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dc.contributor.authorCheng, Kuo-Mingen_US
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dc.description.abstract公差配置的目的在於如何分配或指定合適的公差規格於工件或組件上,最佳化配置準則往往建立在製造成本的考量上,本論文探討如何以最佳化理論搭配Lagrange multipliers (LM)方法建構尺寸公差最佳化課題,以最低製造成本為目標,以組件組合公差即尺寸鏈以及製程能力為限制條件,配合不同成本-公差關係式,進行最惡狀況與統計公差的最佳化配置,同時也建立最佳化公差配置完整分析與設計過程。 本研究首先探討倒數次方與倒數指數之一般成本公差模式,配合等式與不等式限制條件推導應用此方法求解最佳化公差配置問題,且進一步研究探討最惡狀況與統計公差模式下的最佳化公差配置。在應用LM法處理倒數指數型之成本公差模式時,因為微分面臨超越函數問題,本研究特別引入Lambert W函數以解決此課題,進而得到一封閉形式之數學表示式。應用文中所推導的表示式,配合聯立方程式求解在等式限制條件下之限制條件最佳化問題,可解決使用非傳統最佳化方法求解所得近似最佳解不一致現象,並且免去傳統LM方法所需要的微分過程複雜計算,更大大地降低數值方法所產生的截去誤差以及肇因於電腦精確度不足所衍生的捨去誤差。 文中同時舉例說明本方法之應用與驗證本方法的效果,並且經由與傳統LM方法所配置之公差與成本作一比較,結果顯示此法可快速、有效以及準確地執行最低成本之公差配置。zh_TW
dc.description.abstractTolerance allocation is the process to distribute or to assign suitable tolerance specifications to a part or to an assembly. The distribution criteria are often based on manufacturing costs. As mathematical models are required for optimal tolerance allocation, this dissertation explores a comprehensive analysis method for optimal tolerance allocation using Lagrange multipliers for minimizing manufacturing cost subject to constraints on dimensional chains and machining capabilities. A series of systematic design procedures is also conducted to resolve the tolerance optimization problem in mechanical design. The general reciprocal power and exponential cost-tolerance models with both equality and inequality constraints are investigated for employing this method. Moreover, worst-case and statistical tolerancing are also applied in this investigation. In particular, we further derive a closed-form expression of the tolerance optimization problem for reciprocal exponential cost-tolerance model by introducing Lambert W function for which the transcendental equation can be solved. As the near-optimal solutions obtained using nontraditional optimization techniques are probably inconsistent, the optimization problem is solved by applying the algorithmic approach. Therefore, for constrained minimization problems with only equality constraints, the optimum design can be obtained by solving simultaneous equations with closed-form solutions in order to reduce complicated computations while keeps a reasonable accuracy. This computing result displays that truncation errors and round-off errors can be decreased greatly. Several case studies are illustrated to demonstrate the feasibility of this approach. Through comparisons with the regular Lagrange multipliers method and the proposed approach applied on traditional tolerance analysis methods, the result also reveals that tolerance can be allocated quickly, effectively and accurately using this method.en_US
dc.description.tableofcontents摘要 i ABSTRACT ii TABLE OF CONTENTS iii LIST OF TABLES v LIST OF FIGURES vi NOTATION vii CHAPTER 1 INTRODUCTION 1 1.1 Background 1 1.2 Problem Formulation 3 1.3 Research Objective 4 1.4 Contributions of This Research 5 1.5 Contents of the Dissertation 6 CHAPTER 2 LITERATURE REVIEW 8 2.1 Tolerance Analysis 8 2.1.1 Worst-case tolerance analysis 8 2.1.2 Statistical tolerance analysis 9 2.2 Tolerance Allocation 9 2.2.1 Tolerance design for minimum quality loss and manufacturing cost 9 2.2.2 Tolerance assignment with optimization techniques 10 2.3 Cost-Tolerance Modeling 12 CHAPTER 3 THE PROPOSED METHOD 15 3.1 The Lagrange Multipliers Method 15 3.1.1 Constraints of equalities 16 3.1.2 Constraints of inequalities 17 3.1.3 Miscellaneous constraints 18 3.2 The Lambert W Function 18 3.3 Efficient Solution Technique 20 CHAPTER 4 OPTIMUM WORST-CASE TOLERANCE ALLOCATION 22 4.1 Dimensional Chain of an Assembly 22 4.2 Tolerance Allocation for Reciprocal Power Cost-Tolerance Model 23 4.3 Tolerance Allocation for Reciprocal Exponential Cost-Tolerance Model 23 4.4. Case Studies 24 CHAPTER 5 OPTIMUM STATISTICAL TOLERANCE ALLOCATION 42 5.1 Statistical Tolerance Stacks of Assemblies 42 5.2 Tolerance Allocation with Reciprocal Power Cost-Tolerance Model 43 5.3 Tolerance Allocation with Reciprocal Exponential Cost-Tolerance Model 44 5.4 Case Studies 46 CHAPTER 6 CONCLUSIONS AND FUTURE WORK 56 6.1 Summary of Accomplished Research 56 6.2 Recommendations for Future Work 57 REFERENCES 59 APPENDIX 65 AUTHOR’S VITA 70 Educational Background 70 Working Experience 70 Major Certificates 70 Publications and Presentations 71zh_TW
dc.subjectoptimal tolerance allocationen_US
dc.subjectLagrange multipliersen_US
dc.subjectLambert W functionen_US
dc.subjectcost-tolerance modelen_US
dc.subjectworst-case and statistical tolerancing.en_US
dc.subjectLambert W函數zh_TW
dc.title以Lagrange Multiplier為基礎之最佳公差配置探討zh_TW
dc.titleAn Investigation on Optimal Tolerance Allocation Based on Lagrange Multipliersen_US
dc.typeThesis and Dissertationzh_TW
item.openairetypeThesis and Dissertation-
item.fulltextno fulltext-
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