吳文方臺灣大學：機械工程學研究所何鴻翔Ho, Hung-HsiangHung-HsiangHo2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/61166在以往的研究中，有許多學者建立過不同的軌道車輛動態分析模型，但這些模型許多都太過簡易，以致表現出的動態特性與列車的實際行駛狀況有所差異，因此本研究在不考慮車輛縱向加速度及上下顛簸兩種情況，但考慮車輪圓錐度、軌道不平整、潛滑力等因素後，提出了一28個自由度的軌道車輛動態分析模型，並依據美國聯邦鐵路局所訂定的軌道不平整能量頻譜密度函數為主要輸入，來模擬軌道車輛於各種不同的行駛條件下的動態響應。本論文除針對軌道車輛懸吊系統、行駛速度、負重、鋼輪磨平、軌道等級等不同因素，進行模擬、比較外，也探討車輛於高承載狀況下，在直軌和彎軌行駛時動態響應的不同，並以Nadal ratio與輪軸減重率兩種安全指標進行安全評估；最後也對台北捷運局規定捷運車輛在遭遇四級地震時必須停駛的措施作評比，探討車輛遇到此突發狀況是否會出軌，以確保行車安全。研究結果顯示，列車於高承載並行駛於彎軌時，其輪軸組的橫向位移量較無承載時大了數倍，且隨著曲率的增加而增大；而軌道等級的不同也會影響橫向位移的大小，其中一級軌道狀況對輪軸組所造成的位移量幾為其他軌道等級的數倍；此外，高承載下的行駛，會使得輪軸組的橫向位移量較低承載時早超出規定的上限值6 mm，並增加出軌的風險；最後，列車在直軌段行駛突遇四級地震時，輪軸組的橫向位移雖超出規定值而有輪緣接觸的情況，但在安全評估方面，則因計算出來的Nadal ratio與輪軸減重率皆仍在標準範圍內，所以乘客在搭乘列車遇此突發狀況時，仍應是安全的。A 28-degree–of-freedom dynamical model is established in the present study to simulate the responses of rapid transit vehicles. The model takes wheel conicity, creep force, track irregularity, etc. into consideration. Among them, the power spectral density function of track irregularity proposed by US Federal Railroad Administration (FRA) is considered the major input. Dynamical simulation of rapid transit vehicles under various suspensions, vehicle velocities, loads, wheelflats, and track irregularities are performed and compared. The investigation also covers situations when the vehicle is fully loaded of passengers and moves on either straight or curved tracks. Both Nadal ratio and wheel load reduction ratio are used to evaluate the possibility of vehicle derailment. Whether it is necessary to stop operation at the occurrence of an earthquake of intensity four as the regulation set by Taipei Rapid Transit Corporation is investigated as well. Through the study, it is found that, when the railway vehicle is fully loaded of passengers and runs at curved tracks, the lateral displacement of the wheelset is several-time greater than that of the empty train. The displacement increases as the curvature increases. The degree of track irregularity also affects the lateral displacement of the wheelset. In particular, the displacement caused by track irregularity of level one is several-time greater than that caused by track irregularities of other levels. It may exceed the limit value of 6 mm set by Taipei Rapid Transit Corporation when the vehicle is fully loaded of people. Finally, when an earthquake of intensity four occurs, although the phenomenon of wheel contact may occur, the calculated Nadal ratio and wheel load reduction ratio remain within their limit values. Therefore, it is still considered safe to passengers.目錄 誌謝.......................................................................................................................................Ⅴ 摘要.......................................................................................................................................Ⅵ ABSTRACT.........................................................................................................................Ⅶ 目錄.......................................................................................................................................Ⅷ 表目錄..................................................................................................................................XI 圖目錄.................................................................................................................................XII List of Notations............................................................................................................XVIII 第一章 導論......................................................................................................1 1-1 前言.................................................................................................................................1 1-2 文獻回顧.........................................................................................................................2 1-3 本文架構.........................................................................................................................3 第二章 軌道車輛之建模分析..........................................................................5 2-1 座標設定.........................................................................................................................5 2-2 輪軸組受力關係式.........................................................................................................5 2-3 轉向架受力關係式.........................................................................................................9 2-4 