Centrifugal Force Formulas

In summary, an imbalance in an object causes a force that is inversely proportional to the distance between the point of imbalance and the center of rotation.
  • #1
jhetfield
1
0
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.
 
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  • #2
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
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 ?
 
  • #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
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
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, let's 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.
 

1. What is the formula for calculating centrifugal force?

The formula for calculating centrifugal force is F = m x v² / r, where F is the centrifugal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the object's circular path.

2. How does centrifugal force differ from centripetal force?

Centrifugal force is the outward force experienced by an object moving in a circular path, while centripetal force is the inward force that keeps the object in its circular path. They are equal in magnitude but act in opposite directions.

3. What is the relationship between centrifugal force and angular velocity?

The relationship between centrifugal force and angular velocity is directly proportional. As the angular velocity increases, the centrifugal force also increases. This means that the faster an object rotates, the greater the centrifugal force acting on it.

4. How does the mass of an object affect the centrifugal force?

The mass of an object has a direct influence on the centrifugal force. An object with a greater mass will experience a greater centrifugal force when moving in a circular path compared to an object with a smaller mass. This is because the formula for calculating centrifugal force includes mass as a factor.

5. Can centrifugal force be greater than gravity?

Centrifugal force can appear to be greater than gravity when an object is rotating in a circular motion, but it is not actually a true force. It is an apparent force that is a result of the object's inertia and the centripetal force acting on it. In reality, gravity is always the dominant force acting on an object.

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