A sequential greedy search algorithm with Bayesian updating for testing in high-speed milling operations

This paper describes a probabilistic greedy search optimization algorithm for stability testing in high-speed milling. The test parameters (i.e., the experiment setup decisions) consist of the axial depth of cut and the spindle speed. These parameters are selected to maximize the expected value of profit using a greedy search approach (an approach that maximizes the expected value of each stage one step at a time). After a test is performed, Bayesian updating is applied to determine the posterior distribution of stability. The algorithm is then repeated to identify a new test point. The motivation for this work is that, while deterministic models for milling stability prediction are available, uncertainty in the inputs always exists. In this study, it is assumed that the tool point frequency response function, which is required for stability lobe diagram development, is unknown. Therefore, the probability of stability over the selected axial depth-spindle speed domain must be determined experimentally. The greedy search algorithm identifies the maximum expected value of profit within the selected domain, where profit is determined from the product of the profit function and the stability cumulative distribution function, referred to as the probability of stability. This optimal point is then tested to evaluate stability. Whether stable or unstable, the results are used to update the probability of stability. A stable test updates all axial depths smaller than test depth to be stable at the selected spindle speed, while an unstable test specifies that all axial depths above the test depth are unstable. After updating, a new test point is selected by the greedy search algorithm and the process is repeated. This select/test/update sequence is repeated until a preselected stopping criterion is reached. This paper presents both numerical results and experimental validation that the optimization/updating approach quickly converges to the well-known stability lobe behavior described in the literature. However, in this probabilistic technique the issue of uncertainty is also addressed and results can be obtained even if no information about the dynamic system is available.