Optimization of rotations for six-axis machining

Five-axis machines with three translational and two rotation axes are becoming increasingly popular in serving the needs of the mass production industry due to their ability to handle geometrically complex workpieces using the rotational axes. Theoretically, the combination of the five axes offers a minimal number of the degrees of freedom required to transport the tool into a prescribed spatial position and establish a required orientation. However, the rotation axes lead to an inevitable nonlinearity of the tool tip trajectory and the so-called kinematics errors appearing due to the specific kinematics of the machine. Eventually, one arrives at an interesting question. Is it possible to compensate this error by introducing an additional rotation axis? In other words, ??does an additional rotation axis offer any optimization benefits in the sense of the above mentioned error??? In this paper, we answer this question positively by analyzing a hypothetical six-axis milling machine with two rotation axes on the table and one additional rotation axis on the tool. The sixth axis is build on the top of the existing five-axis machine MAHO600E by Deckel Gildemeister. We present an extension of an optimization algorithm developed earlier by the authors for five-axis machining based on an optimal angle sequencing (the shortest path optimization). The extension is a combination of the shortest path strategy and the use of the additional axis. The algorithm leads to an increase in the machining accuracy, in particular, for rough milling. Numerical experiments and cutting by a virtual six-axis machine built in Vericut 5.0 validates the results of the optimization. The proposed optimization procedure is capable of upgrading the existing five-axis G-codes to the case of six-axis machine.