Showing papers in "Vehicle System Dynamics in 1992"
TL;DR: The Magic Formula model as mentioned in this paper provides a set of mathematical formulae from which the forces and moment acting from road to tyre can be calculated at longitudinal, lateral and camber slip conditions, which may occur simultaneously.
Abstract: An account is given of the latest version 3 of the Magic Formula tyre model. The model provides a set of mathematical formulae from which the forces and moment acting from road to tyre can be calculated at longitudinal, lateral and camber slip conditions, which may occur simultaneously. The model aims at an accurate description of measured steady-state tyre behaviour. The coefficients of the basic formula represent typifying quantities of the tyre characteristic. By selecting proper values, the characteristics for either side force, aligning torque or fore and aft force can be obtained. The new version of the model contains physically based formulations to avoid the introduction of correction factors. Double-sided, possibly non-symmetric pure slip curves are employed as the basis for combined slip calculations. Suggestions are given to estimate the driving part of the longitudinal slip curve and to represent the characteristic at rolling backwards.
941 citations
TL;DR: In this article, the authors considered the problem of linear preview control of vehicle suspension as a continuous time stochastic optimal control problem and proposed a solution for a two-degree-of-freedom (2-DOF) vehicle model.
Abstract: SUMMARY The problem of linear preview control of vehicle suspension is considered as a continuous time stochastic optimal control problem. In the proposed approach minimal a priori information about the road irregularities is assumed and measurement errors are taken into account. It is shown that estimation and control issues can be decoupled. The problem formulation and the analytical solution are given in a general form and hence they apply to other problems in which the system disturbances are unknown a priori, even in a stochastic sense, but some preview information is possible. The solution is applied to a two-degree-of-freedom (2-DOF) vehicle model. The effects of preview information on ride comfort, road holding, working space of the suspension and power requirements are examined in time and frequency domains. The results show that the greatest potential is for improving road holding properties. This effect could not have been observed in previous studies based on a 1-DOF vehicle model. It is also ...
178 citations
TL;DR: In this article, the state-of-the-art in the field of independent rotating wheel systems (IRW) for railway vehicles is surveyed and various methods that have been adopted to provide guidance capability to the system are discussed.
Abstract: SUMMARY This paper surveys the state-of-the-art in the field of Independently Rotating Wheel systems (IRW) for railway vehicles. Various methods that have been adopted to provide guidance capability to the system are discussed. Results of the stability and response characteristics of such systems obtained through both experimental and analytical efforts by various researchers are reviewed. Some critical research needs are identified.
59 citations
TL;DR: In this article, the authors derived control laws which minimize specified performance indices for a vehicle moving on a rough surface with preview of the surface elevation, based on linear optimal tracking theory and consequently the system elements are taken to be linear and the performance index is constrained to be of quadratic form.
Abstract: SUMMARY The problem of deriving control laws which minimize specified performance indices for a vehicle moving on a rough surface with preview of the surface elevation is considered. The approach is based on linear optimal tracking theory and consequently the system elements are taken to be linear and the performance index is constrained to be of quadratic form. The ideas of overtaking optimality are applied to the problem in order to achieve a closed form solution for the control. Then, using the control laws derived, computer simulations of performance are conducted and time histories are shown. In the absence of limitations on either processing or actuator speeds, and for cases in which the preview is sufficient to give good control laws, the value of the preview in enhancing vehicle suspension performance is assessed. Comparisons are made with results in the literature.
57 citations
TL;DR: In this article, the stability problems of the active suspension system is analyzed and the stable parameter regions are determined. And the stability of the controlled suspension systems will be examined in the present paper.
Abstract: SUMMARY The suspension system has to fulfil a large number of partly contradictory requirements which can be improved by the application of controllable elements in the wheel suspension system. A number of studies dealing with the improvement of suspension characteristics have been published. In the present paper the stability of the controlled suspension systems will be examined. In the paper the stability problems of the active suspension system is analysed and the stable parameter regions are determined.
49 citations
TL;DR: In this article, a typical UK articulated vehicle is used to measure dynamic tyre forces and sprung mass accelerations to validate two and three-dimensional computer models of the vehicle and the conditions under which a two-dimensional model can accurately simulate vehicle behaviour are examined.
