本研究透過反應曲面最佳化法進行工具機熱親和(Thermo-Friendly)結構設計優化分析以及熱平衡(Thermal-Balance)精度調控與參數分析。熱親和結構設計是藉由結構優化，使工具機的熱變形複雜度降低、熱穩定性提升，有利於溫升熱補償技術的效果。在考慮結構熱親和設計優化的同時，本研究亦同步優化工具機結構的靜剛性、動剛性與輕量化，並分析四個目標物理量(靜剛性、動剛性、重量與熱變形)間的權衡關係。為有效率地進行此多目標最佳化分析，本研究以反應曲面法(Response Surface Methodology, RSM)進行多目標最佳化，規劃設計參數，接著搭配有限元素分析模擬，獲得 Pareto front，達成同時優化工具機結構的靜剛性、動剛性、重量與熱變形的目標，計算得到各種最佳解組合，供設計者挑選。研究使用一個重型龍門加工機為目標機台，原始設計的模擬結果經過實機實驗驗證，熱變形方向相同，誤差約為33%，因此模擬具有合理的可信度。經過RSM輔助分析優化之後的機台結構，在重量減輕6%的條件下，不損失靜剛性，同時動剛性提升6.4%，熱變形量減少10.3%。與傳統上常用於RSM的實驗設計法，如BBD (Box-Behnken Design)與CCD (Central Composite Design)相比，本研究使用的實驗設計法(Design of experiments, DOEs)為OACD (Orthogonal Array Composite Design)，相對於以BBD建立的反應曲面模型，預測精度提升約38%；相對於以CCD建立的反應曲面模型，預測精度可提升約30%。
熱親和結構設計優化雖然可以提升工具機的靜剛性、動剛性與熱變形，但是機台在動態運轉的情況下，結構仍有動態的熱變形；尤其是導致切削點(Tool Cutting Point, TCP)產生熱傾斜的加工誤差，難以使用一般的溫升熱補償技術予以消弭。本研究將RSM應用於智能化熱平衡調控系統的參數優化分析，透過DOEs，以少量但極有效率的實驗建立反應曲面模型，可以精準地估測加工端熱傾斜誤差與關鍵結構位置的溫度之間的相對關係。以此模型為基礎，優化關鍵結構位置的雙向(冷-熱)溫度調控，保持機台主軸的垂直度，達成動態熱親和設計的目標。此部分使用一台超音波加工中心機進行實機驗證，以RSM輔助建立的熱平衡調控模型，可將切削點的熱傾斜誤差於主軸穩定運轉3小時的情況下，全程抑制在±1 µm以內，同時於實際加工實驗中，可將垂直精度提升49.5%，實現超高精度的機台結構動態熱穩定性。

This study uses the Response Surface Methodology (RSM) for the optimization analysis of Thermo-Friendly design and Thermal-Balance control in machine tool structures. Thermo-Friendly design aims to reduce the complexity of thermal deformations and enhance thermal stability in machine tools, benefiting the effectiveness of thermal error compensation techniques. Simultaneously, this study optimizes static stiffness, dynamic stiffness, lightweight, and thermal errors at the tool cutting point (TCP) of a machine tool structure. The trade-off relationships among those four target physical quantities were also investigated. To efficiently conduct this multi-objective optimization analysis and obtain the Pareto front, this study uses the Responsive Surface Methodology (RSM). By planning the design parameters and applying the finite element (FEM) simulation, simultaneous optimization of static stiffness, dynamic stiffness, lightweight performance, and thermal deformation in the machine tool structure were achieved. The results provide a series of Pareto optimal solutions for designers to choose from. To demonstrate this optimization process, a heavy-duty gantry-type machining center was used. The simulation results of the original structure design were validated by experiments. It is shown that the same trend of thermal deformation as the experimental results are obtained with an error of approximately 33%. The multi-objective optimization was then conducted by using the validated FEM model. The RSM-aided designing machine tool structure achieves a 6% reduction in weight while maintaining static stiffness, with a 6.4% improvement in dynamic stiffness and a 10.3% reduction in thermal deformation. Compared to the most commonly used design of experiments (DOEs) methods such as Box-Behnken Design (BBD) and Central Composite Design (CCD), this study uses Orthogonal Array Composite Design (OACD) as the design of experiments, leading to a 38% and a 30% improvement, for BBD and CCD respectively, in the prediction accuracy of response surface model.
Thermo-Friendly structure design optimization can improve the static stiffness, dynamic stiffness, and thermal deformation of the machine tool. However, the structure still exhibits dynamic thermal deformations during operation, especially the thermal tilting machining errors of the Tool Cutting Point (TCP) which cannot be effectively resolved by conventional thermal-error compensation technology. In this study, RSM is applied to the parameter control optimization of an intelligent Adaptive Thermal Balance (ATB) technology. By utilizing DOEs, with a small number but highly efficient experiments, a response surface model is established to estimate the relationship between the thermal tilting error at TCP and the temperature at critical structural positions. Based on this model, the temperature distribution of critical structures position is optimized through bidirectional (cooling-heating) temperature control, ensuring the verticality of the machine tool spindle and achieving the goal of dynamic Thermo-Friendly design. To demonstrate the ability and performance of this RSM enabled ATB, an ultrasonic machining center was used as for experiments. Through experiments verification, the Thermal-Balance control model established by RSM can effectively suppress the thermal tilting error at TCP within ±1 µm throughout 3 hours continuous operation, realizing the goal of ultra-high precision and dynamic thermal stability of the machine tool structure.

