How can I calculate the burst speed of a rotating disk?

[michaeldouglassewell]

How do I determine the theoretical burst speed of a rotating disk, such as a flywheel? I went through my physics textbooks from 30 years ago with no luck. I googled, and found WAY too much information, but still no equation.

Is this similar to the formula for hoop stress in a pressure vessel, only using centrifugal force instead of gas pressure?

Could I figure that the entire mass was at the radius of gyration?

I'm not sure how to determine the stress distribution.

I've been out of school for 3 decades now and I'm not as sharp at integral calculus as I used to be...

Thank you,
Michael

 

[OlderDan]

It may be you have not found the equation because nobody can really nail it down. It's not my area of expertise, but I vaguely remember thinking about this problem once before. I'll pass along what comes to mind, for what little it might be worth.

One way a disk might fail is to break in two at a diameter. It would involve some calculus, but you could find the centripetal force components applying a tensile stress along a diameter plane.

With no calculus, you could consider a volume element at the edge of the disk bounded by two diameter planes and an inner cylindrical surface. You could use the tensile strength of the materal to calculate the maximum force that could be achieved from the inner cylindrical surface, plus the radial components at the diameter surfaces for any such element. (You might know how to throw in some sheer force stuff at these surfaces.) You could then calculate the spin rate that would be needed to exceed the maximum force. You might try different shapes with different angular separations between the diameter surfaces, and different cylindrical surface radii and see if there is a weakest case. I have no idea if this would even get you close to the right answer, but I think it would be relatively easy to program the model and see what comes out of it.

 

[actionintegral]

There are engineering forums further down on the home page. Give those guys a crack at your question.

 

[Astronuc]

How do I determine the theoretical burst speed of a rotating disk, such as a flywheel? I went through my physics textbooks from 30 years ago with no luck. I googled, and found WAY too much information, but still no equation.

Is this similar to the formula for hoop stress in a pressure vessel, only using centrifugal force instead of gas pressure?

Could I figure that the entire mass was at the radius of gyration?

I'm not sure how to determine the stress distribution.

I've been out of school for 3 decades now and I'm not as sharp at integral calculus as I used to be...

Thank you,
Michael

There is probably a general solution already worked out for the stress within a rotating disc, which of course is a function of the mass distribution and rotational speed.

Then one would have to determine the failure criterion, e.g. the local principal stress exceeds the yield stress, or perhaps ultimate tensile stress, or still more appropriately the local stress intensity and use elastic (or elastic-plastic) fracture mechanics, which presupposes critical flaw at the peak stress location (likely at the junction of disk surface and bore).

The yield stress, UTS and fracture toughness are mechanical properties of the material.

 

[actionintegral]

The yield stress, UTS and fracture toughness are mechanical properties of the material.

What is UTS?

 

[michaeldouglassewell]

Ultimate Tensile Strength

 

[Oracle6]

Flywheel burst calculation

I've been down this road myself. LOTS of calculations will get you many different answers. Real life will be a defect, even microscopic where crack initiation and fast fracture occurs. If you are just looking for theoretical -go with fast fracture calcs. This is what really happens. I've developed a test method with Detroit Testing Laboratories to perform these tests for an actual application. They offered software development for modelling and help us in future projects. I turned it down because it seemed the code would have to be tailored specific -meaning empirical test data to modify calcs/modelling to agree with the test results. But, in 5-10 years -maybe they've made headway. If he's still there, the contact is Mr. Bairin You. Good luck.

 

[pervect]

As far as the theory goes, a couple of useful links are:

http://www.utm.edu/departments/engin/lemaster/Machine%20Design/Lecture%2016.pdf

(probably the most useful). and

http://arxiv.org/abs/physics/0211004

 

[michaeldouglassewell]

Got it.

Thank you all very much,
Michael