control of the entire manufacturing operation. The result can be the inability to obtain the required properties of the manufactured part (dimensional accuracy or surface quality) [1]. The described problem may occur during rough machining [2; 3; 4], while it may be particularly relevant during finishing [5] and precision and ultraprecision machining, especially for low-rigidity parts. There can be multiple causes of instability during machining. Among the most important and significant ones, the following are often mentioned [6; 7]: varying undeformed chip thickness caused by vibration (trace regeneration phenomenon), the coupling of two natural modes of vibration, and excessive friction in the cutting zone at the contact area between the cutting tool and the machined layer of the workpiece. The vibration may result in characteristic marks (vibration effect between tool and workpiece), the so-called chatter marks, which usually results in a quality reduction in the machined surfaces [8; 9]. In addition, vibration may cause adverse effects in the form of tool wear (reduced tool life), damage to the toolholders and even the entire machining assemblies (as a result of high vibration amplitudes), and health hazards for machine operators (as a result of excessive noise and its high frequencies) [10; 11; 12]. The presence of vibrations, unfortunately, quite often necessitates a limitation of the applied machining parameters, and thus considerably reduces the productivity of the machining and consequently increases the time of manufacturing. In order to avoid this, diverse methods of vibration reduction are applied. Paper [13] presents different ways and types of damping of chatter vibration, and also includes a description of damping method selection with regard to the machinability of the workpiece and machining system rigidity, that is, the different conditions existing during machining. In the Stability Lobe Diagram (SLD), it is possible to consider tool diameter importance, as a bigger tool diameter can positively extend the stable areas. Moreover, it is also advantageous to use tools with a greater number of cutting edges, as this can result in an increase in the usable range of rotational speed (shifting the SLD to the right) [14; 15]. Unfortunately, the use of SLD plots also has some disadvantages. Among the most commonly mentioned ones are the static approach to input data acquisition and the creation of SLD curves, during the standstill of the machining machine. Such a test therefore does not consider the key process dynamics parameters of the spindle system (for example, thermal expansion or system stiffness), or various other factors related to the characteristics of the workpiece (for example, changes in undeformed chip thickness cross-section, material defects, or damping properties) [13; 16]. The process stability studies often also use [17; 18] spectra analysis, the Poincare method, and the chase plane method, which allows, e.g., to discuss the relationship between the milling parameters and the maximum Lyapunov exponent. Using the Lyapunov exponent criterion, it is possible to determine the vibration stability zone for machining operations (0.61 in this case). An interesting analysis was also performed in paper [7], where external forcing was used to enable the control of the milling process. Tests and numerical analyses were executed with the use of the Runge-Kutta method. The susceptibility of the tool and workpiece to vibration and other non-linear phenomena was considered. An SLD was determined and an analysis of the influence of external forcing was performed. In addition, a proportional-integral controller was used to make closed-loop control possible. The application of the presented methodology allowed for the observation of a decrease in vibration levels during machining. Trochoidal milling is a machining strategy that involves the cutting tool's movement along circular paths. This method is much less popular than the commonly used milling along straight paths.