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Centrifugal Force Formulas

  1. Jul 20, 2004 #1
    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. jcsd
  3. Jul 20, 2004 #2


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    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.
  4. Jul 21, 2004 #3


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    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
    the force as a radius function at some partial radius
    for the tool lenght, or a moment around an axis or something ?
  5. Jul 26, 2004 #4
    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)
    Head in Feet= 2.31 PSIG

    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
  6. Oct 15, 2008 #5
    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.
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