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研究生:陳俊宇
研究生(外文):Chun-Yu Chen
論文名稱:牙科手機內超高速轉子-軸承系統動態特性分析與實驗研究
論文名稱(外文):Dynamic Analysis and Experimental Verification of Ultra- high-speed Rotor-bearing System for Dental Handpiece
指導教授:謝廣文謝廣文引用關係
學位類別:碩士
校院名稱:國立中興大學
系所名稱:生物產業機電工程學系所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
畢業學年度:96
語文別:中文
論文頁數:136
中文關鍵詞:牙科手機有限元素法臨界轉速
外文關鍵詞:Dental HandpieceFinite Element MethodCritical speed
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本研究是以市售醫療廠商所提供的2款牙科手機為對象,對其內部的微型渦輪轉子-軸承系統進行動態特性分析。在轉子-軸承系統數值分析方面,則利用有限元素法之理論,以MATLAB軟體為程式設計平台,撰寫分析轉子-軸承系統的數值分析程式。轉子-軸承系統中包括彈性軸、剛性圓盤以及具有阻尼和剛性的徑向軸承。軸元素的理論推導過程中將其考慮為Timoshenko樑做探討,其中包括平移慣性、轉動慣性、剪力效應與陀螺力矩的影響。
為了驗證分析程式的可靠性,文中先針對前人文獻所分析過的轉子-軸承系統,利用有限元素模型計算求取臨界轉速,並與文獻進行比對;爾後以旋轉試驗轉子(Rotor-Kit)為對象,利用有限元素模型計算求取臨界轉速。最後再進一步分析牙科手機內轉子-軸承系統並繪出坎貝爾圖、模態振型以及臨界轉速與軸承剛性的關係圖,搭配上動態特實驗將微型渦輪轉子-軸承系統的動態特性趨勢分析出來。
本研究所使用的轉子-軸承系統有限元素分析程式,經過文獻以及試驗轉子的驗證,其誤差值都在1%以內,並且成功的分析出牙科手機內微型渦輪轉子的動態特性,所以在設計牙科手機內微型渦輪轉子-軸承系統時,可以藉由有限元素法精準的分析轉子的動態特性。這些分析結果將可作為牙科手機內微型渦輪轉子-軸承系統設計修改的依據,有限元素分析程式也可以作為未來設計微型渦輪轉子-軸承系統的分析工具。
This study researches on the two types of dental handpiece provided by the medical manufacturer, and focus on analyzing their dynamic characteristics of internal rotor-bearing system. In the numerical analysis of rotor-bearing system, this paper uses the finite element method and takes the MATLAB design software as platform to complete the numerical analysis program for this rotor-bearing system. The system consists of elastic shaft, rigid disks and bearing which has damping and stiffness. During analyzing the shaft elements, the research will probe into the beam of Timoshenko. The model of the shaft element includes the effects of translation inertia, rotational inertia, gyroscopic moments, and shear deformations.
In order to confirm the reliability of the analysis program, firstly, we calculate the critical speed of rotor - bearing system by using the finite element model, and compare to the literatures. Then we obtain critical speeds of Rotor-Kit by using the finite element mode, and further analyze the rotor-bearing system in dental handpiece. We draw the Campbell diagram, mode shape and the critical speed versus bearing stiffness diagram and get a trend of dynamic characteristics of rotor-bearing system in experiments.
This finite-element analysis program on rotary-bearing system used in this department is verified in various scientific literatures and proven by many rotor tests. The error percentage is within one percent and it successfully illustrates the dynamic characteristics of the internal microscopic turbine rotor in the dental handpiece. Therefore, in designing this system the finite element method is very useful to precisely analyze the rotor in motion. The experimental data can be used as reference for future modification and refinement of the rotor-bearing system. And this finite-element analysis program can be used as a fundamental design tool for the system.
