KEVOS® 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.
Open the calculatorRuns in your browser. No account needed.
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). |
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.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
