Centrifugal Force Formulas

  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. 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. drag

    drag 1,341
    Science Advisor

    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. 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. 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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