Convergence Analysis of the Multi-Frequency Approach around a Variable-Helix Instability Island

摘要

Variable helix tools are known to have unusual regenerative chatter stability behaviour that can be difficult to predict. This paper explores the convergence and accuracy of a multi-frequency approach (MFA) to stability prediction. An island of instability was identified using the MFA, and the stability boundary was compared to predictions from the semi-discretisation method (SDM) and experimental data. A convergence study for the MFA and SDM showed that the SDM approach was very slow to converge for this specific case, in contrast to its performance at higher spindle speeds. The MFA approach exhibited fast convergence which led to orders of magnitude improvements in the computational speed of the predictions.