Orthogonal cutting scenario: If depth of cut is halved and feed is doubled (chip-thickness ratio unchanged), how does the actual chip thickness change?

Introduction / Context:
In orthogonal cutting, the uncut chip thickness primarily depends on feed, while depth of cut influences chip width. Understanding how process parameters map to chip dimensions is essential for predicting cutting forces, surface integrity, and tool wear. This problem explores the effect of changing feed and depth of cut on chip thickness when the chip-thickness ratio remains constant.

Given Data / Assumptions:

• Orthogonal cutting assumption (chip flows normal to cutting edge).
• Chip-thickness ratio r = t1 / t2 remains constant.
• t1 = uncut chip thickness (mainly governed by feed), t2 = actual chip thickness.
• Depth of cut affects chip width, not thickness, for a given setup.

Concept / Approach:
For orthogonal turning/planing, uncut chip thickness is proportional to feed, while depth of cut sets the chip width. If feed doubles, t1 doubles. Since r = t1 / t2 is unaffected, t2 must scale in the same proportion as t1 to keep r constant.

Step-by-Step Solution:

Verification / Alternative check:
Because chip-thickness ratio is unchanged, any proportional change in uncut thickness must reflect identically in chip thickness. The halved depth of cut does not alter t1 in orthogonal assumptions; it only narrows the chip.

Why Other Options Are Wrong:

• Halved/unchanged/quarter: contradict the constant ratio requirement when feed is doubled.
• Quadrupled: overstates the effect; only a factor of 2 is required to preserve the ratio.

Common Pitfalls:
Confusing effects of feed versus depth of cut; assuming depth of cut changes thickness rather than width; ignoring the definition of chip-thickness ratio r.

Final Answer:
doubled