Merchant’s force analysis assumptions in metal cutting According to Merchant’s classical analysis of orthogonal cutting, which of the following assumptions are made?

Introduction / Context:Merchant’s force analysis provides foundational insight into chip formation, shear angle, and cutting forces in orthogonal cutting. The analysis relies on idealized assumptions to yield tractable relationships.

Given Data / Assumptions:

• Orthogonal cutting model with a sharp tool.
• Steady-state cutting with a continuous chip.
• Defined friction along the rake face resulting in a resultant force.

Concept / Approach:Key assumptions include a perfectly sharp tool with no flank contact, continuous chip (no built-up edge) to avoid transient effects, and constant cutting velocity for steady-state force balance. These yield the classic shear plane analysis and the Merchant shear-angle relation under a minimum energy criterion.

Step-by-Step Solution:Evaluate (A): Sharp tool with no flank contact → assumed in the ideal model.Evaluate (B): Continuous chip, no BUE → steady-state simplifies analysis.Evaluate (C): Constant velocity → permits static force triangle and constant shear plane.Therefore, select “all of the above”.

Verification / Alternative check:Textbook derivations explicitly list these simplifying assumptions before constructing force and velocity triangles.

Why Other Options Are Wrong:(E) contradicts the assumption of a single resultant friction force at the rake face employed in the model.

Common Pitfalls:Applying Merchant’s conclusions directly to interrupted cuts or built-up-edge conditions; ignoring tool wear and thermal effects not captured in the idealization.

Final Answer:all of the above