Boundary-conformed machining for trimmed free-form surfaces based on mesh mapping

Boundary-conformed iso-parametric or streamline-like tool paths are highly desired for machined surfaces requiring extra high finish quality or superior aerodynamic effect in some applications. However, for a trimmed free-form surface, its trimmed boundaries usually do not follow the original iso-parametric curves. As a result, conventional iso-parametric tool path methods are not applied readily on the trimmed surface to generate boundary-conformed tool path, especially on the multiple-trimmed surfaces. In this study, a new method to the problem of boundary-conformed tool path generation on the trimmed surfaces is proposed. The basic idea of the method is to map directly the trimmed surface onto a 2D parametric square domain using mesh mapping technique. Then, the iso-parametric lines on the parametric domain are inversely mapped onto the original trimmed surface to regenerate boundary-conformed tool paths. As the method does not rely on processing on the original parametric domain of the surface patches, it is not limited to the single-trimmed surface and is also well applicable to the multiple-trimmed surfaces and mesh surfaces. The proposed method is implemented and tested on several typical examples to demonstrate its validity and significance.