Hard whirling is a highly efficient and green process for precision ball screw machining. Due to the intermittent cutting characteristics and the helical motion of the tool, the cutting forces are periodic and time-varying, making it extremely challenging to establish an accurate cutting force model. This paper proposes a cutting force modelling method based on the transient geometric characteristics of uncut chips, subject to the essential link between uncut chips and cutting forces. The time-varying features of the chip are revealed by building an accurate 3D digital model of the uncut chip. An equivalent cutting simulation model is developed using the discrete cross-section of the chip, and the effect of cutting parameters and tool edge on the cutting forces are investigated. A combination of simulation and experiment is presented to identify cutting force model coefficients, and the theoretical cutting force model for ball screw hard whirling is established. The results show that the uncut chip cross-sectional area and edge length involved in cutting first increase and then decrease, and the equivalent numerical simulation method based on the transient geometry of uncut chips can obtain more accurate cutting forces. The combined simulation and experimental strategy achieve fast and low-cost identification of cutting force coefficients, and the established cutting force model has good prediction accuracy. This study supports the investigation of the cutting mechanism of hard whirling, the optimisation of process parameters and the improvement of machining quality.

The profile of the hard whirling tool for ZC1 worm machining is challenging to design precisely. An inaccurate tool profile results in irreversible overcutting or additional machining allowance. This study aimed to develop an accurate tool profile design method and digital verification approach to enhance the quality of ZC1 worms. The precise measurement and axial section data acquisition of the worm are conducted. A tool profile design method is proposed based on the envelope of the equidistant axial section. The motion law of whirling is studied, and a 3D model generation procedure for worm teeth is developed. The effect of the tool profile design is verified, and the impact of cutting parameters on worm tooth profile error is analyzed. The results show that the presented tool design method can effectively avoid overcutting. The employed modeling approach of worm teeth provides an intuitive verification means for tool profile design. Variable cutting parameters lead to different machining errors, and the maximum error is less than 3 μm. Changing the cutting parameters will not induce macro profile error but will impact the micromorphology. These findings should be valuable for designing envelope machining tools with complex motion and realizing the superior performance of hard whirling for ZC1 worm machining.