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Milling a m ster comprising tool life compared to ball-mills H208514H20852. Ip and Loftus H208515H20852 demon- strated the competency of an inclined end mill machining strategy on 3-axis machines in producing low curvature surfaces. How- surface is decomposed into triangular patches. An occupancy test of the patches is conducted on a triangular-represented unit sphere Downloaded 11 Dec 2009 to 222.190.117.204. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfm ever, to machine a surface with large curvature variation, it is necessary to determine a set of machining orientations and carry out multiple 3-axis machining operations in a sequential manner with respect to each of those orientations. Therefore, an effective machinability analysis is of critical importance to the successful implementation of multiple orientation 3-axis machining for cre- ating complex parts. Many researchers have studied machinability analysis and its closely related workpiece setup problem. Most of the approaches are 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 is constructed to make each face of the part orthogonally visible to to 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 using computer hardware H20849graphics cardsH20850. Frank et al. H2085117H20852 analyzed two-dimensional H208492DH20850 global visibility on stereolithography H20849STLH20850 slices and searched the necessary machining orientations for fourth-axis indexable machining by executing a GREEDY search algorithm. All these visibility-based approaches determine the necessary condition for machinability; however, they ignore tool geometry and, therefore, true accessibility H20849machinabilityH20850 is not guaranteed. Figure 1 shows that the accessibility cone H20849H9251,H9252H20850 based 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 by constructing a new part model through offsetting the original part surface by the amount of the cutter radius. Machinability was further guaranteed by checking the topology of this offset part Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received October 13, 2004; final manuscript received August 8, 2005. Review conducted by D.-W. Cho. 454 / Vol. 128, MAY 2006 Copyright 2006 by ASME Transactions of the ASME Ye Li e-mail: yeliiastate.edu Matthew C. Frank Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, IA 50011 Machinability Flat End This paper presents of the strategy determines 3-axis machining operations file geometry from a of the line segments orthogonal to the axis machinability analysis respectively. This machinability analysis for the rapid machining. H20851DOI: 10.1 Keywords: machinability, 1 Introduction Machinability analysis is taking an increasingly important role as complex surfaces are used in the design of a wide variety of parts. Current computer-aided manufacturing H20849CAMH20850 software is readily capable of generating toolpaths given a set of surfaces of a part and a cutting orientation H208493-axis machiningH20850. However, deter- mining the setup orientation can be difficult and moreover, it may be very challenging to determine if the part can be created using machining at all. An appropriate setup orientation can guarantee an effective cutting of the surface, whereas an inappropriate one will leave too much material in certain regions. The advancement of 5-axis computer numerically controlled H20849CNCH20850 milling ma- chines seems to alleviate this situation; however, often the cost and/or difficulty of programming a 5-axis machine have limited their widespread use. Three-axis machines, as economical and technologically 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-type indexer to provide an alternative to 5-axis ball end milling. Suh et al. H208512H20852 provided a theoretic basis for machining with additional axes. Recently, Frank et al. H208513H20852 employed a 3-axis milling center with a fourth axis indexer as an effective rapid prototyping ma- chine. End mills have been shown to offer a better match to the part surface geometry, a higher material removal rate, and a longer Analysis for 3-Axis ethod for geometric machinability analysis. The implementation the machinability of a part being processed using a plurality of about a single axis of rotation for setup orientations. Slice eolithography model is used to map machinable ranges to each the polygonal chains of each slice. The slices are taken of 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 visibility manufacturing and prototyping of components using CNC 115/1.2137748H20852 tool accessibility, CNC machining, slice geometry the planes of the enclosing object. The part is then considered to be machinable from the normal-vector directions of the enclosing object planes. Later, computational geometry on the sphere was utilized to analyze visibility by Chen and Woo H208517H20852 who performed pioneering work on computational geometry algorithms that could be used for determining workpiece setup and machine selection. Tang et al. H208518H20852 formulated the problem of workpiece orientation as finding the maximum intersection of spherical polygons. Gan et al. H208519H20852 discussed the properties and construction of spherical maps and presented an efficient way to compute a visibility map from a Gaussian 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 ball end milling. A visibility map is generated by using the normal vectors of a specified portion of the surface of a part; therefore, it cannot guarantee global accessibility. Yang et al. H2085111H20852 computed visibility cones based on convex hull analysis, instead of relying on visibility maps. Yin et al. H2085112H20852 defined complete visibility and partial visibility, and presented a C-space-based method for com- puting visibility cones.Asculptured surface is approximated by its convex hull H2085111H20852, and the spherical algorithms H208517,13H20852 are used in the approach of Yin H2085112H20852. The convex hull may, in some cases, have a significant deviation from the true surface. Suh and Kang H2085114H20852 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 part Downloaded 11 Dec 2009 to 222.190.117.204. