Circular-cantilever screen

Tool deflection

Inputs

Declared lateral forceFSingle lateral tip force for the ideal circular cantilever screen.

Free overhangLFree cantilever length from the effective clamp plane to force application point.

Declared core diameterdCircular effective core diameter; flute, neck, holder, and contact geometry are excluded.

Declared elastic modulusEUser-entered linear-elastic modulus for the stated cutter material.

Circular core second momentI

0.000000001

Ideal tip deflectionδ

0.010234

Outer-fiber bending stressσ

44.21

I = πd⁴/64; δ = FL³/(3EI); σ = 32FL/(πd³)

A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.

Calculation snapshot

Formula version 1.0.0

I = πd⁴/64 · δ = FL³/(3EI) · σ = 32FL/(πd³)

Expand Machinery tool deflection guidance: https://www.expandmachinery.com/2021/07/20/how-to-reduce-tool-deflection-in-cnc-machining/

This printout is a record of displayed inputs and deterministic formula output. It is not an approval, certification, or engineering conclusion.

Method

Calculate elementary circular-cantilever tip deflection and outer-fiber bending stress from force, overhang, core diameter, and modulus.

I = πd⁴/64; δ = FL³/(3EI); σ = 32FL/(πd³)

When

Don’t

Elementary circular constant-section cantilever only; flutes, taper, holder/spindle/fixture compliance, contact distribution, runout, dynamics, chatter, fatigue, tool selection, safety, and production approval are excluded.