Piecewise Decoupling Tool Orientation Re-Scheduling for Four-Axis Reciprocal Toolpaths of Blades Based on S-θ Plane with Monotonicity Constraint

Abstract

Reciprocal toolpaths with four-axis simultaneous motion of five-axis or four-axis machine tools are commonly used in the machining of blades which are widely applied in high-end equipment such as the aero-engine and the marine steam turbine. Due to the complex geometry of the blades, the tool orientation always suffers from frequent swing for this kind of toolpaths, which induces unnecessary acceleration/deceleration of the feed axes, thus degrading processing efficiency and quality. Although there are tool orientation optimization methods aiming at solving the above problem, they are mainly proposed for universal processing of the toolpaths for complex surfaces. Different from them, this paper proposes a piecewise decoupling tool orientation re-scheduling method for this kind of toolpath specifically, which takes full use of the characteristic of the reciprocal toolpaths of the blades, and takes the monotonous variation of rotation axes as an additional constraint. The re-scheduling process is realized based on the construction of a S-θ plane, where the scheduling problem is converted to the adjustment of a S-θ curve inside a feasible channel. Through two procedures, namely linearization scheduling and control-point assigning-based smoothing, the tool orientation path expressed by the S-θ curve can be effectively scheduled in a piecewise manner, and the smoothness between two adjacent pieces of the toolpaths can be ensured directly. The whole algorithm is lightweight and does not involve complex iterative operations or functional optimization solutions. Simulation and experimental tests verify the feasibility and superiority of this method. The results show that the machining efficiency of the blade is improved by 24.5%, due to the reduction of the requirement on highest feed-axis kinematics parameters after rescheduling. In addition, compared with the existing methods, the proposed method not only can improve the dynamics of feed axes in multi-axis machining, but also has advantages in computational complexity and monotonic variation property of the tool orientation.