A Dynamical Analysis of a Towed Two-Wheel Trailer1

The towed trailer method for skid resistance measurements is a practical one for characterizing the friction characteristics of highway pavements, and has been standardized by the ASTM 11). Numerous papers have been published about the improvement of equipment and field-testing techniques but little has been done toward a theoretical explanation.

This paper presents a mathematical model of the trailer which includes roll, pitch, and vertical motion. The skid resistance calculated by using this model gives an excellent check on the standard ASTM skid number formula. The response time and damping effect after locking one test wheel can be clearly seen in this model. Possible effects of the dimensions of trailer, stiffness of suspension system, tire pressure, etc. to skid resistance can also be examined.     

A Theoretical Analysis of the Ride Vibration of Agricultural Tractor and Trailer Combinations

SUMMARY

A six degree of freedom model of an agricultural tractor and trailer combination has been developed. Results from eigenvalue and frequency response calculations indicated that tractor operator vibration levels will be higher when operating with a trailer than for the tractor alone, due mainly to increased tractor pitch motion.

Although minor improvements could be made to present tractor and trailer combinations by moving the hitch forward of the tractor rear axle or providing some damping at a sprung hitch, the scope for a significant improvement in ride lies in changing the configuration. If higher speed specialised transport vehicles prove economical for agriculture, there are some advantages in ride vibration to be gained by changing the layout of the tractor and trailer combination to resemble an off-road version of a commercial articulated lorry.     

Ride Vibration Measurements of Agricultural Tractor and Trailer Combinations

SUMMARY

Tractor ride vibration levels have been measured when operating with and without a two wheel (2W) unbalanced and a four wheel (4W) balanced trailer. Measurements were made in the vertical, pitch, longitudinal and roll directions with the trailers unladen and laden over four typical farm surfaces

The results showed that tractor ride vibration levels were usually increased in all directions-particularly the longitudinal direction- when operating with the laden trailers. But for the unladen trailers, they were increased only in the longitudinal direction. Predominant tractor frequencies tended to be lower with the trailers attached, and coupling between the tractor longitudinal, vertical, roll and pitch co-ordinates was generally increased

Comparisons of the results with the trends predicted by a simplified theoretical model of a tractor and 2W trailer, suggested that the model should be extended to include, (a) the roll direction, (b) more realistic ground inputs, and (c) a 4W trailer     

Frequency Response Analysis of Canadian Logging Trucks

SUMMARY

This paper examines the frequency responses often logging truck configurations currently operating in the interior of British Columbia in Canada. The work is an extension of a previous study conducted at the National Research Council (NRC) in 1990. The previous study presented an extensive analysts of the directional responses and frequency responses of four Canadian log-hauling truck configurations; a tractor/pole trailer, a tractor/triaxle trailer, a tractor/quadaxle trailer (with a single load), and a tractor/single-axle-jeep/pole trailer. In the current study, the frequency responses of these four configurations are compared with those of six more log-hauling truck configurations; a tractor/ tandem-axle-jeep/pole trailer, a doglogger, a double doglogger, a tractor/quadaxle trailer (with a dual load), a tractor/jeep/triaxle trailer, and a tractor/jeep/quadaxle trailer. The current study makes use of three models developed by NRC in the previous study, and a new model developed at NRC in cooperation with the University of Victoria.

The frequency response method has been applied in this study to predict the lateral acceleration at the centre of gravity of each articulated vehicle unit, and the rearward amplification ratio. The logging truck simulation results have been compared with corresponding results, obtained using UMTRI's simplified models, for three conventional highway vehicles; a tractor/semitrailer, a B-train, and an A-train. The comparison provides a useful indication of the differences between the behaviours of logging trucks and conventional highway trucks in their shared environment.     

The Tyre as a Sensor to Estimate Friction

SUMMARY

Continuously updated knowledge of the friction potential and the friction demand can help to improve manoeuvrability and thereby safety of vehicles under slippery road conditions. An on line friction estimation method is presented using a simple brush type tyre model. First the method is verified by outdoor experiments using a tyre test trailer. Then the setup of a low-cost measurement system in a vehicle is discussed and results from both simulations and outdoor experiments are presented. Neural networks have been used both for modelling and identification of friction potential and friction demand.     

