Overview
ISO 3002-2:1982 - "Basic quantities in cutting and grinding - Part 2: Geometry of the active part of cutting tools - General conversion formulae to relate tool and working angles" - provides a standardized method to convert between tool-centered angles (tool-in-hand) and working or process-centered angles (tool-in-use). The standard defines coordinate axes, sign conventions and general conversion formulae that are applicable to all cutting conditions. It also includes worked examples, transformation derivations and multilingual term lists.
Key topics
- Coordinate systems: Definitions of the tool-in-hand, tool-in-use and machine reference axes; axes and plane definitions are based on ISO 841 where applicable.
- Angle definitions: Clear definitions and sign conventions for the three setting angles (plan G, elevation H, roll L) and the three motion angles (plan M, elevation N, roll T).
- Conversion formulae: General direct and inverse transformation formulae (using Euler angles and transformation matrices) to calculate working angles from tool angles and vice versa.
- Auxiliary methods: Alternative method using components of feed speed and cutting speed when motion angles cannot be deduced from simple workshop data.
- Supporting material: Annexes with elaboration of formulae, methods for obtaining rotation/transformation matrices, and lists of equivalent terms (English, French, Russian; German and Dutch equivalents included).
Practical applications
- Tool setup and alignment on machine tools - converting specified tool angles into machine-setting positions.
- CAM programming and simulation - ensuring correct orientation of cutting edges relative to resultant cutting direction.
- Tool design and selection - evaluating active-part geometry in the context of intended cutting motions.
- Metrology and inspection - verifying that measured tool geometry corresponds to intended working angles.
- Process planning for turning, drilling, milling and other operations where orientation and resultant cutting direction affect cutting performance.
Who will use this standard
- Manufacturing and process engineers
- Tool designers and cutting-tool manufacturers
- CNC programmers and CAM engineers
- Machine-tool setup technicians and inspectors
- Researchers and educators in machining and abrasive processes
Related standards
- ISO 3002-1 - definitions of tool and working angles (referenced by this part)
- ISO 841 - machine tool axis/plane conventions used to define the machine reference system
ISO 3002-2 is valuable when accurate, reproducible conversion between tool geometry (tool-in-hand) and operational geometry (tool-in-use) is required for machining, grinding and tool development.
Open preview (PDF)Basic quantities in cutting and grinding — Part 2: Geometry of the active part of cutting tools — General conversion formulae to relate tool and working angles
