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摩托车后轮轮毂低压铸造模具设计【8张CAD图纸+毕业答辩论文】【模具优秀资料】

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摩托车 后轮 轮毂 低压 铸造 锻造 模具设计 全套 cad 图纸 毕业 答辩 论文 冲压 模具
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目   录

1   绪论

1.1   摩托车车轮发展概况………………………………………………………… 1

1.2   铝合金轮毂成形方法的选择与对比………………………………………… 2

1.3   铝合金轮毂铸造方法的选择和对比………………………………………… 3

1.4   国内外低压铸造发展概况…………………………………………………… 4

2   低压铸造基本知识

2.1   低压铸造原理………………………………………………………………… 5

2.2   低压铸造工艺流程…………………………………………………………… 6

2.3   低压铸造的特点……………………………………………………………… 7

2.4   低压铸造工艺规范…………………………………………………………… 8

3   模具总体方案设计

3.1   铝合金轮毂低压铸造模具一般方案………………………………………… 10

3.2   模具总体方案设计与对比…………………………………………………… 12

3.2.1 零件轮辋的主要形式………………………………………………………… 12

3.2.2 轮毂零件的分析……………………………………………………………… 13

3.2.3 铸件毛坯的工艺分析………………………………………………………… 15

3.2.4 模具总体方案1………………………………………………………………  16

3.2.5 模具总体方案2及与方案1的比较………………………………………… 17

3.3   模具的动作方式……………………………………………………………… 18

3.3.1 模具的分模动作方式………………………………………………………… 19

3.3.2 模具的合模复位动作方式…………………………………………………… 20

4   模具设计

4.1   铸件的材料及其性能………………………………………………………… 22

4.2   机械加工余量的确定………………………………………………………… 22

4.3   铸件收缩率的确定…………………………………………………………… 22

4.4   起模斜度的确定……………………………………………………………… 23

4.5   分型面的确定………………………………………………………………… 23

4.6   模架的设计…………………………………………………………………… 24

4.7   冒口的设计…………………………………………………………………… 25

4.7.1 冒口设计的基本原则………………………………………………………… 25

4.7.2 冒口设置的原因……………………………………………………………… 25

4.7.3 冒口的设置与原理分析……………………………………………………… 26

4.8   推出机构的设计……………………………………………………………… 27

4.8.1 推出机构的组成及特点……………………………………………………… 27

4.8.2 推出距离的计算……………………………………………………………… 28

4.8.3 推杆截面积的计算…………………………………………………………… 29

4.9   尺寸公差的确定……………………………………………………………… 31

4.10  涂料的使用…………………………………………………………………… 31

5   边模的工艺路线

5.1   定位基准的选择……………………………………………………………… 33

5.1.1 精基准的选择原则…………………………………………………………… 33

5.1.2 粗基准的选择原则…………………………………………………………… 33

5.1.3 精基准和粗基准的确定……………………………………………………… 33

5.2   边模表面加工工序的确定…………………………………………………… 34

5.2.1 加工工序顺序的原则………………………………………………………… 34

5.2.2 加工阶段的划分……………………………………………………………… 34

5.2.3 边模的工艺路线……………………………………………………………… 35

5.2.4 边模的工艺规程……………………………………………………………… 35

6   总结 ……………………………………………………………………………  37

参考文献……………………………………………………………………………… 38

致谢……………………………………………………………………………………  39

附录……………………………………………………………………………………  40


摘要:轮毂是踏板摩托车上极为重要的行驶部件和安全部件,应具有良好的综合力学性能,在正常行驶过程中不应发生变形和疲劳失效。而轮毂又属于形状复杂的零件,一般采用铸造方法使其成型。现在,广泛采用低压铸造来生产轮毂。模具在铸造成型方法中是至关重要的一部分,因此,它的设计和制造成了铸造质量的关键所在。

本文对轮毂进行实体造型更形象的了解轮毂的外形。并主要从摩托车轮毂的发展状况、铝合金的成型与铸造方法、低压铸造的工艺及特点,模具总体方案的选择以及模具结构的设计等方面介绍了轮毂低压铸造的模具设计。

该款轮毂的材料采用了铝合金材料(ZL101A),对轮毂的铸造毛坯进行了设计,使其能够满足铸造的工艺要求。设计中将低压铸造与压力铸造、金属型重力铸造、挤压铸造以及差压铸造等铸造方法进行了对比。分析了轮毂零件的特点以及轮辋的主要形式及其特点。另外,主要从铸件收缩率、铸型分型面、冒口的设置以及推出机构等几个方面介绍了模具设计的要点。通过示意图描述了模具的分模与合模的动作方式。并对铸造轮毂的边模进行工艺分析。




关键词:轮毂 低压铸造 模具设计


Abstract: Wheels is an extremely important safety components and moving parts of aPedaling Motorcycle , which should have good mechanical properties, in the normal courseof driving should not be taken deformation and fatigue failure. And Wheel is a part of complex shape. Generally casting method used to shapee. It widely used low-pressure casting to produce wheel currently. Die Casting is a vital part in molding method. So its design andmanufacture is the key of casting quality.

