半自动液压专用铣床液压系统的设计【说明书+CAD】
收藏
资源目录
压缩包内文档预览：
编号：120945055
类型：共享资源
大小：4.93MB
格式：ZIP
上传时间：2021-04-11
上传人：221589****qq.com
认证信息
个人认证
李**（实名认证）
湖南
IP属地：湖南
40
积分
- 关 键 词：
-
半自动
液压
专用
铣床
系统
设计
说明书
CAD
- 资源描述：
-
半自动液压专用铣床液压系统的设计【说明书+CAD】,半自动,液压,专用,铣床,系统,设计,说明书,CAD
- 内容简介：
-
Ye Lie-mail: yeliMatthew C. FrankDepartment of Industrial and ManufacturingSystems Engineering,Iowa State University,Ames, IA 50011Machinability Analysis for 3-AxisFlat End MillingThis paper presents a method for geometric machinability analysis. The implementationof the strategy determines the machinability of a part being processed using a plurality of3-axis machining operations about a single axis of rotation for setup orientations. Slicefile geometry from a stereolithography model is used to map machinable ranges to eachof the line segments comprising the polygonal chains of each slice. The slices are takenorthogonal to the axis of rotation, hence, both two- and three-dimensional (2D and 3D)machinability analysis is calculated for perpendicular and oblique tool orientations,respectively. This machinability approach expands upon earlier work on 2D visibilityanalysis for the rapid manufacturing and prototyping of components using CNCmachining. ?DOI: 10.1115/1.2137748?Keywords: machinability, tool accessibility, CNC machining, slice geometry1IntroductionMachinability analysis is taking an increasingly important roleas complex surfaces are used in the design of a wide variety ofparts. Current computer-aided manufacturing ?CAM? software isreadily capable of generating toolpaths given a set of surfaces of apart and a cutting orientation ?3-axis machining?. 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 ?CNC? 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 ?e.g., a programmable indexer?.Suh and Lee ?1? used a 3-axis machine with a rotary-tilt-typeindexer to provide an alternative to 5-axis ball end milling. Suh etal. ?2? provided a theoretic basis for machining with additionalaxes. Recently, Frank et al. ?3? 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 longertool life compared to ball-mills ?4?. Ip and Loftus ?5? demon-strated the competency of an inclined end mill machining strategyon 3-axis machines in producing low curvature surfaces. How-ever, 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 ?6? presented a method to determine ma-chinability of polyhedral objects. A convex enclosing object isconstructed to make each face of the part orthogonally visible tothe 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 ?7? who performedpioneering work on computational geometry algorithms that couldbe used for determining workpiece setup and machine selection.Tang et al. ?8? formulated the problem of workpiece orientation asfinding the maximum intersection of spherical polygons. Gan etal. ?9? discussed the properties and construction of spherical mapsand presented an efficient way to compute a visibility map from aGaussian map. Chen et al. ?10? 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. ?11? computedvisibility cones based on convex hull analysis, instead of relyingon visibility maps. Yin et al. ?12? defined complete visibility andpartial visibility, and presented a C-space-based method for com-puting visibility cones.Asculptured surface is approximated by itsconvex hull ?11?, and the spherical algorithms ?7,13? are used inthe approach of Yin ?12?. The convex hull may, in some cases,have a significant deviation from the true surface. Suh and Kang?14? 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 partsurface is decomposed into triangular patches. An occupancy testof the patches is conducted on a triangular-represented unit sphereto generate global visibility. Dhaliwal et al. ?15? 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. ?16? analyzed visibility by usingcomputer hardware ?graphics cards?. Frank et al. ?17? analyzedtwo-dimensional ?2D? global visibility on stereolithography ?STL?slices and searched the necessary machining orientations forfourth-axis indexable machining by executing aGREEDYsearchalgorithm. All these visibility-based approaches determine thenecessary condition for machinability; however, they ignore toolgeometry and, therefore, true accessibility ?machinability? is notguaranteed. Figure 1 shows that the accessibility cone ?,?based on line-of-light visibility cannot guarantee the true accessi-bility using a sized tool in machining a segment ij.Su and Mukerjee ?6? 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 OFMANUFACTURINGSCIENCE ANDENGINEERING. Manuscript receivedOctober 13, 2004; final manuscript received August 8, 2005. Review conducted byD.-W. Cho.454 / Vol. 128, MAY 2006Copyright 2006 by ASMETransactions of the ASMEDownloaded 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 ?18? and Radzevichand Goodman ?19? 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. ?16,20? 