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

超高速磨削需要开发新型陶瓷结合剂砂轮。在发展之际，必须首先设计砂轮的结构。然而，由于砂轮表面磨粒的空间分布及其形貌表现出高度的复杂性和不规则性，传统的建模技术很难对砂轮的结构进行描述。因此，为了刻画不能用欧几里得几何表示的砂轮表面形貌，本研究引入了分形几何的概念，研究表明，通过磨粒与修整工具之间的运动相互作用形成的不规则、随机的砂轮表面形貌可以用分维来定量表征。这一事实提醒我们，与真实车轮地形在统计上惊人的相似之处是由分形布朗运动(FBM)产生的。通过FBM对各种人造车轮地形的描述，并与实际车轮地形进行比较，证实了FBM在车轮结构几何造型中的应用，在充分的事实和观察的基础上，可以形成清晰的车轮结构设计概念。这一方面将继续得到进一步的考虑，并将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.