Centrifugal expansion of bore of a steel rotating ring 4

This much:

Wow, That was fast. Thank you so much, mintjulep.

I did some calculation based on some theory from my college days and was off by a factor of 1000 (222 mm), which I knew was ridiculous. I have got to my math again correctly.

Thanks again.

Muthu

I used this approximation formula

Change in radius = [(Density in gm/cm[sup]3[/sup]) X (original radius in cm)[sup]3[/sup] X (angular velocity)[sup]2[/sup]] / [Young’s modulus in gm/cm[sup]2[/sup]]

Still trying to figure out where it went wrong.

Muthu

If you scroll down on the link that MintJulep posted, it shows the formulas used. Also, check your units, Young's modulus has units of force/area, not mass/area as you specified in your equation (you had it right in your first post with GPa). I'm not sure exactly what you did, but that unit mix-up could lead to being off by about 1000 in a few different ways.

FAG's Precision Spindle bearing catalog used to discuss inner ring expansion at high speeds I believe.

Sometimes our spindles needed an extra .0005-.001" Ø interference to remain "tight" at high rpm.

Thank you, stick.

I checked with the formula at the bottom of mintjulep's link (I assume u in that formula is actually Poisson's ratio v) in Excel spreadsheet with for following data

Inner Radius - 0.3685 meter
Outer Radius - 0.4125 meter
Density of steel - 7800 Kg/M[sup]3 [/sup]
Poisson's Ratio - 0.3
Speed - 3000 RPM
Angular velocity - 314 Radians/sec
Young's modulus of steel 200 GPa = 20,394,324,260 Kg/M[sup]2[/sup] (is this correct?)

I got inner radius expansion as 2.28 mm, which is high by a factor of 10 (it should be 0.228 mm).

At least my last error has come down now by a factor of 100.

Muthu

Young's modulus units: gigapascals (GPa), or Newton-per-square-meter (N/m2). It is NOT kilogram-per-square-meter (Kg/m2).

Steel is typically given as 2.0 x 10E11 N/m2 (which falls in the range of 190-215 GPa).

Check your unit conversions again.

Converting energy to motion for more than half a century

edison123 said:

Young's modulus of steel 200 GPa = 20,394,324,260 Kg/M2 (is this correct?)

Click to expand...

It's technically correct if the units are kgf/m^2 (kgf being kilogram-force), but I am of the opinion that kilogram-force is a bastard unit that shouldn't be used, and this is exactly why.

The conversion from Newtons to kilogram is to divide by 9.81 m/s^2 (or 10 if you want to round), which is conveniently the same factor that you're off by. If you do the calc out by hand, use Pascals for the units of Young's modulus, and keep meticulous track of your units, everything should work out smoothly and get you the right answer.

Thank you, stick. I was stuck on kg and missed the kgf point.

With 200,000,000,000 N/M[sup]2[/sup], I got 0.2326 mm.

Thank you, Gr8blu. Yes, my unit conversion was the mistake.

I thank you all once again for your valuable tips.



Muthu