Optimization of a pipe end upsetting process

This paper discusses the application of Design of Experiments, Response Surface Methodology and Robust Optimization techniques for efficient optimization of pipe end upsetting with a non-uniform and transient temperature field. First, target pipe end shape and objective functions are defined, and constraints on the final shape, forging pressures, temperatures and strain rates are specified. Second, parametric initial work piece shape and initial temperature distributions are defined. Material data are obtained from independent compression tests. Third, a Box-Behnken experimental design (BBD) is defined for a set of shape and temperature variables. A set of ABAQUS simulations is run according to the BBD. The results from the simulation runs are processed by a MATLAB-script. The script calculates regression relations for all essential responses and estimates the value of the object functions and constraints in the entire design space. Further, it performs both standard and robust constrained optimization. The robust optimization considers the effects of variability in design variables. Finally, MATLAB plots several 2D cross-sections of objective and constraints functions in the multi-dimensional design space. Such process windows make prediction of the capability of the upsetting process possible and are very valuable input to the design and quality assurance work.