The shear angle for two-dimensional cutting operation is given by an equation

where r = cutting ratio, α = rake angle and ϕ = shear angle.

1
\(\tan \phi = \frac{{r\cos \alpha }}{{1 + r\sin \alpha }}\)
2
\(\tan \phi = \frac{{r\cos \alpha }}{{1 - r\sin \alpha }}\)
3
\(\tan \phi = \frac{{1 - r\sin \alpha }}{{r\cos \alpha }}\)
4
\(\tan \phi = \frac{{1 + r\sin \alpha }}{{r\cos \alpha }}\)

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