安全帽的注塑模具设计及成型工艺-抽芯塑料注射模含9张CAD图带开题
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DOI 10.1007/s00170-004-2374-2ORIGINAL ARTICLEInt J Adv Manuf Technol (2006) 28: 370378C.L. Li K.M. Yu Y.H. LeeAutomatic datum dimensioning for plastic injection mould designand manufacturingReceived: 7 May 2004 / Accepted: 10 August 2004 / Published online: 20 April 2005 Springer-Verlag London Limited 2005Abstract Datum dimensioning (or ordinate dimensioning) tech-nique is very popular in plastic injection mould drawings wherethe location dimensions of a large number of hole features mustbe specified in the drawings of the mould plates. Although com-mercial CAD/CAM systems provide semi-automatic tools to as-sist the designer in the dimensioning process, it is still a verytedious process, as the user has to specify the location of each di-mension tag. This paper reports a completely automatic methodwhere optimal placements of the dimension tags can be deter-mined. The method employs dynamic programming technique tooptimize the dimension process with respect to several criteriathat can be selected by the user. The method has been imple-mented and incorporated into a commercial CAD/CAM system,and examples are given to illustrate the important features of theprogram.KeywordsAutomatic dimensioning Datum dimensioning Dynamic programming Optimal dimensioning Ordinate dimensioning1 IntroductionCAD/CAM systems are now widely used in the plastic injec-tion mould-making industry. Many companies are using a solidmodeling system to design the injection mould. They use a CADsystem to model not only the core and cavity inserts of the mould(which are the most important components that form the im-pression of the mould), but also all other components in theC.L. Li (u) Y.H. LeeDepartment of Manufacturing Engineering and Engineering Management,City University of Hong Kong,Tat Chee Avenue, Kowloon, Hong KongE-mail: meclli.hkTel.: +8-52-27888432Fax: +8-52-27888423K.M. YuDepartment of Industrial and Systems Engineering,The Hong Kong Polytechnic Universityentire mould assembly. With the advance in Internet technologyand the recent development of Internet-enabled CAD, the de-sign information of the injection mould can be communicatedelectronically between the product engineer (who designs theplastic part) and the tooling engineer (who designs the injectionmould), even though they may be located in different geographicregions of the world. While flow of design information betweenproduct design and tooling design are communicated effectivelythrough an electronic means, the communication of manufac-turing information to the shop floor is done by both electronicand traditional techniques. Computer Numerical Control (CNC)machining toolpath or inspection instructions can be generateddirectly from the CAD/CAM system and downloaded througha network to the CNC controller for the machining or inspectionoperations. However, set-up instructions for a particular machin-ing job may be specified in an engineering drawing. Moreover,not all machining tasks are done using CNCmachine tools. Sometraditional machining processes, such as drilling and grinding,are done using conventional machine tools because of cost con-sideration. Conventional engineering drawings are thus still play-ing an important role in communicating engineering informationto the shop floor. The orthographic projections in engineeringdrawings can be generated automatically from the CAD modelof the parts. Automatic tools for dimensioning of the parts arealso provided by many commercial CAD systems. However, aspointed out by Chen et al. 1, those automatic dimensioningtools are not able to generate dimensions according to the draw-ing standards and engineering practices adopted in the shop floor.In the specific application of injection mould design, datumdimensioning (or ordinate dimensioning) of hole features areused extensively. Figure 1 shows a typical detail drawing that canbe found on the shop floor of a mould making company. Shownin the figure are the hole features and datum dimensions whichare used to specify the locations of the holes. It can be seenthat the dimensions are very crowded and it is a tedious task tomanually adjust the placement of all the datum dimensions. Thequality of the final fully-dimensioned drawing thus depends verymuch on the experience of the draftsman who produces the draw-ing. The purpose of this research is to develop a tool that can371Fig.1. Use of datum dimensioning in a drawing of a plastic injection mould partgenerate the datum dimensions automatically from a given partof the injection mould. The resulting dimensions must satisfytwo obvious requirements: first, that