Rearward Amplification Research Articles

Effects of configuration parameters on lateral dynamics of tractor–two trailer combinations

The optimum configuration parameters of tractor–trailer combinations for lateral stability performance are proposed by adjusting the length of dolly and the second trailer’s center of gravity. A linear yaw plane model of vehicle combinations is adopted for dynamic analysis, and the model is calibrated by TruckSim. According to the yaw rate rearward amplification ratio of lateral response index, and combining the simulation results of MATLAB/Simulink, dolly and the second trailer are the dominate factors for lateral stability of vehicle combinations. Simulation results show that the distance between articulation joints of dolly is 1.6 m; simultaneously, the rate of distance between front hitch and center of gravity of the second trailer to its front and rear wheelbase is 0.41 and may gain the best lateral performance. Compared with configuration parameters of the original vehicle combinations, the results also illustrate that the one derived from adjustment approach reduces high-speed rearward amplification ratio by 11.4%. The proposed approach might be used for identifying desired design variables of the tractor–two trailer combinations and provided theoretical basis for stability tests.

Articulated heavy vehicle lateral dynamic analysis using an automated frequency response measuring technique

This paper proposes the application of an automated frequency response measuring (AFRM) technique to the lateral dynamic analysis in the frequency-domain for articulated heavy vehicles (AHVs). The AFRM method can be used to automatically acquire the frequency response function of the rearward amplification (RWA) ratio, an important performance measure of the lateral stability of AHVs. A numerical simulation in the time-domain can only achieve the corresponding dynamic response at a specified frequency; to achieve dynamic responses over a frequency band, numerous simulations at various frequencies have to be conducted, and this is a tedious and time consuming process. The RWA measure is frequency-dependent, and the measure in the frequency-domain is of critical importance for the stability evaluation and design synthesis of AHVs. The feasibility and effectiveness of the proposed method is examined using numerical simulations of a tractor/semitrailer combination represented by a linear and a nonlinear AHV model.

Dynamic behaviour of a tractor/quadaxle trailer with variable length drawbar

This paper describes the results of a study of the directional performance of a common Canadian log–hauling truck making use of a tridem–axle tractor, equipped both with and without a forced–steering tag–axle or pusher–axle, in comparison to the conventional fixed tandem–axle tractor. The entire vehicle chosen for analysis consists of a tractor/quadaxle trailer combination; it includes a tractor, a dolly, and a trailer joined to the tractor by a long payload (logs). The dolly, too, is joined to the tractor by a variable length drawbar. The objective is to develop and apply a mathematical model to examine the influence on the vehicle's directional performance of different steering ratios between the tractor's front wheels and the tag–axle or pusher–axle. Different methods for selecting the steering ratios are discussed. The vehicle's directional performance is evaluated against selected performance measures, namely, friction demand at the tractor drive axles, degree of understeer, offtracking, and rearward amplification.

A three-dimensional model of an articulated frame-steer vehicle for coupled ride and handling dynamic analyses

The ride and directional stability properties of an articulated frame steer vehicle (ASV) are investigated through formulation of a comprehensive three-dimensional vehicle model. The model integrates a kineto-dynamic formulation of the frame steering system, a torsio-elastic rear axle suspension, and random roughness of two parallel terrain tracks. The validity of the model is illustrated on the basis of the field-measured ride vibration data and steering strut responses to a 90-degree-turn manoeuvre. The model is applied to determine the ride and yaw/roll dynamic responses of an articulated dump truck with and without a rear-axle suspension under steady and transient steering inputs. The ride responses are evaluated in terms of weighted and un-weighted rms accelerations at the operator location, while the directional responses are obtained in terms of static and dynamic rollover thresholds, rearward amplification ratio, and critical speed corresponding to snaking instability. The results suggest that the rear-axle torsio-elastic suspension yields slightly lower yaw and roll stability limit of the vehicle but substantial reductions in the ride vibration levels. Tyre interactions with the rough terrains affect the stability limits in a highly adverse manner. The results suggest that suspension design with greater lateral and torsional stiffness could yield enhanced directional stability limits while preserving the ride performance.

