Constructing and Studying a
Levitating Frictionless
Bearing
Ruth Toner
Superconductors:
The Basics
-First discovered 1911 by Heike Kamerlingh Onnes.
-Above critical temperature, superconductor behaves like normal material, with high resistivity
- Below Tc, has zero
resistance
- If current is established in loop of superconducting material, will continue indefinitely.
- Other conditions:
Type I Superconductors -- The Meissner Effect
-Zero resistivity of superconductor means that material can act as “perfect dimagnet”
-When superconductor is exposed to magnetic flux, field induces current on surface
-Induced current creates opposing magnetic field which leads to force of repulsion between magnet and
superconductor
-In case of Type I superconductor, magnetic field is completely expelled from superconductor
- force strong enough to cause
Type II Superconductors – Flux Pinning
-Type II Superconductor: contains small impurities which allows some
magnetic flux to pass through filaments in the material
-flux lines become “pinned” in place: any attempt to move the superconductor up or down will create a restoring force
-combination of Meissner Effect repulsive force and flux pinning restorative force causes levitation
-Advantages:
-Higher critical temperatures - horizontal position of
superconductor also fixed
Materials
YBCO Superconductor:
Critical Temperature 90°K (-183°C)
NdFeB magnet:
Surface strength = 1.6 Tesla
Creating the Mount
[CAD drawing]
Materials – base: aluminum handle: G10
A Levitating Frictionless Bearing: Photos
Before:
The magnet rests on supports on top of the superconductor, not levitating.
During cooling:
The mount is lowered into liquid nitrogen and allowed to cool to
77°K, under YBCO’s critical temperature. The YBCO becomes
A Levitating Frictionless Bearing: Photos
The mount is removed from the liquid nitrogen, and the supports are knocked out. The magnet floats in midair, and can only be moved by
Studying the Bearing – Part #1:
Finding the Spring Constant and Resonant Frequency
-The restoring force F applied by objects like the bearing can be described by Hooke’s law: F=-kx, where k is some constant
-The frequency of vibration f is described by
-Increments of weight were placed on the magnet at three different initial heights, and the resulting displacement was measured; these data points were graphed, and the regression line slope was used to calculate constant k, and then frequency f:
Studying the Bearing – Part #2:
Finding the Spin Down Time Constant
-Because the bearing doesn’t make surface contact with anything, it is presumed nearly frictionless
-Some drag forces do exist, however (e.g., air drag), so that the rotational frequency f behaves
according to , where τ is the time constant for rotational decay, the time it takes for f to decrease by 63%.
-The time constant was calculated by monitoring the number of rotations in a 10 second period every minute; a regression time was plotted to achieve a value for τ. This was tested at four separate heights.
Example: rotational frequency decay at 12.70 mm
Initial elevation (mm)
Time constant (seconds)
3.00 246.81
6.54 814.11
9.67 1162.79