車體受力關係式...........................................................................................................10 2-5 懸吊系統平衡關係式...................................................................................................11 2-6 潛滑力...........................................................................................................................15 2-7 運動方程式...................................................................................................................16 第三章 數值模擬與安全指標探討................................................................32 3-1 軌道不平整輸入...........................................................................................................32 3-2 振幅分析.......................................................................................................................34 3-3 安全指標.......................................................................................................................34 3-3-1 Nadal ratio.................................................................................................................35 3-3-2 輪軸減重率..............................................................................................................36 3-4 數值模擬.......................................................................................................................36 第四章 懸吊系統設計與車輛穩定度分析....................................................47 4-1 懸吊設計.......................................................................................................................47 4-1-1 次懸吊系統設計......................................................................................................47 4-1-2 主懸吊系統設計......................................................................................................48 4-2 軌道車輛穩定度分析...................................................................................................49 4-2-1 數值模擬結果..........................................................................................................50 4-2-2 實車測試..................................................................................................................51 第五章 鋼輪磨平下的動態效應....................................................................66 5-1 鋼輪磨平.......................................................................................................................66 5-2 鋼輪磨平的出軌評比...................................................................................................66 5-3 影響衝擊力的參數研究...............................................................................................67 5-3-1 負重和列車速度的影響..........................................................................................67 5-3-2 軌道不平整的影響..................................................................................................68 5-3-3 鋼輪磨平深度的影響..............................................................................................68 5-3-4 軌道勁度的影響......................................................................................................68 5-3-5 主懸吊系統勁度的影響..........................................................................................69 5-4 鋼輪磨平對橫向力的影響...........................................................................................69 5-4-1 鋼輪磨平對主懸吊系統垂直作用力的影響..........................................................70 5-4-2 鋼輪磨平對次懸吊系統垂直作用力的影響..........................................................70 5-4-3 鋼輪磨平對次懸吊系統橫向作用力的影響..........................................................71 5-4-4 鋼輪磨平對出軌比的影響......................................................................................71 第六章 高承載下的安全評估........................................................................87 6-1 承載狀況與彎軌...........................................................................................................87 6-2 動態分析與安全評估...................................................................................................87 6-3 不同軌道等級下的行駛狀況.......................................................................................90 第七章 軌道車輛遇地震時之模擬探討......................................................115 7-1 自由度的改變.............................................................................................................115 7-2 地震輸入.....................................................................................................................115 7-3 遇地震時之直軌動態分析與安全評估.....................................................................116 第八章 結論..................................................................................................127 8-1 