3D surface representation and trajectory optimization with a learning-based adaptive model predictive controller in incremental forming

摘要

In this work, a novel learning-based on-line adaptive shape predictive model is developed to represent the 3D surface of the formed shape after springback in single point incremental forming (SPIF). The model can be updated in each step to predict the forming shapes in future prediction horizons given a new potential tool path, with on-line collected historic geometrical data and their corresponding tool path in previous steps. Furthermore, this model is incorporated into a sequential coupled constrained model predictive control algorithm (MPC), to optimize the potential step-down and step-over sizes in future steps, to minimize the geometric error of the whole formed part in SPIF. Two different geometric shapes, a benchmark truncated cone (with only convex geometric feature) and a non-convex dog-bone (with varying convex and concave feature), are selected for the experimental testing of the new developed on-line adaptive model predictive control algorithm (AMPC). This paper presents the detailed data acquisition and modelling process, on-line feedback control algorithms and experimental validation. The experimental results indicated that the maximum geometric error in the concerned region for the benchmark truncated cone shape and the complex non-convex dog-bone shape can be successfully decreased from above 1.25 mm without control to below 0.75 mm with the current adaptive MPC controller, which cannot be achieved with our previous non-adaptive MPC controller. This is believed to be the first attempt to incorporate a learning-based nonlinear adaptive predictive model with a model predictive controller for tool path optimization in incremental forming. The adaptive model predictive controller (AMPC) demonstrated in this work may provide a powerful tool for geometric accuracy improvement for production of complex geometric shapes in varying forming conditions in incremental sheet forming in the future.