Lab #10 Sheet Rolling Objective:
To cold roll aluminum sheet, and to compare experimentally determined roll pressures with pressures predicted by theory. To observe formability limits of two different aluminum alloys.
Materials
1100-0 aluminum strips about 0.250 inch thick and 2 inches wide. 2024-T351 aluminum strips about 0.250 inch thick.
Equipment
Rolling mill (manufactured by Fenn) located in the department of metallurgical engineering. Diameter of working rolls is 5.25 inches.
Measurements
Roll the 1100-0 aluminum in about 9 successive roll passes of about 0.025 inch reduction each, without lubrications, and record the roll separating force. Be sure to record the new thickness and new width after each step. Roll the 2024 aluminum until failure is observed.
Results – Calculations and Graphs
Plot average reduced roll pressure – Pav/2_{} - obtained from experiment as a function of cumulative strain. Do not use expanded scales, i.e. start with zero. Also plot the predicted average reduced rolling pressure adjusted for friction on the same graph. Check the effect of roll flattening for one of your reductions only (the last one is suggested) upon the predicted roll forces.
Discussion of Results
Discuss all experimental results and observations. Compare theoretical pressure predictions with experimental results and evaluate the significance of your observations. Indicate and discuss any departures from a constant friction correction factor postulated in the literature and indicated in the next section. Discuss the effect of accounting for roll flattening upon the predicted roll separating forces and upon agreement with experiment. Devise an experiment to determine the mill modulus of the rolling mill.
Simplified Analysis of Roll Separating Force in Flat Rolling The analysis of roll separating forces has received much attention since they are important for the determination of deflections of equipment components (e.g. rolls) and rolling torque. A number of solutions is based on the slab technique, perhaps the most also applied, such as slip line theory, upper bounds, and the finite element method. Since all of these methods are rather involved, only very simple approaches will be considered here.
Projected Contact Length L^{2} = (L)^{2} + _{} but (L)^{2} = R^{2} – (R - _{})^{2} = Rh - _{} _{} L = _{} Roll Separating Force in Flat Rolling Homogeneous Deformation Force due to pressure based on mean yield stress per unit width is _{} = 2_{} where W = sheet width _{}= _{} = mean yield shear strength and _{}_{o} = _{} σ_{oi} = yield strength at roll gap entry σ_{of} = yield strength at roll gap exit or _{}_{o} = _{} if functional relationship between stress and true strain in known A multiplying factor of 1.3 may be used in the force equation to account for friction Another simplified approach suggests that _{} = 2_{} _{} where b_{av} = _{}
Roll Flattening can be accounted for starting with the force equation. It provides a first approximation of roll separating force if the nominal roll radius is used the flattened roll radius is then determined from Hitchcock’s equation, which is based on Hertzian contact stress consideration. Flattened roll radius R = R _{} or R = R _{} where typically for steel C = 2.4 x 10^{-5 }_{}^{ }or 1.6 x 10^{-7} _{}
Reference: G.W. Rowe: An Introduction to the Principles of Metalworking. W.F. Hosford and R.M. Caddell: Metal Forming Mechanics and Metallurgy. Lab 10 Page |