Modeling, measurement, and control of the multi-axis bending process

Computer numerically controlled multi-axis bending is a relatively new metal forming process for fabricating long slender workpieces of arbitrary shape and cross section. Although this process can achieve high levels of productivity and flexibility over conventional forming processes, generating CNC programs for a newly-designed workpiece involves a laborious trial-and-error procedure by the manufacturing engineer. A methodology was developed to determine multi-axis control commands from the given 3D geometric shape of the designed part, based on the theory of differential geometry and learning control.; In this methodology, a CAD model is first created from the design data. The model contains the extrinsic representation of the part geometry as well as the die geometry. Since the multi-axis bending is inherently a local deformation process, an open-loop process model was formed by applying intrinsic geometry. With the proper compensation for the elastic springback, the process model can be used to compute a set of initial control commands for fabricating the first-trial workpiece.; There is inevitably a mismatch between the designed and fabricated shape due to the approximation of the open-loop process model. A feedback control scheme for the multi-axis bending process is presented. The closed-loop control is derived from transfer functions that represent the bending and twisting processes. The dynamics of these processes is due to the convection of shape between the bending dies during deformation. The success of the feedback control also depends on the accurate measurement of part shape. To obtain the intrinsic functions of the fabricated part, a method was developed for reconstructing part geometry from inspection data. From the shape errors, incremental control commands are generated using the inverse transfer functions of the linearized process model, and then superimposed upon the previous commands to correct the shape deviation. This iterative learning process proceeds until the desired part geometry is achieved.; On the basis of the methodology, a software package has been developed and used by industry. The package established data communication among design, manufacture, and inspection. The study presented in this dissertation has proved very helpful for the manufacturing industry to develop flexible metal forming technology.