KEVOS® MAKEOS · Manufacturing
Ball-Nose Effective Diameter
What cutting diameter is engaged at this shallow axial depth?
Calculate the maximum engaged diameter of an untilted ball nose, its boundary cutting speed and RPM for a specified speed.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Nominal ball diameter | mm | Spherical ball diameter from the tool drawing. |
| Axial engagement from the tip | mm | Depth from the ball tip into a flat surface, no greater than the radius. |
| Spindle speed | rpm | Actual or proposed spindle setting. |
| Specified surface speed | m/min | Validated cutting speed at the maximum engaged diameter. |
Method and formulas
- Effective diameter = 2√[a(D − a)] for 0 < depth a ≤ D/2.
- Surface speed = π × effective diameter × RPM/1000. Required RPM = 1000 × speed/(π × effective diameter).
- Example: a 10 mm ball at 1 mm depth has 6 mm effective diameter. At 5000 rpm its boundary speed is 94.247780 m/min; 100 m/min requires 5305.164770 rpm.
Limitations
- An untilted cutter and flat surface are assumed. Tilt, scallop height and general 3D contact are excluded.
- Speed varies over the contact and remains zero at the rotational centre; the reported speed is the maximum engaged boundary speed.
- A large calculated RPM may exceed equipment limits. Feed and chip thinning are separate.
- Default values are worked examples, not recommended settings or material properties.
Typical uses
- ball nose
- effective diameter
- shallow milling
Who it is for
- CNC programmers
- Tooling engineers
What you get
- Maximum effective diameter
- Boundary surface speed
- RPM for specified speed
Interpreting the result
- Review actual contact geometry in CAM.
- Verify spindle, tool and workholding limits.
References
- Sandvik Coromant: Milling formulas and definitions — https://www.sandvik.coromant.com/en-gb/knowledge/machining-formulas-definitions/milling-formulas-definitions
- Harvey Performance: Ball nose milling strategy guide — https://www.harveyperformance.com/in-the-loupe/ball-nose-milling-strategy-guide/
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