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MCE311_HW03_sol_fall2011(2)

# MCE311_HW03_sol_fall2011(2) - 17.1 A 42.0-mm-thick plate...

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17.1 A 42.0-mm-thick plate made of low carbon steel is to be reduced to 34.0 mm in one pass in a rolling operation. As the thickness is reduced, the plate widens by 4%. The yield strength of the steel plate is 174 MPa and the tensile strength is 290 MPa. The entrance speed of the plate is 15.0 m/min. The roll radius is 325 mm and the rotational speed is 49.0 rev/min. Determine (a) the minimum required coefficient of friction that would make this rolling operation possible, (b) exit velocity of the plate, and (c) forward slip. Solution: (a) Maximum draft d max = μ 2 R Given that d = t o - t f = 42 - 34 = 8.0 mm, μ 2 = 8/325 = 0.0246 μ = (0.0246) 0.5 = 0.157 (b) Plate widens by 4%. t o w o v o = t f w f v f w f = 1.04 w o 42( w o )(15) = 34(1.04 w o ) v f v f = 42( w o )(15)/ 34(1.04 w o ) = 630/35.4 = 17.8 m/min (c) v r = 2 π rN = 2 π (0.325)(49.0) = 100.06 m/min s = ( v f - v r )/ v r = (17.8 – 100.059)/100.059 = - 0.056 17.26 A 5 cm-long billet with diameter = 3.1 cm is direct extruded to a diameter of 1.25 cm. The extrusion die angle = 90°. For the work metal, K = 310 MPa, and n = 0.20. In the Johnson extrusion strain equation, a = 0.8 and b = 1.5. Determine (a) extrusion ratio, (b) true strain (homogeneous deformation), (c) extrusion strain, and (d) ram pressure at L = 5.0, 3.75, 2.5, 1.25 and zero cm. Use of a spreadsheet calculator is recommended for part (d).

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MCE311_HW03_sol_fall2011(2) - 17.1 A 42.0-mm-thick plate...

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