索尼游戲鼠標(biāo)上蓋注塑模設(shè)計(jì)-抽芯塑料注射模含4張CAD圖帶開題
索尼游戲鼠標(biāo)上蓋注塑模設(shè)計(jì)-抽芯塑料注射模含4張CAD圖帶開題,索尼,游戲,鼠標(biāo),注塑,設(shè)計(jì),塑料,注射,cad,開題
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畢業(yè)設(shè)計(jì)（論文）題目
索尼游戲鼠標(biāo)上蓋注塑模設(shè)計(jì)
學(xué)生姓名
專業(yè)班級(jí)
指導(dǎo)教師姓名
職稱
一、課題背景
隨著市場經(jīng)濟(jì)的發(fā)展，機(jī)械制造業(yè)的生產(chǎn)類型正在由原來的大批量生產(chǎn)方式被小批量多品種的生產(chǎn)方式代替，為滿足客戶對(duì)產(chǎn)品多樣化的要求，一些先進(jìn)制造技術(shù)應(yīng)運(yùn)而生。例如DT、CAD、CAPP、CAM、CIMS、CE、AM、LP等。CAD是先進(jìn)制造技術(shù)的核心與關(guān)鍵，而各種模具的計(jì)算機(jī)輔助設(shè)計(jì)與制造是目前先進(jìn)制造技術(shù)的重要組成部分，也是機(jī)械制造業(yè)中很實(shí)用的部分，發(fā)展相當(dāng)迅速。隨著塑料工業(yè)的飛速發(fā)展，各種塑料制品已廣泛應(yīng)用于國民經(jīng)濟(jì)的各個(gè)領(lǐng)域，其中大部分塑料制品皆是通過注塑成型工藝來加工的，塑料模具也因此成為被廣泛使用的一類模具。目前，CAD在我國的應(yīng)用正處于初級(jí)階段，一些企業(yè)單位還只停留在二維的計(jì)算機(jī)輔助設(shè)計(jì)階段，當(dāng)然也有不少單位引入了國外大型的先進(jìn)設(shè)計(jì)軟件，真正實(shí)現(xiàn)了三維計(jì)算機(jī)輔助設(shè)計(jì)。因此，本設(shè)計(jì)題目具有極強(qiáng)的實(shí)用性與前沿性模具制造能力和水平。模具設(shè)計(jì)、生產(chǎn)水平已經(jīng)成為衡量一個(gè)國家機(jī)械制造技術(shù)水平的重要標(biāo)志之一。注塑成型是現(xiàn)代塑料工業(yè)中的一種重要的加工方法，世界上注塑模的產(chǎn)量約占塑料成型模具總產(chǎn)量的50%以上。在現(xiàn)代機(jī)械制造業(yè)中，模具工業(yè)已成為國民經(jīng)濟(jì)中的基礎(chǔ)工業(yè)，許多新產(chǎn)品的開發(fā)和生產(chǎn)在很大程度上依賴于模具制造技術(shù)，特別在汽車電子和航天等行業(yè)中尤其重要。在討論注塑模設(shè)計(jì)之前，先要對(duì)國內(nèi)外的塑料模具工業(yè)的狀況、塑料模具工業(yè)的發(fā)展方向有一個(gè)較清晰的了解，這也就使我們對(duì)本課題的意義有所了解。首先要對(duì)模具有一個(gè)整體的認(rèn)識(shí)。
模具是機(jī)械、汽車、電子、通訊、家電等工業(yè)產(chǎn)品的基礎(chǔ)工藝裝備之一。作為工業(yè)基礎(chǔ)，模具的質(zhì)量、精度、壽命對(duì)其他工業(yè)的發(fā)展起著十分重要的作用，在國際上被稱為“工業(yè)之母”，對(duì)國民經(jīng)濟(jì)發(fā)展起著不容質(zhì)疑的作用.模具工業(yè)是制造業(yè)中的一項(xiàng)基礎(chǔ)產(chǎn)業(yè)，是技術(shù)成果轉(zhuǎn)化的基礎(chǔ)，同時(shí)本身又是高新技術(shù)產(chǎn)業(yè)的重要領(lǐng)域，在歐美等工業(yè)發(fā)達(dá)國家被稱為“點(diǎn)鐵成金”的“磁力工業(yè)”；美國工業(yè)界認(rèn)為“模具工業(yè)是美國工業(yè)的基石”;德國則認(rèn)為是所有工業(yè)中的“關(guān)鍵工業(yè)”;日本模具協(xié)會(huì)也認(rèn)為“模具是促進(jìn)社會(huì)繁榮富裕的動(dòng)力”，同時(shí)也是“整個(gè)工業(yè)發(fā)展的秘密”，是“進(jìn)入富裕社會(huì)的原動(dòng)力”。日本模具產(chǎn)業(yè)年產(chǎn)值達(dá)到13000億日元，遠(yuǎn)遠(yuǎn)超過日本機(jī)床總產(chǎn)值9000億日元。如今，世界模具工業(yè)的發(fā)展甚至己超過了新興的電子工業(yè)。在模具工業(yè)的總產(chǎn)值中，沖壓模具約占50%，塑料模具約占33%，壓鑄模具約占6%，其它各類模具約占11%。 塑料模具工業(yè)是隨塑料工業(yè)的發(fā)展而發(fā)展的。塑料工業(yè)是一門新興工業(yè)。自塑料問世后的幾十年以來，由于其原料豐富、制作方便和成本低廉，塑料工業(yè)發(fā)展很快，它在某些方面己取代了多種有色金屬、黑色金屬、水泥、橡膠、皮革、陶瓷、木材和玻璃等，成為各個(gè)工業(yè)部門不可缺少的材料。