Developments of Ultra-High-Speed Grinding Wheel Based on Fractal Analysis

超高速磨削要求研制新型陶瓷结合剂砂轮。在发展之际，首先必须设计砂轮的结构。然而，砂轮的结构不能很容易地使用传统的建模技术来描述，因为磨粒在砂轮表面的空间分布和它们的形态表现出高度的复杂性和不规则性。因此，本文引入分形几何的概念来表征无法用欧氏几何表达的砂轮形貌，研究表明，砂轮形貌是由磨粒与修整工具之间的运动相互作用而形成的不规则、随机的，可以用分形维数来定量表征。这一事实提醒我们，分形布朗运动（fBM）可以产生与真实的车轮形貌惊人的统计相似性。用fBm描述了各种人造车轮形貌，并与真实的车轮形貌进行了实际对比，证实了fBm在车轮结构几何造型中的作用，从而在充分的事实和观察的基础上，形成清晰的车轮结构设计概念。这方面的工作将继续进行下去，并将设计一个车轮结构的计算机辅助设计系统。

Developments of new vitrified bonded grinding wheels are required for the ultra-high-speed grinding. On the occasion of developments, a structure of the grinding wheel will have to be designed first thing. However, the structure of the wheel can not easily be described using traditional modeling techniques, because the spatial distribution of abrasive grains over the wheel surface and their morphology show a high degree of complexity and irregularity. Therefore, in this study fractal geometry was introduced for the purpose of characterizing the wheel topography which can not be expressed in terms of Euclidean geometry.Closely research revealed that the irregular and random wheel topography formedby the kinematic interaction between the abrasive grains and the dressing tool could be quantitatively characterized by means of fractal dimensions. This fact reminded us that a striking statistical resemblance to real wheel topography was producible by fractinal Brownian motions (fBm). Describing various artificial wheel topographies through the fBm and comparing them with the real wheel topographies practically, it was confirmed that the fBm would avail much in the geometric modeling of the wheel structure.On the sufficient basis of fact and observation, we could form the clear design conception of the wheel structure in consequence. This aspect will be continuously considered further and a computer aided design system of the wheel structure will be devised.