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.     

“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.     

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.     

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.     

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.     

Comparing the NRMM (VCI), MMP and VLCI traction models

A military vehicle’s ability to traverse soft soil is a significant aspect of its performance. It is therefore important to be able to accurately predict and compare the soft soil performance of wheeled and tracked vehicles. The paper compares the vehicle cone index (VCI) model used in the NATO Reference Mobility Model (NRMM) with the mean maximum pressure (MMP) and vehicle limiting cone index (VLCI) models. The wheeled vehicle models compare reasonably well but the VLCI model for tracked vehicles indicates markedly higher limiting go/no-go soil strengths compared to the VCI and MMP models. Some of the relationships used in the VCI model appear rather irrational and could be significantly simplified. There is a considerable lack of reliable experimental data for tracked vehicles especially in the low traction region.     

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.     

Long-term effects of off-road vehicle traffic on tundra terrain

Traffic tests were conducted at two sites in northern Alaska with an air cushion vehicle, two light tracked vehicles, and three types of wheeled Rolligon vehicles. The traffic impact (surface depression, effect on thaw depth, damage to vegetation, traffic signature visibility) was monitored for periods of up to 10 years. Data show the immediate and long-term effects from the various types of vehicles for up to 50 traffic passes and the rates of recovery of the active layer. The air cushion vehicle produced the least impact. Multiple passes with the Rolligons caused longer-lasting damage than the light tracked vehicles because of their higher ground contact pressure and wider area of disturbance. Recovery occurs even if the initial depression of the tundra surface by a track or a wheel is quite deep (15 cm), as long as the organic mat is not sheared or destroyed.     

Lane-change maneuver of high speed tracked vehicles

This paper presents the theoretical and experimental analysis of steering performance of tracked vehicles under lane-change maneuver to reveal controllability and stability in steering motion. The theoretical results of trajectories and required sprocket torques considerably coincide with the test results of actual vehicles and scale model. As the results, it was found that the controllability and stability of high speed tracked vehicles are significantly influenced by various factors such as mode of steering input, steering ratio, vehicle speed and adhesion of track-ground contact area.     

Development of high-mobility tracked vehicles for over snow operations

This paper describes a detailed investigation into the effects of some of the major design features on the mobility of tracked vehicles over snow. The investigation was carried out using the latest version of an advanced computer simulation model, known as NTVPM, developed under the auspices of Vehicle Systems Development Corporation (VSDC), Ottawa, Ontario, Canada. Results show that the road wheel system configuration, initial track tension (i.e., the tension in the track system when the vehicle is stationary on a level, hard ground) and track width have significant effects on vehicle mobility over snow. On deep snow where the vehicle belly (hull) contacts the snow surface, the location of the centre of gravity (C.G.) of the sprung weight in the longitudinal direction has a noticeable effect on vehicle mobility, as it affects the attitude of the belly and the belly–snow interaction. Based on the investigation, a conceptual high-mobility tracked vehicle for over snow operations is discussed. Results of this study will provide the vehicle designer with guiding principles for the development of high-mobility tracked vehicles. It also demonstrates that NTVPM is a useful and effective tool for design and performance evaluation of tracked vehicles from a traction perspective.     

The applicability of the MMP concept in specifying off-road mobility for wheeled and tracked vehicles

A review is given of the use of mean maximum pressure (MMP) in specifying off-road performance of vehicles. The need to quote a single mobility criterion which is unbiased in favour of either wheeled or tracked vehicles is recognised. The difficulties which researchers have encountered in developing expressions for MMP for both wheeled and tracked vehicles which correctly describe their relative performance are highlighted. Predictions of MMP for wheeled vehicles are compared with ground pressure measurements for a number of vehicles and it is shown that the MMP parameter does not actually represent the ground pressure accurately. Finally it is argued that the only safe route for the specifier is to quote a range of soil types, conditions and gradients on which the vehicle is to operate. This shifts the responsibility to the designer but also clears the way for innovative design, beyond the constraints of the MMP formulae.     

Lateral slide sinkage tests for a tire and a track shoe

Previous field studies have shown the influence of turning vehicles on rut formation or sinkage. In order to further investigate the relationships, laboratory tests were conduced on a 14.5–20.3 6-PR trailer tire and an Armored Personnel Carrier (APC) track shoe in sand. Lateral displacements, and resulting lateral forces, were applied to the tire and track shoe under constant normal forces. The tire was pulled laterally and the track shoe was pulled back and forth to represent actual movement during vehicle turning. Results show that the lateral force and lateral displacement generated by turning maneuver affect sinkage severely for wheeled and tracked vehicles. The final sinkage caused by the lateral force for the tire is 3–5 times to the static sinkage. For the track shoe, the final sinkage caused by the lateral displacement is about three times to the static sinkage.     

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.     