This paper making solid mode-ling for wheels in order to understanding more image about the shape of the wheel ,and it mainly introduces the Wheel mold design of low pressure die casting, fromthe development of motorcycle wheelAluminum alloy molding and casting methods, process and characteristics of Low-Pressure Casting,the choice of the overall program dies the design of die structure Introduced die casting the wheel design by low pressure

Materials of this wheel used alloy material (ZL101A) .The paper Analyses the wheel parts and wheels characteristics of the main forms and characteristicsduring the program design the low-pressure casting and pressure casting, metal-gravity casting, pressure squeeze casting and pressure casting, and other methods are compared. . The Casting blank of the wheel enables it to meet the technological casting requirements. In addition, to introducethe principal Mold design elements, it covers several aspects including the contraction rate of type-casting, Riser set up the institutions and the launch. The actions of Die-Die and mold are described by the cess analysis he side-mode for casting wheel


Keywords:  Wheels  low-pressure casting  mold design  

1  绪论

1.1摩托车车轮发展概况

随着工业的飞速发展,摩托车工业也快速的壮大起来,摩托车成为了人们出行所使用的主要交通工具之一。尤其是在发展中国家里,摩托车的拥有数量非常庞大。在我国各大城市里,摩托车已经成为许多家庭的主要交通工具。正是由于摩托车市场的庞大的需求量,从而促使了摩托车企业的快速发展,制造摩托车的工艺也在不断进步。

摩托车车轮是摩托车中极其重要的部件之一,它的质量好坏直接影响着摩托车行驶的安全和可靠。早期的摩托车速度较低,其车轮结构为刚性连接,轮胎为高压胎。随着轮胎及车轮技术的发展,低压轮胎逐渐取代了高压轮胎。与此同时,低压轮胎又出现了无内胎轮胎。

目前,摩托车车轮主要有三种结构形式:轮圈辐条组合式车轮、辐板式整体车轮和轻合金车轮。

轮圈辐条组合式车轮是一种传统的结构型式,该种车轮与早期刚性连接的车轮相比,减震性能较好。但是,这种车轮受结构的限制,车轮的外形变化比较困难,不能适应摩托车外观造型日新月异的需要。并且由于这种结构车轮受轮圈冲孔的限制,不能装配无内胎轮胎,使它的发展大受影响。

辐板式整体车轮分为辐板式整体钢车轮和辐板式整体铝车轮。辐板式整体钢车轮主要用于中、低挡小轮径摩托车。其钢制轮圈的工艺方法是用钢板卷制后焊接成型,使用一段时间后,焊接部位易生锈造成无内胎车轮漏气。辐板式整体铝车轮有质量小、铝辐板形状容易变化等优势。另外,铝合金轮圈和铝辐板通过表面处理后,可以形成车轮所需要的各种颜色,满足了消费者对多种颜色的需求。


