帶輪的沖壓工藝與模具設(shè)計【三維UG工件圖】

喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請放心下載，，有疑問咨詢QQ:414951605或者1304139763 ======================== 喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請放心下載，，有疑問咨詢QQ:414951605或者1304139763 ======================== INDUSTRIAL APPLICATIONAutomated design of thin-walled packaging structuresChing-Jui Chang&Bin Zheng&Hae Chang GeaReceived: 12 March 2007 /Accepted: 28 April 2007 / Published online: 24 August 2007#Springer-Verlag 2007Abstract This paper presents an automated method togenerate thin-walled packaging structures with reinforce-ment. This method first obtains a thin-walled design spacecompose of hexahedral elements, which covers the modelsto be packaged without undercut effect. After the properboundary conditions are assigned by designers, topologyoptimization is applied to identify the optimal placement ofreinforcement. This automated method can also be used togenerate foam packaging structures. Design examples arepresented to demonstrate the efficiency of this method.Keywords Topologyoptimization.Thin-walledpackaging.Optimalreinforcement1 IntroductionAll industrial products require proper packaging duringtransportation. Packaging technologies not only provideproduct protection but also enhance product presentation. Awell-designed and well-constructed packaging can deliverbetter transportability and consequently increase productvalues. Packaging method can be categorized as two types:free format and fixed format. In the free format packaging,there is no predefined form or shape for packagingmaterials and product is loosely surrounded and protectedby some flexible packaging materials. Although free formatpackaging is very economical, it cannot utilize thepackaging materials and space very efficiently; therefore,it is normally not used for industrial packaging. There aremany different fixed format methods for various industrialpackaging applications. Among all fixed format methods,the thin-walled protective packaging has been evolving asthe most important one because it features space saving andlightweight while delivering conspicuous property in shockabsorption, moisture resistance, and most noticeable,environmental friendly when it is constructed by moldedpulp.Thin-walled packaging structures are normally strength-ened by adding rib-shaped features on the thin wall toincrease its stiffness. However, when designing a thin-walled packaging structure, the spaces for holding productsshould be determined before the rib-shaped reinforcementcan be placed. Generally, the packaging company receivesorders for products to be packaged in the form of computer-aided design (CAD) models or physical products. The CADmodels sometimes will not be given in its native CADformats but only in their surface representation formats dueto the product confidentiality. If physical models areprovided, they can also be digitalized to generate 3D datafor surface representation. For both approaches, StereoLithography (STL) file (Jacobs and Reid 1992) is acommonly used data format to describe surface informationbecause triangle is the most basic primitive for computergraphics, and it is easy to be manipulated. The arrangementof product, such as orientation and distribution, and theoverall size packaged box is pre-determined based on itsdisplay requirement and/or weight distribution. The task ofpackaging company is to obtain the supporting spacebetween the bounding box and the products first, and thena thin-walled structure can be generated from the surface ofthe supporting space. Finally, rib-shaped reinforcement areStruct Multidisc Optim (2008) 35:601608DOI 10.1007/s00158-007-0170-yC.-J. Chang:B. Zheng:H. C. Gea (*)Mechanical and Aerospace Engineering, Rutgers,The State University of New Jersey,Piscataway, NJ 08854, USAe-mail: gearci.rutgers.eduC.-J. Change-mail: chingjuirutgers.eduplaced to enhance its stiffness. Currently, the entire processis accomplished by repeated trial-and-errors. Althoughthere are some existing methods for identifying thesupporting space between the product and its boundingbox, e.g., Boolean-based operations for creating a negativeimage model and parting line detection method (Fu et al.1999, 2001; Wong et al. 1998) or injection mold generationmethod (Priyadarshi and Gupta 2004; Li 2002) forgenerating molded foam, these methods may produce faultydesigns for concave shapes. To remedy this deficiency,additional steps before applying these methods, such as theorientation of objects, should be recalculated to obtain anundercut free orientation (Majhi et al. 1999), or concaveobjects should be convexified first. Furthermore, packagingdesigners also need to consider offsets as well as partinglines and draft angle for packaging molds when createpackaging molds (Qu and Stucker 2003; Tokuyama andBae 1999). As these procedures often require experiencedengineers to intervene, it is very desirable to have anautomated design method for thin-walled packagingstructures.To address these challenges, an automated process fordesigning thin-walled