Abstract: SUMMARY Tests were performed on a typical UK articulated vehicle to measure dynamic tyre forces and sprung mass accelerations. The measured road profile data and vehicle response data are used to determine some of the important characteristics of articulated vehicle vibration behaviour. In particular, roll motions and their effect on dynamic tyre forces are examined. The measured data are used to validate two and three-dimensional computer models of the vehicle. Attention is given to modelling the tandem leaf-spring trailer suspension. The conditions under which a two-dimensional model can accurately simulate vehicle behaviour are examined.
47 citations
TL;DR: In this paper, the Magic Formula Tyre Model is compared with the Monte Carlo version of the model and the comparison between the two versions shows that the latest version results in better fitting results especially for camber influences and (even more important) in an improvement on the fitting process.
Abstract: Tyre behaviour plays an important role in vehicle dynamics studies. The Magic Formula Tyre Model is a semi-empirical tyre model which can describe tyre behaviour quite accurately. A set of Magic Formula parameters constitutes the basis of the model. The determination of these parameters out of tyre measurement data produced by the Delft tyre measurement trailer is dealt with in this paper. Problems that may occur during the "fitting process' are indicated as well. The comparison between the latest version and the 'Monte Carlo version' of the tyre model shows that the latest version results in better fitting results especially for camber influences and (even more important) in an improvement on the fitting process.
45 citations
TL;DR: In this paper, the power requirements of a vehicle due solely to its suspension system, neglecting the important powers associated with air and rolling resistance, were analyzed using the simplest possible mathematical model.
Abstract: SUMMARY This paper attempts to analyze the power requirements of a vehicle due solely to its suspension system, neglecting the important powers associated with air and rolling resistance. Power requirements for active and passive suspensions are compared using the simplest possible mathematical model. A mass in a gravity field moves at constant velocity over a surface and is supported by a point contact on the surface by a massless but otherwise arbitrary suspension system. It is shown that the average propulsive power required is equal to the average power lost in the suspension. In the limit cases of very stiff or very soft suspensions this power vanishes. Passive suspensions require no other power, but active suspensions may require significant extra power from the prime mover to generate the suspension forces.
44 citations
TL;DR: In this article, the authors presented the results of a refined investigation of the dynamical behaviour of Cooperrider's complex bogie, showing that one of the solution branches in [4] and [5] was one of an asymmetric, periodic oscillation -albeit with a very small offset, but it indicates, that the asymmetric oscillation is the generic mode at speeds much lower than has hitherto been found.
Abstract: SUMMARY In this paper we present the results of a refined investigation of the dynamical behaviour of Cooperrider's complex bogie. The earlier results were presented in [4] and [7]. It was discovered, that one of the solution branches in [4] and [5] was one of an asymmetric, periodic oscillation - albeit with a very small offset, but it indicates, that the asymmetric oscillation is the generic mode at speeds much lower than has hitherto been found. The bifurcation diagram has been completed, a new type of bifurcation discovered and the other asymmetric branch determined. Furthermore we discovered chaotic motion of the bogie at much lower speeds than reported in [5] and [8][, and we present the result here. Finally we present a new solution branch, which represents an unstable, symmetric oscillation. It has the interesting property, that it turns stable in a small speed range for very high speeds. It has a smaller amplitude than the coexisting chaos. Such behaviour is not uncommon in dynamical systems, see...
41 citations
TL;DR: The calculation results show that this driver model is able to control a mathematical vehicle model such as an ordinary driver-vehicle system, and is useful for the investigation of vehicle handling and stability.
Abstract: SUMMARY This paper constitutes the first step in developing a new driver model. This model includes mental influence as a risk from the environment which a driver uses to decide his course and also to decide the inputs to the vehicle, not only steering but also fore and aft force. A fuzzy control method is used to decide the risk level, and to control the vehicle as an expert system. The calculation results show that this driver model is able to control a mathematical vehicle model such as an ordinary driver-vehicle system, and is useful for the investigation of vehicle handling and stability.