Berechnung des extremen Lenk- und Bremsverhaltens von Sattelkraftfahrzeugen

SUMMARY

Simulation of Steering and Braking Behaviour of Tractor-Semitrailer Vehicles in Extreme Situations

This paper deals with the simulation of the behaviour of tractor-semitrailer vehicles at braking on wet, slippery road surface. The nonlinear model used for the computation enables to simulate extreme situations at wheel locking and swerving

The instabilities during braking such as jackknifing and trailer swing as well as non steerability are investigated. Straightline braking shows the influence of cornering on the behaviour during braking in a turn.     

The Steering Characteristics of Multiple Axle Bogie Systems

SUMMARY

Legislation limits the load that may be transferred to the roadway by the axies of a commercial vehicle and this has resulted in the development of multi axle bogies for both the tractor and trailer units of articulated vehicles and at the rear of rigid vehicles, some of these bogies contain self steering or articulation steered axles

Experience shows that the tyre wear characteristics of multi axle bogies may be unsatisfactory. The paper analyses the role of such bogies in the context of vehicle handling and shows how the lateral tyre forces vary between the axles. An hypotheses relating the forces in a steady state turn to wear is given. The analysis may also be applied to the general case of vehicle handling.     

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.     

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.     

Skid Prediction

SUMMARY

In this paper, available information about anti-skid devices is reviewed with the specific purpose of bringing out the importance of skid prediction. Then the merits and demerits of three methods of prediction are studied.     

Optimization for Vehicle Suspension I: Time Domain

SUMMARY

A numerical procedure for finding the optimum values of a number of parameters describing a model vehicle suspension has been studied. The vehicle has been modelled by dynamic systems of linear springs and dampers, and the goal is to obtain lower acceleration peaks at an elected design point in the vehicle.

The problem is stated as a mathematical programming problem which can be solved by means of the sequential linear programming technique. The procedure has been implemented for a four wheel independent suspension model capable of being subjected to road irregularities and to centrifugal and braking accelerations.     

HAP(石屑)封层在市政道路沥青路面的应用

在沥青路面上实施雾封层措施后的一段时间内,路面抗滑性能会有一定程度地降低。因此,在实际工程应用中提出了基于HAP路面防护剂的HAP(石屑)封层措施。文中依托试验路工程研究HAP(石屑)封层措施的抗滑性能和防水性能,结果表明该措施能够减少抗滑性能的降低或略微提高抗滑性能,同时可保持雾封层良好的防水性能。     

Validation of an Articulated Vehicle Simulation

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.     

路面抗滑性能影响弯道行车安全的仿真分析

为研究车辆制动工况下路面抗滑性能对弯道行车安全的影响,以车辆动力学分析软件AD-AMS为仿真平台,提出采用轮胎解析参数、整车参数、路面抗滑值构建耦合关联的车辆-轮胎-路面模型,在此基础上研究不同湿滑路面状态下弯道行驶车辆的运动学参数值变化情况,探索路面抗滑性能与表征行车安全风险的运动学参数值之间的关系.研究结果表明,路面抗滑性能影响车辆运动学参数值变化是诱发交通事故的主要因素.较低的弯道路面抗滑性能易使车辆在制动时出现急速横摆、甚至侧翻的交通事故;车辆两侧轮胎接地面抗滑值不均衡对弯道行车安全的影响高于对直道行车安全的影响,车辆极易在弯道制动时出现因抗滑值不均衡而无法保持有效转弯半径、进而冲出车道的交通事故.研究可为制定弯道行车安全的保障措施提供理论依据.      

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.     

Hydroplaning simulation of a tire in thin water using fem and an estimation method and its application to skid number estimation

To simulate the hydroplaning of a tire, many analytical studies have been performed using commercial explicit FE (Finite Element) codes such as MSC.DYTRAN and LS-DYNA. However, most previous studies on this subject have addressed simulation of hydroplaning for water more than 5 mm deep. Additionally, because a great number of Eulerian elements and Lagrangian elements are typically used to analyze hydroplaning and because multiple analyses should be performed for various water depths, long CPU times are required. In this study, it was found that the traction force and the lift and drag forces between the tire and the road surface could be easily estimated for water shallower than 5 mm using an exponential function based on tire rolling FE simulation results. Furthermore, changes in skid resistance, expressed as SN (skid number), could be estimated for various water depths and vehicle speeds using the method proposed in this study, and the results were proven to be in good agreement with results obtained using the ASTM E274 Pavement Friction Tester.     

