# Investigation of Titanium Alloy Cutting Dynamics in Thin-Layer Machining
###### Abstract
Meanwhile, in [21], a model was proposed that incorporates the influence of the cutting edge radius and friction angle. [PERSON] [25] analyzed methods for determining the minimum undeformed chip thickness across different materials. [PERSON] et al. [26] developed a 2D micro-turning model for Ti Gr5 and estimated \(h_{min}\) to be approximately 5-6 \(\upmu\)m for a tool edge radius of 20 \(\upmu\)m. Several researchers have observed the existence of a stagnation zone--also referred to as the dead metal zone--at the tool nose, which acts as a secondary cutting edge. Based on this phenomenon, models have been developed to estimate the effective uncut chip thickness [27; 28; 29; 30]. However, a major limitation of mechanistic models is the need for a precise determination of cutting force coefficients, typically obtained through labor-intensive cutting calibration experiments, as shown in [31; 32]. In [33], an intuitive tool for simulating vibrations, cutting forces, and surface quality control in the milling process is described. To address these challenges and reduce the need for costly experiments, the finite element method (FEM) has also been employed to predict cutting forces [34; 35; 36; 37]. Mechanistic cutting force prediction methods incorporate the effects of minimum chip thickness, plastic deformation, and elastic recovery [38; 39]. These models typically begin with a detailed simulation of the material removal mechanism. Subsequently, FEM-based predictions are used to investigate the influence of a varying tool edge radius on this mechanism [40]. The chip morphology at different cutting thicknesses is also studied. Based on such analyses, the minimum chip thickness is determined--below this threshold, chip formation does not occur [41; 42; 43]. Additionally, FEM enables the modeling of the dead metal zone at the tool edge [44; 45]. As previously indicated, the minimum undeformed chip thickness \(h_{min}\) is typically determined using experimental or theoretical-experimental methods [46]. When the material properties and tool geometry are known, it is possible to identify the region ahead of the cutting edge where the material separates into a chip-forming zone and a plastically deformed (ploughed) zone [47]. This value is most often determined under orthogonal cutting conditions, while preserving the characteristic properties of the workpiece material [48]. For small uncut chip cross-sections, irregularities in chip formation and dynamic instabilities are frequently observed. These include chaotic variations in cutting forces, self-excited vibrations (chatter), and difficulties in maintaining consistent machining parameters [49; 50; 51; 52]. These challenges are exacerbated when machining difficult-to-cut materials such as titanium alloys, which are commonly used in applications requiring a high corrosion resistance and performance under elevated temperatures [53]. Due to their mechanical properties--strength and low weight--titanium alloys are used in the aerospace industry, and where biocompatibility is also required, in medicine. They also have applications in the chemical, sports, and automotive industries. More information on the properties and development of various materials can be found in [54]. Although titanium alloys exhibit favorable mechanical and thermal properties, they pose significant challenges during machining [55]. Common problems include accelerated tool wear, vibration, and low material removal rates [56]. Titanium's low thermal conductivity leads to heat accumulation in the cutting zone, resulting in higher temperatures, reduced tool life, and deteriorated surface quality [57; 58]. This often causes undesirable chip morphologies, burr formation, and material adhesion to the cutting edge [59]. Consequently, the machinability of commercially pure titanium, such as Ti Grade 2, remains a limiting factor in its broader industrial application.