内容简介:
Int J Adv Manuf Technol (2000) 16:739747 2000 Springer-Verlag London LimitedAutomated Assembly Modelling for Plastic Injection MouldsX. G. Ye, J. Y. H. Fuh and K. S. LeeDepartment of Mechanical and Production Engineering, National University of Singapore, SingaporeAn injection mould is a mechanical assembly that consists ofproduct-dependent parts and product-independent parts. Thispaper addresses the two key issues of assembly modellingfor injection moulds, namely, representing an injection mouldassembly in a computer and determining the position andorientation of a product-independent part in an assembly. Afeature-based and object-oriented representation is proposedto represent the hierarchical assembly of injection moulds.This representation requires and permits a designer to thinkbeyond the mere shape of a part and state explicitly whatportions of a part are important and why. Thus, it providesan opportunity for designers to design for assembly (DFA). Asimplified symbolic geometric approach is also presented toinfer the configurations of assembly objects in an assemblyaccording to the mating conditions. Based on the proposedrepresentation and the simplified symbolic geometric approach,automatic assembly modelling is further discussed.Keywords: Assemblymodelling;Feature-based;Injectionmoulds; Object-oriented1.IntroductionInjection moulding is the most important process for manufac-turing plastic moulded products. The necessary equipment con-sists of two main elements, the injection moulding machineand the injection mould. The injection moulding machines usedtoday are so-called universal machines, onto which variousmoulds for plastic parts with different geometries can bemounted, within certain dimension limits, but the injectionmould design has to change with plastic products. For differentmoulding geometries, different mould configurations are usuallynecessary. The primary task of an injection mould is to shapethe molten material into the final shape of the plastic product.This task is fulfilled by the cavity system that consists of core,cavity, inserts, and slider/lifter heads. The geometrical shapesCorrespondence and offprint requests to: Dr Jerry Y. H. Fuh, Depart-ment of Mechanical and Production Engineering, National Universityof Singapore (NUS), 10 Kent Ridge Crescent, Singapore 119260.E-mail: mpefuhyhK.sgand sizes of a cavity system are determined directly by theplastic moulded product, so all components of a cavity systemare called product-dependent parts. (Hereinafter, product refersto a plastic moulded product, part refers to the component ofan injection mould.) Besides the primary task of shaping theproduct, an injection mould has also to fulfil a number oftasks such as the distribution of melt, cooling the moltenmaterial, ejection of the moulded product, transmitting motion,guiding, and aligning the mould halves. The functional partsto fulfil these tasks are usually similar in structure and geo-metrical shape for different injection moulds. Their structuresand geometrical shapes are independent of the plastic mouldedproducts, but their sizes can be changed according to theplastic products. Therefore, it can be concluded that an injectionmould is actually a mechanical assembly that consists ofproduct-dependent parts and product-independent parts. Figure1 shows the assembly structure of an injection mould.The design of a product-dependent part is based on extractingthegeometryfrom theplasticproduct.Inrecentyears,CAD/CAM technology has been successfully used to helpmould designers to design the product-dependent parts. TheMouldMouldbaseCoolFillLayoutPlugSocketCav_1Cav_2CA-plateGuild-bushTCP-plateBep-plateCb-plateEa-plateEb-plateGuid-pinIp-plateRet-pinSliderbodyguideStop-blkHeel-blkheadCoreCavityProduct-independent partProduct-dependent partMove-halfFixed-halfFig. 1. Assembly structure of an injection mould.740X. G. Ye et al.automatic generation of the geometrical shape for a product-dependent part from the plastic product has also attracted alot of research interest 1,2. However, little work has beencarried out on the assembly modelling of injection moulds,although it is as important as the design of product-dependentparts. The mould industry is facing the following two difficult-ies when use a CAD system to design product-independentparts and the whole assembly of an injection mould. First,there are usually around one hundred product-independent partsin a mould set, and these parts are associated with each otherwith different kinds of constraints. It is time-consuming forthe designer to orient and position the components in anassembly. Secondly, while mould designers, most of the time,think on the level of real-world objects, such as screws, plates,and pins, the CAD system uses a totally different level ofgeometrical objects. As a result, high-level object-oriented ideashave to be translated to low-level CAD entities such as lines,surfaces, or solids. Therefore, it is necessary to develop anautomatic assembly modelling system for injection moulds tosolve these two problems. In this paper, we address the follow-ing two key issues for automatic assembly modelling: rep-resenting a product-independent part and a mould assembly ina computer; and determining the position and orientation of acomponent part in an assembly.This paper gives a brief review of related research inassembly modelling, and presents an integrated representationfor the injection mould assembly. A simplified geometric sym-bolic method is proposed to determine the position and orien-tation of a part in the mould assembly. An example of auto-matic assembly modelling of