Directional Dynamics of a Tractor-Loader-Backhoe

This paper presents a study of the directional dynamics of large industrial tractors. These vehicles have special properties which make their dynamics interesting, including soft rear tires, large yaw moments of inertia and low or negative understeer gradients.

A linear yaw plane model was used for the analysis. The lateral compliance of the tires was included via a simplified version of the stretched-string model. Measurements were performed in support of the modeling effort, including inertial parameters, understeer gradient and transient response. A comparison between calculations and test results indicated that lateral compliance was an important influence on the transient response of these vehicles.     

On the handling performance of a vehicle with different front-to-rear wheel torque distributions

ABSTRACT

The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied by analyzing the understeer coefficient in quasi-steady-state maneuvers. In this paper, experimental tests are performed on an electric vehicle with four independent motors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. The study presents a procedure to compute the longitudinal and lateral tire forces, which is based on a first estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the understeer coefficient, and allow to infer a relationship between the understeer coefficient and the yaw moment analysis. The handling characteristics vary with speed and front-to-rear wheel torque distribution. An apparently surprising result arises at low speed: the RWD architecture is the most understeering configuration. This is discussed by analyzing the yaw moment caused by the longitudinal forces of the front tires, which is significant for high values of lateral acceleration and steering angle.     

Optimal Control of Four Wheel Steering Vehicle

SUMMARY

This paper derives a method of controlling four wheel steering using optimal control theory. The purpose of control is to minimize the sideslip angle at the center of gravity. The control method feeds forward the steering wheel angle and feeds back the yaw velocity and the sideslip angle to the front and rear wheel angles. Theoretical studies show that the sideslip angle is reduced to zero even in the transient state, and that the understeer characteristic and frequency response can be changed regardless of the vehicle static margin. This Paper also examines various characteristics of the influence of the side force nonlinearities of tires and crosswinds.     

How well a single-track linear model captures the lateral dynamics of long combination vehicles

ABSTRACT

The effect of centre-of-gravity heights on the high-speed performance measures of long combination vehicles including truck with double centre-axle trailers, Nordic, and A-double combination vehicles is investigated. The high fidelity three-dimensional models, used in this research, are validated against physical test data. These models are often accurate in terms of the actual dynamic behaviours of the vehicle. On the other hand, the simple yaw-plane single-track models with linear tires require less number of vehicle parameters. In this paper, it is investigated how accurate the estimations of performance measures are at high forward speeds by such single-track linear (STL) models. The influence of load height is especially studied. The high-speed performance-based standard or PBS measures considered are rearward amplifications of both lateral acceleration and yaw velocity; lateral load transfer; yaw damping and high-speed transient offtracking. The results show that tire relaxation has a large effect and it is rather easy to add to an STL model, so it is assumed to be modelled in STL. With realistically high payload and a required accuracy of PBS measures of approximately 10%, only the accuracy of rearward amplification of yaw velocity calculated by the frequency response is fulfilled by the STL. With low payload, the same statement is valid, but with around 5% in required accuracy. The roll dynamics effects are more important than the tire non-linearities.     

The Static Stability of Articulated Commercial Vehicles

SUMMARY

This review of the state of the art emphasizes recent results that have been obtained in extending conventionalanalysis techniques to the treatment of “Highway Trains”, that is, to heavy trucks that have multiple articulation points and employ suspensions with multiple axles. Equations of motion applicable to the equilibrium turning performances of articulated vehicles are examined with respect to using analysis techniques involving steering gains, understeer gradients, effective wheel-bases, handling diagrams, and critical speeds. These examinations provide the basis for in sights into simplified approaches for understanding the steady turning mechanics of articulated, multi-axle vehicles riding on pneumatic tires.     

An Investigation of High-Speed Automobile Steering Response

SUMMARY

The significance of the effects of steering compliance and aerodynamic life on high speed automobile's steering response was investigated on two vehicles, a Ford Falcon XW (1969) station-wagon and a GM-Holden Kingswood HQ (1974) sedan. An aerofoil was mounted above the front bumper bar of the Ford Falcon to enable the simulation of vehicles with very degraded aerodynamic characteristics. Mathematical analysis showed the importance of the inclusion of steering compliance effects in determining stability factor, and hence the vehicle's high speed yaw rate sensitivity. Both experiments and theory showed that the actual high speed yaw rate response is not significantly less than that predicted from a low speed skid pad test, however, slight errors were found which are likely to be due to steering system nonlinearity and the effects of aerodynamic lift.     

