Open Access

This paper presents the implementation of a recently developed continuous second-order dynamic friction model (FrD2) in the commercial multibody system software Simpack, where it is evaluated against Simpack's discontinuous friction model for stick-slip applications in terms of performance. A method for adapting parameters from the well-known LuGre model to the FrD2 model is introduced. The FrD2 model accurately captures complex friction phenomena, including the Stribeck effect, which is essential for simulating friction-induced vibrations. Tested on a festoon cable system and a belt model, the FrD2 model demonstrates itself as a robust alternative to both the LuGre and Simpack models, especially for applications requiring continuous transitions between static and dynamic friction states, long-term stiction effects, and other complex friction behaviors.

Dieses Lehrbuch stellt die Methoden der Mehrkörpersimulation anschaulich dar und erläutert an einfachen Beispielen die Vor- und Nachteile bei der praktischen Anwendung. In den Text integrierte Matlab-Skripte und -Funktionen verdeutlichen die einzelnen Methoden. Die Modellbildung, die mathematische Beschreibung und die numerische Simulation von Systemen starrer Körper bilden dabei die Schwerpunkte. Konkrete Beispiele beinhalten die Eigendynamik eines Traktors mit Vorderachsfederung, das Hubschrauberrotorblatt sowie eine Pkw- Vorderachse. Die entsprechenden Matlab-Skripte und Lösungen zu den Übungsaufgaben können auf der Springer-Homepage beim Buch heruntergeladen werden. Neu aufgenommen wurden SparseMatrix Operationen sowie ein Beispiel zu einfach geschlossenen kinematischen Schleifen.

This paper introduces a method to predict wear behavior in conveyor belt systems using a lumped mass modeling approach. While previous research has focused primarily on lateral belt walking, this study shifts attention to belt deformation and its associated wear. Both significantly affect system efficiency and component lifespan. The authors propose using local frictional power as a wear indicator, leveraging its direct relation to frictional work in established wear models. To validate the method, the study simulates a conveyor belt with three flexible rollers and a deformable belt modeled through rigid spheres connected by spring-damper elements. The authors quantify and visualize frictional power density across the belt width, distinguishing between running and transverse directions. The results demonstrate that the frictional power distribution depends heavily on discretization quality, particularly due to the polygon effect inherent in the lumped mass approach. A convergence analysis reveals a minimum discretization of nine sphere rows with 557 spheres per row to achieve reliable qualitative insights. This method enables researchers to evaluate wear distribution in flexible conveyor systems and adapt the approach for broader applications in multibody dynamics. Future work should refine discretization techniques and friction models to enhance quantitative accuracy.

The LuGre model is widely used in the analysis and control of systems with friction. Recently, it has even been made available in the commercial multibody dynamics simulation software system Adams. However, the LuGre model exhibits well-known drawbacks like, too low and force rate dependent break-away forces, drift problems during sticking periods, and significant differences in non-stationary situations between the pre-defined friction law and the one produced by the LuGre model. In the present literature, these problems are supposed to come from the model dynamics or its nonlinear nature. However, most of these drawbacks are not simple side effects of a dynamic friction model but are caused in the LuGre approach, as shown here, by a too simple and inconsistent model of the bristle dynamics. Standard examples and a more practical application demonstrate, that the LuGre model is not a “what you see is what you get” approach. A dynamic friction model with accurate bristle dynamics and consistent friction force is set up here. It provides insight into the physical basis of the LuGre model dynamics. However, it results in a nonlinear and implicit differential equation, whose solution will not be easy because of the ambiguity of the friction characteristics. The standard workaround, a static model based on a simple regularized characteristics, produces reliable and generally satisfactory results, but definitely cannot maintain stick. The paper presents a second order dynamic friction model, which may serve as an alternative. It can maintain stick and produces realistic and reliable results.