Cutting tool strategies for multifunctional part configurations: Part I—analytical economic models for cutting tools

The optimisation problem of multifunctional cutting tools, including multistep and combination tools, has been investigated. The tools' concepts for their physical understanding are discussed in order to provide the necessary background for the reader. Since they are not available in the literature, the necessary mathematical models for the optimsation are analysed based on constant tool speed (rpm), constant surface speed and variable speed or feed for each tool step and/or function. The integration of the mathematical models in optimisation schemes results in an analytical design tool for modelling and simulation of the advanced multifunctional tools in an early part processing stage that refines the process and tooling approaches while determining the sensitivity of these tools to the performance and production cost of individual machines. The aforementioned problem has been theoretically analysed here, while heuristic optimisation algorithms for determining the optimum cutting speed(s) and feed(s) for the multifunctional tools are presented in Part II of this paper. Experimental results and analytical examples which demonstrate the effectiveness and advantages of the proposed approach utilising the described mathematical models are presented in Part II.