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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.
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.
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.
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.
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.
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.