ANALYSIS OF SURFACE FINISHED BY ULTRA-PRECISION DIAMOND CUTTING BASED ON THEORY OF COMPLEX SYSTES

基于复杂系统理论，对超精密切削得到的表面轮廓进行了分析。镜面轮廓由刀具进给和刀尖半径定义的理论轮廓和由晶界步进、位错等随机因素产生的不规则轮廓组成。为了从表面轮廓中分离出单个因素的轮廓并了解其特征，我们应用了小波变换技术和混沌理论。通过对有效性的调查，得到了以下几点评价：1。提出了小波系数的平均值作为表征超精密切削表面的新参数。用小波变换评价表面轮廓的有效性。基于复杂系统理论，对小波变换后的轮廓进行了分析。通过分析三维相空间重建的吸引子模式和Lyapunov指数，发现几种剖面具有混沌特征。从1级到-8级的小波分量具有混沌特性。从李雅普诺夫谱的角度看，-4和-5能级的谱线表现出较强的混沌特征。结果表明，超精密切削面轮廓由周期、随机和混沌三种波动分量组成。期望通过对各个小波剖面的分析，可以了解切割表面的未知特征。

The surface profiles obtained by an ultra-precision cutting were analyzed based on theory of the complex systems. The mirror surface profiles consists of the theoretical profile defined by feed and nose radius of the tool and the irregular profile generated by random factors such as the step of grain boundary, the dislocation and so on. In order to separate the profiles by the individual factors from the surface profile and understand the characteristics, we applied the technique of the wavelet transform and the theory of the chaos. Through the investigation of the validity, the following remarks were obtained.1. The average of the wavelet coefficients was suggested as a new parameter for the characterization of the ultra-precision cut surface. The validity of the method to evaluated the surface profile by applying the wavelet transform.2. The wavelet-transformed profiles were analyzed based on the theory of the complex systems. It was found that several profiles had the chaotic characteristics by analyzing the pattern of attractor reconstructed in three-dimensional phase space and Lyapunov exponents. The wavelet components from level -1 to level -8 have the chaotic characteristics. Particularly, the profiles of level -4 and -5 presented the strong chaotic characteristics from point of view of Lyapunov spectrum.3. It was identified that the profiles of the ultra-precision cut surface consisted of three fluctuating components of periodic, random and chaotic ones. It is expected that an unknown characteristics of cut surface can be understood by analyzed the individual wavelet profiles.