@inproceedings{HacklHirschbergLexetal., author = {Hackl, Andreas and Hirschberg, Wolfgang and Lex, Cornelia and Rill, Georg}, title = {Tyre Dynamics: Model Validation and Parameter Identification}, series = {Proceedings of the European Automotive Congress EAEC-ESFA 2015}, volume = {45}, booktitle = {Proceedings of the European Automotive Congress EAEC-ESFA 2015}, editor = {Andreescu, Cristian and Clenci, Adrian}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-27275-7}, doi = {10.1007/978-3-319-27276-4_20}, pages = {219 -- 232}, abstract = {The present paper deals with the experimental validation of tyre dynamics approaches as it is widely applied in tyre models for vehicle dynamics and handling. Firstly it gives a brief derivation of two modelling principles regarding the deflection velocity in the considered direction of the tyre's deformation. This is than followed by a brief description of the performed measurement procedure. From the measurements, a set of model parameters of the considered tyre, depending on different manoeuvre speeds and frequencies, is identified, where no particular fitting parameters for the tyre dynamics are needed. Based on these model parameters, the related dynamic simulations are carried out. The comparisons show that the applied first-order model describes the behaviour quite well within a certain operation range, whereas the second-order approach cannot deliver better results in spite of the longer computational time. However, for investigations within an enlarged frequency range of the steer input and at high slip angles, a more detailed model is recommended.}, language = {en} } @inproceedings{DessortChucholowskiRill, author = {Dessort, Ronnie and Chucholowski, Cornelius and Rill, Georg}, title = {Parametrical approach for modeling of tire forces and torques in TMeasy 5}, series = {Proceedings of the 16. Internationales Stuttgarter Symposium Automobil- und Motorentechnik}, booktitle = {Proceedings of the 16. Internationales Stuttgarter Symposium Automobil- und Motorentechnik}, editor = {Bargende, Michael and Reuss, Hans-Christian and Wiedemann, Jochen}, publisher = {Springer}, address = {Wiesbaden}, isbn = {978-3-658-13254-5}, pages = {435 -- 449}, abstract = {For the dynamic simulation of on-road vehicles, the model-element "tire/road" is of special importance, according to its influence on the achievable results. Sufficient description of the interaction between tire and road is one of the most challenging tasks of vehicle modeling. Two groups of tire models can be classified: handling models and structural or high-frequency models. Usually, various assumptions are made in modeling vehicles as multibody systems. Therefore, in the interest of balanced modeling, the precision of the complete vehicle model should stand in reasonable relation to the performance of the applied tire model. Handling tire models are characterized by a useful compromise between user friendliness, model complexity, and efficiency in computation time on the one hand, and precision in representation on the other hand. The present paper describes the general approach of the semi-physical tire model TMeasy for vehicle dynamics and handling simulation and its enhancement for bore torque simulation in Version TMeasy 5. A parameter fitting process realized by TESIS DYNAware and the validation of real tire behavior by simulation with DYNA4 is presented. Even with first guess parameters, the TMeasy tire model behaves in a realistic and plausible manner. Parameter estimation is intuitive and datasets from previous model versions can be easily migrated. After parameter fitting, the simulation results correlate well with both the tire test rig and full vehicle measurements. The enhancement of a three-dimensional slip calculation in the latest version does not modify the model behavior for high slip conditions, but improves the results not only for highly dynamic situations but also for low speed maneuvers such as parking.