Data of an orthogonal cutting is:

Chip thickness ratio = 0.4

Rake angle = 20°

What will be the shear plane angle?

[given, $cos 2 0^{\circ} = 0.94$ , $sin 2 0^{\circ} = 0.34$ ]

Question

Question

This question was previously asked in

SJVN ET Mechanical 2019 Official Paper

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Answer 1

Concept:

The shear plane angle $ \phi $ in orthogonal cutting is calculated using:

$ \tan \phi = \frac{r \cos \alpha}{1 - r \sin \alpha} $

Given:

Chip thickness ratio $ r = 0.4 $, Rake angle $ \alpha = 20^\circ $

$ \cos(20^\circ) = 0.94 $, $ \sin(20^\circ) = 0.34 $

Calculation:

$ \tan \phi = \frac{0.4 \cdot 0.94}{1 - 0.4 \cdot 0.34} = \frac{0.376}{0.864} \approx 0.435 $

$ \phi = \tan^{-1}(0.435) $