目前在國民經(jīng)濟(jì)的各個(gè)部門中都廣泛地使用著各式各樣的塑料制品。特別是在辦公設(shè)備、照相機(jī)、汽車、儀器儀表、機(jī)械制造、交通、電信、輕工、建筑業(yè)產(chǎn)品、日用品以及家用電器行業(yè)中的電視機(jī)、收錄機(jī)、洗衣機(jī)、電冰箱和手表的殼體等零件，都已經(jīng)向塑料化方向發(fā)展。近幾年來由于工程塑料制件的強(qiáng)度和精度等得到很大的提高，因而各種工程塑料零件的使用范圍正在不斷擴(kuò)大，預(yù)計(jì)今后隨著微型電子計(jì)算機(jī)的普及和汽車的微型化，塑料制件的使用范圍將會(huì)越來越大，塑料工業(yè)的生產(chǎn)量也將迅速增長，塑料的應(yīng)用將覆蓋國民經(jīng)濟(jì)所有部門，尤其在國防和尖端科學(xué)技術(shù)領(lǐng)域中占有越來越重要的地位。目前，世界的塑料產(chǎn)量 電信、輕工、建筑業(yè)產(chǎn)品、日用品以及家用電器行業(yè)中的電視機(jī)、收錄機(jī)、洗衣機(jī)、電冰箱和手表的殼體等零件，都已經(jīng)向塑料化方向發(fā)展。近幾年來由于工程塑料制件的強(qiáng)度和精度等得到很大的提高，因而各種工程塑料零件的使用范圍正在不斷擴(kuò)大，預(yù)計(jì)今后隨著微型電子計(jì)算機(jī)的普及和汽車的微型化，塑料制件的使用范圍將會(huì)越來越大，塑料工業(yè)的生產(chǎn)量也將迅速增長，塑料的應(yīng)用將覆蓋國民經(jīng)濟(jì)所有部門，尤其在國防和尖端科學(xué)技術(shù)領(lǐng)域中占有越來越重要的地位。世界的塑料產(chǎn)量已超過有色金屬產(chǎn)量的總和。塑料模具就是利用特定形狀去成型具有一定形狀和尺寸的塑料制品的工藝基礎(chǔ)裝備。用塑料模具生產(chǎn)的主要優(yōu)點(diǎn)是制造簡便、材料利用高、生產(chǎn)率高、產(chǎn)品的尺寸規(guī)格一致，特別是對(duì)大批量生產(chǎn)的機(jī)電產(chǎn)品，更能獲得價(jià)廉物美的經(jīng)濟(jì)效果。塑料模具的現(xiàn)代設(shè)計(jì)與制造和現(xiàn)代塑料工業(yè)的發(fā)展有極密切的關(guān)系。隨著塑料工業(yè)的飛速發(fā)展，塑料模具工業(yè)也隨之迅速發(fā)展。 在我國，隨著國民經(jīng)濟(jì)的高速發(fā)展，模具工業(yè)的發(fā)展也十分迅速。1999年中國大陸制造工業(yè)對(duì)模具的總市場需求量約為330億元，今后幾年仍將以每年10%以上的速度增長。對(duì)于大型、精密、復(fù)雜、長壽命模具需求的增長將遠(yuǎn)超過每年10%的增幅。汽車、摩托車行業(yè)的模具需求將占國內(nèi)模具市場的一半左右。1999年，國內(nèi)汽車年產(chǎn)量為183萬輛，保有量為1500萬輛，預(yù)計(jì)到2005年汽車年產(chǎn)量將達(dá)600萬輛。僅汽車行業(yè)就將需要各種塑料件36萬噸，而目前的生產(chǎn)能力僅為20多萬噸，因此發(fā)展空間十分廣闊。家用電器，如彩電、冰箱、洗衣機(jī)、空調(diào)等，在國內(nèi)的市場很大。目前，我國的彩電的年產(chǎn)量己超過3200萬臺(tái)，電冰箱、洗衣機(jī)和空調(diào)的年產(chǎn)量均超過了100萬臺(tái)。家用電器行業(yè)的飛速發(fā)展使之對(duì)模具的需求量極大。到2010年，在建筑與建材行業(yè)方面，塑料門窗的普及率為30%，塑料管的普及率將達(dá)到50%，這些都會(huì)大大增加對(duì)模具的需求量。其它發(fā)展較快的行業(yè)，如電子、通訊和建筑材料等行業(yè)對(duì)模具的需求，都將對(duì)中國模具工業(yè)和技術(shù)的發(fā)展產(chǎn)生巨大的推動(dòng)作用
注塑成型能一次成型形狀復(fù)雜，尺寸精確的制品，適合高效率、大批量的生產(chǎn)方式，已發(fā)展成為熱塑性塑料和部分熱固性塑料最主要的成型加工方法。而傳統(tǒng)的生產(chǎn)方法不僅使產(chǎn)品的生產(chǎn)周期延長，生產(chǎn)成本增加，而且難以保證產(chǎn)品的質(zhì)量。要解決這些問題必須有科學(xué)分析的方法，研究各個(gè)車型過程的關(guān)鍵技術(shù)，為實(shí)現(xiàn)注塑產(chǎn)品的更新?lián)Q代，提高企業(yè)的競爭能力，必須進(jìn)行注塑模具設(shè)計(jì)制造及成型過程分析的CAD/CAM /CAE集成技術(shù)的研究。
設(shè)計(jì)技術(shù)以計(jì)算機(jī)及周邊設(shè)備和系統(tǒng)軟件為基礎(chǔ)，它包括二維繪圖設(shè)計(jì)，三維幾何造型設(shè)計(jì)，有限元分析及優(yōu)化設(shè)計(jì)，數(shù)控加工編程，仿真模擬及產(chǎn)品數(shù)據(jù)管理等內(nèi)容。
