Self-induced vibrations, known as chatter, are one of the main limitations to the productivity of cutting processes. Prediction of unstable areas is therefore very important but is analytically difficult to achieve due to the many non-linearities in the process. This thesis analyses the stability of turning in the time domain by solving delay differential equations. We presented the theoretical foundations of the mechanics and dynamics of turning. We carried out turning experiments to determine the force components as a function of feed and depth of cut and approximated them by a polynomial. We conducted modal analysis of the tool with the toolholder and determined the transfer function of the response to excitation in the feed direction. We used the results from both measurements in the equation of motion of the chatter system, which we solved numerically with the code dde23 in Matlab. By analyzing the results of the simulations, we formulated the stability diagram, considering the non-linear dependence of the force on the thickness of the chip and the non-linearity that occurs when the tool jumps out of the material. We have shown that by solving delay differential equations it is possible to simulate chatter in the turning process while accounting for the nonlinearities, which is not possible in frequency domain analysis.
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