Chaos theory applied to analyze tool wear during machining of titanium metal matrix composite (TiMMCs)

• Main Author: Duong, Xuan Truong
• Format: Dissertation
• Language: English
• Published: Ann Arbor ProQuest Dissertations & Theses 2015
• Subjects: Mechanical engineering
• ISBN: 1369486510; 9781369486513

This research work focused on developing a new method to investigate the tool wear and tool life during machining of titanium metal matrix composite (TiMMCs). That novel generation material offers many other advantages compared to titanium alloys and metal matrix composites. Due to high strength, high stiffness, and creep resistance at high temperatures, TiMMCs is considered as a material of choice for applications in aerospace and automotive industries in the near future. However, the combination of all the hard machining characteristics of titanium alloys and metal matrix composites makes the TiMMCs an extremely difficult to cut material while their machinability is still not fully understood in the open literature.
In various studies on tool wear and tool life, three distinctive regions of tool wear have widely been classified according to the increase of tool wear versus cutting time. They are the initial wear, steady wear and accelerated wear periods. However, the initial tool wear phenomenon and its influence on the tool life are not yet clearly understood. This fact can be explained by noting that most of these studies have been performed within the steady wear period which intuitively seems to be the right method to handle tool life problem.
Accordingly, with the aim of contributing to a better understanding of the initial tool wear phenomenon as well as how it affects to the tool life, an investigation on initial tool wear behavior during machining of TiMMCs has been conducted in this thesis. The results have shown that the initial wear occurs at the first instant and extends to only ten seconds at the most; it is a result of complicated mechanisms such as coating layer damage, friction - tribological wear diffusion and adhesion. The low thermal conductivity and high reactivity of titanium alloys lead to plastic deformation and forming of a built-up-edge (BUE) at elevated temperatures under all experimental cutting conditions in the first or initial, wear zone. This wear mechanism is indeed opposite to the wear mechanism of abrasion found in the steady wear period.
More importantly, by analyzing the wear mechanism at the first transition wear period we report herein a new wear form. The effect of chemical stresses under high cutting force and high temperatures was the main reason for the resulting diffusion wear; the by-products of that cutting process can spontaneously react with atmospheric oxygen. These oxidized titanium and aluminum based materials then diffuse from the coating layer and the TiMMCs at high pressure and elevated temperature. All together, these mechanisms in association with the coating layer (Ti,Al)N of the cutting tool and TiC reinforcement of the workpiece material generated a new hard thin layer involved in the machining process. This new wear layer which authors have coined "wear shield" is mostly found on the flank face at the first transition wear period. The formulation of the wear shield layer allows a better explanation why the wear rate increases very fast during initial wear and then decreases abruptly at the transition point to the steady wear period on one hand; and interpreting how significantly the initial tool wear and initial cutting conditions affect the tool wear evolution and the entire tool life on the other.
In this work, chaos theory is applied, for the first time to the best of our knowledge, to investigate the effect of initial conditions on the tool wear. The mathematic of chaos theory has been proved efficient in describing how something changes in time based on it sensitive dependence on initial conditions. More importantly, it is reported that chaos theory can apply to a simple dynamical system. This new philosophy can notably change the methodologies for the studies of machining technology. Analyzing dynamical cutting and tool wear during machining process based on the chaos theory is thus of interest. This implies a thorough analysis of the initial parameters of the machining process. We therefore considered these characteristics of chaos to demonstrate the dependence of the tool life on the initial cutting conditions. In fact, almost all applications of chaos have concerned a nonlinear dynamical system while its application in the tool wear investigation has not been reported in the literature so far. Hence to investigate how sensitively the tool life is affected by the initial cutting conditions the chaotic tool wear should be quantified numerically. In this case, the wear curves evolution during the machining processes that are being used to calculate Lyapunov exponents need to be modeled by a continuous function.
Accordingly, two new mathematical models are proposed in this thesis. First, a new mathematical model so called "chaotic tool wear" is proposed to quantify a chaotic tool wear during machining based on the Lyapunov exponent and fractal dimension. In order to solve the chaotic wear phenomena, another mathematical model is developed to characterize the variation in wear curves under different initial parameters. In the present work, the multistep method and cubic B-splines collocation methods are used to solve an ordinary differential equation of a chaotic tool wear model.
As a result, a new concept of tool wear, "chaotic tool wear", is proposed in the study of tool wear. The chaotic tool wear model provides for the first time with a full explanation of the wear rate behavior at the first initial wear period and brings more insight on how the tool life depends significantly on the initial cutting conditions. More importantly, application of the chaotic tool wear model to change initial cutting conditions when machining TiMMCs improved the tool life by up to 24.5%.