本研究主要推導軌道車輛脫軌係數，藉以探討在不同的車輛自由度參數考慮下，獲得一接近實際狀況下的脫軌準則，亦即一脫軌係數公式；並可在營運車輛上佈置感測器，量測所需之參數即可獲得脫軌係數值。在推導脫軌係數的過程中，結合輪重減載率與前人的脫軌係數推導方式，並且考慮列車動力振動分析下，藉由各剛體釋放不同的自由度以建立運動方程式，此時的自由度包含側滾角、浮沉、及側移；最後在輪對的分析上，在臨界脫軌時，輪軌接觸面會有四種不同的接觸點位置情況來描述脫軌的情形，以及在爬軌脫軌與跳軌脫軌的不同脫軌行為下，分析輪軌接觸間的垂向力與橫向力平衡，來獲得脫軌係數與不同參數之關係。 接著數值模擬的部分，利用LS-DYNA建立單一輪對與軌道的有限元模型模擬真實跳軌脫軌行為，並輸出脫軌係數公式中所需之參數值，代入本論文所提之脫軌係數公式後，求得脫軌時的脫軌係數臨界值，發現當輪重減載的情況偏向輪緣貼靠之車輪時，臨界值越小；而摩擦係數與輪緣角的改變，並不會影響臨界值變化。 ;This study derives formulas about derailment quotients of train to investigate derailment criterions that can response the real conditions by different parameters. Then, it would be obtained on-line derailment quotients on in-situ testing by using these formulas. The computational theory was developed by considering the wheel unloading rates and theories of derailment quotients as well as vehicle system dynamics. To establish the Equations of Motion by vehicle system dynamics, releasing the degrees of freedom including horizontal movement, bounce, and roll on the rigid bodies is needed. In addition, there are four conditions about different positions of contact points at wheel-rail contact area at the derailment impending instant. Moreover, this theory separates two different types of derailment, which is climbing derailment and lifting derailment, to analyze the wheel-rail contact forces balance, including lateral and vertical contact forces, and obtain the relationship of derailment quotients and parameters of mechanical factors. On the part of numerical simulation, a FEM model which is including one wheelset and two rail tracks is built by using LS-DYNA software to simulate the behavior of lifting derailment and obtain the limits of derailment quotients. Numerical examples demonstrate that, the larger the wheel unloading rates at the flange contact wheel are made, the smaller the limits of derailment quotients are. The variation of friction coefficients and flange angles cannot make the limits of derailment quotients obvious change.