}, language = {en} } @inproceedings{DessortChucholowskiRill, author = {Dessort, Ronnie and Chucholowski, Cornelius and Rill, Georg}, title = {Parametrical approach for modeling of tire forces and torques in TMeasy 5}, series = {16. Internationales Stuttgarter Symposium, Automobil- und Motorentechnik, Bd. 1}, booktitle = {16. Internationales Stuttgarter Symposium, Automobil- und Motorentechnik, Bd. 1}, editor = {Bargende, Michael and Reuss, Hans-Christian and Wiedemann, Jochen}, publisher = {Springer}, address = {Wiesbaden}, isbn = {978-3-658-13254-5}, doi = {10.1007/978-3-658-13255-2_31}, pages = {435 -- 449}, abstract = {For the dynamic simulation of on-road vehicles, the model-element "tire/road" is of special importance, according to its influence on the achievable results. Sufficient description of the interaction between tire and road is one of the most challenging tasks of vehicle modeling. Two groups of tire models can be classified: handling models and structural or high-frequency models. Usually, various assumptions are made in modeling vehicles as multibody systems. Therefore, in the interest of balanced modeling, the precision of the complete vehicle model should stand in reasonable relation to the performance of the applied tire model. Handling tire models are characterized by a useful compromise between user friendliness, model complexity, and efficiency in computation time on the one hand, and precision in representation on the other hand.}, language = {en} } @inproceedings{HacklHirschbergLexetal., author = {Hackl, Andreas and Hirschberg, Wolfgang and Lex, Cornelia and Rill, Georg}, title = {Parameterization Process of the Maxwell Model to Describe the Transient Force Behavior of a Tire}, series = {WCX 17: SAE World Congress Experience 2017}, booktitle = {WCX 17: SAE World Congress Experience 2017}, publisher = {SAE}, doi = {10.4271/2017-01-1505}, abstract = {The present technical article deals with the modeling of dynamic tire forces, which are relevant during interactions of safety relevant Advanced Driver Assistance Systems (ADAS). Special attention has been paid on simple but effective tire modeling of semi-physical type. In previous investigations, experimental validation showed that the well-known first-order Kelvin-Voigt model, described by a spring and damper element, describes good suitability around fixed operation points, but is limited for a wide working range. When aiming to run vehicle dynamics models within a frequency band of excitation up to 8 Hz, these models deliver remarkable deviations from measured tire characteristics. To overcome this limitation, a nonlinear Maxwell spring-damper element was introduced which is qualified to model the dynamic hardening of the elastomer materials of the tire. However, the advantage of a more realistic description of the transient behavior leads to a more complex parametrization process. Therefore, in the proposed article attention is paid to describe the identification process including defined maneuvers to parameterize the tire model, where the accuracy of the parameter strongly depends on the quality of the available input data from measurement. In order to study this important aspect of parameterization, the reference data from simulation of the full physical tire model FTire is applied like a "virtual measurement" of specified testing maneuvers. The procedure of simulation by means of the enhanced first order dynamics model is implemented by the semi-physical tire model TMeasy. Finally, the improvements of the extended model are discussed and an outlook for future work is given.}, language = {en} } @inproceedings{RillArrietaCastro, author = {Rill, Georg and Arrieta Castro, Abel}, title = {A Novel Approach for Parametrization of Suspension Kinematics}, series = {Advances in Dynamics of Vehicles on Roads and Tracks: Proceedings of the 26th Symposium of the International Association of Vehicle System Dynamics (IAVSD 2019), August 12-16, 2019, Gothenburg, Sweden}, booktitle = {Advances in Dynamics of Vehicles on Roads and Tracks: Proceedings of the 26th Symposium of the International Association of Vehicle System Dynamics (IAVSD 2019), August 12-16, 2019, Gothenburg, Sweden}, editor = {Klomp, Matthijs and Bruzelius, Fredrik and Nielsen, Jens and Hillemyr, Angela}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-030-38076-2}, doi = {10.1007/978-3-030-38077-9_210}, pages = {1848 -- 1857}, abstract = {n the automotive industry, simulations are needed to analyse the dynamics of vehicles and also of its main components and subsystems, e.g. tires, brakes and suspension systems. These simulations are required for an early-stage development and in consequence, they must deliver realistic results. Suspension systems plays a key