TY - CHAP A1 - Rill, Daniel A1 - Butz, Christiane A1 - Rill, Georg ED - Kecskeméthy, Andrés ED - Geu Flores, Francisco T1 - Dynamic Interaction of Heavy Duty Vehicles and Expansion Joints T2 - Multibody Dynamics 2019, Proceedings of the 9th ECCOMAS Thematic Conference on Multibody Dynamics N2 - The “Smart Bridge (Intelligente Brücke)” project cluster, initiated by the German Federal Highway Research Institute (Bundesanstalt für Straßenwesen, BASt) and the Federal Ministry of Transport and Digital Infrastructure (BMVI), focuses on “smart” monitoring devices that allow an efficient and economic maintenance management of bridge infrastructures. Among the participating projects, the one presented herein focuses on the development of a smart expansion joint, to assess the traffic parameters on site. This is achieved by measuring velocity and weight of crossing vehicles. In reference measurements, performed with a three-axle truck and a typical tractor semi-trailer combination with five axles in total, it was shown that the interaction between the vehicle and the expansion joint is highly dynamic and depends on several factors. To get more insight into this dynamic problem, a virtual test rig was set up. Although nearly all vehicle parameters had to be estimated, the simulation results conform very well with the measurements and are robust to vehicle parameter variations. In addition, they indicate a significant influence of the expansion joint dynamic to the peak values of the measured wheel loads, in particular on higher driving velocities. By compensating the relevant dynamic effects in the measurements, a “smart” data processing algorithm makes it possible to determine the actual vehicle weights in random traffic with reliability and appropriate accuracy. Y1 - 2020 SN - 978-3-030-23131-6 U6 - https://doi.org/10.1007/978-3-030-23132-3_56 VL - 53 SP - 471 EP - 478 PB - Springer International Publishing CY - Cham ER - TY - CHAP A1 - Hackl, Andreas A1 - Hirschberg, Wolfgang A1 - Lex, Cornelia A1 - Rill, Georg T1 - Parameterization Process of the Maxwell Model to Describe the Transient Force Behavior of a Tire T2 - WCX 17: SAE World Congress Experience 2017 N2 - 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. Y1 - 2017 U6 - https://doi.org/10.4271/2017-01-1505 PB - SAE ER - TY - CHAP A1 - Hackl, Andreas A1 - Hirschberg, W. A1 - Lex, C. 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 - Andreescu, Cristian ED - Clenci, Adrian T1 - Tyre Dynamics: Model Validation and Parameter Identification T2 - Proceedings of the European Automotive Congress EAEC-ESFA 2015 N2 - 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. KW - Semi-physical model KW - Tyre dynamics modelling KW - Tyre testing KW - vehicle dynamics Y1 - 2016 SN - 978-3-319-27275-7 U6 - https://doi.org/10.1007/978-3-319-27276-4_20 VL - 45 SP - 219 EP - 232 PB - Springer CY - Cham ER - TY - CHAP A1 - Dessort, Ronnie A1 - Chucholowski, Cornelius A1 - Rill, Georg ED - Bargende, Michael ED - Reuss, Hans-Christian ED - Wiedemann, Jochen T1 - Parametrical approach for modeling of tire forces and torques in TMeasy 5 T2 - Proceedings of the 16. Internationales Stuttgarter Symposium Automobil- und Motorentechnik N2 - 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. KW - Drehmoment KW - dynamische Simulation KW - Einparken KW - Fahrzeugdynamik KW - Mehrkörpersystem KW - Parameterabschätzung KW - Rechenzeit KW - REIFENKRAFT KW - Reifentest KW - simuliertes Ergebnis Y1 - 2016 UR - https://www.researchgate.net/publication/317037138_Parametrical_Approach_for_Modeling_of_Tire_Forces_and_Torques_in_TMeasy_5 SN - 978-3-658-13254-5 SP - 435 EP - 449 PB - Springer CY - Wiesbaden ER - TY - JOUR A1 - Hirschberg, W. A1 - Rill, Georg A1 - Weinfurter, H. T1 - Tire model TMeasy JF - Vehicle System Dynamics N2 - 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. Y1 - 2007 U6 - https://doi.org/10.1080/00423110701776284 VL - 45 IS - sup1 SP - 101 EP - 119 PB - Taylor&Francis ER - TY - CHAP A1 - Arrieta Castro, Abel A1 - Weber, Hans Ingo A1 - Rill, Georg T1 - Design an integrate vehicle control based-on hierarchical architecture for improve the performance of ground vehicles T2 - COBEM2015 : 23rd ABCM International Congress of Mechanical Engineering, December 6-11, 2015, Rio de Janeiro, RJ, Brazi Y1 - 2015 U6 - https://doi.org/10.20906/cps/cob-2015-1970 ER - TY - CHAP A1 - Dessort, Ronnie A1 - Chucholowski, Cornelius A1 - Rill, Georg ED - Bargende, Michael ED - Reuss, Hans-Christian ED - Wiedemann, Jochen T1 - Parametrical approach for modeling of tire forces and