Definition precision — shear angle in orthogonal cutting In metal cutting theory, the shear angle is defined as the angle between the shear plane and which reference direction?

Difficulty: Easy

Correct Answer: Direction of cutting velocity

Explanation:


Introduction / Context:
The shear angle is central in chip-formation mechanics. It appears in Merchant's analysis and affects chip thickness, cutting force, and heat generation.



Given Data / Assumptions:

  • Orthogonal cutting with a straight cutting edge normal to the cutting velocity.
  • Shear occurs along a single shear plane.


Concept / Approach:
The shear angle φ is defined as the angle between the shear plane and the direction of cutting velocity. With chip thickness t_c, uncut chip thickness t_o, and rake angle α, the relationships include geometry and force models (e.g., Merchant's minimum energy criterion).



Step-by-Step Solution:

Establish cutting kinematics → velocity direction is tangential to workpiece motion past the tool.Define shear plane → plane along which primary plastic deformation concentrates.By definition, φ is measured from cutting velocity direction to the shear plane → correct reference is the direction of cutting velocity.


Verification / Alternative check:
Alternative equivalent definition uses 90° − φ as the angle between the shear plane and the work surface; hence choosing the work surface would be incorrect without that complement.



Why Other Options Are Wrong:
Work surface relates by complement (90° − φ), not φ itself. Tool rake face angle is α, not φ. Spindle axis and normal to work surface are unrelated reference directions for defining φ.



Common Pitfalls:
Interchanging φ with 90° − φ, leading to errors in chip-thickness ratio and force predictions.



Final Answer:

Direction of cutting velocity

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