1. Home
  2. ⚙ Mechanical Engineering
  3. Formula - maximum rev/s?

Formula - maximum rev/s?

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)

Thanks for reading,

Russell

Reply to
Russell Harper
Loading thread data ...

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.

Reply to
jim andrews

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?

Thanks for reading,

Russell

Reply to
Russell Harper

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.

Reply to
jim andrews

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

Reply to
Brian Whatcott

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.

To reply remove AT

Reply to
Jonathan Barnes

PolyTech Forum website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.