Stability Criteria for Automobile-Trailer Combinations

The characteristic equation for a simple automobile-trailer combination is analyzed, revealing the parameter groups which are important in determining the stability characteristics. Application of Routh's method results in separate criteria for oscillatory and non-oscillatory criteria which can be evaluated algebraically, and which can also be displayed graphically showing a region of stability on a two-dimensional plot. The stability region is bounded by limits of oscillatory and non-oscillatory stability, and the evaluation of a specific case corresponds to the location of a point relative to the boundaries.     

Closed-Loop Directional Stability of Car-Trailer Combinations in Straight-Line Motion

SUMMARY

This work focuses on the interaction between a driver and a car-trailer combination. A model characterizing human operator behavior in regulation task is employed to study directional stability of the overall system. The vehicle-trailer model retains nonlinear cornering force and other kinematic nonlinearities. Linear stability of the straight line motion is analyzed by the application of Routh-Hurwitz criteria and stability boundaries in parameter space are constructed by setting appropriate Hurwitz determinant to zero. It is shown that two types of transition in stability are possible in the driver/car-trailer system. They correspond to one pair or two pairs of complex conjugate eigenvalues crossing the imaginary axis simultaneously. The implications in terms of resulting motions for the nonlinear system are also discussed. It is shown that stabilization of the combination can be achieved by adding a passive controller at the articulation point. Articulation damper turns out to be a more useful device for controlling trailer oscillations instability although a combination of damper and torsional spring would be a more ideal solution.     

Stability Criteria for Articulated Railway Vehicles Possessing Perfect Steering

SUMMARY

The general form of the equations o f motion o f multi-body articulated railway vehicles are used to establish the conditions which the elastic stiffness matrix, which describes the nature and configuration o f the suspension elements connecting the various bodies, must satisfy in order to achieve both perfect steering on circular curves and dynamic stability. The resulting criteria are then used to discuss the properties of various multi-axle configurations which are either typical of current practice or possibilities for future designs.     

Investigation on Stability and Possible Chaotic Motions in the Controlled Wheel Suspension System

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.     

Automotive Stability and Handling Dynamics in Cornering and Braking Maneuvers

SUMMARY

Automotive steering behaviour is classified for steady-state cornering and the definitions of over-/understeer and stability/instability are well known. In this paper it is intended to apply these definitions to combined cornering and braking maneuvers i.e. to extend the criteria to quasi-steady-state conditions. This way of investigation was chosen because it gives a clear idea of the typical handling behaviour. Furthermore, the vehicle behaviour is analyzed using the cornering stiffness of the axles and front/rear cornering stiffness ratio because this is always of primary significance. The following contribution is based on a theoretical analysis considering the most important non-linear vehicle properties.

The paper deals with two groups of vehicles: single vehicles (passenger cars) and combinations (passenger car/caravan and tractor/semitrailer). In the case of combinations the effect of trailers on the towing vehicles is examined. So, careful attention is paid to the coupling forces, which alter the wheel loads and influence steerability and stability.     

A Simplified Framework for String Stability Analysis of Automated Vehicles∗

SUMMARY

Automated vehicles traveling in platoons must exhibit stability both individually and as a group, a property referred to as “string stability”. We propose a new framework for evaluating the longitudinal string stability properties of platoons of automated vehicles. In this framework, the platoon is considered to be a mass-spring-damper system with linear characteristics. The resulting closed-loop representation yields transfer functions and impulse responses that can be analyzed to determine the string stability properties of the platoon. This framework facilitates qualitative comparisons of the effects of various controller characteristics, such as time headway and intervehicle communication, on string stability.     

A Nonlinear Analysis of the Generic Types of Loss of Stability of the Steady State Motion of a Tractor-Semitrailer∗

SUMMARY

All different types of loss of stability which occur generically for a tractor semitrailer vehicle are studied when varying two parameters namely the speed V of the vehicle and the position d of the center of mass of the trailer. For a fixed value of d and varying V it turns out that only two cases either a divergence or a Hopf bifurcation can occur typically. By means of a nonlinear analysis the post-bifurcation behavior for both cases is treated showing that it is critical in both cases. This latter result means that the system is an imperfection sensitive one for which the calculation only of the linear stability limit, does not have very much practical meaning, because small perturbations of the system (changes of parameters) can lead to a drastic reduction of the critical speed. Our paper furthermore indicates how a nonlinear investigation of stability problems in vehicle dynamics with no restriction to the number of degrees of freedom of the system can be done in a straight forward manner.     

