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Section: Machining
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Machining

Tool Geometry

Quick Cheat Sheet

Summary

Single-point tool geometry — defined by rake, relief and cutting-edge angles in the ASA or ORS systems — controls chip flow direction, cutting forces, surface finish and tool life.

Key Points

  • Rake angles (back, side) decide chip flow and cutting force
  • Relief angles (end, flank) prevent the tool from rubbing the work
  • Cutting-edge angles set chip thickness, width and tool entry behaviour
  • Nose radius affects surface finish, tool strength and chatter
  • ASA system (machine reference) vs ORS system (orthogonal reference)
  • Tool signature lists 7 elements in standard order

Remember This

  • 1ASA signature: back rake, side rake, end relief, side relief, end cutting edge, side cutting edge, nose radius
  • 2Positive rake → lower cutting force, weaker tool (used for ductile metals)
  • 3Negative rake → stronger tool, used for hard/brittle materials & interrupted cuts
  • 4Typical relief angles: 5–10° (too small = rubbing; too large = weak edge)
  • 5Surface roughness Rₐ ≈ f² / (8R) — larger nose radius R → better finish

Quick Formulas

Theoretical surface finish

Rₐ ≈ f² / (8R)

Single Point Cutting Tool

A single point cutting tool has one cutting edge and is used for operations like turning, boring, and shaping.

Tool Angles and Surfaces

Key Surfaces

  1. Rake Surface - Surface over which the chip flows
  2. Flank Surface - Surface facing the newly generated workpiece surface
  3. Cutting Edge - Edge formed by intersection of rake and flank surfaces

Important Angles

Rake Angle (α)

  • Angle between rake surface and reference plane perpendicular to cutting velocity
  • Controls chip flow direction
  • Positive rake - rake surface inclined away from cutting edge (easier cutting, weaker tool)
  • Negative rake - rake surface inclined toward cutting edge (stronger tool, more cutting force)
  • Zero rake - rake surface perpendicular to cutting direction

Clearance/Relief Angle (β)

  • Angle between flank surface and cutting surface of workpiece
  • Prevents rubbing between tool flank and workpiece
  • Typical values: 5° to 15°
  • Too small → rubbing and friction
  • Too large → weak cutting edge

Cutting Edge Angle

  • Angle of cutting edge orientation relative to direction of tool travel

Tool Signature (ASA System)

Tool geometry specified by 7 elements in order:

  1. Back rake angle
  2. Side rake angle
  3. End relief angle
  4. Side relief angle
  5. End cutting edge angle
  6. Side cutting edge angle
  7. Nose radius

Example: 0-10-6-6-8-15-0.8 (all angles in degrees, nose radius in mm)

Orthogonal vs Oblique Cutting

Orthogonal Cutting

  • Cutting edge perpendicular to direction of tool motion
  • Chip flows directly away from cutting edge
  • 2D analysis (simpler to analyze)
  • Used in theoretical studies

Oblique Cutting

  • Cutting edge at an angle (not 90°) to direction of tool motion
  • Chip flows at an angle
  • 3D analysis (more complex)
  • More common in actual machining operations
  • Produces longer, thinner chips

Chip Formation

Types of Chips

  1. Continuous Chip

    • Long, continuous ribbon
    • Formed with ductile materials at high cutting speeds
    • Good surface finish
    • Steady cutting forces

  2. Discontinuous/Segmented Chip

    • Small segments or particles
    • Formed with brittle materials
    • Low cutting speeds
    • Poor surface finish
    • Fluctuating cutting forces

  3. Continuous Chip with Built-Up Edge (BUE)

    • Layers of work material adhere to rake face
    • Forms at moderate speeds with ductile materials
    • BUE periodically breaks off
    • Poor surface finish
    • Can protect tool but causes dimensional inaccuracy

Tool Wear

Types of Tool Wear

  1. Flank Wear

    • Occurs on flank surface
    • Most common and predictable
    • Measured as wear land width (VB)
    • Gradual and uniform

  2. Crater Wear

    • Occurs on rake surface
    • Caused by chip sliding over rake face
    • High temperatures accelerate crater formation

  3. Nose Wear

    • Wear at tool nose radius
    • Affects surface finish

Tool Life

  • Tool life = cutting time until tool must be replaced
  • Measured by amount of flank wear
  • Criterion: VB = 0.3 mm (typical for HSS), 0.6 mm (for carbides)

Cutting Forces

Three mutually perpendicular force components:

  1. Fc - Cutting force (tangential/main cutting force)

    • In direction of cutting velocity
    • Largest component
    • Used to calculate power

  2. Ft - Thrust force (feed force)

    • In direction of tool feed
    • Perpendicular to cutting force

  3. Fr - Radial force

    • Perpendicular to both Fc and Ft
    • Pushes tool away from workpiece

Power Calculation

Pc = Fc × v

Where:

  • Pc = Cutting power (W)
  • Fc = Cutting force (N)
  • v = Cutting speed (m/s)

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