Tool deflection screening calculator

Solid round cantilever tool under a supplied lateral tip force; flute compliance omitted.

cnc-tool-deflection.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	inertiamm^4	deflectionmm
	63.6173	0.0047157
	63.6173	0.00377256

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

deflection budget0.00 mm✓ passes

BASELINE INPUTS

force20 Nstickout30 mmdiameter6 mmmodulus600 GPa

CALCULATED

inertia63.617 mm^4

deflection0.0047157 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Tool deflection screening
# Scope: Solid round cantilever tool under a supplied lateral tip force; flute compliance omitted.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

force = 20 N
stickout = 30 mm
diameter = 6 mm
modulus = 600 GPa

inertia := pi*diameter^4/64 [mm^4]
deflection := force*stickout^3/(3*modulus*inertia) [mm]

check deflection budget: deflection <= 0.01 mm

scenario alternative: force = 16 N

Calculated from your source · not saved

Baseline · Baseline

deflection budget0.00 mm ✓ passes

alternative · alternative

deflection budget0.00 mm ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

inertia: inertia = pi*diameter^4/64 [mm^4]
deflection: deflection = force*stickout^3/(3*modulus*inertia) [mm]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

force: 20 N
stickout: 30 mm
diameter: 6 mm
modulus: 600 GPa

Calculated

inertia: 63.6173 mm^4
deflection: 0.0047157 mm

Assumptions and limits

Solid round cantilever tool under a supplied lateral tip force; flute compliance omitted.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Tool deflection screening. Inputs: tool geometry; overhang; cutting-force estimate; modulus. Outputs: tip deflection; bending stress. Model scope: Tool, stock and machine-specific cutting data. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: tool geometry, overhang, cutting-force estimate, modulus
Outputs: tip deflection, bending stress
Modes: calculate, compare, sweep
Drawing: Tool engagement and material-removal preview

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS