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To improve the quality of tool paths in surface machining, different machining requirements are considered in the tool path generation algorithm. In the traditional tool path generation algorithm, due to the lack of a unified mathematical calculation framework, these requirements often need to be considered separately, but they often compete with each other, so that different requirements cannot be satisfied at the same time and the tool path cannot achieve the optimal. To resolve this issue, an extensive tool path generation algorithm framework for arbitrary surfaces was proposed. The proposed algorithm transforms the tool path calculation framework into a constrained functional optimization problem by establishing an optimization function based on the potential energy field and an inequality function based on the gradient field in the machining area. By establishing finite element approximation, the functional optimization problem is transformed into a numerical optimization problem, which reduces the difficulty of solving. According to the machining requirements of die surface such as tool path smoothness, line width constraint and cutting direction constraints were transformed into the constraints of potential energy field isopotential line, and the method of generating reciprocating cutter path and cutter contact path isosection cutter path was proposed by optimizing the method. It is evident from the simulation and machining experiments results that continuous and smooth tool paths can be generated by using this algorithm, and machining quality and machining efficiency can be improved. By adding different machining requirements into the framework, a tool path with different optimization objectives can be generated.

Tool Path Generation Algorithm Based on Rough Machining of Jade Carving Surface