According to the Ernst and Merchant theory, the relation between the shear angle (ϕ), friction angle (β) and rake angle (α) in single point cutting tool in turning is as follows:

1
2ϕ + β + α = 90°
2
2ϕ + β - α = 90°
3
ϕ + 2β - α = 45°
4
2ϕ + β - α = 45°

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