包裝方面翻譯文獻(xiàn).pdf

Development of a design system for EPS cushioning package of a monitor using axiomatic design Jeong Wook Yia Gyung Jin Parkb aMechanical Design and Production Engineering Hanyang University 1271 Sa 1 Dong Ansan City Kyunggi Do 426 791 South Korea bDepartment of Mechanical Engineering College of Engineering Science Hanyang University 1271 Sa 1 Dong Ansan City Kyunggi Do 426 791 South Korea Received 21 August 2003 revised 17 May 2004 accepted 10 June 2004 Available online 7 January 2005 Abstract A monitor is packed by cushioning materials because it could be damaged during transportation However the addition of the cushioning material increases the volume of the product Therefore it is required that the cushioning material be minimized In practice design engineers have used ad hoc design along with the experiences of their predecessors Automation of the design process is very important for the reduction of engineering cost and it can be achieved by an appropriate design process and software development According to axiomatic design a design fl ow is defi ned and a software system is developed for the automated design At fi rst a basic model is defi ned The user can modify the model from menus and the design is carried out according to the input from the user Finite element models are automatically generated based on the design A nonlinear fi nite element analysis program is linked for the impact analysis The process of design of experiments DOE using orthogonal arrays is installed to minimize the maximum acceleration in the drop test and a new design can be proposed by the system The program is designed according to the independence axiom of axiomatic design Functional requirements FRs and design parameters DPs of the software system are defi ned and decomposed by zigzagging process Independent modules can be generated by analysis of the full design matrix and each module is coded as a class in Object Oriented Programming OOP The design results are discussed q 2004 Elsevier Ltd All rights reserved Keywords Axiomatic design Independence axiom EPS expanded polystyrene Cushioning package Orthogonal arrays 1 Introduction These days cushioning materials are popularly utilized to protect various products They help safe transportation of fragile products A large volume of cushioning material can protect a product more safely however the cost is increased Therefore much attention is needed for the proper design of the cushioning package Since the outside of monitors is generally made of brittle materials the cushioning materials have to be well designed The cushioning part of a monitor is mostly made of expanded polystyrene EPS 1 2 Although it is lightweight the usage of EPS considerably increases the volume of the packing box Therefore industries are trying to minimize the volume while maintaining the strength Currently the cushioning package of monitors is designed based on past experience not with a systematic approach When a design is fi nished the strength is validated by drop tests that are very expensive If the design is not satisfi ed an iterative process with trial and error is carried out In recent years software for simulating drop tests by computer is used in the conceptual design stage 3 7 It is well known that fl exible use of the software is quite diffi cult due to tedious modeling procedure and tricky analysis skills Therefore we need a software system that automatically analyzes and designs the cushioning package of monitors Axiomatic design AD provides a framework for general design It consists of two axioms which are the independence axiom and the information axiom When a design process is defi ned according to the independence axiom the design can be performed sequentially without 0965 9978 see front matter q 2004 Elsevier Ltd All rights reserved doi 10 1016 j advengsoft 2004 06 016 Advances in Engineering Software 36 2005 273 284 Corresponding author Tel C82 31 400 5246 fax C82 31 407 0755 E mail address gjpark hanyang ac kr G J Park feedback 8 10 Since the design process is well organized a software system can be easily developed for automatic design by using the axiomatic approach 11 Various software systems have been developed by axiomatic design 12 13 Recently the axiomatic approach is adopted for object oriented programming OOP 14 15 Software design is carried out by the AD framework It is noted that the software design and the design process are almost identical and the design process is automated by the software system The design process of the EPS cushioning for monitors is analyzed and constructed based on axiomatic design A software system is designed and coded according to the design process The software system is also designed based on the axiomatic approach Therefore the manual design is automated and the automated process is coded by using axiomatic design A basic model for the monitor is defi ned to restrict excessive freedom of the design and new designs are made based on the basic model The system generates fi nite element FE models of the EPS cushioning according to the user s defi nition and shows the results of the FE simulation Design of experiments DOE is installed to evaluate various design cases and choose an optimum design Orthogonal arrays OA are utilized for the DOE process 16 18 The system is developed by the object oriented program ming language The V model has been proposed for the idea of object oriented software design with an AD framework 14 15 The system is designed by using the V model and coded according to the design 2 Conceptual design for the design system 2 1 Cushioning package design In practice the cushioning package design is treated less important than the monitor design Therefore it is designed after the monitor design is fi nished The period of the cushioning design is very short in the entire design process Generally it should be conducted during the molding process of the monitor It is common that a design engineer