Probabilistic analysis of dynamic stability for milling process

Self-excited vibrations known as regenerative chatter arise in milling operations, causing excessive tool wear or breakage, along with poor surface finish on the machined workpiece. Consequently, it is critical to understand regenerative chatter and predict stability boundary for the milling process. Traditionally, stability analysis for milling processes is developed based on the assumption that parameters of the milling system are deterministic. However, in many cases, parameters of the milling system are uncertain. Successfully taking parameter uncertainty into account would increase reliability for modeling of chatter stability in milling. Considering impact of uncertain factors, this paper presents a practical method for probabilistic analysis of dynamic stability of the milling process. Dimension reduction method is applied to compute statistical moments of the limit state function. Saddlepoint approximation is employed to estimate probability density function, cumulative distribution function and, more specifically, reliability of the dynamic stability of the milling process. Finally, a discussion of the practical application of this method along with a detailed analysis to evaluate efficiency of the proposed method is presented.