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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.
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.
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 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.
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.
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.
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.
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.