注塑模具設(shè)計(jì)是典型的設(shè)計(jì)分析一體化過程。計(jì)算機(jī)輔助設(shè)計(jì)計(jì)算機(jī)輔助求解以及計(jì)算機(jī)輔助制造的技術(shù)已經(jīng)越來越廣泛的應(yīng)用到模具的開發(fā)設(shè)計(jì)和生產(chǎn)中。
目前，國內(nèi)在電器產(chǎn)品外觀零件設(shè)計(jì)制造方面的研究還處于初級(jí)階段，與發(fā)達(dá)國家的差距很大。由于電器產(chǎn)品美觀性的要求，零件外形多為復(fù)雜曲面，傳統(tǒng)的設(shè)計(jì)方法在對(duì)零件成形過程分析以及對(duì)產(chǎn)品存在缺陷的處理方面顯得無能為力，產(chǎn)品成形過程數(shù)值模擬技術(shù)跟不上的現(xiàn)狀己經(jīng)成為制約產(chǎn)品開發(fā)和生產(chǎn)的一個(gè)瓶頸。面對(duì)日益激烈的國際競爭，必須緊跟國際先進(jìn)水平，不斷提高電器產(chǎn)品外觀零件的質(zhì)量，降低設(shè)計(jì)和生產(chǎn)成本，加快生產(chǎn)周期。因而，鼠標(biāo)上蓋成形技術(shù)的研究與開發(fā)具有相當(dāng)重要的理論意義和實(shí)用價(jià)值。以此作為一個(gè)突破口，帶動(dòng)和促進(jìn)相關(guān)電器產(chǎn)品外觀零件注塑成形技術(shù)的發(fā)展和技術(shù)創(chuàng)新。
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二、畢業(yè)設(shè)計(jì)方案
2.1研究內(nèi)容及實(shí)驗(yàn)方案 本文將對(duì)鼠標(biāo)上蓋成型的幾個(gè)關(guān)鍵問題:鼠標(biāo)制品外形的設(shè)計(jì)與建模、最佳成型方法的選擇，分析最佳成型工藝，模具設(shè)計(jì)并進(jìn)行理論和試驗(yàn)研究。
2.2鼠標(biāo)上蓋制品外形設(shè)計(jì) 本課題利用Pro/E軟件對(duì)鼠標(biāo)上蓋進(jìn)行實(shí)體建模，Pro/E的圖形設(shè)計(jì)是基于三維的，它與傳統(tǒng)的二維繪圖有著本質(zhì)的區(qū)別。生成的模型直觀，立體感強(qiáng)，可以在任何角度進(jìn)行觀察。另外系統(tǒng)還能計(jì)算出實(shí)體的表面積、體積、重量、慣性距、重心等。使設(shè)計(jì)者很容易、很清楚地知道零件的特性。而且可由立體圖生成三視圖，大大提高工作的效率和準(zhǔn)確性。
2.3 最佳成型方法的選擇 比較幾種可用于成型鼠標(biāo)外殼這種薄壁單分型面制品的常用塑料加工方法，根據(jù)產(chǎn)品開發(fā)依據(jù)和使用要求選擇合理的成型方法。
2.4 分析最佳成型工藝 鼠標(biāo)上蓋為薄壁制件，比表面積大，可能的工藝方案較多，工藝方案的優(yōu)劣直接影響到產(chǎn)品質(zhì)量、生產(chǎn)成本以及生產(chǎn)效率。
本文在對(duì)塑件進(jìn)行分析的基礎(chǔ)上，確定并優(yōu)化了工藝方案。具體內(nèi)容如下： (1)對(duì)塑件成型工藝性進(jìn)行分析，對(duì)可能的工藝方案進(jìn)行比較分析，初步得出可能的工藝方案以及其可行的條件。 (2)根據(jù)產(chǎn)品開發(fā)依據(jù)及成型要求，確定工藝方案。
2.5 模具設(shè)計(jì)
2.5.1模具結(jié)構(gòu)分析和確定 針對(duì)鼠標(biāo)上蓋尺寸小，精度高的特點(diǎn)，根據(jù)工藝方案和零件的形狀特點(diǎn)、精度要求、生產(chǎn)批量、模具加工條件、操作方便與安全的要求，對(duì)模具進(jìn)行分析，確定模具的合理結(jié)構(gòu)。
2.5.2模具主要零部件的結(jié)構(gòu)設(shè)計(jì) 根據(jù)模具結(jié)構(gòu)型式和特點(diǎn)，確定模具工作、導(dǎo)向以及固定等并確定模具主要零件的形式以及尺寸。
三、畢業(yè)設(shè)計(jì)（論文）預(yù)期成果及創(chuàng)新
本研究的主要目的是通過一個(gè)具有代表性模具的分析研究，從而達(dá)到掌握具有復(fù)雜曲面模具的設(shè)計(jì)制造以及加工的方法。國內(nèi)在電器產(chǎn)品外觀零件設(shè)計(jì)制造方面的研究還處于初級(jí)階段，與發(fā)達(dá)國家的差距很大。由于電器產(chǎn)品美觀性的要求，零件外形多為復(fù)雜曲面，傳統(tǒng)的設(shè)計(jì)方法在對(duì)零件成形過程分析以及對(duì)產(chǎn)品存在缺陷的處理方面顯得無能為力，產(chǎn)品成形過程數(shù)值模擬技術(shù)跟不上的現(xiàn)狀己經(jīng)成為制約產(chǎn)品開發(fā)和生產(chǎn)的一個(gè)瓶頸。論文目的在于設(shè)計(jì)鼠標(biāo)上殼，使之使用高效快捷，設(shè)計(jì)人性化，使用壽命長，產(chǎn)品外形美觀。