結論.............................................................................................................................127 參考文獻........................................................................................................129 表目錄 表2-1 軌道車輛運動模型各自由度代表變數...............................................20 表2-2 自訂係數表（輪軸組）...........................................................................21 表2-3 自訂係數表（轉向架）...........................................................................23 表2-4 自訂係數表（車體）...............................................................................25 表3-1 軌道不平整能量頻譜密度函數表(PSD).............................................38 表3-2 輪軸組與軌道不平整之位移與速度變數表.......................................39 表3-3 世界各國軌道車輛系統所設定之Nadal ratio (出軌比)......................40 表3-4 台北捷運局軌道車輛標準參數表.......................................................41 表3-5 潛滑係數與輪軌接觸參數表...............................................................42 表4-1 動態穩定性之模擬結果.......................................................................53 表4-2 車體橫向位移量之模擬結果...............................................................54 表4-3 轉向架之最大橫向加速度...................................................................55 表5-1 鋼輪磨平深度1mm下Nadal ratio變化值.............................................73 表5-2 時速80 km/hr下，不同軌道等級與鋼輪磨平深度之Nadal ratio........................................................................................................74 表7-1 世界各國震度分級表.........................................................................118 表7-2 地震輸入之位移與速度變數表.........................................................119 圖目錄 圖2-1 軌道車輛模型示意圖.............................................................................27 圖2-2 軌道車輛運動座標系.............................................................................27 圖2-3 第一組輪軸組自由體圖.........................................................................28 圖2-4 第二組輪軸組自由體圖.........................................................................28 圖2-5 第三組輪軸組自由體圖.........................................................................29 圖2-6 第四組輪軸組自由體圖.........................................................................29 圖2-7 前轉向架自由體圖.................................................................................30 圖2-8 後轉向架自由體圖.................................................................................30 圖2-9 車體之自由體圖.....................................................................................31 圖2-10 輪軌接觸力示意圖.................................................................................31 圖3-1 高低不整與方向不整示意圖.................................................................43 圖3-2 水平與方向軌道不平整能量頻譜密度函數 (車速80 km/h)...............43 圖3-3 軌道之勁度係數與阻尼係數示意圖.....................................................44 圖3-4 軌道車輛行駛於彎軌示意圖.................................................................44 圖3-5 軌道車輛行駛之衝擊角示意圖.............................................................45 圖3-6 爬上型出軌之過程圖.............................................................................45 圖3-7 輪軌接觸受力示意圖.............................................................................46 圖3-8 滾動接觸示意圖.....................................................................................46 圖4-1 次懸吊橫向勁度係數與次懸吊橫向振幅關係圖.................................56 圖4-2 次懸吊垂向勁度係數與次懸吊垂向作用力關係圖.............................56 圖4-3 主懸吊橫向勁度係數與主懸吊橫向振幅關係圖.................................57 圖4-4 主懸吊橫向勁度係數與主懸吊橫向作用力關係圖.............................57 圖4-5 主懸吊垂向勁度係數與主懸吊垂向作用力關係圖.............................58 圖4-6 一級軌道狀況下轉向架之橫向加速度關係圖 (車速80 km/h)...........58 圖4-7 一級軌道狀況下轉向架之橫向加速度關係圖 (車速90 km/h)...........59 圖4-8 一級軌道狀況下轉向架之橫向加速度關係圖 (車速145 km/h).......................................................................................................59 圖4-9 一級軌道狀況下轉向架之橫向加速度關係圖 (車速148 km/h).......................................................................................................60 圖4-10 六級軌道狀況下轉向架之橫向加速度關係圖 (車速150 km/h).......................................................................................................60 圖4-11 一級軌道狀況下車體之橫向位移量關係圖 (車速148 km/h).......................................................................................................61 圖4-12 六級軌道狀況下車體之橫向位移量關係圖 (車速150 km/h).............61 圖4-13 一級軌道狀況下輪軸組之橫向位移量關係圖 (車速145 km/h).......................................................................................................62 圖4-14 一級軌道狀況下輪軸組之橫向位移關係圖 (車速150 km/h).......................................................................................................62 圖4-15 六級軌道狀況下輪軸組之橫向位移關係圖 (車速150 