Nonlinear Dynamics of Orthogonal Metal Cutting

An in depth study on the nonlinear dynamic interactions occuring during metal cutting process is given. A general mathematical model of the machine tool-cutting process is established, and then a high accuracy numerical algorithm for a multibody dynamic system excited by a cutting process is developed. Next, a simple model of orthogonal metal cutting, where all nonlinearities have been accounted for in the cutting process has been investigated in the first instance. Then stochastic properties of the material being cut were introduced to reflect variations in the workpiece properties, in particular in the cutting resistance. Nonlinear dynamics techniques such as constructing bifurcation diagrams and Poincaré maps are employed to ascertain dynamics responses for both the deterministic and the stochastic model. Untypical routes to chaos and unusual topology of Poincaré cross-sections were observed. The analysis conducted has led to formulation of some practical design recommendations. Finally, occurrence of chatter was investigated experimentally using a specially designed rig.