packaging structures with the optimalplacement of reinforcements is presented in this paper. Inthis automated process, CAD models of the products areplaced in a pre-specified fashion first. Then, a design spacefor supporting structures is generated between the productsand the overall package by an automated computerprocedure. The design space is further reduced to a one-layered finite element mesh for modeling the thin-walledstructure. Then, a topology optimization method is incor-porated to generate the optimal reinforced structure. Theoptimal criterion is based on the mean complianceformulation to produce the stiffest structure. The final resultfrom the topology optimization can be used to suggest theoptimal reinforcements in the thin-walled structures. In thefollowing sections, detailed discussion on the proposedmethod will be given. Then, some practical designexamples are included to demonstrate the effectiveness ofthe proposed method.2 Design space identificationTo create thin-walled packaging structures with the optimalplacement of reinforcements, a thin-walled design spaceshould be determined from a pre-specified packagingbounding box and product arrangement. There are threesteps in the design space identification: (1) facet reduction,(2) height detection, and (3) design space generation. Thefacet reduction eliminates unnecessary calculation byreducing the number of facets of the CAD model. Theheight detection creates an evenly distributed supports forproducts and prevents undercuts. The design space gener-ation forms a thin-wall mesh surrounding the products. Thedetails of these steps will be presented in this section. Oncethe thin-walled design space is identified, topology optimi-zation can be applied to determine the optimal placement ofreinforcement, which will be discussed in the next section.2.1 Facet reductionAs the products are often given in the form of surfacerepresentation, a commonly used data format, STL format,is implemented in our current study. The STL file formatsimply describes the surface model of solid parts usingtriangles, which is one of the basic graphic primitives.Each triangle is specified with its three vertices, arrangedin counterclockwise order, along with its surface normalcalculated using the right hand rule from its vertices asshown in Fig. 1, which indicates the direction leaving themodel. The surface normal is normalized to have unitylength. A typical ASCII data of a facet in a STL fileconsists of its normal vector (u, v, w) and three sets ofcoordinates of vertices, (xi, yi, zi).To construct the supporting space between the boundingbox and the products, a set of evenly spaced supportinglines is created from the bottom of the bounding boxtowards the products. Although there is no specialrequirement on the spacing between supporting lines, itshould be slightly smaller than the size of the smallestdownward facing triangle such that all features of theproduct model can be captured. From our numericalexperiments, using the spacing as an 80% nominal lengthof the smallest feature can always produce satisfactoryresults. Once the spacing is determined, a set of 2D meshgrids can be generated on the bottom plane of boundingbox. These mesh grids are positioned as the starting pointsof the vertical supporting lines, and the ending points arethe intersections of supporting lines to the products asshown in Fig. 2a. The intersections between each sup-porting line and products will be calculated as shown inFig. 2b.Fig. 1 Triangle primitive of a 3D model602Chang et al.As there are a lot of facets involved in the intersectioncalculation, we need to reduce the computational effort byreducing the number of facets in the STL files first.Considering an object as shown in Fig. 3, it is obviousthat all facets with green normal vectors should not beincluded in the intersection test.To remove all facets with non-downward normal vector,we need to transform all entities in the model to have thesame coordinate system and then rotate the z-axis to be thedirection pointing upwards as the supporting lines. Oncethese transformations are completed, all facets with apositive z component in the normal vectors should beremoved from the comparison pool. This selection processcan reduce a great number of facets before the intersectioncalculation.2.2 Height detectionFor each supporting line, the height from the base to theproduct must be calculated. Although the number of facetshas been greatly reduced after the first step, there still hasno obvious pattern to locate the corresponding facet foreach mesh grid. Because it is computationally expensive tocheck every grid on the mesh for corresponding points, apre-test using a blue bounding rectangle enclosed theprojected triangle, as shown in Fig. 4, is applied first tolimit the grids to be checked. This pre-test is very straight-forward because the mesh grids are pre-defined and spacedregularly. To further improve the efficiency of the calcula-tion, each facet is projected into the mesh grid plan to traceback the mesh grids