Study on steerability of articulated tracked vehicles — Part 1. Theoretical and experimental analysis

This paper presents theoretical and experimental analysis of steering performance of articulated tracked vehicles on level ground. A mathematical model for predicting the steerability of articulated units has been developed and computerized for numerical application. The accuracy of the analog has been verified by scale model tests.From the results of the simulation and scale model tests it was found that steerability was significantly improved and required sprocket torques for steering and track slippage were considerably decreased in articulated tracked vehicles when compared with a single and coupled tracked vehicles.     

Etude de la direction des véhicules articulés à chenille (l analyse théorique et expérimentale)

This paper presents theoretical and experimental analysis of steering performance of articulated tracked vehicles on level ground. A mathematical model for predicting the steerability of articulated units has been developed and computerized for numerical application. The accuracy of the analog has been verified by scale model tests.From the results of the simulation and scale model tests it was found that steerability was significantly improved and required sprocket torques for steering and track slippage were considerably decreased in articulated tracked vehicles when compared with a single and coupled tracked vehicles.     

A theoretical analysis of steerability of tracked vehicles

This paper presents a theoretical analysis of steerability of tracked vehicles during uniform turning on level pavement.

Considering all possible factors related to steering problems such as track slippage, centrifugal force and vehicle configuration, equations for uniform turning motion have been developed in order to analyze and predict steering dynamics, and steerability in plane motion of vehicles.

These equations have been numerically solved by a digital computer in terms of turning radius, side slip angle, shift of instantaneous center of vehicle and track slippage.     

An optimal method for the design of a robotic tracked vehicle to operate over fresh concrete under steering motion

The objective of this paper is to find an optimal method for the design of tracked base travel systems for special purpose vehicles and robotic machines that may be required to steer over a light bonded terrain composed of fresh concrete. For the case of a vehicle traveling on a weak fresh concrete during construction, the paper presents detailed comparative studies of the steering performances of a small model tracked test vehicle with alternative amount of steering ratio for various concrete slump values. For these studies a detailed simulation analytical method has been developed. From this work it is proven, in comparison to experiment, that the simulation analytical method is useful for predicting various steering performances of a test tracked vehicle running upon soft fresh concrete of various consistencies.     

Advanced mobility in difficult terrain

The development and success of the Swedish Combat Vehicle CV90 has demonstrated the abilities of the author in the field of terramechanics related to tracked military vehicles. The honour of the Bekker–Reece–Radforth Award 2002 has been granted in recognition of these achievements made during the author's employment at Hägglunds Vehicle AB since 1975. Hägglunds Vehicle AB has been a producer of military vehicles since the late 1950s, although the first years concentrated on production only. From the early 1960s, Hägglunds developed a number of its own tracked vehicles, all of which were influenced by the mobility demands dictated by their intended use in severe terrain conditions, such as those found in Northern Scandinavia. This paper presents a brief history of the advancement of tracked vehicle technology at Hägglunds Vehicle AB. The concepts discussed include: ground pressure, the number of road-wheels, articulated steering, track tension, track attack angle, sinkage, belly effects, and the use of terramechanic simulation. The success of the CV90 demonstrates that the combination of practical experience, terrain knowledge, and terramechanic simulations can effect substantial improvements in vehicle mobility. Evaluation of the CV90 versus other modern combat vehicles of the same class has shown that the CV90 possesses considerably higher mobility and speed under severe terrain conditions. These two attributes provide CV90 with the ability to access terrain that similar vehicles cannot, thus giving the military user greater mobility options.     

A new contact & slip model for tracked vehicle transient dynamics on hard ground

This study presents a new general transient contact and slip model for tracked vehicles on hard ground which is simple, accurate, and in agreement with the test results to a satisfactory level. Simulating zero track speed instances become possible with the new contact/shear model which is the major proposed improvement in addition to more accurate results for transient steering and tractive inputs. The model represents a general tracked vehicle having rear or front sprockets, with parameters for center of gravity, wheel positions, number of wheels, and track-pretention. To calculate longitudinal and lateral forces, a transient shear model is used. Shear stress under each track pad is assumed to be a function of shear displacement. The contact time formulation used in shear displacement calculation is improved to gain accuracy for transient and zero track speed conditions.The model is implemented on the Matlab/Simulink platform and verified with a comprehensive program of road tests composed of transient steering and tractive/braking scenarios. The results of the simulations and the road tests are satisfactorily similar for both constant and transient input maneuvers. Moreover, sensitivity simulations for vehicle parameters are conducted to show that the model responses are inline with the expected vehicle dynamics behaviours.     

