STUDY ON EVALUATION OF ULTRA-PRECISION CUT SURFACE AND PERFORMANCE BY FRACTAL AND CHAOS CHARACTERIZATION

采用基于分形和混沌理论的新方法对超精密切削和常规车削加工得到的表面轮廓进行了评价。通过对有效性的调查，得到了以下几点评价：1。采用变分法对金刚石刀具加工表面轮廓的分形维数进行了评价。在本研究的实验条件下，分形维数的取值范围为1.1 ~ 1.5。该值随着进给速率的降低而增加，并根据工作材料和有无切削液而变化。提出了一种基于分形维数概念的切削面轮廓建模新方法。结果表明，ARMA模型具有分形特征。研究了ARMA模型参数和分形维数与切削条件的关系。研究发现，具有近似周期轮廓的车削面具有混沌特性，具有复杂轮廓的车削面不是确定性波动而是随机过程。李雅普诺夫指数的取值和相关维数与切削条件（如机头半径、进给速度和切削速度）有关。提出了一种基于径向基函数网络的切削面轮廓混沌建模方法。模型得到的表面轮廓与实测轮廓基本吻合。模型的预测性能与模型阶数有关。

The surface profiles obtained by an ultra-precision cutting and a conventional turning were evaluated with a new method based on Fractal and Chaos theories to characterize the cut surface. Through the investigation of the validity, the following remarks were obtained.1.The fractal dimensions of the surface profiles machined with a diamond cutting tool were evaluated by using the variation method. The values of the fractal dimensions are in a range of 1.1-1.5 under the experimental conditions of this study. The values increase in a decrease of the feed rate rate and also change depending on the work materials and with or without the cutting fluids.2.A new approach for modeling the cut surface profiles was suggested based on the concept of the fractal dimension. It was found that the ARMA model had the fractal characteristics. Three factors, the parameters and the fractal dimensions of ARMA model and the cutting conditions, were related.3.It was found that the cut surface by turning with approximately periodical profile possess the chaotic characteristics and the cut surface with a complicated profile was not the determinative fluctuation but the stochastic process. The values of Lyapunov exponents and the correlation dimensions were associated with the cutting conditions such as the nose radii, the feed rate and the cutting speed.4.The chaos modeling approach for a cut surface profile was presented by using the radial basis function network. The surface profile obtained by the model was approximately coincident with the measured profile. The prediction properties of the model was associated with the model order.