Implementation of Trailer Steering Control on a Multi-Unit Vehicle at High Speeds

A high-speed path-following controller for long combination vehicles (LCVs) was designed and implemented on a test vehicle consisting of a rigid truck towing a dolly and a semitrailer. The vehicle was driven through a 3.5 m wide lane change maneuver at 80 km/h. The axles of the dolly and trailer were steered actively by electrically-controlled hydraulic actuators. Substantial performance benefits were recorded compared with the unsteered vehicle. For the best controller weightings, performance improvements relative to unsteered case were: lateral tracking error 75% reduction, rearward amplification (RA) of lateral acceleration 18% reduction, and RA of yaw rate 37% reduction. This represents a substantial improvement in stability margins. The system was found to work well in conjunction with the braking-based stability control system of the towing vehicle with no negative interaction effects being observed. In all cases, the stability control system and the steering system improved the yaw stability of the combination.

Effect of Terrain Roughness on the Roll and Yaw Directional Stability of an Articulated Frame Steer Vehicle

Compared to the vehicles with conventional steering, the articulated frame steer vehicles (ASV) are known to exhibit lower directional and roll stability limits. Furthermore, the tire interactions with relatively rough terrains could adversely affect the directional and roll stability limits of an ASV due to terrain-induced variations in the vertical and lateral tire forces. It may thus be desirable to assess the dynamic safety of ASVs in terms of their directional control and stability limits while operating on different terrains. The effects of terrain roughness on the directional stability limits of an ASV are investigated through simulations of a comprehensive three-dimensional model of the vehicle with and without a rear axle suspension. The model incorporates a torsio-elastic rear axle suspension, a kineto-dynamic model of the frame steering struts and equivalent random profiles of different undeformable terrains together with coherence between the two tracks profiles. The simulations are performed to determine the stability limits of the ASV models while operating on different terrains, namely: a perfectly smooth surface, plowed field, pasture, gravel road, and the MVEE random course. The directional stability limits are defined in terms of the static and dynamic rollover thresholds, rearward amplification ratio, and critical speed corresponding to snaking instability under steady and transient steering inputs. The results suggest that the tire interactions with the rough terrains affect the stability limits of both the unsuspended and suspended vehicles in a highly adverse manner. The suspended vehicle responses, however, show less sensitivity to variations in the road roughness profile.

A generic controller for improving lateral performance of heavy vehicle combinations

A generic controller for improving the lateral performance of heavy vehicle combinations by steering the axles of the towed units is proposed. The lateral performance of nine heavy vehicle combinations, including conventional combinations and existing and prospective longer combinations, are studied with and without the controller. The performance of the passive vehicles clearly indicates a need for improvements, which can be achieved by the proposed controller. The results obtained for controller verification in the frequency and time domains demonstrate that the controller reduces the yaw rate rearward amplification and off-tracking of all studied vehicles significantly, and diminishes trailer swings without reducing manoeuvrability. Furthermore, as a by-product, it moderately reduces the lateral acceleration rearward amplification. The improvements obtained by the proposed controller can promote the use of longer combination vehicles in traffic, which will result in a reduction of congestion, as well as substantial environmental and economic benefits.

Analysis of the lateral dynamic behaviour of articulated commercial vehicles

The challenge of designing stability control functions for trucks is to guarantee robustness for all variations in truck and trailer combinations. The method proposed in this study can be used to quickly narrow down the number of truck and trailer combinations to a critical set to be evaluated with complex nonlinear simulation software or full-scale tests. To reach this goal, equations of motion are derived for single track linear vehicle models to understand the fundamental differences between the dynamic yaw performance of the truck and trailer combinations. The Hurwitz criterion is used to determine approximate analytical stability boundaries. It is shown that stability does not provide discrimination between combinations as most combinations are stable during normal driving conditions. In contrast, rearward amplification is a discriminatory performance measure. A frequency domain approach is used to study the fundamental differences between vehicle combinations. A comparison with complex nonlinear simulation model results indicates that the proposed method can be used to select critical vehicle combinations and to study the effect of parameter changes.