an injection mould is illustrated.2.Related ResearchAssembly modelling has been the subject of research in diversefields, such as, kinematics, AI, and geometric modelling. Lib-ardi et al. 3 compiled a research review of assembly model-ling. They reported that many researchers had used graphstructures to model assembly topology. In this graph scheme,the components are represented by nodes, and transformationmatrices are attached to arcs. However, the transformationmatrices are not coupled together, which seriously affects thetransformation procedure, i.e. if a subassembly is moved, allits constituent parts do not move correspondingly. Lee andGossard 4 developed a system that supported a hierarchicalassembly data structure containing more basic informationabout assemblies such as “mating feature” between the compo-nents. The transformation matrices are derived automaticallyfrom the associations of virtual links, but this hierarchicaltopology model represents only “part-of” relations effectively.Automatically inferring the configuration of components inan assembly means that designers can avoid specifying thetransformation matrices directly. Moreover, the position of acomponent will change whenever the size and position of itsreference component are modified. There exist three techniquesto infer the position and orientation of a component in theassembly: iterative numerical technique, symbolic algebraictechnique, and symbolic geometric technique. Lee and Gossard5 proposed an iterative numerical technique to compute thelocation and orientation of each component from the spatialrelationships. Their method consists of three steps: generationof the constraint equations, reducing the number of equations,and solving the equations. There are 16 equations for “against”condition, 18 equations for “fit” condition, 6 property equationsfor each matrix, and 2 additional equations for a rotationalpart. Usually the number of equations exceeds the number ofvariables, so a method must be devised to remove the redundantequations. The NewtonRaphson iteration algorithm is used tosolve the equations. This technique has two disadvantages:first, the solution is heavily dependent on the initial solution;secondly, the iterative numerical technique cannot distinguishbetween different roots in the solution space. Therefore, itis possible, in a purely spatial relationship problem, that amathematically valid, but physically unfeasible, solution canbe obtained.Ambler and Popplestone 6 suggested a method of comput-ing the required rotation and translation for each componentto satisfy the spatial relationships between the components inanassembly.Sixvariables(threetranslationsandthreerotations) for each component are solved to be consistent withthe spatial relationships. This method requires a vast amountof programming and computation to rewrite related equationsin a solvable format. Also, it does not guarantee a solutionevery time, especially when the equation cannot be rewrittenin solvable forms.Kramer 7 developed a symbolic geometric approach fordetermining the positions and orientations of rigid bodies thatsatisfy a set of geometric constraints. Reasoning about thegeometric bodies is performed symbolically by generating asequence of actions to satisfy each constraint incrementally,which results in the reduction of the objects available degreesof freedom (DOF). The fundamental reference entity used byKramer is called a “marker”, that is a point and two orthogonalaxes. Seven constraints (coincident, in-line, in-plane, parallelFz,offsetFz, offsetFx and helical) between markers are defined.For a problem involving a single object and constraints betweenmarkers on that body, and markers which have invariant attri-butes, action analysis 7 is used to obtain a solution. Actionanalysis decides the final configuration of a geometric object,step by step. At each step in solving the object configuration,degrees of freedom analysis decides what action will satisfyone of the bodys as yet unsatisfied constraints, given theavailable degrees of freedom. It then calculates how that actionfurther reduces the bodys degrees of freedom. At the end ofeach step, one appropriate action is added to the metaphoricalassembly plan. According to Shah and Rogers 8, Kramerswork represents the most significant development for assemblymodelling. This symbolic geometric approach can locate allsolutionsto constraintconditions, andis computationallyattractive compared to an iterative technique, but to implementthis method, a large amount of programming is required.Although many researchers have been actively involved inassembly modelling, little literature has been reported on fea-ture based assembly modelling for injection mould design.Kruth et al. 9 developed a design support system for aninjection mould. Their system supported the assembly designfor injection mouldsthrough high-level functionalmouldobjects (components and features). Because their system wasAutomated Assembly Modelling741based on AutoCAD, it could only accommodate wire-frameand simple solid models.3.Representation of Injection MouldAssembliesThe two key issues of automated assembly modelling forinjection moulds are, representing a mould assembly in com-puters, and determining the position and orientation of a pro-duct-independent part in the assembly. In this section, wepresent an object-oriented and feature-based representation forassemblies of injection moulds.The representation of assemblies in a computer involvesstructural and spatial relationships between individual parts.Such a representation must support the construction of anassembly from all