本研究主要探討線性滑軌滾動介面剛性對門型結構動態特性之影響，進而評估整機結構自然振動頻率隨動件位置之變化趨勢，以作為工具機設計或加工精度控制依據。線性滑軌是加工機進給定位機構之重要導引元件，其中鋼珠在滑槽中形成滾動接觸之剛性與接觸負荷之間的非線性關係，是影響結構剛性與動態特性之重要因素。因此，本研究提出鋼珠接觸剛性與滾動介面模擬法則，並導入門型結構之有限元素模型中，以正確預測其動態行為，藉以評估滾動線軌中鋼珠預力對門型定位結構動態特性之影響，進一步比較滾動介面模式與傳統式固定介面模式之間的差異。研究結果發現，採用滾動介面模式之有限元素模型所預測之振頻與振動實驗所得結果甚為吻合，其間的最大誤差9.4％以內，而固定介面模式所預測之頻率與實驗結果有較大誤差（3～28％）。顯示在相同分析模型中使用固定介面與滾動介面的方式，將產生不同結果。相較於固定介面模式，滑軌滾動介面能真實地呈現門型結構之動態特性。進一步探討門型受簡諧力之激振響應，經由量測溜板之加速度響應，可預測出門型受切削力之最薄弱環節。結果顯示，經實驗分析門型結構之動剛性將隨外力激振頻率而變化，若在頻率1300Hz以下，結構將顯現較低的動剛性結構將顯現較低的動剛性，此為整龍門結構最薄弱環節，此項結果將是衡量門型結構動態性能的重要依據。

In this paper, the linear guide along with the rolling contact stiffness on the dynamic characteristics of a gantry structure was investigated. For a linear guide, the contact mode between rolling ball and groove can be characterized as a nonlinear problem according to the Hertzian theorem, in which the contact stiffness is varied with the preload set on the rolling balls. To deal with the nonlinearity, a linear spring element with adequate contact stiffness was introduced at the rolling interface of the guideway and hence the dynamic characteristic of a gantry could be predicted by the finite element method. As a validation, a series of modal tests were performed on the gantry prototype. Results predicted from gantry model with a rolling interface, rather than a fixed interface, are shown to agree well with experimental data, a maximum error of 9.4% being estimated. In addition, the fundamental natural frequencies of the gantry were shown to change with position of the moving carriage due the variation in structural stiffness. Current results clearly suggest that the modeling of a rolling interface with linearized contact stiffness can be a feasible way to accurately predict the dynamic characteristics of a machine tool with linear guides.

中 文 摘 要 i
英 文 摘 要 ii
誌 謝 iii
目 錄 iv
表 目 錄 vi
圖 目 錄 vii
符 號 說 明 ix
第一章 導論 1
1.1 研究背景 1
1.2 文獻回顧 3
1.3 研究動機與目的 6
1.4 全文概述 7
第二章 相關理論 9
2.1 滾動接觸剛性理論 9
2.2有限元素法 11
2.2.1 結構模態分析 13
2.2.2 結構靜剛性分析 14
2.2.3 結構動剛性分析 16
第三章 門型工具機有限元素模型 18
3.1有限元素模型建立 18
3.2滑軌滾動介面與固定介面模擬 20
3.3 有限元素收斂分析 23
第四章 門型結構振動實驗 26
4.1 實驗設備說明 26
4.2 振動實驗 30
4.3 振動頻譜 31
第五章 門型結構模態分析 32
5.1 有限元素-模態分析 32
5.2 結果與討論 36
第六章 振頻變化分析與實驗驗証 40
6.1 振頻變化分析 40
6.3 振動實驗 47
6.4 結果與討論 51
第七章 門型結構剛性分析 53
7.1 有限元素-靜剛度分析 53
7.2 有限元素-動剛度分析 57
7.3振動實驗驗証 58
7.4結果與討論 65
第八章 結論與未來展望 68
8.1結論 68
8.2 未來展望 69
參考文獻 70

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