A new path planning strategy based on level set function for layered fabrication processes

In this paper, a new equidistant filling theory based on the level set function and a corresponding numerical algorithm based on the dynamic finite difference method were proposed. Firstly, a closed curve is defined as the zero-value contour of the level set function. Then, the level set equation, a partial differential equation, was built to get the level set function, and a dynamic finite difference method was proposed to solve the level set function. Secondly, three types of cross sections, simple polygon, multi-island polygon, and multi-hole polygon, were used to test the equidistant filling effect of the algorithm. The test results show that the proposed theory and algorithm in this paper solved the equidistant filling problem of these cross sections well. In addition, any complex section can be equidistant filled by the algorithm proposed. The calculation cost is significantly related to the number of the offsets, but not directly related to the section complexity. Finally, the remanufacturing of a typical crankshaft hot forging die proves that the algorithm proposed in this paper can effectively produce the remanufacturing repair path of a complex forging die. The surface of the remanufactured die is smooth, and there is no efects such as porosity and slag inclusion after machining. Compared with making a new die, the manufacturing cost can be saved more than 50%, and the efficiency of die manufacturing can be improved more than 60%. This is because the machining allowance of the die after additive manufacturing is very small, and it can be quickly repaired on site.