KEVOS® MAKEOS · Manufacturing
Small Cutter and Drill Stiffness and Deflection
How much stiffness do I lose by choosing a smaller or longer micro end mill or drill, and how far will it deflect?
Change in torsional stiffness of small end mills and drills when the diameter or flute length changes, using the handbook’s proportionalities (diameter⁴, flute length⁻²), and the bending deflection of the new tool under a radial cutting force as a cantilever with an effective fluted diameter.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Original tool diameter | mm | Diameter of the current tool. |
| Original flute length | mm | Flute length of the current tool. |
| New tool diameter | mm | Diameter of the proposed tool. |
| New flute length | mm | Flute length of the proposed tool. |
| New tool stick-out from the holder | mm | Length from the holder face to the cutting point. |
| Effective diameter factor for flutes | Ratio of the fluted section’s equivalent diameter to the nominal diameter (about 0.8 for two flutes). | |
| Tool material modulus | GPa | Elastic modulus of the tool (about 600 GPa for carbide). |
| Radial cutting force | N | Radial force at the tool tip. |
Method and formulas
- Torsional stiffness ∝ D⁴ and ∝ L⁻² (handbook): change = (D₂⁴ − D₁⁴) ÷ D₁⁴ and (L₂⁻² − L₁⁻²) ÷ L₁⁻².
- Combined ratio = (D₂ ÷ D₁)⁴ × (L₁ ÷ L₂)².
- Deflection δ = F L³ ÷ 3 E I with I = π (k D₂)⁴ ÷ 64 (cantilever).
- Example: going from 1 to 0.8 mm cuts torsional stiffness by 59.04% (the handbook’s −59%).
Limitations
- Proportional scaling only; shank, neck and holder stiffness also matter.
- Deflection treats the whole stick-out as the fluted section, which is conservative.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Compare tool options before micromilling or microdrilling
- Estimate deflection error on a small cutter
- Choose the shortest flute length that reaches the feature
Who it is for
- Machinists
- CNC programmers
- Manufacturing engineers
What you get
- Torsional stiffness change from diameter and flute length
- Combined change
- Bending deflection of the new tool
Interpreting the result
- Flute length matters almost as much as diameter: choose the shortest that reaches.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1093–1094. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Small Cutter and Drill Stiffness and Deflection calculator