the given parts, changes in the relativepositioning of parts, and manipulation of the assembly as awhole. Moreover, the representations of assemblies must meetthe following requirements from designers:1. It should be possible to have high-level objects ready touse while mould designers think on the level of real-world objects.2. The representation of assemblies should encapsulate oper-ational functions to automate routine processes such aspocketing and interference checks.To meet these requirements, a feature-based and object-orientedhierarchical model is proposed to represent injection moulds.An assembly may be divided into subassemblies, which in turnconsists of subassemblies and/or individual components. Thus,a hierarchical model is most appropriate for representing thestructural relations between components. A hierarchy impliesa definite assembly sequence. In addition, a hierarchical modelcan provide an explicit representation of the dependency ofthe position of one part on another.Feature-based design 10 allows designers to work at asomewhat higher level of abstraction than that possible withthe direct use of solid modellers. Geometric features areinstanced, sized, and located quickly by the user by specifyinga minimum set of parameters, while the feature modeller worksout the details. Also, it is easy to make design changes becauseof the associativities between geometric entities maintained inthe data structure of feature modellers. Without features,designers have to be concerned with all the details of geometricconstruction procedures required by solid modellers, and designchanges have to be strictly specified for every entity affectedby the change. Moreover, the feature-based representation willprovide high-level assembly objects for designers to use. Forexample, while mould designers think on the level of a real-world object, e.g. a counterbore hole, a feature object of acounterbore hole will be ready in the computer for use.Object-oriented modelling 11,12 is a new way of thinkingabout problems using models organised around real-world con-cepts. The fundamental entity is the object, which combinesboth data structures and behaviour in a single entity. Object-oriented models are useful for understanding problems anddesigning programs and databases. In addition, the object-oriented representation of assemblies makes it easy for a“child” object to inherit information from its “parent”.Figure 2 shows the feature-based and object-oriented hier-archical representation of an injection mould. The represen-tation is a hierarchical structure at multiple levels of abstraction,from low-level geometric entities (form feature) to high-levelsubassemblies. The items enclosed in the boxes represent“assembly objects” (SUBFAs, PARTs and FFs); the solid linesrepresent “part-of” relation; and the dashed lines representother relationships. Subassembly (SUBFA) consists of parts(PARTs). A part can be thought of as an “assembly” of formfeatures (FFs). The representation combines the strengths of afeature-based geometric model with those of object-orientedmodels. It not only contains the “part-of” relations betweenthe parent object and the child object, but also includes aricher set of structural relations and a group of operationalfunctions for assembly objects. In Section 3.1, there is furtherdiscussion on the definition of an assembly object, and detailedrelations between assembly objects are presented in Section Definition of Assembly ObjectsIn our work, an assembly object, O, is defined as a unique,identifiable entity in the following form:O = (Oid, A, M, R)(1)Where:Oid is a unique identifier of an assembly object (O).A is a set of three-tuples, (t, a, v). Each a is called anattribute of O, associated with each attribute is a type,t, and a value, v.M is a set of tuples, (m, tc1, tc2, %, tcn, tc). Eachelement of M is a function that uniquely identifies amethod. The symbol m represents a method name; andmethods define operations on objects. The symbol tci(iFig. 2. Feature-based, object-oriented hierarchical representation.742X. G. Ye et al.= 1, 2, %, n) specifies the argument type and tc specifiesthe returned value type.R is a set of relationships among O and other assemblyobjects.Therearesixtypesofbasicrelationshipsbetween assembly objects, i.e. Part-of, SR, SC, DOF,Lts, and Fit.Table 1 shows an assembly object of injection moulds, e.g.ejector. The ejector in Table 1 is formally specified as:(ejector-pinF1, (string, purpose, ejecting moulding),(string, material, nitride steel), (string, catalogFno,THX),(checkFinterference(), boolean), (pocketFplate(), boolean),(part-of ejectionFsys), (SR Align EBFplate), (DOF Tx,Ty).In this example, purpose, material and catalogFno areattributes with a data type of string; checkFinterference andpocketFplate are member functions; and Part-of, SR and DOFare relationships.3.2Assembly RelationshipsThere are six types of basic relationships between assemblyobjects, Part-of, SR, SC, DOF, Lts, and Fit.Part-ofAn assembly object belongs to its ancestor object.SRSpatial relations: explicitly specify the positionsandorientationsofassemblyobjectsinanassembly.Foracomponentpart,itsspatialrelationship is derived from spatial constraints(SC).SCSpatial constraints: implicitly locate a componentpart with respect to the other parts.DOFDegrees of freedom: are allowable translational/rotational directions of motion after assembly, withor without limits.LtsMotion limits: because of obstructions/interferences,the DOF may have unilateral or bilateral limits.FitSize constraint: is applied to dimensions, in orderto maintain a given class of fit.Table 