## 1 Introduction
[PERSON] and [PERSON] [42] constructed cutting force models that include not only the shear zone processes, but also the constituents of the plowing force [43; 44] related to the cutting tool wear. [PERSON] et al. [45] reviewed the estimates of the cutting geometry of the cutting part and the geometry that are used to predict cutting forces, torque, power and the possibility of vibration and other states of the process along the tool path. [PERSON] et al. [46] experimentally and computationally tested methods for modeling milling of complex triaxial and five-axis examples, as well as for predicting cutting forces. [PERSON] and [PERSON] [47] developed a model of cutting forces in milling of hard-to-cut Inconel 718. Despite the fact that many papers take into account the relative positioning of the work-mill [35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47], none of them are concerned with developing the conditions that ensure the optimum difference between the work-mill which will provide the minimum surface roughness. The following papers are dedicated to theoretical and experimental studies of face milling processes [48; 49; 50; 51; 52; 53]. [PERSON] et al. [48] investigated measurement of the cutting force in face milling and proposed a novel rotating dynamometer for this purpose. [PERSON] et al. [49] focused on applying the novel method of dynamic register cutting forces using predictive statistical methods. [PERSON] et al. [50] presented a novel approach to monitoring the spindle title and deflection with the help of HDM (high-definition metrology) surface data. [PERSON] [51] developed a mathematical model for the main drive power expended in face milling, taking into consideration the wear of teeth on the back surface of the tool. [PERSON] and [PERSON] [52] investigated full immersion face milling with round inserts and proposed an approach for determining specific cutting force coefficients (SCFCs). [PERSON] et al. [53] structured a predictive model for power in face milling used in the manufacturing processes. However, papers [48; 49; 50; 51; 52; 53] are not concerned with developing the conditions that ensure the optimum position of the face mill and the workpiece which provides the minimum surface roughness. A few papers [54; 55; 56; 57; 58; 59; 60] are also dedicated to studying acceleration of vibration in face milling. [PERSON] et al. [54] investigated variable speed cutting as a method for vibration control in face milling. [PERSON] and [PERSON] [55; 56] proposed in their works an analytical method for predicting vibrations during face milling and implemented an analytical explanation of dynamic phenomena. [PERSON] et al. [57], in their paper, using the finite element method, performed a dynamic evolution during the milling of a thin-walled part. [PERSON] et al. [58] proposed a novel energy-saving acceleration control method that involves a synchronized state between the acceleration of spindle and the feed unit. [PERSON] et al. [59] presented the selection of optimal design variety of components integrated in the verbal message system (VBS). [PERSON] et al. [60] studied the effects of radial depth of cut and cutter geometry on cutting forces and vibration amplitudes. [PERSON] et al. [61], in their article, presented a sustainability analysis for a milling operation with one degree of freedom in a thin-walled workpiece. However, papers [54; 55; 56; 58; 59; 60; 61] are not concerned with developing the conditions that ensure the optimum position of the face mill and the workpiece which provides the minimum surface roughness in addition to acceleration. The main conclusion of this review is that no previous research seems to have posed the problem of investigating the complex relationship between the relative position of the face mill towards the workpiece, the milling kinematics and the surface roughness, cutting forces, and acceleration of vibrations.