# Investigation of Titanium Alloy Cutting Dynamics in Thin-Layer Machining
## 6 Conclusions  
This study investigated the stability and dynamics of the titanium alloy cutting process, focusing on Ti Grade 5 and Ti Grade 2. A key parameter analyzed was the minimum undeformed chip thickness, which significantly influences cutting stability, chip formation, and surface quality. 1. This research confirms that the minimum undeformed chip thickness \(h_{min}\) is not a constant, but a variable parameter influenced by machining conditions. Its fluctuations can significantly destabilize the cutting process, especially at low feed rates, where the transition from continuous to intermittent cutting becomes more likely. This highlights the importance of accurately identifying \(h_{min}\) in order to maintain a consistent cutting performance. 2. In orthogonal cutting conditions, a linear relationship was established between the undeformed chip thickness and the cutting force. This allowed for the development of a linear force model, from which slope coefficients were calculated. Additionally, the determination of a critical angle enabled the identification of the exact point where material separation into the chip and remaining workpiece occurs. A deeper analysis of this angle made it possible to derive the \(h_{min0}\) coefficient, representing the minimum chip thickness independent of the cutting edge radius. 3. The \(h_{min0}\) coefficients were determined for both Ti Grade 2 and Ti Grade 5 alloys, with average values found to be approximately 0.313. While the mean values were similar, Ti Grade 2 exhibited significantly lower variation around the mean, indicating more stable and predictable cutting behavior. This contrast can be attributed to the simpler, more homogeneous structure of Ti Grade 2 compared to the more complex microstructure of Ti Grade 5. 4. For oblique cutting, \(h_{min}\) values were estimated based on the determined \(h_{min0}\) and experimentally measured tool edge radii. These values reached up to a few micrometers. A physical model was developed to show how increasing \(h_{min}\) shifts the material separation point away from the cutting edge, resulting in increased lateral material flow. When feed is reduced at a constant \(h_{min}\) (e.g., 6 \(\upmu\)m), a material stagnation zone emerges, indicating a loss of efficient chip formation and an increased risk of built-up edge and surface damage. 5. This study confirmed that \(h_{min}\) has a particularly strong effect at low feed rates, where the process becomes more sensitive to instability and vibration. In the case of Ti Grade 2, this effect was observed even at medium feed rates, reinforcing the alloy's greater susceptibility to dynamic disturbances. The findings underscore the need for careful feed rate selection, especially when machining pure titanium grades. 6. To assess the dynamic stability of the process, the 0-1 test for chaos was applied to cutting force signals. The results showed that Ti Grade 2 transitioned into chaotic behavior much more rapidly than Ti Grade 5. The threshold time product (\(T\cdot dt\)) for the onset of chaos was 6 s for Ti Grade 2 and 50 s for Ti Grade 5. Furthermore, the dominant frequencies of chaotic fluctuations were 0.17 Hz and 0.02 Hz, respectively. This clearly indicates that Ti Grade 2 is more prone to localized, high-frequency dynamic instability during cutting. 7. The results collectively demonstrate that the feed rate relative to \(h_{min}\) plays a critical role in determining the stability and predictability of the cutting process. Operating above \(h_{min}\) promotes stable, periodic cutting, while working below this threshold can lead to chaotic fluctuations in cutting forces, ultimately compromising surface quality and tool life. Therefore, maintaining machining stability requires the integration of multiple factors--including material properties, cutting tool geometry, thermal effects,and real-time monitoring--particularly when machining titanium alloys, which are inherently difficult to machine. Conceptualization: A.Z.-T.; Methodology: A.Z.-T.; Investigation: A.Z.-T. and E.Z.