for the height detection. The red meshgrids enclosed by the projected triangle as shown in Fig. 4are the corresponding mesh grids which need to beprocessed further for height detection.To verify whether the mesh grids are the correspondingones for a given facet, the following procedure is used.Because all the projected facets have their surface normalpointing downwards, if one looks from the top of thebounding rectangle, the edge vectors of the projectedtriangle must run clockwise; consequently, the inner gridsmust be always on the right side of every edge. Hence, theeasiest way to select the inner points is to compare the zvalue of the cross product between the edge vector and thevector formed by the end vertex and the targeting grid.When the z value of the outer product is less than or equalto zero, then the grid is inside the triangle as shown inFig. 5. This test is performed along each edge of the facet.Fig. 3 All facets with green normal vectors should not be included inthe intersection testFig. 2 a Supporting lines from the bottom of the bounding box; bintersections between supporting lines and productFig. 4 Grids enclosed by a projected facetFig. 5 Inner test for a grid and a facetAutomated design of thin-walled packaging structures603If any of the tests confirms that the grid is outside theprojected triangle, the point will be removed immediately.After collecting all inner grids for each facet, it is verysimple to calculate the intersection point. The plane thatembraces a given triangle with facet normal (uk, vk, wk) canbe defined as:ukx vky wkz ukxa vkya wkzawhere (xa, ya, za) is one of the vertex coordinates of thefacet. The z coordinate at the product end of the supportingline with respect to a mesh grid (xi, yj) can be calculatedeasily as:zi;j zaukxa? xi vkya? yj?wkIn some cases, a supporting line from one mesh grid mayintersect with more than one facet. In this case, the shortestheight will be assigned to be the actual height on that gridto avoid penetration.2.3 Design space generationAlthough the heights of all supporting lines from the meshgrids are obtained after the height detection, the packagingsupporting surface still cannot be formed by simplyconnecting these points because there are some portionsof the models may have interference. To overcome thisproblem, heights of supporting lines at the location wheresurface normal changes from down facing to up facing needto be relaxed as follows. For a given supporting line, wecompare all possible eight neighboring supporting lines fortheir heights, and the lowest value among all neighboringheights is assigned to be the new height. This methodapplies to every supporting line to adjust its height to a newone to avoid interferences. After the height relaxationmethod, all new heights can be connected to form asupporting surface as shown in the blue lines of Fig. 6a.One interesting by-product of this method is that apackaging foam model is obtained immediately beforegenerating a thin-walled design space and topologyoptimization. As the foam type of packaging method isalso very popular in some industrial applications, thecurrent implementation can also be used to create the foammodel very efficiently.To generate thin-walled design space, a continuouslyconnected mesh is formed using the heights on the gridsbecause a continuous connected layer of mesh is required toprevent pivot effect from hinge-like meshes. Therefore, aset of four neighboring height grids is used to createcontinuously connected mesh. For grids with the sameFig. 6 An example of forming aFEA mesh layer. a supportingsurface, b first pass mesh, c finalmesha bcFig. 7 a A ball model with1,596 facets, b supportingspace for a bounding box withheight of 45% of the diameter ofthe ball, and c supporting spacefor a bounding box with heightof 70% of the diameter of theball604Chang et al.height, simply connected mesh can be formed. However,for grids with different heights, the lowest height value ofthe set of grids is chosen as the base height and an array ofconnecting hexahedron is generated from the base to thetop as shown in Fig. 6b and c.3 Topology optimizationOnce the thin-walled design space is generated, designercan assign proper boundary conditions including supportsand loadings to simulate various packaging conditions.Because thin-walled structures have very low stiffnessagainst off-plane loading and vibration, they are normallyreinforced by proper placement of stiffeners. There are tworesearch directions related to the optimal stiffener design:the composite structure optimization problem and thereinforcement problem. The former models the thin-walledstructures using orthotropic material and calculate theoptimal thickness and orientation of orthotropic materials(Gea and Luo 2004; Luo and Gea 1998a Pedersen 1989,1990, 1991), and the latter utilizes the topology optimiza-tion to identify the optimal locations and orientation undervarious static and vibration applications (Luo and Gea1997, 1998b, c, 2003; Gea and Luo 1999; Gea and Fu1995, 1997). The validity