學(xué)部審核意見
學(xué)部主任（簽字） 年 月 日
注：此表中的一、二、三項(xiàng)，由學(xué)生在教師的指導(dǎo)下填寫。
資料來源：
文章名：一種基于分枝定界算法的注塑模架基工藝規(guī)劃系統(tǒng)
書刊名：《Advanced Manufacturing Technology》
作 者： P. Y. Gan, K. S. Lee and Y. F. Zhang
出版社：Department of Mechanical Engineering, National University of Singapore, Singapore
章 節(jié)：A Branch and Bound Algorithm Based Process-Planning System for Plastic Injection Mould Bases
頁 碼：10.1007/s0017001一種基于分枝定界算法的注塑模架基工藝規(guī)劃系統(tǒng)
70022
文 章 譯 名：
A Branch and Bound Algorithm Based Process-Planning System for Plastic Injection Mould Bases
P. Y. Gan, K. S. Lee and Y. F. Zhang
Department of Mechanical Engineering, National University of Singapore, Singapore
This paper describes the use of artificial intelligence in the process planning of plastic injection mould bases. The com- puter-aided process-planning system, developed for IMOLDò will extract and identify the operations required for machining. These operations are considered together with their precedence constraints and the available machines before the process plan for the mould base plate is generated. The process plan is optimised by a branch and bound based algorithm. Overall machining time has been proposed as the objective function for optimisation. The ability of this algorithm to search intelli- gently for a feasible optimised solution is illustrated by an industrial case study. A brief comparison with a genetic algor- ithm based process planning system is also made. The result of this development will allow users to optimise process plans easily for any given mould base, with options to suit dynamic changes on the manufacturing shop floor.
Keywords: Branch and bound algorithm; Computer-aided process-planning (CAPP); Optimisation; Plastic injection mould base
1. Introduction
Computer-aided process planning (CAPP) has received much attention in recent years. It has long been identified as the bridge between computer-aided design (CAD) and computer- aided manufacturing (CAM) systems to achieve a fully auto- mated factory. Despite the need, insufficient CAPP systems have been developed for the different industries requiring them. This work focuses on developing a CAPP system for mould base makers. At present, most process planning for the pro- duction of mould bases is done manually. The process plans depend very much on the decisions of the process planner. The introduction of CAPP systems should ensure consistently good process plans with more comprehensive consideration of
