【溫馨提示】====【1】設(shè)計包含CAD圖紙 和 DOC文檔，均可以在線預(yù)覽，所見即所得，，dwg后綴的文件為CAD圖，超高清，可編輯，無任何水印，，充值下載得到【資源目錄】里展示的所有文件======【2】若題目上備注三維，則表示文件里包含三維源文件，由于三維組成零件數(shù)量較多，為保證預(yù)覽的簡潔性，店家將三維文件夾進行了打包。三維預(yù)覽圖，均為店主電腦打開軟件進行截圖的，保證能夠打開，下載后解壓即可。======【3】特價促銷，，拼團購買，，均有不同程度的打折優(yōu)惠，，詳情可咨詢QQ：1304139763 或者 414951605======【4】 題目最后的備注【JA系列】為店主整理分類的代號，與課題內(nèi)容無關(guān)，請忽視
Int J Adv Manuf Technol 2001 17 297 304 2001 Springer Verlag London Limited Optimum Gate Design of FreeForm Injection Mould using the Abductive Network J C Lin Department of Mechanical Design Engineering National Hu Wei Institute of Technology Yunlin Taiwan This study uses the injection position and size of the gate as the major control parameters for a simulated injection mould Once the injection parameters gate size and gate position are given the product performance deformation can be accurately predicted by the abductive network developed To avoid the numerous influencing factors first the part line of the parameter equation is created by an abductive network to limit the range of the gate The optimal injection parameters can be searched for by a simulation annealing SA optimisa tion algorithm with a performance index to obtain a perfect part The major purpose is searching for the optimal gate location on the part surface and minimising the air trap and deformation after part formation This study also uses a prac tical example which has been and proved by experiment to achieve a satisfactory result Keywords Abductive network Injection mould Simulation annealing SA 1 Introduction Owing to the rapid development of industry and commerce in recent years there is a need for rapid and high volume production of goods The products are manufactured using moulds in order to save the time and cost Plastic products are the majority Owing to these products not requiring complicated processes it is possible to cope with market demand speedily and conveniently In traditional plastic production the designs of the portions of the mould are determined by humans However because of the increased performance requirements the complexity of plastic products has increased First the geometric shapes of the plastic products are difficult to draw and the internal shape is often complex which also affects the production of the product Injection processing can be divided into three stages Correspondence and offprint requests to Dr J C Lin Department of Mechanical Design Engineering National Hu Wei Institute of Technology Yunlin 632 Taiwan E mail linrcKsunws nhit edu tw 1 Heat the plastic material to a molten state Then by high pressure force the material to the runner and then into the mould cavity 2 When the filling of the mould cavity is completed more molten plastic should be delivered into the cavity at high pressure to compensate for the shrinkage of the plastic This ensures complete filling of the mould cavity 3 Take out the product after cooling Though the filling process is only a small proportion of the complete formation cycle it is very important If filling in incomplete there is no pressure holding and cooling is required Thus the flow of the plastic fluid should be controlled thoroughly to ensure the quality of the product The isothermal filling model of a Newtonian fluid is the simplest injection mould flow filling model Richardson 1 produced a complete and detailed concept The major concept is based on the application of lubrication theory and he simplified the complex 3D flow theory to 2D Hele Shaw flow The Hele Shaw flow was used to simulate the potential flow and was furthermore used in the plasticity flow of the plastic He assumed the plasticity flow on an extremely thin plate and fully developed the flow by ignoring the speed change through the thickness Kamal et al used similar methods to obtain the filling condition for a rectangular mould cavity and the analyti cal result obtained was almost identical to the experimental result Plastic material follows the Newtonian fluid model for flow in a mould cavity and Bird et al 2 4 derived mould flow theory based on this When the shape of a mould is complicated and there is variation in thickness then the equilibrium equa tions changes to nonlinear and has no analytical solution Thus it can be solved only by finite difference or numerical solutions 2 5 Of course as the polymer is a visco elastic fluid it is best to solve the flow problem by using visco elasticity equations In 1998 Goyal et al used the White Metzner visco elasticity model to simulate the disk mould flow model for central pouring Metzner using a finite difference method to solve the governing equation fould the visco elasticity effect would not change the distribution of speed and temperature However it affects the stress field very much If it is a pure visco elastic 298 J C Lin flow model the popular GNF model is generally used to perform numerical simulation Currently finite element methods are mostly used for the solution of mould flow problems Other methods are pure visco elastic models such as C FOLW and MOLD FLOW software We used this method