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. Regli?21?, Regli et al. ?22?, and Gupta and Nau ?23? discussed featureaccessibility and checked it by calculating the feature accessibilityvolume and testing the intersection of the feature accessibilityvolume with the part. Gupta and Nau ?23? 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. ?24? reviewed representative feature-based manufac-turability evaluation systems. Shen and Shah ?25? checked featureaccessibility by classifying the feature faces and analyzing thedegree of freedom between the removal volume and the work-piece. TheMEDIATORsystem reported by Gaines et al. ?26? 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 ?27?discussed the accessibility of both 2.5-D positive and negativefeatures. Other researchers presented featured-based approachesto determine workpiece setups ?2831?.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. ?3? 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 ?Fig. 2?. 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 ?b? ?shown in the Fig. 2? 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 ?Dtmax? used to calculate the collisionoffset ?b? makes the setting of collision offset for each new partunnecessary. The feature-free nature of this method suggests thatit 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 ?i? 2D orthree-dimensional?3D?visibilityconesemployedbytheFig. 1Accessibility based on light ray and a sized toolFig. 2Setup for rapid machiningFig. 3Process steps for rapid machiningJournal of Manufacturing Science and EngineeringMAY 2006, Vol. 128 / 455Downloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmvisibility-based approaches convey no size information of the tooland workpiece and, therefore, cannot guarantee true accessibility;or ?ii? the feature-based approaches cannot cope with complex?free-form? 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.2DefinitionsAlthough 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 ?TS?,obstacle space ?OS?, and machinable range ?MR? 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 S?p?S? is visible by a lightray emanated from an external point q if pq?suffices thecondition of pq?Sp?=?.Machinability: A point p on a surface S?p?S? is machinableby a certain type and size of tool T?CL,? if p?T?CL,?and T?CL,?Sp?=?. T?CL,? represents the tool sur-face at the cutter location CL, approaching from the orien-tation?.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?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 ?a line, a curve, or a patch of surface that isgeometrically composed of a set of points? is the intersection ofthe machinability of each point belonging to that feature. Similarto the concept of partial visibility ?PV?, partial machinability?PM? of a feature can also be defined in addition to the concept ofcomplete machinability ?CM?.Partial Machinability: A feature is partially machinablealong an orientation?if there exists at least one point onthat feature such that no cutter location CL exists for it tosuffice the condition of p?T?CL,? and T?CL,?Sp?=?.Complete Machinability: A feature is completely machin-able along an orientation?if for each point on that featureat least one cutter location CL can be found to guarantee thecondition of p?T?CL,? and T?CL,?Sp?=?.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?, 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 p from an orientation?forms a region calledtoolspace,writtenasTS?p,?=?CL:p?T?CL,? and T?CL,?Sp?=?.Tool space of a feature F is the union of the tool space of everypoint belonging to F; that is, TS?F?=?TS?p,?:p?F?. A toolspace reaches its maximum value maximum tool space ?MTS?when there is no obstacle around the geometric entity. Here, weconsider the entire part surface except the portion under consider-ation to be obstacles. Thus, the corresponding space for obstaclesis defined as obstacle space.Obstacle Space: The aggregate of all unfeasible cutter loca-tions with respect to an orientation?due to the existence ofan obstacle i ?Obi? is called the obstacle space of obstacle i,written as OS?i,?=?CL:T?CL,?Obi?.The cutter cannot enter the domain of obstacle space because itwill gouge into the obstacle.Tool space can be computed by subtracting all the obstaclespaces from maximum tool space.TS= MTS?iOS?1?If the computed tool space using Eq. ?1? is not empty, thenmachinability exists; otherwise, the geometric entity is nonma-chinable. The machinability analysis method presented in this pa-per is based on Eq. ?1?. Tool space is actually a measure of ma-chinability since it tells the existence of machinability and themagnitude of machinability, if it exists.Once the tool space is determined, the machinable range result-ing from it can be obtained.Machinable Range: The maximum machinable portion of afeature given the tool space is called machinable range ofthat feature, written as MR=?p:p?F and TS?p,?.The above definitions will be used throughout the