km/h).......................................................................................................63 圖4-16 六級軌道狀況下輪軸組之橫向位移關係圖 (車速160 km/h).............63 圖4-17 感測器裝置位置示意圖.........................................................................64 圖4-18 空空車重量下軌道車輛之穩定度測試結果 (車速80 km/h)...............65 圖4-19 空車重量下軌道車輛之穩定度測試結果 (車速90 km/h)...................65 圖5-1 鋼輪磨平示意圖.....................................................................................75 圖5-2 有鋼輪磨平之Nadal ratio變化圖 (車速80 km/h).................................75 圖5-3 有鋼輪磨平之Nadal ratio變化圖 (車速150 km/h)...............................76 圖5-4 不同負重且有無鋼輪磨平時之衝擊力對速度變化圖.........................76 圖5-5 不同軌道等級之衝擊力對速度變化圖 (考慮W1負重且無鋼輪磨平)............................................................................................................77 圖5-6 不同軌道等級之衝擊力對速度變化圖 (考慮W1負重且有鋼輪磨平)............................................................................................................77 圖5-7 不同鋼輪磨平深度之衝擊力對速度變化圖 (W1負重)......................78 圖5-8 不同鋼輪磨平深度之衝擊力對軌道勁度係數變化圖 (考慮W1負重且時速80 km/h)......................................................................................78 圖5-9 不同鋼輪磨平深度之衝擊力對主懸吊勁度係數變化圖 (考慮W1負重且時速80 km/h)..................................................................................79 圖5-10 不同軌道等級之輪軸組橫向力對速度變化圖 (W1負重)..................80 圖5-11 不同軌道等級之輪軸組橫向力對速度變化圖 (W3負重)..................80 圖5-12 不同軌道等級之主懸吊系統垂向力對速度變化圖 (考慮W1負重且無鋼輪磨平無鋼輪)...................................................................................81 圖5-13 不同軌道等級之主懸吊系統垂向力對速度變化圖 (考慮W1負重且有鋼輪磨平)............................................................................................81 圖5-14 不同軌道等級之次懸吊系統垂向力對速度變化圖 (考慮W1負重且無鋼輪磨平)............................................................................................82 圖5-15 不同軌道等級之次懸吊系統垂向力對速度變化圖 (考慮W1負重且有鋼輪磨平)............................................................................................82 圖5-16 不同鋼輪磨平深度之次懸吊系統垂向力對速度變化圖 (W1負重)............................................................................................................83 圖5-17 次懸吊系統垂向力對鋼輪磨平深度變化圖 (考慮不同負重且時速80 km/h).......................................................................................................83 圖5-18 不同鋼輪磨平深度之次懸吊系統垂向力對軌道勁度變化圖 (考慮W1負重與時速80 km/h)........................................................................84 圖5-19 不同軌道等級之次懸吊系統橫向力對速度變化圖 (考慮不同負重且時速80 km/h)..........................................................................................84 圖5-20 不同軌道等級之次懸吊系統橫向力對鋼輪磨平深度變化圖 (考慮不同負重且時速80 km/h)..........................................................................85 圖5-21 不同軌道等級之前15秒Nadal ratio對速度變化圖 (考慮W1負重且無鋼輪磨平)............................................................................................85 圖5-22 不同軌道等級之前15秒Nadal ratio對速度變化圖 (考慮W1負重且有鋼輪磨平)............................................................................................86 圖5-23 不同鋼輪磨平深度之Nadal ratio對速度變化圖 (W1負重).................86 圖6-1 直軌高承載下第一輪軸組之橫向位移關係圖.....................................92 圖6-2 直軌高承載下第四輪軸組之橫向位移關係圖.....................................92 圖6-3 直軌高承載下第一輪軸組之垂向位移關係圖.....................................93 圖6-4 直軌高承載下第四輪軸組之垂向位移關係圖.....................................93 圖6-5 直軌高承載下輪軸組之橫向加速度關係圖.........................................94 圖6-6 直軌高承載下輪軸組之垂向加速度關係圖.........................................94 圖6-7 直軌高承載下前轉向架之橫向位移關係圖.........................................95 圖6-8 直軌高承載下車身之橫向位移關係圖.................................................95 圖6-9 直軌高承載下前轉向架之垂向位移關係圖.........................................96 圖6-10 直軌高承載下車身之垂向位移關係圖.................................................96 圖6-11 直軌高承載下之Nadal ratio變化圖.......................................................97 圖6-12 直軌高承載下之輪軸減重率變化圖.....................................................97 圖6-13 彎軌無承載下第一輪軸組之橫向位移關係圖 (曲率半徑3,500 m)............................................................................................................98 圖6-14 彎軌無承載下之Nadal ratio變化圖 (曲率半徑3,500 m)............................................................................................................98 圖6-15 彎軌無承載下之輪軸減重率變化圖 (曲率半徑3,500 m)............................................................................................................99 圖6-16 彎軌高承載下第一輪軸組之橫向位移關係圖 (曲率半徑3500 m)............................................................................................................99 圖6-17 彎軌高承載下之Nadal ratio變化圖 (曲率半徑3,500 m)..........................................................................................................100 圖6-18 彎軌高承載下之輪軸減重率變化圖 (曲率半徑3,500 m)..........................................................................................................100 圖6-19 彎軌無承載下第一輪軸組之橫向位移關係圖 (曲率半徑1,500 m)..........................................................................................................101 圖6-20 彎軌無承載下之Nadal ratio變化圖 (曲率半徑1,500 m)..........................................................................................................102 圖6-21 彎軌高承載下第一輪軸組之橫向位移關係圖 (曲率半徑1,500 m)..........................................................................................................103 圖6-22 彎軌高承載下之Nadal ratio變化圖 (曲率半徑1,500 m)..........................................................................................................104 圖6-23 彎軌無承載下第一輪軸組之橫向位移關係圖 (曲率半徑200 m)..........................................................................................................105 圖6-24 彎軌無承載下之Nadal ratio變化圖 (曲率半徑200 m)..........................................................................................................106 圖6-25 彎軌高承載下第一輪軸組之橫向位移關係圖 (曲率半徑200 m)..........................................................................................................107 圖6-26 彎軌高承載下之Nadal ratio變化圖 (曲率半徑200 m)..........................................................................................................108 圖6-27 直軌高承載下第一輪軸組之橫向位移關係圖 (class 3)............................................................................................................109 圖6-28 直軌高承載下轉向架、車身之橫向位移關係圖 (class 3)............................................................................................................109 圖6-29 直軌高承載下第一輪軸組之垂向位移關係圖 (class 3)............................................................................................................110 圖6-30 直軌高承載下轉向架、車身之垂向位移關係圖 (class 3)..................110 圖6-31 直軌高承載下第一輪軸組之橫向位移關係圖 (class 6)............................................................................................................111 圖6-32 直軌高承載下轉向架、車身之橫向位移關係圖 (class 6)..................111 圖6-33 直軌高承載下第一輪軸組之垂向位移關係圖 (class 6)............................................................................................................112 圖6-34 直軌高承載下轉向架、車身之垂向位移關係圖 (class 6)..................112 圖6-35 彎軌高承載下第一.輪軸組之橫向位移關係圖 (class 3，曲率半徑3,500 m).................................................................................................113 圖6-36 彎軌高承載下第一輪軸組之橫向位移關係圖 (class 6，曲率半徑3,500 m)...........................................................................................................113 圖6-37 彎軌高承載下不同軌道等級之輪軸組橫向位移關係圖 (曲率半徑1,500 m).................................................................................................114 圖6-38 彎軌高承載下不同軌道等級之輪軸組橫向位移關係圖 (曲率半徑200 m)...........................................................................................................114 圖7-1 前半車體的轉向架之橫向加速度關係圖 (車速80 km/h).....................................................................................................120 圖7-2 TAP005橫向地表加速度歷程..............................................................120 圖7-3 TAP005垂向地表加速度歷程..............................................................121 圖7-4 TAP005橫向地表位移歷程..................................................................121 圖7-5 TAP005垂向地表位移歷程..................................................................122 圖7-6 考慮地震與軌道不平整下前輪軸組之橫向位移關係圖 (車速80 km/h).....................................................................................................122 圖7-7 考慮地震與軌道不平整下前輪軸組之垂向位移關係圖 (車速80 km/h).....................................................................................................123 圖7-8 四級地震輸入之Nadal ratio (車速80 km/h)........................................123 圖7-9 四級地震輸入之輪軸減重率 (車速80 km/h).....................................124 圖7-10 僅考慮橫向地震與軌道不平整下前輪軸組之橫向位移關係圖 (車速80 km/h)................................................................................................124 圖7-11 僅考慮橫向地震與軌道不平整下前輪軸組之垂向位移關係圖 (車速80 km/h)................................................................................................125 圖7-12 僅考慮垂向地震與軌道不平整下前輪軸組之橫向位移關係圖 (車速80 km/h)................................................................................................125 圖7-13 僅考慮垂向地震與軌道不平整下前輪軸組之垂向位移關係圖 (車速80 km/h)................................................................................................1265936819 bytesapplication/pdfen-US軌道車輛軌道不平整穩定度鋼輪磨平出軌彎軌地震railway vehicletrack irregularitystabilitywheelflatderailmentcurved trackearthquakethesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/61166/1/ntu-96-R94522529-1.pdf