Fractal Estimation of Flank Wear in Turning. Part 1: Theoretical Foundations and Methodology.

Abstract : In this two-part paper, a novel scheme of sensor-based on-line cutting tool flank wear estimation, called fractal estimation is developed, implemented and evaluated. This paradigm is unique in the sense that we extract fractal properties of sensor signals. The metric invariants of the sensor signals called fractal dimensions are related to the instantaneous flank wear using a recurrent neural network to implement a fractal estimator. The performance of the fractal estimator, evaluated using actual experimental data, establishes this scheme as a viable flank wear estimation paradigm. This methodology is general enough to be applied to many classes of estimation problems related to several manufacturing processes. We have developed the necessary theoretical formalisms and obtained implementation experiences through the research on tool wear monitoring in turning. The feature extraction methods used in this work are vital to the image analysis research and form the foundation for our future work. In this first part, theoretical foundations leading to the development of the fractal estimator are presented. New schemes of wavelet transform-based signal separation and fractal dimensions based feature extraction are described in detail.