Optimization of Tool Path Planning in 5-Axis Flank Milling of Ruled Surfaces with Improved PSO

5-Axis machining has been widely used in manufacturing of complex ruled geometries in automobile, aerospace, energy, and mould industries. Compared with traditional 3-axis machining, this machining operation offers better shaping capability and productivity with additional degrees of freedom in the tool motion. Tool path planning is a challenging task in most 5-axis machining operations, with tool collision and machining error control as two major concerns. It is highly difficult, if not impossible, to completely avoid tool overcut and undercut when a cylindrical cutter is used to create complex shapes. The machined surface is considered acceptable in practice as long as the amount of machining error is limited within a given tolerance. Previous studies have shown that the machining error in 5axis flank milling can be effectively reduced by means of global (or near global) optimization of tool path planning. The optimization approach also provides a systematic mechanism of machining error control. Wu and Chu proposed the first attempt to transform the tool path planning into a curve matching problem. Discrete dynamic programming techniques were then applied to generate an optimal matching with the total error on the machined surface as the objective function. Chu et al. solved the similar problem with Ant Colony Systems (ACS) algorithms Simulation results showed that the computation time can be thus significantly reduced with a minor sacrifice at the final solution. Hsieh and Chu allowed the cutter to contact at any point on the boundary curves of the ruled surface. This relaxes the constraint in the two previous studies that the cutter can only contact at pre-defined discrete points on the boundary curves. They also adopted GPU computing technologies to accelerate the optimization process, which is usually computationintensive and limits the practicality of optimization-based tool path planning. All the previous methods mentioned above suffer from unsatisfactory solution quality of the optimization due to the assumption that the cutter must make contact with the boundary curves. This assumption greatly restricts the solution space in search for optima, resulting in worse tool paths. To overcome this deficiency, we propose to use a new scheme for encoding cutter location in the PSO-based tool path planning. The cutter can deviate from the surface to be machined along the normal, tangent, and binormal directions on the points of the boundary curves. The solution space in the optimization is thus significantly enlarged. Factorial experiment techniques are applied to systematically determine the parameter setting in the PSO algorithms. In addition, the objective function is re-formulated as a weighted sum of the Optimization of Tool Path Planning in 5-Axis Flank Milling of Ruled Surfaces with Improved PSO