Ride dynamics mathematical model for a single station representation of tracked vehicle

Tracked vehicles are exposed to severe ride environment due to dynamic terrain-vehicle interactions. Hence it is essential to understand the vibration levels transmitted to the vehicle, as it negotiates different types of terrains at different speeds. The present study is focused on the development of single station representation of tracked vehicles with trailing arm hydro-gas suspension systems, simulating the ride dynamics. The kinematics of hydro-gas suspension system have been derived in order to determine the non-linear stiffness characteristics at various charging pressures. Then, incorporating the actual suspension kinematics, non-linear governing equations of motion have been derived for the sprung and unsprung masses and solved by coding in Matlab. Effect of suspension non-linear dynamics on the single station ride vibrations have been analyzed and validated with a multi-body dynamics model developed using MSC.ADAMS. The above mathematical models would help in estimating the ride vibration levels of the tracked vehicle, negotiating different types of terrains at various speeds and also enable the designers to fine-tune the suspension characteristics such that the ride vibrations are within acceptable limits. The mathematical ride model would also assist in development of non-linear ride vibration model of full tracked vehicle and estimate the sprung mass dynamics.     

Longitudinal vehicle dynamics control for improved vehicle safety

The aim is to investigate the improvements in vehicle safety that can be achieved by limiting the vehicle speed based on GPS path information. The control strategy is aimed at reducing vehicle speed before a potentially dangerous situation is reached, in contrast with widely used stability control systems that only react once loss of control by the driver is imminent. An MSC.ADAMS/View simulation model of an off-road test vehicle was developed and validated experimentally. A longitudinal speed control system was developed by generating a reference speed based on the path information. This reference speed was formulated by taking into account the vehicle’s limits due to lateral acceleration, combined lateral and longitudinal acceleration and the vehicle’s performance capabilities. The model was used to evaluate the performance of the control system on various tracks. The control system was implemented on the test vehicle and the performance was evaluated by conducting field tests. Results of the field tests indicated that the control system limited the acceleration vector of the vehicle’s centre of gravity to prescribed limits, as predicted by the simulations, thereby decreasing the possibility of accidents caused by rollover or loss of directional control due to entering curves at inappropriately high speeds.     

Hydro-gas suspension system for a tracked vehicle: Modeling and analysis

Tracked vehicles fitted with torsion bar suspensions are limited in their ability to achieve high mobility. This limitation is due to the linear characteristics and the consequent poorer ride performance. Hydro-gas suspensions due to their inherent non-linear behavior can provide higher mobility and better ride comfort performance. The hydro-gas suspension model has usually been developed from experimental force-displacement characteristics, which requires availability of suspension hardware.In this paper, a hydro-gas suspension system is modeled using polytropic gas compression model to represent the spring characteristics, while the damper orifices are modeled using hydraulic conductance. The analytical model is then validated with experiments individually for spring and damper flow characteristics and then as a suspension-wheel assembly in a test rig. The validated suspension model is incorporated in an in-plane model. Using this model, simulation is carried out for sinusoidal inputs of different wavelengths, amplitudes and vehicle speeds. The simulation model is validated with data measured on a vehicle traversing an APG course. The proposed model agrees very well with the measured data. Based on the validated model, studies on the influence of suspension parameters on the ride comfort of a tracked vehicle are carried out.     

Semi-active hydro-gas suspension system for a tracked vehicle

A semi-active hydro-gas suspension is proposed for a tracked vehicle to improve ride comfort performance, without compromising the road holding and load carrying capabilities of the passive suspension. This is achieved through an active damper used in parallel with a gas spring. The suspension damper parameters are varied by a control mechanism based on sky-hook damping theory, which alters the flow characteristics. A damper prototype has been developed, tested for its flow characteristics, after which it has been integrated into an existing hydro-gas suspension system. An analytical model has been proposed from first principles rather than developing a phenomenological model based on experimental characteristics. This model is validated with experiments carried out on a suspension test rig. In order to compare the performance with the original passive system, an in-plane vehicle model is developed and the simulations clearly show that the semi-active system performance is superior to the passive system.     

Prediction of the tractive performance of a flexible tracked vehicle

In this study, we describe a mathematical model designed to allow for the determination of the mechanical relationship existing between soil characteristics and the primary design factors of a tracked vehicle, and to predict the tractive performance of this tracked vehicle on soft terrain. On the basis of the mathematical model, a computer simulation program (Tractive Performance Prediction Model for Tracked Vehicles; TPPMTV) was developed in this study. This model took into account the characteristics of the terrain, including the pressure-sinkage, the shearing characteristics, and the response to the repetitive loading, as well as the primary design parameters of the tracked vehicle. The efficacy of the developed model was then confirmed via comparison of the drawbar pulls of tracked vehicles predicted using the simulation program TPPMTV, with those determined as the result of traction tests. The results indicated that the predicted drawbar pulls, with the change in slip, were quite consistent with the ones measured in the traction test, for the changes in the weight of the vehicle, the initial track tension, and the number of roadwheels within the entire slip range. Thus, we concluded that the simulation program developed in this study, named TPPMTV, proved useful in the prediction of the tractive performance of a tracked vehicle, and that this system might be applicable to the design of a vehicle, possibly enabling a significant improvement in its functions.     

