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Tiny metal spheres are needed for tiny ball valves and tiny ball bearings, which are needed for all kinds of miniaturized machines. Hollow spheres are lighter, and thus have less inertia, and thus can be made to move faster in these very small applications, where response time is often critical. But how do you make a hollow metal sphere 2mm across? Turns out you can do it with one of the lost foam processes I'm always going on about. Tiny styrofoam beads are first coated with fine metal powder and a binder, then heat-treated to evaporate both binder and bead, leaving only a fragile hollow metal powder shell, which is then sintered into a continuous shell at higher temperature. Read more over at Science Daily.
Turns out that Spherical shells (hollow spheres) have higher moments of inertia(rotational inertia) than solid spheres. Which has always bothered me but is true nonetheless.
http://en.wikipedia.org/wiki/List_of_moments_of_inertia
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That is true only if they have the same mass. Obviously hollow spheres are lighter too, and therefore the intertia is smaller.
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If both spheres had the same radius, the hollow one should have less than 60% of the solid spheres mass in order to have less moment of inertia (according to the above mentioned wikipedia article). On the other hand, the wikipedia formula also presumes the hollow spheres shell is of negligible thickness, which probably isn't the case either. My guess is that the hollow spheres are preferable in most cases though. Interesting.
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From the Science Daily article, "The hollow spheres are 40 to 70 percent lighter than solid ones."
So, they are 30% to 60% of the mass of a solid sphere the same diameter, meeting the need in the wiki article.
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Thank you. So they would, in fact, be less responsive in ball bearings than solid spheres. But I think the ball-valve claim is safe, anyway.
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Thanks to you guys, too, for pointing out that the conclusions David and I drew from the forms of the two moment-of-inertia equations would only be true if both solid and hollow spheres had the same mass which, if they have the same diameter and are made of the same material, they clearly do not.
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Not sure what physics class you guys took. The moment of inertia will decrease if it is hollow when compared to a solid of the same diameter and same density material. The mass changes, the radius does not when compared to another bearing of "equal size".
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I can see this being useful for the ball valves they talked about, where the ball is free floating, but they won't be much use in a bearing, at least not as they are described here. Moment of inertia is only one consideration and for bearings, stiffness, wear resistance and thermal response are going to be much more important. A hollow sphere is not going to be a good fit for these requirements and in general the bearing itself forms only a small part of the rotational inertia of a rotation system, thus this property is not as important.
That said, this is a very cool application for power met. technology and I hope they scale this up for larger spheres in the future.
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We've already been able to make big hollow balls for a while now. The cool thing to note about these is their small size because making tiny things is a technical challenge. Saying "I hope they scale this up for larger spheres in the future" slightly misses the point.
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