remainder ofthis paper.456 / Vol. 128, MAY 2006Transactions of the ASMEDownloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfm3Machinability AnalysisThe machinability analysis approach presented in this paper isbased on the concept of configuration space ?C-space?. The con-cept of C-space first applied in robotic spatial motion planningwas documented by the work of Lozano-Perez ?32?. The basicidea of C-space is to find the aggregate of the valid spatial con-figurations for a moving mechanism in an environment with ob-stacles around it. Recently, C-space has been applied in tool-pathplanning for multiaxis machining. Choi et al. ?33? presented aC-space-based approach to generate 3-axis numerically controlled?NC? tool paths for sculpture machining by transforming the de-signed part surface and stock-surface into elements in C-space andtreating the cutter as a moving object in the safe space. TheC-space is represented and computed using a Z-map model of thepart. Choi and Ko ?34? incorporated C-space into computer-automated process planning ?CAPP? for freeform die-cavity ma-chining. Morishige et al. ?35? used C-space to generate tool pathsfor 5-axis ball end milling. Jun et al. ?36? optimized tool orienta-tions for 5-axis flat end milling by a search method in C-space.C-space of the cutting tool, which is defined as tool space in Sec.2, provides the safe space for tool-path planning; therefore, toolpaths based on C-space are always gouge-free and collision-free.The tool space can be seen as the aggregate of all possible toolpaths. If tool space exists, then at least one tool path can be gen-erated to machine the corresponding geometric point on the partsurface, and hence, this point has machinability. Therefore, bytesting the tool space of each point on a surface, the machinabilityof this surface can be theoretically determined.The input for the machinability method of this paper is the slicefile of an STL model of the part along the intended axis of rota-tion. An STL model is an approximation of the part surface byusing triangular facets and is currently the de facto standard fileformat for rapid prototyping systems. The tessellation process tocreate an STL model can keep the approximation errorthe de-viation between the part surface and the tessellation triangleswithin a specified tolerance. The size and shape of each trianglecreated is adaptive to its local region on the part surface. There-fore, compared to the Z-map model employed by Choi et al. ?33?,which is essentially a virtually equal-spacing sampled model, theslice file of an STL model is a more precise and efficient repre-sentation of the original part surface. The slicing process for theSTL model of the part, which may be either a feature-based partor a free-form geometry, breaks the part surface into many linesegments comprising the polygonal chains of each slice. Theseline segments are essentially the only representation of a “feature”in the method presented in this paper. In this manner, it is notimportant that any set of segments be machinable in any particularsetup orientation. The intent is to map the segments or portions ofsegments machinable from each orientation?, in order for a mini-mum set of orientations to be found such that all segments aremachined after all setup orientations are completed.Each line segment of the slice file is either perpendicular oroblique with respect to the tool approach orientation. If the per-pendicular case occurs, the obstacles and their corresponding ob-stacle spaces for each point on that line segment are the same.This is actually a static-obstacle case. A two-dimensional C-spaceanalysis can be performed for all those points at the same time,considering all the adjacent segments above the segment to beobstacles. Section 3.1 discusses the perpendicular case in moredetail. However, if the line segment to be checked is oblique withrespect to the tool approach orientation, the obstacles for eachpoint on that segment are variable. This dynamic-obstacle envi-ronment creates difficulty for the machinability analysis process.The solution for this case will be presented in Sec. Perpendicular Case. The coordinate system used in thispaper is consistent with that of a 3-axis milling center, wherebythe slicing of the part occurs along the x-axis of the machinecoordinate frame and each slice is in the y-z plane ?Fig. 4?a?. Weuse Pi,jPi,j+1to represent a segment that is currently undergoingthe machinability analysis process, where i denotes the number ofthe slice on which that segment resides, and j and j+1 denote thetwo consecutive points forming that line segment. In the casewhere the segment Pi,jPi,j+1is perpendicular to the tool-cuttingorientation, all the segments on slice i and its adjacent slices witha portion having a greater height than that of Pi,jPi,j+1along thetool-cutting orientation are obstacles. The obstacle spaces associ-ated with these obstacles remain