Understanding shear velocity in metal cutting In orthogonal/oblique machining, “shear velocity” refers to the velocity of material flow along the shear plane within the work material (relative to the work), not along the tool face or relative to the tool. Which option best matches this definition?

Introduction / Context:
In metal cutting theory (Merchant analysis), three fundamental velocities are used: cutting velocity, chip (sliding) velocity, and shear velocity. Students often confuse these with one another because they occur simultaneously at different interfaces of the cutting zone.

Given Data / Assumptions:

• Conventional turning or orthogonal cutting is considered.
• The tool is sharp and the chip forms by primary shear along a well-defined shear plane.
• Steady-state cutting (constant speed, feed, and depth of cut).

Concept / Approach:
Cutting velocity V is the velocity of the work surface past the tool (work relative to tool). Chip (or sliding) velocity Vc is the velocity of chip flow up the rake face (chip relative to tool). Shear velocity Vs is the material flow velocity along the shear plane, i.e., inside the work material across the primary deformation zone, typically taken relative to the work.

Step-by-Step Solution:

Verification / Alternative check:
Standard machining texts depict the velocity triangle and label Vs along the shear plane, distinct from V (work-tool) and Vc (chip-tool) directions.

Why Other Options Are Wrong:
Tool relative to the workpiece: that is the cutting velocity V, not Vs.Chip relative to the tool: that is chip/sliding velocity Vc, not Vs.Tool motion along the tool face: describes Vc direction, not Vs.

Common Pitfalls:
Assuming the largest velocity must be the shear velocity or equating chip sliding with shearing. Always relate each velocity to its physical interface.

Final Answer:

None of these