Magnetic levitation by rotation

A permanent magnet can be levitated simply by placing it in the vicinity of another permanent magnet that rotates in the order of 200 Hz. This surprising effect can be easily reproduced in the laboratory with off-the-shelf components. Here, we have investigated this novel type of magnetic levitation experimentally and clarified the underlying physics. Using a 19-mm-diameter spherical Nd-Fe-B magnet as the rotor magnet, we have captured the detailed motion of levitating spherical $\mathrm{Nd}$-$\mathrm{Fe}$-$\mathrm{B}$ magnets, denoted floater magnets, as well as the influence of the rotation speed and magnet size on the levitation. We have found that as levitation occurs, the floater-magnet frequency locks with the rotor magnet and, noticeably, that the magnetization of the floater is oriented close to the axis of rotation and toward the like pole of the rotor magnet. This is in contrast to what might be expected by the laws of magnetostatics, as the floater is observed to align its magnetization essentially perpendicular to the magnetic field of the rotor. Moreover, we have found that the size of the floater has a clear influence on the levitation: the smaller the floater, the higher the rotor speed that is necessary to achieve levitation and the further away the levitation point shifts. Despite the unexpected magnetic configuration during levitation, we have verified that magnetostatic interactions between the rotating magnets are responsible for creating the equilibrium position of the floater. Hence, this type of magnetic levitation does not rely on gravity as a balancing force to achieve an equilibrium position. Based on theoretical arguments and a numerical model, we show that a constant vertical field and eddy-current-enhanced damping are sufficient to produce levitation from rest. This enables a gyroscopically stabilized counterintuitive steady-state moment orientation and the resulting magnetostatically stable midair equilibrium point. The numerical model displays the same trends with respect to the rotation speed and the floater-magnet size as seen in the experiments.

Figure 1

The experimental setup, including a closeup of the rotor and floater magnet. The closeup is an image taken with the high-speed camera and where the floater magnet has been painted to indicate its magnetic poles. The floater magnet can clearly be seen to be levitating.

Figure 2

The phase angle, $\phi$, between the floater and the rotor magnets. The phase angle is the angle between the projection onto the $x$-$y$ plane of the respective magnetization vectors of the two magnets, ${\mathbf{m}}_r$ and ${\mathbf{m}}_f$. The levitation distance is the center-to-center distance between the rotor and the floater magnets.

Figure 3

(a) The levitation time as a function of the rotor speed and (b) the initial levitation distance as a function of the rotor speed. For both figures, the color of the dots denotes the mode occurring during levitation. The multicolored dots mean that the mode changes from the left colored mode to the right colored mode, e.g., for the red-blue case, the mode changes from an up-down mode exclusively to a side mode exclusively. The levitation distance is defined as the distance from the center of the spherical magnet of the rotor to the center of the spherical magnet of the floater.

Figure 4

The fall rate of the floater magnet as a function of the motor speed for the semistable region. The error bars are the standard deviation of three experiments for each rotor speed.

Figure 5

(a) The minimum rotation speed to achieve levitation as a function of the diameter of the floater-magnet spheres (blue points, bottom $x$ axis) and remanence (red points, top $x$ axis). (b) The initial levitation distance as a function of the diameter of the floater-magnet spheres (blue points, bottom $x$ axis) and remanence (red points, top $x$ axis) at a rotor speed of 150 Hz for the remanence variation and 300 Hz for the variation of the floater-magnet diameter. The error bars given on (b) are the standard deviation of the position as determined by the tracker software.

Figure 6

The simulation results at various rotor frequencies with the floater position fixed. The rotor is displaced by ${\delta }_r=1\mathrm{mm}$ relative to the rotation axis, yielding a slight vertical $B$ field, the effective damping is $\eta =1\mathrm{Pa}\cdot \mathrm{s}$, both magnetizations are 1.18 T, and the diameters are 12.7 and 19 mm for the floater and rotor, respectively. (a)–(c) The steady-state behavior in the three different dynamical phases for $d=20\mathrm{mm}$: (a),(b) the phase lag, $\phi$, and floater polar angle, ${\theta }_f$, versus time over 25 ms; (c) the transverse components of the normalized floater moment over 150 ms. (d) The dynamical phase of every simulation at various rotor frequencies, $f_r$, and rotor and/or floater distances $d$. The orange crosses mark stable force equilibria. (e),(f) ${\theta }_f$ and the vertical force $F_z$ for all simulations in the blue phase between 270 and 360 Hz. The stable equilibria are the points where spline fits of the force curves in (f) cross from positive (attractive) to negative (repulsive) as $d$ decreases.