unchanged for the analysis ofevery point on Pi,jPi,j+1. In this situation, the cutting tool is mov-ing in an environment with static obstacles. The problem is sim-plfied as finding the tool space for segment Pi,jPi,j+1as a geomet-ric primitive on a two-dimensional plane, instead of analyzingeach point separately. Figure 4?a? shows that there are left ob-stacles and right obstacles on each side of segment Pi,jPi,j+1. Ob-stacles may also exist on the slice where Pi,jPi,j+1resides. Plane?contains segment Pi,jPi,j+1and is perpendicular to the tool-cuttingorientation?. Any segment that has a portion above plane?isconsidered an obstacle. Figure 4?b? is the top view of Fig. 4?a?.The boundary of the maximum tool space and the obstacle spacesare constructed by offsetting segment Pi,jPi,j+1and obstacle seg-ments by the amount of the tool radius. The curves in the dashed-dottedlinedenotetheboundariesofleftobstaclespace?mOS?Lm,? and right obstacle space ?nOS?Rn,?. Thecurves in the dashed line denote the boundaries of current sliceobstacle space ?OS?i,? and the closed curve in the solid linedenotes the boundary of the maximum tool space ?MTS?. Theactual tool space ?TS?, represented by the shaded region in Fig.4?b?, is computed using Eq. ?1? as follows:TS= MTS?mOS?Lm,? ?nOS?Rn,? OS?i,?If tool space results in an empty set, then the segment Pi,jPi,j+1contains no machinable portion. If tool space exists, then the ma-chinable range ?MR? boundary can be obtained by offsetting theboundary of tool space by the amount of the tool radius ?Fig.4?c?. It should be noted that the tool space may consist of severalsubregions in practice ?the tool space shown in Fig. 4?b? consistsof only one region?. Therefore, the machinable range may also beseparated into subsections. If the machinable range subsectionscover the entire segment, Pi,jPi,j+1, that is, Pi,jPi,j+1?MR?,then segment Pi,jPi,j+1has complete machinability; otherwise, itonly has partial machinability. Figure 4?c? shows that Pi,jPi,j+1haspartial machinability and the portions outside of the machinablerange boundary are nonmachinable portions of segment Pi,jPi,j+1.3.2Oblique Case.3.2.1Dynamic-Obstacle Environment. For most cases, thecutting orientation is not perpendicular, but oblique to the linesegment being analyzed for machinability. This makes the ma-chinability analysis significantly different from the previously de-scribed perpendicular case that only had static obstacles. The fun-damental reason is that the static-obstacle machinability analysisapproach based on two-dimensional C-space does not work forthe oblique case, which is characterized by dynamic obstacles.The maximum tool space for machining each point under the ob-lique case is invariantly a half-circle arc, which is shown in Fig. 5.However, the obstacle spaces that the points on Pi,jPi,j+1are sub-ject to are dynamically changing, as the point under analysis ismoving along Pi,jPi,j+1. Figure 6 shows segment Pi,jPi,j+1on slicei and an obstacle segment Pi+n,kPi+n,k+1on adjacent slice i+n.Polygon Pi+n,kPi+n,k+1Pi+n,k+1?Pi+n,k?is the obstacle polygon result-ing from segment Pi+n,kPi+n,k+1with respect to the cutting orien-tation?. It is clear that the effective obstacles affecting point P1and P2, denoted by Ob1and Ob2, respectively, are different, eventhough they are caused by the existence of the same obstaclesegment Pi+n,kPi+n,k+1. Hence, the obstacle spaces associated withJournal of Manufacturing Science and EngineeringMAY 2006, Vol. 128 / 457Downloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmthese two obstacles are also different. The variation of obstaclespaces is because the heights of the points on Pi,jPi,j+1with re-spect to the cutting orientation?are different from one another.The obstacle spaces of a certain height are determined by theprojections of the obstacle segments above that height on theplane perpendicular to the cutting orientation?at that height. Thisis actually a problem of three-dimensional C-space. The toolspace for Pi,jPi,j+1could be computed by constructing a three-dimensional C-space. However, since the “part surfaces” beingworked on consist of segments from STL slice geometry, there isno information about what kind of feature Pi,jPi,j+1resides onand/or the local surface description in the vicinity of Pi,jPi,j+1.Therefore,testingmachinabilitybyconstructingathree-dimensional C-space for each segment is inappropriate.3.2.2Relative Movement of Effective Obstacles. Although theentire three-dimensional C-space will not be constructed for eachline segment, the effective obstacle spaces of each obstacle seg-ment at different heights can be considered to have relative move-ment with the point under analysis if one sets a convention formachinability analysis. Referring to the example in Fig. 6, if oneanalyzes the point along the direction traversing the line segmentPi,jPi,j+1, the relative linear movement of the effective obstaclesshows three stages