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GENERATION OF STRONG CENTRIFUGAL FIELDS
In the work of Beams and his collaborators Young and Moore*) the authors set themselves the task of bringing centrifugal fields up to the maximum permitted by the strength of the rotor material. From experience with high-speed turbines it is known that in rotating homogeneous elastic rotors the maximum stress is proportional to the square of the linear peripheral speed
$$ v^2=(2\pi\nu)^2 r^2. $$
It follows from this that rotors of similar shape, made of the same material, must burst at the same peripheral speeds. Thus, in order to obtain the highest centrifugal fields, whose intensity is measured by the acceleration
$$ \frac{v^2}{r}=(2\pi\nu)^2 r, $$
the radius of the rotor must be as small as possible. It turns out that, for rotors made of a given elastic material, the highest speed can be achieved provided that the radial and tangential shears have a constant value throughout the rotor. This condition is most simply satisfied if ordinary steel balls from ball bearings are used as rotors.
In the experiments of Beams, Young, and Moore, the ball-rotor was supported in vacuum by the magnetic field of a solenoid and was spun up by a rotating magnetic field. To become acquainted with the rather complex supply circuits of the supporting solenoid and of the coils that produced the rotating field, one should consult the original paper.
The problem of sufficiently accurately determining the peripheral speed was solved by the authors in a simple and ingenious way. One half of the ball-rotor was polished, and the other was blackened. For the latter purpose the balls were immersed halfway in dilute sulfuric acid, which was in contact with metallic antimony. The resulting dark layer was very thin and did not break down under the highest centrifugal forces. To determine the speed, the light of an incandescent lamp was focused on the surface of the rotating ball (special measures were taken to keep the ball exactly in the same place and to eliminate vibrations both in the vertical and in the horizontal plane). Next, the light scattered by the ball was focused by another lens onto the sensitive surface of a photomultiplier. The alternating voltage produced, after amplification, was applied to one pair of plates of a cathode-ray oscilloscope, while to the other pair was applied the voltage of a calibrated high-frequency generator. In this way the two frequencies could be compared with one another.
) J. W. Beams, J. L. Joung and J. W. Moore, J. Applied Phisics 17*, 886, November 1946.
As already indicated, the rotation speed of the ball increased until the ball was torn apart by centrifugal forces. The results obtained with different balls are compared in the table:
| Rotor diameter, mm | Rotor speed, rev/sec | Peripheral speed, cm/sec | Centrifugal acceleration | Maximum calculated elastic stress, pounds/dm |
|---|---|---|---|---|
| 3.97 | 77,000 | \(9.60 \cdot 10^4\) | \(4.7 \cdot 10^7\) | 410,000 |
| 2.38 | 123,500 | \(9.25 \cdot 10^4\) | \(7.20 \cdot 10^7\) | 385,000 |
| 1.59 | 211,000 | \(1.05 \cdot 10^5\) | \(1.43 \cdot 10^8\) | 498,000 |
| 0.795 | 386,000 | \(9.65 \cdot 10^4\) | \(2.40 \cdot 10^8\) | 420,000 |
As can be seen, the maximum peripheral speed for all the balls is about \(10^5\) cm/sec \(= 1\) km/sec. It is precisely this that characterizes the strength limit of the steel that served as the material of the balls. In accordance with expectation, the maximum centrifugal acceleration, exceeding the acceleration due to gravity by \(240\) million times, was obtained with the smallest ball.
E. V. Shpolsky