# Surface Quality Evaluation in the Milling Process Using a Ball Nose End Mill
## 1 Introduction
The results obtained by [PERSON] [43] show that surface topography is affected by the plastic deformation of the machined surface and, in the latter case, by cutting vibration generated during machining. The machining process incorporates a factor referred to as \"cycle time,\" encompassing the duration for the machine to interpret a single line of NC code and subsequently transmit this information to control machine movement. Another facet involves the time required for the control unit to rectify the machine's motion, adjusting parameters like position, velocity, or acceleration [44]. Different toolpaths are generated in the machining process using linear interpolation, which is defined as the path between two successive cutting tool positions (CL). In a CAM system, a tolerance band, also known as chord error, can be defined to modify the toolpath segments. When the user reduces the tolerance zone, the toolpath becomes increasingly closer in resemblance to the CAD model [45]. [PERSON] [46; 47] described in more detail the problem of interpolation of linear segments (Figure 3a) and curved toolpaths Figure 3b, where the number of segments increases, and the increasing number of segments affects the size of the NC program. Figure 3 shows the trajectory view calculation for the free-shaped toolpath for the forward step (Figure 3a) and for size length, as shown in Figure 3b. [PERSON] et al. [48] found that the toolpaths in a CAM system appear to be the same, but each CAM system generates a different NC code when processing identical geometry. According to this different NC code, a different machining process is generated, which affects the real machining time, surface roughness, or feed rate oscillation. According to [PERSON] et al. [49], segment length decomposition is used as an indicator of geometric composition. They used histograms to verify the relationship between surface radius and segment length, where they obtained that a small radius of curvature corresponds to a smaller segment length. [PERSON] et al. [50] studied surface topography in the production of molded surfaces using the ball milling process, where he investigated machining errors caused by tool deflection. He proposed a surface generation model to predict the resulting machining errors. The surface obtained was used to predict dimensional accuracy prior to actual cutting. Surface topography in ball milling machining and surface roughness evaluation were similarly dealt with by [PERSON] et al. [51], who looked at the effect of machining parameters and the choice of milling strategies on the machined surface. The results emphasized the importance of obtaining the surface topography, which is necessary to determine the influence of the different parameters on the surface roughness. [PERSON] et al. [52] dealt with characteristics such as chip geometry, cutting force, and roughness in the production of shaped surfaces, using a copy-milling cutter as a tool. He predicted roughness values by defining an algorithm that accounted for tool and workpiece motions. The evaluation of surface topography and surface roughness was investigated by [PERSON] et al. [53], who evaluated these surface characteristics in five-axis machining. He proposed a model that was able to predict the surface texture and roughness parameters with a 20% deviation of the correct answer. Extensive research in reviewing methods for obtaining surface topography as well as analyzing the various factors that affect the milling process was described by [PERSON] in his study [54]. He analyzed the mechanism of machined surface topography and discussed the factors that influence it. [PERSON] et al. [55] found that as the tool inclination angle increases beyond 6 degrees, the surface roughness improves with the use of a ball milling cutter. [PERSON] et al. [56] focused on designing a model that could obtain the surface topography directly from the cutting parameters, workpiece surface geometry, and cutter placement.