KEVOS® MAKEOS · Manufacturing
Small Tool Substitution Check (Stiffness Change, Deflection, Feed to Hold Tolerance)
If I swap to a smaller or longer micro tool, how much stiffness do I lose, how far will it deflect under the cutting force, and what feed keeps deflection within my limit?
Check of a substitute small end mill or drill: the stiffness change from the new diameter and flute length, and the bending deflection of the new tool under the radial cutting force at its stick-out (as the small cutter stiffness tool), compared with the deflection your tolerance allows, with the force and feed (proportional to force) that keep the deflection within the limit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Original tool diameter | mm | Diameter of the tool the process was proven with. |
| Original flute length | mm | Flute length of that tool. |
| New tool diameter | mm | Diameter of the substitute tool. |
| New flute length | mm | Flute length of the substitute. |
| New tool stick-out from the holder | mm | Stick-out of the substitute from the holder face. |
| Effective diameter factor for flutes | Diameter of an equivalent solid round as a share of the tool diameter (fluted section). | |
| Tool material modulus | GPa | Elastic modulus of the tool (carbide about 600 GPa). |
| Radial cutting force at the planned feed | N | Radial cutting force at the planned feed (from measurement or a force estimate). |
| Planned feed per tooth | mm | Feed per tooth planned for the substitute. |
| Largest deflection the tolerance allows | µm | Largest tool deflection the part tolerance can absorb. |
Method and formulas
- Stiffness change from diameter = (D₂ ÷ D₁)⁴; from flute length = (L₁ ÷ L₂)²; combined ratio (as the small cutter stiffness tool).
- Deflection = F L³ ÷ 3EI with I = π (k D₂)⁴ ÷ 64 at the stick-out (as the small cutter stiffness tool).
- Force for the limit = F × limit ÷ deflection; feed scaled in the same proportion (force taken as proportional to feed).
- Example: the new tool is 28.444% as stiff and deflects 3.6428 µm; the feed for 5 µm is 0.01 mm.
Limitations
- Cantilever deflection of the tool alone; holder and spindle compliance add to it.
- Force assumed proportional to feed; at very small feeds rubbing breaks this.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a smaller replacement end mill
- Set a reduced feed for a long-reach tool
- Explain why a micro tool cut out of tolerance
Who it is for
- CNC programmers
- Machinists
- Manufacturing engineers
What you get
- Stiffness change from diameter and length
- Deflection of the new tool
- Force and feed for the deflection limit
Interpreting the result
- Stick-out matters most: deflection grows with its cube, so the shortest holder pays back immediately.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1093–1094. Topic reference; no source tables or recommended settings are reproduced.
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