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Computer-Aided Design 44 (2012) 1229–1234Contents lists available at SciVerse ScienceDirectComputer-Aided Designjournal homepage: www.elsevier.com/locate/cadTechnical noteSimultaneous optimization of tool path and shape for five-axis flank millingLiMin Zhu a, ∗ , Han Ding a , YouLun Xiong ba School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, PR Chinab State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, 430074, PR Chinaa r t i c l e i n f oArticle history:Received 22 May 2011Accepted 1 June 2012Keywords:Rotary cutterFlank millingTool pathTool shapeDistance functiona b s t r a c tBy representing the swept envelope of a generic rotary cutter as a sphere-swept surface, our previouswork on distance function based tool path optimization is extended to develop the model and algorithmforsimultaneousoptimizationofthetoolpathandshapeforfive-axisflankmilling.Ifthetoolpathisfixed,a novel tool shape optimization method is obtained. If the tool shape is fixed, a tool path optimizationmethod applicable to any rotary cutter is obtained. The approach applies to non-ruled surfaces, andalso finds applications in cutter dimension optimization and flank millable surface design. Numericalexamples are given to confirm its validity.© 2012 Elsevier Ltd. All rights reserved.1. IntroductionFlank milling is performed by employing the side of a cutterto touch the desired surface. Compared with point milling, flankmilling has its unique advantages. It can increase the materialremoval rate, lower the cutting forces, eliminate necessary handfinish, ensure improved component accuracy and result in longertool life. Thus it offers a good choice for machining slender parts,like turbine blades and impellers. Recently, increasing attentionwas drawn onto the problem of optimum positioning of the cutterfor flank milling. In most of the works, a tool path is represented byahugedatasetofcutterlocations(CLs),andeachCLisgeneratedtoeliminate or reduce the local interference between the cutter andworkpiece. However, the machined surface is formed by the sweptenvelope of the cutter surface. The true machining errors are thedeviationsbetweenthedesignsurfaceandcutterenvelopesurface.It is well known that the shape of the cutter envelope surface cannot be completely determined unless all the CLs are obtained. So,only a few works addressed the cutter positioning problem fromthe perspective of approximation of the cutter envelope surface todesign surface.Chiou [1] described a swept envelope-based method for toolpositioning. The initial cutter positions were located to contactwith two directrices. Then the swept profile of the cutter wascalculated based on the cutter motion. Finally the cutter locationswere adjusted to reduce the machining errors by comparing theswept profile with the designed ruled surface. By considering theenvelope surface, Senatore et al. [2] analyzed the performance of∗Corresponding author. Tel.: +86 2134206545.E-mail address: zhulm@sjtu.edu.cn (L.M. Zhu).an improved positioning method for flank milling of ruled surfaceswith cylindrical cutters. Lartigue et al. [3] proposed a methodto deform the two curves that define the tool axis trajectory sothat the tool envelope surface fitted the design surface as muchas possible. The geometric deviation between the two surfaceswas evaluated by the sum of the squared distances of the pointson the design surface to the envelope surface. To simplify thecomputation, an approximate distance measure was employed.Pechard et al. [4] stated that control of the trajectory smoothnesswas as essential as control of the geometrical deviations, anddeveloped a method that aims at minimizing the geometricaldeviations between the tool envelope surface and design surfacewhilepreservingthetrajectorysmoothness.Forcylindricalcutters,Gong et al. [5] presented the error propagation principle, andformulated the problem of tool path optimization as that of leastsquares (LS) fitting of the tool envelope surface to the pointcloud on the offset surface of the design surface. Later, Gong andWang [6] extended this idea to deal with generic rotary cutters,and determined the optimum CL by LS fitting of a spatial line toa series of post-processed point data. Although the LS methodwas easy for implementation and efficient in computation, itdid not conform to the minimum zone criterion recommendedby ANSI and ISO standards for tolerance evaluation [7,8], whichrequires the maximum norm of the error vector be minimized.More importantly, the geometric deviation of the machinedsurface from the nominal one was not clearly defined and theinfluence of the change of the tool axis trajectory on the changeof this deviation was not quantitatively analyzed. Based on thedifferential properties of the signed point-to-surface distancefunction [9,10], we developed the model and algorithm for toolpath planning from the perspective of surface approximationfollowing the minimum zone criterion. The envelope surface of0010-4485/$ – see front matter © 2012 Elsevier Ltd. All rights reserved.doi:10.1016/j.cad.2012.06.003同时优化的刀具路径和形状为五轴侧铣削