Nonlinear Lateral and Yaw Dynamics and Stability of Snow mobiles

SUMMARY

This paper takes a close look at the mechanism of locomation in snowmobiles. A mathematical model is developed taking into account the inherent nonlinearities of the system. A piece-wise linear approach is presented. A nonlinear methodology is used to construct stability maps for the yaw dynamics. The strategy can be extended to assess the stability in lateral slip of the snowmobile when negotiating a turn. The developed models and strategies are useful design tools for a wide class of snowmobiles.     

Stationar- und Ubergangsverhalten von Sattel- und Lasttugen bei der Kreisfahrt: Lineare Berechnungen

ABSTRACT

Steady and Transient Turning of Tractor-Semitrailer and Truck-Trailer Combinations: A Linear Analysis

A simplified analysis is made of the yaw stability and control of the two types of the commercial vehicle combinations (tractor-semitrailer, truck-trailer) at a constant forward velocity during steady and transient turning. The combined vehicle is treated as a linear dynamic system (Fig. 2). The steer angle at the front wheels of the tractor (or truck) and the steady-state responses if the road verhicle train (yaw rate, articulation angles and sideslip angle) are calculated (Equations 18 to 25). Exploratory calculations are performed to determine the influence of the cornering stiffness of the tires for the two types of the vehicle combinations upon the steady-state responses (Figs. 7 to 10). For a linear simplified model of articulated vehicle the steady-state turning behaviour is stable also under conditions of rather high driving speed (70 km/h). A simplified analysis of the transient turning behaviour of the two types of road trains has shown the tractor-semitrailer to preserve stability even under driving speeds exceeding 70 km/h (Fig. 13), whereas the truck-trailer combinations appear to become oscillatory unstable if the driving speed rises above the 60 km/h margin (Fig. 14).     

Zur Stabilität der Kurvenfahrt eines Kraftfahrzeuges mit und ohne Tangentialbeschleunigung

SUMMARY

(Title: On the Stability of Turns of a Motor Vehicle with and without Tangential Acceleration) As can be shown in the treatment of the steady-state turn, the conditions for stability of a possible turning motion give rise to a limitation of the speed of travel which lies partly under the boundary due to friction limitations. In particular, at transient turns (braking or accelerating in a turn) the stability changes considerably at large absolute values of the tangential acceleration and may lead to a considerable further decrease of the maximum possible speed of travel.     

Railway Vehicles with Perfect Curving Behaviour Which are Asymptotically Stable at Vanishing Speed

SUMMARY

Paper deals with the linear behaviour of a railway vehicle with any arbitrary number of wheelsets, body parts and connecting elements. A vehicle which has both perfect curving properties and asymptotical stability at vanishing speed, has to satisfy a twofold condition, indicated by Wickens in 1978. In the present paper this condition is derived in reliance upon the dimension theorem for linear mappings. How the investigation can be executed in practice, is shown for the case of a two-axled vehicle. At last the behaviour in a transition curve is discussed.     

A Comparision of Spacing and Headway Control Laws for Automatically Controlled Vehicles1

SUMMARY

This paper investigates two different longitudinal control policies for automatically controlled vehicles. One is based on maintaining a constant spacing between the vehicles while the other is based upon maintaining a constant headway (or time) between successive vehicles. To avoid collisions in the platoon, controllers have to be designed to ensure string stability, i.e the spacing errors should not get amplified as they propagate upstream from vehicle to vehicle. A measure of string stability is introduced and a systematic method of designing constant spacing controllers which guarantee string stability is presented. The constant headway policy does not require inter-vehicle communication to assure string stablity. Also, since inter-vehicle communication is not required it can be used in systems with mixed automated-nonautomated vehicles, e.g for AICC (Autonomous Intelligent Cruise Control). It is shown in this paper that for all the autonomous headway control laws, the desired control torques are inversely proportional to the headway time.     

Comparison of Ride Comfort Criteria for Computer Optimization of Vehicles Travelling on Randomly Profiled Roads

SUMMARY

This paper discusses and compares some ride comfort criteria which may be suitable for randomly vibrating vehicles. The criteria consider single-figure measures based on response mean square spectral densities for plane linear combined vehicle-passenger models. Eight different measures divided into three groups are studied. The two vehicle suspension damper stiffnesses are numerically optimized with respect to the eight measures of ride comfort. The results are compared and discussed. Two optimizations with respect to five vehicle parameters are also reported.     

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.     