no two dimension tags mayoverlap; and second, that a dimension tag be placed as close aspossible to the feature being dimensioned. The key issue in thisresearch is to develop a method that can optimize the placementof the datum dimensions.2 Related workWhile dimensioning and tolerancing are two closely related pro-cesses in specifying the size and location information of thefeatures in a mechanical part or an assembly, most of the pastresearch work has focused on tolerancing. The major researchissues in tolerancing are representation, analysis and synthesis.Tolerancing representation is concerned with the incorporationof tolerance information into a product modeling scheme. Exam-ples include the solid offset approach developed by Requicha 2,the feasibility space approach proposed by Turner 3, and theTTRS by Desrochers and Clement 4. More detailed review canbe found in Roy et al. 5 and Yu et al. 6. Tolerance analy-sis aims to determine the combined effect of part tolerances onthe assembly tolerance. It can be used to verify the functional-ity of a design given known or assumed variations of individualpart dimensions. Examples of technique in tolerance analysis in-clude Monte Carlo simulation 7 and the direct linearizationmethod 8. The main objective of tolerance synthesis or tol-erance allocation is to allocate part tolerances based on givenfunctional requirements of the assembly. Recently, Islam 9 re-ported a concurrent engineering approach to address this prob-lem. Based on a systemic analysis of the functional requirementsfrom different customer requirements and the technical require-ments from engineering considerations, a methodology for ex-tracting dimensional requirements is developed. A software pro-totype FDT 10 is also developed for supporting the implemen-tation of the methodology. FDT provides tools for representingthe functional requirements, dimensions, tolerances and processcapability into a functional requirement/dimensions matrix. Thefunctional equations captured in the matrix are then separatedinto groups, and each group is then solved using a solution strat-egy specific to the functional requirement and the tolerancingproblem involved. More detailed review intolerance analysis andsynthesis can be found in Roy et al. 5, Ngoi and Ong 11 andHong and Chang 12.Several methods have been developed for generating dimen-sions automatically from the CAD model of a part. Yuen etal. 13 reported an early attempt in automatic dimensioning ofparts represented in Constructive Solid Geometry (CSG) solidmodeling technique. Points from planar faces and axes of cylin-ders are extracted from the solid model. The coordinates of thepoints are arranged in a tree structure to generate linear dimen-sions in the three principal directions. A simple technique fordiametric and radial dimensions was also reported. Other earlyworks in automatic dimensioning have been summarized by Yuet al. 6. Recently, Chen et al. 1,14 reported a more in-depthstudy of automatic dimensioning. Their method analyzed di-mension redundancy, determined dimensioning schemes that arespecific to feature patterns, selected appropriate views for spec-ifying the dimension, and determined the appropriate locationof the dimension using an expert system approach 15. The ex-pert system analyses the geometry and topology of the featureto be dimensioned, and determined a position for placing thedimension based on a set of rules that is relevant to the cur-rent dimensioning feature. With the placement of one dimension,a forbidden region is constructed so that all subsequent dimen-sions will not be placed in this region. This avoids overlap orintersection between two dimensions.372A limitation in the existing approach for the placement ofthe dimension is due to the sequential nature of the method.For example, in Chens 1,14 method the features to be dimen-sioned are prioritized, and the positions of the dimensions aredetermined one after another. The approach is not appropriatefor determining the placement of datum dimensions, especiallywhen the dimensions are very crowded, as in the case of injectionmould plates. This is because the placement of one datum di-mension may have an effect on the placement of another dimen-sion that may be located far away from the current dimension.This paper reports our work in solving the placement problemin datum dimensioning. The major contribution of our work isthe development of a new method that determines the optimalplacement of each datum dimension. Using the dynamic pro-gramming approach to optimization, this new method overcomesthe limitation of the sequential approach used in the existingmethod.3 Basic characteristicof