Bifurcation analysis of thin-walled structures trimming process with state-dependent time delay

Abstract

Our previous study [1] revealed that trimming of thin-walled structures has a strongly nonlinear nature, hence this investigation delves into nonlinear dynamic analysis. Specifically, a perturbation method was applied to analyze the linear stability, whilst a direct numerical integration approach was employed to construct bifurcation diagrams, where unsafe cutting caused by multiple stabilities had been found. Basins of attraction were computed to evaluate the cutting safety. Finally, the stability charts for both linearized and fully nonlinear models were constructed showing a good degree of similarity but the linear one has a larger area of stable trimming. The data from our focused experimental studies was then superimposed on both diagrams and it is clear that more refinements in models’ calibration are needed. This work has laid firm foundations for further advanced modelling investigations and experimental studies to gain more insights into nonlinear dynamics of the machining process.