Direct Covariance Analysis for the Calculation of Creepages and Creep-Forces for Various Bogies on Straight Track with Random Irregularities

In this paper creep-forces and creepages for an ICE express train coach and an electric locomotive BR 120 of the DB on straight track with random irregularities are investigated. The calculations are made with the multibody program MEDYNA using direct covariance analysis. One of the aims of this article is to emphasize the advantages of the direct covariance method (time domain) compared with the power spectral density method (frequency domain).     

A Procedure for Optimization of Truck Suspensions

SUMMARY

The purpose of this paper is to develop a procedure based on covariance analysis and nonlinear programming techniques which can be used for the parameter selection of optimum truck suspensions. The procedure is applied to explore the differences in parameter selection caused by the changes in the frequency content of the road input or by changes in the criteria for optimization. The equations of motion for a tractor-semitrailer truck are cast in state space form. The road excitations are represented by the output of a white noise excited shaping filter taking into consideration the time delays between the different vehicle axles. Shape filters to represent human perception of vibration in both the vertical and longitudinal directions in the time domain are presented and realized in terms of state variables. The suspension parameters of the road-vehicle-human body system are optimized using a direct search algorithm.     

Vehicle Response to Stochastic Roadways

SUMMARY

Dynamic response calculations for vehicles traversing irregular surfaces are usually accomplished using frequency domain methods involving spectral densities and transfer functions. Here an alternative procedure is developed which allows direct computation of mean square values and correlations of system variables for both transient and steady-state conditions. The method is based upon the differential equation for the covariance matrix which is directly related to the state equations for the vehicle. Multiple white noise inputs can be incorporated as well as inputs at two wheels which follow the same track at a distance from one another..The method is suitable for computer implementation without the complex algebra associated with finding all necessary transfer functions and the necessity of evaluating integrals in order to find mean square values using the conventional approach. As an illustration, a simple vehicle model is worked out completely and the variation of pitch and heave motion as a function of vehicle speed is plotted.     

Robust Stability Analysis of LQG-Controlled Active Suspension with Model Uncertainty Using Structured Singular Value, μ, Method

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.     

Analyses of Vision-based Lateral Control for Automated Highway System

SUMMARY

The stability and performance of a vision-based vehicle lateral control system are analyzed. Effects of look-ahead distance, vision delay, and vehicle speed on the performance of vision feedback control system are examined by using frequency domain and time domain methods. A measurement model of the vision system is derived from the point of view of multiple sensors. The quantization error of the vision system is analyzed and the way of extracting essential information for control is studied. Based on this analysis, some guidelines for the design of vision-based controllers are proposed. A design example is further illustrated for a vision system with a substantial time delay.     

Precision analysis and dynamic stability in the numerical solution of the two-dimensional wheel/rail tangential contact problem

ABSTRACT

In this paper the two-dimensional contact problem is analysed through different mesh topologies and strategies for approaching equations, namely; the collocation method, Galerkin, and the polynomial approach. The two-dimensional asymptotic problem (linear theory) associated with very small creepage (or infinite friction coefficient) is taken as a reference in order to analyse the numerical methods, and its solution is tackled in three different ways, namely steady-state problem, dynamic stability problem, and non-steady state problem in the frequency domain. In addition, two elastic displacements derivatives calculation methods are explored: analytic and finite differences. The results of this work establish the calculation conditions that are necessary to guarantee dynamic stability and the absence of numerical singularities, as well as the parameters for using the method that allows for maximum precision at the minimum computational cost to be reached.     

An H2 Formulation for the Design of a Passive Vibration-Isolation System for Cars

SUMMARY

Optimal design of an active suspension system for road vehicles can be solved using LQR techniques. Such a problem is equivalent, in the frequency domain, to determine the state feedback gain matrix that minimizes the H₂ norm of a suitable transfer matrix.

A passive suspension system can be seen as the physical realization of a suitable state feedback law whose gains are function of the system parameters. This law, and thus the characteristic elements of the passive suspension, can be determined as an approximation of the H₂ optimal solution. This methodology allows one to choose the best controller from a constrained subset (i.e., all possible passive suspensions of a particular form) of all possible controllers.     

