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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.
LuGre or not LuGre
(2022)
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.
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.
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.
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.
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.
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.
Road Vehicle Dynamics
(2020)
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.
A review of the current use of multibody dynamics methods in the analysis of the dynamics of vehicles is given. Railway vehicle dynamics as well as road vehicle dynamics are considered, where for the latter the dynamics of cars and trucks and the dynamics of single-track vehicles, in particular motorcycles and bicycles, are reviewed. Commonalities and differences are shown, and open questions and challenges are given as directions for further research in this field.
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.