Question
Download Solution PDFWhich of the following relation is correct for Ernst-Merchant Theory? [where ϕ = Shear angle, α = Rake angle, β = Friction angle]
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
From the merchant first analysis
\(2\phi + \beta - \alpha = \frac{\pi }{2}\)
Where, ϕ = shear angle, β = friction angle, α = cutting rake angle
There are several theories for the relationship between α (rake angle), β (friction angle), and ϕ (shear angle).
Ernst – Merchant theory:
\(\phi = \frac{\pi }{4} - \frac{\beta }{2} + \frac{\alpha }{2}\)
Stabler theory (Modified Ernst – Merchant theory):
\(\phi = \frac{\pi }{4} - \beta + \frac{\alpha }{2}\)
Lee and Shaffer theory:
\(\phi = \frac{\pi }{4} - \beta + \alpha \)Last updated on Jul 1, 2025
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