## Centrifugal expansion of bore of a steel rotating ring

## Centrifugal expansion of bore of a steel rotating ring

(OP)

How much the bore of a steel ring expands under speed?

Bore at standstill is 737 mm.

Speed is 3000 RPM.

Young’s modulus of steel = 210 GPa

Bore at standstill is 737 mm.

Speed is 3000 RPM.

Young’s modulus of steel = 210 GPa

Muthu

www.edison.co.in

## RE: Centrifugal expansion of bore of a steel rotating ring

## RE: Centrifugal expansion of bore of a steel rotating ring

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

www.edison.co.in

## RE: Centrifugal expansion of bore of a steel rotating ring

Change in radius = [(Density in gm/cm

^{3}) X (original radius in cm)^{3}X (angular velocity)^{2}] / [Young’s modulus in gm/cm^{2}]Still trying to figure out where it went wrong.

Muthu

www.edison.co.in

## RE: Centrifugal expansion of bore of a steel rotating ring

## RE: Centrifugal expansion of bore of a steel rotating ring

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

## RE: Centrifugal expansion of bore of a steel rotating ring

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

^{3 }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

^{2}(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

www.edison.co.in

## RE: Centrifugal expansion of bore of a steel rotating ring

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## RE: Centrifugal expansion of bore of a steel rotating ring

It's technically correct if the units are kg

f/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.

## RE: Centrifugal expansion of bore of a steel rotating ring

With 200,000,000,000 N/M

^{2}, 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

www.edison.co.in