Reliable Tension Leveling Process Design Using Stochastic Optimization

Abstract

In this paper, reliability based design optimization method for the determination of tension leveling process combining Finite Element (FE) simulation and numerical stochastic optimization method has been proposed. For the tension leveling calculation, steady state analysis based on the incremental deformation theory of plasticity is adopted. In the simulation, Chaboche-Rousselier hardening rule is used for accurate cyclic stress-strain calculation. Since only steady state of a metallic strip is calculated and contact analysis can be avoided the computing cost of the FE simulation is very small compare to other non-steady FE simulations.
The optimization problem is formulated to minimize the probability of failure. In this problem, it is assumed that a failure product appears due to the tolerances of design variables such as tension load, roll-intermesh and so on, and uncontrollable variables like geometric parameters and mechanical properties. Tolerances of such parameters are assumed to appear in stochastic manner. For probability of failure estimation, Monte Carlo simulation, which virtually demonstrates a mass production by iteratively generating the design and uncontrollable variables randomly, is employed. Additionally, the response surface with Moving Least Square Method is used to reduce the computing time. The proposed optimization has been applied on the four-work-roll tension leveling process design problem. The obtained result is more reliable than the optimum obtained by the ordinary deterministic optimization method. Additionally, it is found that the tolerances of the initial yield stress and Young's modulus have a great influence on the residual curvature.