Non-Linear Control and Numerical Analysis Applied in a Non-Linear Model of Cutting Process Subject to Non-Ideal Excitations - Angelo M. Tusset; Jonierson A. Cruz; Jose M. Balthazar; Maria E. K. Fuziki; Giane G. Lenzi (Modelling)
This work presents a non-linear mathematical model of a machining system subjected to a non-ideal vibration source. Computer simulations have shown chaotic behavior for specific parameters of the proposed mathematical model. The chaotic behavior is proven using time histories, phase diagrams, bifurcation diagrams, and the Lyapunov exponent. Considering that cutting tool vibration in the machining process is one of the main problems of productivity and machining accuracy, the introduction of a magnetorheological damper was considered in the proposed model to reduce the vibration amplitudes of the cutting tool and suppress the chaotic behavior. Hysteresis was considered in the magnetorheological damper model and its application in the system as both a passive and active absorber. The active control strategy considered the application of two non-linear control signals: feedforward to maintain the vibration with a desired behavior and state feedback to drive the system to the desired behavior. The numerical results demonstrated that the proposed controls efficiently reduced the vibration amplitude by introducing the MR damper. Active control has proven effective in controlling the force of the MR damper by varying the electrical voltage applied to the damper coil.