STATISTICAL-ANALYSIS OF THE DYNAMIC CUTTING COEFFICIENTS AND MACHINE-TOOL STABILITY

Machine tool chatter is a statistical phenomenon since it is dependent on the interaction of two statistical quantities, these being the dyn amic characteristics of the machine tool structure and the transfer fu nction of the cutting process. In this paper, a generalized statistica l theory of machine tool chatter has been developed. This takes into c onsideration the scatter of the dynamic data of the machine structure and/or that of the cutting process. The dynamics of the cutting proces s have been represented by a mathematical model which derives the cutt ing coefficients from steady state cutting data, based on a nondimensi onal analysis of the cutting process. The dynamics of the machine tool structure and the cutting process, being the input data to the theory , were determined experimentally. The predicted stability charts were plotted to take into consideration the scatter in the machine structur e dynamics and/or the cutting process. At the threshold of stability, the statistical variations due to the dynamic cutting coefficients amo unt to +/-29.5 percent at 99 percent confidence level while the statis tical variations due to the structure dynamics amount to +/-4.5 percen t only, at the same confidence level. Therefore, the threshold of stab ility can be specified only in terms of mean values with confidence li mits.