role in comfort and safety of road vehicles. They usually consist of rigid links and force elements that are arranged with a specific topology. In addition, some of their functionalities are to carry the weight of the car and the passengers, and maintain a correct wheel alignment. In simulations involving suspension systems, lookup-tables are frequently used. They are obtained from a Kinematic and Compliance (KnC) test and then standardized for a specific vehicle simulation software. Nonetheless, lookup-tables require a reasonable number of characteristic points. Additionally, derivatives, interpolation, and extrapolation are not necessarily smooth. This produces results that depend on the interpolation technique and may be inaccurate. In this paper, a novel method called "design kinematics" is proposed. This method can describe the kinematic properties of almost any type of suspension systems. Comparisons with an analytic calculation and a KnC measurement shown that the design kinematics is able to represent the kinematic and compliance properties of suspension systems extremely well and very efficiently.}, language = {en} } @inproceedings{RillArrietaCastro, author = {Rill, Georg and Arrieta Castro, Abel}, title = {The Influence of Axle Kinematics on Vehicle Dynamics}, series = {Interdisciplinary Applications of Kinematics. Proceedings of the Third International Conference (IAK)}, volume = {71}, booktitle = {Interdisciplinary Applications of Kinematics. Proceedings of the Third International Conference (IAK)}, editor = {Kecskem{\´e}thy, Andr{\´e}s and Geu Flores, Francisco and Carrera, Eliodoro and Elias, Dante A.}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-030-16422-5}, doi = {10.1007/978-3-030-16423-2_2}, pages = {23 -- 31}, abstract = {The automotive industry employs many different kinds of axle suspension systems at modern passenger cars. Important criteria are costs, space requirements, kinematic properties, and compliance attributes. This paper illustrates that in particular the kinematic properties of a suspension system have a significant influence on the dynamics of vehicles. As a consequence, the kinematics of a suspension system must be modeled very precisely and nonlinear. Typical kinematical features of a suspension system are discussed by analyzing the most common double wishbone axle suspension system. The influence of the axle kinematics on vehicle dynamics is finally demonstrated by simulation results generated with a fully nonlinear and three-dimensional multibody vehicle model.}, language = {en} } @incollection{Rill, author = {Rill, Georg}, title = {Multibody Systems and Simulation Techniques}, series = {Vehicle Dynamics of Modern Passenger Cars}, booktitle = {Vehicle Dynamics of Modern Passenger Cars}, editor = {Lugner, Peter}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-79007-7}, doi = {10.1007/978-3-319-79008-4_6}, pages = {309 -- 375}, abstract = {This part begins with an introduction to Multibody Systems (MBS). It presents the elements of MBS and discusses different modeling aspects. Then, different methods to generate the equations of motion are presented. Solvers for ordinary differential equations (ODE) as well as differential algebraic equations (DAE) are discussed. Finally, techniques for "online" and "offline" simulations including real-time applications are presented like necessary for car development. Special examples show the connection between simulation and test results.}, language = {en} } @book{RillArrietaCastro, author = {Rill, Georg and Arrieta Castro, Abel}, title = {Road Vehicle Dynamics}, publisher = {CRC Press}, address = {Boca Raton, Fla.}, isbn = {9780429244476}, doi = {10.1201/9780429244476}, abstract = {Road Vehicle Dynamics: Fundamentals and Modeling with MATLAB®, Second Edition combines coverage of vehicle dynamics concepts with MATLAB v9.4 programming routines and results, along with examples and numerous chapter exercises. Improved and updated, the revised text offers new coverage of active safety systems, rear wheel steering, race car suspension systems, airsprings, four-wheel drive, mechatronics, and other topics. Based on the lead author's extensive lectures, classes, and research activities, this unique text provides readers with insights into the computer-based modeling of automobiles and other ground vehicles. Instructor resources, including problem solutions, are available from the publisher.