KEVOS® MAKEOS · Manufacturing
Cutting Tool Deflection and Depth-of-Cut Limit
How far will this end mill or boring bar deflect under the cut, and what depth keeps it within tolerance?
Cutting force on an end mill (average tangential force from removal rate and specific cutting force) or a boring bar (chip area × specific cutting force), the resultant with the radial component, the tool’s cantilever deflection with an effective fluted diameter, the overhang ratio, and the largest depth of cut that keeps deflection within the allowance.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tool | choice | End mill or boring bar. |
| Tool or bar diameter | mm | Diameter of the tool or bar. |
| Overhang (stick-out) | mm | Distance from the holder face to the cutting edge. |
| Effective diameter factor (fluted section) | Equivalent stiff diameter as a share of nominal (about 0.8 for fluted end mills, 1 for solid bars). | |
| Tool modulus | GPa | Elastic modulus (about 600 GPa carbide, 210 GPa steel). |
| Specific cutting force | N/mm² | Specific cutting force for the material. |
| Radial ÷ tangential force | Radial (deflecting) force as a share of the tangential force (about 0.3–0.6). | |
| End mill cut | ||
| Teeth | Teeth on the end mill. | |
| Feed per tooth | mm | Feed per tooth. |
| Radial width of cut | mm | Radial engagement of the end mill. |
| Axial depth of cut (end mill) | mm | Axial depth of the end mill cut. |
| Boring cut | ||
| Feed per revolution (boring) | mm/rev | Feed per revolution for boring or turning. |
| Depth of cut (boring, radial) | mm | Radial depth of cut for boring. |
| Limit | ||
| Allowable deflection | mm | Deflection you can accept (a share of the tolerance). |
Method and formulas
- End mill average tangential force F_t = a_e a_p f_z z k_c ÷ π D (removal rate × k_c ÷ cutting speed).
- Boring: F_t = a_p × f × k_c.
- Resultant F = F_t √(1 + ratio²); deflection δ = F L³ ÷ 3 E I with I = π (k D)⁴ ÷ 64 (as the boring-bar tool).
- Force is proportional to depth, so the largest depth = depth × allowable ÷ δ.
- Example: a 10 mm end mill at 40 mm stick-out deflects 50.347 µm; keep the depth below 3.9724 mm.
Limitations
- Average force; peak force on few-tooth cutters is higher.
- Holder and spindle compliance add to tool deflection.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set depth of cut for a long-reach end mill
- Hold bore tolerance with a long boring bar
- Choose a shorter or carbide tool before cutting
Who it is for
- Machinists
- CNC programmers
- Manufacturing engineers
What you get
- Cutting force
- Tool deflection and overhang ratio
- Largest depth of cut for the allowance
Interpreting the result
- Deflection rises with the cube of overhang: shorten the tool before reducing feed.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1093–1094, 1162–1167. Topic reference; no source tables or recommended settings are reproduced.
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