# Evaluation of Non-Planar Tool Interaction in Milling of Shaped Surfaces Using a Copy Milling Cutter
## 1 Introduction
[PERSON] [25] investigated the contact point in the interaction of the cutting tool and the machined surface in multi-axis machining, where he changed the angle of inclination of the tool in the cutting process. The comparison of milling finishing strategies in the production of shaped surfaces and the analysis of different methods for the evaluation of surface topography with respect to the effective tool diameter for three different heights on the workpiece was investigated by [PERSON] [26]. The author showed that the changes in the observed parameters were due to the variation of the tool effective diameter as well as the influence of the strategy used. The best results were obtained with the Constant Z strategy, in which uniform toolpaths were achieved over the whole height of the specimen. The cutting edge was displaced in height during machining when the setting angle was changed stepwise. This resulted in the approximation of a semi-spherical shape by a series of low tapered surfaces. [PERSON] [27] studied the influence of the effective tool diameter in the production of dies, in which the material investigated was Super Plast \({}^{\text{\textregistered}}\) 300 (SP300) grade steel and where a Ti(CN) coated copy tool was used. The cutting mechanism based on the changing effective diameter of the cutter when milling free-form surfaces was also investigated, in which the authors focused mainly on the change of cutting forces when the tool contacts the workpiece [28; 29]. The optimisation of the selection of finishing strategies was studied by [PERSON] [30], focusing on high-speed machining for HSM. [PERSON] et al. [31] investigated the machining of a part that equally contained concave and convex surfaces, compared different strategies such as linear strategy, beams, and 3D offset, and evaluated their effect on texture and roughness. The worst results for machined surface texture and roughness were obtained with the linear strategy and the best with the 3D offset strategy. The effect of toolpath on milling a low curvature convex surface using hardened material was investigated by [PERSON] et al. [32]. The authors also investigated the influence of milling strategies, namely linear, beam, 3D offset, and helix in the workpiece-tool relationship, evaluating cutting forces, surface texture, and machining time. The results showed that the beam strategy achieved the best surface quality, while the spiral strategy was the worst machined surface quality. [PERSON] and [PERSON] [33] analysed the effect of four milling strategies (circle, square, beams, and Z level) on the production of a freeform surface where the material was an aluminium alloy. The lowest roughness parameter was obtained only for the circular toolpath due to the defined requirement of achieving roughness. [PERSON] et al. [34] investigated the effect of different strategies (linear, 3D offset, spiral, and beam) and machining parameters on the microhardness of a convexly curved surface of 1.4903 stainless steel, and the design of experiments was carried out using the Taguchi's method. The results showed that different toolpaths have different effects on the microhardness of the milled surfaces, where the spiral strategy reached the maximum hardness and the beam strategy reached the minimum hardness. The tool-workpiece contact relationship in freeform ma chining was investigated by [PERSON] [35], who compared descending, ascending milling, and tool-centred machining. In addition to virtual modelling, a reverse engineering method is also used to obtain a 3D model from a physical (real) part. One of the possible methods is digitisation of the physical part using a non-contact optical scanner. The output format is the so-called cloud of points. Currently, various aspects focused on the milling of shaped surfaces and their evaluation are being investigated. Previous studies have assessed the selection of a suitable copying tool based on a cloud of points, without considering the specific shape of the machined surface [36; 37; 38].