Correspondence and offprint requests to: K.-S. Lee, Department of Mechanical and Production Engineering, The National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260. E-mail: mpeleeks@nus.edu.sg
the manufacturing parameters. CAPP systems are required in industry for the following reasons:
1. Mould base companies are receiving an increasing number of requests to manufacture customised mould bases, in which additional features are added to a standard mould base. Therefore, extra operations are required to create these new features. Usually, standard mould bases have a predetermined process plan, which is optimised for the amount of machining required. As new operations are added, this optimised process plan is disrupted and manual process planning is unable to keep up with the changes. CAPP systems are able to re-optimise the process plan constantly to ensure optimality of the process plans used.
2. Overall shop floor conditions should be taken into account during process planning. Manual process planning is unable to consider all shop floor changes and apply them efficiently. Only CAPP systems allow rigorous consideration of optimis- ation.
The goal of this work is to develop a CAPP system for process planning mould bases. IMOLDò (Intelligent Mold Design) is a knowledge-based application software developed at the Department of Mechanical Engineering, NUS to facilitate plastic injection mould design. The system is an addition to IMOLDò, and it process plans the mould bases created using IMOLDò. Databases of machines, tools, precedence constraints, and the model part file are read together with real-time inputs of machine availability during process planning. An operator is required to enter the customised features and a process plan is then generated using some form of artificial intelligence. The branch and bound technique is the chosen search algor- ithm here.
