How Do You Calculate Centrifugal Force in CNC Tools?

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Discussion Overview

The discussion focuses on calculating centrifugal force in CNC tools, particularly in relation to tool imbalance during operation. Participants explore various formulas and concepts related to centrifugal force, velocity, and the specifics of measuring imbalance in the context of CNC machining.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a formula for calculating centrifugal force based on known values: rpm, amount of imbalance (gmm), and diameter.
  • Another participant requests clarification on the nature of the "imbalance" and its orientation to provide more targeted assistance.
  • A third participant presents a general formula for force, suggesting it depends on mass, velocity, and radius, but asks for specifics regarding the desired calculation.
  • A participant shares Affinity Laws for centrifugal applications, noting their origin from liquid applications and suggesting potential adaptation for CNC tools.
  • One participant explains the conversion of unbalance from g-mm to oz-in and proposes an approximation formula for calculating force based on unbalance and rpm, while also clarifying terminology differences between "imbalance" and "unbalance."

Areas of Agreement / Disagreement

Participants express varying interpretations of "imbalance" and its implications for calculations. There is no consensus on a single formula or approach, and multiple perspectives on the topic remain unresolved.

Contextual Notes

Some participants note the need for clarity on units and definitions, as well as the specific context of the calculations, which may affect the applicability of proposed formulas.

jhetfield
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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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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.
 
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 ?
 
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
 
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.
 

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