A strip is to be rolled from a thickness of 36 mm to 20 mm using a two-high mill having rolls of diameter 400 mm. The approximate value of the coefficient of friction for unaided bite will be:

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Question

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HPCL Engineer Mechanical 04 Nov 2022 Official Paper (Shift 2)

Answer 1

Concept:

The relationship between reduction or draft, coefficient of friction and radius of rolls is as follows:

\(Δ h = μ^2 R \)

where, Δ h = Reduction or draft = (h_initial) - (h_final)

R = Radius of rolls, μ = Coefficient of friction

Calculation:

Given:

Given, h_i = 36 mm, h_f = 20 mm, D = 400 mm ⇒ R = D/2 = 200 mm

Δ h = (36-20) =16 mm
\(Δ h = μ^2 R \Rightarrow 16 = μ ^2 \times 200 \)

\(\mu = \sqrt{0.08} = 0.2828\)