Forming forces in incremental forming of a geometry with corner feature: investigation into the effect of forming parameters using response surface approach

Single-point incremental forming (SPIF) is an emerging sheet forming process. The force-parameter correlation is yet not well clear in this process, specifically for geometries with corners. In the present study, a new level of understanding on the parameter-force relationship is presented. A simple shape with corners (i.e., frustum of pyramid containing corners and oblique wall) is opted as the test geometry. Following the response surface method, a design of experiments (DoE) comprising of 47 runs obtained by varying five forming parameters namely sheet thickness, tool diameter, wall angle, step size, and flow stress is performed. The analysis of the results reveals that the parameter-force relation in SPIF is complex and interactive, explaining that the effect of variation in a parameter on the force magnitude is closely associated with the value and the type of the other parameters employed for forming. From the analysis of the forces involved in forming the pyramid, it is found that the corner requires more force than does the wall. Further, the normal force (i.e., force along normal to sheet plane) is greater than the in-plane force. The use of very small tools, especially low d/to where d is the tool diameter and to is the sheet thickness, is observed to cause fabrication defects leading to substantial rise in the magnitude of forming force thus endangering the machine tool. Finally, a set of force models is proposed using which one can predict a set of forming parameters simultaneously minimizing the force and preventing the fabrication problems.