列車運轉時空特性分析

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Title:	列車運轉時空特性分析
Other Titles:	The Analysis of Train Operation Characteristics
Authors:	鍾志成
Contributors:	淡江大學運輸管理學系
Keywords:	列車運轉模擬;平均加速度;煞車摩擦係數;Train Operation Simulation;Average Acceleration Rate;Braking Friction Coefficient
Date:	2000-10
Issue Date:	2013-04-10 15:34:33 (UTC+8)
Abstract:	列車運轉模擬的運算基礎大多係根據時間或空間的推進，假設列車在一小段時間或空間距離內所受的淨力為定值，再以運動學基本公式來計算列車的時間、空間及速度的關係，以此種方式來模擬列車的運轉動態基本上係一近似解，其誤差隨時間或空間增量的大小而定，本篇論文考慮列車加速度隨速度而變的特性，提出以速度推進來模擬列車運轉動態的理論基礎，此一方式可精確描述列車的運轉行為，而不受速度增量的影響。本篇論文同時將介紹以時間、空間及速度為基礎的三種不同概念之列車平均加速度，並根據其物理及數學性質提出三項定理，定理一說明以時間為基礎的列車平均加速度配合簡單的運動學基本公式可精確計算列車的行駛時間；定理二說明以空間為基礎的平均加速度配合簡單的運動學基本公式可精確計算列車的行駛距離；定理三說明三種平均加速度相等的充分及必要條件。台鐵在計算列車緊軔時間及緊軔距離時採用的閘瓦平均摩擦係數公式係取材自日本鐵路，本篇論文將根據定理一及定理二來證明該公式，以便使用者能理解該公式的原理。 Traditional train operation simulation is usually based on the increments of time or space, while assuming the force acts on the train is constant during each simulation step. The basic kinematic equations are then applied to calculate the relationships among time, space, and speed. The train dynamics resulted from such approach is an approximate solution, where the error depends on the magnitude of time or space increment. Since train acceleration force is a function of speed, a speed increment approach for train simulation is thus proposed in this paper. By using integration and change of variable, train dynamics can be precisely determined. In analyzing train operation, sometimes it may be necessary to compute the average acceleration rate. This paper introduces three different concepts of average acceleration rates, including time-average, space-average, and speed-average accelerations. Based on their physic and mathematic characteristics, three theorems are developed in this paper. Theorem 1 indicates that plugging the time-average acceleration into the basic kinematic equation can precisely determine train traveling time, while theorem 2 states that the space-average acceleration can be used to precisely calculate train traveling distance. The necessary and sufficient conditions for these three average accelerations being identical are illustrated in theorem 3. The average coefficients of braking friction that Taiwan Railway Administration used to calculate train braking time and braking distance are originally from Japan Railway without any proof. These formulas can be easily proved via theorem 1 and 2, and are given at the end of this paper.
Relation:	新世紀軌道運輸國際學術研討會論文集Proceedings of the International Conference on Rail Transportation of New Century，頁255-266
Appears in Collections:	[Graduate Institute & Department of Transportation Management] Proceeding

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