ORIGINAL ARTICLE A new approach for predicting wear overlap geometry in ball end finish milling De-Jun Cheng 1,2 & Young-Jin Oh 2 & Su-Jin Kim 2 Received: 9 February 2018 /Accepted: 27 June 2018 /Published online: 20 July 2018 # Springer-Verlag London Ltd., part of Springer Nature 2018 Abstract The inclination angles of sculptured surface and tilting angles of 5-axis machining change cutting time distributions (CTD) on cutting contact (CC) points. The models of element wear (EW) function of the CTD on each CC points are overlapped to form wear overlap (WO) geometry. However, the WO geometry has not been taken into account in most current tool wear models. This paper proposes a new approach for modeling of the WO geometry associated with the overlapping zones in the 5-axis machining of sculptured surfaces. The EWs in response to CTD at each CC points are modeled using probability density function. The EW is changed to the linear function of time by deforming the tool wear unit. Afterward, for each overlapping point, the WO value is calculated by using the method of the linear addition of linearized EWs. Then, the WO geometry is obtained by the inverse deformation of the unit. The proposed approach is demonstrated and validated through a case study. The predictions of WO geometry present good accordance with experimental observations in constant tilting angle and flat convex surface finish milling process. Keywords Cutting time distribution . Element wear . Tool wear unit deformation . Overlapping zone . Wear overlap geometry 1 Introduction The 5-axis ball end milling are commonly used in generating complex shapes on high hardened steels in various industries such as aerospace, automotive, and die-mold industries. A complex sculptured surface involves a continuous variation in surface inclination angles and cutting contact (CC) points, which generates very complex overlapping zones in the mill- ing process. During the curved surface milling process, there is always tool wear associated with surface inclination angles and overlapping zones, which not only affects the machining accuracy but also the integrity of the machined surface. Therefore, it is necessary to consider the effect of surface inclination angle and overlapping zone on the tool wear dur- ing machining. In reality, tool wear is one of the key challenges in machining of hardened materials which are com- monly used in precision engineering. With 5-axis ball end milling process, a complex curved surface is composed of many curved surfaces with different curvatures. The inclination angles change during the curved surface milling process, owing to changes in the surface normal vector, thus affecting the tool wear and surface in- tegrity. Ko et al. [1] have focused on the inclination angle and cutter path by considering the cutting force, surface roughness, and tool wear. The results indicated that an in- clination angle of 15° was optimal and that horizontal downward milling was the best cutter path. Gani et al. [2] have discussed the effect of tool orientation on the cutting process in 5-axis milling by using the geometric model of machining process. Daymin et al. [3] reported that the best surface finish was obtained when inclination angle of work- piece was 15°, and the mean surface stress decreased slight- ly as the inclination angle increased. Lim [4] has focused on the high-speed finish milling and investigated the effects of four different cutter paths on surface roughness. The results indicated that the horizontal downward cutting orientation satisfied the processing requirements in multi-axis CNC machining. Zhou et al. [5] have discussed that the complex curved surface design technology and CNC machining * Su-Jin Kim sujinkim@gnu.ac.kr 1 School of Mechanical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, Jiangsu Province, China 2 School of Mechanical and Aerospace Engineering, Gyeongsang National University, 900 Gajwa-dong, Jinju, Gyeongnam 660-701, South Korea The International Journal of Advanced Manufacturing Technology (2018) 98:2677–2691 https://doi.org/10.1007/s00170-018-2380-4