TY - CHAP A1 - Hackl, Andreas A1 - Hirschberg, Wolfgang A1 - Lex, Cornelia A1 - Rill, Georg ED - Bargende, Michael ED - Reuss, Hans-Christian ED - Wiedemann, Jochen T1 - Experimental validation of the Maxwell model for description of transient tyre forces T2 - 16. Internationales Stuttgarter Symposium, Automobil- und Motorentechnik N2 - Modelling and simulation of safety relevant Driver Assistance Systems (DAS) and Vehicle Dynamics Controllers (VDC) which act in standard and limit situations lead to increasing accuracy demands in the description of dynamic reactions of tyre contact forces, e.g. For that purpose, first-order approaches are widely applied in this field of vehicle dynamics and handling, which originate from Schlippe & Dietrich, were modified by Pacejka and later on refined by Rill. Y1 - 2016 SN - 978-3-658-13254-5 U6 - https://doi.org/10.1007/978-3-658-13255-2_29 SP - 401 EP - 418 PB - Springer CY - Wiesbaden ER - TY - CHAP A1 - Hackl, Andreas A1 - Hirschberg, Wolfgang A1 - Lex, Cornelia A1 - Rill, Georg ED - Spiryagin, Maksym ED - Gordon, Timothy ED - Cole, Colin ED - McSweeney, Tim T1 - Tyre type dependent transient force behaviour by means of a maxwell model T2 - The Dynamics of Vehicles on Roads and Tracks : Proceedings of the 25th Symposium of the International Association of Vehicle System Dynamics (IAVSD 2017), Rockhampton, Queensland, Australia, 14-18 August 2017 N2 - The present papers deals with the usability of an extended Maxwell model to describe the tyre dynamics during transient driving manoeuvres. In the present article, the para-metrisation process of a dynamic tyre model is investigated in a first step, using measurement data of tyre forces from a flat trac tyre test bench, (IABG 2016). Two tyre types of dimensions 255/50 R19 and 175/55 R15 are used. The practical applicability is discussed, considering the measurement procedure and the parameter optimisation process. In a second step, the performance of the dynamic tyre model is validated using measurements of manoeuvres under higher dynamic excitation. As a last step, an outlook is given on further research planned in which the presented model and parametrisation are adapted to a larger frequency range. Y1 - 2018 SN - 1351057170 U6 - https://doi.org/10.1201/9781315265506 SP - 157 EP - 162 PB - CRC Press CY - London ER - TY - RPRT A1 - Rill, Georg T1 - Second-Order Dynamic Friction Model Goes Bi-Dimensional N2 - Dynamic friction models can handle not only slip-stick-slip transitions but also stick as long as the external load does not exceed the friction limit. The recently developed second-order dynamic friction model (FrD2) uses two internal states. It models standard friction characteristics by a smooth analytical function, which includes the Stribeck effect and also a viscous component. A horizontal shift of the regularized friction characteristics provides non-vanishing friction forces required to keep stick. Unlike the well-known LuGre model, the FrD2 model reproduces predefined friction characteristics very accurately and shows no drift under pulsating loads. This paper shows how to extend FrD2 to its bi-dimensional version FrD2bd. KW - Second-Order Dynamic Friction Model KW - Shifted Regularization KW - Bi-Dimensional Friction KW - Planar Oscillator KW - Sliding Pendulum Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:898-opus4-80791 CY - Regensburg ER - TY - RPRT A1 - Rill, Georg T1 - Second-Order Dynamic Friction Model In Three-Dimensional Applications N2 - The second-order dynamic friction model (FrD2) is a reliable alternative to the LuGre model. It can compete with commercial friction models and has been successfully tested in standard one- and two-dimensional friction problems. The FrD2 approach is based on a fictitious bristle with a fictitious mass that automatically adjusts to viscoelastic properties. The FrD2 model approximates standard friction characteristics using a smooth analytical function that incorporates the Stribeck effect and a viscous component. The two-dimensional FrD2 version enables users to specify different bristle and friction properties in each direction. This working paper demonstrates how to apply the FrD2 model to three-dimensional friction problems, such as distributed contacts and ball joints. KW - Second-Order Dynamic Friction Model (FrD2) KW - Three-Dimensional Friction KW - Distributed Friction KW - Ball Joint Friction Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:898-opus4-84288 CY - Regensburg ER - TY - RPRT A1 - Rill, Georg T1 - Second-Order Dynamic Friction Model (FrD2) in a Nutshell N2 - The well-known LuGre friction model generates dynamic friction forces. This force results from the