39 citations
TL;DR: In this paper, a comprehensive directional dynamics model of a tractor-tank trailer is developed by integrating a non-linear dynamic fluid slosh model to the three-dimensional vehicle dynamics model.
Abstract: SUMMARY A comprehensive directional dynamics model of a tractor-tank trailer is developed by integrating a non-linear dynamic fluid slosh model to the three-dimensional vehicle dynamics model. The nonlinear fluid slosh equations are solved in an Eulerian mesh to determine dynamic fluid slosh loads caused by the dynamic motion of the vehicle. The dynamic fluid slosh forces and moments are coupled with the vehicle dynamics model to study the directional response characteristics of tank vehicles. The directional response characteristics of partially filled tank vehicles employing dynamic slosh model are compared to those employing quasi-dynamic vehicle model, for steady as well as transient directional maneuvers. Simulation results reveal that during a steady steer maneuver, the dynamic fluid slosh loads introduce oscillatory directional response about a steady-state value calculated from the quasi-dynamic vehicle model. The directional response characteristics obtained using the quasi-dynamic and dynamic fl...
TL;DR: In this article, a method to avoid discontinuities calculating the contact forces of one wheelset using a rigid profile process associated to a limited number of equivalent parameters, as functions of the lateral wheelset relative displacement "y", is presented.
Abstract: SUMMARY Computing contact forces is rather quick if rigid profiles are used but the results are numerically uncertain because of discontinuities in contact locations. Using elastic profiles is physically correct but gives rise to new difficulties to locate multi contacts (2 or 3 at the same time on the same wheel) and implication of high frequency modes due to wheel and rail separation through high stiffnesses. This paper presents a method to avoid discontinuities calculating the contact forces of one wheelset using a rigid profile process associated to a limited number of equivalent parameters, as functions of the lateral wheelset relative displacement “y”. These parameters are precomputed once for all using a time consuming elastic multicontact program associated with an identification process. Comparisons between forces calculated by this quick new method and the slow complex code are good.
TL;DR: A survey of the state-of-the-art in predicting wheel/rail interaction can be found in this article, where the authors present several methods for calculating contact geometry, defining the wheel and rail kinematic expressions, and obtaining contact plane forces due to creep.
Abstract: SUMMARY This paper presents a survey of the state-of-the-art in predicting wheel/rail interaction. Current methods are presented for calculating contact geometry, defining the wheel/rail kinematic expressions, and obtaining contact plane forces due to creep. The paper concludes by examining where future research should be focused. While techniques for predicting wheel/rail interaction have developed considerably over the last twenty years, there is room for still further improvement.
TL;DR: The Magic Formula model can be used in all phases of a vehicle project, from the specifications of a new car to tuning the handling In the final stage of the developement as discussed by the authors.
Abstract: The Magic Formula tyre model can be used In all phases of a vehicle project, from the specifications of a new car to tuning the handling In the final stage of the developement. The applications of the model at Volvo, shown in this paper, are from different parts of this process, with several examples, which together with test results show the wide applicability of the model. The implementation of the model in different simulation programs is also discussed, as well as the creation of model parameters from the measurements. Also, the influence of varying the model parameters on the vehicle behaviour is presented.
TL;DR: In this article, a ring model is used to simulate the dynamic behavior of a real tire rolling on the road, where the road contact is kinematically represented by two displacement constraints, one in radial and one in tangential direction.
Abstract: SUMMARY The dynamic behavior of tires rolling on the road is predicted based on a ring model that is experimentally verified to well represent a real tire. The road contact is kinematically represented by two displacement constraints, one in radial and one in tangential direction. The displacement constraints are enforced via the receptance theory. The receptance matrix developed for the rolling tire is found to be Hermitian. Numerical results show that the natural (or eigen-) frequencies of the rolling tire with road contact are, as expected, higher than those of the tire with no contact. The influence of the rotating speed to the eigen-frquencies of the tire is also shown. Analytic expressions for the mode shapes of a rolling tire with ground contact are derived.
TL;DR: In this paper, a model of a vehicle where the front and the rear springs are connected by a capillary tube is presented, and the effect of the capillary flow coefficient and that of the phase angle between front and rear axle excitation is studied.