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfm surface. This method is effective for the machinability analysis of a ball end cutter, but not for that of a flat end cutter, because the effective radius of a flat end cutter is variable with the change of tool tilting angle. Haghpassand and Oliver H2085118H20852 and Radzevich and Goodman H2085119H20852 considered both part surface and tool geom- etry. However, tool size was not taken into account because Gaussian mapping does not convey any size information of the part 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 an active field among the manufacturing research community. Regli H2085121H20852, Regli et al. H2085122H20852, and Gupta and Nau H2085123H20852 discussed feature accessibility and checked it by calculating the feature accessibility volume and testing the intersection of the feature accessibility volume with the part. Gupta and Nau H2085123H20852 recognized all machin- ing operations that could machine the part, generated operation plans, and checked and rated different plans according to design needs. A comprehensive survey paper on manufacturability by Gupta et al. H2085124H20852 reviewed representative feature-based manufac- turability evaluation systems. Shen and Shah H2085125H20852 checked feature accessibility by classifying the feature faces and analyzing the degree of freedom between the removal volume and the work- piece. The MEDIATOR system reported by Gaines et al. H2085126H20852 used the 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 H2085127H20852 discussed the accessibility of both 2.5-D positive and negative features. Other researchers presented featured-based approaches to determine workpiece setups H208512831H20852. Although feature-based approaches are capable tools to handle feature-based design, they cannot lend themselves to free-form surfaces where definable features may not exist. In addition, feature-based approaches suggest that all the geometric elements comprising of a feature are treated together as an entity. This actually imposes a constraint to the analysis of a part model. For example, it might be feasible to machine a portion of a part fea- ture in one orientation and then finish the remaining surfaces of the feature in one or more successive orientations. The current problem that this paper addresses is based on a rapid machining strategy proposed by Frank et al. H208513H20852 whereby a part is machined with a plurality of 3-axis machining operations from multiple setup orientations about a single axis of rotation. The strategy is implemented on a 3-axis CNC milling machine with a fourth-axis indexer H20849Fig. 2H20850. Round stock material is fixed between 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 the collision offset H20849bH20850H20849shown in the Fig. 2H20850 on each side of the workpiece, the implementation of rapid machining can avoid the risk of collision between tool holders and the holding chucks. The diameter of largest tool H20849D tmax H20850 used to calculate the collision offset H20849bH20850 makes the setting of collision offset for each new part unnecessary. The feature-free nature of this method suggests that Fig. 1 Accessibility based on light ray and a sized tool Journal of Manufacturing Science and Engineering it is unnecessary to have any surface be completely machined in any particular orientation. The goal is to simply machine all sur- faces after all orientations have been completed. The number of rotations required to machine a model is dependent on its geomet- ric complexity. Figure 3 illustrates the process steps for creating a typical complex part using this strategy. Currently, the necessary cutting orientations are determined by 2D 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. The visibility of those slices approximates the visibility of the entire surface of the part along the axis of rotation since the slices are generated orthogonal to that axis. The above literature review sug- gests that existing approaches to machinability cannot calculate the set of orientations for setups such that one can machine all machinable surfaces after all orientations, because either H20849iH20850 2D or three-dimensional H208493DH20850 visibility cones employed by the Fig. 2 Setup for rapid machining Fig. 3 Process steps for rapid machining MAY 2006, Vol. 128 / 455 visibility-based approaches convey no size information of the tool and workpiece and, therefore, cannot guarantee true accessibility; or H20849iiH20850 the feature-based approaches cannot cope with complex geometrically composed of a set of pointsH20850 is the intersection of the machinability of each point belonging to that feature. Similar to the concept of partial visibility H20849PVH20850, partial machinability Downloaded 11 Dec 2009 to 222.190.117.204. Redistribution subject to ASME license or copyright; see http:/www.asme.org/terms/Terms_Use.cfm H20849free-formH20850 surface machining because few traditional features can be identified on parts with free-form surfaces. An effective machinability analysis method is a prerequisite