where machinability is affected. They includestage 1, where the obstacle space begins to gouge into the maxi-mum tool space ?Fig. 7?a? and the gouged tool space increases?Fig. 7?b? until it reaches its maximum gouged tool space arc,?mL?mU?Fig. 7?c?; stage 2, where the obstacle space maintains itsmaximum gouged tool space arc?mL?mU?Figs. 7?c? and 7?d?; andstage 3, where the obstacle space begins to move away from Om,the point being examined. Gouged tool space then begins to de-crease ?Fig. 7?e? until the obstacle space does not affect machin-ablity ?Fig. 7?f?. In Fig. 7, ? denotes the slicing spacing and k? isthe distance from the slice i to slice i+k, where the obstacle seg-ment is located. The variable d is the relative distance of theeffective obstacle segment to the segment under analysis. EF rep-resents the effective obstacle, point Fmoves along edgePi+n,k+1Pi+n,kand Pi+n,kPi+n,k?, and point E moves along edgePi+n,k+1Pi+n,k+1?of the polygon Pi+n,kPi+n,k+1Pi+n,k+1?Pi+n,k?in Fig. 6.Fig. 5Illustration of maximum tool space under obliquecuttingFig. 4Illustration of machinability for perpendicular case458 / Vol. 128, MAY 2006Transactions of the ASMEDownloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmThe variable dsdenotes the distance from F to Omalong they-axis, at which tool space begins to be gouged by the obstaclespace of EF; while dmdenotes the distance from F to Omalongthe y-axis, at which the maximum gouged tool space is reached?Fig. 7?c?, and also denotes the distance from E to Omalong they-axis, at which gouged tool space begins to reduce ?Fig. 7?d?.From Fig. 7. it can be seen that if there exists a point p?EF withits distance to Omalong the y-axis equal to dm, then the maximumgouged tool space can be attained. The variable dedenotes thedistance from point E to Omalong the y-axis, at which the toolspace becomes unaffected by the obstacle space of EF. Note thateach obstacle segment may have all or only one or two of thesethree typical stages in practice depending on the relative locationof the obstacle segment and the segment under analysis. This willbe discussed further in Sec. 3.2.3.For the above case, once the stage the effective obstacle be-longs to and the value of d is known, the gouged tool space arc?dL,?dU? can be computed as follows:For stage 1 where dm?d?ds?dL= arccos?k?k2?2+ d2? +?2?k2?2+ d2?R?dU= arccos?k?k2?2+ d2? ?2?k2?2+ d2?R?For stage 2 where d=dm?dL= 0?dU= arccos?k? RR?For stage 3 where de?d?dmwhen de?d?0?dL= 0?dU= arccos?k?k2?2+ d2? +?2?k2?2+ d2?R?when 0?d?dm?dL= 0?dU= arccos?k?k2?2+ d2? ?2?k2?2+ d2?R?ds=?2R?2 ?k?2dm=?R2 ?k? R?2de= ?R2 ?k? R?2?=?k2?2?k2?2+ d2?2 ?d2+ k2?2?3+ 4d2R2?d2+ k2?2?R is the tool radius.3.2.3Characterization of the Relative Movement. The abovediscussion demonstrates that the relative movement of the effec-tive obstacle with respect to the point under analysis provides theinformation necessary to calculate the gouged tool space resultingfrom the corresponding effective obstacle space, and thus the toolspace can be computed. Therefore, if the relative movement ofeach effective obstacle with respect to the point under analysis canbe precisely determined, then machinability can be computedwithout constructing a three-dimensional C-space.Geometric transformation. The relative movement ofeach effective obstacle with respect to the point under analysis canbe precisely determined by performing a geometric transformationto both the segment to be analyzed and the obstacle segment.ConsideraninclinedlinesegmentPi,jPi,j+1?Pi,j?yi,j,zi,j?Pi,j+1?yi,j+1,zi,j+1? on slice i, and supposethat zi,jis greater than zi,j+1?zi,j?zi,j+1? ?Fig. 8?. The parameter tis from the parametric representation of Pi,jPi,j+1. The parameter tis 0 at the end point with smaller z coordinate and is 1 at the endpoint with greater z coordinate. For the segment Pi,jPi,j+1shownin Fig. 8, t is 0 at Pi,j+1and is 1 at Pi,j. Point E?yE,zE? is anFig. 6Variation of effective obstaclesFig. 7Variation of machinable range due to the existance of an obstacle segmentJournal of Manufacturing Science and EngineeringMAY 2006, Vol. 128 / 459Downloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmarbitrary point in the plane y-z and lies on line AB, determined bypoint A?yA,zA? and B?yB,zB?. Point E can be transformed andmapped uniquely as a point E?dE,tE? in plane D-T as shown inFig. 8. The dEis the horizontal distance from E to line Pi,jPi,j+1along the y-axis. It is the distance from E to IE?yiE,zE?, the inter-section point of line Z=zEand the line where segment Pi,jPi,j+1lies. The tEis the parametric value at the intersection point IE.Similarly, A and B are mapped as A?and B?in plane D-T. Thetransformation from a 2D plane y-z to the 2D plane D-T ?D-Ttransformation? can be represented as a map F: R2R2of theformF?p? = M p + nfor all point p?R2, whereM =?1yi,j+1 yi,jzi,j zi,j+101zi,j zi,j+1?N =?zi,j+1yi,j zi,jyi,j+1zi,j zi,j+1zi,j+1zi,j zi,j+1?for line segments withzi,j+1? zi,j;M =? 