1. Definition of an assembly object-ejector.Object Oidejector-pinF1Instance-ofEjectorFpinDerived from ejector classAPurpose “ejecting moulding” Type stringMaterial “nitrided steel”Type stringCatalogFno “THX”Type stringMCheckFinterferenceCheck interference(coolFobj)between ejectors andcooling linesPocketFplate()Make a hole on plate toaccommodate ejector pinsRPart-ofejectorFsysSRalign with EBplateDOFTx, TyAmong all the elements of an assembly object, the relation-ships are most important for assembly design. The relationshipsbetween assembly objects will not only determine the positionof objects in an assembly, but also maintain the associativitiesbetween assembly objects. In the following sub-sections, wewill illustrate the relationships at the same assembly level withthe help of examples.3.2.1Relationships Between Form FeaturesMould design, in essence, is a mental process; mould designersmost of the time think on the level of real-world objects suchas plates, screws, grooves, chamfers, and counter-bore holes.Therefore, it is necessary to build the geometric models of allproduct-independent parts from form features. The moulddesigner can easily change the size and shape of a part,because of the relations between form features maintained inthe part representation. Figure 3(a) shows a plate with acounter-bore hole. This part is defined by two form features,i.e. a block and a counter-bore hole. The counter-bore hole(FF2) is placed with reference to the block feature FF1, usingtheir local coordinates F2and F1, respectively. Equations (2)(5) show the spatial relationships between the counter-borehole (FF2) and the block feature (FF1). For form features,there is no spatial constraint between them, so the spatialrelationships are specified directly by the designer. The detailedassembly relationships between two form features are definedas follows:SR(FF2, FF1):F2i= F1i(2)F2j= F1j(3)Fig. 3. Assembly relationships.Automated Assembly Modelling743F2k= F1k(4)r2F= r1F+ b22*F1j+ AF1*F1i(5)DOF:ObjFhasF1FRDOF(FF2, F2j)The counter-bore feature can rotate about axis F2j.LTs(FF2, FF1):AF1, b11 0.5*b21(6)Fit (FF2, FF1):b22= b12(7)WhereF and r are the orientation and position vectors of fea-tures.F1= (F1i, F1j, F1k),F2= (F2i, F2j, F2k).bijis the dimension of form features, Subscript i isfeature number, j is dimension number.AF1is the dimension between form features.Equations (2)(7) present the relationships between the formfeature FF1and FF2. These relationships thus determine theposition and orientation of a form feature in the part. Takingthe part as an assembly, the form feature can be consideredas “components” of the assembly.The choice of form features is based on the shape character-istics of product-independent parts. Because the form featuresprovided by the Unigraphics CAD/CAM system 13 can meetthe shape requirements of parts for injection moulds and thespatial relationships between form features are also maintained,we choose them to build the required part models. In additionto the spatial relationships, we must record LTs, Fits relation-ships for form features, which are essential to check thevalidity of form features before updating the models in theCAD system.3.2.2Relationships Between PartsIn an assembly, the position and orientation of a part is usuallyassociated with another part. Figure 3(b) shows a plate (PP1)and a screw (PP2). The relative placement of the screw isconstrained by the counter-bore hole on the plate. The relation-ships between the screw and the plate are defined as follows:SR(PP2, PP1):P2= MpP1(8)r2= Mrr1(9)SC(PP2, PP1):mate(f1,f2) axisFalign(axisF1, axisF2)DOF:ObjFhasF1FRDOF(PP2, P2j)The screw can rotate about P2jof the plate.LTs(PP2, PP1):A22, A12(10)Fits(PP2, PP1):A13= A21+ cc(11)Where:P1and P2are the orientation vectors of the plate andthe screw, and P1= (P1i, P1j, P1k), P2= (P2i, P2j, P2k).Mpand Mrare the transformation matrix between thescrew and the plate. is a Boolean operator.mate and axisFalign are constraints (detailed discussionabout them are given in the next section).r is a position vector.Aijis dimension of parts. Subscript i is part number, andj is dimension number.cc is the clearance between the screw and the plate.As we can see in Eqs. (8) and (9), it is essential to calculatethe matrix Mpand Mrto determine the position and orientationof the screw with reference to the plate. Mpand Mrcan bederived from the spatial constraints (SC). This derivationrequires the task of inferring the configuration of a part in anassembly, which will be discussed in the next section.We have presented a representation of the injection mouldassembly in a computer. At this stage, it might be worthwhileto summarise the benefits of this representation. Assembliesare represented as a collection of subassemblies that in turnmay consist of subassemblies and/or component parts, and acomponent part can further be considered as the assembly ofform features. Such hierarchical relationships imply an orderingon the assembly sequence and a parentchild link. The feature-based representation not only allows designers to work at ahigh-level of abstraction while designing individual parts, butalso extends the feature paradigm to assembly modelling,because this representation allows a component to be changedparametrically with the other components consequently havingtheir positions changed accordingly. The object-oriented rep-resentation can combine both the data structure and operationin an object. The encapsulated operational functions in anassembly object can help to automate the routine processessuch as the pocketing and interference check.4.Inferring Part Configuration