as well Some software employs the visco elastic White Metzner model but it is limited to 2D mould flow analysis Simple mould flow analysis is limited by CPU time For the complicated mould shapes Papthanasion et al used UCM fluid for filling analysis using a finite difference method and BFCC coordination system application for the solution of the more complicated mould shape and filling problem but it was not commercialised 6 Many factors affect plastic material injection The filling speed injection pressure and molten temperature holding press ure 7 12 cooling tube 13 14 and injection gate affect the accuracy of the plastic product because when the injection processing is completed the flow of material in the mould cavity results in uneven temperature and pressure and induces residual stress and deformation of the workpiece after cooling It is difficult to decide on the mould part surface and gate positions Generally the mould part surface is located at the widest plane of the mould Searching for the optimal gate position depends on experience Minimal modification to the mould is required if you are lucky However the time and cost required for the modification of most injection moulds exceeds the original cost if the choice of the part line is poor For the mould part surface many workers used various methods to search for the optimal mould part line such as geometric shape and feature based design 15 17 Some workers used finite element methods and abductive networks to look for the optimal gate design for a die casting mould 18 This study used an abductive network to establish the para meter relationship of the mould part line and used this formula for searching for 22 points on the injection mould part line to serve as the location for an injection gate Abductive networks are used to match injection pressure and pressure holding time to perform injection formation analysis and to establish a relationship between these parameters and the output result of the injection process It has been shown that prediction accuracy in abductive networks is much higher than that in other networks 19 Abductive networks based on the abductive modelling tech nique are able to represent complex and uncertain relationships between mould flow analysis results and injection parameters It has beeen shown that the injection strain and injection stress in a product can be predicted with reasonable accuracy based on the developed networks The abductive network has been constructed once the relationships of gate location that are input and simulated have been determined an appropriate optimisation algorithm with a performance index is then used to search for the optimal location parameters In this paper an optimisation method for simulated annealing 20 is presented The simulated annealing algorithm is a simulation of the annealing process for minimising the perform ance index It has been successfully applied to filtering in image processing 21 VLSI layout generation 22 discrete tolerance design 23 wire electrical discharge machining 24 deep draw clearance 25 and casting die runner design 26 etc It provides an experimental foundation based on theory for the development and application of the technologies 2 Mould Flow Theory The mould flow analysis include four major parts 1 Filling stage 2 Pressure holding stage 3 Cooling and solidification stage 4 Shrinkage and warp i e stress residue stage Thus the major mould flow equations are divided into four groups In the filling stage the mould cavity is filled with molten plastic fluid at high presssure Thus the governing equations include 1 Continuity equation The plastic deformation or shape change accompany the flow during the filling process mass conservation r t V 0 1 r plastic density V vector velocity 2 Momentum equation Newton s second law is used to derive the momentum acceleration condition or force balance generated by plastic flow r F V t V V G VP t rf 2 P flow pressure f body force t stress tensor 3 Energy equation The energy conservation of system and laws of conservation of flow material if the fluid is incom pressible rC P F T t V T G q t V 3 T temperature C P specific heat of constant pressure q heat flux 4 Rheology equation t f n g T P 4 g V V T 5 V deform tensor V T transport vector Holding pressure analysis The holding pressure process is to maintain the pressure after the mould cavity is filled in order to inject more plastic to compensate for the shrinkage in cooling r V 1 t P x 1 F t 11 x 1 t 21 x 2 t 31 x 3 G 6 r V 2 t P x 2 F t 12 x 1 t 22 x 2 t 32 x 3 G 7 r V 3 t P x 1 F t 13 x 1 t 23 x 2 t 33 x 3 G 8 Optimum Gate Design of FreeForm Injection Mould 299 Cooling analysis The analysis of the cooling process con siders the relationship of the plastic flow distribution and heat transmission The homogenous mould temperature and the sequence of filling will be affected by the shrinkage of the product formed If the temperature is distributed non uniformly it tends to produce warp This is mainly due to heat transfer and crystallisation heat of the plastic rC