This paper presents the operation of a flexible CAPP system aimed at assisting process planners in more comprehensive considerations during operations planning. A brief literature survey is provided of some forms of artificial intelligence used in process planning and related work in this field. Problem formulation and the branch and bound algorithm implemented are included in the following sections. Lastly, a case study demonstrates the usability and potential of this system. A comparison between branch and bound based CAPP and genetic algorithm based CAPP is shown in a second case study.
2. Background
Process planning is the preparation of a set of detailed instruc- tions for all the steps required to create the final product from a piece of raw material [1]. The quality of a process plan depends very much on the skills of the process planner, as extensive knowledge of the available tools, the machines and the operations needed to create a part is required [2]. A CAPP system is therefore seen as an important tool for assisting in process planning.
A CAPP system should optimise a part for all possible methods of manufacturing. However, many reported CAPP systems are not able to generate globally optimised process plans [3]. As a result, there has been an increasing use of artificial intelligence to search for global solutions [4,5]. Many of the reported methods involve only feature sequencing with- out including details of the operations required [6,7]. Details of the operations are necessary for allocating shop floor resources for performing the operations.
The performance measure is the objective function to be maximised or minimised in all optimisation problems. For process planning, the objective is either to minimise time, cost, or sometimes both. There is a variety of work done using cost as the performance measure [8]. However, there is also a range of cost models that can be used to consider and calculate cost [9,10], but there is no universal method to account for costs. It is known that to minimise work-in-progress and the flow- time of jobs in a job shop, process plans with the least overall machining time should be used [11]. We therefore use time, as it is a more definite basis on which to quantify the quality of generated process plans. This choice is further justified, as the delivery time of mould bases is very important in mould- making industries.
An exhaustive sequential search for a process plan solution leads to unacceptable computation times when a large number of operations are required. This work uses a branch and bound algorithm to search intelligently for the optimal or near optimal process plan. The branch and bound algorithm is a well-known search algorithm for implicit enumeration of the search space [12]. Its use as an artificial intelligence method has been reported widely in the areas of scheduling, process planning, and problem solving [13].
Some work has been reported using the branch and bound technique for process planning [14–16]. However, the nature of process plans in those works is different from the process planning required for the mould making industry. This work uses the branch and bound technique to process plan all the operations considering all tool access directions on all the available machines and tools for each mould base plate. To the best of our knowledge, such a level of consideration has not been dealt with in other related studies.
3. Problem Formulation
A process-planning problem is constrained to the number of operations, precedence relations, machines, machining direction, and tools. The optimised solution is a way to sequence the
operations with their associated machines to produce a process plan, which takes the least possible production time.
3.1 Process Planning Model
The information required for optimisation is extracted from mould bases modelled using IMOLDò. This database of oper- ations, machines, machining direction, tools, and precedence constraints is used for process planning together with machine availability. A schematic representation of this model is shown in Fig. 1 and the following assumptions are made:
1. Only one operation can be processed by one machine at a time.
2. All the machines can access the part at only one particular face. If machining is to be done on another face, the part has to be taken down and set-up time has to be incurred to replace the part facing a different direction.
3. Cranes or robots are available at all times. No waiting time is allowed for time wasted while waiting for machinery or labour to move the parts.
Customised features require the process planner to input the necessary data manually. This is because a single feature can be created by many possible methods and this allows the process planner more control over the system. The assigned operations and the final generated process plan should satisfy the following conditions:
1. The features of the mould base plate are recognised with the operations assigned to them. The operations assigned should produce the desired shape, dimension, tolerance, and finish to the feature.
Fig. 1. The process planning model.
2. The sequence of operations obtained from the process plan should not violate any precedence relations governing the operations.
machining direction, but no change of machine between the two operations. It is defined as,
3
n—1
3. Operations can only be carried out on available machines with the available tools, which are capable of machining
MDST =
i=1
(K(MDi+1,MDi)
that particular feature.
