臺灣博碩士論文加值系統

本研究是以靈敏度分析的方式找出目標參數在一個模擬模型中的影響度，並依照此靈敏度對參數進行修正以建立出符合實驗數據的模擬模型。本篇研究之模擬模型建立方法為有限元素法，由分析套裝軟體ANSYS取得初始模型的數據建立有限原模型，在依照實際需求定立設計參數(介面剛性、支撐剛性等)並計算出對於模型目標值(位移量、自然頻率等)的靈敏度。而本研究的目的為降低模擬模型的目標值與實驗的量測值間的誤差。以最佳化的形式透過不斷的迭代找尋出能計算出與實驗相同數據的設計參數。

本研究以兩個案例為主要研究目標： (1).薄壁鋁件與虎鉗間的介面剛性搜尋 (2). 工具機底座模型支機腳等效剛性搜尋。兩者皆以模態測試實驗取得自然頻率並依ANSYS的數據建立有限元素模型，以最佳化的方法計算出目標參數。本研究依更新結果探討目標剛性與自然頻率間的關聯。更進一步，利用模型更新的方法找尋出工具機底座機腳是否有鬆脫的現象。本研究將移除一支撐於工具機底座模型的機腳，並取得實驗的自然頻率，在以模型更新計算出所有機腳的等效剛性值，驗證模型更新是否能找尋出有鬆脫情況的機腳。

The purpose of this research is establish a computer model that make a low level of the difference between the identified results and the measured data. This research would analyze the sensitivity of the parameters and identified the correction values of parameters. This research identified the stiffness of the model with the measured data, such as displacement or the natural frequencies and the model would be established by the finite element method. It established an initial computer model by the analysis software, such as ANSYS. The object of this research is reducing the difference between the simulation prediction and the measured results by solving the optimization problem.

Two main cases are involved in this research: (1) Identifying the value of the contacted stiffness between an aluminum thin wall and a vise, (2) Identifying the equivalent stiffness of footings of a machine tool model. It would measure natural frequency by the modal testing. The finite element model was built with the data got in ANSYS and the objective stiffness was identified by the model updating. This research would be analyzed the relationship between the updated stiffness and the measured natural frequency. Furthermore, this research would be found the improper installation of the footings of the machine tool model by the model updating. One footing would be removed for simulating the improper installation and the natural frequencies were measured by the modal testing. The equivalent stiffness of all footings was identified by model updating and the improper installation of the footing would be found out.

Acknowledgement i
摘要 ii
Abstract iii
Table of Contents iv
List of Tables iv
List of Figures vii
List of Symbols ix
Chapter 1. Introduction 1
1.1 Background 1
1.2 Literature Review 2
1.2.1 Modeling machine tools 2
1.2.2 Modal analysis & Reduction 3
1.2.3 Model Updating 4
1.2.4 Foundation of the machine tool 7
1.3 Objectives 8
1.4 Structure of thesis 8
Chapter 2. Sensitivity – Based Model Updating Analysis 9
2.1 Modal analysis & model reduction 9
2.1.1 Estimation of natural frequencies and mode shapes 9
2.1.2 Model reduction and reduced system matrices of perturbed model 10
2.2 Linearization of the relationship between measured data and estimated parameters 12
2.3 Subset selection and parameter prediction 13
2.4.1 Objective function 13
2.4.2 Subset selection 14
2.4.3 Parameters prediction with sensitivity matrix 16
2.4 Regularization approach 18
Chapter 3. Model Updating in Practice 20
3.1 3 DOF Statically load System 20
3.1.1 Underdetermined & overdetermined systems 21
3.1.2 Case 1. Model updating of underdetermined systems 22
3.1.3 Case 2. Model updating of overdetermined systems 23
3.1.4 Case 3. Effect of Noise and Regularization 24
3.2 Identification of bearing stiffness in a simulated 26
3.3 Correcting the interface stiffness between an aluminum thin wall and vise 33
3.3.1 Shape function for the Spring bed 33
3.3.2 Stiffness correction 35
Chapter 4. Model Updating for the Machine Tool Footing stiffness 37
4.1 Introduction 37
4.2 Identification of the footings stiffness 39
4.2.1 Numerical model of scaled machine tool base 39
4.2.2 Stiffness of the foundation 40
4.3 Iteration & Results 43
4.4 Effect of Height 45
4.5 Random initial stiffness 49
4.6 Simulation for improper installation of the machine tool footings 50
4.7 Random initial stiffness for improper installation of footing 58
Chapter 5. Conclusion and future work 61
5.1 Conclusion 61
5.2 Future work 62
References 63

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