A New Algorithm to Solve the Extended-Oxley Analytical Model of Orthogonal Metal Cutting in Python

This paper presents a new implementation method of the Extended-Oxley analytical model, previously proposed by Lalwani in 2009, for orthogonal cutting of metals with a Johnson–Cook thermo-elastoplastic flow law. The present work aims to improve the implementation of this analytical model in order to propose a unified solution that overcomes the main shortcomings of the original model: the non-uniqueness of the solution, the low accuracy of the obtained solution, and the relatively long computational time for a purely analytical approach. In the proposed implementation, the determination of the optimal set of model parameters is based on an optimization method using the Python LMFIT library with which we have developed a dual Levenberg–Marquardt optimization algorithm. In this paper, the performance and efficiency of the developed model are presented by comparing our results for a 1045 steel with the simulation results obtained in the original paper proposed by Lalwani. The comparison shows a considerable gain in terms of computational speed (more than 2000 times faster than the original model), uniqueness of the obtained solution, and accuracy of the obtained numerical solution (almost zero force imbalance).