OBRABOTKAMETALLOV technology Vol. 27 No. 1 2025 Fig. 4 illustrates the variation of feed force (Ph), acting along the table feed direction), lateral force (Pv, perpendicular to the feed direction), and axial force (Px, acting along the milling cutter axis, i.e., vertically in end milling) as a function of minimum chip thickness (fmin). When feeding across the specimen, the maximum feed force (Phmax) and maximum lateral force (Pvmax) are larger, and their increase with increasing feed is more pronounced, indicating an influence of the build direction in WAAM. The maximum axial force (Pxmax) remains relatively constant with increasing feed, but exhibits a slightly higher value when feeding across the specimen. In Fig. 4, graph 2 (Pvmax along) exhibits an inflection point at fmin = 80 mm/min, an effect not observed when feeding across the specimen in graph 5 (Pvmax across). Furthermore, at fmin = 80 mm/min, a decrease in the maximum feed force (Phmax along) is apparent in graph 1; however, the remaining data points for this force lie on a linear trend. Analysis of the cutting force graphs shown in Fig. 4 reveals characteristic force interactions between the milling cutter and the workpiece. The force vector Pv is measured by a dynamometer with a negative value. This indicates that this force component, which arises from the radial impact of the cutter teeth, is directed away from the operator, i.e., opposite to the OY axis. For ease of visualisation, the vector Pvmax is shown in the positive direction of the axis in the figure, although its actual direction is opposite. Similarly, the force Px, also having a negative value, is directed against the OZ axis. This is a consequence of the positive helix angle ω of the milling cutter, which results in a vertical pull-up of the workpiece. It is important to note that the absolute values of the forces Pv and Px are considered in the analysis, as these reflect the intensity of the force impact. At the same time, the force Ph has a positive value, corresponding to the direction of the OX axis, which defines the primary cutting force. An analysis of the maximum cutting forces values Phmax and Pvmax as a function of the minimum feed rate fmin (see Fig. 4), with a cutting depth of 3 mm and other constant cutting parameters, demonstrates their approximately linear relationship. This allows for the use of linear equations to approximate these dependencies within the considered parameter range. A pattern is observed: when synthesizing workpieces and directing the feed along the machining axis, the values of the maximum forces Phmax, Pvmax and Pxmax are slightly smaller than when the feed direction is perpendicular. This difference, as seen in Fig. 4, is not significant but shows the influence of the feed direction on the force characteristics of the milling process. The difference in force values may be due to changes in the contact conditions between the tool and the workpiece, specifically changes in the contact area of the cutting edge and the depth of cut, depending on the feed direction. Further studies, including analysis of the helix angle of the milling cutter, the geometry of the cutting edge, and the properties of the workpiece material, are needed for a more accurate explanation of this phenomenon. Moreover, some factors, such as the presence of vibrations and the influence of the coolant, may also contribute to the observed differences. A more accurate model, considering all these factors, will allow for more precise prediction of force characteristics and optimization of the technological process. Fig. 5 demonstrates an unexpected phenomenon during milling with a four-tooth tool at a cutting depth of 3 mm. Despite the theoretical assumption of only one tooth is in contact with the workpiece at any given time, which should lead to periodic zeroing of the cutting force, continuous force exertion is observed, most prominently expressed in the feed force (Ph) graph (purple curve). Moreover, the increase in the minimum Ph value with increasing feed rate indicates a complex interaction between the tool and the workpiece that goes beyond a simple single-tooth cutting model. Analysis of the Ph cutting force curve reveals a distinct pattern of four pronounced peaks and valleys. This periodicity unequivocally indicates that all four teeth of the milling cutter participate in the cutting process, each leaving its imprint on the curve. Small but noticeable amplitude variations of these peaks are observed, indicating a slight radial runout of the teeth. However, it is important to note that the maximum Ph values for adjacent teeth are almost identical. This equality of amplitudes for adjacent teeth suggests that the radial distance of each tooth from the axis of rotation of the milling cutter is the same. This fact allows us to confidently rule out any displacement of the milling cutter axis relative to the collet chuck as the cause of the recorded cutting force fluctuations.
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