Handling and stability performance of four-track steering vehicles

The advantages of using a four-track steering (4TS) vehicle are less slippage and sinkage of the tracks in turning, compared with conventional skid-steering tracked vehicles. This paper describes the steerability and the mobility of the 4TS vehicle for on- and off-road conditions. Mathematical models have also been developed to predict the effects of various types of differential torque transfer on the handling behavior of a vehicle. A turning vehicle motion was simulated and compared with the experimental data. The results demonstrate that the proposed mathematical model could accurately assess the steering performance of a 4TS vehicle.     

A method for predicting the internal motion resistance of rubber-tracked undercarriages,Pt. 1. A review of the state-of-the-art methods for modeling the internal resistance of tracked vehicles

This article summarizes the known methods for calculating the internal resistance of tracked undercarriages. The values of the coefficient of internal resistance for sample tracked vehicles are available in the literature and presented in this paper. Although they are suitable for simple computations, they cannot be used to optimize the energy efficiency of new generation tracked undercarriages. This problem might be solved by the models where every phenomenon leading to energy dissipation during vehicle motion is described by a separate submodel as a function of vehicle speed, track tension, undercarriage layout, design features of the undercarriage components, etc. This kind of model is still missing for vehicles with conventional rubber tracks. The article presents multiple state-of-the-art models describing rolling resistance of road wheels, bending resistance of rubber belts, etc., including the models of belt conveyors resistance. A vast majority of the phenomena discussed herein are described by several incompatible models whose parameters have not yet been determined for conventional rubber tracks. Consequently, in the second and the third part of the article, the authors have undertaken a theoretical and experimental studies on the methods for calculating and optimizing the internal motion resistance of vehicles with conventional rubber tracks.     

A spatial motion analysis model of tracked vehicles with torsion bar type suspension

A spatial motion analysis model for high-mobility tracked vehicles was constructed for evaluation of ride performance, steerability, and stability on rough terrain. Ordinary high-mobility tracked vehicles are equipped with independent torsion bar type suspension system, which consists of road arms and road wheels. The road arm rotates about the axis of torsion bar, and rigidity of the torsion bar and cohesion of damper absorb sudden force change exerted by interaction with the ground. The motion of the road arms should be considered for the evaluation of off-road vehicle performance in numerical analysis model. In order to obtain equations of motion for the tracked vehicles, the equations of motion for the vehicle body and for the assembly of a road wheel and a road arm were constructed separately at first. Two sets of equations were reduced with the constraint equations, which the road arms are mechanically connected to the vehicle body. The equations of motion for the vehicle have been expressed with minimal set of variables of the same number as the degrees of freedom for the vehicle motion. We also included the effect of track tension in the equations without constructing equations of motion for the tracks. Numerical simulation based on the vehicle model and experiment of a scale model passing over a trapezoidal speed bump were performed in order to examine the numerical model. It was found that the numerical results reasonably predict the vehicle motion.     

Turning characteristics of multi-axle vehicles

This paper presents a mathematical model for multi-axle vehicles operating on level ground. Considering possible factors related to turning motion such as vehicle configuration and tire slip velocities, equations of motion were constructed to predict steerability and driving efficiency of such vehicles. Turning radius, slip angle at the mass center, and each wheel velocity were obtained by numerically solving the equations with steering angles and average wheel velocity as numerical inputs. To elucidate the turning characteristics of multi-axle vehicles, the effect of fundamental parameters such as vehicle speed, steering angles and type of driving system were examined for a sample of multi-axle vehicles. Additionally, field tests using full-scale vehicles were carried out to evaluate the basic turning characteristics on level ground.     