datum dimensioningIn datum dimensioning, the location of a feature is specifiedby the horizontal and vertical distances from the reference lo-cation of the feature and a reference datum. The default formof datum dimension is shown in Fig. 2a. When the vertical dis-tance between two features to be dimensioned is less than thedimension tag size (i.e. the sum of the dimension text heightand the minimum spacing between adjacent dimension texts),Fig.2. Basic characteristics of datum dimensioningthe alternative forms shown in Fig. 2b are required.1The di-mension tags are shifted upward or downward from the defaultlocation to prevent overlap. As shown in Fig. 2c, the shiftingof the dimension tag is achieved by breaking the single exten-sion line of the dimension into three segments: two horizontalsegments which are connected by one inclined segment. The ex-tent to which a dimension tag can be shifted is governed bythree parameters: (i) the dogleg angle , which is the angle be-tween the inclined segment and the horizontal segments of thedimension line; (ii) the margin distance m between the dimen-sion text and the part boundary; and (iii) the location (xfi, yfi) ofthe feature fi. The two extreme positions (i.e. the uppermost pos-ition ymaxiand lowermost position ymini) of the dimension tag aregiven by:ymaxi= yfi+(xfi+m)tanymini= yfi(xfi+m)tan(1)4 Automaticdatum dimensionThe objective of the automatic datum dimensioning system is tofind an optimal position for each datum dimension. The processconsists of two phases of operation: the preparation phase andthe optimization phase. In the preparation phase, major param-eters that facilitate the optimization process will be established.Feasibility for placing the dimensions for all the features usingthe given dogleg angle, margin offset and dimension tag sizewill also be tested. In the optimization phase, a dynamic pro-gramming approach is used. The dimension tag locations can beoptimized with respect to different sets of criteria, including theminimization of the shift of every dimension from their defaultlocations, or maximization of the use of the default form as muchas possible.4.1 The preparation phaseThe features to be dimensioned are first grouped into one ormore feature sets. For each feature in a feature set, there existat least one other feature in the set such that the vertical dis-tance between them is less than the dimension tag size. In otherwords, the features in a feature set cannot be dimensioned usingthe default form exclusively without overlap between adjacentdimension tags. Instead, at most one feature can use the de-fault form while all others require the use of the alternativeform. The set of dimension tags associated with a feature setis called a dimension block. The configuration of a dimensionblock refers to the forms and locations of each datum dimen-sion within the dimension block. For each position of a dimen-sion block, its configuration is uniquely defined. Figure 3 showstwo feature sets and their dimension blocks at two differentconfigurations.1To simplify the explanation of the technique, only vertical dimensionsplaced on the left hand side of the part are discussed. The method developedis general and can be applied to the other sides of the part.373Fig.3. Feature sets and different con-figurations of dimension blocksDefinition 1: Validity of a configuration. A configuration of a di-mension block is valid if there is no overlap between any dimen-sion tags in the dimension block, and each dimension tag lieswithin its extreme positions.The configurations of the dimension blocks shown in Fig. 3bare valid. Two examples of invalid configuration are shown inFig. 4. The configuration shown in Fig. 4a is invalid because twoof the dimension tags overlap. For the configuration shown inFig. 4b, the extension line of the dimension tag 14.00 is at itslowermost position, while the required position for the dimen-sion tag is beyond this lowermost position.Fig.4. Invalid configurations of a dimension blockFig.5. Dimension block at extreme configurationsDefinition 2: Extreme configurations. There are two extremeconfigurations: the uppermost and lowermost configurations.A dimension block is at its uppermost (lowermost) configurationif the dimension block is valid and is at a position such that anyother higher (lower) position results in an invalid configuration.The extreme configurations of a dimension block diare denotedby Ymaxiand Ymini.Figure 5a shows a dimension block at its uppermost config-uration. It cannot move further upward because the dimensiontag 29.5 is at its highest position. Figure 5b shows a dimen-sion block at its lowermost configuration. It