1yi,j+1 yi,jzi,j+1 zi,j01zi,j+1 zi,j?N =?zi,j+1yi,j zi,jyi,j+1zi,j+1 zi,jzi,jzi,j+1 zi,j?for those with zi,j+1?zi,j.Mapping an obstacle polygon on D-T plane. Based onthe D-T transformation, an obstacle segment on adjacent slice i+mQi+m,kQi+m,k+1anditsassociatedobstaclepolygonQi+m,kQi+m,k+1Qi+m,k+1?Qi+m,k?Fig. 9? can be mapped onto D-TplaneassegmentQi+m,k*Qi+m,k+1*andobstaclepolygonQi+m,k*Qi+m,k+1*Qi+m,k+1?*Qi+m,k?*?Fig.10?.ThecoordinatesofQi+m,k*,Qi+m,k+1*,Qi+m,k+1?*,Qi+m,k?*are?di+m,k,ti+m,k?,?di+m,k+1,ti+m,k+1?, ?di+m,k+1,0?, and ?di+m,k,0?, respectively. Anyline segment formed by truncating a horizontal line in the D-TplanebytheboundaryoftheobstaclepolygonQi+m,k*Qi+m,k+1*Qi+m,k+1?*Qi+m,k?*is actually the effective obstacle ofQi+m,kQi+m,k+1at the height t along the T-axis, as shown in Fig.10. The end point with a smaller D value can be considered as afront point and the one with a larger D value can be considered asa rear point. The front points and rear points of all the effectivesegments resulting from Qi+m,kQi+m,k+1form the front point trajec-tory and the rear point trajectory. In Fig. 10, the front point tra-jectoryisQi+m,k*Qi+m,k?*andtherearpointtrajectoryisQi+m,k*Qi+m,k+1*and Qi+m,k+1*Qi+m,k+1?*.The three stages discussed in Sec. 3.2.2 can also be reflectedclearly on the obstacle polygon in plane D-T, as illustrated in Fig.10. JK, along the front point trajectory, truncated by the line d=dsand d=dm, corresponds to stage 1, KG, along the line d=dmtruncated by the front point trajectory and the rear point trajectorycorresponds to stage 2, and GH, along the trajectory of the rearpoint, truncated by line d=dmand d=de, corresponds to stage 3.As mentioned previously, not all the obstacle segments possess allof these three stages. How many stages an obstacle segment mayhave depends on the shape of the obstacle polygon in the D-Tplane. The mapping of these three stages onto the D-T plane canprovide a precise calculation for the gouged tool space because,given a t value, the corresponding d value, which denotes therelative distance of the segment under analysis and one obstaclesegment, can be easily mapped on plane D-T and, therefore, thegouged tool space can be precisely calculated with the d value,using the method described in Sec. 3.2.2.Fig. 8Geometric TransformationFig. 9An obstacle polygon in y-z planeFig. 10An obstacle polygon in D-T plane460 / Vol. 128, MAY 2006Transactions of the ASMEDownloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmThus far, we have shown that d is a function of t and gougedtool space is a function of d. Therefore, the gouged tool space canalso be considered as a function of t. This leads to the constructionof a graph of machinability versus the parameter t for each linesegment to be examined.3.2.4Machinability Graph. Figure 11 illustrates the composi-tion of the machinability graph for line segment Pi,jPi,j+1underthe interference of one obstacle Qi+m,kQi+m,k+1. It consists of thesame three stages as those shown in Fig. 10 and is bounded bytwo curves: Upper boundary curve?Uand lower boundary curve?L. The region bounded within these two curves is the gouged toolspace obstructed by the obstacle Qi+m,kQi+m,k+1and is denoted asOSi+m,k,k+1. The rectangular frame shown in Fig. 11 with length 1and width?is the maximum tool space ?MTS?. Once the gougedtool space for each obstacle segment is obtained, the machinabil-ityanalysiscanbeconductedbycomputingMTS?n?kOSi+n,k,k+1. If the subtraction operation yields an empty re-sult, then the segment Pi,jPi,j+1is not machinable with respect tothe machining orientation. Otherwise, this segment is at least par-tially machinable.Since the upper boundary curve?Uand lower boundary curve?Lare not of regular shapes, the analytic computation of toolspace is not feasible. In this paper, a sweeping line method wasused to incrementally check the existence of tool space. The stepsto the method are as follows:Step 1. Assign tsto t. ?tscan be either 1 or 0, depending on theincremental direction?.Step 2. Check and store the intersections of line t=tswith theupper and lower boundary curves of each obstacle segmentQi+m,kQi+m,k+1.Step 3. If there is no intersection, then t=tsis machinable. Goto Step 8. If there are intersections, sort all the intersections indecreasing order into a sequence.Step 4. If the maximum intersection is ?180 deg, or the mini-mum intersection is greater than 0 deg, then t=tsis machinable.Go to Step 8. Otherwise, search the reverse order pair in theintersection points list. The reverse order pair is defined as a lowerintersection point ?LIP, an intersection with a lower boundarycurve? immediately in front of an upper intersection point ?UIP, anintersection with an upper boundary curve? in the sorted intersec-tion points sequence.Step 5. If there is no reverse order pair, then t=tsis nonma-chinable. Go to step 8. Otherwise, store the reverse order pairs.Step 6. For each