The process plan obtained should include the number of operations to be carried out, the sequence of these operations, the machines, machining direction, and corresponding tools used. Such details are necessary so that time can be saved for operations to be carried out on a particular machine using the same set-up. For example, a blind hole must be drilled in the
+x direction whereas a through hole can be drilled from the
+x or —x directions. It can be seen by considering just these two operations, that the process plan should try to perform these two operations on the same machine from the +x direc- tion so that extra set-up time is not incurred.
3.2 The Objective Function
To quantify the objective function, which is the overall machin- ing time (OMT), we use a calculation framework similar to that used by Zhang et al. [17]. The objective function is calculated for each successive sequence of the process plans, and the sequence that yields the minimum OMT will be taken as the final process plan. There are 3 areas which contribute to the calculation of OMT, and they are machine set-up times, machining direction set-up times, and machining times.
3.2.1 Machine Set-up Time
3
Machine set-up time (MST) is considered whenever there is a change of machines between two operations. It is defined as the time required to move between machines and the set-up time of the mould baseplate onto the machine in a particular direction. It is defined for a total of all n operations as,
n—1
×[1 — K(Mi+1,Mi)] × MDSTIi+1) (3)
MDi is the machining direction selected to process operation i and MDSTIi is the machining direction set-up time index for the machine used in operation i. MDSTIi and MSTIi are related by the difference in time to move the part between the old and new machine.
MSTIi = MDSTIi (4)
+ (Time to move part between machines)
As no waiting time for the cranes or robots is assumed, we take MDSTIi and MSTIi to be the same.
3.2.3 Machining Time
3
Machining time MT is the actual time to perform all machining operations such as drilling, milling, or grinding on the assigned machines with the respective tools.
n
i i
MT = (MTM ,T )i (5)
i=1
The machining time for a single operation can vary according to the assigned machine and tool selected. From this, there exists one or more possible MTi for a single operation.
3.2.4 Overall Machining Time
Overall machining time is the total of all machine change set- up times, machining direction change set-up times and all machining times.
OMTmin = (MST + MDST + MT)optimised sequence (6) The objective is to produce a sequence of operations that will
MST =
where,
i=1
(K(Mi+1,Mi) MSTIi+1) (1)
K(Mi+1,Mi) =
1 if i = 1
1 if Mi+1 G Mi (i > 1)
(2)
0 if M
i+1
= M
i
(i > 1)
{
require the least OMT.
Table 1. Types of machines, MSTI, MDSTI and types of suitable tool.
Machines (M)
MSTI, MDSTI
(min)
Tool types Suitable (T)
1. FARTWARTH VBM-5VL
5, 5
1
vertical surface miller
2. HAMAI-4DS horizontal gang
6, 6
1
surface miller
3. Manual chamfering machine
2, 2
5
4. OKAMATO grinding machine
4, 4
2
5. HUACHONG grinding
3, 3
2
machine
6. Radial drilling machine
2, 2
4, 6
7. MORI SEIKI MV65-50
3, 3
1,3,4,6,7,8,9
vertical CNC milling
8. MAKINO MC98 vertical
4, 4
1,3,4,6,7,8,9
Mi refers to the machine selected to process operation i,
MSTIi refers to the machine set-up time index for the machine
used in operation i, and n is the number of operations selected for the whole series of operations identified from the mould fea- tures.
3.2.2 Machining Direction Set-up Time
CNC milling
Machining direction set-up time (MDST) is the time required
to change the orientation of the mould baseplate on the same machine. MDST is calculated only when there is a change in
1. Face mill cutter; 2. Grinding wheel; 3. End mill; 4. NC spot drill;
5. Edge-grinding wheel; 6. Drill; 7. Reamer; 8. Boring tool; 9. Tap drill
Fig. 2. Customised core plate part with 11 additional operations.
4. Branch and Bound Algorithm
A branch and bound algorithm was chosen as the search algorithm to be used as it has a proven track record in this area. Its robust and enumerative nature should yield an optimal or near optimal solution. The search space of most branch and bound algorithms is inherently large and computationally complex. This means that effective heuristic and efficient lower bound calculations are important for decreasing search space to help arrive at a good solution earlier.
