International Journal of Mechanical Sciences 157–158 (2019) 293–303 Contents lists available at ScienceDirect International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci Kinematics performance oriented smoothing method to plan tool orientations for 5-axis ball-end CNC machining Jinting Xu a , Dayuan Zhang b , Yuwen Sun b,∗ a School of Automotive Engineering, Dalian University of Technology, Dalian 116024, China b School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China a r t i c l e i n f o Keywords: 5-axis machine CNC machining Tool orientation Kinematics performance Angular acceleration a b s t r a c t When adopting 5-axis machine to mill the parts, it is desired to avoid the drastic change of tool orientation for improving the kinematics performance of 5-axis machining while ensuring no machining interferences. For this purpose, a kinematics performance oriented smoothing method is proposed to plan the tool orientations, which is focused specifically on minimizing the angular accelerations imposed on the rotary axes of 5-axis machine. In this method, with several specified representative tool orientations (RTOs), two B-spline curves, which represent the displacements of the rotary axes, are used to join smoothly the RTOs together and then to determine the tool orientations at other areas. The solutions for the two B-spline curves are achieved by solving a least-square objective function which minimizes the angular accelerations of the rotary axes. To restricting simultaneously the interpolated tool orientations in the geometric feasible domains (GFDs) of tool motion, a simple alternate strategy of first smoothing the tool orientation and then checking the machining interference is developed so that tool orientation planning and its geometric constraints are decoupled and the complicated constraint optimization process of tool orientation can be greatly simplified. Since the proposed method works in the machine coordinate system (MCS), it can not only ensure the smooth motions of the rotary axes without the machining interferences, but also can generate directly the rotary axis orders. Finally, the proposed method is validated by the experiments. 1. Introduction Within the context of 5-axis CNC machining, the rotary axes of the machine usually have low capacities of acceleration comparatively to the translation axes, thus the change of the tool orientation has to be controlled reasonably to achieve the smooth rotary axis motions and the required surface quality. At present, the methods, which determine the tool orientation, have focused mainly on finding the best tool orien- tation so that the local gouging and the global collision can be avoided [1]. For these methods, sometimes to avoid the local gouging and the collision with the obstacles, the tool has to make a abrupt change of orientation between two adjacent cutter location (CL) points. Although the machining interference is effectively eliminated, the kinematics per- formance of 5-axis machine is deteriorated possibly due to the abrupt change of tool orientation which causes significant times of deceleration and reacceleration of the rotary axes, leaving the apparent unfavorable tool marks on the parts and slowing down the tool movement. Actually, such extreme change of the tool orientation is not allowed in the actual machining due to the limits of the kinematics capacities of the rotary axes of 5-axis machine [2–4]. Thus, when planning the tool orientations, ∗ Corresponding author. E-mail address: ywsun@dlut.edu.cn (Y. Sun). the smoothness of the rotary axis motion has to be taken into considera- tion. To address this challenging issue of 5-axis machining, the objective of this paper is to present an in-depth study on tool orientation planning with a new solution that can improve the kinematics performance of 5- axis ball-end machining while ensuring no machining interferences. Its focus is mainly on how to generate the smooth tool orientations, and the machining interference is checked by the existing methods, such as [5,6]. In the following, some background and past works for planning tool orientations from a kinematics perspective are first reviewed. 1.1. Related works Initially, smoothing tool orientation from the kinematics perspective is conducted in the workpiece coordinate system (WCS) to control the change of the tool orientation by adjusting the discrete tool orientations along the tool path. For example, Jun et al. [5] proposed a feasible C- space based tool orientation smoothing method, in which the forward and backward searching algorithms were presented to find two paths from the boundary of the feasible C-space, and the one with smaller angle change was selected as the optimal tool orientations to raise the https://doi.org/10.1016/j.ijmecsci.2019.04.038 Received 8 January 2019; Received in revised form 31 March 2019; Accepted 19 April 2019 Available online 26 April 2019 0020-7403/© 2019 Elsevier Ltd. All rights reserved.