Abstract: SUMMARY Airsprings have been used for vehicle suspensions over the last 40 years. They are mostly used as independent suspensions. Analysis of air springs available in literature is mostly limited to a single-degree-of-freedom system or a two-degrees-of-freedom system only in the translation mode. This paper deals with a model of a vehicle where the front and the rear springs are connected by a capillary tube. A two-degrees-of-freedom model having motion in bounce and pitch mode is presented. Equations of mass flow are linearized on the assumption of small variations in volume and pressure. Expressions for the transmissibility and the phase angle in the bounce and the pitch mode are derived. Road inputs to the front and the rear axles are assumed to be identical except for a phase difference between them. The effect of the capillary flow coefficient and that of the phase angle between the front and the rear axle excitation are studied. It is shown that an optimum value of the capillary flow coefficient ex...
TL;DR: In this paper, the simulation results of a wheelset modelled with two different wheel-rail elements are compared to each other for three different simulation scenarios: the first model is a wheel-set element together with a track element.
Abstract: SUMMARY The simulation results of a wheelset modelled with two different wheel-rail elements are compared to each other. The first model is a wheelset element together with a track element. The contact between wheel and rail is treated as constraint and the kinematics of the wheelset is solved in advance. The second model is a wheel-rail interconnection element. The contact between wheel and rail is flexible. The results of the two models are compared for three different simulations. In the first simulation the wheelset modelled with the flexible contact patch is oscillating around a position with two contact points on one wheel. The second simulation is hunting of the wheelset with flange contact and the third is a hunting movement with small amplitudes. The normal forces calculated with the two elements differ in all three simulations. Beside flexibility and two point contact the reason for differences is the variation of the curvature in the contact points. In simulations governed by two point contact ...
TL;DR: In this article, the authors describe the implementation of a preview control scheme on the Iltis and test two preview control schemes using simulations using a full-vehicle model developed with the A'GEM multibody dynamics package.
Abstract: SUMMARY Recent work has resulted in the production of a microcomputer controlled, hydraulically actuated, active suspension for the ¼ ton, 4 wheel drive vehicle called the Iltis. The system has been designed to accommodate various control schemes through relatively straightforward changes to software and to transducers. This paper describes the implementation of a preview control scheme on the Iltis. Following an extensive review of sensor technology, ultrasonic sensors were selected for use in a preview mode. These sensors are rugged, sufficiently accurate and cost effective for this purpose. Two preview control schemes are tested through the use of simulations using a full-vehicle model developed with the A'GEM multibody dynamics package. One algorithm, taken from the literature, was developed from optimal control theory using a quarter-car model as a basis. The other algorithm tested was developed from the full-vehicle model. This one, of necessity due to the complexity of the model, did not use optima...
TL;DR: In this paper, a more general surface model has been formulated and compared with the experimental data, and a simple parametric approximation is developed for the coherence function on the basis of the extended unevenness model.
Abstract: SUMMARY The properties of real roads along the lateral axis cannot not be adequately explained with the classic model of the isotropic road. With a realistic assumption of spatial invariance (homogeneity), a more general surface model has been formulated and compared with the experimental data. A good match of measurements and “theory” has been achieved. A simple parametric approximation is developed for the coherence function on the basis of the extended unevenness model. In addition to the undulation exponent of the road surface and the track width, the curve is characterized by three other key figures. The adaptation to the experimental data results in comparatively small yet justifiable parameter intervals. Due to the further development of filter methods for the synthesis of random irregularities, a model family is now available which facilitates a satisfactory balance between model accuracy and numerical complexity for most applications. The main difficulties would appear to lie in the formulation o...
TL;DR: This paper describes how quasi-static and dynamics analysis methods are combined to simulate of a “full-scale” passenger car model and describes a novel method for combining symbolic and numerical equation formulations to generate quasi- static analysis algorithms.