摘要 i
Abstract iii
誌謝 v
目錄 vi
圖目錄 x
表目錄 xvi
符號表 xix
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 3
第二章 理論簡介 5
2.1 ANSYS運算理論 5
2.1.1靜剛性 5
2.1.2 動剛性 5
2.1.3 穩態熱傳導方程式 6
2.1.4 熱彈性力學方程式 7
2.2 反應曲面最佳化法 7
2.2.1反應曲面法 7
2.2.2 實驗設計 13
2.2.3 Pareto front 20
2.2.4 反應曲面最佳化法 21
2.3 灰色關聯分析 23
第三章 數值模擬與實驗 25
3.1 模擬模型簡介 25
3.2 材料性質設定 25
3.3 邊界條件設定 27
3.3.1 接觸面設定 27
3.3.2 自然對流 27
3.4 實驗設置 28
3.5 實驗結果 32
3.6 模擬結果 38
第四章 結果與討論 43
4.1 實驗設計法擬合反應曲面模型誤差比較 43
4.2 機台特性分析 48
4.1.1 靜剛性特性 48
4.1.2 動剛性特性 49
4.1.3 熱變形特性 51
4.3 橫樑肋板構型最佳化 53
4.3.1 肋板設計方案 53
4.3.2 最佳化設定 60
4.3.3 最佳化結果 62
4.4 橫樑肋板數量最佳化 63
4.4.1 設計參數 63
4.4.2 最佳化設定 65
4.4.3 最佳化結果 66
4.5 橫樑肋板尺寸最佳化 69
4.5.1 設計參數 69
4.5.2 最佳化設定與反應曲面模型精度 71
4.5.3 尺寸最佳化結果 73
4.5.4 敏感度分析與設計參數響應 77
4.6 橫樑尺寸最佳化(考慮熱變形) 81
4.6.1 設計參數 81
4.6.2 最佳化設定與反應曲面模型精度 82
4.6.3 尺寸最佳化結果 84
4.6.4 敏感度分析與設計參數響應 90
4.7 橫樑最佳化設計方向總結 94
第五章 動態結構熱平衡 96
5.1 實驗設置 96
5.2 動態結構熱平衡實驗 99
5.2.1 機台熱變位分析與熱傾斜誤差預測模型 100
5.2.2 熱平衡參數搜尋 109
5.2.3 熱平衡溫控模型與結構溫度最佳化 113
5.2.4 熱平衡實機驗證 117
5.3 熱平衡加工驗證 121
5.3.1 加工驗證規劃 121
5.3.2 加工驗證結果 124
5.3 Complex System Response 簡介 127
5.4 Complex System Response模擬 129
5.5 以CSR建立熱傾斜預測模型 135
5.5.1 實驗設計與CSR函數擬合 135
5.5.2 CSR預測結果比較 137
第六章 結論 140
Reference 142

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