The dynamic stability of the machining set and the entire cutting process, together with the appropriate form of chips generated during machining under the given conditions, are the basic prerequisites for autonomous machining in accordance with the Industry 4.0 trend. The research, based on a newly designed method, aims to study the frequency response of the machining system to different values of tool wear and cutting speed, which cause the worsening of the machined parts’ quality and the instability of the whole cutting process. The new idea is based on the inverse principle, in which the wear with various values of VB was artificially prepared in advance before machining. Consequently, the effect of artificial wear and cutting speed on vibration and chip shape characteristics were studied. Three types of brass alloys were used within the experiments as the machined materials. Measured data were statistically processed and the desired dependencies were plotted. Chips were collected for each combination of machining conditions, while the article presents a database of the obtained chip shapes at individual cutting speeds so that they can be compared and classified. The results showed that brass alloys CW510L and CW614N exhibit an average of three times lower vibration damping compared to the CW724R alloy, while relatively good chip formation was noted in the evaluated machining conditions even without the use of a chip breaker. The problematic chip shape occurred only in some cases at the machining of CW510L and CW724R, which cannot be generalized.