No abstract

Rotary-draw tube bending operation is one of the most universal methods used for the tube forming processes. Similar to the other forming methods, some problems such as wall thinning, cross-section distortion, wrinkling, and springback can also be seen on the tubes formed by rotary-draw bending operations. Springback is a very common problem and its prediction plays a crucial role in increasing the efficiency of the tube bending operations and also to overcome the difficulties in the assembly processes. Tube diameter, wall thickness, bend radius, bend angle, and coefficient of friction can be considered as the most effective parameters that cause the variation of springback magnitude. In this study, not a simple one-at-a-time sensitivity analysis, but a thorough investigation of the springback phenomena involving interactions between the geometrical and mechanical parameters is done and surrogate models are developed via the data obtained from finite element analysis using a multi-purpose explicit and implicit finite element software LS-DYNA to analyze the non-linear response of structures. The constructed surrogate models can be utilized to perform fast prediction of springback for a given combination of parameters. Three different surrogate modeling techniques are exploited and it is found that the linear polynomial response surface approximations can provide acceptable accuracy. Finally, experiments are conducted to validate the accuracy of surrogate models. It is observed that the cross-validation error predictions are close to the errors observed in the experiments.

Many automobile companies are actively exploring the use of high-strength dual-phase steels as an alternative to aluminum and magnesium alloys owing to their light weight, low cost and durability. However, dual-phase steels have a tendency to springback more than other structural steels in a forming operation owing to their high tensile strength. In addition, variations in manufacturing process parameters and material properties cause springback variation over different manufactured parts. Therefore, it is an important task to reduce the magnitude of springback, as well as its variation within, to produce robust and cost-effective parts. This article investigates minimization of the magnitude and variation of springback of DP600 steels in U-channel forming within a robust optimization framework. The computational cost was reduced by utilizing metamodels for prediction of the springback and its variation during optimization. Three different allowable sheet thinning levels were considered in solving the robust optimization problem, and it was found that, as the allowable thinning increased, the die radius decreased, thereby the magnitude and variation of springback reduced. A simple sensitivity analysis was performed and the yield stress was found to be the most important random variable. Finally, a double-loop Monte Carlo simulation method was proposed to calculate part-to-part and batch-to-batch springback variations. It was found that, as the batch-to-batch variation of yield stress increased, the batch-to-batch springback variation increased, while the part-to-part springback variation remained unchanged.

In this study, surrogate models are constructed to approximate the behavior of simulation models for springback angles, sidewall curl, and sheet thickness reduction in U-bending process. The surrogate-modeling techniques used here are: (i) polynomial response surface (PRS), (ii) Kriging (KR) and (iii) radial basis functions (RBF). While constructing surrogate models, the following procedure is pursued. First, a set of training points is generated using Latin hypercube sampling method, and finite element simulations are performed at these points. Then, surrogate models are constructed utilizing the training data. The accuracies of the surrogate models are evaluated by using the leave-one-out cross validation errors. First-order PRS is found to be most accurate surrogate model for prediction of the springback angles, side wall curl, and sheet thickness reduction.