to the successful implementation of multisetup 3-axis end milling in order to achieve the needs of 4- and perhaps 5-axis machining.An effective machinability analysis method will determine, given a machining orientation and an end mill of a particular size, how much of the part surface can be machined with respect to this machining orientation. The focus of this paper is to present a feature-free machinability analysis that can determine the number of setups required to completely machine the surfaces of a part with one-axis-of-rotation setups. The machinability analysis method presented in this paper is unlike any previous work in its completely feature-free treatment of the part geometry. We reduce the surfaces of the part down to simple line segments on the slices; therefore, any CAD model can be exported as an STL file and studied. This approach is done because we are only assuming that the part is machined about one axis of rotation; therefore, it is much simpler to simply analyze the 2D slices rather than 3D surface 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 machinability analysis approach. Last, conclusions and future research endeav- ors are provided. 2 Definitions Although 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 also derived. The definitions provided in this section are used for the subsequent discussion in the remainder of this paper. Visibility:Apoint p on a surface SH20849pH33528SH20850 is visible by a light ray emanated from an external point q if pqH6023 suffices the condition of pqH6023H33370H20849SpH20850=H9021. Machinability:Apoint p on a surface SH20849pH33528SH20850 is machinable by a certain type and size of tool TH20849CL,H9251H20850 if pH33528TH20849CL,H9251H20850 and 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 machinability takes into account the size and shape of the cutting tool instead of treating it simply as a line of light. Therefore, machinability can guarantee true accessibility, whereas visibility is only a necessary condition of machinability. Hence, the aggregate of orientations satisfying machinability is a subset of that satisfying visibility. In other words, machinability can guarantee visibility, but not vice versa. Unlike the expression of visibility in angular orientations, the bundle of which forms a cone, there are two parameters used to describe 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 exists only if there is a cutter location that allows the cutting tool to approach and touch the point p without intersecting any other part surface. 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 is 456 / Vol. 128, MAY 2006 H20849PMH20850 of a feature can also be defined in addition to the concept of complete machinability H20849CMH20850. Partial Machinability: A feature is partially machinable along an orientation H9251 if there exists at least one point on that feature such that no cutter location CL exists for it to suffice the condition of pH33528TH20849CL,H9251H20850 and TH20849CL,H9251H20850H33370H20849S pH20850=H9021. Complete Machinability: A feature is completely machin- able along an orientation H9251 if for each point on that feature at least one cutter location CL can be found to guarantee the condition of pH33528TH20849CL,H9251H20850 and TH20849CL,H9251H20850H33370H20849SpH20850=H9021. Note that Complete Machinability may exist for either a point or a feature, whereas partial machinability exists only for a fea- ture, because a point can only be said to be either machinable or nonmachinable. If machinability exists with respect to an approaching orienta- tion H9251, the number of feasible cutter locations CLs may vary with different points on a surface. Points with more feasible CLs trans- lates to easier machining because the more possible CLs provide more options for tool-path and setup planning. The need to mea- sure the space of cutter locations leads to the concept of tool space. Tool Space: The aggregate of all feasible cutter locations to cut a point p from an orientation H9251 forms a region called tool space, written as TSH20849p,H9251H20850=H20853CL:p H33528TH20849CL,H9251H20850 and TH20849CL,H9251H20850H33370H20849SpH20850=H9021H20854. Tool space of a feature F is the union of the tool space of every point belonging to F; that is, TSH20849FH20850=H20853H33371TSH20849p,H9251H20850:pH33528FH20854. A tool space reaches its maximum value maximum tool space H20849MTSH20850 when there is no obstacle around the geometric entity. Here, we consider the entire part surface except the portion under consider- ation to be obstacles. Thus, the corresponding space for obstacles is defined as obstacle space. Obstacle Space: The aggregate of all unfeasible cutter loca- tions with respect to an orientation H9251 due to the existence of an obstacle i H20849ObiH20850 is called the obstacle space of obstacle i, written as OSH20849i,H9251H20850=H20853CL:TH20849CL,H9251H20850H33370ObiHS11005H9021H20854. The cutter cannot enter the domain of obstacle space because it will gouge into the obstacle. Tool space can be computed by subtracting all the obstacle spaces from maximum tool space. TS= MTS H20858 i OS H208491H20850 If the computed tool space using Eq. H208491H20850 is not empty, then machinability exists; otherwise, the geometric entity is nonma- chinable. The machinability analysis method presented in this pa- per is based on Eq. H208491H20850. Tool space is actually a measure of ma- chinability since it tells the existence of machinability and the magnitude 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 a feature given the tool space is c
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