The application of springback compensation to the CAD geometries of forming tools: Milestone 2

For car body parts, generally a surface modeling CAD system is used. The geometry of the tools that are used for forming the parts is based directly on this description. To compensate for springback after forming, the tools have to be modified. This turns out to be a complicated and time consuming task. Also, because the surface description is generally not flexible enough, the springback compensation cannot be transferred to the CAD geometry entirely, and the accuracy of the compensation is heavily reduced. For parts with Class-A surface quality, such as outer car body panels, the tolerances for the surface accuracy and smoothness are extremely tight. This is because the human eye is capable of detecting the smallest defects in the light reflections on the surfaces. It is hard to retain such tight tolerances during modification. However, the CAD surfaces are generally modeled orderly, making them easier to modify. For internal panels the tolerances are not so stringent. Unfortunately, these geometries are also hard to modify since the mathematical structure of the geometry is generally bad. The all-purpose CAD systems that are used for the creation of these geometries tend to produce many trimmed surfaces and T-junctions between surfaces. Surface-modeling CAD is based on a group of mathematical spline surfaces called NURBS. The two most basic and most used surfaces are the Bezier surfaces and the piecewise polynomial B-spline surfaces. The boundary conditions between these surfaces, defining the smoothness of the geometry, can be imposed by certain rules for their control points. Trimmed surfaces are based on NURBS surfaces, but only a specified region of the surface, defined by boundary curves, is used. Trimmed surfaces are used frequently in CAD systems because they are easy to generate. However, it is impossible to impose exact boundary conditions on the surface edges, so they are very hard to modify smoothly. Trimmed surfaces form the main problem in modifying CAD geometries. A new development in surface mathematics is the T-spline surface. These surfaces allow local refinement of the control point grid. Therefore, generally a large amount of irrelevant control points can be avoided, and local control over the surface shape is improved. Possibly, trimmed surfaces can be avoided by using T-spline surfaces. The FFD method is the most well known strategy for changing collections of CAD surfaces (or solids). In this method, the geometry is embedded in an imaginary volume. When this volume is changed, the geometry follows the change in shape. The springback compensation algorithm can be regarded as a variant of this. Another way to generate and modify free form surfaces is based on ’sketched’ curves. Both methods are of great use for designers, but not suited for exact shape modification