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Computer-Aided Design 67–68 (2015) 87–106Contents lists available at ScienceDirectComputer-Aided Designjournal homepage: www.elsevier.com/locate/cadCNC double spiral tool-path generation based on parametric surfacemapping ?Bo Zhou a,b , Jibin Zhao a, ∗ , Lun Li aa Shenyang Institute of Automation, Chinese Academy of Sciences, Liaoning, 110016, Chinab University of Chinese Academy of Sciences, Beijing, 100049, Chinah i g h l i g h t s• We study a new double spiral tool-path generation algorithm for 5-axis HSM.• We call a smoothness optimization method during solving PDEs to smooth curves.• Machining parameters (e.g., path interval and step length) can be guaranteed.• Mapping rules are based on the same ranges of NURBS curve and parametric domain.• Our tool-paths have a self-complementary structure and can be suitably linked.a r t i c l e i n f oArticle history:Received 9 December 2014Accepted 12 June 2015Keywords:High-speed machiningPartial differential equationsParameter domainMapping ruleDouble spiral tool-patha b s t r a c tHigh-speed machining (HSM) has been an important method for machining complex parametric surface.Tool-path planning for HSM has a significant impact on processing efficiency and surface quality. A newdouble spiral tool-path generation algorithm for HSM is proposed in this paper. First, the isothermal lineswhich satisfy the machining parameters in the mapping parametric domain are computed by means ofconstructing a thermal conductivitymodel and solving partial differential equations(PEDs). Furthermore,a smoothness optimization method is proposed to improve the smoothness of the isothermal lines andavoid taking up too much memory. Then, the mapping rules are constructed and the trajectory is plannedout in the standard parametric domain in order to generate double spiral trajectory in the correspondingparametric domain. Finally, the trajectory is mapped onto the parametric surface to obtain the tool-paths,and the tool-paths linking method is planned for complex multi-domains. This method can realize theprecision milling of complicated parametric surface without tool retractions, and meanwhile it improvesthe uniformity of the tool-paths and machining efficiency. Our method has been experimented in severalsimulations and validated successfully through the actual machining of a complicated pocket. The resultsindicate that this method is superior to other existing machining methods, and it can realize HSM ofcomplicate-shaped pocket based on parametric surface.© 2015 Elsevier Ltd. All rights reserved.1. IntroductionPocket components with aspheric surfaces have been ex-tensively applicated in different industrial sectors, includingaerospace, space exploration, mold, powertrain system and so on[1]. At present, HSM has emerged as a key technology in machin-ing components with aspheric surfaces and other manufacturingapplications, which possesses obvious superiority in complicated?This paper has been recommended for acceptance by Gershon Elber.∗Corresponding author. Tel.: +86 13998809239.E-mail addresses: zhoubo@sia.cn (B. Zhou), jbzhao@sia.cn (J. Zhao).surfacemachining withmuchhigher rotationalspeedand feedrateof the spindle than traditional milling methods. So HSM has be-come one of the most widely adopted approaches to increase ma-chining efficiency, improve machining quality and reduce cost [2].HSM has not only brought higher requirements for the lathe,clamp, cutter, etc., but also proposed further requests for thetopology geometric shape and dynamics performance of the tool-path. Spiral tool-path is an ideal tool-path planning method forHSM. Generally speaking, splintery machining trajectories rarelyoccur during machining, and furthermore, load fluctuation of thecutter can be effectively restrained and the times of cutter liftingcan be reduced so as to achieve higher machining quality. Inorder to effectively avoid sudden direction changes of the velocityhttp://dx.doi.org/10.1016/j.cad.2015.06.0050010-4485/ © 2015 Elsevier Ltd. All rights reserved.基于参数曲面映射的数控双螺旋刀具轨迹生成