uses the experience of predecessors and engineering intuition Therefore many errors can occur in the design Drop tests are performed to verify the strength to consider the results in the design process Generally drop tests are carried out for the directions of 1 angle 3 edges and 6 planes as illustrated in Fig 1 2 3 The impact acceleration ratio in Eq 1 is evaluated for each test G Za g 1 where a is the acceleration measured on the center of a front CRT cathode ray tube monitor and g is the gravity acceleration If it is larger than the critical value the design should be changed and the tests are performed again for the new design The design is tedious and costly due to the repeated process Computer simulations are replacing the drop tests However the simulation results are not yet well incorpor ated into the design Through design automation the simulation results can be easily accommodated in the design process and the lead time for the design is considerably shortened 2 2 Defi nition of the basic model of a cushioning package It is almost impossible to include all the imaginary shapes of the cushioning package in a design automation system It is found that common aspects exist in most designs Also some design variables are identifi ed to be important to reduce the impact acceleration ratio G in Eq 1 A basic model is established to have common aspects and important variables Because the two parts are symmetric as illustrated in Fig 1 only one part is designed A basic model is presented in Fig 2 The inner part and the outer part are defi ned separately As illustrated in Fig 2 each part is divided into eight areas for the design As can be seen in the fi gures some sizes are linked For instance a thickness of one area can be utilized in other areas Changeable design variables are defi ned based on the basic model The entire size for the cushioning package is given at the beginning Changeable variables have con siderable infl uence on the value of the impact acceleration ratio G in Eq 1 Suppose four contact points with the monitor are chosen to be varied for the new design At each point the sizes of the contact planes are the design variables as illustrated in Fig 3 The shapes of the ribs on the contact planes are selected as design variables as illustrated in Fig 4 They are called the main ribs Also the design variables are defi ned for the center ribs as illustrated in Fig 5 We call them assistant ribs Then the design variables are the positions the numbers and the shapes of Fig 1 Directions of the drop test J W Yi G J Park Advances in Engineering Software 36 2005 273 284274 them These design variables can be changed by the user from the menu display 2 3 Design of experiment using orthogonal arrays A matrix experiment for DOE consists of a set of experiments In the matrix experiment the settings of design variables are defi ned to obtain the characteristics After all of the experiments are conducted analyses such as ANOVA analysis of variance and ANOM analysis of means are performed to investigate the effects of the design variables and to determine the optimum levels 16 If the matrix experiment is set up with an orthogonal array the minimum number of experiments would have an effect that substitutes the full factorial experiments When the interaction among the design variables is strong the interaction should be considered in choosing the smallest size of an orthogonal array However it is not easy to comprehend the strong interaction among the design variables in structural design In this research the effect of the interaction is ignored Thus the smallest orthogonal array is selected as the orthogonal array with minimum experiments that can assign all the design variables to their columns The process to determine the optimum levels of design variables using ANOM is as follows 17 18 Suppose that we have four design variables of A B C and D and each design variable has three levels For a problem with four design variables and three levels the minimum orthogonal array is selected as L9 34 of Table 1 since the interactions among the design variables are ignored In Table 1 the characteristics from h1to h9in the rows are obtained by some experiments or calculations For simulation analysis Fig 2 Subdivision of the basic model Fig 3 Contact area for the inner cushioning material Fig 4 Main rib for the cushioning material J W Yi G J Park Advances in Engineering Software 36 2005 273 284275 each row means one fi nite element calculation Then the ANOM is conducted with these values Considering the fi rst level of design variable A A1 the main effect of A1 MA1 is calculated as Eq 2 MA1ZmA1Km mA1Z 1 3 h1Ch2Ch3 m Z 1 9 X 9 iZ1 hi 2 where m is the mean of all characteristics and mA1is the mean of the characteristics corresponding to A1 The mean of the characteristics corresponding to each level for any design variable is calculated as Table 2 Then the optimum level of each design variable is chosen by the level with the minimum mean If each level with minimum mean is the combination of mA1 mB1 mC2 and mD3 the optimum levels are determined as A1 B1 C2 and D3 A confi rmation test should be performed with the optimum levels If interactions between design variables exist we have to consider them when we allocate the variables upon columns of the orthogonal arrays However the problem is that we have to identify them before the experiments and it is almost impossible to fi nd them in the design Thus the interactions are not accounted for and this oversight may cause a poor design In this research a best design is selected from the rows of the orthogonal array and selected optimum levels Therefore if interactions exist the obtained solution may not be optimum but is one of the good solutions Details are referred in Ref 16 2 4 Design fl ow of the system As illustrated in Fig 6 the automatic design system for the EPS cushioning package consists of the steps of user input modeling impact analysis and design proposal After