reverse order pair j, check the number of netupper intersection points ?Num?NUIP? before reverse order pair j?denoted by ?j? and the number of net lower intersection points?Num?NLIP? after reverse order pair j ?denoted by ?j? in theintersection points sequence.Num? NUIP?j? = number of UIP?j? number of LIP?j?Num? NLIP?j? = number of LIP?j? number of UIP?j?Step 7. If Num?NUIP=1 and Num?NLIP=1, then t=tsis ma-chinable. If Num?NUIP?1 and Num?NLIP?1, then t=tsisnonmachinable.Step 8. Update t by an increment and check if stopping crite-rion is met. If not met, go to Step 1.4ImplementationTo validate the approach proposed in this paper, the machin-ability algorithms were implemented in the C programing lan-guage on a Pentium IV, 3.06 GHz PC running Windows XP. Themachinability software uses slice-visibility data, the size of theflat-end tool chosen and a specified cutting orientation as inputs. Itgenerates the machinable portion of each slice segment with re-spect to the cutting orientation as output. We present two examplepart surfaces to verify the machinability analysis approach. Thefirst part was chosen to be quite simple so that the nonmachinableregions should seem intuitive to the reader. The second part is amore complex part, a toy “jack,” and this part is evaluated with3D inspection software that is used for reverse engineering.Example 1. Figure 12?a? shows a block with a half cylindricalextruded cut. We chose the direction of 45 deg on a plane or-thogonal to the axis of rotation as the cutting orientation. The flatend tool diameter is set to be 0.25 in. ?6.35 mm?. The slice spac-ing is 0.01 in. ?0.254 mm?. Results from the machinability analy-Fig. 11Machinability graphFig. 12Machinability of a half cylinder extrusion pocketJournal of Manufacturing Science and EngineeringMAY 2006, Vol. 128 / 461Downloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmsis are displayed in Fig. 12?b?, which indicates that there are twononmachinable regions, denoted as S1 and S2. Since this model isan extrusion, the geometric shape along the axis of rotation doesnot change. Therefore, the results of the machinability analysis ofthis part should be the same on every slice along the axis ofrotation. The machinable profile of one slice is displayed in Fig.13?a?. O-A-B, C-D and E-F-G are machinable regions whileB-C and D-E are nonmachinable regions. This part was also vir-tually machined in Mastercam. A screen shot of the part beingvirtually machined from a block of material is shown in Fig. 14.The virtually machined volume was saved as an STL file andimported into RapidForm 2004 ?reverse engineering software?.Figure 13?b? shows a cross-sectional profile of this STL by usingthe inspection function of RapidForm. The orientation of the pro-file displayed in Fig. 13?b? is 45 deg with respect to the horizon,the same direction as the machining setup shown in Fig. 14. O?-A?-B?, C?-D?and E?-F?-G?are the machinable regions, whileB?-C?and D?-E?are the nonmachinable regions in Fig. 13?b?. Toverify the results from the machinability analysis, two local coor-dinate systems are set up on point O ?X-O-Y in Fig. 13?a? and O?X?-O?-Y?in Fig. 13?b?, respectively. Coordinates of the nonma-chinable boundary points B, C, D, and E are computed from theresults of the machinability analysis software we developed andthen the coordinates of B?, C?, D?, and E?are measured in Rapid-Form 2004. The coordinates of the points from each approach areshown in Table 1. The data are very close, and the error is withinthat which can be expected using an STL approximation and aline-sweeping algorithm for finding machinable regions.Example 2. The second part model used as an example is a toy“jack” that is analyzed first for visibility and then for machinabil-ity using the approach of this paper. Figure 15?a? shows the STL-model of the “jack.” The visibility software developed previously?17? first processed this model and gave the result that the modelis 100% visible through four orientations ?50, 155, 228, 335 deg?.To demonstrate the deficiency of visibility analysis, the “jack”model was machined with these four orientations using a0.125 in. dia ?3.175 mm dia? flat-end tool. Figure 15?b? shows themachined “jack” with nonmachinable regions indicated by thefour rectangles.Since the shape of slices of the “jack” model varies along theaxis of rotation, the nonmachinable regions change accordinglyand, therefore, are not regular shapes. To demonstrate that themachinability analysis approach can predict the nonmachinableregions, we virtually machined the “jack” from a 50 deg orienta-tion in MasterCAM and saved the result as an STL file after vir-tual machining. The file was imported into RapidForm 2004 andwas overlapped with the original CAD model. Using the inspec-tion function of RapidForm, we are able to map the deviations ofFig. 132D views of machinable profilesFig. 