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%.
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