Tool Path Generation Algorithm Based On Offset-projection In Multi-axis Blade Machining

Tool path generation algorithm,as a critical technology in a multi-axis program,determines machining accuracy,machining efficiency as well as surface quality.It is so hard for the current tool path generation algorithms to simultaneously solve the following problems:(1)Fluctuation of the tool orientations and tool paths due to unstable curvature distribution on surfaces;(2)Gouging and undercutting on the machining region;(3)Cannot Adapt to arbitrary APT cutter and free-form surfaces;(4)Cannot satisfy high machining accuracy.To solve the above issues,this paper presents a tool path generation algorithm based on offset-projection in five-axis blade machining.This algorithm can be divided into drive path computation based on offset triangulation surface and tool path computation based on cutter projection onto original surface.Drive path computation algorithm includes offset-triangulation surface construction,CC drive path generation and smooth,tool-axis optimization,and drive path calculation.An unified mathematical framework is proposed for tool-axis optimization based on covariant functional.Machining requirements,including gouging-free,preferred direction,and tool-axis stability,are incorporated into this optimization problem as constraints functional which is covariant so that the result is independent of surface parameterization and applicable to non-Euclidean geometry.This algorithm avoids successive iterations for tool orientations,and enables the smoothness of tool orientations and tool paths.Tool path computation algorithm consists of cutter projection onto triangulated surfaces and cutter projection onto original surfaces.An efficient cutter projection onto triangulated surfaces along any predetermined direction is addressed,with focus on solving the most complicated torus-edge projection problem.We prove that the two special but widely used cases,the torus-edge projection along tool-axis direction and ball-edge projection along any predetermined direction,can be solved analytically.We also developed three numerical methods to solve the general issue of the torus-edge projection along any predetermined direction.The initial CC point is calculated by cutter projection onto triangulated surfaces.Motivated by the Newton-Raphson algorithm,the tangent plane-based search method is developed to find cutter contact points on surfaces.Simulation on five-axis blade finishing indicate that the proposed algorithm is capable of producing uniform and smooth tool paths as well as ensuring high machining accuracy.