Estimation of the Stability of the Machining Technological System Using Nonlinear Dynamics Mathematical Models

In the present work is investigated the technological processing system stability at high-speed turning. Increasing the cutting speed causes machining process instability, which drastically reduces the accuracy and machined surface quality, and the parts durability. A series of experiments was carried out to study the technological processing system stability using mathematical models based on the parametric method by I. Prigozhin and the friction systems behavior laws. The parametric approach conditions are perfectly combined with the classical systems of Lorentz and Rössler: these systems are dissipative, consist of three ordinary differential equations and contain control parameters. Therefore, dynamic system stability modeling is based on them. The models are built on the vibroacoustic signal time series generated by the machining. The technological processing system model is a system of ordinary differential equations capable of reproducing experimentally obtained time series with a given accuracy. The model shows that in the friction system chaotic attractors are formed under certain parameters, which is due to the presence of deterministic chaos in the system. The regulated and control parameters are revealed and depending on their set the system dynamics changes on the attractor on various models are investigated. The control parameter values intervals are shown forms stable or unstable system behavior. A comparative analysis of nonlinear dynamics mathematical models for the technological system behavior study and ones adequacy verification are carried out. The conclusion is made that the Lorenz and Rössler models can be used to assess the machining process stability at high-speed finishing turning.