P T t k F 2 T x 2 1 2 T x 2 2 2 T x 3 3 G rC P rDH 9 r crystallisation rate DH crystallisation heat 3 Abductive Network Synthesis and Evaluation Miller 22 observed that human behaviour limits the amount of information considered at a time The input data are summar ised and then the summarised information is passed to a higher reasoning level In an abductive network a complex system can be decom posed into smaller simpler subsystems grouped into several layers using polynomial function nodes These nodes evaluate the limited number of inputs by a polynomial function and generate an output to serve as an input to subsequent nodes of the next layer These polynomial functional nodes are specified as follows 1 Normaliser A normaliser transforms the original input variables into a relatively common region a 1 q 0 q 1 x 1 10 Where a 1 is the normalised input q 0 q 1 are the coefficients of the normaliser and x 1 is the original input 2 White node A white node consists of linear weighted sums of all the outputs of the previous layer b 1 r 0 r 1 y 1 r 2 y 2 r 3 y 3 r n y n 11 Where y 1 y 2 y 3 y n are the input of the previous layer b 1 is the output of the node and the r 0 r 1 r 2 r 3 r n are the coefficients of the triple node 3 Single double and triple nodes These names are based on the number of input variables The algebraic form of each of these nodes is shown in the following single c 1 s 0 s 1 z 1 s 2 z 2 1 s 3 z 3 1 12 double d 1 t 0 t 1 n 1 t 2 n 2 1 t 3 n 3 1 t 4 n 2 t 5 n 2 2 t 6 n 3 2 t 7 n 1 n 2 13 triple e 1 u 0 u 1 o 1 u 2 o 2 1 u 3 o 3 1 u 4 o 2 u 5 o 2 2 u 6 o 3 2 u 7 o 3 u 8 o 2 3 u 9 o 3 3 u 10 o 1 o 2 u 11 o 2 o 3 u 12 o 1 o 3 u 13 o 1 o 2 o 3 14 where z 1 z 2 z 3 z n n 1 n 2 n 3 n n o 1 o 2 o 3 o n are the input of the previous layer c 1 d 1 and e 1 are the output of the node and the s 0 s 1 s 2 s 3 s n t 0 s 1 t 2 t 3 t n u 0 u 1 u 2 u 3 u n are the coefficients of the single double and triple nodes These nodes are third degree polynomial Eq and doubles and triples have cross terms allowing interaction among the node input variables 4 Unitiser On the other hand a unitiser converts the output to a real output f 1 v 0 v 1 i 1 15 Where i 1 is the output of the network f 1 is the real output and v 0 and v 1 are the coefficients of the unitiser 4 Part Surface Model This study uses an actual industrial product as a sample Fig 1 The mould part surface is located at the maximum projection area As shown in Fig 1 the bottom is the widest plane and is chosen as the mould part surface However most important is the searching of gate position on the part surface This study establishes the parameter equation by using an abductive neuron network in order to establish the simulated annealing method SA to find the optimal gate path position The parameter equation of a part surface is expressed by F Y X First use a CMM system to measure the XYZ coordinate values in this study z 0 of 22 points on the mould part line on the mould part surface as illustrated in Table 1 and the gate position is completely on the curve in this space Prior to developing a space curve model a database has to be trained and a good relationship msut exist between the control point and abductive network system A correct and Fig 1 Injection mould product 300 J C Lin Table 1 X Y coordinate Set number X coordinate Y coordinate 1 0 02 4 6 2 1 63 4 33 3 3 28 3 5 4 5 29 2 04 5 7 31 0 56 6 9 34 0 9 7 11 33 2 35 8 12 98 3 94 9 13 85 5 57 10 14 12 7 34 11 13 69 9 67 12 12 96 11 9 13 10 00 21 03 14 9 33 23 16 15 8 64 25 28 16 7 98 27 39 17 7 87 28 31 18 7 80 29 29 19 7 83 30 34 20 7 60 31 30 21 7 07 32 15 22 6 11 32 49 precise curve Eq is helpful for finding the optimal gate location To build a complete abductive network the first requirement is to train the database The information given by the input and output parameters must be sufficient A predicted square error PSE criterion is then used to determine automatically an optimal structure 23 The PSE criterion is used to select the least complex but still accurate network The PSE is composed of two terms PSE FSE K P 16 Where FSE is the average square error of the network for fitting the training data and K P is the complex penalty of the network shown by the following equation K P CPM 2s 2 p K N 17 Where CPM is the complex penalty multiplier K P is a coef ficient of the network N is the number of training data to be used and s 2 p is a prior estimate of the model error variance Based on the development of the database and the prediction of the accuracy of the part surface a three layer abductive network which comprised design factors input various Y coordinate and output factors X coordinate is synthesised automatically It is capable of predicting accurately the space curve at any point under various control parameters All poly nomial equations used in this network are listed in Appendix A PSE 5 8 10 3 Table 2 compares the error predicted by the abductive model and CMM measurement data The measurement daa is excluded from the 22 sets of CMM measurement data for establishing the model