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.     

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).     

Full drive-by-wire dynamic control for four-wheel-steer all-wheel-drive vehicles

Most of the controllers introduced for four-wheel-steer (4WS) vehicles are derived with the assumption that the longitudinal speed of the vehicle is constant. However, in real applications, the longitudinal speed varies, and the longitudinal, lateral, and yaw dynamics are coupled. In this paper, the longitudinal dynamics of the vehicle as well as its lateral and yaw motions are controlled simultaneously. This way, the effect of driving/braking forces of the tires on the lateral and yaw motions of the vehicle are automatically included in the control laws. To address the dynamic parameter uncertainty of the vehicle, a chatter-free variable structure controller is introduced. Elimination of chatter is achieved by introducing a dynamically adaptive boundary layer thickness. It is shown via simulations that the proposed control approach performs more robustly than the controllers developed based on dynamic models, in which longitudinal speed is assumed to be constant, and only lateral speed and yaw rate are used as system states. Furthermore, this approach supports all-wheel-drive vehicles. Front-wheel-drive or rear-wheel-drive vehicles are also supported as special cases of an all-wheel-drive vehicle.     

Optimal Control of Four Wheel Steering Vehicle

This paper derives a method of controlling four wheel steering using optimal control theory. The purpose of control is to minimize the sideslip angle at the center of gravity. The control method feeds forward the steering wheel angle and feeds back the yaw velocity and the sideslip angle to the front and rear wheel angles. Theoretical studies show that the sideslip angle is reduced to zero even in the transient state, and that the understeer characteristic and frequency response can be changed regardless of the vehicle static margin. This Paper also examines various characteristics of the influence of the side force nonlinearities of tires and crosswinds.     

Effect of Frame Compliance on the Lateral Dynamics of Motorcycles

SUMMARY

The lateral dynamics of an uncontrolled motorcycle, running on a straight, level road surface, is investigated in this paper. The structural compliances in the front and the rear frames of the motorcycle are taken into account by introducing additional degrees of freedom in the analysis. The kinematics of the tires is represented by linear differential equations which are based on the taut-string model of pneumatic tires. The linear differential equations of motion are solved to yield the eigensolutions of the system. Numerical results, obtained for parameters corresponding to a Honda CB750 motorcycle, are presented and discussed.     

The Influence of Structural Flexibilities on the Straight-running Stability of Motorcycles

SUMMARY

A new tyre model for studies of motorcycle lateral dynamics, and three new motorcycle models, each incorporating a different form of structural compliance, are developed. The tyre model is based on “taut string” ideas, and includes consideration of tread width and longitudinal tread rubber distortion and tread mass effects, and normal load variation. Parameter values appropriate to a typical motorcycle tyre are employed. The motorcycle models are for small lateral perturbations from straight running at constant speed, and include (a) lateral compliance of the front wheel in the front forks, (b) torsional compliance of the front forks, and (c) torsional compliance in the rear frame at the steering head about an axis perpendicular to the steering axis.

Results in the form of eigenvalues, indicating modal damping properties and natural frequencies are presented for each model. The properties of four large production machines for a range of forward speeds, and the practicable range of stiffnesses are calculated, and the implications are discussed.

It is concluded that typical levels of structural compliance in models (a) and (c) contribute significantly to the steering behaviour properties of large motorcycles, and their observed behaviour can be understood better in terms of the new results than of those existing previously. Some conclusions relating to optimal structural stiffness properties are also drawn.     

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.     

