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

利用分形和混沌理论对超精密切削和普通车削加工的表面轮廓进行了表征。通过对该方法的有效性研究，得到以下结论：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计算。在本研究的实验条件下，分形维数的值在1.1-1.5之间。该值随进给速度的减小而增大，并随切削材料的不同以及有无切削液而变化。2.提出了一种基于分形维数的切削表面轮廓建模方法。结果表明，阿尔马模型具有分形特征。研究了阿尔马模型的参数、分形维数与切削条件之间的关系。3.发现具有近似周期性轮廓的车削加工表面具有混沌特性，复杂轮廓的车削加工表面不是确定性波动，而是随机过程。研究表明，李雅普诺夫指数和关联维数的大小与刀尖圆弧半径、进给量和切削速度等切削条件有关。4.提出了基于径向基函数网络的切削表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.