# Determination of the Depth of Cut via Surface Integrity
## 1 Introduction and Literature Review  
An important part of process planning refers to establishing the machining parameters. The depth of cut is the parameter that directly influences the machined-surface quality because it interacts with both the surface and subsurface layers of the processed material. The machined-surface quality must not be appreciated only by the surface roughness. A correct assessment must consider the condition and characteristics of the surface, as well as of the subsurface of the processed material. Thus, surface integrity becomes a very important criterion for assessing the quality of the machined surface [1; 2]. Surface integrity refers to certain aspects of the surface, such as form, roughness, waviness, lay, and subsurface characteristics such as residual stress, granular plastic flow orientation, and defects (porosity, micro cracks, tears, laps, etc.) [3]. Surface integrity is influenced by various factors, including the machining parameters [4; 5; 6]. [PERSON] et al. [7] approach the connection between the rough and finishing tool passes considering the final surface integrity. The final surface integrity is influenced by the previous operations/passes. Surface integrity is specific to each operation. Thus, the concept of Current-Previous Machining Process--CPMP [8] becomes very important. This concept considers that surface roughness \(\mathrm{R}\mathrm{z}_{\mathrm{P}}\) and the components of \(\mathrm{S}_{\mathrm{P}}\) generated during the machining process and caused by the casting process must be considered when calculating \(\mathrm{d}_{\mathrm{cf}}\) (current depth of cut), following Figure 1. \(\mathrm{R}\mathrm{z}_{\mathrm{P}}\) refers to the surface roughness obtained after the previous operation. \(\mathrm{S}_{\mathrm{P}}\) refers to the subsurface layer degraded after the previous operation (subsurface defects). The depth of cut must also contain dimensional tolerance obtained at the previous operation (\(\mathrm{\delta}_{\mathrm{P}}\)), flatness deviation obtained after the previous operation (\(\mathrm{\epsilon}\mathrm{F}_{\mathrm{P}}\)), and axial clamping error related to the current operation (\(\mathrm{\epsilon}\mathrm{C}\mathrm{a}\mathrm{c}_{\mathrm{c}}\)). Among the first researchers who have considered the connection between the depth of cut and machined-surface quality wasKovan [9; 10], whose ideas were overtaken by [PERSON] [11], as well. However, at that time, the term surface integrity was not known. This term was first used by [PERSON], [PERSON] in 1964. In accordance with these papers, the components of \(\mathrm{d_{cf}}\) are colinear vectors, as Formula (1) illustrates. \[\mathrm{d_{cf}}\geq\mathrm{Rz_{p}}+\mathrm{S_{p}}+\delta_{\mathrm{p}}+\varepsilon \mathrm{F_{p}}+\varepsilon\mathrm{Cax_{c}} \tag{1}\]  
index \(\mathrm{p}\) is used for the previous operation, and index \(\mathrm{c}\) is used for the current operation, so \(\mathrm{d_{cf}}\) is to be calculated. In the literature, establishing the depth of cut is approached with respect to the issue of cutting parameters optimization. The depth of cut, as well as the other machining parameters, results based on a mathematical optimization model. Usually, the optimization criterion is an economic one (minimization of cost and time regarding machining operations). The constraints from the mathematical models are connection relations among the parameters related to machining operations. [PERSON] [12] overviews the software for modeling certain parameters related to machining operations. The paper considers expert systems. Regarding the turning processes, the considered parameters are feed, depth of cut, speed, and surface roughness. [PERSON] et al. [13] present connection relations among surface roughness, work piece speed, tool speed, depth of cut, and feed. [PERSON] et al. [14] created relations among surface roughness, cutting speed, feed rate, depth of cut, and nose radius. [PERSON] and [PERSON] [15] have studied how vibration amplitude and tool flank wear were influenced by machining parameters.