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Improving optimization of tool path planning in 5-axis f l ank millingusing advanced PSO algorithmsHsin-Ta Hsieh, Chih-Hsing ChunDepartment of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwana r t i c l e i n f oArticle history:Received 12 December 2011Received in revised form28 March 2012Accepted 29 April 2012Available online 22 May 2012Keywords:5-axis machiningFlank millingParticle swarm optimizationRuled surfacea b s t r a c tThis paper studies optimization of tool path planning in 5-axis f l ank milling of ruled surfaces usingadvanced Particle Swarm Optimization (PSO) methods with machining error as an objective. Weenlarge the solution space in the optimization by relaxing the constraint imposed by previous studiesthat the cutter must make contact with the boundary curves. Advanced Particle Swarm Optimization(APSO) and Fully Informed Particle Swarm Optimization (FIPS) algorithms are applied to improve thequality of optimal solutions and search eff i ciency. Test surfaces are constructed by systematicvariations of three surface properties, cutter radius, and the number of cutter locations comprising atool path. Test results show that FIPS is most effective in reducing the error in all the trials, while PSOperforms best when the number of cutter locations is very low. This research improves tool pathplanning in 5-axis f l ank milling by producing smaller machining errors compared to past works. It alsoprovides insightful f i ndings in PSO based optimization of the tool path planning.& 2012 Elsevier Ltd. All rights reserved.1. Introduction5-axis machining provides a higher productivity and bettershaping capability compared to traditional 3-axis machining withtwo additional degrees of freedom in tool motion. It has beencommonly used in manufacturing of complex parts in automobile,aerospace, energy, and mold industries since the late 90’s. The5-axis machining operation contains two different milling meth-ods: end milling and f l ank milling. The cutting edges near the endof a cutter perform actual material removal in end milling whilethe circumferential part of a cutter mainly does the cutting inf l ank milling. Tool path planning is a critical task in both millingoperations, with avoidance of tool collision and machining errorcontrol as two major concerns [1].In 5-axis f l ank milling, it is highly diff i cult to produce amachined surface exactly the same as its design specif i cationsusing a cylindrical cutter. Unless for simple geometries likecylindrical and conical surfaces, the cylindrical cutter cannotmake a contact with a surface ruling without inducing overcutor undercut around the ruling due to local non-developability of aruled surface [2]. The machined surface is considered acceptablein practice as long as the amount of machining deviation islimited within a given tolerance. A common method used inindustry is to make the cutter follow the surface rulings, althoughserious machining errors often occur on twisted surfaces [3].Various approaches have been proposed to reduce the machiningerror induced in this way.Previous studies [4–6] have shown that the machining error in5-axis f l ank milling of ruled surfaces can be effectively reducedthrough optimization of tool path planning in a global (or nearglobal) manner. Such an optimization approach works as asystematic mechanism for precise control of machining error.Wu and Chu [4] transformed tool path planning in 5-axis f l ankmilling into a curve matching problem and applied discretedynamic programming to solve for an optimal matching withthe total error on the machined surface as an objective function inthe optimization. They solved the similar curve matching problemwith Ant Colony Systems (ACS) algorithm to reduce the lengthytime required by the dynamic programming approach [5]. Hsiehand Chu [6] allowed the cutter to freely make contact with thesurface to be machined, rather than moving among pre-def i nedsurface points in previous works [4,5]. They also adopted GPUcomputing technologies to accelerate PSO based search in sameoptimization process and thus enhanced the practicality ofmachining error control by optimization of tool path planningin 5-axis f l ank milling.All the previous studies mentioned above imposed a majorconstraint to simplify the optimization problem. They assumed thatthe cutter must make contact with the boundary curves of the ruledsurface to be machined. This assumption seriously restricts theContents lists available at SciVerse ScienceDirectjournal homepage: www.elsevier.com/locate/rcimRobotics and Computer-Integrated Manufacturing0736-5845/$-see front matter & 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.rcim.2012.04.007n Corresponding author.E-mail address: chchu@ie.nthu.edu.tw (C.-H. Chu).Robotics and Computer-Integrated Manufacturing 29 (2013) 3–11利用改进的粒子群优化算法改进五轴侧铣削刀具路径规划