# Surface Quality Evaluation in the Milling Process Using a Ball Nose End Mill
## 1 Introduction
[27] verified a method for the estimation of vibration and roughness during free surface milling with a ball end mill. They concluded that the tool overhang length has a significant effect on the roughness parameters. The effect of the tool path on the milling of the convex surface was evaluated by [PERSON] et al. [28] when hardened material was used. The results showed that the radial strategy achieved the best  
Figure 2: Tool contact with machined surface (**a**) machining with the center of the tool (**b**) ascendant direction (**c**) ascendant direction in the lower area of the sample. surface texture and the spiral strategy the worst. [PERSON] et al. [18] studied the effect of tool orientation on cutting speed and tool life. They came to the conclusion that machining with the center of the tool, where the cutting speed is zero, leads to a worse roughness parameter. [PERSON] et al. [29] examined the influence of the cutting direction in free-form surface milling. The result showed that the effective radius of the tool was larger when cutting upwards, resulting in a more favorable value of effective cutting speed. On the other hand, in the opposite direction, in a downward movement, the effective tool radius was found to be much smaller, and the cutting speed may be reduced to a critical value. A suitable, effective cutting speed is usually achieved when the tool cuts approximately tangentially. Changes in cutting speed during full surface milling can cause process instability [26] in terms of roughness parameters [30], dimensional accuracy [27] as well as geometric deviations. In the downward-cutting method of free-form surface milling, elastoplastic deformation of the material in the form of a notched effect [24] may occur on the surface of the part. In the process of cutting through the center of the tool, where the cutting speed is low, the vibrations are maximum in this area [31; 32]. For this reason, the correct selection of the milling strategy is very important [33]. It can affect the contact area in the machining process, which affects the tool wear, surface texture, roughness, and vibration. According to [PERSON] [34], the choice of milling strategy for free-form surfaces has a significant impact because their selection can affect the contact area between the tool and the surface, vibration, roughness parameters, or tool wear. In this case, it is important to understand the relationship between tool-workpiece contact in free-form milling [35]. The surface quality is influenced by various inputs, including feed rate, cutting speed, or depth of cut, which are referred to as controlled inputs, and uncontrolled inputs, such as the workpiece, tool usage, or machine vibration [36; 37]. Numerous studies, as reported by [PERSON] [38], have investigated the roughness parameters in free surface milling and various geometrical features such as the scallop height, the influence of the toolpath strategy, or the cutting conditions during milling. [PERSON] and [PERSON] [39; 40] elaborated on the possibilities of free-form surface machining where surface roughness and dimensional accuracy were evaluated. [PERSON] [28] investigated spiral, raster, radial, and 3D feed strategies in free-form milling of low-curvature convex surfaces and evaluated cutting force and surface texture. This experiment concluded that the radial strategy produced the best surface quality, and the helical strategy resulted in the worst surface quality. [PERSON] [41] complemented the results by stating that the poor quality of the sculpted machined surface may be influenced by the lower cutting force. [PERSON] and [PERSON] [42] analyzed the effect of milling strategies on the free surface topography of aluminum alloy when Z-level, radial, offset, and circular strategies were used. It was found that the lowest roughness parameter, as required, was obtained only when the tool path was circular.