Modelling and simulation of an agricultural tracked vehicle

A new approach to the dynamic modelling of tracked vehicles is proposed in this paper, resulting in a 3D, 8 degrees of freedom dynamic model of an agricultural tracked vehicle, having the two independently applied sprocket torques as input variables. The main features of the approach are a new dynamic model of the shear displacement and the adoption of an innovative modelling and simulation environment: MOSES, based on Object-Oriented tools and techniques. Simulation results are reported for a qualitative validation of the model.     

Design and mobility evaluation of tracked lunar vehicle

Past lunar vehicles have had difficulty traveling through soft sand areas due to the thick, soft and dry regolith. This paper describes the design and evaluation results of a tracked lunar vehicle which aims at achieving greater mobility, particularly improved climbing ability on pure sand slopes, by reducing contact pressure with a crawler link. The tracked vehicle uses mesh crawler links to reduce complexity, weight and parts count. Single-crawler tests on simulated lunar soil revealed that the crawler’s slip ratio was lower than that of a rigid wheel at any slope angle, and that its power consumption was lower than that of a wheel on slopes of 10° or more. Furthermore, the crawler’s slip ratio was stable or decreasing along the traveling distance on steep slopes, contrary to the wheel. Our tracked lunar vehicle, the “Light Crawler”, is equipped with four such mesh-crawlers, each of which is independently driven and steered. It is intended to realize high climbing ability, a small turning circle, and an obstacle-crossing capability using a unique suspension system. The vehicle’s climbing and obstacle-crossing capabilities were tested on both simulated lunar soil and a rock-scattered field, and its mobility performance was successfully confirmed.     

A study of soil thrust exerted by a tracked vehicle

This paper deals with soil thrust exerted by a tracked vehicle. Measurements of the ground pressure beneath the tracks of a tracked vehicle were carried out and it was shown that the ground pressure distribution is approximately represented by discontinuous triangles which have their maxima under the roadwheels. The relationship between soil shear curve (shear stress or force-deformation curve) obtained from shear test and thrust curve (soil thrust-slip ratio curve) of the tracked vehicle is analyzed by using the above mentioned ground pressure distribution, and it is shown that there is a transformation law between both curves. Namely, the thrust curve due to soil shear under any wheel portion is given as a function of soil and vehicle parameters. Further, the reliability of the above method is confirmed experimentally.     

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.     

Ride quality analysis of a tracked vehicle suspension with a preview control

The feasibility of a preview control is examined for tracked vehicle’s suspension systems to improve the performance of tracked vehicle systems. Numerical results are compared with LQ, robust H_∞, reference model tracking and hybrid preview control methods. The ride quality analysis is performed based on the vertical acceleration at the driver’s position. On the simulations, it is proven that the hybrid preview controller is the most efficient and practical method.     

External motion resistance caused by rut sinkage of a tracked vehicle

This paper deals with the external motion resistance of a tracked vehicle caused by rut formation (sinkage) or compression of soil under the tracks. It is shown that the relationship between the applied load and the sinkage for a loading test using a plate is represented by a hyperbola. Based on the above relationship, the external motion resistance caused by the rut formation of a tracked vehicle is estimated by considering the work done by overcoming the ground pressure and the resistance. Further, measurements of the external motion resistance were carried out by using a tracked vehicle and the experimental results are compared with the theoretical ones, and the reliability of the above method is confirmed experimentally.     

Assessment of tracked vehicle suspension system using a validated computer simulation model

A non-linear, in-plane computer simulation model of a typical high-mobility tracked vehicle is developed for suspension dynamic analysis and ride quality assessment. The Langrangian model formulation of the tracked vehicle is derived considering an arbitrary rigid terrain profile and constant vehicle speed. The model incorporates detailed representations of a trailing arm suspension system and dynamic wheel-track-terrain interactions. The computer model predictions are validated against field measurements, which were gathered from tests of an armoured personnel carrier traversing a discrete half-round bump and a random course. A parametric sensitivity analysis was carried out using the validated computer model in order to assess the influence of conventional suspension parameters on the ride performance of the test vehicle. In addition, the ride performance potentials of an alternate hydrogas suspension configuration were investigated.     

Prediction of sinkage and motion resistance of a tracked vehicle using plate penetration test

The relationship between contact pressure and sinkage must be represented by a mathematical model to estimate the sinkage and the motion resistance due to a vehicle. In this study an approximate and simple pressure-sinkage model is proposed. This model takes into account the effect of the size of the penetration plate on soil response, and includes two soil values that can be obtained by a single plate penetration test. It is submitted that the sinkage and the motion resistance of a tracked vehicle can be estimated by means of the proposed model.     

