Machine tool chatter is a statistical phenomenon since it is dependent on the interaction of two statistical quantities, these being the dynamic characteristics of the machine tool structure and the transfer function of the cutting process. In this paper, a generalized statistical theory of machine tool chatter has been developed. This takes into consideration the scatter of the dynamic data of the machine structure and/or that of the cutting process. The dynamics of the cutting process have been represented by a mathematical model which derives the cutting coefficients from steady state cutting data, based on a nondimensional 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 structure dynamics and/or the cutting process. At the threshold of stability, the statistical variations due to the dynamic cutting coefficients amount to ±29.5 percent at 99 percent confidence level, while the statistical variations due to the structure dynamics amount to ±4.5 percent only, at the same confidence level. Therefore, the threshold of stability can be specified only in terms of mean values with confidence limits.
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Statistical Analysis of the Dynamic Cutting Coefficients and Machine Tool Stability
M. A. El Baradie
School of Mechanical and Manuf. Engr., Dublin City University, Dublin 9, Ireland
El Baradie, M. A. (May 1, 1993). "Statistical Analysis of the Dynamic Cutting Coefficients and Machine Tool Stability." ASME. J. Eng. Ind. May 1993; 115(2): 205–215. https://doi.org/10.1115/1.2901651
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