粗细集料磨光值对沥青路面长期抗滑的影响

良好的路面抗滑性能是车辆安全行驶的重要保障,而集料品质是影响沥青路面抗滑性能的重要因素之一。集料的耐磨光性能直接决定路面抗滑性能的衰变规律和抗滑终值。因此,集料磨光值的表征和评价对沥青路面全寿命周期抗滑性能的研究具有重要意义。为充分明确粗、细集料对沥青路面长期抗滑性能的影响,引入了3种新的试验方法：①使用Wehner/Schulze (W/S)加速磨光试验对不同种类粗、细集料的磨光值进行评价;②使用自主研发的轮式加速磨光机对9组试样进行加速磨光试验;③使用W/S试验仪抗滑测试机体在速度为60 km·h^-1和水膜覆盖条件下测量试件磨光后的动摩擦因数。结果表明：①集料矿物成分是决定磨光值的重要因素,且磨光值越高沥青路面的长期抗滑性能越好;②密级配沥青路面细集料对路面长期抗滑性能的影响比粗集料更大;③W/S加速磨光试验不仅较Polished Stone Value (PSV)试验结果精度更高,还能评价细集料的抗磨光值;④不同抗滑检测设备与试验方法间具有较大的差异性,轮式加速磨光试验能对试件的全磨耗周期行为进行表征,W/S抗滑检测则可在高速动态旋转和水膜覆盖条件下进行检测(且不受人为操作影响和可重复性高),二者的工况模拟和工作原理具有较强的科学性与可靠性。未来工程应用中,应尽量提高细集料的磨光值,以进一步提高路面抗滑性能;同时,如需精确地表征集料磨光值差异性与路面抗滑性能之间的关系,建议使用W/S试验进行研究。     

Computer-Aided Analysis of Urban Railway Vehicles

SUMMARY

Computer-aided dynamic simulations are usually employed when designing modern urban railway vehicles. Even if the modeling procedure is similar to the one used for trains, specific features have to be taken into account for tramways: they are designed for low speeds (less than 80 km/h) and narrow curves (less than 20 m of radius). Moreover, in order to improve accessibility, low floor designs have been developed (the floor lying at about 300 mm above the rails level). The simulation procedure has therefore to take account of the occurence of multiple wheel/rail contacts or the modelization of independent wheels. A specific software well adapted to the computer-aided design of urban railway vehicles has been developed by the Faculte Polytechnique de Mons. It performs the following classical analyses:

lateral linearization, modal analysis and root locii plots;

vertical linearization and comfort prediction;

non-linear time simulation in straight track (limit cycles) and in curve (derailment study)

parametric analyses

The vehicle model is formed by combination of bodies ( or flexible bodies, rotating bodies like wheelsets or independent wheels) and interconnection elements ( spring and damper elements). Contact between rails and wheels is treated as a part of the rotating bodies. A residual formulation has been preferred. When combined with the use of a complete iteration matrix, this formulation is well adapted to the treatment of stiff differential equations. It is based on a fast determination of the residues of the dynamic equations combined with the calculation of the iteration matrix through a numerical derivation procedure. The advantages of the approach are discussed. The model of a partial low floor vehicle with wheelsets and independent wheels is described.     

A Modular Computer Model for the Design of Vehicle Dynamics Control Systems1

SUMMARY

This paper describes a multiport approach to computer-aided modeling of vehicle dynamics. The modeling approach produces models that are suitable for the interactive design and evaluation of complex control strategies. The vehicle model which can be used for ride and handling analysis, is built from modular components. The components are programmed using the syntax of the computer aided control system design (CACSD) program EASYS. Seven modeling components are used to create a three-dimensional vehicle dvnamics model. The model is flexible enoug-h to simulate any suspension design with revolute joints.

Each component of the model consists of a FORTRAN subroutine and a main calling module called a macro. To simplify the process of model building, the modeling components in the car model are designed to represent physical elements, such as the spring, damper, link or tire. To create a model, the components, which are represented by blocks, are interconnected through points, located on the blocks, called pons. These ports have been designed to simulate the location of the connection points between the physical elements, as observed in real systems. The construction of multibody models within a CACSD program offers the flexibility of simultaneous interactive simulation of the three-dimensional dvnamics and evaluation of the desien of the controls.

Although modeling of multibody systems using FORTRAN components has been pioneered by Chace, Haug and Orlandea; and bond graph modeling of multibody systems has been investigated by Bos, this approach is novel because:-

The model is included in the control system design program (EASYS). This arrangement allows the designer to exploit the advanced control design tools available in the program. Furthermore, this approach significantly reduces the computation time required for running the model after parameters modification.

The model is built from components that are interconnected by ports which represent the actual physical location of the connection points between the elements. The multiport approach simplifies the model building process for multibody systems. This simplification is achieved by reducing the model of a multibody system to a block diagram form.