BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Original tool diameter
- What it is
- The diameter of the end mill or drill the process was proven with, the reference for the change in stiffness.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It only enters the stiffness ratio; the deflection is calculated from the new tool alone.
What this means: Original flute length
- What it is
- The flute length of the original tool, the reference for the change in stiffness caused by flute length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: New tool diameter
- What it is
- The diameter of the substitute tool; it sets the stiffness and the bending deflection under the cutting force.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.8 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deflection falls with the fourth power of diameter, so a slightly smaller tool bends much more.
What this means: New flute length
- What it is
- The flute length of the substitute tool, compared with the original flute length in the stiffness ratio.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The deflection uses the stick-out, not the flute length; this value only feeds the stiffness ratio.
What this means: New tool stick-out from the holder
- What it is
- The length of the substitute tool projecting from the holder face to the tip, where the cutting force is taken to act.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deflection rises with the cube of the stick-out.
What this means: Effective diameter factor for flutes
- What it is
- The diameter of a solid round bar with the same bending stiffness as the fluted section, as a fraction of the tool diameter.
- Units and format
- Enter a plain number with no unit. The form accepts 0.4 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.8 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter a fraction, not a percentage; take it from the tool maker or a test, as it depends on flute count and core size.
What this means: Tool material modulus
- What it is
- The elastic modulus of the tool material, from the tool maker’s data.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1200 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deflection is inversely proportional to the modulus.
- Get it right
- Enter GPa, not MPa: the tool multiplies by 1000 internally.
What this means: Radial cutting force at the planned feed
- What it is
- The force pushing the tool sideways, at right angles to its axis, at the planned feed, from measurement or a cutting force estimate.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N to 100000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Deflection is proportional to the radial force.
What this means: Planned feed per tooth
- What it is
- The feed per tooth planned for the substitute tool; the tool scales it down in proportion if the deflection exceeds the limit.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.01 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter feed per tooth, not feed per revolution or table feed in mm/min.
What this means: Largest deflection the tolerance allows
- What it is
- The largest sideways bending of the tool tip that the part tolerance can absorb, decided from the tolerance band and other error sources.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0.01 µm to 10000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter micrometres, not millimetres: 0.01 mm is 10 µm.
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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