Determination of the stability lobes in milling operations based on homotopy and simulated annealing techniques

The stability of a thin wall workpiece milling process is investigated through a single degree of freedom system that mimics the milling machine operation. The stability lobes were computed by using the Enhanced Multistage Homotopy Perturbation Method (EMHPM), the Chebyshev Collocation, the Semi-Discretization and Full-Discretization methods. A comparison of these methods with respect to experimental data and computational time was made to identify the method with the best performance in terms of accuracy and computational time in order to optimize the material removal rate by using the Simulated Annealing algorithm (SA). Then, we have used the EMHPM with the SA algorithm to establish the optimal cutting conditions. Based on numerical simulation computed by combining the SA algorithm with the EMHPM and experimental data, we have determined the optimum cutting condition in less than 400 ms which is 100 times faster than the off-line methods used to find the stability lobes.