in theAssemblyAs we can see from Eqs (8) and (9), the positions andorientations of parts in an assembly are eventually representedby the transformation matrices. For the sake of convenience,the spatial relationships are usually specified by the high-levelmating conditions such as “mate”, “align” and “parallel”. Thus,it is essential to derive automatically the explicit transformationmatrices between parts from implicit constraint relationships.Three techniques to infer the configurations of parts in anassembly have been discussed in Section 2. Because the sym-bolic geometric approach can locate all solutions to constraintequations withpolynomial time complexity, we use thisapproach to determine the positions and orientations of partsin an assembly. To implement this approach in assemblymodelling software, a large amount of programming is required.Therefore, a simplified geometric approach is proposed todetermine the positions and orientations of parts in an assembly.744X. G. Ye et al.In the symbolic geometric approach, determining positionsand orientations of parts is performed symbolically by generat-ing a sequence of actions to satisfy each constraint incremen-tally. The information required to satisfy each constraintincrementally is stored in a table of “plan fragments”. Eachplan fragment is a procedure that specifies a sequence ofmeasurements and actions that move parts in such a way asto satisfy the corresponding constraint. The plan fragment alsorecords the objects new degrees of freedom (DOFs) andassociated geometric invariants. Conceptually, Kramers planfragment table is a 3D dispatch table. We use TDOF torepresent translational degrees of freedom and RDOF to rep-resent rotational degrees of freedom. Then an entry in the planfragment table has the following form:planFfragment: kTDOF, RDOF, constraintFtypelTDOF = 0, 1, 2, 3RDOF = 0, 1, 2, 3constraintFtype=coincident,in-line,in-plane,parallelFz, offsetFz, offsetFx and helicalThe plan fragment table is an exhaustive enumeration of allthe states in the search space for the problem of moving anobject to satisfy a series of constraints between markers onthe object and markers fixed in the global coordinate frame.To enumerate the combination of different values of the abovethree parameters, 82 entries will be generated 7. If the searchspace for the problem can be reduced the number of entriesin a plan fragment table will decrease. To achieve this, thenumber of enumerate values for entry parameters must bedecreased. For example, for a specified constraint type, if theenumeration values of TDOF change from 0,1,2,3 to 0,3,then the search space is reduced.After a careful analysis of the constraints between compo-nents of an injection mould, four basic primitive constraints areintroduced: in-line, parallelFz, parallelFz1 and parallelFoffset.Their definitions and algebraic equations are as follows:in-line(M1, M2): M1lies on the line through M2parallel to theZ-axis of M2.ugmp(M1) gmp(M2)u gmz(M2)u = 0(12)parallelFz(M1, M2): the Z-axes of markers M1and M2areparallel and have the same direction.gmz(M1) gmz(M2) = 1(13)parallelFz1(M1, M2): the Z-axes of markers M1and M2areparallel and have the opposite direction.gmz(M1) gmz(M2) = 1(14)paralleFoffset(M1, M2, d): Applicable only in conjunctionwith parallelFz or parallelFz1, specifies the distancebetween M1position and M2position.gmp(M1) gmp(M2) = d(15)Where:M1and M2are markers.gmp(M) is the global marker position.gmz(M) is the global marker Z-axis.gmx(M) the global marker X-axis.d is the distance between M1and M2.In our simplified symbolic geometric approach, the enumer-ation vales of constraint types are inFline, parallelFz, par-relFz1, paralleFoffset. Compared with Kramers symbolic geo-metric approach, our constraint types are reduced from sevento four. This simplification will reduce the number of entriesin the plan fragment table. Based on these four primitiveconstraints, three high-level constraints were synthesised fortheusersconvenience.Theyaremate(M1,M2,d),planeFalign(M1, M2, d), and axisFalign(M1, M2). Their defi-nitions are given as follows:mate(M1, M2, d):parallelFz1(M1, M2) parallelFoffset(M1, M2, d)planeFalign(M1, M2, d):parallelFz(M1, M2) parallelFoffset(M1, M2, d)axisFalign(M1, M2):parallelFz(M1, M2) inFline(M1, M2)The assembly objects in an injection mould can have one,two or three synthesised constraints. For two and three syn-thesised constraints, the constraint sequence is further restricted.The sequences are as follows:mate(M1, M2, d) planeFalign(M3, M4, d2)mate(M1, M2, d1) axisFalign(M3, M4)planeFalign(M1, M2, d) axisFalign(M3, M4)mate(M1,M2,d1)axisFalign(M3,M4,d2)axisFalign(M5, M6).Because of these restrictions on the constraint sequences,the number of entries in our plan fragment table is substantiallyreduced. To solve for one, two or three constraints allowed inour system, only nine entries are required. For interactiveaddition of components to the assembly, more constraint typesand free sequences will increase the flexibility for users. How-ever, in automatic assembly modelling for an injection mould,as the spatial relationships are predefined in assembly objects,some of the sequence restrictions do not matter. With theabove-defined synthesised constraints, the structural relation-ships of a component part can be specified in the database ofthe components. When adding a component part to the mouldassembly, the system will first decompose the synthesisedconstraints into primitive constraints, then generate a groupof fragment plans to orient and position the component inthe assembly.5.Automated Assembly Modelling ofInjection