approximation of the dynamics of a massless fictitious bristle. However, it has several drawbacks and fails to reproduce predefined friction characteristics. The second-order dynamic friction model (FrD2) avoids these drawbacks and accurately reproduces friction characteristics. The FrD2 model is based on a fictitious bristle whose mass automatically adapts to visco-elastic bristle properties. The FrD2 model describes friction characteristics using piecewise-defined analytical functions and applies shifted regularization, which allows for smooth handling of stick-slip transitions. FrD2 parameters can easily be derived from LuGre model parameters. KW - Second-Order Dynamic Friction Model KW - Shifted Regularization KW - Fictitious Bristle KW - FrD2 Model Parameter KW - LuGre to FrD2 Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:898-opus4-80770 ER - TY - CHAP A1 - Rill, Georg ED - Apetaur, Milan T1 - Vehicle Dynamics in Real-Time Simulation T2 - The dynamics of vehicles on roads and on tracks N2 - This paper presents some ideas on a new concept, named COMPACT (Computer Simulation of Passenger Cars and Trucks). COMPACT was developed for the mathematical description of vehicles in all driving situations. As COMPACT is completely adopted to the particular problems in road vehicle dynamics, it results in a computer code where execution time is minimized. Thus, even real-time application at the Daimler-Benz driving simulator is possible. Previous Chapter Next Chapter Y1 - 2021 SN - 9781003210894 U6 - https://doi.org/10.1201/9781003210894-40 SP - 337 EP - 347 PB - CRC Press CY - Boca Raton ER - TY - BOOK A1 - Rill, Georg A1 - Schaeffer, Thomas A1 - Borchsenius, Fredrik T1 - Grundlagen und computergerechte Methodik der Mehrkörpersimulation N2 - 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 einen Bungee-Sprung, die Eigendynamik eines Traktors mit Vorderachsfederung, das Hubschrauberrotorblatt sowie eine Pkw-Vorderachse. Die Lösungen zu den Übungsaufgaben und die im Text integrierten Matlab-Beispiele, die zum Teil durch Animationen angereichert sind, sowie zusätzliche Beispiele und Anwendungen stehen auf der Verlagshomepage beim Buch zum Download zur Verfügung und ermöglichen dadurch auch ein effizientes Selbststudium. Y1 - 2020 SN - 978-3-658-28911-9 U6 - https://doi.org/10.1007/978-3-658-28912-6 PB - Springer Fachmedien CY - Wiesbaden ET - 4. Aufl. ER - TY - BOOK A1 - Rill, Georg A1 - Schaeffer, Thomas T1 - Grundlagen und Methodik der Mehrkörpersimulation N2 - 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. Y1 - 2017 SN - 978-3-658-16008-1 U6 - https://doi.org/10.1007/978-3-658-16009-8 PB - Springer CY - Wiesbaden ET - 3. Aufl. ER - TY - BOOK A1 - Rill, Georg A1 - Schaeffer, Thomas T1 - Grundlagen und Methodik der Mehrkörpersimulation : Vertieft in Matlab-Beispielen, Übungen und Anwendungen N2 - Dieses Lehrbuch vermittelt nicht nur Grundlagen, sondern stellt auch 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 und ermöglichen es, Aufwand und Problematik bei der Umsetzung der Theorie innerhalb von Simulationsprogrammen einzuschätzen. Die Modellbildung, die mathematische Beschreibung und die numerische Simulation von Systemen starrer Körper bilden dabei die Schwerpunkte. Konkret behandelte Beispiele sind die Eigendynamik eines Traktors mit gefederter Vorderachse, das Rotorblatt eines Hubschraubers sowie die Vorderachse eines Pkws. Die entsprechenden Matlab-Skripte und Lösungen zu den Übungsaufgaben können auf der Springer-Homepage beim Buch heruntergeladen werden. Der Inhalt Dynamik des starren Körpers - Bewegungsgleichungen - Starre Körper mit elastischen und kinematischen Verbindungselementen - Integrationsverfahren - Rekursiver Algorithmus - Differential-Algebraische Gleichungen - Analyse von Mehrkörpersystemen - Anwendungs- und Übungsbeispiele aus der Technik Die Zielgruppen Studenten des Maschinenbaus, der Elektrotechnik und Mechatronik sowie der Biomechanik an Hochschulen und Universitäten Ingenieure in der Praxis, die sich mit Fragestellungen der Mehrkörpersimulation (MKS) befassen Entwickler aus der Kfz-Technik sowie Fachleute aus F+E Die Autoren Dr.-Ing. Georg Rill ist Professor mit den Lehrgebieten Technische Mechanik, Ingenieurinformatik, Fahrdynamik, Mehrkörperdynamik sowie Laborleiter Fahrdynamik. Dr.