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Millinga mstercomprisingtool life compared to ball-mills H208514H20852. Ip and Loftus H208515H20852 demon-strated the competency of an inclined end mill machining strategyon 3-axis machines in producing low curvature surfaces. How-surface is decomposed into triangular patches. An occupancy testof the patches is conducted on a triangular-represented unit sphereDownloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmever, to machine a surface with large curvature variation, it isnecessary to determine a set of machining orientations and carryout multiple 3-axis machining operations in a sequential mannerwith respect to each of those orientations. Therefore, an effectivemachinability analysis is of critical importance to the successfulimplementation of multiple orientation 3-axis machining for cre-ating complex parts.Many researchers have studied machinability analysis and itsclosely related workpiece setup problem. Most of the approachesare based on visibility, which is essentially line-of-light accessi-bility. Su and Mukerjee H208516H20852 presented a method to determine ma-chinability of polyhedral objects. A convex enclosing object isconstructed to make each face of the part orthogonally visible toto generate global visibility. Dhaliwal et al. H2085115H20852 presented a simi-lar approach for computing global accessibility cones for polyhe-dral objects, but with exact mathematical conditions and algo-rithms. Balasubramaniam et al. H2085116H20852 analyzed visibility by usingcomputer hardware H20849graphics cardsH20850. Frank et al. H2085117H20852 analyzedtwo-dimensional H208492DH20850 global visibility on stereolithography H20849STLH20850slices and searched the necessary machining orientations forfourth-axis indexable machining by executing a GREEDY searchalgorithm. All these visibility-based approaches determine thenecessary condition for machinability; however, they ignore toolgeometry and, therefore, true accessibility H20849machinabilityH20850 is notguaranteed. Figure 1 shows that the accessibility cone H20849H9251,H9252H20850based on line-of-light visibility cannot guarantee the true accessi-bility using a sized tool in machining a segment ij.Su and Mukerjee H208516H20852 took into account the cutter information byconstructing a new part model through offsetting the original partsurface by the amount of the cutter radius. Machinability wasfurther guaranteed by checking the topology of this offset partContributed by the Manufacturing Engineering Division of ASME for publicationin the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript receivedOctober 13, 2004; final manuscript received August 8, 2005. Review conducted byD.-W. Cho.454 / Vol. 128, MAY 2006 Copyright 2006 by ASME Transactions of the ASMEYe Lie-mail: Matthew C. FrankDepartment of Industrial and ManufacturingSystems Engineering,Iowa State University,Ames, IA 50011MachinabilityFlat EndThis paper presentsof the strategy determines3-axis machining operationsfile geometry from aof the line segmentsorthogonal to the axismachinability analysisrespectively. This machinabilityanalysis for the rapidmachining. H20851DOI: 10.1Keywords: machinability,1 IntroductionMachinability analysis is taking an increasingly important roleas complex surfaces are used in the design of a wide variety ofparts. Current computer-aided manufacturing H20849CAMH20850 software isreadily capable of generating toolpaths given a set of surfaces of apart and a cutting orientation H208493-axis machiningH20850. However, deter-mining the setup orientation can be difficult and moreover, it maybe very challenging to determine if the part can be created usingmachining at all. An appropriate setup orientation can guaranteean effective cutting of the surface, whereas an inappropriate onewill leave too much material in certain regions. The advancementof 5-axis computer numerically controlled H20849CNCH20850 milling ma-chines seems to alleviate this situation; however, often the costand/or difficulty of programming a 5-axis machine have limitedtheir widespread use. Three-axis machines, as economical andtechnologically mature pieces of equipment, have been paid spe-cial attention with respect to complex surface machining if as-sisted with multisetup devices H20849e.g., a programmable indexerH20850.Suh and Lee H208511H20852 used a 3-axis machine with a rotary-tilt-typeindexer to provide an alternative to 5-axis ball end milling. Suh etal. H208512H20852 provided a theoretic basis for machining with additionalaxes. Recently, Frank et al. H208513H20852 employed a 3-axis milling centerwith a fourth axis indexer as an effective rapid prototyping ma-chine. End mills have been shown to offer a better match to thepart surface geometry, a higher material removal rate, and a longerAnalysis for 3-Axisethod for geometric machinability analysis. The implementationthe machinability of a part being processed using a plurality ofabout a single axis of rotation for setup orientations. Sliceeolithography model is used to map machinable ranges to eachthe polygonal chains of each slice. The slices are takenof rotation, hence, both two- and three-dimensional (2D and 3D)is calculated for perpendicular and oblique tool orientations,approach expands upon earlier work on 2D visibilitymanufacturing and prototyping of components using CNC115/1.2137748H20852tool accessibility, CNC machining, slice geometrythe planes of the enclosing object. The part is then considered tobe machinable from the normal-vector directions of the enclosingobject planes. Later, computational geometry on the sphere wasutilized to analyze visibility by Chen and Woo H208517H20852 who performedpioneering work on computational geometry algorithms that couldbe used for determining workpiece setup and machine selection.Tang et al. H208518H20852 formulated the problem of workpiece orientation asfinding the maximum