torques in TMeasy 5 T2 - 16. Internationales Stuttgarter Symposium, Automobil- und Motorentechnik, Bd. 1 N2 - 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. Y1 - 2016 SN - 978-3-658-13254-5 U6 - https://doi.org/10.1007/978-3-658-13255-2_31 SP - 435 EP - 449 PB - Springer CY - Wiesbaden 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 - JOUR A1 - Rill, Georg A1 - Bauer, Florian A1 - Kirchbeck, Mathias T1 - VTT - a virtual test truck for modern simulation tasks JF - Vehicle system dynamics N2 - The development of new technologies like advanced driver assistance systems or automated driving requires a flexible simulation environment of sufficient complexity. In general this flexibility is not provided by commercial software packages. This paper presents a three-dimensional and nonlinear hand-made model for heavy commercial vehicles including tractor and trailer as well as tractor and semitrailer combinations that can be used in different simulation environments, as well as in real-time applications. As typical for trucks, the torsional flexibility of the frame and a suspended driver's cabin are taken into account. The design kinematics makes it possible to handle different and quite complex axle suspensions very efficiently. Appropriate force elements are used to model various couplings between tractor and trailer or tractor and semitrailer, respectively. The virtual test truck environment (VTT) coded in ANSI C is extremely portable and can easily be embedded in commercial simulation packages like MATLAB/Simulink. It includes the TMeasy tyre model and offers flexible interfaces to third-party software tools. KW - coupled air springs KW - design Kinematics KW - heavy commercial vehicles KW - MATLAB KW - Simulink KW - TMeasy tyre model KW - vehicle coupling KW - Vehicle modelling Y1 - 2021 U6 - https://doi.org/10.1080/00423114.2019.1705356 VL - 59 IS - 4 SP - 635 EP - 656 PB - Taylor&Francis ER - TY - CHAP A1 - Arrieta Castro, Abel A1 - Rill, Georg ED - Orlova, Anna ED - Cole, David T1 - Kinematic Versus Elasto-Kinematic Model of a Twistbeam Suspension T2 - 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 N2 - 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. KW - Design kinematics KW - Twistbeam suspension KW - Multibody model KW - Vehicle dynamics Y1 - 2022 U6 - https://doi.org/10.1007/978-3-031-07305-2_59 SP - 505 EP - 605 PB - Springer Nature ER - TY - JOUR A1 - Rill, Georg A1 - Bauer, Florian A1 - Topcagic, Edin T1 - Performance of leaf spring suspended axles in model approaches of different complexities JF - Vehicle System Dynamics N2 - Axles with leaf spring suspension systems are still a popular choice in many commercial vehicles. However, leaf springs are not in perfect conformity to standard multibody vehicle models because they combine guidance and suspension in one single element. Combining standard multibody vehicle models with sophisticated finite element leaf spring models results in rather complex and computing time-consuming solutions. Purely kinematic models, defined by lookup tables or the design kinematics approach, cover only some but not all features of the leaf spring suspension. As shown here, the five-link model, which incorporates a quasi-static solution of the leaf spring compliance, provides a very practical model. It is comparatively lean and provides results of sufficient accuracy in the whole application range. KW - beam-model KW - commercial vehicles KW - design kinematics KW - five-Link model KW - Leaf spring suspension KW - vehicle dynamics Y1 - 2021 U6 - https://doi.org/10.1080/00423114.2021.1928249 VL - 60 IS - 8 SP - 2871 EP - 2889 PB - Taylor&Francis ER - TY - CHAP A1 - Bünte, Tilman A1 - Rill, Georg A1 - Ruggaber, Julian A1 - Tobolář, Jakub ED - Orlova, Anna ED - Cole, David T1 - Modelling and Validation of the TMeasy Tyre Model for Extreme Parking Manoeuvres T2 - 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 N2 - The TMeasy is a tyre model suitable for vehicle handling analyses and enables easy parametrisation. Recently, a convenient interface to Modelica was implemented by DLR to support the TMeasy also for vehicle modelling in multi-physical domains. This paper focuses especially on the particular problem of reliable reproduction of the tyre’s bore torque which occurs during parking manoeuvres. It outlines the theory behind it, discusses the Modelica interface implementation, and presents the results of parameter identification which were achieved based on real experiments with DLR’s research platform ROboMObil. Y1 - 2022 SN - 978-3-031-07305-2 