Orthogonal cutting system basics: Which statements properly describe orthogonal cutting kinematics and chip flow?

Introduction / Context:
Orthogonal cutting is an idealized 2D model used to analyze chip formation, shear angle, and cutting forces. It assumes a straight cutting edge oriented perpendicular to the cutting velocity, with plane strain and no side flow. Understanding this idealization helps interpret Merchant’s analysis and tool-chip friction models.

Given Data / Assumptions:

• Two-dimensional cutting (plane strain) with width much larger than uncut chip thickness.
• Cutting edge perpendicular to tool velocity.
• Chip flows straight up the rake face without lateral spread.

Concept / Approach:
The orthogonal model contrasts with oblique cutting where the cutting edge is inclined, producing side flow. In orthogonal cutting, chip velocity is normal to the cutting edge, simplifying force decomposition into cutting and thrust components and enabling closed-form relations for shear angle and force ratios.

Step-by-Step Solution:

Verification / Alternative check:
Classic texts on metal cutting illustrate these three defining statements in orthogonal cutting diagrams and derivations.

Why Other Options Are Wrong:
Each of (a), (b), and (c) is essential to the orthogonal model; thus “all of the above” is correct. “None” is inconsistent with the model.

Common Pitfalls:
Applying orthogonal results directly to oblique turning or milling where chip flow is three-dimensional; corrections are needed for inclination and helix angles.

Final Answer:
all of the above