intersection of spherical polygons. Gan etal. H208519H20852 discussed the properties and construction of spherical mapsand presented an efficient way to compute a visibility map from aGaussian map. Chen et al. H2085110H20852 partitioned the sphere by spheri-cally convex polygons to solve the geometric problem of deter-mining an optimal workpiece orientation for 3-, 4-, and 5-axis ballend milling. A visibility map is generated by using the normalvectors of a specified portion of the surface of a part; therefore, itcannot guarantee global accessibility. Yang et al. H2085111H20852 computedvisibility cones based on convex hull analysis, instead of relyingon visibility maps. Yin et al. H2085112H20852 defined complete visibility andpartial visibility, and presented a C-space-based method for com-puting visibility cones.Asculptured surface is approximated by itsconvex hull H2085111H20852, and the spherical algorithms H208517,13H20852 are used inthe approach of Yin H2085112H20852. The convex hull may, in some cases,have a significant deviation from the true surface. Suh and KangH2085114H20852 constructed a binary spherical map to compute the point vis-ibility cone in order to algebraically solve machining configura-tion problems, including workpiece setup orientation. The partDownloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmsurface. This method is effective for the machinability analysis ofa ball end cutter, but not for that of a flat end cutter, because theeffective radius of a flat end cutter is variable with the change oftool tilting angle. Haghpassand and Oliver H2085118H20852 and Radzevichand Goodman H2085119H20852 considered both part surface and tool geom-etry. However, tool size was not taken into account becauseGaussian mapping does not convey any size information of thepart surface and/or the tool. Balasubramaniam et al. H2085116,20H20852 veri-fied tool posture from visibility results by collision detection be-fore interpolating the tool path for 5-axis machining.Over the past years, feature-based technologies have been anactive field among the manufacturing research community. RegliH2085121H20852, Regli et al. H2085122H20852, and Gupta and Nau H2085123H20852 discussed featureaccessibility and checked it by calculating the feature accessibilityvolume and testing the intersection of the feature accessibilityvolume with the part. Gupta and Nau H2085123H20852 recognized all machin-ing operations that could machine the part, generated operationplans, and checked and rated different plans according to designneeds. A comprehensive survey paper on manufacturability byGupta et al. H2085124H20852 reviewed representative feature-based manufac-turability evaluation systems. Shen and Shah H2085125H20852 checked featureaccessibility by classifying the feature faces and analyzing thedegree of freedom between the removal volume and the work-piece. The MEDIATOR system reported by Gaines et al. H2085126H20852 usedthe knowledge of manufacturing equipment to identify manufac-turing features on a part model. Accessibility is examined by test-ing the intersection of removal volumes with the part. Faraj H2085127H20852discussed the accessibility of both 2.5-D positive and negativefeatures. Other researchers presented featured-based approachesto determine workpiece setups H208512831H20852.Although feature-based approaches are capable tools to handlefeature-based design, they cannot lend themselves to free-formsurfaces where definable features may not exist. In addition,feature-based approaches suggest that all the geometric elementscomprising of a feature are treated together as an entity. Thisactually imposes a constraint to the analysis of a part model. Forexample, it might be feasible to machine a portion of a part fea-ture in one orientation and then finish the remaining surfaces ofthe feature in one or more successive orientations. The currentproblem that this paper addresses is based on a rapid machiningstrategy proposed by Frank et al. H208513H20852 whereby a part is machinedwith a plurality of 3-axis machining operations from multiplesetup orientations about a single axis of rotation.The strategy is implemented on a 3-axis CNC milling machinewith a fourth-axis indexer H20849Fig. 2H20850. Round stock material is fixedbetween two opposing chucks and rotated between operations us-ing the indexer. For each orientation, all visible surfaces are ma-chined using simple layer-based tool-path planning. By setting thecollision offset H20849bH20850H20849shown in the Fig. 2H20850 on each side of theworkpiece, the implementation of rapid machining can avoid therisk of collision between tool holders and the holding chucks. Thediameter of largest tool H20849DtmaxH20850 used to calculate the collisionoffset H20849bH20850 makes the setting of collision offset for each new partunnecessary. The feature-free nature of this method suggests thatFig. 1 Accessibility based on light ray and a sized toolJournal of Manufacturing Science and Engineeringit is unnecessary to have any surface be completely machined inany particular orientation. The goal is to simply machine all sur-faces after all orientations have been completed. The number ofrotations required to machine a model is dependent on its geomet-ric complexity. Figure 3 illustrates the process steps for creating atypical complex part using this strategy.Currently, the necessary cutting orientations are determined by2D visibility maps with tool access restricted to directions or-thogonal to the rotation axis. Cross-sectional slices of the geom-etry from an STL model are used for 2D visibility mapping. Thevisibility of those slices approximates the visibility of the entiresurface of the part along the axis of rotation since the slices aregenerated orthogonal to that axis. The above literature review sug-gests that existing approaches to machinability cannot calculatethe set of orientations for setups such that one can machine allmachinable surfaces after all orientations, because either H20849iH20850 2D orthree-dimensional H208493DH20850 visibility cones employed by theFig. 