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5-Axis tool path smoothing based on drive constraintsXavier Beudaerta , Pierre-Yves Pechard b , Christophe Tournier a, na LURPA, ENS Cachan, Universite ´ Paris Sud 11, 61 av du pdt Wilson, 94235 Cachan, Franceb Missler Software, 7 Rue du Bois Sauvage, 91055 Evry, Francea r t i c l e i n f oArticle history:Received 9 March 2011Received in revised form14 August 2011Accepted 15 August 2011Available online 22 August 2011Keywords:5-axis machiningTool path smoothingDrive constraintsMachine tool kinematica b s t r a c tIn high speed machining, the real feedrate is often lower than the programmed one. This reduction ofthe feedrate is mainly due to the physical limits of the drives, and affects machining time as well as thequality of the machined surface. Indeed, if the tool path presents sharp geometrical variations thefeedrate has to be decreased to respect the drive constraints in terms of velocity, acceleration and jerk.Thus, the aim of this paper is to smooth 5-axis tool paths in order to maximize the real feedrate and toreduce the machining time.Velocity, acceleration and jerk limits of each drive allow to compute an evaluation of the maximumreachable feedrate which is then used to localize the areas where the tool path has to be smoothed. Sostarting from a given tool path, the proposed algorithm iteratively smoothes the joint motions in orderto raise the real feedrate. This algorithm has been tested in 5-axis end milling of an airfoil and in f l ankmilling of an impeller for which a N-buffer algorithm is used to control the geometrical deviations.An important reduction of the measured machining time is demonstrated in both examples.& 2011 Elsevier Ltd. All rights reserved.1. IntroductionWithin the context of high speed machining, the tool path andmachine motions have to be smooth to achieve the required surfacequality. Mathematically, the smoothness is usually def i ned by acontinuous second derivative. But it is important to make a cleardistinction between a smooth tool path and a smooth motion.A smooth tool path considers only the geometry which means asecond derivative with respect to a geometrical parameter (thedisplacement for example) whereas a smooth motion deals withthe temporal movement (i.e. the second derivative with respect tothe time). Indeed, you can have a jerky motion even along a straightline or a really quiet travel along a curvy path.In the literature, several articles deal with the smoothness ofthe motion. First works were carried out by robotics researchers[1,2]. Nowadays, it is important to limit the jerk in the trajectoryplanning to produce a soft motion [3–7]. The aim of these articlesis to f i nd a velocity prof i le which respects all the kinematicalconstraints of the drives and of the machine tool structure for agiven tool path. Industrial numerical controllers also offer thepossibility to have a jerk limited motion along the tool path [8].On the other hand, few works have been carried out aboutgeometrical smoothing. A corner optimization is proposed in[9–11] but it is applied only in 3-axis machining. In 5-axis,different methods were proposed to smooth the rotary drives ofa 5-axis milling machine [12–14]. The fundamental idea is thatthe slowdowns on the feedrate come from the rotary drives,which appears to be too restrictive. The method proposed in [15]increases the smoothness by minimizing the energy of deforma-tion of the tool path in the context of 5-axis f l ank milling. Thisallows a global optimization of the tool path but as it is realized inthe Part Coordinate System, machine tool constraints are nottaken into account. Industrial numerical controllers also providesolutions to smooth the geometry of the tool path, such as cornerrounding functions or tool path compressors [8]. These functionslead to a shorter machining time but the user cannot control thegeometrical error generated on the part. Indeed the tolerance ishandled axis by axis, which means that the resulting errors on thepart in 5-axis milling cannot be controlled.The main problem of these approaches is that the machine toolcharacteristics are not considered. Actually, the results of thealgorithms will be the same whatever the desired feedrate andthe kinematical capacities of the machine tool. However, it is clearthat depending on the relative abilities of each drive the solutionshould change (see Section 3 of [16]).The prediction of the velocity prof i le generated by the CNC wasused in [17,18] to improve the machining time by changing theorientation of the tool. Although the complete motion planning is thebest way to see where the feedrate is decreasing, it is time consumingand not necessary for the purpose of trajectory smoothing.Another way to improve the machining time is to use a poly-nomial description of the tool path with a good parameterization as itContents lists available at SciVerse ScienceDirectjournal homepage: www.elsevier.com/locate/ijmactoolInternational Journal of Machine Tools & Manufacture0890-6955/$-see front matter & 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijmachtools.2011.08.014n Corresponding author. Tel.: þ33 1 47 40 29 96; fax: þ33 1 47 40 22 11.E-mail address: tournier@lurpa.ens-cachan.fr (C. Tournier).International Journal of Machine Tools & Manufacture 51 (2011) 958–965基于驱动约束的五轴刀具轨迹平滑