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For studying the metal’s three-dimentional platic flow mechanism along the longitudinal direction and lateral direction in rail universal rolling, the relationship between the metal flow volume and the elongation coefficient of different parts of rail was proposed, then the elongation coefficient of different parts of rail were derived on the base of the law of volume constancy, then the flow volume between different parts of rail were obtained. Moreover, the integrated deformation influence factor was introduced into this model to express the influence of the spread coefficient and the reduction coefficient of different parts of rail on the metal’s three-dimentional plastic flow. Compared with the experimental results, the prediction error of analytical model for elongation coefficient is less than  5%, and the the prediction error of analytical model for flow volume is not greater than  16%. Introduction The universal rolling method has been applied in rail rolling for 40 years. At present, the process of the rail universal rolling has been studied by FEM and experimental methods generally. In the Reference [1-3] , the process of rail universal rolling was studied by FEM software and the rolling experiments, then the stress distribution and deformation law of rail universal rolling were analyzed. In the Reference [5] , the spread model of the base and head of rail in rail rough rolling was proposed on the base of existing empirical functions. In the Reference [6, 7] , the spread and elongation law of heavy rail universal rolling were analyzed by the nerve network method based on a number of measured data. As mentioned above, these analytic model for calculating the spread and elongation of rail universal rolling were all derived by the empirical equation directly or indirectly, and the metal’s lateral flow between the base of rail, the head of rail and the waist of rail were neglected. However the volume of metal’s lateral flow will influence the cross-section profile of outgoing workpiece and the elongation coefficient of the base of rail, the head of rail and the waist of rail. Therefore, the elongation coefficient and the lateral flow of different parts of rail interrelate with each other. Consequently, if an accurate mathematical model can be built to predict the volume of metal’s lateral flow and the elongation coefficient of different parts of rail, a rational rolling schedule and processing parameters for rail universal rolling could be preset to improve the cross-section size precision and decrease the degree of curvature and the residual stress of finished rail effectively. So the performance of rail can be improved greatly based on a precise mathematical model of three-dimensional plastic flow. Building the Mathematical Model of Plastic Flow in Rail Universal Rolling There are significant differences between the pass profile and cross-section profile of the base, head and waist of rail, and the deformation mechanism of different parts of rail are quite distinct. So the elongation coefficient of the base, head and waist of rail are different generally, there are metal’s lateral flow existing in different parts of rail to reduce the discrepancy of elongation coefficient for 2nd Annual International Conference on Advanced Material Engineering (AME 2016) © 2016. The authors Published by Atlantis Press 444 keeping the deformation’s compatibility and consistency. The following equations can be proposed according to the volume constancy .

A Research on the Metal's Three-dimentional Plastic Flow Mechanism in Rail Universal Rolling