# Investigation of Titanium Alloy Cutting Dynamics in Thin-Layer Machining
###### Abstract  
Manufacturing in modern industrial sectors involves the machining of components where the undeformed chip thickness inevitably decreases to values comparable to the tool edge radius. Under such conditions, the ploughing effect between the workpiece and the tool becomes dominant, followed by the noticeable formation of a stagnation zone. This paper presents research focused on the analysis of the cutting process for small cross-sections of the removed layers, based on cutting force components. This study investigated the machining of two titanium alloy grades--Ti Grade 5 (Ti-6 Al-4V) and Ti Grade 2--with the main focus on process stability. A material separation model was analyzed to demonstrate the mechanism of material flow within the cross-section of the machined layer. It was found that the material has a limited ability to flow sideways at the boundary of the chip thickness, thus determining the probable size of the stagnation zone in front of the cutting edge. Orthogonal cutting experiments enabled the determination of the minimum chip thickness coefficient for constant temperature conditions, independent of the tool edge radius, as \(h_{min0}=0.313\). In oblique cutting tests, the sensitivity of thin-layer machining was demonstrated for the determined values of minimum undeformed chip thickness. By applying the 0-1 test for chaos, the measurement time (parameter \(T\)-\(dt\)) was determined for both titanium alloys to determine the range of observable chaotic behavior. The analyses confirmed that Ti Grade 2 enters chaotic dynamics much more rapidly than Ti Grade 5 and displays local cutting instabilities independent of the uncut chip thickness. [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], D.  
Furthermore, in [8], the influence of the cutting edge radius on ploughing force generation was investigated, revealing that in the machining of Ti Grade 5 (Ti-6 Al-4V), ploughing occurs even with ideally sharp tools. The transition from classical shearing to ploughing leads to increased friction and localized thermal effects, which influence the chip morphology and tool wear [9]. In studies estimating the minimum undeformed chip thickness during micro-milling of Ti Grade 5 under various machining conditions, the minimum thickness was found to range between 25% and 49% of the cutting edge radius [10]. Numerous authors have confirmed that the minimum chip thickness depends on material properties, tool geometry (particularly the cutting edge radius), rake angle, and the thermodynamic conditions of the cutting process [11; 12; 13; 14]. Unlike conventional machining, in the processing of thin layers, the tool radius may be comparable to the undeformed chip thickness. This results in the occurrence of ploughing effects and an effectively negative rake angle [15]. When the layer thickness falls below the minimum value required for chip formation, the material is not sheared but instead plastically deformed beneath the tool. In such cases, surface effects, friction, and the influence of the cutting edge radius become dominant. As the thickness of the cut layer decreases further, there is a noticeable increase in surface plastic deformation rather than complete chip separation [16; 17; 18]. This can lead to the dominance of material smearing (burnishing) over proper cutting, causing a deterioration in surface quality and accelerated tool wear [19; 20]. Therefore, an accurate assessment of the minimum undeformed chip thickness is crucial, as it directly affects both the quality and dimensional accuracy of the machining process [21; 22]. Analyses of the probable minimum thickness of the machined layer have been the subject of numerous studies. Some of these analyses focus on developing models based on simplified assumptions regarding material behavior and tool geometry [23]. In [24], an orthogonal cutting model was developed and validated, based on the assumption of zero shear stress at the stagnation point under constant thermodynamic conditions.