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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.
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.
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.
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.
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.
Parameterization Process of the Maxwell Model to Describe the Transient Force Behavior of a Tire
(2017)
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.
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.
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.
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.
LuGre or not LuGre
(2023)
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 simple regularized characteristics, produces reliable and generally satisfactory results but definitely cannot maintain a stick. The paper presents a second-order dynamic friction model, which may serve as an alternative. It can maintain a stick and produces realistic and reliable results.