Improving the Safety and Road Wear Performance of Heavy Vehicles in South Africa Using a Performance-Based Standards Approach

As a result of successful initiatives in Australia, New Zealand and Canada, the introduction of a Smart Truck or performance-based standards (PBS) approach in the heavy vehicle sector in South Africa was identified by the CSIR as a research area warranting funding because of the potential benefits in terms of transport efficiency, road/vehicle safety and the protection of road infrastructure. The PBS approach involves setting standards to specify the performance required from the operation of a vehicle on a network rather than prescribing how the specified level of performance is to be achieved. A need was identified to design, manufacture and operate a number of PBS demonstration projects in South Africa in order to gain practical experience in the PBS approach and to quantify and evaluate potential benefits. The Smart Truck demonstration projects have been designed and manufactured to comply with the safety standards of the Australian PBS system. These include directional and non-directional manoeuvres such as acceleration capability, slow speed swept path, static rollover threshold and rearward amplification. In order to evaluate the impact of the PBS vehicles on pavements, the South African Mechanistic-Empirical Design and Analysis Methodology was used to calculate the road wear characteristics of various baseline and PBS vehicle combinations. In most cases, the PBS vehicles were found to be significantly more road-friendly per ton of payload than the corresponding baseline vehicles. Modifications for reducing road wear were identified such as load redistribution in order to reduce the load on the steering axle, replacing wide-based single tyres with dual tyres and, where appropriate, replacing a single steer axle with a twin steer axle unit. The paper describes the results of road wear analyses of five PBS vehicles and the corresponding baseline vehicles.

Active steering of a tractor–semi-trailer

This paper develops a path-following steering control strategy for an articulated heavy goods vehicle. The controller steers the axles of the semi-trailer so that its rear end follows the path of the fifth wheel coupling: for all paths and all speeds. This substantially improves low-speed manoeuvrability, off-tracking, and tyre scrubbing (wear). It also increases high-speed stability, reduces ‘rearward amplification’, and reduces the propensity to roll over in high-speed transient manoeuvres. The design of a novel experimental heavy goods vehicle with three independent hydraulically actuated steering axles is presented. The path-following controller is tested on the experimental vehicle, at low and high speeds. The field test results are compared with vehicle simulations and found to agree well. The benefits of this steering control approach are quantified. In a low-speed ‘roundabout’ manoeuvre, low-speed off-tracking was reduced by 73 per cent, from 4.25 m for a conventional vehicle to 1.15 m for the experimental vehicle; swept-path width was reduced by 2 m (28 per cent); peak scrubbing tyre forces were reduced by 83 per cent; and entry tail-swing was eliminated. In an 80 km/h lane-change manoeuvre, peak path error for the experimental vehicle was 33 per cent less than for the conventional vehicle, and rearward amplification of the trailer was 35 per cent less. Increasing the bandwidth of the steering actuators improved the high-speed dynamic performance of the vehicle, but at the expense of increased oil flow.

High-speed optimal steering of a tractor–semitrailer

A high-speed optimal trailer steering controller for a tractor–semitrailer is discussed. A linear model of a tractor–semitrailer with steered trailer axles is described, and an optimal trailer steering controller is introduced. A path-following controller is derived to minimise the path-tracking error in steady-state manoeuvres using active trailer steering. A roll stability controller is introduced by adding the lateral acceleration of trailer centre of gravity as another objective in the steering controller, so as to improve roll stability in transient manoeuvres. A strategy to switch between these two control modes is demonstrated. Simulation results show that the steering controller can ensure good path tracking of articulated vehicles in steady-state manoeuvres and improve roll stability significantly in transient manoeuvres, while maintaining the path-tracking deviation within an acceptable range. Tests with an experimental tractor–semitrailer equipped with a high-bandwidth active steering system validate the controller design and simulation results. The roll stability controller reduces the measured rearward amplification by 27%.