This set of data is used to test the appropriateness of the model established above We can see from Table 2 that the error is approximately 2 13 which shows that the model is suitable for this space curve Table 2 CMMS coordinate and neural network predict compared it is not included in any original 22 sets database Items CMMS neural network Error values coordinate predict CMMS predict coordinate CMMS Coordinate 11 25 16 0 11 01 16 0 2 13 5 Create the Injection Mould Model Similarly the relationship is established between input para meters gate location and gate size and the output parameter deformation during the injection process To build a complete abductive network the first requirement is to train the database The information given by the input and the output data must be sufficient Thus the training factor gate location for abductive network training should be satisfactory for making defect free products Figure 2 shows the simulation of FEM mould flow Table 3 shows the position of the gate and the maximum deformation of the product obtained from mould flow analysis Based on the development of the injection mould model three layer abductive networks which are comprised of injec tion mould conditions and the injection results deformation are synthesised automatically They are capable of predicting accurately the product strain the result of injection moulded product under various control parameters All polynomial equations used in this network are listed in Appendix B PSE 2 3 10 5 Table 4 compares the error predicted by the abductive model and the simulation case The simulation case is excluded from the 22 sets of simulation cases for establishing the model This set of data is used to test the appropriateness of the model established above We can see from Table 4 that the error is Fig 2 The deformation of FEM mould flow Optimum Gate Design of FreeForm Injection Mould 301 Table 3 Gate location and the maximum strain relationship Set number X coordinate Y coordinate Gate width Gate length Produce max strain 1 0 02 4 6 0 525 1 1475 0 348 2 1 63 4 33 0 7 1 53 0 3153 3 3 28 3 5 0 875 1 9125 0 2710 4 5 29 2 04 1 05 2 295 0 2858 5 7 31 0 56 0 525 1 1475 0 3017 6 9 34 0 9 0 7 1 53 0 526 7 11 33 2 35 0 875 1 9125 0 2369 8 12 98 3 94 1 05 2 295 0 2517 9 13 85 5 57 0 525 1 1475 0 2788 10 14 12 7 34 0 7 1 53 0 2773 11 13 69 9 67 0 875 1 9125 0 2988 12 12 96 11 9 1 05 2 295 0 2997 13 10 00 21 03 0 525 1 1475 0 2576 14 9 33 23 16 0 7 1 53 0 2624 15 8 64 25 28 0 875 1 9125 0 2542 16 7 98 27 39 1 05 2 295 0 2495 17 7 87 28 31 0 525 1 1475 0 2503 18 7 80 29 29 0 7 1 53 0 2456 19 7 83 30 34 0 875 1 9125 0 2596 20 7 60 31 30 1 05 2 295 0 2457 21 7 07 32 15 0 525 1 1475 0 2499 22 6 11 32 49 0 7 1 53 0 2511 Table 4 Mould flow simulated and neural network predict compared it is not included in any original 22 set database Items FEM mould flow Neural network simulation predict X coordinate 11 01 11 01 Y coordinate 16 0 16 0 Gate width 1 8 1 8 Gate height 0 9 0 9 Produce max deformation 0 3178 0 3325 Error values 4 62 FEM predict FEM approximately 4 62 which shows that the model is suitable for this model requirement 6 Simulation Annealing Theory In 1983 a theory that was capable of solving the global optimisation problem was developed for the optimised problem The concept was a powerful optimisation algorithm based on the annealing of a solid which solved the combinatorial optimisation problem of multiple variables When the tempera ture is T and energy E the thermal equilibrium of the system is a Boltzman distribution P r 1 Z T exp S E K B T D 18 Z T normalisation factor K B Boltzman constant Exp E K B T Boltzman factor Metropolis 24 proposed a criterion for simulating the cool ing of a solid to a new state of energy balance The basic criterion used by Metropolis is an optimisation algorithm called simulated annealing The algorithm was developed by Kirk patrick et al 20 In this paper the simulation annealing algorithm is used to search for the optimal control parameters for gate location Figure 3 shows the flowchart of the simulated annealing search First the algorithm is given an initial temperature T s and a final temperature T e and a set of initial process vectors O x The objective function obj is defined based on the injection parameter performance index The objective function can be recalculated for all the different perturbed compensation para meters If the new objective function becomes smaller the peturbed process parameters are accepted as the new process parameters and the temperature drops a little in scale That is T i 1 T i C T 19 where i is the index for the temperature decrement and the C T is the decay ratio for the temperature C T 1 However if the objective function becomes larger the prob ability of acceptance of the perturbed process parameters is given as P r obj exp F Dobj K B T G 20 Where K B is the Boltzman constant and Dobj is the different in the objective function The procedure is repeated until the temperature T i approaches zero It shows the energy dropping to the lowest state Once the