# Formula - maximum rev/s?

• posted

For a small solid sphere, cylinder or disk, I came up with the maximum rev/s that such an object could be spun as:

w = [2p/(dr^2)]^(1/2)

where:

p = ultimate tensile strength d = density r = radius

As an example, for a diamond disk 1 cm in radius...

p = 90 GPa d = 3520 kg/m^3 r = 0.01 m

w = 720,000 /s

This corresponds to a surface velocity of 45 km/s. Empirically this is within the right ballpark, but I suspect the constant '2' is wrong. Does anyone know where I can find the correct formula?

Also, is there a concise way to describe the 'obvious' axis to spin a cylinder or disk? (e.g. the way a top spins)

Russell

• posted

Empirically, I cannot believe that's even *close* to the "right ballpark". I don't know of many cylinders that can be spun to even

1 km/sec, and I have a hard time believing you could achieve well over an order of magnitude improvement with a spherical geometry.

I don't have the time or the inclination to check your formula or your math, but I'm skeptical.

jim andrews active power, inc.

• posted

Sorry to use such an extreme example, but this was the only case I could find with real numbers quoted.

Vertically, a sphere of micrometer scale size is suspended in a vacuum using a high powered laser beam. Horizontally, another laser with an asymetric beam imparts a slight difference on the surface causing the sphere to rotate. Maybe twenty years ago, the experiment was tried with fused silica achieving surface velocities of several km/s before the sphere fragmented. I was incorrect in using "empirical" for diamond, that apparently hasn't been done (yet?), but perusing Google I've seen estimates of 100-200 km/s as the maximum surface velocity.

In any case, is there somewhere on the web where I can check this formula? Or alternatively, some less extreme empirical cases? Are the maximum rated RPM of power tools some fixed percentage of the predicted maximum before failure?

Russell

• posted

Well, I hope somebody is looking long and hard at the engineering issues one would face in trying to "commercialize" such a thing, because it would positively crush "modern" flywheels in terms of energy density. Of course, the thing is spinning in free space -- coupling it to a "shaft" in order to transmit torque would quite likely reduce its efficacy by a large margin. Any references in this regard?

jim andrews active power, inc.

• posted

This note caught my eye - it didn't seem intuitive, so I did a quickie google - where the current contents are all about maximizing kinetic energy for flywheels, in general. They talk about surface speeds around 1 km/s. I do recall reading a limiting spin rate that is supposed to be characteristic of a given material; you would expect this to be a function of allowable stress/density. One number sticks in my mind - about 25 krpm for steel That would be 400 rev/sec, so 2 pi r times 400/sec = 1000 meters/sec and

• posted

My Kemp's ( 1943 Ed ) says flywheel stress is dependent on rim speed, and for cast iron 6000 ft / min is regarded as safe....

The phrasing suggests to me that those who found the limit had to duck :-)

It also notes a steel plate with wire wound rim has been run at 15,000 ft / min.

It is commercially important to run grind stones as fast as possible, and a lot of work on maximum safe speeds for them has been done. Might be worth looking this up.

Hope this helps.

-- Jonathan

Barnes's theorem; for every foolproof device there is a fool greater than the proof.