A simulation model for the prediction of the ground pressure distribution under tracked vehicles

A computer based simulation model for the prediction of the ground pressure distribution beneath tracked vehicles under static conditions has been developed. The model can differentiate between various track designs and is based on an analytical method developed and described by Garber and Wong. Simulating the model with the parameters of a rubber tracked forestry vehicle (FARMI TRAC 5000) led to several conclusions. The road wheel arrangement has a considerable effect on the ground pressure distribution: increasing the number of road wheels reduces the maximum ground pressure and improces the uniformity of the pressure distribution. The radius of the road wheel, the stiffness of the suspension and the stiffness of the track tensioning device have an insignificant effect on the ground pressure distribution. In contrast, the initial track tension and the width of the track have a significant effect on the ground pressure distribution: increasing the initial track tension reduces the maximum ground pressyre and improves the uniformity of the pressure distribution. The same conclusions are valid for an increase of the track width. This model can be used as a tool to assist in the design of off-road vehicles, and is currently being used in the design of forestry vehicles in Ireland.     

A method for predicting the internal motion resistance of rubber-tracked undercarriages,Pt. 2. A research on the motion resistance of road wheels

In spite of an increasing number of rubber-tracked crawlers, the literature provides few guidelines and calculation models suitable for minimizing their internal motion resistance. This article presents a model where the internal resistance of double-flanged road wheels for rubber-tracked vehicles is calculated as a sum of the losses resulting from the indentation of the wheels into the track surface and friction of the wheels against the track guide lugs. The model allows for vertical and lateral load of the wheels, the non-uniform distribution of the wheel pressure on the track, and the relationship between the friction coefficient and normal reaction force in the interface between the wheel and track guide lugs. The model has been verified by experiments. According to the results of model computations and experiments discussed in the article, the internal losses of a given rubber-tracked undercarriage might be reduced if: the road wheels are covered with a material that exhibits low friction coefficient and mechanical hysteresis, the vehicle suspension system features oscillating bogie wheels, the undercarriage is fitted with the largest possible number of road wheels, and the vehicle weight is evenly distributed to all of the road wheels.     

Comparison between centrifugal and vertical vibro-compaction of high-lifted decomposed weathered granite sandy soil using a tracked vehicle

The aim of this research was to develop a new vibro-compaction machine by comparing experimentally and theoretically the effects of a tracked vehicle of total weight 9.8 kN mounted with a centrifugal or vertical oscillator on a high lifted decomposed weathered granite sandy soil. By measuring the amount of sinkage of the terrain surface, the dry density distribution with depth, the normal earth pressure distribution with depth, and the vertical and horizontal acceleration distribution with depth, the compacting effect of centrifugal and vertical vibro-tracked vehicles on the increment of dry density in a deep soil stratum were compared for a frequency of about 54 Hz. It was observed that the centrifugal vibro-tracked vehicle showed a 25% increase in the final amount of sinkage and a 11.3% increase in the maximum dry density of compacted soil compared to the vertical vibro-tracked vehicle. We believe that the centrifugal vibro-tracked vehicle can be shown from the analysis of the stress and acceleration propagation to be a better compaction machine at a high frequency of oscillation for a high lifted soil stratum when compared to conventional vertical vibro-tracked vehicles.     

Analytical track models for ride dynamic simulation of tracked vehicles

This paper presents various modelling strategies to account for track in the ride dynamic simulation of high mobility tracked vehicles negotiating rough off-road terrains. Four analytical track representations of varying complexities are formulated in conjuction with an in-plane ride dynamic model of a typical tracked vehicle. These track models are conceived in view of the tracked vehicle kinematics while ignoring the track belt vibrations. The ride dynamic response of a conventional armoured personnel carrier is evaluated in conjunction with different track methods, and validated against field-measured ride data. The relative performances of these track models are thus assessed based on the accuracy of response predictions, and associated computational time.     

Prediction of track forces in skid-steering of military tracked vehicles

Track forces for outer and inner tracks have been calculated for a military tracked vehicle in a skid-steer situation. The present work is an attempt to improve the understanding of track force variation with turning radius. Furthermore, a reasonable estimate of transmission loads is required for the design of steering transmission for turning a tracked vehicle. This may also be obtained from the track forces. The understanding of track force variation with turning radius has been rather poor. In literature, the reason for lower track force at larger turning radius has been explained in terms of the deflection of the various suspension components like the track shoes, bushings, etc., which are associated with steer action. Deflection of the suspension components does not seem to be an adequate explanation for the variation of track forces with turning radius. In the present work, track forces have been obtained from the dynamics of the moving vehicle. The variation of tractive coefficient (coefficient of friction) due to lateral track slippage has also been considered. This is where the present work differs from the conventional track force estimation where a constant value of coefficient of lateral friction has been used. The estimation of tractive coefficient is made by using pull-slip equation found in literature. The explanation of decreasing track force with increasing radius is given in terms of variation of slip with speed and turning radius. It is found from the study that the concept of variation of coefficient of friction (tractive coefficient) is very important and probably a realistic one in the prediction of track forces. The results of the calculations compare reasonably well with the trends of test result plots obtained in the literature.     

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.