Frequency Spectral Analysis of Bridge-Vehicle System due to Road Surface Roughness

SUMMARY

The paper presents a new method to study the dynamic properties of the bridge-vehicle system. The transfer function of the system is obtained by iteration in the frequency domain instead of the time domain. The relationship between vehicle speed and the lowest natural frequency of the system is investigated and a parametric study of the system stability is made. The varying parameters concerned are the vehicle speed, the ratio of vehicle mass to bridge mass, the ratio of vehicle eigenfrequency to bridge eigenfrequence, and the relative damping of the vehicle and bridge.     

Improvement of Vehicle Maneuverability by Direct Yaw Moment Control

SUMMARY

This paper deals with a study to theoretically formulate an effective method of improving vehicle performance, particularly, its characteristics in the nonlinear region, and to verify the feasibility of the proposed method by calculations and examinations. In order to analyze vehicle characteristics in the nonlinear region, a new method of analysis was developed for determining yaw moment and side force of the vehicle with a parameter of the side slip angle at the center of gravity when its center of gravity point was fixed. The study with this new method found that direct yaw moment control by proper distribution of traction and braking forces on the right and left tires could provide a very effective means of stabilizing vehicle characteristics, specifically for acceleration and deceleration, and enlarging the limit of vehicle maneuverability.     

Properties of Non-Linear Two-Force Elements Used in Vehicle Dynamic Systems under Stationary Stochastic Excitation. Part 1 - Ideal Elements

SUMMARY

Non-linear two-force elements (springs, dampers, etc.) are commonly found in vehicle dynamic systems. Their mathematical idealization by expressing their force-excitation relation by a real function is called to be an ideal element. Excitation of these elements can be often considered as being stationary stochastic. Their general properties under such excitation are discussed and computation of the stochastic properties of the output force for known excitation are shown in this paper. Transfer functions of the elements, i.e. output force - input relations in the frequency domain, under the given excitational conditions form the base for the evaluation.     

Vehicle Response to Stochastic Roadways

Dynamic response calculations for vehicles traversing irregular surfaces are usually accomplished using frequency domain methods involving spectral densities and transfer functions. Here an alternative procedure is developed which allows direct computation of mean square values and correlations of system variables for both transient and steady-state conditions. The method is based upon the differential equation for the covariance matrix which is directly related to the state equations for the vehicle. Multiple white noise inputs can be incorporated as well as inputs at two wheels which follow the same track at a distance from one another..The method is suitable for computer implementation without the complex algebra associated with finding all necessary transfer functions and the necessity of evaluating integrals in order to find mean square values using the conventional approach. As an illustration, a simple vehicle model is worked out completely and the variation of pitch and heave motion as a function of vehicle speed is plotted.     

Uncertainty quantification in vehicle dynamics

ABSTRACT

This paper presents a review of various works that highlight the importance of introducing the variability of the road-track/vehicle system into dynamic simulations as soon as this latter is meant to be predictive. The first section of the paper presents the Uncertainty Quantification, Verification and Validation method (UQ-VV). This latter proposes tools to model uncertainties, to associate a confidence to the prediction of quantities of interest and to estimate the probability of occurrence of different scenarios. The method is illustrated by various examples mainly from the rail domain but also from the road sector. The second section summarises application examples of predictive modelling, robust optimisation and calibration.     

Gyroscopic stabilisers for powered two-wheeled vehicles

ABSTRACT

This paper illustrates the potential of a gyroscopic stabiliser for the stabilisation of single-track vehicles, at low and high speed as well as during braking. Alternative systems are considered, including single and twin counter-rotating gyroscopes, spinning and precessing with respect to different axes, either freely (passive stabilisers) or in a controlled way (active stabilisers). A suitable mathematical model has been developed and stability has been investigated both by eigenvalue calculation and time domain simulations. It has been found that the most effective configuration is one where the gyroscope(s) spin with respect to an axis parallel to the wheels' spin axis and swing with respect to the vehicle yaw axis. Passive systems may effectively stabilise both weave and wobble at medium and high speed, but cannot stabilise the vehicle at low and zero speed. On the contrary, actively controlled gyroscopes are capable of stabilising the vehicle in its whole range of operating speed, as well as during braking. The alteration of the original vehicle handling characteristics is negligible when active counter-rotating gyroscopes are used, and still acceptable if a single gyroscope is adopted instead.     

