A novel method for solving shortest tool length based on compressing 3D check surfaces relative to tool postures

Solving the shortest tool length quickly under a known tool trajectory in multi-axis machining of complex channel parts is an urgent problem in industrial production. To solve this problem, a novel and efficient method is proposed which is featured by extracting only a few necessary curves from the check surface instead of sampling the entire surface. By rotating and compressing the 3 D check surface relative to all tool postures, the boundaries of the area occupied by the 2 D compressed surfaces are the essential elements for determining the shortest tool length. A tracking-based numerical algorithm is introduced to efficiently solve the silhouette curves which are formed in compressing. To define the multi-taper shaped tool holding system(THS) which is commonly used in production, a characterization model for THS profile is established. A model for solving the shortest tool length is finally constructed based on the critical interference relationship between the THS profile and all compressed boundary curves. For acceleration, the boundary splines are segmented according to their knot vectors. Then a new concept called the axis-aligned tool length box(AATB) is introduced,which can provide a conservative range of tool length for a spline segment. By scanning the AATBs of all spline segments, the very few effective spline segments that may ultimately determine the shortest tool length are filtered out. This acceleration method makes the solution for the shortest tool length more focused and efficient. The results of experimental examples are also reported to validate the efficiency and accuracy of the proposed algorithm.