Elastic Deformation

Your Teachers Assistant will be a good source of information.

I'm having trouble visualizing this. Can you post a sketch?

Is this one piece? Has it gyroscope purposes? Or acts as a flywheel? Do you want to know when you get 2% deformation, due to centripetal force? On the outer diameter?

What is the disc and shafts made off? And what are the shaft diameters and thickness of the disc.

Any elastic deformation will probably result in catastrophic failure of the system

Are you storing energy with a flywheel?

a = v²/r, for starters.

A system like the one you describe is dynamically balanced for a specific rpm. So, the moment you change the rpm you are likely to turn it into an unbalanced and therefore unstable system. You need to work backwards - decide the rpm first and then balance the system for that rpm. Of course, this assumes that all components of the system have been designed correctly. Though I have not done any calculations my feeling is that for your system running at around 12000 rpm hoop stress in the disk may be the limiting factor.

This might help...

http://matperso.mines-paristech.fr/Donnees/data04/450-maziere08a.pdf

1- in all basic books you find equations for "rotating discs" stress computation (mostly for the elastic domain) you ONLY need to have a look at them after using google to find the texts

2- a rotating disc will present elastic deformations due to loading and if the load becomes too high even elastoplastic deformations. such "events" can occur in high speed turbines when the speed limits are due to a regulator failure not respected. as long as material stays elastic no failure will happen.

3- a disc is in general statically balanced since the ratio width to diameter is small, dynamic balances are required for rotating parts with a not too low ratio b/d. So if it is really a disc and not a cylinder rotating speed will NOT generate disbalances only since balance is not perfect an increase of radial forces.

4- I think that your disc will explode (yes explode) before you reach the 2% (not any more elastic) deformation. In machine design the elasticity limit is considered as the stress which leads to a 0.2% remanent deformation after unloading. You are 10x further with your limit of 2%. Assuming that you go over the elasticity limit material does NOT behave any more "elastically" so that you must use other equations (elastoplasticity) for the stress/ strain computation.

The disc is a rotor from an electric asynchroon motor 2 pole 1 hp 3 phase.

Outside diameter 64 mm weight 1,950 kg

For an application we want to let the motor run at 200 Hz (12 000 RPM).

The problem is to know the maximal rotating speed.

When informing the motor manufacture; they says the maximum speed is limited to 4000 RPM.

Motor from other brands with a similar rotor ( even bigger diameter) run at 12 - 15 000 RPM.

As a test we let run the motor (no load) for a couple hours at 250 Hz (= 15 000 RPM)

Maximum bearing speed (6204) is 18 000 RPM.

The manufacturer says the maximum speed is 4000 rpm.

You are willing to test run the motor at 15,000 rpm.

Do you have a containment shell to safely conduct this test for when it fractures and comes apart?

How good is your companies insurance plan for when someone is injured (or killed) by your using equipment well beyond the manufacturers specification?

Are you seriously asking anonymous individuals to ease your conscience in conducting this test and possible future use under these conditions?

If you want to run something at 15,000 rpm, get a product designed for it. Don't attempt to use one manufacturers product simply because it may be cheaper than another one actually designed for how you want to use it.

First remark is that you do not know the definition of a "disc" although it is the same meaning in all the language you may master (french and/ or flamish). What you have is NOT a disc it is a cylinder since to have a weight mass of 1.95 kg (it is a mass unit) at d= 64mm its length should be not small to respect to diameter.

You already run it at 15 krpm and it did not broke then why the question? I could have understood that before such a risky test you would like to know how risky it could be.

In general a stress/strain evaluation is made before a test and not after.

Now another question : is the rotor uniform as a cylinder or does it have a profile, windings aso? In such a case your question is out of range.

If with this motor you rotate a disc then your test with the motor alone has a limited value. A rotor is dynamically balanced and excessive radial loads

due to higher rpm could shorten bearings life expectancy quite a lot since dynamic equivalent load affects it at power 3 and loads increase with rpm power 2. So that life shorten proportional to rpm power 5!!!!

interesting, a motor driven high speed shrapnel generator. And to think I had been using explosives all this time.......