}, subject = {Fahrdynamik}, language = {en} } @article{Rill2017, author = {Rill, Georg}, title = {Reducing the cornering resistance by torque vectoring (X International Conference on Structural Dynamics, EURODYN 2017)}, series = {Procedia Engineering}, volume = {199}, journal = {Procedia Engineering}, publisher = {Elsevier}, doi = {10.1016/j.proeng.2017.09.393}, pages = {3284 -- 3289}, year = {2017}, abstract = {Usually, torque vectoring is used to reduce a significant understeer behavior at high speed cornering. Thus, providing larger vehicles with a sportive touch. Even on typical front wheel driven cars torque vectoring control is available now. Torque vectoring is nearly a standard on electric driven vehicles. Complex control and optimization strategies are applied to improve the maneuverability in particular or to enhance the driving behavior and reduce the energy consumption in addition. This paper shows, that a quite simple strategy will enhance the maneuverability and simultaneously reduce the cornering resistance in sharp bends. At first, a case study with a fully non-linear and three-dimensional vehicle model is performed. It turned out that a full drive torque shift to the outer wheels improves the maneuverability and reduces the cornering resistance in addition. This results are verified by an optimization performed with a simpler four-wheeled handling model. Here, the front steering angles and the driving torques at each of the four wheels are considered as free parameters. Minimizing the cornering resistance by taking the equations of motion for the four-wheeled handling model as constraints will deliver an optimal set of parameters then.}, language = {en} } @inproceedings{ArrietaCastroChavesRilletal., author = {Arrieta Castro, Abel and Chaves, Rafael B. and Rill, Georg and Weber, Hans I.}, title = {Use of Integrated Control to Enhance the Safety of Vehicles in Run-Off-Road Scenarios}, series = {Proceedings of DINAME 2017 : Selected Papers of the XVII International Symposium on Dynamic Problems of Mechanics}, booktitle = {Proceedings of DINAME 2017 : Selected Papers of the XVII International Symposium on Dynamic Problems of Mechanics}, editor = {Fleury, Agenor de T. and Rade, Domingos A. and Kurka, R. G.}, edition = {1. Auflage}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-91217-2}, issn = {2195-4356}, doi = {10.1007/978-3-319-91217-2_30}, pages = {431 -- 443}, abstract = {In this work, an integrated vehicle control system (IC) is tested in run-off-road scenarios. The integrated approach was employed in order to coordinate vehicle control systems, i.e. the Anti-Lock Brake System (ABS), Four-wheel Steering (4WS) and the Electronic Stability Program (ESP). To perform a run-off-road maneuver, a fuzzy virtual test driver was designed. By receiving the lateral position of an obstacle and the vehicle's relative yaw angle, the virtual test driver is capable of following a reference trajectory. Furthermore, to test the performance of the standalone controllers, i.e. ABS, ESP and 4WS, individual maneuvers are performed using a multibody vehicle model. The vehicle without any coordination between the control systems is used as reference. For the simulation results, it is concluded that the IC improves the vehicle stability and maneuverability in comparison with the non-integrated approach.}, language = {en} } @inproceedings{Rill, author = {Rill, Georg}, title = {TMeasy 6.0-A handling tire model that incorporates the first two belt eigenmodes}, series = {Proceedings of the XI International Conference on Structural Dynamics (EURODYN 2020): Athens, Greece, 23.11.2020 - 26.11.2020}, booktitle = {Proceedings of the XI International Conference on Structural Dynamics (EURODYN 2020): Athens, Greece, 23.11.2020 - 26.11.2020}, publisher = {EASD Procedia}, doi = {10.47964/1120.9054.18673}, pages = {676 -- 689}, abstract = {TMeasy 6.0, an extension to the standard TMeasy tire model of version 5.3, takes the relevant first two rigid body eigenmodes of the belt into consideration. These modes represent the in plane longitudinal and rotational movements of the belt relative to the rim. The dynamics of the longitudinal force is of higher order then and reproduces the tire wheel vibrations, required for indirect tire-pressure monitoring systems (iTPMS), sufficiently well. A tailored implicit solver, which takes the stiff coupling between the longitudinal force and the belt motions into account, still provides real-time performance in addition. Simulation examples show that a rigid body vehicle model equipped with TMeasy 6.0 makes it possible to investigate second generation indirect tire-pressure monitoring systems.