Statistical Theory of Machine Tool Stability

Abstract

Machine tool chatter is essentially a statistical phenomenon. The dynamic characteristics of the machine tool structure as well as the dynamic coefficients of the cutting process are statistical quantities that show scatter when determined in repeated tests. In this paper a generalized statistical theory of chatter has been developed. This takes into consideration the scatter of the dynamic data of the machine structure and/or that of the dynamic cutting coefficients. The dynamics of the cutting process has been presented by a mathematical model, based on deriving the cutting coefficients from steady state cutting data. The dynamics of the machine tool structure and the cutting process, being input to the theory, were determined experimentally. At the thresholds of stability, the statistical variations due to the dynamic cutting coefficients amount to ±17 per cent at the 99 per cent confidence level, while the statistical variations due to the structure dynamics amount to ±5.2 per cent only, at the same confidence levels. Therefore the predicted thresholds of stability can be specified only in terms of mean values with confidence limits.