Generation of cubic Hermite spline-based trochoidal milling toolpath by introducing a coefficient factor in machining curved slots

Trochoidal milling has become popular in high-speed milling due to its ability to reduce cutting force, enhance thermal dissipation, and prolong tool life. Among other toolpath patterns, the cubic Hermite spline offers significant advantages in generating trochoidal milling toolpath in machining complex and curved slots. However, determining those two different relation coefficients in the polynomial function of cubic Hermite spline remains complicated and empirical. This paper introduces a coefficient factor to simplify the determination process, which only requires the position and tangent vector parameters of each endpoint pair. The coefficient factor combines an instantaneous in-process slot width (IISW)-related width factor and a tangent vector direction-related direction factor. Two complex-curved slots are used to validate the performance of the proposed method. The results show that this method is straightforward and effective in generating trochoidal milling toolpaths for machining complex-curved slots while matching the slot geometry. Additionally, compared with a direct 5-axis trochoidal milling (one-step slotting strategy) in trochoidal milling of 3D slots on both serial and hybrid machining tools, a two-step slotting strategy (3-axis trochoidal milling and a successive 5-axis perpetual milling) is preferable in improving machining efficiency.