本研究提出一種基於〝輪/軌接觸幾何合成〞所發展出適用於鋼輪/鋼軌軌道系統之簡易評估方法，可用於車輪與鋼軌輪廓設計初期優劣評估，無需建立複雜之數值模擬模型及繁複之現場測量。此簡易評估方法使用車輪與鋼軌輪廓方程式及輪/軌接觸幾何合成方法，探索每一側車輪與鋼軌之間所有可能的接觸位置，藉由輪/軌接觸點分析輪軸運動之動態軌跡線；依據動態軌跡線變化量，可得知輪軸於車輪與鋼軌接觸踏面變化時之運動行為；若輪/軌接觸踏面位於瞬時旋轉中心軌跡線(Centrode)變化量較小之區域，則可獲得較佳的乘坐舒適度，亦可定義為輪/軌接觸踏面甜蜜點(Sweet spot)範圍，作為乘坐舒適度之簡易評估指標。在本研究中，參考G1曲線連續性之機械製圖方法設計輪廓繪製機構，及描述可靠之現行車輪與鋼軌輪廓，進而透過機械分析法推導其輪廓方程式；亦將推導所得之車輪與鋼軌輪廓方程式，轉換為可輸入電腦數值控制工具機之G代碼(G-Code)，採用刀具路徑模擬軟體進行驗證。且本研究為瞭解台灣高速鐵路(THSR)現行之新幹線車輪匹配其他鋼軌是否可提供更佳之乘坐舒適度，應用新幹線車輪匹配UIC60和JIS60二種鋼軌輪廓作為案例研究；研究結果顯示，新幹線車輪匹配UIC60鋼軌比新幹線車輪匹配JIS60鋼軌具有更寬的甜蜜點接觸範圍，使得軌道車輛於彎道行駛時，新幹線車輪可更有效地與UIC60鋼軌匹配。最後，將新幹線車輪、UIC60鋼軌及JIS60鋼軌之輪廓方程式，應用輪/軌接觸幾何合成方法研究輪/軌接觸點位置，導入軌道車輛數值模擬軟體進行分析，及比對不同輪/軌配對產生之車廂垂向及側向振動響應；數值模擬分析結果顯示，當軌道車輛於彎道行駛時，新幹線車輪匹配UIC60鋼軌，無論垂向或側向振動加速度皆小於新幹線車輪搭配JIS60鋼軌，並提供更好的乘坐舒適度。此外，將新幹線車輪匹配UIC60鋼軌及JIS60鋼軌之垂向及側向接觸力用於計算Nadal脫軌係數(Q/P值)；其結果顯示，無論新幹線車輪匹配UIC60鋼軌或JIS60鋼軌，其Nadal脫軌係數(Q/P值)最大值皆約0.24，雖皆符合各國高速鐵路脫軌係數標準。綜合上述研究分析結果與簡易評估方法具有相同之結果，證明動態軌跡線方法可適用於簡易評估乘坐舒適度，進而作為一種輪/軌適用性評估簡易評估方法。

This study proposes a simplified methodology to assess the initial design of the wheel/rail contact profile for the railway system. This method does not require complicated simulation models or measurements, but simply applies wheel/rail contact geometry synthesis to explore all possible contact positions between the wheel and the rail on either side of the track. In addition, the dynamic motion of the wheelset obtained from the obtained wheel/rail contact points is analyzed. Based on the synthesis results, moving and fixed centrodes of the wheelset motion are determined. According to the smoothness of the moving and fixed centrodes, the wheelset motion behavior in response to the change in the tread contact of wheel/rail is determined. The wheel/rail contact area is located in the most degree of smoothness of the moving and fixed centrodes that will obtain a better ride comfort than other contact area, which is further applied to define the range of the “sweet spot” to derive a simplified assessment of ride comfort. Herein, a mechanical drawing method with reference to G1 continuity is used for drawing the mechanism in order to describe a wheel/rail contact profile and to derive a profile equation by mechanical analysis. The wheel/rail contact profile equation is then converted into the G-Code equation, which can be input to the computer numerical control machine to improve its practicality. The Taiwan High Speed Rail (THSR) uses the Shinkansen standard wheel profile. It is generally discussed whether the UIC60 rail, which is widely used in the domestic railway business, provides a better degree of comfort than the existing JIS60 rail used in the THSR system. The Shinkansen wheel contact conditions with the UIC60 rail and the JIS60 rail are analyzed and applied in the contact geometry synthesis. The results show that the Shinkansen wheel in contact with the UIC60 rail is more effective because the UIC60 rail has a wider range of contact sweet spots than the JIS60 rail for rolling stock running on a curved track. Finally, the Shinkansen wheel profile and each rail profile equation are applied in simulation software for a vehicle/track system under different wheel/rail match conditions. This is done to verify whether the contact geometry synthesis can be used to assess the ride comfort of a vehicle and can serve as a simplified assessment method for wheel/rail matching. A dynamic simulation program with parameters adjusted to fit the experimental values is used to compare the results. The results indicate that both the vertical and lateral vibration acceleration responses of a carbody with the Shinkansen wheels in contact with the UIC60 rail are lower than those with the JIS60 rail. Furthermore, the UIC60 rail provides a better degree of ride comfort of a carbody equipped with the Shinkansen wheels. In addition, the vertical and lateral contact forces of the Shinkansen wheels in contact with the UIC60 rail and the JIS60 rail are used to calculate the Nadal derailment coefficient (Q/P ratio); it is approximately 0.24 for both wheel/rail contact types, which meets the international high-speed rail derailment criteria. The results of the numerical analysis and the proposed method agree with each other. Therefore, the wheel/rail contact geometry synthesis can be used to assess the motion behavior of rolling stock and to derive a simplified index for ride comfort.

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