}, language = {en} } @inproceedings{Rill, author = {Rill, Georg}, title = {A Three-Dimensional and Nonlinear Virtual Test Car}, series = {ENOC 2022, book of abstracts, 10th European Nonlinear Dynamics Conference: July 17-22, 2022, Lyon, France}, booktitle = {ENOC 2022, book of abstracts, 10th European Nonlinear Dynamics Conference: July 17-22, 2022, Lyon, France}, address = {Lyon}, pages = {49 -- 58}, abstract = {Virtual testing procedures have become a standard in vehicle dynamics. The increasing complexity of driver assistance sys- tems demand for more and more virtual tests, which are supposed to produce reliable results even in the limit range. As a consequence, simplified vehicle models, like the classical bicycle model or 4-wheel vehicle models, have to be replaced by a fully three-dimensional and nonlinear vehicle model, which also encompasses the details of the suspension systems. This paper presents a passenger car model, where the chassis, the four knuckles, and the four wheels are described by rigid bodies, the suspension system is modeled by the generic design kinematics, and the TMeasy tire model provides the tire forces and torques in all driving situations.}, language = {en} } @inproceedings{ArrietaCastroRill, author = {Arrieta Castro, Abel and Rill, Georg}, title = {Kinematic Versus Elasto-Kinematic Model of a Twistbeam Suspension}, series = {Advances in Dynamics of Vehicles on Roads and Tracks II, proceedings of the 27th Symposium of the International Association of Vehicle System Dynamics (IAVSD 2021): August 17-19, 2021, Saint Petersburg, Russia}, booktitle = {Advances in Dynamics of Vehicles on Roads and Tracks II, proceedings of the 27th Symposium of the International Association of Vehicle System Dynamics (IAVSD 2021): August 17-19, 2021, Saint Petersburg, Russia}, editor = {Orlova, Anna and Cole, David}, publisher = {Springer Nature}, doi = {10.1007/978-3-031-07305-2_59}, pages = {505 -- 605}, abstract = {The Twistbeam axle suspension is a cheap and robust layout for rear axles at front wheel driven midsize cars. Appropriate models have to take the elastic deformation of the torsion beam into account. A Finite Element approach requires detailed informations of the material properties and the shape which are usually only available in the final production stage. This paper presents a lumped mass model which can easily be integrated into a multibody vehicle model and can be used in the early stage of development. An approximation by the design kinematics further reduces the complexity of the model and considers only the kinematic properties of the Twistbeam suspension. Simulations using a nonlinear and three-dimensional vehicle model with different maneuvers, such as steady-state cornering, step steer input, and driving straight ahead on random road, demonstrate the performance and, in particular, the difference of the presented Twistbeam suspension models.}, language = {en} } @inproceedings{Rill, author = {Rill, Georg}, title = {Real-Time capable Multibody Model of dual Truck Front Axles}, series = {Proceedings of DINAME 2023 - Selected Papers of the XIX International Symposium on Dynamic Problems of Mechanics, 26 Feb - 03 Mar 2023, Piren{\´o}polis, Brazil}, booktitle = {Proceedings of DINAME 2023 - Selected Papers of the XIX International Symposium on Dynamic Problems of Mechanics, 26 Feb - 03 Mar 2023, Piren{\´o}polis, Brazil}, editor = {Fleury, Agenor de T.