Abstract: SUMMARY This paper describes how quasi-static and dynamics analysis methods are combined to simulate of a “full-scale” passenger car model. It also describes a novel method for combining symbolic and numerical equation formulations to generate quasi-static analysis algorithms. A quasi-static model is first used to simulate three-dimensional suspension kinematics and compliance properties. The results from this analysis are then used to fit coefficients to polynomials that describe the suspension motions. These coefficients are then employed in a dynamics model that is formulated using the same polynomial equations. The method is illustrated for an automotive vehicle model, using a suspension representation with 11 degrees of freedom (DOF), and a full-vehicle model with 14 DOF. The symbolic multibody program AUTOSIM is used to derive the equations and optimize them for computer solution. The overall simulation is sufficiently detailed to captures the influences of bushing compliances, and yet is computatio...
TL;DR: In this article, a time-domain direct identification method is presented for the identification of vehicle system mass, damping and stiffness matrices, as well as for parameters of nonlinear components which are linear-in-the-parameters.
Abstract: SUMMARY In this paper a time-domain direct identification method is presented for the identification of vehicle system mass, damping and stiffness matrices, as well as for parameters of nonlinear components which are “linear-in-the-parameters”. The method is based on least-square type of error costs which are constructed from system dynamic equations. The estimated system parameters are then tuned to minimize each of these cost functions. The parameters are directly identified from the deduced algorithm without iteration. To demonstrate the proposed identification procedure, the method is applied to a four degree-of-freedom vehicle; different nonlinear suspension components, such as cubic springs, nonlinear hydraulic and frictional dampers and their combinations are considered. It can be seen that by using the proposed method, all the unknown system parameters are identified with sufficient accuracy, low memory and computation time.
TL;DR: In this article, a system for reducing automotive body roll response to steering inputs by active control is described, which involves the use of electro-hydraulic actuation of anti-roll bars under lateral acceleration feedback control.
Abstract: SUMMARY A system for reducing automotive body roll response to steering inputs by active control is described. It involves the use of electro-hydraulic actuation of anti-roll bars under lateral acceleration feedback control. The system is suitable for use as an optional fitment to a conventional vehicle or as original equipment. A mathematical model of the arrangement, including sectors for the vehicle, the sensing, the signal processing, the flow control valves and the actuators is set up and, using a set of basic parameters which describe a large saloon car, design and performance studies are conducted. Conclusions are drawn relating to test schedules, the potential effectiveness of the scheme, the hardware requirements, best use of the hardware and energy costs.
TL;DR: In this article, the authors analyze the system's response when the internal tyre pressure in the rear wheels is lower than the normal, and the question is whether the control system is able to stabilize the motion of the vehicle.
Abstract: SUMMARY The four-wheel-steering systems of the cars are becoming more and more wide-spread. In addition to the conventional 4WS systems (e.g. the steering-wheel-angle dependent four-wheel-steering and the speed dependent 4WS) there already exist some so called active 4WS systems. The front wheels and rear wheels are steered autonomously by the feedback compensation and in this manner the behaviour of the car during high-speed turning manoeuvre and under the side wind gust is improved. But what happens if some of the parameters of the car are changed? In the present paper, the author will analyze the system's response when the internal tyre pressure in the rear wheels is lower than the normal. Due to this the under-steered car becomes over-steered and the question is whether the control system is able to stabilize the motion of the vehicle.
TL;DR: In this article, a robust stability analysis of LQG-con-trolled active suspension systems is presented, where the robust stability of an active suspension system in the presence of assumed parameter variations is analyzed.
Abstract: SUMMARY This paper presents a systematic approach toward robust stability analysis of LQG-con trolled active suspension systems. To perform this task, the paper starts with a brief background information on LQG control, its relation to H 2 method, and showing how H 2 could be formulated to become the frequency domain equivalent of LQG. Then unstructured and structured uncertainties of active suspension are formulated. The paper continues with the definition of maximum singular values and structured singular values of a transfer function matrix. Using these definitions, the robust stability of an active suspension system in the presence of assumed parameter variations are analyzed. These steps are illustrated by means of a numerical example of an active suspension system.
TL;DR: In this paper, a semi-empirical tire model is described and used in examining the influences of changes in tire tread depth and pavement mean texture depth and skid number on tire forces.
