MS08.5: Non-Smooth Dynamics

Nonlinear dynamics of impact oscillators have been widely studied for the design and control of practical systems with amplitude constraining stop. In this study, we theoretically and experimentally investigated the hunting motion in a single railway wheelset with impact to rails.The system above a critical running speed is self-excited due to special contact force, which is called the creep force, between the rail and wheel and can be regarded as a flutter-type self-excited oscillator with double-side impact, because the growth of amplitude is constrained by the impact between rails and wheels. Numerical study of a mathematical model and experimental results using a simple apparatus demonstrate asymmetric oscillation that collides with one of the left or right rails in a single oscillation cycle.

There is an ongoing effort to develop nonsmooth versions of high-order schemes for the simulation of mechanical systems with frictional contact. In this paper, we introduce a particular version of the principle of virtual action, which allows to derive a nonsmooth extensions to the Lobatto IIIA-IIIB methods. The discretization is performed using the ideas of Discrete Mechanics. The schemes are derived by pairing the discretization of the principle of virtual action with a discretization of the contact laws that is consistent with the bilateral constraints of the system. Finally, the properties of the presented schemes, e.g., their convergence behavior, are analyzed using a suitable numerical benchmark example.

This contribution introduces the application of control barrier functionals in turning processes to maintain acceptable surface quality while increasing productivity. An illustrative simple example is presented to control an unstable turning process by applying an optimal feedback loop with input saturation.