謝誌......................................................i
摘要.....................................................ii
Abstract.................................................iv
目錄.....................................................vi
圖目錄....................................................x
表目錄...................................................xv
符號說明...............................................xvii
第一章 緒論..............................................1
1.1前言...............................................1
1.2研究目的...........................................3
第二章 文獻探討..........................................4
2.1轉子-軸承系統有限元素法探討........................4
2.2牙科手機...........................................6
第三章 轉子-軸承系統有限元素模型.....................9
3.1連續樑理論........................................10
3.1.1連續樑理論介紹...............................10
3.1.2 Timoshenko樑理論............................11
3.1.3剪切係數的含義...............................12
3.2轉子-軸承系統有限元素模型的建立...................13
3.2.1基本假設.....................................13
3.2.2剛性圓盤之運動方程式.........................18
3.2.3彈性軸之運動方程式...........................20
3.2.4軸承之運動方程式.............................25
3.2.5轉子-軸承系統運動方程式......................26
3.3轉子-軸承系統動立方程式求解.......................27
3.3.1轉子系統自然頻率之計算.......................27
3.3.1轉子系統臨界轉速之計算.......................28
3.4小結...........................................30
第四章 試驗設備與方法...................................31
4.1試驗材料..........................................31
4.1.1牙科手機介紹.................... ............31
4.1.2 旋轉試驗轉子介紹............................32
4.2研究方法......................................... 33
4.2.1研究流程規劃................................ 36
4.2.2臨界轉速計算................................ 38
4.2.3動態特性分析................................ 39
4.3旋轉試驗轉子(Rotor-Kit)動態特性分析.............. 41
4.3.1旋轉試驗轉子靜模態有限元素分析與實驗方法.....41
4.3.2旋轉試驗轉子動態特性有限元素分析與實驗方法...46
4.3.3旋轉試驗轉子動態測試設備及測試流程...........48
4.4微型渦輪轉子-軸承系統動態特性分析................ 52
4.4.1微型渦輪轉子-軸承系統動態特性有限元素分析....52
4.4.2微型渦輪轉子-軸承系統動態實驗設備及量測方法..56
4.4.3支承剛度變化與臨界轉速關係之分析與動態實驗...59
第五章 結果與討論.......................................61
5.1轉子-軸承系統動態特性有限元素分析程式
與文獻比對結果................. 61
5.1.1單圓盤均勻軸系統.............................61
5.1.2多圓盤均勻軸系統............................ 65
5.1.3多圓盤非均勻軸系統.......................... 68
5.2旋轉試驗轉子-軸承系統動態特性分析結果與討論.......72
5.2.1旋轉試驗轉子-軸承系統靜模態分析與實驗比對....72
5.2.2旋轉試驗轉子-軸承系統動態特性有限元分析結果..73
5.2.3旋轉試驗轉子-軸承系統動態特性實驗結果....... 76
5.2.4實驗結果與數值分析比較...................... 78
5.3牙科手機內微型渦輪轉子-軸承系統動態特性分析...... 80
5.3.1微型渦輪轉子-軸承系統有限元分析結果..........80
5.3.2微型渦輪轉子-軸承系統動態特性實驗結果........85
5.3.3動態實驗測試結果與有限元分析程式比對........ 93
5.4不同支承剛度下轉子臨界轉速測試結果............... 95
5.4.1前後支承剛度變化與臨界轉速測試結果...........95
5.4.2前後支承剛度變化與臨界轉速關係分析..........104
第六章 結論與建議......................................107
6.1結論............................................ 107
6.2建議.............................................108
參考文獻................................................110
附錄、牙科手機轉子動平衡原理與測試......................113


圖目錄
圖3.1 Timoshenko樑......................................11
圖3.2 轉子—軸承系統示意圖..............................14
圖3.3 剖面座標與固定參考座標之相對位置..................15
圖3.4 軸元素之元素位移與節點位移........................20
圖3.5 軸承之數學模型....................................25
圖4.1 牙科手機..........................................32
圖4.2 微型渦輪轉子..................................... 32
圖4.3 旋轉試驗機全貌................................... 33
圖4.4 研究方法架構圖................................... 35
圖4.5 研究流程圖....................................... 37
圖4.6 彎曲平面座標..................................... 38
圖4.7 轉子軸承-系統動態分析流程圖...................... 40
圖4.8 模態測試實驗設備架構圖........................... 43
圖4.9 試驗轉子專用治具與懸吊方式圖..................... 43
圖4.10 轉子敲擊點規劃...................................44
圖4.11 試驗轉子-軸承系統示意圖......................... 47
圖4.12 旋轉試驗轉子及變頻馬達.......................... 48
圖4.13 軸承座...........................................49
圖4.14 渦電流非接觸式位移計.............................49
圖4.15 訊號放大器.......................................49
