## 1 Introduction
#### Trochoidal Milling in CAM (computer-aided machining) systems  
The development of computer technology enabled a wider implementation of CAM systems. Currently, there are several major manufacturers of these systems (e.g., PTC Creo, CATIA, Delcam, SolidCAM, EDGECAM, etc.) which, in addition to programming conventional machining methods, also allow so-called smart machining to reduce tool load through a constant angle of the feed. From the user's point of view, the solution is realized by entering the input parameters of machining or cutting conditions. The cutting parameters which affect the (conventional) cutting process are cutting speed, feed rate (or feed per tooth) and cutting depth. The primary goal of trochoidal milling also referred to as constant-angle machining by CAM systems manufacturers, is to reduce tool loading. If the tool is moving along a path similar to a mathematical trochoid, the feed angle is not constant but is defined as the angle between two vectors describing the tool contact area with the machined material. Load size continuously increases from zero to maximum depending on the tool movement (Figure 3). If this angle is greater than the entered value, a circular motion of the tool with a radius defined by the radius \(R_{\text{P}}\) parameter is executed in a controlled manner in this position. If this angle is smaller than the defined value, then the circular motion is not generated at this position, and the tool moves to the next position. Just for trochoidal milling, today's advanced control of all aspects of the tool path, including collision control, seems to be very effective. When we use trochoidal milling, there are two next parameters (step of trochoid and engagement angle) which define the trochoidal path. Due to this fact, the research of the trochoidal path has been focused on the step of trochoid, the engagement angle and trochoidal radius (Figure 3). Figure 3: Graphic presentation of trochoidal parameters: s—step of trochoid; RP—radius of the trochoid circle; RT—radius of the milling cutting tool; \(\alpha\)—engagement angle. The trochoid step determines the distance between the centres of two adjacent circles that characterize the tool's feed by a given distance. The engagement angle is the angle of stroke that occurs between the two directions at the tool and material contact point. Between two mentioned parameters, there is a relationship which causes the curvature of the path. During the path generation, the CAM system continuously checks the engagement angle at each tool position defined by the step. If the engagement angle is greater than the specified value, the cutting tool at this position performs a circular tool movement with the radius defined by the radius parameter. If the engagement angle is smaller than the specified value, the CAM system does not generate a circular movement at this position; the tool moves to the next position. The trochoid radius is the radius of the circle describing the rolling motion of the milling cutting tool, the centre of the tool as the centre of the actual trochoid circle moving along a solid baseline. The walls of the formed groove are not entirely straight; they have the shape of small circular arcs; the surface quality of the groove wall increases with the set step and the radius of the trochoid. The magnitudes of the forces acting on the milling cutting tool correspond to the magnitudes of the forces-responses of the milling cutting tool acting on the machined material, in accordance with the [PERSON]'s third law [5; 9; 29]. The aim of the research of the dynamics of the trochoidal machining process is to examine the dependence of the total machining force on the trochoid parameters qualitatively and quantitatively. At a relatively small engagement angle, the area of the workpiece material cut width is reduced. If the currently machined surface is theoretically reduced to a single point, the tangent at this point is a common tangent to the radius of the milling cutting tool and to the radius of the current trochoid circle.