cannot move fur-374ther downward because the dimension tag 14.00 is at its lowestposition.The extreme configurations of a dimension block are the twoimportant parameters that will be used by the optimization pro-cess. They are also useful in testing whether it is feasible todimension all the features without any overlap between the di-mension tags. It is observed that two properties are useful indeveloping a method to determine the extreme configurations.Property 1:. For a dimension block at its uppermost (lowermost)configuration, at least one of its dimension tags is at its upper-most (lowermost) position.Property 2:. A dimension block has a valid configuration if andonly if it has extreme configurations.Property 1 can be proved by contradiction. Assume that a di-mension block is at its uppermost (lowermost) configuration, andnone of its dimension tags are at their uppermost (lowermost)positions. Since all the dimension tags are not at their uppermost(lowermost) positions, they can all be moved upwards (down-wards) simultaneously by the same amount until any one of themreaches its uppermost (lowermost) position. As all dimensiontags are moved simultaneously by the same amount, the dimen-sion tags do not overlap, and thus the resulting configurationis still valid and at a higher (lower) position than its originalconfiguration. This violates the assumption that the original con-figuration is the uppermost (lowermost) configuration.Property 2 can be verified directly. Given a valid configura-tion, the dimension block is moved upward (downward) until oneor more of its dimension tags reach its uppermost (lowermost)position. Since all the dimension tags are moved simultaneouslyby the same amount, overlap does not occur. Moreover, the di-mension block cannot be moved upwards (downwards) any fur-ther without invalidating the configuration because at least oneof its dimension tags is at its uppermost (lowermost) position.According to Definition 2, the resulting configuration is thus theuppermost (lowermost) configuration. On the other hand, it isob-vious that if a dimension block has extreme configurations, thenit has a valid configuration because the extreme configurationsare, by definition, valid.Property 1 indicates that the extreme configurations of a di-mension block can be obtained by investigating the extreme pos-itions of the dimension tags in the block. The configuration ofa dimension block can be specified by yi,i =1,2,.,n, whereyiis the location of the dimension tag of the ith feature in thefeature set fi. This assumes that fi are arranged in ascend-ing order by their vertical positions (i.e. yfi yfjif i j). Then,to avoid overlap between dimension tags, the location of the ithdimension tag is given by:yi= (i 1)SIZE+ y1;n i 2(2)where SIZE is the dimension tag size and y1is the location of thedimension tag for the first feature ( f1) of the set. y1is also usedas the reference location of the dimension block.For a configuration to be valid, all dimension tags must liebelow its own uppermost position given by Eq. 1. That is:ymaxi yiand thusymaxi (i 1)SIZE + y1The above relationship must be satisfied by all i. Therefore, thehighest allowable value for y1is given by:Miniymaxi(i 1)SIZE(3)with the y1value given by Eq. 2, and one or more yiequal toymaxi. All other yiare less than its ymaxi. Since no other largervalue of y1results in a configuration that satisfies ymaxi yi, theresulting configuration, if valid, is the uppermost configuration.However, it is possible that at this configuration some of the yigiven by Eq. 2 is less than ymini. Therefore, a check is performedfor each yi. If yi yminifor all i, then the uppermost configura-tion is found. If yii(YmaxjSIZEni)YFmini= Max(Ymini, Maxij1(Yminj+SIZEnj)where niand njare the number of dimension tags in dimensionblocks diand dj, respectively. Using this definition of the feas-ible range, those configurations that always cause overlap withadjacent dimension blocks are excluded from the feasible range.A fixed resolution, say 0.5mm, is specified and the number ofstates for a given stage is obtained by dividing the feasible rangeby the given resolution.4.4 Cost functionsThe overall cost of a stage and the cost function Ci(ti,j,ti1,k)are vector and vector-valued functions, respectively. A cost vec-tor consists of five components ci, i = 1,. ,5 arranged in de-scending order of importance. That is, ciis considered moreimportant than cjifi p?YFmaxiYFmini?, and is set to zerootherwise.When two adjacent dimension blocks at their default loca-tions overlap for a certain amount a, the overlap can be removedby shifting diupwards by ai, and shifting di1downwards byai1, such