of topology optimization result iscurrently under investigation. In common cases, bead rib isa suitable candidate to be applied on the thin-wall structureto increase stiffness. Some extra considerations need to betaken when bead ribs intersecting each other becausestiffness may be decreased in this case.As the main purpose of this paper is to demonstrate anautomated design methodology of thin-walled packagingstructure using topology optimization, only the minimizingmean compliance formulation is used to demonstrate theapplicability of the method. In this paper, a microstructure-based design domain method is employed to formulate thisproblem due to its simplicity (Gea 1996), and theoptimization problem is solved iteratively by generalizedconvex approximation (Chickermane and Gea 1996). Thismethod has been implemented using C#.NET on a PentiumIV 2.66 GHz personal computer with 1.5 GB RAM. In thenext section, examples of automated packaging designusing this method are presented and discussed.Fig. 8 Efficient test result on ball models with different number ofsupporting base gridsab c Fig. 9 a A suspension model, b suspension model and supportingspace with 70% height, and c supporting spaceAutomated design of thin-walled packaging structures6054 Design examplesFour examples are presented in this section. The first twoexamples are foam packaging designs: example 1 is asimple convex object and example 2 consists of anautomobile suspension model with multiple components.These two examples are used to demonstrate the efficiencyof the proposed method. The last two examples are thin-walled packaging structures: example 3 is a simple box andexample 4 is a toy car model with multiple components.Designs of optimal reinforcement of both models usingtopology optimization under mean compliance formulationare presented.4.1 Example 1: a ball modelA simple ball model is presented in the first examplebecause it is a strictly convex model as shown in Fig. 7a.The ball contains 1,596 facets, and the bottom of sup-porting space is divided into 200200 mesh grids. First, theheight of bounding box is chosen as 45% of the diameter ofthe ball, which is slightly below the center of ball. Aconcave foam packaging structure is generated in 0.15 s ina personal computer as shown in Fig. 7b. When the heightof bounding box elevates to 70% of the diameter of the ball,the foam packaging structure cannot be obtained by asimple negative model from Boolean operation. However,our method can still produce a correct form packagingspace automatically by creating a cylindrical cavity after thesupporting space passes the half ball as shown in Fig. 7c.The entire operation is completed within 0.16 s.To further demonstrate the efficiency of the algorithm ofgenerating the supporting surface, the ball model isgenerated and saved to have a different number of facets,and the supporting space is divided into different amount ofgrids to compare the time required to generate thesupporting surface. Fifty percent of the height is designedto be covered. The result is shown in Fig. 8. The resultshows that the amount of facets has minor effect on the timeneeded to obtain the supporting surface, while the number ofbase grids plays a major role on that. The complexity of thealgorithm is verified to be linear, which can be observed fromFig. 8.4.2 Example 2: automobile suspension modelIn the second example, an automobile suspension model isused. This model consists of 55 individual components:wheels, motor, transmission gears, differential gears,frames, etc., totaling 140,640 facets. A 300524 meshgrids are created in the bottom plane of supporting space.The height of the bounding box is chosen as the 75% of theheight of the model. It is obvious that models with multi-component will pose great challenge when the parting lineFig. 10 Detection of designspace. a bounding box and cut-ting plane, b supporting space, cfinal design spaceFig. 11 Topology optimizationresult for a box model. a designspace with loading and supports,b final design from topologyoptimization, c location ofreinforcements606Chang et al.algorithm is use. However, the method presented here canstill generate the correct foam packaging structure automat-ically. The final supporting space is generated in 0.83 s.The results are shown in Fig. 9.4.3 Example 3: a box modelA simple square box model is presented in the thirdexample for thin-walled packaging structure design becauseit is a simple convex model. First, the box is placed in abounding space that is 30% larger along all its edges. Abounding plane is set at the height equals 50% of the totalheight as shown in Fig. 10a. Then, the height detection gridis defined to have 3030 points, and the heights areaccordingly obtained as shown in Fig. 10b. Followed by thedesign space generation, a thin-walled design space isobtained as shown in Fig. 10c.The loadings and constraints are assigned by designeraccording to its applications. As an example to demonstratethis method, a simply supported four corners are modeledwith a concen