分配曲线是重力选煤效果评定的基础，分配曲线形态可用分选密度、可能偏差、四分位偏度、尾态系数4阶特性参数表示，粒度对重选效果的影响可分解成粒度对分配曲线形态参数的影响。以无压三产品重介旋流器在不同粒度下的分配曲线数据为基础，采用基于四分位数的广义正态分布分配曲线数学模型，利用非线性回归方法，分别提取了精煤段和中煤段不同粒级下分配曲线的4阶形态参数，揭示了粒度对无压三产品重介旋流器分选效果影响的基本规律：分选密度随粒度增大先减小后增大，可能偏差随粒度的增大而减小，偏度与尾态系数随粒度增大而趋近于0。即粒度越大，分选精度越高，分配曲线对称性越好，长尾程度越小，分配曲线形态越接近于正态分布。采用幂函数与指数函数相结合的形式，构建了分选密度-粒度数学模型；采用幂函数形式，构建了可能偏差-粒度数学模型；采用幂函数形式，给出了四分位偏差-粒度、尾态系数-粒度数学模型。在4阶形态参数下将重选过程中密度、粒度相互影响统一在基于四分位数的广义正态分布函数中，建立了一个模型参数可扩展的高精度的密度-粒度双变量分配曲面数学模型，为量化分析各类水力分级和重力分选过程粒度密度的相互影响，提供一个通用的数学工具，对于揭示粒度对分选的影响机理具有重要意义。

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.

1 分配曲线和分配曲面数学模型

2 分配曲线数据及处理方法

3 粒度对分配曲线形态参数的影响

4 分配曲面数学模型构建与优化

   4.1 基于四分位数的密度-粒度双变量分配曲面数学模型构建

   4.2 密度-粒度双变量分配曲面数学模型优化

   4.3 曲面与曲线形态特性参数比较

   4.4 宽粒级分配曲面形态

5 结论