the input from a user is given for a design the design model is evaluated by the impact analysis for the drop test Since nonlinear fi nite element analysis is performed a fi nite element model should be established from the input prior to the simulation A pre processor called LS INGRID is utilized in the background for the mesh generation 19 When all the decisions for the input are made LS INGRID is automatically called and the fi nite element meshes are generated When an orthogonal array is selected one model is generated for each row LS DYNA3D is employed for the fi nite element simulation with the FE model 20 21 Since the nonlinear fi nite element analysis is very sensitive to inputs many skills are required to make an input fi le The skills are proprietary and beyond the scope of this paper Drop tests are performed for each model of a row in an orthogonal array And then the system proposes an optimum design of the cushioning material by virtue of ANOM 3 Software design using the axiomatic approach 3 1 Axiomatic design Axiomatic design AD is the framework for a good design It helps to create synthesized solutions that satisfy Fig 5 Assistant rib for the cushioning material Table 1 L9 34 orthogonal array Expt no Column number and factor assignedResults 1234 ABCD 11111h1 21222h2 31333h3 42123h4 52231h5 62312h6 73132h7 83213h8 93321h9 Table 2 Mean of h corresponding to each level Design variablesLevels 123 AmA1Z h1Ch2Ch3 3mA2Z h4Ch5Ch6 3mA3Z h7Ch8Ch9 3 BmB1Z h1Ch4Ch7 3mB2Z h2Ch5Ch8 3mB3Z h3Ch6Ch9 3 CmC1Z h1Ch6Ch8 3mC2Z h2Ch4Ch9 3mC3Z h3Ch5Ch7 3 DmD1Z h1Ch5Ch9 3mD2Z h2Ch6Ch7 3mD3Z h3Ch4Ch8 3 J W Yi G J Park Advances in Engineering Software 36 2005 273 284276 perceived needs through mapping between functional requirements FRs and design parameters DPs An FR is the goal to achieve and is defi ned in the functional domain while a DP is determined in the physical domain as the means to achieve the goal Mapping is a process to choose a relevant DP in the physical domain which satisfi es a given FR in the functional domain According to axiomatic design the essence of the design process lies in the hierarchies as illustrated in Fig 7 Designers begin the design from comprehensive FRs A design can decompose FRs into many hierarchies But the decomposition of FRs must be carried out at the same time with the decomposition of DPs The zigzagging between FRs and DPs is necessary because the two sets of each level are connected and mutually dependent Axiomatic design consists of two axioms which are the independence axiom and the information axiom The fi rst axiomtellsusabouttheselectionofFRsandDPs Thesecond axiom shows a quantitative method of judging which design is more desirable The design axioms are defi ned as follows Axiom 1 The independence axiom Maintain the independence of functional requirements Axiom 2 The information axiom Minimize the information content The two axioms present the most fundamental means needed to choose the best design For a design to be acceptable the design must satisfy the fi rst axiom A design matrix DM is defi ned to pursue the relationship between FRs and DPs as following fFRsg Z A fDPsg 3 where FRs is a vector for FRs DPs is a vector for DPs and A is a design matrix If we have three FRs and DPs Eq 3 can be expressed as following FR1 FR2 FR3 8 9 Z XOO OXO OOX 2 6 4 3 7 5 DP1 DP2 DP3 8 9 4 where X means a relation exists and O means there is no relation The components in the design matrix can be expressed by constants or equations instead of X and O When the independence axiom is satisfi ed the design matrix takes the form of a diagonal matrix or a triangular matrix A diagonal matrix in Eq 4 represents a perfectly uncoupled design and is the most desirable form A triangular matrix represents a decoupled design This form of design is also a proper design but the DPs need to be arranged in a specifi c order The third form is the coupled design where some diagonal elements are not zero in the design matrix This type of design is undesirable because when a DP is modifi ed multiple FRs are changed That is the independence axiom is not satisfi ed The information axiom is related to the complexity of a design and implies that the simpler design is the better one 8 15 Generally information content is quantitatively defi ned by the probability of success The information axiom is utilized to select the best one out of multiple designs which satisfy the independence axiom The information content is not yet defi ned rigorously in software development Therefore only the independence axiom is employed in this research Fig 6 Design fl ow of the design system for EPS cushioning package Fig 7 Concept of domain mapping and spaces J W Yi G J Park Advances in Engineering Software 36 2005 273 284277 3 2 Axiomatic design for object oriented programming System modules should be independently constructed to design an effi cient software system 23 It is needed to introduce the axiomatic design approach so that modules in the functional domain can be maintained independently in the physical domain Do and Park have developed a software for the glass bulb design with a conventional language using axiomatic design 12 Recently object oriented programming OOP is utilized with the axiomatic approach and the V model is proposed as the design process for the object oriented software system 14 15 In the V model the fi rst step is to build the hierarchy which follows the top down approach and is the generation of the full design matrix table for module defi nition The second step is to build the object oriented model with a bottom up approach As illustrated in Fig 8 several steps are needed as follows 15 Step 1 Defi nition of FRs for the system FRs are defi ned in the functional domain based on the needs of the customer An FR is expressed by a function that the software system should achieve For example they are receiving data changing control data executing Fig 8 Axiomatic design process for object oriente