Parameter that completely characterizes chip formation kinematics In the orthogonal metal cutting model, which single parameter is used to completely describe the chip formation geometry for a given uncut thickness and rake angle?

Introduction / Context:
In orthogonal cutting theory, chip formation is modeled as simple shear along a plane characterized by a shear angle. This kinematic description connects uncut chip thickness, chip thickness, and tool rake angle, providing a compact way to discuss chip compression and deformation.

Given Data / Assumptions:

• Orthogonal cutting with constant rake angle and steady-state conditions.
• Uncut chip thickness and rake are specified.
• Friction and thermal effects are excluded from the purely geometric description.

Concept / Approach:
The chip thickness ratio r and shear plane orientation are governed by the shear angle. Once the shear angle is set, the geometric relation among uncut thickness, chip thickness, and rake is fixed. Chip–tool contact length is a frictional/tribological outcome influenced by speed, lubrication, and material; it does not by itself define chip formation kinematics.

Step-by-Step Solution:
Define geometry: uncut thickness t1, chip thickness t2, rake angle α, shear angle φ.Use geometric relations (e.g., r = t1/t2 as a function of φ and α) to characterize chip compression.Conclusion: shear angle φ completely describes the chip formation geometry for given t1 and α.

Verification / Alternative check:
Standard derivations relate φ to measurable quantities (like r and α), confirming φ as the single kinematic descriptor of chip formation in the 2D orthogonal model.

Why Other Options Are Wrong:
Chip–tool contact length is a result, not a defining geometric parameter. Saying both are required mixes cause and effect. Cutting speed influences temperature and friction but does not set the geometric chip relation directly.

Common Pitfalls:
Conflating geometric descriptors (φ) with process outcomes (contact length, temperature). Ensure model scope is clear.

Final Answer:
Shear angle