A new formulation of the understeer coefficient to relate yaw torque and vehicle handling

The handling behaviour of vehicles is an important property for its relation to performance and safety. In 1970s, Pacejka did the groundwork for an objective analysis introducing the handling diagram and the understeer coefficient. In more recent years, the understeer concept is still mentioned but the handling is actively managed by direct yaw control (DYC). In this paper an accurate analysis of the vehicle handling is carried out, considering also the effect of drive forces. This analysis brings to a new formulation of the understeer coefficient, which is almost equivalent to the classical one, but it can be obtained by quasi-steady-state manoeuvres. In addition, it relates the vehicle yaw torque to the understeer coefficient, filling up the gap between the classical handling approach and DYC. A multibody model of a Formula SAE car is then used to perform quasi-steady-state simulations in order to verify the effectiveness of the new formulation. Some vehicle set-ups and wheel drive arrangements are simulated and the results are discussed. In particular, the handling behaviours of the rear wheel drive (RWD) and the front wheel drive (FWD) architectures are compared, finding an apparently surprising result: for the analysed vehicle the FWD is less understeering than for RWD. The relation between the yaw torque and the understeer coefficient allows to understand this behaviour and opens-up the possibility for different yaw control strategies.     

A Tractor Handling Study

SUMMARY

Agricultural tractors are relatively slow moving vehicles but a good steer response under all working conditions is generally required. This paper evaluates the effect of ground slope, axle load, ground speed, tyres and ground surface on yaw rate response to steer input.     

Effects of Model Complexity on the Performance of Automated Vehicle Steering Controllers: Controller Development and Evaluation

SUMMARY

Due to increased traffic congestion and travel times, research in Advanced Vehicle Control Systems (AVCS) has focused on automated lateral and headway control. Automated vehicles are seen as a way to increase freeway capacity and vehicle speeds while reducing accidents due to human error. Recent research in automated lateral control has focused on vehicle control during low-g maneuvers. To increase safety, automated lateral controllers will need to recognize and react to emergency situations.

This paper investigates the effects of vehicle and tire model order on the response of automated vehicles to an emergency step lane change using a controller based on linear vehicle and tire models. From these studies it is concluded that control strategies based solely on linear vehicle and tire models are inadequate for emergency vehicle maneuvers.

A strategy is then proposed to automatically control vehicles through emergency maneuvers. Here the response of a nonlinear vehicle model is used with a linear state model to optimize controller gains for nonlinear maneuvers. An emergency step lane change is used as a preliminary test of the method.     

Steady State Steering Response

The yaw rate response for a two-degree-of-freedom car model requires a family of curves for different degrees of oversteer or understeer. By use of non-dimensional co-ordinates this family is reduced to one single curve. The ordinate ρ is the ratio of yaw rate response to that of a neutral steering car at the same speed and is less than 1 for understeer and greater than 1 for oversteer. Since ρ is also the ratio of the side-slip angle response it is hence, a unique measure of the steady-state steering characteristics.     

Optimal control of brakes and steering for autonomous collision avoidance using modified Hamiltonian algorithm

ABSTRACT

This paper considers the problem of collision avoidance for road vehicles, operating at the limits of friction. A two-level modelling and control methodology is proposed, with the upper level using a friction-limited particle model for motion planning, and the lower level using a nonlinear 3DOF model for optimal control allocation. Motion planning adopts a two-phase approach: the first phase is to avoid the obstacle, the second is to recover lane keeping with minimal additional lateral deviation. This methodology differs from the more standard approach of path-planning/path-following, as there is no explicit path reference used; the control reference is a target acceleration vector which simultaneously induces changes in direction and speed. The lower level control distributes vehicle targets to the brake and steer actuators via a new and efficient method, the Modified Hamiltonian Algorithm (MHA). MHA balances CG acceleration targets with yaw moment tracking to preserve lateral stability. A nonlinear 7DOF two-track vehicle model confirms the overall validity of this novel methodology for collision avoidance.     

The Influence of Tire Factors on the Stability of Trucks and Tractor Trailers

SUMMARY

The mechanical properties of tires and trucks are contrasted with comparable properties of the motor car to explain why the motor truck and the tractor-trailer can exhibit fixed-control instability at moderate levels of lateral acceleration. The (1) rearward bias in the distribution of roll stiffness, (2) large ratio of e.g. height to track, and (3) low torsional stiffness of the parallel-rail frame (as typically employed in heavy commercial vehicles) are found to be the major factors implicated in this phenomenon. Experimental and analytical evidence is provided to show how tire inflation pressure and mixes of (a) tire-carcass construction and (b) tread design also influence stability at moderate levels of lateral acceleration. Conclusions relating to the safety of commercial vehicle operations are drawn.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.