BIZOMAT MAKEOS · Manufacturing
CNC Arc Segmentation and Feed Check (Chord Tolerance, Block Rate, Achievable Feed)
If my CAM output breaks this arc into straight segments within my tolerance, how short are the segments, can the control process them fast enough at my feed, and what feed can it actually hold?
Check of a curved toolpath output as short linear moves: the segment length that keeps the chord error within your tolerance on the arc radius, the angle per segment and number of segments over the arc (as the CNC chord error tool), the block rate the control must process at the programmed feed, the largest feed the control’s block processing rate allows, and the time for the arc.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Arc radius | mm | Radius of the curve being machined. |
| Chord tolerance | mm | Largest chord error allowed between segment and true arc. |
| Arc angle | ° | Angle of the arc. |
| Programmed feed | mm/min | Feed programmed along the path. |
| Control block processing rate | blocks/s | Blocks per second the control can read and execute (from the control maker; look-ahead settings change it). |
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: Arc radius
- What it is
- The radius of the curved toolpath that is being output as short straight segments.
- 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 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger radius allows longer segments, so fewer blocks per second are needed.
What this means: Chord tolerance
- What it is
- The largest gap allowed between a straight segment and the true arc, at the middle of the chord, as set in the CAM system.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.005 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Segment length grows roughly with the square root of the tolerance.
What this means: Arc angle
- What it is
- The angle the arc sweeps from start to end, used for the number of segments and the time for the arc.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.001° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Programmed feed
- What it is
- The feed rate programmed along the toolpath.
- Units and format
- Enter a number in mm/min: millimetres per minute. The form accepts 0.000001 mm/min to 1000000 mm/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 mm/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The block rate needed rises in proportion to the programmed feed.
What this means: Control block processing rate
- What it is
- The number of program blocks per second the control can read, process and execute, from the control maker.
- Units and format
- Enter a number in blocks/s: blocks/s. The form accepts 0.000001 blocks/s to 100000 blocks/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 blocks/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Look-ahead and smoothing settings change it; use the value for the settings you will run.
Method and formulas
- Segment length for a chord error e: L = 2√(2Re − e²); angle per segment = 2 sin⁻¹(L ÷ 2R); segments = ⌈arc angle ÷ segment angle⌉ (as the CNC chord error tool).
- Blocks per second = feed ÷ (60 L).
- Largest feed = rate × 60 × L; arc time = arc length ÷ the lower of the two feeds.
- Example: 0.005 mm tolerance gives 1.4142 mm segments (56 over the arc); at 3000 mm/min the control needs 35.356 blocks/s and can hold 8,485.1 mm/min.
Limitations
- Constant radius; tight curvature in freeform paths needs the smallest local radius.
- Block rate only: acceleration limits can slow the feed further.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set CAM tolerance without starving the control
- Explain why a contour runs slower than programmed
- Choose between arcs (G2/G3) and segments
Who it is for
- CNC programmers
- Manufacturing engineers
- Machinists
What you get
- Segment length, angle and number
- Block rate needed at the programmed feed
- Largest feed for the control and arc time
Interpreting the result
- Halving the tolerance shortens the segments by about √2, raising the block rate needed by the same factor.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1279–1300, 77–80. Topic reference; no source tables or recommended settings are reproduced.
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