Abstract: Distribution curve is the basis for evaluating the effect of gravity concentration.The shape of distribution curve can be expressed by the 4-order characteristic parameters including separation density,probable error,quartile skewness and tail state coefficient.The influence of particle size on the effect of gravity concentration can be decomposed into the influence of particle size on the shape parameters of distribution curve.Based on the distribution curve data of non-pressure three-product heavy medium cyclone at different particle sizes,the generalized skew-normal distribution model was adopted.It extracted the 4-order morphological parameters of distribution curve at different particle sizes of first coal stage and second stage respectively by using nonlinear regression method,revealing the basic law of the influence of particle size on the separation effect of non-pressure three-product heavy medium cyclone.The separation density first decreases and then increases with the increase of particle size.The probable error decreases with the increase of particle size.The skewness and tail coefficient approach 0 with the increase of particle size.That is,the larger the particle size is,the higher the separation accuracy is,the better the symmetry of the distribution curve is,the smaller the degree of the long tail is,and the closer the distribution curve is to the normal distribution.The mathematical model of separation density-particle size was established by combining power function and exponential function,the probable error-particle sizes mathematical model is constructed by using power function.The mathematical models of quartile deviation-particle size and tail coefficient-particle size are given for the first time in the form of power function.The interaction of density and particle size in gravity concentration process was unified into the generalized skew-normal distribution function based on quartile under the 4-order morphological parameters.And a high-precision density-particle size distribution surface mathematical model with the extensibility of model parameters was established to quantitatively analyze the interaction of particle size and density in various hydraulic classification and gravity concentration processes.It provides a general high-precision mathematical tool,which is of great significance to reveal the influence mechanism of particle size on separation.