that ai+ai1= a. It may be desirable that ai= ai1.That is, the required total shift is being shared equally betweentwo dimension blocks. The sub-cost function DV(ti,j) is not ableto achieve this purpose because it only measures the total shiftamount and not the distribution of the amount between adjacentdimension blocks. DE(ti,j) is devised to equalize the amount ofshift between adjacent dimension blocks. It is set to the differ-ence between the extent of deviations of the adjacent dimensionblocks.DE(ti,j,ti1,k) = |DV(ti,j) DV(ti1,k)|.The four optional sub-cost functions are freely selected andassigned to the second to fifth cost components by the user toachieve different objectives. In the next section, examples aregiven to illustrate the different results obtained by choosing dif-ferent optional sub-cost functions.5 Illustrative examplesThe proposed optimization method has been implemented usingC+ and incorporated into the Unigraphics II CAD/CAMsystemthrough its Application Program Interface (API). To illustrate theeffects of the sub-cost functions, consider the example illustratedin Fig. 6. There are five dimension blocks in the figure. All thedimension blocks are at their default configurations and overlapoccurs between d1and d2, and between d4and d5. These dimen-sions are generated automatically by the optimization program,with the cost function contributed only by the sub-cost functionDV. As a result, the dynamic programming procedure selectsa set of states where the lowest cost corresponds to the minimumdeviation from the default location of each dimension block.Fig.6. Dimension blocks at their default configurationFig.7. Minimizing the amount of shift and the number of dimension blocksto be shifted to remove overlaps between dimension blocks377Fig.8. Comparison of the effects obtained from DNand DEFig.9. Execution of the optimization program to gen-erate datum dimensions for an example part378By activating the cost component equation c1which dealswith overlaps, and setting cost component c2to DVand c3toDN, the optimization program shifts the dimension blocks fromtheir default configurations by a minimum amount to removethe overlaps, and also the number of dimension blocks that haveto be shifted are also minimized. The resulting dimensions areshown in Fig. 7. Only two dimension blocks d1and d4are shifteddownwards to remove overlaps with d2and d5.Figure 8 shows another example which compares the effectof DNand DE. Figure 8a shows the result obtained by using DVand DN. The lower block is shifted while the upper block re-mains at its default configuration. Figure 8b shows the result ob-tained by using DVand DE. Both dimension blocks are shiftedby a small amount to remove the overlap.Figure 9 shows the execution of the optimization program inthe Unigraphics II CAD/CAM system. After invoking the userfunction that contains the optimization program, a sequence ofdialogue boxes appear to prompt user input. The user selects theface of a part where datum dimensions are to be generated andthe reference datum to be used through the first and second di-alogue boxes, respectively. Finally, the user is prompted for thefont size of the dimension text and the margin offset to be used.A drawing that contains 120 datum dimensions for all hole fea-tures associated with the selected face is generated automaticallywithin a second, as shown in the figure. Several typical exampledrawings in injection mould design with 50 to 250 hole featureshave been used to test the performance of the program. The testsshow that datum dimensions can be generated within a second,which confirms that the performance of the program is suitablefor interactive use.A limitation of the current implementation is that the dog-leg angle is set to a fixed value, and cannot be adjusted by theoptimization program. When it is not feasible to place all thedatum dimensions, the program execution terminates at the prep-aration phase and prompts the user for an alternative font sizeof the dimension text and the margin offset. It is desirable thatthe program attempts to solve the problem first by finding anoptimal dogleg angle within a given range before promptingthe user to change the two parameters. Further investigation isneeded to incorporate the dogleg angle as an additional variablefor optimization.6 ConclusionAutomatic dimensioning is a useful tool in improving the pro-ductivity of the design process. Datum dimensions are frequentlyused in an injection mould workshop, and thus automatic datumdimensioning is particularly useful. A major problem in auto-matic datum dimensioning is to determine the proper
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