-Ing. Thomas Schaeffer ist Professor mit den Lehrgebieten Konstruktion, CAD, Maschinenelemente und Getriebetechnik, Mehrkörpersysteme und Bewegungstechnik sowie Laborleiter Mehrkörpersimulation, beide an der Ostbayerischen Technischen Hochschule (OTH) Regensburg. Y1 - 2014 U6 - https://doi.org/10.1007/978-3-658-06084-8 PB - Springer CY - Berlin ER - TY - JOUR A1 - Schuderer, Matthias A1 - Rill, Georg A1 - Schaeffer, Thomas A1 - Schulz, Carsten T1 - Friction modeling from a practical point of view JF - Multibody System Dynamics N2 - AbstractRegularized static friction models have been used successfully for many years. However, they are unable to maintain static friction in detail. For this reason, dynamic friction models have been developed and published in the literature. However, commercial multibody simulation packages such as Adams, RecurDyn, and Simpack have developed their own specific stick-slip models instead of adopting one of the public domain approaches. This article introduces the fundamentals of these commercial models and their behavior from a practical point of view. The stick-slip models were applied to a simple test model and a more sophisticated model of a festoon cable system using their standard parameters. KW - Multibody dynamics KW - Friction KW - Stick-slip effect KW - Adams KW - RecurDyn KW - Simpack Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:898-opus4-72513 SN - 1384-5640 N1 - Corresponding author: Matthias Schuderer PB - Springernature ER - TY - GEN A1 - Schuderer, Matthias A1 - Rill, Georg A1 - Schulz, Carsten A1 - Schaeffer, Thomas T1 - Influence of fictitious bristle parameters in dynamic friction models T2 - Global Annual Meet on Mechanical and Aerospace Engineering (GAMMAE2025), March 10-12, 2025, Rome, Italy N2 - In this study, the influence of bristle parameters in dynamic friction models is investigated, in particular in the LuGre and FrD2 models. These models contain internal states to better capture the friction behavior. The FrD2 model, a second-order dynamic friction model, aims at higher accuracy. The investigation focuses on how the independent variation of the bristle stiffness and the damping parameters affects the model behavior, especially considering the practical approximations used in determining the damping coefficient. Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:898-opus4-80348 ER - TY - BOOK A1 - Rill, Georg A1 - Schaeffer, Thomas A1 - Borchsenius, Fredrik T1 - Grundlagen und computergerechte Methodik der Mehrkörpersimulation BT - Vertieft in Matlab-Beispielen, Übungen und Anwendungen N2 - Dieses Lehr- und Übungsbuch vermittelt auf anschauliche Weise die Methoden der Mehrkörpersimulation und verdeutlicht deren Vor- und Nachteile bei der praktischen Anwendung anhand konkreter Beispiele. Die einzelnen Methoden werden durch Matlab-Skripte und -Funktionen verdeutlicht, wobei die Modellbildung, die mathematische Beschreibung und die numerische Simulation von Systemen starrer Körper die Schwerpunkte bilden. Die vorliegende Auflage wurde unter anderem um Matlab-Live-Skripte erweitert, welche kleine Animationen zur Veranschaulichung der Dynamik der Probleme enthalten. Die Lösungen zu den Übungsbeispielen und die integrierten Matlab-Skripte sowie weitere Beispiele und Anwendungen stehen über QR-Codes zum Download zur Verfügung und ermöglichen dadurch auch ein effizientes Selbststudium. KW - ADAMS-Modell KW - McPherson-Achse KW - Euler-Parameter KW - Bushings KW - Kontaktelement KW - Kinematische Bindung KW - Räumliches Doppelpendel KW - Analyse MKS KW - Lumped Mass Modelle KW - SIMPACK-Modell KW - Sparse Matrix KW - Mehrkörpersystem KW - MATLAB KW - Dynamik KW - Simulation Y1 - 2023 U6 - https://doi.org/10.1007/978-3-658-41968-4 PB - Springer Nature ER - TY - CHAP A1 - Rill, Georg A1 - Schaeffer, Thomas A1 - Borchsenius, Fredrik T1 - Analyse von Mehrkörpersystemen T2 - Grundlagen und computergerechte Methodik der Mehrkörpersimulation N2 - Nach dem Aufbau eines Mehrkörper-Simulationsmodells muss dieses auf Richtigkeit, Funktionalität und Wirtschaftlichkeit getestet werden. Die Ermittlung der Gleichgewichtslage stellt dabei eine erste Plausibilitäts-Kontrolle dar. Eine Linearisierung mit anschließender Analyse der Eigendynamik liefert Aussagen über die Frequenzen und das Dämpfungsverhalten des Modells. Einfache Erregersignale ermöglichen einen ersten Einblick in das nichtlineare dynamische Verhalten des Modells. Modell-Parameter, die nicht genau bekannt sind, können durch gezielte Variationen plausibel geschätzt oder über eine Optimierung sogar mit optimalen Werten belegt werden. Nach all diesen Tests steht das Mehrkörper- Simulationsmodell dann für praktischeUntersuchungen zurVerfügung, die neben reinen Zeitsimulationen auch Methoden der Inversen Kinematik und der Inversen Dynamik mit einschließen. KW - Gleichgewicht KW - Linearisierung KW - Eigendynamik KW - Fremderregung KW - Optimierung KW - Inverse Kinematik KW - Inverse Dynamik Y1 - 2023 U6 - https://doi.org/10.1007/978-3-658-41968-4_5 SP - 198 PB - Springer ER - TY - JOUR A1 - Rill, Georg A1 - Schaeffer, Thomas