BIZOMAT 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.
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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 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. |
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 tool you use now, the reference for the stiffness comparison.
- 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.
- Effect on the result
- Stiffness varies with the fourth power of diameter, so the ratio is very sensitive to it.
- Get it right
- Use the cutting diameter of the tool, not its shank diameter.
What this means: Original flute length
- What it is
- The flute length of the tool you use now, the reference for the length part of the stiffness comparison.
- 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.
- Effect on the result
- Stiffness varies inversely with the square of flute length.
- Get it right
- Use the fluted length, not the overall tool length.
What this means: New tool diameter
- What it is
- The diameter of the proposed new tool. It is compared with the original and also used for the bending deflection.
- 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 the new diameter.
- Get it right
- Small changes matter: stiffness follows the fourth power of this diameter.
What this means: New flute length
- What it is
- The flute length of the proposed new tool, compared with the original 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 1.2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer flute lowers the stiffness ratio with the square of the length ratio.
- Get it right
- This affects only the stiffness ratio; the deflection uses the stick-out instead.
What this means: New tool stick-out from the holder
- What it is
- How far the new tool sticks out from the face of the holder to the cutting point, treated as a cantilever for the deflection.
- 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, so keep it as short as possible.
- Get it right
- Measure from the holder or collet face, not from the end of the flutes.
What this means: Effective diameter factor for flutes
- What it is
- The ratio of the equivalent solid diameter of the fluted section to the nominal tool diameter, allowing for metal removed by the flutes in the bending stiffness.
- 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.
- Effect on the result
- Deflection falls with the fourth power of this factor.
- Get it right
- Type it as a ratio, not a percentage; the guide notes the usual figure for two flutes.
What this means: Tool material modulus
- What it is
- The elastic modulus of the tool material, such as solid carbide or high-speed steel, from the tool or material supplier’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
- This is in gigapascals; 1 GPa is 1000 MPa.
What this means: Radial cutting force
- What it is
- The sideways cutting force pushing on the tip of the new tool, at right angles to its axis.
- 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 directly proportional to the radial force.
- Get it right
- Use the radial force, not the axial thrust or the tangential cutting force alone.
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.
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Open the Small Cutter and Drill Stiffness and Deflection calculator