The initial tool wear during machining of titanium metal matrix composite (TiMMCs) is the result of several wear mechanisms: tool layer damage, friction - tribological wear, adhesion, diffusion and brace wear. This phenomenon occurs at the first instant and extends to only ten seconds at most. In this case the adhesive wear is the most important mechanism while the brace wear is considered as a resistance wear layer at the beginning of the steady wear period. In this paper, the effect of the initial tool wear and initial cutting conditions on tool wear progression and tool life is investigated. We proposed herein a new mathematical model based on the scatter wear and Lyapunov exponent to study quantitatively the “chaotic tool wear”. The Chaos theory, which has proved efficient in explaining how something changes in time, was used to demonstrate the dependence of the tool life on the initial cutting conditions and thus contribute to a better understanding of the influence of the initial cutting condition on the tool life. Based on the chaotic tool wear model, the scatter wear dimension and Lyapunov exponents were found to be positive in all case of the initial cutting conditions such as initial speed, feed rate and depth of cut. The initial cutting speed appears however to have the most significant impact on tool life. In particular, the mathematical model was successfully applied to the case of machining TiMMCs. It was clearly shown that changing the initial cutting speed by 20 m/min for the first two seconds of machining instead of keeping it constant at 60 m/min during the whole cutting process leads to an increase in the tool life (up to 24%).

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