Influence of Strain Hardening on the Force in Cold Strip Rolling

Abstract

The boundary problem in cold strip rolling with plane strip deformation is solved on the basis of the Amontons–Coulomb frictional law for materials whose strengthening is described by the formula σ_s/σ_s0 = 1 + mεⁿ. When n = 1, solution in quadratures is employed; when n ≠ 1, a power series is adopted. The influence of the parameters m and n of the strain-hardening curve on the position of the strip’s neutral cross section and the rolling force is established. Increase in n shifts the strip’s neutral cross section in the rolling direction. For materials with the same strengthening coefficient on emerging from the reduction zone, the rolling force increases with decrease in n. The new solution is compared with its predecessors. Note that the difference in the results for the rolling force given by the proposed method and the Tselikov formula increases with decrease in n and with increase in m and λ_c. It is 20–30% when n ≤ 0.35 and λ_c ≥ 1.3.