A1 - Schuderer, Matthias T1 - LuGre or not LuGre JF - Multibody System Dynamics N2 - 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 simple regularized characteristics, produces reliable and generally satisfactory results but definitely cannot maintain a stick. The paper presents a second-order dynamic friction model, which may serve as an alternative. It can maintain a stick and produces realistic and reliable results. KW - Dynamic friction model KW - LuGre model KW - Asymmetric regularization KW - Break-away force KW - Stick-slip KW - Multibody dynamics Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:898-opus4-65653 N1 - Corresponding author: Georg Rill PB - Springer ER - TY - INPR A1 - Rill, Georg A1 - Schaeffer, Thomas A1 - Schuderer, Matthias T1 - LuGre or not LuGre N2 - 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. Y1 - 2022 U6 - https://doi.org/10.21203/rs.3.rs-2266522/v1 ER - TY - GEN A1 - Schuderer, Matthias A1 - Rill, Georg A1 - Schulz, Carsten A1 - Schaeffer, Thomas T1 - Dynamic Stick-Slip Models based on Continuous and Discontinuous Friction Characteristics T2 - ENOC - European Nonlinear Dynamics Conference, 11th, 2024, Delft N2 - 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. KW - Multibody Simulation KW - Simpack KW - FrD2 KW - LuGre KW - Stick-slip Y1 - 2024 U6 - https://doi.org/10.2139/ssrn.5014569 ER - TY - JOUR A1 - Rill, Georg A1 - Schuderer, Matthias T1 - A Second-Order Dynamic Friction Model Compared to Commercial Stick–Slip Models JF - Modelling N2 - Friction has long been an important issue in multibody dynamics. Static friction models apply appropriate regularization techniques to convert the stick inequality and the non-smooth stick–slip transition of Coulomb’s approach into a continuous and smooth function of the sliding velocity. However, a regularized friction force is not able to maintain long-term stick. That is why dynamic friction models were developed in recent decades. The friction force depends herein not only on the sliding velocity but also on internal states. The probably best-known representative, the LuGre friction model, is based on a fictitious bristle but realizes a too-simple approximation. The recently published second-order dynamic friction model describes the dynamics of a fictitious bristle more accurately. It is based on a regularized friction force characteristic, which is continuous and smooth but can maintain long-term stick due to an appropriate shift in the regularization. Its performance is compared here to stick–slip friction models, developed and launched not long ago by commercial multibody software packages. The results obtained by a virtual friction test-bench and by a more practical festoon cable system are very promising. Thus, the second-order dynamic friction model may serve not only as an alternative to the LuGre model but also to commercial stick–slip models. KW - commercial stick–slip friction models KW - dynamic friction model KW - long-term stick KW - multibody dynamics Y1 - 2023 U6 - https://doi.org/10.3390/modelling4030021 SN - 2673-3951 N1 - Corresponding author: Georg Rill VL - 4 IS - 3 SP - 366 EP - 381 PB - MDPI ER - TY - INPR A1 - Rill, Georg A1 - Schuderer, Matthias T1 - A Second Order Dynamic Friction Model Compared to Commercial Stick-Slip Models N2 - Friction has long been an important issue in multibody dynamics. Static friction models apply appropriate regularization techniques to convert the stick inequality and the non-smooth stick-slip transition of Coulomb’s approach into a continuous and smooth function of the sliding velocity. However, a regularized friction force is not able to maintain long-term stick. That is why, dynamic friction models were developed in the last decades. The friction force depends herein not only on the sliding velocity but also on internal states. The probably best known representative, the LuGre friction model, is based on a fictitious bristle but realizes a too simple approximation. The recently published second order dynamic friction model describes the dynamics of a fictitious bristle more accurately. Its performance is compared here to stick-slip friction models, developed and launched not long ago by commercial multibody software packages. KW - dynamic friction model KW - commercial stick-slip friction models KW - long-term stick KW - multibody dynamics Y1 - 2023 U6 - https://doi.org/10.20944/preprints202306.1233.v1 ER - TY - GEN A1 - Schuderer, Matthias A1 - Rill, Georg A1 - Schaeffer, Thomas A1 - Schulz, Carsten T1 - Friction modeling from a practical point of view T2 - MULTIBODY2023: 11th ECCOMAS Thematic Conference on Multibody Dynamics, Tampa, 24th-28th May 2023 Y1 - 2023 ER -