BIZOMAT 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. |
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: Nominal ball diameter
- What it is
- The full diameter of the spherical end of the ball-nose cutter, from the tool drawing or marking.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- For a fixed depth, a larger ball gives a larger engaged diameter.
- Get it right
- Enter the ball diameter, not its radius or the shank size.
What this means: Axial engagement from the tip
- What it is
- How deep the tip of the untilted ball sinks into a flat surface, measured along the tool axis from the lowest point of the ball.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 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
- Deeper engagement increases the engaged diameter, so less rpm is needed for the same surface speed.
- Get it right
- It must not exceed the ball radius in this model; it is the axial depth, not the stepover.
What this means: Spindle speed
- What it is
- The spindle speed you are running or plan to run, used to calculate the surface speed at the largest engaged diameter.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The boundary surface speed is directly proportional to spindle speed.
- Get it right
- Use the actual programmed speed after any override.
What this means: Specified surface speed
- What it is
- The cutting speed you want at the largest engaged diameter of the ball, from the tool supplier or a proven process.
- Units and format
- Enter a number in m/min: metres per minute. The form accepts 0.001 m/min to 1000000 m/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 m/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The required rpm is directly proportional to the specified surface speed.
- Get it right
- This is surface speed in metres per minute, not rpm; the tool works out the rpm for you.
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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