Impact of Dynamic Fluid Slosh Loads on the Directional Response of Tank Vehicles

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 fluid slosh models during transient steer inputs show good correlation. Based on this study, it can be concluded that the quasi-dynamic model can predict the directional response characteristics of tank vehicles quite close to that evaluated using the comprehensive fluid slosh model.     

Nonlinear Attitude Dynamics of Twin Cycle with Feedback Control

Abstract

The nonlinear attitude dynamics of a twin cycle under output feedback control is studied through bifurcation analysis. Two cases are considered. One assumes no slip and the other assumes small slip. The double zero bifurcation is found to occur in both cases but with different bifurcation sets. Among them heteroclinic orbits are found in both cases and a limit cycle in the second case. The region of feedback gains for stability is obtained. Large negative feedback gains are found necessary to assure stability of the twin cycle. Finally, the tire effect is studied and it causes the distortion of the bifurcation sets.     

Stability Analysis of Constant Speed Transit Vehicles On Straight,Horizontal, Fixed Guideways

SUMMARY

Several methods of motion stability analysis are examined and compared in the context of the problem posed by a simple idealization of a transit vehicle moving at constant speed on a straight, horizontal, fixed guideway, supported by idealized rubber tires, air cushion pads, or semiconical steel wheels on steel rails. Stability analysis methods examined include Liapunov analysis with the Hamiltonian and with a modified Hamiltonian proposed by Walker, and analysis of characteristic equations using theorems due to Routh, Hurwitz, Cronin, and Liénard and Chipart It is concluded that for rubber-tired and aircushioned vehicles a Liapunov analysis employing the Hamiltonian is most efficient, and for the tracked vehicle the criteria of Liénard and Chipart are most useful.     

Advanced Control Methods of Active Suspension

SUMMARY

This paper describes new control methods for the active suspension. For improving ride comfort further, preview control rule is proposed. For improving stability further, roll stiffness distribution control rule is examined by the test vehicle. Simulations and vehicle driving tests are conducted to confirm the effect of these new control methods. The results of simulations and vehicle driving tests show in our research phase that preview control can achieve a substantial improvement in ride comfort and application of roll stiffness distribution control provides a large improvement in stability     

On the Destabilizing Effect of Liquids in Various Vehicles∗ (part 1)

SUMMARY

The unrestrained free surface of a liquid has an alarming propensity to undergo large excursions for even very small motions of the container. This fact may endanger the stability, as well as the riding and maneuvering quality of the vehicle considerably. It is particularly true for fuel- or cargo tanks of automotive vehicles, railroad tank cars, for fuel tanks of large ships and tankers, for which violent sea conditions at times result in fairly large amplitudes of pitching, heaving and rolling, as well as for airplanes and spacevehicles flying through atmospheric disturbances. The response of liquids contained in cargo- or fuel tanks is therefore of quite some concern, especially in those cases where the sloshing liquid masses occupy a large amount of the total mass of the vehicle.

For this reason the theory of liquid motion with a free surface is presented for containers of various geometries. Forces and moments of the liquid exerted upon the vehicle are presented and a simple mechanical model for the representation of the liquid motion is derived. Methods for the reduction of the destabilizing effect of the liquid motion, such as baffles, cross walls and surface coverings are presented and shall exhibit their effectiveness. In addition the interaction of the liquid motion with the elastic structure of the container, as well as the interaction with a controlling system of the vehicle shall be demonstrated. Stability boundaries, design criteria and dynamic responses to disturbances shall be presented for a particular case.     

Literature review and fundamental approaches for vehicle and tire state estimation*

ABSTRACT

Most modern day automotive chassis control systems employ a feedback control structure. Therefore, real-time estimates of the vehicle dynamic states and tire-road contact parameters are invaluable for enhancing the performance of vehicle control systems, such as anti-lock brake system (ABS) and electronic stability program (ESP). Today's production vehicles are equipped with onboard sensors (e.g. a 3-axis accelerometer, 3-axis gyroscope, steering wheel angle sensor, and wheel speed sensors), which when used in conjunction with certain model-based or kinematics-based observers can be used to identify relevant tire and vehicle states for optimal control of comfort, stability and handling. Vehicle state estimation is becoming ever more relevant with the increased sophistication of chassis control systems. This paper presents a comprehensive overview of the state-of-the-art in the field of vehicle and tire state estimation. It is expected to serve as a resource for researchers interested in developing vehicle state estimation algorithms for usage in advanced vehicle control and safety systems.