An Integrated Design Method for Articulated Heavy Vehicles with Active Trailer Steering Systems

This paper presents an integrated design method for active trailer steering (ATS) systems of articulated heavy vehicles (AHVs). Of all contradictory design goals of AHVs, two of them, i.e. path-following at low speeds and lateral stability at high speeds, may be the most fundamental and important, which have been bothering vehicle designers and researchers. To tackle this problem, a new design synthesis approach is proposed: with design optimization techniques, the active design variables of ATS systems and passive design variables of trailers can be optimized simultaneously; the ATS controller derived from this approach has two operational modes, one for improving lateral stability at high speeds and the other for enhancing path-following at low speeds. To demonstrate the effectiveness of the proposed approach, it is applied to the design of an ATS system for an AHV with a tractor and a full trailer. Simulation results illustrate that compared with the baseline vehicle, the one derived from the design synthesis approach decreases low-speed off-tracking by 35.2% and reduces high-speed rearward amplification ratio by 30.0%. The proposed approach may be used for identifying desired design variables and predicting performance envelopes in the early design stages of AHVs with ATS systems.

Command steering of trailers and command-steering-based optimal control of an articulated system for tractor-track following

First the effectiveness of command steering of trailers in reducing off-tracking during a 90° turn for a truck with three trailers is examined. In command steering, front trailer axles are steered proportionately to the articulation angles between the tractor and corresponding trailers. Then, based on insights gained, the approach of an optimal linear quadratic regulator (LQR) controller to minimize off-tracking indirectly, by minimizing rearward amplification, is used. The simulation results demonstrate that command steering is very effective only for low speeds, although it also reduces the turn radius during a 90° turn. Command-steering-based LQR control is, however, very effective for all speeds.

Active trailer steering control of an articulated system with a tractor and three full trailers for tractor-track following

We examine several control strategies to minimise off-tracking of a multi-axle steering system with a tractor and three full trailers, described by a linear yaw-plane model. Given any arbitrary tractor track desired real-time by the driver, control inputs are the steering angles of front axles of the trailers. A minimum Rearward Amplification Ratio (RWA), as a surrogate for minimum off-tracking, is used as the control criterion to arrive at an optimal LQR controller, which is remarkably robust to tyre-parameter variations. Actively steering trailers 1 and 2 is most cost-effective in achieving acceptable levels of RWA, with off-tracking practically eliminated.

A Simple Differential Brake Control Algorithm for Attenuating Rearward Amplification in Doubles and Triples Combination Vehicles

SUMMARYA simple brake control algorithm useful for attenuating rearward amplification tendencies in doubles and triples combination trucks is described. The basic goal was to first design, and then to demonstrate through experimental testing, an automatic brake control system that could intervene—only when needed—to help suppress unwanted trailer yaw oscillations (commonly referred to as ‘rearward amplification’) in large combination vehicles (typically doubles and triples combinations in the U.S.). The system would only be enabled for highway speed operating conditions, and if possible, so simple that the system could be provided on a trailer-by-trailer basis. That is, the proposed system, when implemented on a particular trailer within a combination vehicle train, would not have to depend upon sensor information from units ahead of it or behind it in order to function properly and yet provide significant benefit. The primary focus therefore of this work was on the development and demonstration of a so-called “trailer-only” RAMS (Rearward A mplification Suppression) system [1].

Sensitivity of rearward amplication control of a truck/full trailer to tyre cornering stiffness variations