Abstract: A semi-empirical tire model is described here and used in examining the influences of changes in (a) tire tread depth and (b) pavement mean texture depth and skid number on tire forces. Test results show that changes in tread depth lead to changes in cornering stiffness and the form of the pressure distribution. The ways in which these factors are included in the model and their influences on lateral force characteristics of truck tires are presented and discussed. The influences of tread depth, mean texture depth, and skid number on die sliding friction of truck tires are discussed and equations for representing the frictional characteristics of a worn tire operating on a wet surface (not flooded to a level well over the tops of the road asperities) are presented in an appendix. The body of the paper concludes with a discussion of future approaches for representing frictional effects.
TL;DR: In this article, a linear contact model is presented which completely describes nonsteady state contact mechanics for elliptical contact patches, based on a linearization of Kalker's three dimensional contact theory with respect to a nonlinear reference configuration.
Abstract: SUMMARY A linear contact model is presented which completely describes nonsteady state contact mechanics for elliptical contact patches. The contact model is based on a linearization of Kalker's three dimensional contact theory with respect to a nonlinear reference configuration and is able to consider an oscillating contact patch. As an output one obtaines frequency responses of the tangential forces for oscillating creepages or for an oscillating normal force which occurs when a wheel passes over irregularities of short wavelengths. Simple mechanical models are presented which can be incorporated in multibody systems including wheel/rail dynamics for the high frequency range.
TL;DR: In this paper, a train bogie with independently rotating wheels and half as light as the conventional one was developed to improve the stability of hight speed running on tangent section and the curving performance, and to make it available as a next generation bogie on narrow lines.
Abstract: SUMMARY Railway Technical Research Institute (RTRI) developed a bogie which has independently rotating wheels and weighs half as light as the conventional one, being intended to improve the stability of hight speed running on tangent section and the curving performance, and to make it available as a next generation bogie on JR narrow lines. The performance of the bogie were testd on roller rig and in field tests. From the measurement, it is verified that the independently rotating wheels using a newly developed wheel profile has a gravitational restoring force and its performance we have expected. From eigenvalue and results of simulation, the influence of modeling level and that of the steering mechanism, and the better running stability of the independently rotating wheels are clear.
TL;DR: In this article, a multibody model developed for railway applications and in particular for the study of the lateral dynamics of a non-conventional articulated bogie with independent wheels is presented.
Abstract: This paper presents a multibody model developed for railway applications and, in particular, for the study of the lateral dynamics of a non-conventional articulated bogie with independent wheels. The classical multibody formalism is first briefly reviewed and the generation of the equations in symbolic form is also presented. Moreover, a new wheel/rail contact model compatible with the symbolic output of the MBS software ROBOTRAN has been developed. The validation with results available in the literature and some results concerning the articulated bogie are finally presented.
TL;DR: In this article, a linear technique based on Fourier transform is presented to calculate the dynamic response of railway track and vehicles to non-sinusoidal irregularities on the running surfaces of wheel and rail.
Abstract: SUMMARY A linear technique based on Fourier Transforms is presented to calculate the dynamic response of railway track and vehicles to non-sinusoidal irregularities on the running surfaces of wheel and rail. The model has been validated tentatively by comparison of calculation with data measured in a field experiment with a variety of irregular wheels and types of track. Calculation underestimates the difference in sleeper bending moment and overestimates the difference in contact force arising from the use of stiff and resilient railpads. An example is given in which the model is used to help in design of track by indicating the relative importance of different damage mechanisms.
TL;DR: In this article, the effect of the nonlinearities on the active system performance is studied and the performance of active suspensions with nonlinear passive elements is found to be superior to the corresponding passive suspension systems.
Abstract: SUMMARY Active control of non-stationary response of a single degree of freedom vehicle model with nonlinear passive suspension elements is considered in this paper. The method of equivalent linearization is used to derive the equivalent linear model and the optimal control laws are obtained by using stochastic optimal control theory based on full state information. Velocity squared quadratic damping and hysteresis type of stiffness nonlinearities are considered. The effect of the nonlinearities on the active system performance is studied. The performance of active suspensions with nonlinear passive elements is found to be superior to the corresponding passive suspension systems.