SN - 978-3-031-07304-5 U6 - https://doi.org/10.1007/978-3-031-07305-2_94 SP - 1015 EP - 1025 PB - Springer CY - Cham ER - TY - CHAP A1 - Rill, Georg T1 - A Three-Dimensional and Nonlinear Virtual Test Car T2 - ENOC 2022, book of abstracts, 10th European Nonlinear Dynamics Conference: July 17-22, 2022, Lyon, France N2 - 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. Y1 - 2022 UR - https://enoc2020.sciencesconf.org/data/ENOC2022_proceedings.pdf SP - 49 EP - 58 CY - Lyon ER - TY - CHAP A1 - Rill, Georg A1 - Arrieta Castro, Abel ED - Klomp, Matthijs ED - Bruzelius, Fredrik ED - Nielsen, Jens ED - Hillemyr, Angela T1 - A Novel Approach for Parametrization of Suspension Kinematics T2 - 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 N2 - 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. KW - design Kinematics KW - Kinematic and compliance test KW - Suspension systems Y1 - 2020 SN - 978-3-030-38076-2 U6 - https://doi.org/10.1007/978-3-030-38077-9_210 SP - 1848 EP - 1857 PB - Springer International Publishing CY - Cham ER - TY - JOUR A1 - Rill, Georg T1 - Sophisticated but quite simple contact calculation for handling tire models JF - Multibody system dynamics N2 - Handling tire models like Pacejka (Tire and Vehicle Dynamics, 3rd edn., Elsevier, Amsterdam, 2012) or TMeasy (Rill in Proc. of the XV Int. Symp. on Dynamic Problems of Mechanics, Buzios, RJ, Brazil, 2013) consider the contact patch as one coherent plane. As a consequence, the irregularities of a rough road profile must be approximated by an appropriate local road plane that serves as an effective road plane in order to calculate the geometric contact point and the corresponding contact velocities. The Pacejka/SWIFT tire model employs a road enveloping model that generates the effective height and slope by elliptical cams. TMeasy just uses four representative road points for that purpose. In addition, TMeasy replaces the geometric contact point by the static contact point and shifts it finally to the dynamic contact point that represents the point where the contact forces are applied. In doing so, a rather sophisticated but still simple contact calculation is possible. Simulations obtained with a virtual tire test rig and fully nonlinear three-dimensional multibody system models of a motor-scooter and a passenger car demonstrate the potential of this contact approach. KW - Dynamic contact point KW - Effective road plane KW - Geometric contact point KW - Static contact point KW - Tire road contact KW - TMeasy tire model KW - Vehicle modeling Y1 - 2019 U6 - https://doi.org/10.1007/s11044-018-9629-4 VL - 45 IS - 2 SP - 131 EP - 153 PB - Springer Nature ER - TY - CHAP A1 - Rill, Georg A1 - Arrieta Castro, Abel ED - Kecskeméthy, Andrés ED - Geu Flores, Francisco ED - Carrera, Eliodoro ED - Elias, Dante A. T1 - The Influence of Axle Kinematics on Vehicle Dynamics T2 - Interdisciplinary Applications of Kinematics. Proceedings of the Third International Conference (IAK) N2 - 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. KW - Double wishbone suspension system KW - Multibody system KW - Suspension kinematics KW - vehicle dynamics Y1 - 2019 SN - 978-3-030-16422-5 U6 - https://doi.org/10.1007/978-3-030-16423-2_2 VL - 71 SP - 23 EP - 31 PB - Springer International Publishing CY - Cham ER - TY - CHAP A1 - Rill, Georg T1 - TMeasy 6.0-A handling tire model that incorporates the first two belt eigenmodes T2 - Proceedings of the XI International Conference on Structural Dynamics (EURODYN 2020): Athens, Greece, 23.11.2020 - 26.11.2020 N2 - 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. KW - TMeasy Tire Model KW - Tire Force Dynamics KW - Frequency Analysis KW - Real-time Simulation KW - Virtual Test Rig Y1 - 2020 U6 - https://doi.org/10.47964/1120.9054.18673 SP - 676 EP - 689 PB - EASD Procedia ER - TY - BOOK A1 - Rill, Georg A1 - Arrieta Castro, Abel T1 - Road Vehicle Dynamics N2 - 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. KW - Fahrdynamik Y1 - 2020 SN - 9780429244476 U6 - https://doi.org/10.1201/9780429244476 PB - CRC Press CY - Boca Raton, Fla. ER - TY - CHAP A1 - Rill, Georg ED - Lugner, Peter T1 - Multibody Systems and Simulation Techniques T2 - Vehicle Dynamics of Modern Passenger Cars N2 - 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. KW - Differential equations KW - Equations of motion KW - Multibody systems KW - Numerical solution KW - Vehicle models Y1 - 2019 SN - 978-3-319-79007-7 U6 - https://doi.org/10.1007/978-3-319-79008-4_6 SP - 309 EP - 375 PB - Springer International Publishing CY - Cham ER -