Tool Path Generation Algorithm Based On Covariant Field Theory And Its Applications In Blade Machining And Die Machining

In order to improve the quality of the tool path, different machining requirements have to be considered in the tool path generation process. In traditional tool path generation methods, those requirements are divided and treated individually due to the lack of comprehensive mathematic framework. Tool path generated in this way normally is not fully optimized since different requirements could compete or even conflict with each other. Targeting at this issue, this paper presents a unified mathematic framework based on field theory to generate tool path for both planar and freeform surface, where the three most important factors in NC machining, i.e., the smoothness, uniformness and machining efficiency of tool path are considered.In the proposed framework, a field-based cost functional and a gradient-field based inequality constraints functional is established, so as to convert the optimal tool path computation into a functional minimization problem with inequality constraints. Then, a Finite Element Method(FEM) based numerical method is proposed to solve the multi-variable nonlinear optimization problem. After that, two smooth tool path generation methods are proposed with taking the step-over as constraint.Blade surface roughing and platform surface machining are used as example of generating smooth spiral tool paths by the algorithm. Two methods for control the step over are proposed. To further improve the machining efficiency, this paper also provides a hybrid method that combines zigzag and spiral pattern tool path by dividing the machining area to sub regions. Plus, the method to generate zig-zag and iso-planar tool path for die surface machining are also provided.Experiments on blade machining and simulation show that the proposed method can produce uniform and smooth tool paths while the machining efficiency can be improved at the same time. In addition to the above advantages, the proposed mathematical framework is extensible by incorporating different machining requirements into it, making it possible to generate overall optimized tool path.