Reliability of chatter stability in a turning tool-workpiece system

Abstract

The chatter prediction in orthogonal machining is performed by generating stability lobe diagrams (SLDs) using the measured structural parameters of the machining system. Due to measurement inaccuracies and uncertainties or variations in structural parameters, the probability of stability must be accounted for to predict chatter accurately. The reliability study of dynamic structural systems analyses the probability of turning process stability, which is computed by formulating a probability model. Structural parameters of the tool-workpiece system are considered as random variables with mean value and standard deviation. SLDs for a turning chatter model with a rigid and flexible workpiece are generated. The first-order reliability methods are employed to solve the reliability model by expanding the limit state equation using Taylor series expansion, neglecting higher-order terms. For computing the reliability index of the turning chatter model, the advanced first-order second-moment method (AFOSM) is employed along with the Hasofer-Lind linear mapping method. Machining experiments are carried out to validate SLDs obtained through the reliability study. The reliability method using AFOSM is found to provide a more reliable depth-of-cut for any spindle speed, depicted through reliable stability lobe diagram (RLD), when compared to the conventional SLDs. The proposed reliability-based analysis reveals that the stable depth of cut for tool–rigid and flexible workpiece systems is 8% and 21% lower, respectively, than the critical values predicted by conventional SLDs. To validate these results, machining tests are conducted, and the findings show that the reliability-based SLDs are 90% accurate in predicting stable and chatter conditions. Overall, the proposed method provides a strong framework for improving chatter prediction when parameter uncertainty exists.