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Contents lists available at ScienceDirectInternational Journal of Machine Tools & Manufacturejournal homepage: www.elsevier.com/locate/ijmactoolGlobal tool-path smoothing for CNC machine tools with uninterruptedaccelerationShingo Tajima, Burak Sencer ?Oregon State University, Mechanical Industrial and Manufacturing Engineering Department, Corvallis, OR, USAA B S T R A C TMajority of tool-paths for high-speed machining is composed of series of short linear segments, so-called G01moves. This discrete tool-path format limits the achievable speed and accuracy of CNC machines. To generatecontinuous feed motion along sharp cornered tool-paths, most NC systems smooth corners locally using a pre-specif i ed curve or a spline and slow down to be able to change the feed direction within machine kinematiclimits. Path speed is dramatically reduced for accuracy if sharp corners are within close vicinity. This paperproposes a new real-time interpolation algorithm for NC systems to generate continuous rapid feed motionalong short segmented linear tool-paths by smoothing local and adjacent corners that are within close vicinity.Instead of locally modifying the corner geometry with a spline, the proposed algorithm directly blends axisvelocities between consecutive linear segments based on the jerk limited acceleration prof i le (JLAP) andgenerates cornering trajectories within user-specif i ed contour errors and kinematic limits of the drives. A novelLook-Ahead Windowing (LAW) technique is developed to plan tangential feed prof i le with uninterruptedacceleration to continuously smooth the path. The feed prof i le is optimized to generate rapid motion alongoverlapping adjacent corners. Simulation and experimental results demonstrate ef f ectiveness of the proposedmethod to interpolate accurate Cartesian high-speed motion along short-segmented tool-paths for machiningfree-form surfaces found in dies, molds and aerospace parts.1. IntroductionParts for aerospace, and die-and-mould industries contain complexsculptured geometries that are designed on CAM systems using smoothparametric curves such as splines and NURBS [1]. It has been reportedthat direct interpolation of these curves on CNC (computer numericalcontrolled) machine tools can provide the smoothest, fastest andaccurate motion, and thereby most suitable for high-speed machining[1–3]. However, def i ciencies in the accurate calculation of curvelengths, planning of time-optimal feed prof i les, and feed f l uctuationshinder penetration of “direct spline interpolation” in CNC machines[4–8]. Most CAM systems do not export parametric spline tool-paths[3]. Instead, they discretize original smooth geometry with a series ofshort line segments, and output a “polygonal” tool-path, which is to beinterpolated using basic G01 commands [9]. Based on chord-lengthspecif i cations, the point-to-points G01 moves range from 1 μm to1 mm in length. As the curvature of the tool-path increases discretiza-tion becomes f i ner and denser generating NC part programs composedof thousands of lines. Although size of the NC (numerical control) partprogram is not the bottleneck, its def i nition is. Polygonal tool-paths areonly position continuous, and they do not allow continuous interpola-tion of the feed motion at the junction points, i.e. corners ofconsecutive line segments. As a result, motion must stop momentarilyat corners; otherwise, acceleration and jerk limits of the drives areviolated, which can destroy the surface f i nish. Regardless, this stop-and-go motion planning leads elongated cycle times and generatesrough, cornered surfaces with pronounced feed marks. This process isdepicted in Fig. 1a and b.The well-known approach to generate continuous non-stop motionalong polygonal tool-path geometries is to blend consecutive line seg-ments locally [10–12]. The idea is straightforward. In order to realize acontinuous feed motion, the sharp corner geometry between two linearsegments is replaced by a smooth blending curve in by the NC system ofthe machine tool as shown in Fig. 1b. The f i nal corner prof i le is no longersharp, and the reference path deviates from the original corner geometry.As long as the deviation from original corner geometry is controllable, thisapproach is conveniently applicable to roughing and semi-f i nishing. Basicarcs, cubic, quadratic, quintic, B-splines or various curves are used togenerate a continuous motion transition around the corner prof i le welldocumented in the literature [13–20].http://dx.doi.org/10.1016/j.ijmachtools.2017.03.002Received 4 November 2016; Received in revised form 22 February 2017; Accepted 10 March 2017? Corresponding author.E-mail addresses: tajimas@oregonstate.edu (S. Tajima), burak.sencer@oregonstate.edu (B. Sencer).International Journal of Machine Tools & Manufacture 121 (2017) 81–95Available online 16 March 20170890-6955/ © 2017 Elsevier Ltd. All rights reserved.MARK具有不间断加速的数控机床全局路径平滑