A skid steering model with track pad flexibility

The paper describes a model for predicting the skid-steering performance of tracked vehicles that allows for the flexibility of the track pads. It thus accounts for the reductions in friction moment that are observed as the radius of the turn is increased. The pad model computes a compound slip function and takes account of the shear stiffness of the pad and the limiting friction between the pad and the ground. Vehicle dimensions and the equations of motion are entered into a Microsoft Excel spreadsheet. The equations are solved using the Excel Solver routine. This avoids the need for specialised software or programming skills. It also gives good insight into the mechanics of steering and the factors affecting performance. Predicted sprocket torques for a Jaguar vehicle turning at different radii show good agreement with experimental measurements. The steering performance of an example six axle 24 tonne vehicle is computed and compared with that using the early Merritt/Steeds model that ignored track pad flexibility. The flexible pad model generally shows the vehicle to be slightly oversteer, whereas the Merritt/Steeds model predicts the vehicle to be understeer. At higher speeds the maximum cornering acceleration is likely to be limited by available power at the sprockets. Altering the static weight distribution of the vehicle shows that a forward weight distribution tends to cause a more oversteer response with reduced limiting lateral acceleration. With a rearward weight distribution, the vehicle response tends towards neutral to slight understeer. This is in contrast to Ackerman steered wheeled vehicles with pneumatic tyres where moving the CG forward tends to a more understeer response. Using the concept of static margin as applied to wheeled vehicles, it is suggested that a uniform or slightly forward weight distribution would make tracked vehicles less sensitive to external disturbances (cambered roads for example).     

EXPERIMENTAL ANALYSIS OF ACTIVE STEERING HARDWARE-IN-LOOP BASED ON SLIDING MODE CONTROL 1)

为了提高重型车辆在转向过程中的稳定性和安全性,本文提出了一种基于滑模变结构控制的主动前轮转向控制策略,基于这种策略设计了主动转向控制器,建立了三轴商用车的二自由度车辆动力学简化模型及整车模型,利用TruckSim--Simulink建立联合仿真平台以及进行硬件在环实验。在不同工况、不同车速下,分别对有无主动转向控制器的车辆进行了操纵稳定性分析,并在此基础上进行了滑模变结构控制的主动转向影响因素敏感性分析。实验结果表明,这种控制器策略在不同工况下具有较强的适应性。     

结构振动强度的应用研究

本文根据弯曲波理论和声强测量原理提出了结构振动能量分布和传输特性的新技术方法.理论分析、实验室研究和实际应用结果表明,用振动强度来分析结构振动问题可得到振动能量的流向和分布,测量技术简单且易于掌握,具有可接受的实际应用精度.     

An analysis of horizontal plane motion of tracked vehicles

This paper presents a theoretical analysis of non-stationary motion of a tracked vehicle on level ground. A practical model that includes track slippage, inertia force and the moment of inertia was developed to analyze and predict steering dynamics and steerability on the subject examined.

The system of differential equations was programmed and numerically solved on a digital computer, where the inputs are circumferential velocities of right and left drive sprockets.

The simulations for J-turn maneuver disclose the effects of initial forward velocities on the transient responses of the track slip velocity, side slip angle, yaw rate, and acceleration of the center of gravity of a tracked vehicle.     

“Wheels vs. tracks” – A fundamental evaluation from the traction perspective

The issue of wheeled vehicles vs. tracked vehicles for off-road operations has been a subject of debate for a long period of time. Recent interest in the development of vehicles for the rapid deployment of armed forces has given a new impetus to this debate. While a number of experimental studies in comparing the performances of specific wheeled vehicles with those of tracked vehicles under selected operating environments have been performed, it appears that relatively little fundamental analysis on this subject has been published in the open literature, including the Journal of Terramechanics. This paper is aimed at evaluating the tractive performance of wheeled and tracked vehicles from the standpoint of the mechanics of vehicle–terrain interaction. The differences between a tire and a track in generating thrust are elucidated. The basic factors that affect the gross traction of wheeled and tracked vehicles are identified. A general comparison of the thrust developed by a multi-axle wheeled vehicle with that of a tracked vehicle is made, based on certain simplifying assumptions. As the interaction between an off-road vehicle and unprepared terrain is very complex, to compare the performance of a wheeled vehicle with that of a tracked vehicle realistically, comprehensive computer simulation models are required. Two computer simulation models, one for wheeled vehicles, known as NWVPM, and the other for tracked vehicles, known as NTVPM, are described. As an example of the applications of these two computer simulation models, the mobility of an 8 × 8 wheeled vehicle, similar to a light armoured vehicle (LAV), is compared with that of a tracked vehicle, similar to an armoured personnel carrier (APC). It is hoped that this study will illustrate the fundamental factors that limit the traction of wheeled vehicles in comparison with that of tracked vehicles, hence contributing to a better understanding of the issue of wheels vs. tracks.     

