Large oscillations of a thin cantilever beam: Physical experiments and simulation using absolute nodal coordinate formulation, accepted to appear
- Yoo W.-S, Lee, +6 authors D.Yu
- Journal of Nonlinear Dynamics,
MONDAY, March 1, 2004 09:00 – 10:00 Simulation and Time Integration 10:30 – 12:00 Mechatronic Systems 13:30 – 14:50 Multifield Problems 15:20 – 17:00 Analysis of Dynamical Systems Reliable Simulation of Mechatronic Systems using Newmark Algorithms O. Brüls (University of Liège ASMA, Belgium), P. Duysinx, J.-C. Golinval In the framework of flexible multibody systems simulation, the stability and the accuracy of the time integration process can be guaranteed by a family of implicit integrators derived from the Newmark scheme (Hilber-Hughes-Taylor and Generalized-α methods). This paper deals with the extension of those reliable integrators for the simulation of mechatronic systems. In order to account for the strong coupling between the mechanism and the control system, the coupled set of equations contains mechanical and control variables. The generation of those equations, their numerical treatment and their time integration may become unmanageable for realistic control systems. In many cases, it is however sufficient to consider a weak coupling, which means that the action of the control system is treated as an external force disturbing the dynamic equilibrium. The weak coupling assumption is fully justified when a digital controller is present in the control loop. Then, the control actions exhibit discontinuous transitions at each sampling instant. The standard form of the Newmark scheme assumes continuity of the acceleration variables, and is thus not appropriate for this situation. Therefore, we propose an adapted Newmark scheme which achieves an explicit treatment of the acceleration jumps throughout the integration process, so that the proper simulation of the mechatronic system is guaranteed. The paper describes the detailed modifications of the integration algorithm. Illustrative examples are used to point out the critical situations where they prevent from substantial integration errors. A Modified Implicit Euler Algorithm for Solving Vehicle Dynamic Equations G. Rill (FH Regensburg, University of Applied Sciences, Germany) Vehicle modelling is usually done by Multi Body Systems. Very often the overall model consists of several subsystems, like the drive train and the steering system. Due to the tire forces and torques and due to small but essential compliancies in the axle/wheel suspension systems the resulting differential equations are stiff. To improve the model quality dynamic models for some components like damper, and rubber elements are used. Again these models contain stiff parts. If the implicit Euler Algorithm is adopted to the specific problems in vehicle dynamics a very effective numerical solution can be achieved. Hence, even with very sophisticated vehicle models real time applications are possible. Due its robustness the presented algorithm is very well suited for co-simulations. The modifications in the implicit Euler Algorithm also make it possible to use a simple model for describing the dry friction in the damper and in the brake disks. A quarter car vehicle model with a longitudinal compliance in the wheel suspension and a dynamic damper model including dry friction is used to explain the algorithm and to show its benefits.