Study of fuzzy stochastic limited cutting width on chatter

Abstract

Fuzzy mathematical theory is applied to drawing the fuzzy stability lobes in which each lobe is characterized by a membership grade of experiential distribution of testing data in the theoretical distribution set of chatter signal. The judgement of limit value of free-chatter cutting width is spread over the fuzzy domain in this paper. The fuzzy combination relationship between the spindle speed and the depth of cut in milling is also addressed. According to the limit width, a safety criterion on which the cutting process is stable is developed. Also, the concept and definition of safety criterion for the cutting process stability operation for fuzzy stochastic meaning are given. Analysis indicates that the fuzzy stability lobes have definite physical significance. First, they can tell us in which status the cutting process is for the drawn lobe. Second, they reflect the probability distribution of the limit value of cut width in the fuzzy domain with respect to the identification of chatter status (fuzzy event). Meanwhile, it indicates that there is a transition between unstable lobes and stable lobes in a stability threshold graph with the influence of both fuzzy stochastic parametric excitation and fuzzy stochastic external excitation. Testing value curves of the fuzzy allowed domain of the limited cutting width are developed via experiment.