An approach to computer control for legged vehicles

Observation of the locomotion of animals and human beings in difficult terrain makes it quite obvious that legged locomotion offers substantial mobility advantages over conventional wheeled or tracked systems. However, effective adaptation of legged locomotion principles to off-road vehicles has to date been frustrated by the complexity of the joint coordination control problem and by the lack of suitable sources of power for individual leg joints. This paper is addressed to the first problem and is intended to show that some of the techniques used in aircraft autopilots can be adapted to legged vehicle control. The main results presented are derived from a computer simulation study of a system in which vehicle speed and direction are determined by a human operator while individual joint commands are generated automatically by a digital computer. Present indications are that such a vehicle might be as easy to control as a conventional wheeled or tracked automotive system.     

A skid steering model using the Magic Formula

The paper describes a computer model for predicting the steering performance and power flows of a notional skid steered tracked vehicle. The force/slip characteristics of the rubber track pads are calculated by means of the so-called Magic Formula. Relevant parameters for the Magic Formula are derived from the limited amount of data available from traction tests with a tracked vehicle on a hard surface. The computer model considers the vehicle in steady state motion on curves of various radii and allows for lateral and longitudinal weight transfer, roll and pitch motions and the effects of track tension forces. Vehicle dimensions, Magic Formula parameters and the equations of motion are set up in a Microsoft Excel spreadsheet and solutions obtained using the Solver routine. Model outputs are described in terms of driver control input and various power flows against lateral acceleration. Maximum lateral acceleration is generally limited by the available engine power. In some conditions the outer track sprocket could be transmitting almost twice the maximum net engine power. For vehicles with a single electric motor/inverter driving each sprocket, these units would need to be able to transmit these high intermittent powers.     

Track-terrain modelling and traversability prediction for tracked vehicles on soft terrain

Skid-steered tracked vehicles are the favoured platform for unmanned ground vehicles (UGVs) in poor terrain conditions. However, the concept of skid-steering relies largely on track slippage to allow the vehicle to conduct turning manoeuvres potentially leading to overly high slip and immobility. It is therefore important to predict such vulnerable vehicle states in order to prevent their occurrence and thus paving the way for improved autonomy of tracked vehicles. This paper presents an analytical approach to track-terrain modelling and a novel traversability prediction simulator for tracked vehicles conducting steady-state turning manoeuvres on soft terrain. Traversability is identified by predicting the resultant track forces acting on the track-terrain interface and the adopted models are modified to provide an analytical generalised solution. The validity of the simulator has been verified by comparison with available data in the literature and through an in-house experimental study. The developed simulator can be employed as a traversability predictor and also as a design tool to test the performance of tracked vehicles with different vehicle geometries operating on a wide range of soil properties.     

An analysis of vehicle power requirements in deep snowpack

Power requirements for tracked vehicles moving in deep medium-to-high density snow are calculated. A volumetric constitutive law is used to determine the energy absorbed by the pressure bulb under the vehicle. Also shearing effects along the pressure bulb wall and in the pressure bulb are taken into account. A parametric study is made to determine the effect of initial density, track pressure, vehicle speed and track geometry on track efficiency. The results show that if the snow material properties are expressible in terms of a constitutive law, the method presented can be of considerable use for predicting certain aspects of vehicle performance in snow and for evaluating the structure of the pressure bulb below the vehicle track.