4.1 Implemented Algorithm
The algorithm starts by sequencing one of the available oper- ations and this is called branching the node. By branching a node, a new node is formed and the node is kept in the search space if its lower bound value is better than the upper bound value or vice versa. A heuristic is used to schedule the remaining operations for every node and the best solution found so far will be recorded as the upper bound value. The next node to be branched is the one with the best lower bound value, as it is deemed to have the best potential. As more nodes are branched, more and more operations will be sequenced, and the upper bound value will become smaller and smaller. The
algorithm stops when the upper bound value is smaller than all lower bound values and the process plan is the sequence that yields the upper bound solution.
To balance the quality of the solution and the computation time, a termination condition is set such that the program will exit when there is no more improvement to the upper bound value after a certain number of cycles (Xc). For most problems, it was found that a value of about 10 000 for Xc will yield near optimal solutions while giving a computation time of less than 10 min.
To explain the branch and bound algorithm better, we use the conventions of the A* algorithm. The mathematical rep- resentation of the lower bound function f(Sa) for sequence Sa is defined as
f(Sa) = g(Sa) + h(Sa) (7)
where g(Sa) is the cost incurred to reach Sa and h(Sa) is a function that calculates the estimated cost of reaching the final schedule. When all the operations are sequenced, h(Sk(final)) = 0, the objective function can then be calculated as f(Sk(final)) = g(Sk(final)). The implemented branch and bound algorithm can be briefly summarised as follows:
begin
Step 1. S0 ← Initial situation (no operation sequenced) Open ← S0
do
Step 2. Choose in Open, a node with sequence Sa, which has the best lower bound
Open ← Open — Sa
Step 3. Sequence all the possibilities starting from Sa
for each possibility Sk
Step 4. Use a heuristic to schedule the remaining operations
Sk(final)
objective function = g(Sk(final))
Step 5. Update the upper bound value
if g(Sk(final)) is better
then upper bound = f(Sk(final))
Step 6. Calculated the lower bound
for each possibility k, f(Sk) = g(Sk) + h(Sk)
Step 7. Include branched node into search space
if f(Sk) better than upper bound
then Open ← Open + Sk
end
Step 8. Discard all nodes in Open with f(S) worse than, or equal to, upper bound
while Termination condition G ? OR Open G ?
end
4.2 Constant Machine / Machining Direction Heuristic
A good heuristic will help to generate good solutions as early as possible. When good solutions are generated early, the upper bound value will become lower and has a higher chance of rejecting unpromising nodes with higher lower bound values. This will reduce the search space so that time can be spent more efficiently on nodes, which might give a better solution than the current best. However, when a heuristic becomes too complex and computationally intensive, it causes each branch to take a much longer time and can significantly increase the overall running time. There is thus a need to use a simple and effective heuristic.
When a process planner plans for a particular job, operations that require both the same machine and machining direction will usually be grouped and carried out together. To build on that behaviour, the heuristic will keep looking for the sub- sequent operation that has the same machine and machining direction as the previous one. The heuristic can be briefly summarised as:
do
Step 1. To determine operation i+1,
for all other operations, which can be processed using, machine Mi
choose the operation with a corresponding machine and machining direction which will yield the lowest added time (AT = MDSTi+1 + MSTi+1 + MTi+1)
Step 2. if no operation is chosen, i.e. none of the remaining available operations can be processed by machine Mi, choose the operation with the lowest AT
while there are still unassigned operations, i = i + 1
end
The heuristic will choose an available operation that has the same machine and machining direction as the previous oper- ation if the time is shorter. In cases where time is saved by carrying out that operation on a faster machine, the faster machine is chosen. By having a heuristic like this, the process plan will not always force operations to be carried out on the same machine and in the same machining direction but rather allow different machines to be used if time can be saved.
4.3 Lower Bound Calculation
The lower bound value is an estimate of the best possible solution that can arise from the current sequence of a node. A simple way of calculating the lower bound would be to add up the minimum process times for all remaining operations. However, that will underestimate the lower bound value of that node as no set-up time is included in the estimate. Underestimating lower bound values causes many unpromising nodes to be branched and hence wastes time. To obtain best possible solution, we included the set-up when necessary into the lower bound calculations. It is found tha
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