An updated model of stability prediction in five-axis ball-end milling

The intention of this paper is to present an updated model to predict stability limits of five-axis ball-end milling. Two-degree of freedom five-axis ball-end milling system in consideration of regenerative effect and helix angle is first concluded into a delay differential equation (DDE) with time-varying coefficients. As the time period being carved up evenly into a certain number of elements, the discrete map of system response is determined with the assistance of generalized precise integration method (GPIM). Then, in a single tooth passing period, the analytic cutter-workpiece engagement (CWE) is extracted by an intersection of spatial surface technique to ascertain the instantaneous cutting angles. Taking the advantage of these angles, the transition matrix denoting the given machining state is established to predict the process stability. The validity of the predictive model is verified in a five-axis CNC machine tool by close accordance with the experimental results. Lastly, a set of comparisons and discussions are developed to demonstrate the feature of this updated predictive model.