## 1 Introduction  
To manufacture flat surfaces, face milling is widely used as a method of high productivity [1; 2; 3], and other milling methods [4; 5]. At the same time, when describing cutting modes, such as in [PERSON] et al. [6], usually there are recommendations about the amount of position symmetry of the cutter and workpiece with asymmetric processing circuits as a range \(e=(0.03\)-\(0.06)B\), where \(B\)--depth of milling. Moreover, very often cutting tool manufacturing handbooks only contain the processing circuit with position symmetry of the cutter and workpiece, or there is a given displacement range. For example, [PERSON] [7] recommends using a range; however, there no is specific amount of displacement suggested. The work of [PERSON] and [PERSON] [8] demonstrated that an asymmetric circuit with an offset close to zero provided for the best tool list. The paper of [PERSON] and [PERSON] [9] proved that the cutting force in milling is lower when using an asymmetric scheme as opposed to symmetrical milling. In reference [10], it is shown that the cutting force is pulsating, which is associated with a variable number of the cutter's teeth involved in the process that will certainly cause vibrations in a real system. This is why it is really important to define specific positions of the end of the cutter and the workpiece that provide the minimum roughness of the machined surface. Today, many publications are dedicated to surface roughness models in face milling [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28]. [PERSON] et al. [11], for the operation conducted as face milling, reported the influence of cutter runout errors on surface quality parameters. They have also investigated the role of changes in the feed rate. [PERSON] and [PERSON] [12] optimized cutting parameters for face milling process to optimize the roughness parameter. [PERSON] and [PERSON] [13] experimentally investigated the effects of machining parameters of face milling responses, such as on the material removal amount, then the performance of tool that served, and the surface roughness parameter. On the other hand, the Taguchi technique was applied by [PERSON] and [PERSON] [14] in face milling of Al-Mg alloy. Their target was to maximize the surface quality at the lowest power usage. Considering multiple parameters, [PERSON] et al. [15] performed concurrent optimization of time, cost, and profit. In that problem, the limiting parameters were power, force, speed, feed, and roughness. [PERSON] et al. [16] conducted an experimental investigation of face milling at two different domains of speed--high and super. They have focused on the machining force, the roughness value of surface, and the chip-morphology. [PERSON] et al. [17] conducted several experiments regarding tool wear study to reveal the tool life, taking into account the surface roughness in milling of TC6 alloy. Conversely, [PERSON] [18] formulated the model of height of micro-roughness parameter. In doing so, the author accounted for the wear of tool. Considering the same machining operation but for Inconel 718 superalloy, [PERSON] et al. [19] conducted research to evaluate the influence of machining speed on cutting forces, as well as on tool wear. The study of [PERSON] [20] revealed the influence of face mill wear on the surface roughness parameter when the subject material was steel-45. [PERSON] and [PERSON] [21] studied the machinability of AISI H13 steel, hardened and machined as face milling. The main focus was to observe the behavior of chips, service time of tools, wear mechanism of tools, and quality of surfaces. Also, the comparison was performed based on different conditions. [PERSON] et al. [22] considered the cooling-lubrication mode to be an important index to influence the face milling operation. The role of cooling-lubrication was reported alongside the influence of cutting parameters. In a separate study, the face milling parameters were simulated using FEM (Finite element method) and empirical approach by [PERSON] et al. [23].