摘要：为了研究重质碳酸钙颗粒在超细粉碎过程中的分形维数以及多维分形特征与研磨时间的关系,对重质碳酸钙颗粒进行湿法研磨,提取不同研磨时间的颗粒,测量其粒度分布,并利用单一分形法和多维分形法计算样品的分形维数,建立分形维数与研磨时间的拟合曲线。结果表明:相对于单一分形法,多维分形法更能准确地描述颗粒的尺寸分布状态;通过分形维数与研磨时间拟合曲线中的峰值,可以判断颗粒的最佳研磨时间范围,这与实验中重质碳酸钙颗粒样品的最佳研磨时间60 min相符,从而优化颗粒超细粉碎过程中的研磨时间参数,减少能源消耗。

关键词：重质碳酸钙；超细粉碎；分形维数；单一分形；多维分形

Abstract： To investigate the fractal dimension of ground calcium carbonate particles and the relationship between multifractal characteristics with grinding time， the particle size distribution at different grinding time was studied in the wet ultrafine ball-stirring grinding system. The fractal dimension of samples was computed by the methods of single fractal and multifractal， and fitted curves of fractal dimension and grinding time were established. The results show that the particle size distribution can be described more accurately by the multifractal method comparing with the single fractal method. The best grinding time can be determined by the peak value of the fitted curves of fractal dimension and grinding time， which is consistent with the best grinding time of 60 min about the ground calcium carbonate sample in the experiment. The parameter of grinding time in the process of particle ultrafine can thus be optimized and grinding energy consumption be reduced. 

Keywords: ground calcium carbonate； ultrafine grinding process； fractal dimension； single fractal； multifractal