Shear angle definition in metal cutting In orthogonal cutting, the shear angle (phi) is defined as the angle that the shear plane makes with which reference direction?

Introduction / Context:
The shear angle controls chip thickness, cutting forces, and heat generation in metal cutting. It is a geometric descriptor of the shear plane relative to the cutting direction.

Given Data / Assumptions:

• Orthogonal cutting model with a straight shear plane.
• Cutting velocity vector defines tool travel direction.

Concept / Approach:
By convention, the shear angle is measured between the shear plane and the direction of cutting velocity. Larger shear angles tend to reduce chip thickness and cutting force for a given uncut chip geometry.

Step-by-Step Solution:
Identify the shear plane: plane along which plastic shear occurs.Define reference: cutting velocity direction (tool travel relative to work).Shear angle = angle between shear plane and cutting velocity direction.

Verification / Alternative check:
Merchant’s analysis uses this definition to derive relations involving rake angle and friction angle.

Why Other Options Are Wrong:

• Tool axis or work central plane are not the standard references for shear angle.
• Rake face plane defines rake angles, not shear angle.

Common Pitfalls:
Measuring from the normal to cutting direction instead of the direction itself; confusing shear angle with rake angle.

Final Answer:
the direction of tool travel (cutting velocity direction)