14Screen shot of example part virtually machined in MasterCAMTable1BoundarypointcoordinatesofnonmachinableregionsPointResult of machinabilityanalysis ?in.?Result of virtual machining?in.?B,B?B?0.3173,0.2481?B?0.3170,0.2506?C,C?C?0.4973,0.4294?C?0.4956,0.4291?D,D?D?0.7500,0.4983?D?0.7513,0.4982?E,E?E?1.2500,0.0000?E?1.2496,0.0000?462 / Vol. 128, MAY 2006Transactions of the ASMEDownloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmthe machined STL model to the original part model. Figure 16illustrates the virtually machined surface ?in MasterCAM? by ro-tating the part model to a 50 deg orientation. The region markedby the circle contains the nonmachinable surfaces. Figure 17?b?illustrates the deviation results from RapidForm 2004. The partmodel is displayed in point shading mode to indicate the surfaceprofile. Figure 17?a? illustrates the results from our machinabilityanalysis software, which corresponds well with the graphical dis-play in Fig. 17?b?.The above examples indicate that the machinability softwarenot only predicts machinable and nonmachinable regions for asliced STL model, but also determines the exact coordinate loca-tions of its machinable and nonmachinable portions. Therefore,given a cutting orientation and a sized tool, the precise locationalinformation of the machinable and nonmachinable regions can beobtained, thus, providing a tool for product designers in evaluat-ing the manufacturability of a particular design. Another applica-tion could be found in determining the minimum number of setupsfor machining a part using an indexable 4-axis machine with re-spect to one rotation axis. This could be realized by first runningthe machinability software for cutting orientations from 0 up to360 deg at the interval of a specified incremental angle, and thensearching for the minimum number of setup orientations using anoptimization algorithm. In this manner, the machinability analysisFig. 15Machining result of a “jack” modelFig. 16Machined “jack” surface in MasterCAMFig. 17Identification of nonmachinable regions for “jack”Journal of Manufacturing Science and EngineeringMAY 2006, Vol. 128 / 463Downloaded 11 Dec 2009 to 04. Redistribution subject to ASME license or copyright; see /terms/Terms_Use.cfmpresented in this paper is not relegated to a verification tool,rather, the information it provides can be used to calculate ma-chining setup information and for tool-path planning.5Conclusions and Future ResearchThis paper presents a machinability analysis approach for3-axis flat end milling based on the concept of C-space. The ap-proach is intended to find the true accessibility, which is oftenapproximated by the visibility of line of light. The input informa-tion is the STL slice file of a geometric model with restriction toone axis of rotation. The model can be either feature based orfeature free, as the machinability analysis approach presented inthis paper does not require feature recognition. Instead, it analyzesbasic geometric primitives, line segments from the STL slice file.In addition to checking 2D machinability, the analysis approachcan handle 3D machinability by constructing a machinabilitygraph. The results of this analysis yields the portions of the sur-face segments machinable from a given orientation and tool. Theexpectation is that the machinability results can be used to deter-mine the minimum set of setup orientations necessary to machineall surface segments using simple 3-axis milling operations. Cur-rently, our approach is restricted to 3-axis flat end milling. Themachinability analysis of ball-end mills and fillet-end mills maybe the focus of future research. In addition, how to extend thecurrent research to the application of 4-axis or perhaps 5-axismilling will likely be another consideration.References?1? Suh, S. H., and Lee, J. J., 1998, “Five-Axis Part Machining With Three-AxisCNC Machine and Indexing Table,” ASME J. Manuf. Sci. Eng., 120?1?, pp.120128.?2? Suh, S. H., Lee, J. J., and Kim, S. K., 1998, “Multiaxis Machining WithAdditional Axis NC System: Theory and Development,” Int. J. Adv. Manuf.Technol., 14?12?, pp. 865875.?3? Frank, M. C., Wysk, R. A., and Joshi, S. B., 2004, “Rapid Planning for CNCMachiningA New Approach to Rapid Prototyping,” J. Manuf. Syst., 23?3?,pp. 242255.?4? Vickers, G. W., and Quan, K. W., 1989, “Ball-Mills Versus End-Mills forCurved Surface Machining,” ASME J. Eng. Ind., 111, pp. 2226.?5? Ip, W. L. R., and Loftus, M., 1993, “The Application of An Inclined End MillMachining Str
- 温馨提示:
1: 本站所有资源如无特殊说明，都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
2: 本站的文档不包含任何第三方提供的附件图纸等，如果需要附件，请联系上传者。文件的所有权益归上传用户所有。
3.本站RAR压缩包中若带图纸，网页内容里面会有图纸预览，若没有图纸预览就没有图纸。
4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
5. 人人文库网仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对用户上传分享的文档内容本身不做任何修改或编辑，并不能对任何下载内容负责。
6. 下载文件中如有侵权或不适当内容，请与我们联系，我们立即纠正。
7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
人人文库网所有资源均是用户自行上传分享，仅供网友学习交流，未经上传用户书面授权，请勿作他用。
川公网安备: 51019002004831号