力学讲座-Nonlinear Dynamics and Stability in Machining Processes

Comprehensive understanding of chatter, bifurcations and stability is essential formproving productivity, quality, and efficiency of manufacturing operations. Chatternanifests itself as undesired large amplitude self-excited vibration, whilst bifurcationand stability analysis hold the keys to its effective control and suppression . Bifurcationsin manufacturing processes belong to the most complex ones, where nonlinearities arevery strong and play the dominant role. In this lecture, first I will define nonlinearity.chatter, bifurcations and stability in manufacturing processes with the focus on metalcutting. Then I will discuss on the frictional chatter, which was introduced andinvestigated with my group and collaborators. Chatter in precision grinding has been asubject of many our investigations, where low dimensional strongly nonlinear modelswere used to undertaken in depth analytical and numerical studies. Finally, examples ofadvanced nonlinear dynamics techniques such as path following bifurcation analysis,pasins of attraction, Poincare maps and Lyapunov exponents will be discussed, whichhave been used to examine stability and determine a practically important measure so-called cutting safety.