Question

In an orthogonal machining with a tool of 9° orthogonal rake angle, the uncut chip thickness is 0.2 mm. The chip thickness fluctuates between 0.25 mm and 0.4 mm. The ratio of the maximum shear angle to the minimum shear angle during machining is __________.

Accepted Answer

The correct answer is 1.49 (± 0.05). tanφ = r·cosα/(1−r·sinα), where r=t/tc is the chip-thickness ratio and α=9°. At tc=0.25 mm: r=0.8, tanφ=0.8cos9°/(1−0.8sin9°)≈0.903 → φ≈42.1° (max shear angle, from min chip thickness). At tc=0.4 mm: r=0.5, tanφ=0.5cos9°/(1−0.5sin9°)≈0.536 → φ≈28.2° (min shear angle, from max chip thickness). Ratio = 42.1/28.2 ≈ 1.49.

Explanation