2 Setup for rapid machiningFig. 3 Process steps for rapid machiningMAY 2006, Vol. 128 / 455visibility-based approaches convey no size information of the tooland workpiece and, therefore, cannot guarantee true accessibility;or H20849iiH20850 the feature-based approaches cannot cope with complexgeometrically composed of a set of pointsH20850 is the intersection ofthe machinability of each point belonging to that feature. Similarto the concept of partial visibility H20849PVH20850, partial machinabilityDownloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmH20849free-formH20850 surface machining because few traditional featurescan be identified on parts with free-form surfaces.An effective machinability analysis method is a prerequisite tothe successful implementation of multisetup 3-axis end milling inorder to achieve the needs of 4- and perhaps 5-axis machining.Aneffective machinability analysis method will determine, given amachining orientation and an end mill of a particular size, howmuch of the part surface can be machined with respect to thismachining orientation. The focus of this paper is to present afeature-free machinability analysis that can determine the numberof setups required to completely machine the surfaces of a partwith one-axis-of-rotation setups. The machinability analysismethod presented in this paper is unlike any previous work in itscompletely feature-free treatment of the part geometry. We reducethe surfaces of the part down to simple line segments on theslices; therefore, any CAD model can be exported as an STL fileand studied. This approach is done because we are only assumingthat the part is machined about one axis of rotation; therefore, it ismuch simpler to simply analyze the 2D slices rather than 3Dsurface geometry.The remainder of this paper is organized as follows. In Sec. 2,definitions that are used throughout this paper are presented. Sec-tion 3 discusses the machinability analysis method in further de-tail, and Sec. 4 presents the implementation of the machinabilityanalysis approach. Last, conclusions and future research endeav-ors are provided.2 DefinitionsAlthough previous researchers have defined the concepts of vis-ibility and machinability in their work, similar definitions are pro-vided first in this section to clarify the difference between visibil-ity and machinability. Next, the concepts of tool space H20849TSH20850,obstacle space H20849OSH20850, and machinable range H20849MRH20850 are introduced.A condition to determine the existence of machinability is alsoderived. The definitions provided in this section are used for thesubsequent discussion in the remainder of this paper. Visibility:Apoint p on a surface SH20849pH33528SH20850 is visible by a lightray emanated from an external point q if pqH6023 suffices thecondition of pqH6023H33370H20849SpH20850=H9021. Machinability:Apoint p on a surface SH20849pH33528SH20850 is machinableby a certain type and size of tool TH20849CL,H9251H20850 if pH33528TH20849CL,H9251H20850and TH20849CL,H9251H20850H33370H20849SpH20850=H9021. TH20849CL,H9251H20850 represents the tool sur-face at the cutter location CL, approaching from the orien-tation H9251.By definition, machinability shares the same concept of acces-sibility with visibility, but differs in the sense that machinabilitytakes into account the size and shape of the cutting tool instead oftreating it simply as a line of light. Therefore, machinability canguarantee true accessibility, whereas visibility is only a necessarycondition of machinability. Hence, the aggregate of orientationssatisfying machinability is a subset of that satisfying visibility. Inother words, machinability can guarantee visibility, but not viceversa.Unlike the expression of visibility in angular orientations, thebundle of which forms a cone, there are two parameters used todescribe machinability. They are the cutter location and the ap-proaching orientation, if the type and size of a cutter are specified.Machinability with respect to an approaching orientation H9251 existsonly if there is a cutter location that allows the cutting tool toapproach and touch the point p without intersecting any other partsurface.Similar to the concept of the visibility of a feature, the machin-ability of a feature H20849a line, a curve, or a patch of surface that is456 / Vol. 128, MAY 2006H20849PMH20850 of a feature can also be defined in addition to the concept ofcomplete machinability H20849CMH20850. Partial Machinability: A feature is partially machinablealong an orientation H9251 if there exists at least one point onthat feature such that no cutter location CL exists for it tosuffice the condition of pH33528TH20849CL,H9251H20850 and TH20849CL,H9251H20850H33370H20849SpH20850=H9021. Complete Machinability: A feature is completely machin-able along an orientation H9251 if for each point on that featureat least one cutter location CL can be found to guarantee thecondition of pH33528TH20849CL,H9251H20850 and TH20849CL,H9251H20850H33370H20849SpH20850=H9021.Note that Complete Machinability may exist for either a pointor a feature, whereas partial machinability exists only for a fea-ture, because a point can only be said to be either machinable ornonmachinable.If machinability exists with respect to an approaching orienta-tion H9251, the number of feasible cutter locations CLs may vary withdifferent points on a surface. Points with more feasible CLs trans-lates to easier machining because the more possible CLs providemore options for tool-path and setup planning. The need to mea-sure the space of cutter locations leads to the concept of toolspace. Tool Space: The aggregate of all feasible cutter locations tocut a point

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