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

超高速磨削要求开发新型陶瓷结合剂砂轮。在发展的场合，首先要设计砂轮的结构。然而，由于磨料颗粒在砂轮表面的空间分布及其形态表现出高度的复杂性和不规则性，利用传统的建模技术很难描述砂轮的结构。因此，本研究引入分形几何来表征无法用欧几里得几何表示的车轮形貌。深入研究表明，磨料颗粒与修整工具的运动相互作用所形成的不规则、随机的砂轮形貌可以用分形维数定量表征。这一事实提醒我们，分形布朗运动（fBm）在统计上与真实的车轮形貌有着惊人的相似之处。利用fBm对各种人工车轮形貌进行了描述，并与实际车轮形貌进行了比较，证实了fBm对车轮结构的几何建模有很大的帮助。在充分的事实和观察的基础上，我们可以形成清晰的车轮结构的设计概念。这方面将继续深入研究，并设计出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.