Fractal Estimation of Flank Wear in Turning

A novel fractal estimation methodology, that uses—for the first time in metal cutting literature—fractal properties of machining dynamics for online estimation of cutting tool flank wear, is presented. The fractal dimensions of the attractor of machining dynamics are extracted from a collection of sensor signals using a suite of signal processing methods comprising wavelet representation and signal separation, and are related to the instantaneous flank wear using a recurrent neural network. The performance of the resulting estimator, evaluated using actual experimental data, establishes our methodology to be viable for online flank wear estimation. This methodology is adequately generic for sensor-based prediction of gradual damage in mechanical systems, specifically manufacturing processes. @S0022-0434~00!02401-1# Online damage prediction and estimation are essential for enforcing real-time control of mechanical systems, particularly manufacturing processes. Tool wear, especially flank wear, adversely impacts the accuracy and surface finish of machined products @1#. Conventionally, flank wear is quantified by the height of the flank wear land hw , and hw.0.018 in. is considered to be a good indicator that the tool is fully worn. In many industrial scenarios it takes between 5 to 20 min for a cutting tool to wear out. A viable continuous flank wear estimator must accurately estimate values between 0.0‐0.018 in. over the above-specified time span. Accuracies of <10% of the total range are desirable for practical applicability because the continuous flank wear estimates may be directly used to enforce geometric adaptive control, plan tool changes, and control tool wear rate to meet the surface integrity and other product specifications. Comprehensive solution to flank wear estimation is still elusive @2#. The earlier flank wear estimation schemes were based on either ~i! analytical models providing lumped dynamics differential equations @3,4#, ~ii! traditional empirical models using dimensional principles, ~iii! observes based on Kalman filters@5‐8# ,o r ~iv! neural networks @9,10#. The available analytical models do not capture all the understood physical phenomena. Further, analytical model-based estimation is mathematically intractable. As a result, the estimates are usually off by over 50‐100%. The exponents and coefficients of traditional empirical models are extremely sensitive to the assumed structure of the relationships and variations of process parameters p I . Thus, the accuracy of empirical model-based estimators is very low. The accuracy of observers, without some form of adaptation, is, at most, that of the underlying analytical model. Even with adaptation, the estimates are sensitive to the model structure and hence are not robust. Although observers can perform better than analytical models, empirical models and some neural networks, most of them explicitly or implicitly assume the sensor signals to be predominantly harmonic with additive contaminants. Furthermore, they use sensor signals sampled at low-frequencies to fit Kalman filter estimators, thereby ignoring the overall variations in machining process dynamics captured by the measured signals, henceforth called machining dynamics ~see Sec. 2!. These simplifications adversely affect the observer performance. The knowledge of the exact structure of the underlying dynamical system is not necessary for neural network estimation. However, as the estimator development is entirely data-driven, rich and appropriately processed signals are necessary for neural network training. The available neural network architectures are extremely complicated, entail significant training overhead, and are not guaranteed to converge. The challenge is to obtain accurate algorithmically simple neural network estimators, possibly with guaranteed performance. This can be achieved from the understandings of the heretofore ignored relationships connecting machining dynamics and flank wear. The main objective of the research reported in this paper is to develop a methodology for accurate and algorithmically simple neural network estimation by exploiting the properties of the underlying machining dynamics and its interactions with flank wear dynamics. Our new methodology, called fractal estimation ,i s driven by the results of our previous research, where we have have clearly established that machining dynamics exhibits lowdimensional chaos @11# under normal operating conditions. Since fractal estimation relies on the structural information regarding the chaotic attractor of machining dynamics, it was found to be more robust compared with those developed using the statistical signal properties alone. We employ chaos theory @12‐14# to educe information on machining dynamics from sensor signals. We anticipate that our methodology and the reported results will spur further research on paradigms based on combining chaos theory and neural networks for flank wear estimation and other condition monitoring problems in manufacturing processes and mechanical systems. This paper is organized as follows: the main motivation for this work is provided in Sec. 2, the overall methodology is outlined in Sec. 3, and finally, the results and the pertinent discussion are presented in Sec. 4.