BP artificial neural network modeling for accurate radius prediction and application in incremental in-plane bending

Abstract

Incremental in-plane bending (IIB) is a new and advanced flexible manufacturing technology for small-lot production of strip with various bending radii. The strip of sheet metal is bent incrementally by a beating inclined punch. The bending radius is strongly affected by mechanical properties of the material, geometry of the strip, and processing parameters. It is difficult to predict the bending radius due to the complex synergistic effects of the controlling parameters. How to predict the bending radius accurately has therefore become a key point to be urgently solved in the development of this advanced forming technology. In this paper, a model based on a back propagation neural network (BPNN) is introduced to reveal the relationship of bending radius with angle of die α, indentation s, pitch p, and width of strip w. Out of 14 different BPNN architectures trained, the 4-9-9-1 BPNN with two hidden layers having nine neurons trained with the Levenberg-Marquardt algorithm (trainlm) is found to be the optimum network model, and the prediction error is less than 2 % on average. Otherwise, a 1-9-9-4 reverse BPNN is developed to build the processing window for a given bending radius. Meanwhile, taking section moment of inertia I as a quantitative index of forming stability, α, p, s, w0 are optimized as design variables in order to make objective functions of I maximized simultaneously. Finally, to verify its predictive capability, the present approach is applied to a case study, and the optimal combination of parameters for stable forming during IIB is obtained.