MouldsAnyassemblyofinjectionmouldsconsistsofproduct-independent parts and product-dependent parts. The design ofindividual product-dependent parts is based on the geometryof the plastic part 1,2. Usually the product-dependent partshave the same orientation as that of the top-level assembly,and their positions are specified directly by the designer. Asfor the design of product-independent parts, conventionally,mould designers select the structures from the catalogues,Automated Assembly Modelling745build the geometric models for selected structures of product-independent parts, and then add the product-independent partsto the assembly of the injection mould. This design process istime-consuming and error-prone. In our system, a database isbuiltforallproduct-independentpartsaccordingtotheassembly representation and object definition described in Sec-tion 3. This database not only contains the geometric shapesand sizes of the product-independent parts, but also includesthe spatial constraints between them. Moreover, some routinefunctions such as interference check and pocketing are encapsu-lated in the database. Therefore, the mould designer must selectthe structure types of product-independent parts from the userinterfaces, and then the software will automatically calculatethe orientation and position matrices for these parts, and addthem to the assembly.5.1Mould Base SubassemblyAs can be seen from Fig. 1, the product-independent parts canbe further classified as the mould base and standard parts. Amould base is the assembly of a group of plates, pins, guidebushes, etc. Besides shaping the product, a mould has to fulfila number of functions such as clamping the mould, leadingand aligning the mould halves, cooling, ejecting the product,etc. Most moulds have to incorporate the same functionality,which results in a similarity of the structural build-up. Someform of standardisation in mould construction has been adopted.A mould base is the result of this standardisation.According to the feature-based and object-oriented assemblyrepresentation, the feature-based solid models for componentparts of the mould base are first constructed; next, the assemblyobjectsaredefinedbyestablishingrelationshipsbetweencomponents and encapsulating some functions in the componentparts; then, using these assembly objects, a hierarchical subas-sembly object a mould base can be formed. This mouldbase object can be instantiated by a group of data from thecatalogue database. Figure 4 shows the instantiation of themould base object to generate the specified mould base. Thisspecified mould base instance can be added automatically tothe mould assembly. The structural relations between the mouldbase subassembly and top assembly can be expressed by Eqs.(8) and (9), where Mpand Mrare the unit matrices.5.2Automatic Addition of Standard PartsA standard part is an assembly object. It can be definedaccording to Eq. (1) in Section 3.1. In the database, the spatialconstraints are specified by mate, planeFalign and axisFalign,but unlike the mould base, the position and orientation matricesof a standard part are left unknown. During instantiation,the software then automatically infers the explicit structuralrelationshipsbyusingthesimplifiedsymbolicgeometricapproach described in Section 4.5.3Pocketing for Assembly ObjectsOne of the important issues for automatic assembly design isthe automation of the pocketing process. Pocketing is anFig. 4. Instantiation of mould base.operation that makes an empty space in corresponding compo-nents to accommodate the inserted components. When an ejec-tor is added to the assembly, an empty space is required onthe EA plate to accommodate the ejector, as shown in Fig. 5.Since an object-oriented representation is adopted, eachassembly object can be represented by two solids, the realobject and the virtual object. The virtual object is modelledaccording to the space that a real object will occupy. Wheneveran assembly object is added to an assembly, its virtual objectisalsoaddedtotheassembly.TheoperationfunctionpocketFplate() in M of O will subtract the virtual object fromthe corresponding components (see Eq. (1) and Table 1).Moreover, because there are associativities between the virtualobject and real object, the pockets on the corresponding compo-nents will change with the modification of the real object.Fig. 5. Pocketing of assembled objects.746X. G. Ye et al.This automatic pocketing function further demonstrates theadvantage of an object-oriented representation.6.System ImplementationBased on the Unigraphics system 13, the proposed feature-based and object-oriented assembly scheme and automation ofassembly modelling have been implemented in the IMOLDsystem 14 developed at the National University of Singapore.The Unigraphics system provides a user-friendly applicationprogramming interface (API). Through this interface, the userscan call Unigraphics internal functions such as adding parts toan assembly, modifying parameters, etc. Although Unigraphicsprovides functions for mating conditions, the proposed approachis still needed to infer the component configuration, becauseit is necessary to calculate the degrees of freedom, and checkthe validity of mating conditions before the component can beadded to the assembly. The proposed synthesised constraintsare compatible with Unigraphics constraints.Figure 6 shows an injection moulded product, and thedesigned injection mould assembly for this product is shownin Fig. 7(a). The corresponding parentchild relationships forfix-half subassembly are shown in Fig. 7(b). This assembly is
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