基于分形理论的PIM颗粒表面特性及机理研究

【作者】 邹娜娜；

【导师】 郑洲顺；

【作者基本信息】 中南大学 ， 应用数学， 2009， 硕士

【摘要】 粉末注射成形是塑料注射成形与粉末冶金技术相结合而发展起来的一种新型的近净成形技术。本文在综述粉末注射成形的原理、特点、研究现状及分形理论应用的基础上,利用分形理论对粉末注射成形中粉末颗粒表面分形特性、热传导、接触载荷及孔隙率进行研究。首先,分析粉末注射成形过程中颗粒的分形特性,给出粉末注射成形坯剖面颗粒面积分形维数的计算方法和剖面颗粒的各向异性局部面积占有率；基于多孔介质热传导的计算公式,推导出粉末颗粒和粘结剂串并联时粉末注射成形坯各向异性有效导热率的表达式,及其无量纲有效导热率与剖面颗粒面积分形维数的关系。以铁粉成形坯的相应参数进行计算,得到成形坯有效导热率随着剖面颗粒面积分形维数的增大而增大。其次,用Weierstrass-Mandelbrot分形函数表征粉末颗粒表面轮廓的分形特性,在经典M-B模型的基础上,根据Hertz接触理论,借助于弹性和塑性临界转化面积,分析粉末注射成形过程中粉末颗粒与模具以及颗粒间接触时的弹塑性变形过程,进而推导出当颗粒表面发生弹性、弹塑性、塑性变形等不同接触状态时粉末颗粒表面真实接触面积和接触载荷的计算公式。最后,借助多孔介质孔隙结构的分形理论分析了粉末注射成形坯孔隙结构的分形特性,根据成形坯中孔隙尺寸的分布密度函数,推导粉末注射成形坯孔隙率的表达式,并且得出粉末注射成形坯的孔隙率随着孔隙分布分形维数的增加而减小的结论；用粉末注射成形坯的孔隙体积和总体积求孔隙率的方法,得到带有双重分形维数的粉末注射成形坯孔隙率的计算公式。更多还原

【Abstract】 Powder injection molding is a new near-net-shape technology of combining plastic injection molding and powder metallurgy. In this paper, on the basis of the overview of the principle of powder injection molding, characteristics, research status and application of fractal theory, the fractal properties of powder particle, heat conduction, contact load and porosity are studied by fractal theory in powder injection molding.Firstly, by analyzing the fractal characteristic of compacts in PIM, algorithm of fractal dimension of its section particle area is presented and anisotropic local area share of section particle in compacts with fractal dimension is counted. Then, based on the formula of thermal conductivity in porous media, the anisotropic effective thermal conductivity of compacts and its dimensionless ones are calculated when powder and binder are in series or parallel. Thus, taking Fe compacts for example, the results show that the effective thermal conductivity is enlarger with the increase of fractal dimension.Secondly, the fractal characteristic of powder particle surface in powder injection molding is represented by the Weierstrass-Mandelbrot fractal function. Then, based on the theory of contact mechanics, the process of elastic-plastic deformation as particle contacts with particle or mold is analyzed by means the critical areas of elastic and plastic. So, the real contact area and contact load for particles surface in powder injection molding are calculated, when powder particles are in states of elastic, elastic-plastic and plastic.Finally, the fractal characteristics of pore structure in powder injection molding are analyzed by fractal theory of them in porous media. According to the distribution density function of pore size, the equation of the porosity of compacts in powder injection molding is given. And we can gain that the porosity of compacts is decreasing with the increase of pore distributed fractal dimension. While, the porosity formula with a dual-fractal dimension in powder injection molding is gained using pore volume and total volume.更多还原