}, publisher = {Springer}, abstract = {Dual front steering axles are quite common in multi-axled heavy duty trucks. In standard layouts of such axle combinations, the steer motions of the wheels depend not only on the rotation of the steering wheel but also on the movements of the axles. As a consequence, the model complexity of the steering system should match with the complexity of the suspension model. The development of new technologies like advanced driver assistance systems or autonomous driving can only be accomplished efficiently using extensive simulation methods. Such kind of applications demand for computationally efficient vehicle models. This paper presents a steering system model for dual front axles of heavy duty trucks which supplements the suspension model of the axles. The model takes the torsional compliance of the steering column as well as the stiffness of the tie rods and the coupling rod into account. A quasi-static solution provides a straight forward computation including the partial derivatives required for an efficient implicit solver. The steering system model matches perfectly with comparatively lean, but sufficiently accurate multibody suspension models.}, language = {en} } @article{HirschbergRillWeinfurter, author = {Hirschberg, Wolfgang and Rill, Georg and Weinfurter, H.}, title = {Tire model TMeasy}, series = {Vehicle System Dynamics}, volume = {45}, journal = {Vehicle System Dynamics}, number = {sup1}, publisher = {Taylor\&Francis}, doi = {10.1080/00423110701776284}, pages = {101 -- 119}, abstract = {This paper describes the semi-physical tire model TMeasy for vehicle dynamics and handling analyses, as it was applied in the 'low frequency tire models' section of the research programme tire model performance test (TMPT). Despite more or less weak testing input data, the effort for the application of TMeasy remains limited due to its consequent 'easy to use' orientation. One particular feature of TMeasy is the wide physical meaning of its smart parameter set, which allows to sustain the identification process even under uncertain conditions. After a general introduction, the modelling concept of TMeasy is compactly described in this paper. Taking the standard tire interface (STI) to multibody simulation system (MBS) software into account, the way to apply TMeasy is briefly shown. This includes three selected examples of application. The final comments of the authors on TMPT describe the experiences and earnings received during the participation in that programme.}, language = {en} } @inproceedings{HacklHirschbergLexetal., author = {Hackl, Andreas and Hirschberg, Wolfgang and Lex, Cornelia and Rill, Georg}, title = {Experimental validation of the Maxwell model for description of transient tyre forces}, series = {16. Internationales Stuttgarter Symposium, Automobil- und Motorentechnik}, booktitle = {16. Internationales Stuttgarter Symposium, Automobil- und Motorentechnik}, editor = {Bargende, Michael and Reuss, Hans-Christian and Wiedemann, Jochen}, publisher = {Springer}, address = {Wiesbaden}, isbn = {978-3-658-13254-5}, doi = {10.1007/978-3-658-13255-2_29}, pages = {401 -- 418}, abstract = {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.}, language = {en} } @inproceedings{HacklHirschbergLexetal., author = {Hackl, Andreas and Hirschberg, Wolfgang and Lex, Cornelia and Rill, Georg}, title = {Tyre type dependent transient force behaviour by means of a maxwell model}, series = {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}, booktitle = {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}, editor = {Spiryagin, Maksym and Gordon, Timothy and Cole, Colin and McSweeney, Tim}, publisher = {CRC Press}, address = {London}, isbn = {1351057170}, doi = {10.1201/9781315265506}, pages = {157 -- 162}, abstract = {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.}, language = {en} } @techreport{Rill, type = {Working Paper}, author = {Rill, Georg}, title = {Second-Order Dynamic Friction Model Goes Bi-Dimensional}, address = {Regensburg}, doi = {10.35096/othr/pub-8079}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:898-opus4-80791}, pages = {17}, abstract = {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.}, language = {en} } @techreport{Rill, type = {Working Paper}, author = {Rill, Georg}, title = {Second-Order Dynamic Friction Model In Three-Dimensional Applications}, address = {Regensburg}, doi = {10.35096/othr/pub-8428}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:898-opus4-84288}, pages = {14}, abstract = {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.}, language = {en} } @techreport{Rill, type = {Working Paper}, author = {Rill, Georg}, title = {Second-Order Dynamic Friction Model (FrD2) in a Nutshell}, doi = {10.35096/othr/pub-8077}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:898-opus4-80770}, pages = {9}, abstract = {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.}, language = {en} }