On Geometric Principles And Methods For Non-Ball-End Milling Of Complex Surfaces With Large Machining Strip Width

Five-axis NC machining provides an efficient way to manufacture complex surfaces. The ball-end cutter is widely applied in engineering applications because it is easy to position the cutter. But the lower machining performance and efficiency limit the full use of the five-axis machining. Therefore, the non-ball-end cutters are preferred for complex surface machining. The tool envelope surface is applied to approximate the design surface by adjusting the cutter orientations, so that the cutting performance can be improved and the machining strip width can be increased. However, the complexity of the design surface and the diversity of the cutter surface bring lots of challenges in avoiding the interferences, controlling the machining errors and smoothing the tool orientations during the tool path generation.The tool path optimizations for five-axis flank milling of ruled surfaces and point milling of free-form surfaces are studied in this dissertation. Four aspects are considered including the analytical expression of the swept envelope of a rotary cutter undergoing spatial motion, the global tool path optimization for flank milling of ruled surfaces, cutter size optimization and smooth tool path generation for flank milling of centrigural impellers, and interference-free tool positioning for high-order contact milling of free-form surfaces with a flat-end cutter. The main research work and the novel contributions are listed as follows: Firstly, two methods for analytically computing the swept envelope undergoing general spatial motions are proposed. (1) Based on the tangency condition in the envelope theory and the representation of the body velocity in spatial kinematics, a closed-form solution of the swept envelope of a general rotary cutter moving along a multi-axis tool path is derived. No additional moving frames or local frames are required. (2) Based on the observation that the cutter surfaces can be treated as the envelope surface of a one-parameter family of spheres, the analytical expression of the envelope of the swept volumes are derived using the envelope theory of sphere congruence. The method associates the tool envelope surface with the tool axis trajectory surface, based on which the measure of the geometric errors is proposed.Secondly, the signed distance from a point on the design surface to the tool envelope surface is defined without constructing the swept envelope. This transforms the manipulation of the envelope surface to that of the tool axis trajectory surface. Also the first order differential increment of the signed distance with respect to the differential deformation of the tool axis trajectory surface is derived. It quantitatively characterizes the change in the geometric deviation under the deformation of tool trajectory. On this basis, the tool path optimization for flank milling of ruled surfaces is developed in a unified framework, and a sequential approximation algorithm is developed for the optimization. The numerical examples indicate that the proposed method can improve the machining accuracy greatly, and can handle the optimization with non-overcut constraint effectively.Thirdly, strategies for cutter size optimization and smooth tool path generation are proposed for five-axis flank milling of centrifugal impellers. Aside from the local interference of the cutter with the design surface, the global interferences with the hub surface and the adjacent blade surface are also considered in the optimization models. The distance function is redefined with parameters of both tool trajectory and cutter radius, and used as contraints to avoid interferences. Meanwhile, by characterizing the geometric smoothness by the strain energy of the cutter axis trajectory surface, the tool trajectory is globally smoothed while preserving the geometric accuracy of the machined part. The method applies to both finish and semi-finish flank millings, and the generated tool paths are applied to the practical machining of the centrifugal impellers.Fourthly, based on the local approximation of the tool envelope surface to the design surface, the strategies for interference-free and smooth tool path generation are proposed for five-axis machining of free-form surfaces with a flat-end cutter. The tool feasibility space is established on the basis of analytically computing the second-order contact cutter locations, so that the geometric contact information between the tool envelope surface and the design surface is included into the optimization models while reducing the computational load. On this basis, the optimal contact tool path can be derived by calculating the relative curvature derivatives between the design surface and the tool envelope surface in the normal section orthogonal to the feed direction. Also, the optimal smooth tool path can be generated by globally minimizing the variation of the tool orientations along the whole tool path. The numerical examples indicate that the proposed method can avoid interferences effectively and improve the machining strip width greatly.Based on the modeling of the cutter swept envelope, five-axis non-ball-end milling of complex surfaces with a large machining strip width is focused. A uniform tool path optimization frame is founded with comprehensive consideration of interference avoiding, geometric error controling, and tool trajectory smoothing, etc. The proposed methods enrich the tool path planning strategies for five-axis machining.