Efficient approximation of stochastic turning process based on power spectral density

Abstract In this study, we utilize stochastic cutting force to enhance the existing 1-degree-of-freedom turning model. We adopt a stochastic model to address the stochastic resonance phenomenon occurring near stability boundaries. Additionally, we introduce a simplified stochastic model with additive noise only. Our investigations reveal that, with the recommended noise intensity of 0.1% to 1%, there is no significant difference in the stability charts and mean square characteristics between the two models. As a result, we can bypass time-consuming numerical methods, as the simplified model offers an analytical approach to compute variance based on power spectral density (PSD). By combining efficient techniques such as D-separation to determine stability boundaries and the PSD-based variance calculation, we construct a heatmap that clearly outlines dangerous stochastic resonance regions within the stable domain.