# Evaluation of Non-Planar Tool Interaction in Milling of Shaped Surfaces Using a Copy Milling Cutter
## 1 Introduction
When using the finishing strategies applied to the 3-axis machining process, the cutting tool must always be tangent to the machined surface. Using a copying cutter is a position that is given by the contact point of the cutter, the centre of the tool, the position of the cutter, the radius of the tool, and the vector of the tool orientation [11]. When machining shaped parts, the area of engagement of the cutter when the tool is in contact with the machined surface is also important, which changes from the point of view of the curvature of the surface during the cutting process. It is difficult to predict and analyse the area of capture in a specific position of the tool to the machined surface. The use of copying tools in the field of finishing operations has its advantages due to adaptability to changes in surface curvature. Nevertheless, the tool grip changes during the manufacturing process, resulting in process instability [12; 13]. Many studies have been devoted to applying multi-axis machining in the production of shaped surfaces due to less tool wear owing to its tilting, and to avoid the negative effect known as material ploughing, which appears when the tool is in a perpendicular position relative to the machined surface. An accompanying phenomenon of material ploughing is the action of the vertical position of the tool, while there is no shearing mechanism, as the action of the centre of the tool does not create enough chips for removal, thus there is a zero-cutting speed at the cutting point [14]. In his research, [PERSON] [15] assessed the effect of the vertical position of the tool on the quality and topography of the machined flat surface, evaluated the geometric characteristics of the surface, and compared four strategies. The author also evaluated the roughness of the surface, where the best results were obtained with the circular pocket and Constant step pocket auto boundary strategies. He expanded his research with knowledge regarding the influence of finishing milling strategies on the production quality of the shaped surface applied in 3-axis milling of aluminium samples, while it was a combination of convex and concave curves. [PERSON] also assessed the roughness and choice of a milling strategy, where the Constant \(Z\) strategy achieved the best results in terms of roughness [16]. The author proposed a method of comprehensive assessment of the quality of the machined surfaces (surface topography, surface roughness, shape deviation, etc. ), useful in deciding on the production method and the use of appropriate strategies in 3-axis milling. For the experiment, he selected an aluminium alloy that had a parabolic shape and evaluated the elements of the surfaces with respect to the chosen height of the sample using a digital microscope, where the regular arrangement of the tool paths along the contour lines was achieved only with the Constant Z strategy [17]. In their works, [PERSON] [18] and [PERSON] [19] evaluated the methods dealing with the interaction between the tool and the machined surface. Since CAM systems are important in the production of shaped surfaces, [PERSON] [20] analysed the accuracy of their use due to the difference in the generation of tool paths compared to real production. The difference in the results was up to 30%. [PERSON] [21] investigated the vibrations during the production of shaped surfaces and their estimation, and emphasized the influence of tool overhang. In his results, [PERSON] [22] reported effective cutting speeds in areas where the interaction of the tool with respect to the machined surface reached a tangential level. From the point of view of dimensional and shape accuracy assessment, various surface assessment methods are used, resulting in various analyses and reports providing information on production accuracy, shape deviations, etc. [23]. [PERSON] et al. [24] investigated the design of an algorithm designed to predict the quality of the machined surface where the authors used a copy cutter for the finishing process.