On the numerical solution of tracked vehicle dynamic equations

In this investigation, the solution of the nonlinear dynamic equations of the multibody tracked vehicle systems are obtained using different procedures. In the first technique, which is based on the augmented formulation that employes the absolute Cartesian coordinates and Lagrange multipliers, the generalized coordinate partitioning of the constraint Jacobian matrix is used to determine the independent coordinates and the associated independent differential equations. An iterative Newton-Raphson algorithm is used to solve the nonlinear constraint equations for the dependent variables. The numerical problems encountered when one set of independent coordinates is used during the simulation of large scale tracked vehicle systems are demonstrated and their relationship to the track dynamics is discussed. The second approach employed in this investigation is the velocity transformation technique. One of the versions of this technique is discussed in this paper and the numerical problems that arise from the use of inconsistent system of kinematic equations are reported. In the velocity transformation technique, the tracked vehicle system is assumed to consist of two kinematically decoupled subsystems; the first subsystem consists of the chassis, the rollers, the sprocket and the idler, while the second subsystem consists of the track which is represented as a closed kinematic chain that consists of rigid links connected by revolute joints. It is demonstrated that the use of one set of recursive equations leads to numerical difficulties because of the change in the track configuration. Singular configurations can be avoided by repeated changes in the recursive equations. The sensitivity of the predictor-corrector multistep numerical integration schemes to the method of formulating the state equations is demonstrated. The numerical results presented in this investigation are obtained using a planner tracked vehicle model that consists of fifty four rigid bodies.     

Development of a tracked vehicle to study the influence of vehicle parameters on tractive performance in soft terrain

This paper describes a new special tracked vehicle for use in studying the influence of different vehicle parameters on mobility in soft terrain; particularly muskegg and deep snow. A field test in deep snow was carried out to investigate the influence of nominal ground pressure on tractive performance of the vehicle. The vehicle proved useful for studying vehicle parameters influencing the tractive performance of tracked vehicles. The tests show that the nominal ground pressure has a significant effect on the tractive performance of tracked vehicles in deep snow. The decrease in drawbar pull coefficient when the nominal ground pressure is increased and originates at about the same amount from a decrease of the vehicle thrust coefficient, an increase of the belly drag coefficient and an increase of the track motion resistance coefficient.     

Prediction of trafficability for tracked vehicle on broken soil: real size tests

Full-scale tests were carried out within the broader framework of a study of an operational mechanical mine clearance system. This system is made up of a tracked machine pushing a mine clearance plow that scarifies the soil to approximately 30 cm depth. This study examines the capacity of the tractor to move on a disturbed soil. This paper presents motion resistance tests and drawbar pull tests on four types of soil. The soils have been chosen to be scientifically representative of the broad distribution on our planet: a sand (frictional soil), a silt (cohesive soil), a silty gravel (coarse-grained soil), and a silty sand (cohesive soil). The tests are performed in two configurations: on compacted soils and on soils scarified with an experimental plow. The results of each test condition are described. The effects of the soil type, its state, and the speed of the tested vehicle are presented. Using these results and, in addition, full-scale tests of scarification, we present an operational analysis determining the mobility of a tracked vehicle on broken soil. This method makes it possible to calculate the maximum speed of a mechanical mine clearance system for the whole range of soils tested.     

Development of hybrid electrical air-cushion tracked vehicle for swamp peat

This study presents a developed hybrid electrical air-cushion tracked vehicle (HETAV) for the transportation operation of agricultural and industrial goods on the swamp peat terrain bearing capacity of 5 kN/m². The vehicle’s design parameters are optimized by using the developed mathematical models which are made based on the kinematics and dynamics behaviors of the vehicle. A set of sensors are used with this vehicle to activate the air-cushion system and battery pack recharging system. The vehicle’s air-cushion system is protected by a novel-design auto-adjusting supporting system. The air-cushion dragging motion resistance is overcome with additional thrust which is developed by a propeller. The vehicle is equipped with the air-cushion system to make the vehicle ground contact pressure 5 kN/m².     

A simplified method for the estimation of soil thrust exerted by a tracked vehicle

A simplified method for estimating the soil thrust exerted by a tracked vehicle is proposed. The relationship between the soil shear torque curve (shear torque-deformation curve) obtained from ring shear test and the thrust curve (soil thrust-slip ratio curve) of a tracked vehicle is analyzed and it is shown that there is a transformation law between these curves. A simplified analytical method for estimating the soil thrust exerted by a tracked vehicle is developed by using the above-mentioned transformation law. Soil thrust can be estimated by using the soil shear torque curve, shear ring and vehicle parameters. It is experimentally confirmed that the soil thrust can be easily estimated by using the proposed method.