圖4.16 SigLab頻譜分析儀.................................50
圖4.17 轉子-軸承動態特性測試流程圖..................... 51
圖4.18 TT201T轉子尺寸圖................................ 53
圖4.19 TT201M轉子尺寸圖.................................55
圖4.20 轉速計...........................................56
圖4.21 非接觸式電容位移計...............................57
圖4.22 SigLab頻譜分析儀.................................57
圖4.23 轉速計擷取轉子轉速訊號方式.......................58
圖4.24 微型渦輪轉子動態測試圖...........................58
圖5.1 單圓盤均勻軸轉子模型............................ 62
圖5.2 單圓盤均勻軸系統有限元分析-坎貝爾圖.............. 64
圖5.3 多圓盤均勻軸轉子模型............................. 65
圖5.4 多圓盤均勻軸系統有限元分析-坎貝爾圖.............. 67
圖5.5 多圓盤非均勻軸轉子模型........................... 68
圖5.6 多圓盤非均勻軸系統有限元分析-坎貝爾圖............ 71
圖 5.7 轉速20000rpm,聯軸器剛度2.5×105N/m,前後支承剛度106N/m...................................... 74
圖 5.8 轉速20000rpm,聯軸器剛度2.25×105N/m,前後支承剛度106N/m...................................... 74
圖 5.9 轉速20000rpm,聯軸器剛度2.5×105N/m,前後支承剛度107N/m...................................... 75
圖 5.10 轉速20000rpm,聯軸器剛度2.25×105N/m,前後支承剛度107N/m...................................... 75
圖5.11 試驗轉子階次追蹤圖、加減速頻線瀑布分析圖........ 77
圖5.12 TT201T坎貝爾圖(前支承剛度等於後支承剛度) ........81
圖5.13 TT201T臨界轉速與支承剛性關係圖...................81
圖5.14 TT201M坎貝爾圖(前支承剛度等於後支承剛度) ........83
圖5.15 TT201M臨界轉速與支承剛性關係圖...................83
圖5.16 TT201T Order tracking圖-位移計量測..............86
圖5.17 TT201T Order tracking圖-加速規量測..............87
圖5.18 TT201T Waterfall圖..............................87
圖5.19 TT201T Intensity圖..............................88
圖5.20 TT201T Spectrum圖.............................. 88
圖5.21 TT201M Order tracking圖.........................90
圖5.22 TT201M Waterfall圖............................. 90
圖5.23 TT201M Intensity圖............................. 91
圖5.24 TT201M Spectrum圖...............................91
圖 5.25 TT201T轉子-坎貝爾圖(前支承剛度4×105N/m,後支承剛度5×105N/m) .....................................94
圖 5.26 TT201M轉子-坎貝爾圖(前支承剛度3.5×105N/m,後支承剛度2.5×105N/m) ...................................94
圖5.27 Order tracking圖(使用位移計及加速規量測) ........96
圖 5.28 加速規量測之Waterfall圖.......................................................97
圖 5.29 坎貝爾圖(前支承剛度4×105 N/m,後支承剛度5×105 N/m).....................................97
圖5.30 位移計量測之Order tracking圖.....................99
圖5.31 加速規量測之Order tracking圖.....................99
圖5.32 加速規量測之Waterfall圖.........................100
圖 5.33 坎貝爾圖(前支承剛度7×105 N/m,後支承剛度9×105 N/m)....................................100
圖5.34 位移計量測之Order tracking圖....................102
圖5.35 加速規量測之Order tracking圖....................102
圖5.36 加速規量測之Waterfall圖.........................103
圖 5.37 坎貝爾圖(前支承剛度4.5×105 N/m,後支承剛度9×105 N/m)....................................103
圖 5.38 臨界轉速圖(前支承剛度等於後支承剛度) ....................................................105
圖 5.39 臨界轉速圖(前支承剛度改變、後支承剛度不變) ....................................................105
圖 5.40 臨界轉速圖(前支承剛度不變、後支承剛度改變) ....................................................106


表 目 錄
表4.1 試驗轉子各區段物理參數............................45
表4.2 試驗轉子物理參數資料..............................45
表4.3 TT201T轉子參數................................... 54
表4.4 TT201T渦輪葉片參數................................54
表4.5 TT201M轉子參數....................................55
表4.6 TT201M渦輪葉片參數................................56
表4.7 前後支承剛度變化與臨界轉速關係實驗規劃表......... 60
表5.1 單圓盤均勻軸轉子物理參數..........................63
表5.2 單圓盤均勻軸系統比對結果..........................64
表5.3 多圓盤均勻軸轉子物理參數..........................66
表5.4 多圓盤均勻軸轉子模型..............................66
表5.5 多圓盤均勻軸轉子比對結果..........................67
表5.6 多圓盤非均勻軸轉子物理參數........................69
表5.7 多圓盤非均勻軸轉子建模參數........................70
表5.8 多圓盤非均勻軸系統比對結果........................71
表5.9 試驗轉子模態比較結果..............................79
表5.10 試驗轉子-軸承系統動態模擬分析結果............... 76
表5.11 動態實驗臨界轉速................................ 77
表5.12 動態實驗與有限元模擬比對........................ 79
表5.13 TT201T轉子模態振型圖............................ 82
表5.14 TT201M轉子模態振型圖............................ 84
表5.15 微型渦輪轉子動態測試結果........................ 92
參考文獻

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