Fuzzy stability analysis of regenerative chatter in milling

Abstract

During machining, unstable self-excited vibrations known as regenerative chatter can occur, causing excessive tool wear or failure, and a poor surface finish on the machined workpiece.Consequently it is desirable to predict, and hence avoid the onset of this instability. Regenerative chatter is a function of empirical cutting coefficients, and the structural dynamics of the machine-tool system. There can be significant uncertainties in the underlying parameters, so the predicted stability limits do not necessarily agree with those found in practice.In the present study, fuzzy arithmetic techniques are applied to the chatter stability problem. It is first shown that techniques based upon interval arithmetic are not suitable for this problem due to the issue of recursiveness. An implementation of fuzzy arithmetic is then developed based upon the work of Hanss and Klimke. The arithmetic is then applied to two techniques for predicting milling chatter stability: the classical approach of Altintas, and the time-finite element method of Mann. It is shown that for some cases careful programming can reduce the computational effort to acceptable levels. The problem of milling chatter uncertainty is then considered within the framework of Ben-Haim's information-gap theory.It is shown that the presented approach can be used to solve process design problems with robustness to the uncertain parameters. The fuzzy stability bounds are then compared to previously published data, to investigate how uncertainty propagation techniques can offer more insight into the accuracy of chatter predictions.

MATLAB - A Ubiquitous Tool for the Practical Engineer

“…For monotonic problems this process may be trivial, since the maxima or minima of the inputs will lead to the maxima or minima for the output. Conversely, for non-monotonic problems this is no longer the case (Sims et al, 2010). In addition, the Standard Fuzzy Arithmetic may become problematic and lead to different results for the same problem depending on the form in which the solution procedure is applied, as can be seen in the examples gathered in (Hanss, 2002).…”

Chatter prediction for uncertain parameters

“…Kong et al [3], Kong and Yu [4], Sims et al [5] and Hamann et al [6] have used fuzzy set theory to determine the confidence ranges of the computed stability diagrams. Sims et al [5] reported that explicit fuzzy interval-based arithmetic is impractical in the analysis of machine tool vibrations. Instead, numerical methods with a specific sample of uncertain parameters have been used [5,6].…”

“…Sims et al [5] reported that explicit fuzzy interval-based arithmetic is impractical in the analysis of machine tool vibrations. Instead, numerical methods with a specific sample of uncertain parameters have been used [5,6]. Park and Qin [7] have used the edge theorem combined with the zero exclusion method in robust stability analysis.…”

Prediction of surface location error in milling considering the effects of uncertain factors

“…However, all these models assume that parameters of the milling process such as depth of cut, feed per tooth and cutting force are deterministic. Actually, these parameters are random in practical engineering due to uncertainty factors in real manufacturing environment, which would in turn influence the milling process (Sims et al, 2010;Graham et al, 2013;Hajdu et al, 2016). In this paper, a practical method is proposed to predict SLE in milling considering the effects of uncertain factors.…”