# Centrifugal Force Formulas

1. Jul 20, 2004

### jhetfield

I have a tool that is used in CNC metal cutting machines. This tool rotates and we have a machine that calculates the amount of immbalance. The known values are, rpm, amount of imbalance (gmm), diameter.

I'm trying to find a formula that calculates the centrifugal force that is generated from the known values above.

2. Jul 20, 2004

### Gza

when you say "imbalance," in what manner or orientation is the object not balanced? If you can provide a little more detail, I can help.

3. Jul 21, 2004

### drag

What units are gmm ? What's "imbalance" (pressure, force) ?
For the force in general you have:
Force = Mass * (Velocity)^2 / Radius = Mass * (rpm / 60) * Radius
But, you'll have to be more specific - do you want
for the tool lenght, or a moment around an axis or something ?

4. Jul 26, 2004

### KrazyIBKid

Affinity Laws for Centrifugal Applications:

Flow1/Flow2 = RPM1/RPM2
Pres1/Pres2 = (RPM1)2/(RPM2)2
BHP1/BHP2 = (RPM1)3/(RPM2)3
For Pumps:

BHP= (CFM x PSF)/(33000 x Efficiency of Fan)
BHP= (CFM x PIW)/(6344 x Efficiency of Fan)
BHP= (CFM x PSI)/(229 x Efficiency of Fan)
Where:

BHP = Brake Horsepower
GPM = Gallons per Minute
FT = Feet
PSI = Pounds per Square Inch
PSIG = Pounds per Square Inch Gravity
PSF = Pounds per Square Foot
PIW = Inches of Water Gauge
Specific Gravity of Water = 1.0

I pulled that from a website... it deals with liquids, however hope u can adapt it for your uses.. hope it helps

5. Oct 15, 2008

### GinVT

Hi jhetfield. You've probably solved this long ago but, I just saw it and thought I'd answer. Your question is perfectly legitimate. As I understand it, your toolholder balancer shows the tool has an unbalance. This unbalance is measured in g-mm (grams at a 1mm radius). First, lets convert your unbalance in g-mm to oz-in (ounce-inches). To do this, multiply your g-mm value by 0.00139 (g-mm x 0.00139 = oz-in). A quick approximation (pretty close) of the force generated would be:

F = 1.67U(n/1000)^2

F = force in lbs.
U = unbalance in oz-in
n = speed in rpm.

By the way, not that it really matters but, "imbalance" exists in your checkbook, "unbalance" exists in your rotor. The ISO changed this terminology a few years back.

Hope this helps.