Ultrafast rotation of magnetically levitated macroscopic steel spheres

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Science Advances  05 Jan 2018:
Vol. 4, no. 1, e1701519
DOI: 10.1126/sciadv.1701519
  • Fig. 1 High-speed magnetically levitated spinning ball motor.

    Experimental setup composed of a solid steel sphere rotor (R), which is levitated by means of an electromagnet (EM). The position of the rotor is measured in all dimensions with two orthogonally placed position-sensitive device (PSD) sensors onto which the shadow of the sphere is projected. Light is projected onto the rotor by two infrared light-emitting diodes (LEDs). The output signal is used for the closed-loop control of the levitation height. A centering core (CC) guides the magnetic flux toward the rotor. Four drive coils (DC 1 to 4) produce a rotating magnetic field, which exerts a torque on the rotor. To reduce drag due to air friction, the rotor is enclosed in a glass tube (GT), which is evacuated by a vacuum system. The inset shows a magnification of the rotor and the lower end of the centering core. Aside from spinning around the z axis as desired, the rotor is prone to oscillate horizontally, requiring active damping through closed-loop control. This behavior can be modeled as a weakly damped spring-mass pendulum.

  • Fig. 2 Torque characteristics of the motor including air friction drag and temperature for a 0.5-mm rotor.

    (A) Torque acting on the rotor depending on the slip frequency for a field frequency of 800 kHz (synchronous rotational speed of 48 Mrpm). The shown error bars result from the calculation of the angular acceleration based on rotational speed measurements, which have a resolution of 500 Hz. The shaded blue area represents a ±30% uncertainty related to pressure measurement. The inset shows the residual between the experimentally obtained and the modeled torque using the read pressure value (blue line). Subfigures (a) and (b) show the current density distributions inside the rotor on the horizontal plane through its equator at slip frequencies of 150 and 700 kHz, respectively. (B) Rotor temperature over the same slip frequency range. The inset shows the ratio of heat transfer between the rotor and the environment due to radiation and free molecular conduction.

  • Fig. 3 Acceleration curves and bursting speeds of different rotors.

    (A) Acceleration curves for rotors of different diameters to their bursting speeds. Shown error bars represent the 500-Hz resolution of the measurements. The inset shows the highest of the principal normal mechanical stresses inside the rotor. (B) Achievable rotational speeds for different rotor sizes, materials, and initial stress conditions. Error bars show 95% confidence intervals for the mean. The inset shows a magnification of values for diameters 0.794 and 0.8 mm, illustrating the influence of the material and thermal treatment on the achievable rotational speed. The theoretical curve is based on the tabulated tensile strength value for 100Cr6 material. Short lines with square markers of the respective color correspond to calculated rotational speeds based on the specified UTS values obtained from hardness measurements (see text for details).

  • Fig. 4 Rotors exploding due to high centrifugal force.

    High-speed image sequence showing a rotor (a = 0.4 mm), initially intact one frame before exploding (A), fractured into multiple parts (B), and individual fractures hitting the wall of the vacuum tube (C). Red bars mark the walls of the vacuum tube. Images were recorded at 100,000 frames per second (fps) and a shutter speed of 1/283,000 s. The sequence is assembled by combining images from two different rotor explosions at 21.3 Mrpm (A and C) and 23.4 Mrpm (B) to enhance time resolution.

  • Fig. 5 Microscope images of exploded rotor fragments.

    (A) Overview of recovered larger wedge-shaped rotor fragments of a 0.8-mm-diameter rotor. (B) Detailed view of one exemplary surface of the fragments (red box) exhibiting typical properties of mostly brittle failure. (C) Three-dimensional view of the same surface highlighting its structure.

Supplementary Materials

  • Supplementary material for this article is available at

    fig. S1. Photograph of the experimental setup with levitated rotor.

    fig. S2. Control structure of the magnetic suspension system.

    fig. S3. Rotor dynamics in horizontal direction with and without active magnetic damping.

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Photograph of the experimental setup with levitated rotor.
    • fig. S2. Control structure of the magnetic suspension system.
    • fig. S3. Rotor dynamics in horizontal direction with and without active magnetic damping.

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