Chatter reliability prediction of turning process system with uncertainties

• We model the chatter reliability model of tuning system with uncertainties.
• The reliability probability was calculated using the FOSM method, fourth moment.
• Reliability lobe diagram (RLD) is proposed to identify the chatter vibration.

In this paper, reliability analysis of dynamic structural system is introduced into chatter vibration prediction of a turning process system. Chatter reliability is defined to represent the probability of stability (no chatter occurs) for a turning process system. Probability model (reliability model) of chatter vibration is established to predict turning chatter vibration, in which structural parameters m, c, k and spindle speed Ω are considered as random variables. Choosing chatter frequency ωc as an intermediate variable, reliability model is developed from a model impossible to solve to a new model related to chatter frequency, and the new model can be solved. The first-order second-moment, fourth moment method are adopted to solve the turning process system reliability model and obtain the reliability probability of the system. An example is used to demonstrate the feasibility of the proposed method. The reliability probability of turning chatter system was calculated using the FOSM method, fourth moment and compared with that calculated by Monte Carlo simulation method. The results using the three methods were consistent. Reliability lobe diagram (RLD) is proposed to identify the chatter and no chatter regions for chatter prediction instead of stability lobe diagram (SLD). Comparing with the traditional SLD method, chatter reliability and RLD can be used to judge the probability of stability of turning process system. The RLD and the index of chatter reliability have better prospects in workshop application.

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