration, moment plots for different radial positions and tilt angles of the coils are given for a specific coil geometry. In addition, a way to find the effectiveness of finitely thick diamagnetic plates by using the method of images is also presented with normalized plots for some common, cylindrical NdFeB magnet geometries. Introduction Diamagnetic levitation has been a curiosity for decades [1-2]. All materials are diamagnetic though the phenomenon is weak and is often eclipsed by other magnetic affects like paramagnetism and ferromagnetism. Diamagnetism, like all magnetic effects, comes mainly from quantum mechanical interactions of electrons in atoms with externally applied magnetic fields (see [3-5] for more detailed information about this). For information about stability and stable levitating regions for diamagnetically stabilized magnets, see [1-2]. Though a few applications for diamagnetism have been proposed, but because the effect is very weak [1-2] there are few useful engineering applications. With NdFeB magnets, diamagnetic levitation can be applied to engineering applications at small scales. This paper explores using diamagnetism for creating a millimeter scale levitating rotor that could be scaled to microscales for MEMS applications and focuses on some design issues of a levitating rotor. Structure & Design Figure 1 shows the basic layout for a diamagnetic rotor using a triangular configuration for the levitating magnets. The magnets are bonded to light weight but rigid structure that constrains the levitating magnets in an equilateral triangular configuration. The rotor is levitated by using a lifter magnet placed about the rotor and stabilized by using two plates of pyrolitic graphite placed directly above and below the rotor. Estimating the levitation position below the lifter magnet can be done by using a force balance where the weight of the levitating magnets is balanced by the magnetic attraction from the lifter magnet: mg− ∫ Idl×B = 0 whereB is the field density from lifter magnet, the I is the current along a circular current loop (thin cylindrical magnets can be approximated this way with I = Mt , M is magnetization and t is the magnet’s thickness). Only the radial component of B contributes to vertical forces on the levitating magnets and an approximation for Br is − 1 2 r ∂Bz ∂z , where Bz is the z component along the z axis [4, pg. 62]. Treating the lifting magnet as a cylindrical ribbon current (solenoid) and applying the Biot Savart law gives the following expression for Bz Levitating Rotor top view 10 mm 3 mm side view 1.6 mm 0.7 mm (a) (b) stablizing pyrolitic graphite plates suspending magnet rotor Diamagnetic Suspension H