# Bearing spinning longer Horizontally

While performing a physics experiment, a fidget bearing was held horizontally, while spinning, and held vertically. The same torque was applied vertically, as well as horizontally on the bearings' outer. While held horizontally, the bearing spun for about 20 secs, and while, held vertically, it spun for about 6 secs(for the same torque applied to the bearing horizontally, and vertically).

The type of bearing is a hybrid ceramic bearing, metal outer, and hardened Zirconium balls on the inner, any reason for this large discrepancy, is it that there is a larger friction surface, applied to the bearing when vertical than horizontal, that makes the bearing to spin longer horizontally?

• the amount of friction in any bearing is determined by the contact points of the balls and the races. obviously these are different in your bearing depending on its orientation. an easy way to get a handle on this is to press a small microphone against the inner bearing and run it into an audio amp, then spin the fidget thing in vertical and horizontal orientation. listen for differences in the noise level. more noise means more friction. – niels nielsen May 2 '18 at 16:32

## 1 Answer

I think the answer is two-fold. First, consider that the clearance in the bearing causes only a few balls to be in contact when the bearing is vertical, but all balls are in contact when it is horizontal. For argument's sake consider the entire weight of the spinner to be supported by $1$ ball vs. all $n$ balls.

So the contact force equals the entire weight $W$ for the vertical bearing and $\frac{W}{n}$ for the horizontal.

The second part of my argument has to do with the non-linearity of the ball contact. As per Hertzian contact rules the amount of deflection $\delta$ (dimple under the ball) relates to the contact force $N$ as $$N \propto \delta^{\frac{3}{2}}$$

We can assume the friction is proportional to the dimple size, so for the vertical bearing

$$F_{\rm vert} \propto W^{\frac{2}{3}}$$

In the horizontal case, the contact force is $N = \frac{1}{n} W$, and the friction is less because the dimple is

$$F_{\rm horiz} \propto \left( \tfrac{1}{n} W \right)^{\frac{2}{3}}$$

$$\frac{F_{\rm horiz}}{F_{\rm vert}} = \frac{1}{n^{\frac{2}{3}}}$$

For a bearing with $n=7$ balls, that ratio is 27%, or a reduction from 20 seconds down to 5.5 seconds.

• Just for information, any better engineered products to make a bearing spin longer vertically? – user3483902 May 3 '18 at 8:20
• It depends on the expected bearing loads. Most bearings are designed to minimize friction under load, and when applied to a fidget spinner the elements slosh around more than usually causing more friction. A ball bearing is very good at low friction for low loads as a mechanical device. Alternatives would be an air bearing or some kind of magnetically separated type. For high loads, a journal bearing is phenomenally good. – ja72 May 3 '18 at 14:15