Question

A single-point cutting tool with zero rake angle is used for orthogonal machining. If the chip-compression ratio is 1.25, then the shear angle (in degree) during machining is \(\underline{\hspace{2cm}}\). [round off to one decimal place]

Hint:

Always check whether the problem uses chip-compression ratio ($t_c/t$) or chip-thickness ratio ($t/t_c$); many students mix the two.

Answer 1

Correct Answer: 38 - 39

Chip-compression ratio: \[ r = \frac{t}{t_c} = 1.25 \] For zero rake angle (\(\alpha = 0\)): \[ r = \frac{\sin\phi}{\cos(\phi - 0)} = \tan\phi \] Thus: \[ \phi = \tan^{-1}(1.25) \] Compute: \[ \phi \approx 51.34^\circ \] But in machining, chip-compression ratio is often defined as \[ r_c = \frac{t_c}{t} = 1.25 \Rightarrow r = \frac{1}{1.25} = 0.80 \] Use correct definition: \[ r = 0.8 = \tan\phi \] \[ \phi = \tan^{-1}(0.8) \approx 38.66^\circ \] Thus shear angle lies in: \[ \boxed{38.0\text{ to }39.0^\circ} \]