Abstract
This paper deals with the foundational method of forecasting chatter stability limits with acceleration signals in cutting process by applying time series analysis and forecasting theory. In this study machine tools and cutting process are considered as a black-box and consequently all the factors concerned with chatter are included in the analysis, hence the method proposed in this study is very actual and practical for forecasting chatter stability limits. Firstly it is verified theoretically that chatter stability limits can be predicted from the trend of the acceleration amplitude and next taking variance of sampled data zt is shown to be effective as a method of converting trends of amplitude to those of average level. After the estimation of the time series models for the preprocessed series using the FPE method and Yule-Walker's equation, future values are forecasted precisely by means of the models estimated. As for the prediction of the onset of chatter vibration, three methods of model estimation for each cutting speed and forecast origin viz. (1) using common model, (2) using the same set of model order (p, d) and estimating autoregressive parameters, (3) estimating the new suitable model, are investigated and the three methods are all shown to be capable of forecasting practical limit conditions of chatter applying the acceleration level on the onset of chatter vibration at a cutting speed.