A Procedure for Optimization of Truck Suspensions

The purpose of this paper is to develop a procedure based on covariance analysis and nonlinear programming techniques which can be used for the parameter selection of optimum truck suspensions. The procedure is applied to explore the differences in parameter selection caused by the changes in the frequency content of the road input or by changes in the criteria for optimization. The equations of motion for a tractor-semitrailer truck are cast in state space form. The road excitations are represented by the output of a white noise excited shaping filter taking into consideration the time delays between the different vehicle axles. Shape filters to represent human perception of vibration in both the vertical and longitudinal directions in the time domain are presented and realized in terms of state variables. The suspension parameters of the road-vehicle-human body system are optimized using a direct search algorithm.     

Optimal Control of the Tractor-Semitrailer Truck

SUMMARY

This paper is concerned with the braking performance and the handling behavior of the tractor-semitrailer truck under optimal braking. Optimal control theory is used in order to deal with the problem and a combination of the steepest descent method and the Davidon Fletcher Powell method is used to solve it numerically. Results for some chosen braking maneuvers are obtained for a nonlinear truck model which has 14 degrees of freedom. These results show that, for the chosen maneuvers an idealized anti-skid braking is close to being optimal in the sense defined in this paper. Implementation of an idealized anti-skid braking on the tractor-semitrailer truck, however, may be not desirable.     

Trends in vehicle motion control for automated driving on public roads

ABSTRACT

In this paper, we describe how vehicle systems and the vehicle motion control are affected by automated driving on public roads. We describe the redundancy needed for a road vehicle to meet certain safety goals. The concept of system safety as well as system solutions to fault tolerant actuation of steering and braking and the associated fault tolerant power supply is described. Notably restriction of the operational domain in case of reduced capability of the driving automation system is discussed. Further we consider path tracking, state estimation of vehicle motion control required for automated driving as well as an example of a minimum risk manoeuver and redundant steering by means of differential braking. The steering by differential braking could offer heterogeneous or dissimilar redundancy that complements the redundancy of described fault tolerant steering systems for driving automation equipped vehicles. Finally, the important topic of verification of driving automation systems is addressed.     

A book review of “Dynamik der Kraftfahrzeuge (German)”, Dynamics of Motor Vehicles by M. Mitschke,Springer-Verlag, 1972, 529 pp., 382 figs.

SUMMARY

The demands upon the dynamic behaviour of a vehicle can be stated as an optimization problem. The optimum solution is calculated using an iterative optimization algorithm. Scaling the problem by non-linear transformations reduces the number of iterations. Lagrange multipliers provide useful information about the sensitivity of the optimum with respect to changes of the constraints. The analysis of the dynamic behaviour is performed in the frequency domain. New structural variants are calculated using system synthesis. As an example, the engine, cab and wheel suspension systems of a tractor/semi-trailer have been optimized all together.     

Analysis of wheel speed vibrations for road friction classification

ABSTRACT

With higher level of vehicle automation, it becomes increasingly important to know the maximum possible tyre forces during normal driving. An interesting method in this respect is estimating the tyre–road friction from the resonance peak in the wheel speed signal, excited by road roughness. A simulation environment using the MF-Swift tyre model is proposed, which gives insight in the correctness and functioning of this method. From implementing the estimation algorithm and considering the tyre torsional vibration system, it is concluded that frequencies and damping ratios can be estimated with reasonable accuracy and that the trends observed with changing road friction are consistent. Furthermore, the proposed simulation environment gives opportunity to investigate other issues like robustness of the estimation method to road roughness. Additionally, the tyre modelling aspect of the estimation method is analysed and improvements are proposed.     

An Advanced Steering System with Active Kinesthetic Feedback for Handling Qualities Improvement

SUMMARY

Advanced Steering System with artificial steering wheel torque-active kinesthetic information feedback for improving handling qualities is discussed. Fundamentally the structure of the system may be considered to another form of model following control. In this system, a driver always remains in the control loop and receives steering control information which give him/her a direct hint to steer a steering wheel. This system works as a stability and control augmentation system of the vehicle to improve the vehicle handling qualities both in compensatory and pursuit control task, and is expected to reduce driver's workload. Effects of this system are analyzed in terms of man-machine system characteristics. Identification of driver dynamics was carried out to find why such improvement could be achieved. Availability of the proposed system is verified by analysis, simulator and proving ground tests.