Contact Calculations in Flexible Multibody Systems


Impacts occur in many mechanical systems, such as valve control systems, hammer drills or vehicle gearboxes. Important characteristics of impacts are the short time duration, high contact forces, and high frequency phenomena like wave propagation and structural vibrations.

One possibility to analyze the contact process is the fully elastic modeling of the bodies using the finite element method (FEM). To capture all elastic effects during the impact, a finely discretized mesh, especially in the contact area, is needed. Furthermore, the unilateral contact constraint always leads to a nonlinear problem. These mentioned points result in high computation times and, therefore, the global behavior cannot be simulated in reasonable time using FE models.

The efficient analysis of the global motion of dynamic systems is often possible using the approach of rigid multibody systems (MBS). However, during impact elastic deformations cannot be neglected. For the efficient investigation of these deformations, the traditional approach of MBS can be enhanced by elastically deformable bodies, which leads to the approach of flexible multibody systems (FMBS).

This research project focuses on the precise and efficient analysis of the contact behavior using the approach of flexible multibody systems (FMBS) with reduced flexible bodies.


For the analysis of the local deformation of the contact area and the high frequency wave propagation a combination of reduced FMBS and a nodal contact routine are used in this research.

At first the CAD geometries of the bodies are discretized using FE tools. The description of the contact between the bodies is realized with contact elements. For an exact detection of the contact area a three-dimensional description of the contact surface is needed. These contact elements are available as surface elements from the FE discretization.

In order to save computation time, the number of elastic degrees of freedom can be reduced using different model order reduction techniques such as modal reduction or the Craig-Bampton method.

During impact, kinetic energy of the rigid body motion is transferred into plastic or viscoelastic deformation of the contact area and into waves and structural vibrations. These vibrations propagate away from the contact area. In the modeling these vibrations can be efficiently captured using a moderate number of eigenmodes. However, using only modally reduced models a large number of high frequency eigenmodes is required to capture all local deformation effects in the contact area. Therefore, an efficient coupling of the contact surfaces is not possible. Consequently, it is recommended to use the Craig-Bampton method for model order reduction. In this method, the global deformation of the bodies can be captured with a moderate number of eigen modes. To capture all local deformations in the contact area static shape functions are used. However, this yield numerical challenging problems and the interplay of this reduction technique with the contact dynamic has not been fully explored yet.

The results will be compared with full FE simulations and experiments. For position and speed measurement Laser-Doppler vibrometers are used and for strain measurements special high frequency-capable strain gauges can be employed.

Overview poster of Contact Calculations in Flexible Multibody Systems (click here for PDF file in German).




Selected Publications

  1. Seifried, R.: Numerische und experimentelle Stoßanalyse für Mehrkörpersysteme. Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Band 2. Aachen: Shaker Verlag, 2005.
  2. Seifried, R.; Schiehlen, W.; Eberhard, P.: The Role of the Coefficient of Restitution on Impact Problems in Multibody Dynamics. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, Vol. 224, 2010, pp. 279-306 [DOI: 10.1243/14644193JMBD239].
  3. Seifried, R.; Minamoto, H.; Eberhard, P.: Viscoplastic Effects Occurring in Impacts of Aluminum and Steel Bodies and Their Influence on the Coefficient of Restitution. ASME Journal of Applied Mechanics, Vol. 77, No. 4, 41008 1-7, 2010, [DOI:10.1115/1.4000912].
  4. Minamoto, H.; Seifried, R.; Eberhard, P.; Kawamura, S.: Analysis of Repeated Impacts on a Steel Rod with Visco-Plastic Material Behavior. European Journal of Mechanics - A/Solids, No. 30, pp. 336-344, 2011 [DOI: 10.1016/j.euromechsol.2010.12.002].