Highway safety and vehicle performance are two important considerations in the design of a heavy vehicle combination. In this paper a performance measure called the ‘rearward amplification ratio’ (RWA) is used as a control criterion in the design of a vehicle-handling controller. This approach is different to conventional control techniques. The RWA is defined as the ratio of the peak lateral acceleration at the rearmost trailer's centre of gravity (CG) to that of the lead unit during a lane-change manoeuvre. The vehicle under consideration is a six-axle truck/full trailer, which usually exhibits a high level of RWA leading to roll-over during obstacle avoidance manoeuvres. In this study, several control strategies are examined, namely active yaw control at the truck CG, active yaw control at the dolly CG and active yaw control at the trailer CG. These could be employed individually or in combination. The effect of an active control torque applied to various vehicle units is examined by using an optimal linear quadratic regulator approach combined with a simplified four degrees-of-freedom linear vehicle model. The controller performance index parameters are determined for the vehicle based on acceptable RWA target values. The sensitivity of the controller to tyre cornering stiffness variation is further evaluated. Simulation results indicate that the RWA can be reduced without significant change of the uncontrolled vehicle trajectory when active yaw torque is applied to the dolly. The controller can be more effective in improving the dynamic performance and roll stability of this type of commercial vehicle, if applied to the lead unit (truck) or to the last unit (trailer). However, the path of the vehicle will be strongly influenced and driving difficulties can be experienced. For active yaw control at the dolly CG, the optimal controller is found to be most sensitive to the dolly's tyres' cornering stiffness variations and least sensitive to steering axle from the RWA point of view. It is also found that the controller is most sensitive to steering axle parameter variations for path following.

Directional performance analysis of an A-train double with externally mounted dampers

An A-dolly with externally mounted dampers is proposed to enhance the yaw and lateral directional performance of an A-train double. A kinematic analysis of the external dampers is performed to derive damping forces and moments imposed on the coupled A-dolly and the first semitrailer of the combination. The resulting kinematic model of the external dampers is integrated within the non-linear yaw-plane model of the A-train to study the performance potentials of the dampers. The directional response characteristics of the combination are evaluated under closed-loop path-change and double path-change manoeuvres, in conjunction with a path-follower driver-vehicle model based upon preview/predictive strategy. An analytical function based on the Magic Formula is further proposed to describe the path co-ordinates for the closed-loop manoeuvres. The results of the study show that damped articulation integrated between the first semitrailer and the A-dolly offers considerable potential for enhancement of the directional performance of the vehicle combination in terms of peak lateral acceleration, yaw rate, and rearward amplification.

Rearward Amplification Control of a Truck/Full-Trailer

In this paper an attempt is made to use a performance measure called the “Rearward Amplification Ratio (RWA)” as a control criterion in the design of a vehiclehandling controller as an alternative to conventional control techniques. The RWA is defined as the ratio of the peak lateral acceleration at the rearmost trailer's centre of gravity (cg) to that at the cg of the lead unit during a lane-change manoeuvre. The vehicle under consideration is a 6-axle truck/fiill-trailer, which usually exhibits high level of rearward amplification ratio leading to rollover during obstacle avoidance manoeuvres.In this study, the control performance index criteria are determined for the vehicle based on acceptable RWA target value. Several control strategies are examined, namely active yaw control at the truck cg, active yaw control at the dolly cg, and active yaw control at the trailer cg. The active yaw torque could be employed individually to each unit of the vehicle or in combination. The effect of the active control torque applied to various vehicle units are examined by using the Linear Quadratic Regulator (LQR) approach combined with a simplified four degrees of freedom (DOF) linear vehicle model.Simulation results indicate that the rearward amplification ratio can be reduced without significant change of the uncontrolled vehicle trajectory when active yaw torque is applied to the dolly. However, the controller can be more effective if applied to the lead unit (truck) or to the last unit (trailer), but the path of the vehicle will be strongly influenced and driving difficulties can be experienced. However, the improvement of the rearward amplification will result in improving the dynamic performance and roll stability of this type of heavy commercial vehicles.

A Computer Simulation Study of the Closed-Loop Stability and Maneuverability of Articulated Coach/Driver Systems

Results of a computer simulation study conducted to examine the directional stability and maneuverability of an articulated coach/driver system are presented. Findings suggest that: (a) the ability of drivers to stabilize and control articulated coaches within the linear operating regime is approximately the same as that required of automobile drivers, (b) maneuverability of the driver/vehicle system is strongly influenced by driver control characteristics, but driver-related improvements to the maneuverability of the system are severely limited by large rearward amplification properties of the vehicle, and (c) drivers may exchange (within limits imposed by the rearward amplification phenomenon) decreased stability of the closed-loop system for increased maneuverability (and vice versa) by simple alteration of their preview control strategies. For the covering abstract of the conference see TRIS 395019. (Author/TRRL)