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.     

Fast dynamic modeling for off-road track vehicles

The paper presents a simple, fast, and reliable dynamic model for an off-road track vehicle operating on terrain with obstacles. The method has been proven previously for wheeled-vehicle formulation. The model is based on a discrete body dynamics (DBD) method, which leads to simplistic linear decoupled motion equations. In this method, joints and bodies with relatively small mass are replaced with stiff springs and dampers, eliminating the system’s constraints and reducing the number of system bodies; this is important for accelerating the simulation runtime of the track vehicle model. The track in this approach is based on modeling each link as a point-mass. Two consecutive links are connected by stiff springs and dampers. This approach reduces the calculation time and increases system stability. The track–soil interaction was modeled using Bekker’s and Janosi’s formulation (Bekker, 1956; Hanamoto and Janosi, 1961). Specific soil properties were obtained for each link–soil interaction from soil classification and GIS. The link–ground contact was determined from topographic surface and adjustment of the force and direction acting on the track. The results of the simulation using the DBD method were compared with Siemens' VL commercial multibody dynamics program and with experiments reported in the literature. Results using the proposed method were found to be similar to the commercial program based on published experiments. The solution runtimes obtained for unpaved soil were two orders faster with the DBD method compared with the Siemens' VL program. The model was written as an independent software infrastructure, enabling easy integration with any other software component, such as a control system. The algorithm is in a suitable form for parallel processing calculation to speed up the runtime simulation close to real-time.     

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.     

Soft soil track interaction modeling in single rigid body tracked vehicle models

Single rigid body models are often used for fast simulation of tracked vehicle dynamics on soft soils. Modeling of soil-track interaction forces is the key modeling aspect here. Accuracy of the soil-track interaction model depends on calculation of soil deformation in track contact patch and modeling of soil resistive response to this deformation. An algorithmic method to calculate soft soil deformation at points in track contact patch, during spatial motion simulation using single body models of tracked vehicles, is discussed here. Improved calculations of shear displacement distribution in the track contact patch compared to existing methods, and realistically modeling plastically deformable nature of soil in the sinkage direction in single body modeling of tracked vehicle, are the novel contributions of this paper. Results of spatial motion simulation from a single body model using the proposed method and from a higher degree of freedom multibody model are compared for motion over flat and uneven terrains. Single body modeling of tracked vehicle using the proposed method affords quicker results with sufficient accuracy when compared to those obtained from the multibody model.     

Modelling of off-road wheeled vehicles for real-time dynamic simulation

Simulation of wheel-ground and vehicle-ground interactions is very important in many applications. Achieving accuracy and efficiency is challenging for both soft and hard terrains. This is not only because of the simulation and numerical challenges, but also due to the questionable nature of the existing terrain models. For example, the most widely used terramechanics model is not a representative constitutive relation for a full range of dynamic conditions and applications, but rather a parametrization of steady state conditions. In general, the selection and development of the proper constitutive model and the parametrization of the ground properties are very challenging. Here, we present a unified framework for general wheel-ground interaction which can be used with different terramechanics models. The framework is based on a complementarity formulation and also uses the concept of kinematic constitutive relations, beside the other known concepts for modelling and parametrizing the soil properties. The framework makes it possible to consider the appropriate modelling of the terrain for a broad range of dynamic behaviours and simulation conditions. We will illustrate the material with several examples for off-road conditions.     

Investigation of the soil thrust interference effect for tracked unmanned ground vehicles (UGVs) using model track tests

The traction force of a tracked unmanned ground vehicle (UGV) depends on the soil thrust generated by the shearing action on the soil-track interface. In the development of soil thrust, because the continuous-track system consists of a number of single-track systems connected to each other, interference occurs between the adjacent single-track systems through the surrounding soil. Thus, the total soil thrust of the continuous-track system is not equal to the sum of the soil thrust of each single-track system, and the interference effect needs to be carefully considered. In this study, model track tests were conducted on model single-, double-, and triple-track systems according to relative density of soil and shape ratio (i.e., the length of the track plate to grouser depth). The test results indicated that the interference effect reduced soil thrust due to the overlapping shear zones between adjoining single-track systems. The loss of soil thrust increased as the relative density of the soil increased and the shape ratio decreased. Based on these findings, a soil thrust multiplier that can be utilized to assess the soil thrust of a continuous-track system was developed.     

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.     

Analytical models of mesh stiffness for cracked spur gears considering gear body deflection and dynamic simulation

Meccanica - Accurate mesh stiffness models for cracked spur gears are critical to obtain gearbox failure characteristics. However, the influence of crack on gear body deflection is often ignored by...     

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.     

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.     

Modeling of terrain impact caused by tracked vehicles

Analytical models that can predict the terrain impact caused by tracked vehicles on a horizontal plane were developed and tested. The models included a disturbed width model and an impact severity model. Inputs of the terrain impact models included vehicle static properties, vehicle dynamic properties, and terrain properties. The tested vehicles included an M1A1 tank, an M577 Armored Personal Carrier (APC), and an M548 cargo carrier. The models were verified with field tests conducted in Yakima Training Center in Yakima, WA, Fort Riley, KS, and Camp Atterbury, Indiana. The average percentage errors of the disturbed width model for the M1A1, M577, and the M548 were 10.0%, 27.3%, and 8.5%, respectively. The average percentage errors of the impact severity model of the M1A1 and M577 were 25.0% and 21.4%, respectively.     

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 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 mathematical model for spatial motion of tracked vehicles on soft ground

A mathematical model which predicts spatial motion of tracked vehicles on non-level terrain has been developed. The motion of the vehicle is represented by three translational and three rotational degrees of freedom. In order to incorporate the inelastic deformation of soil, a soil-track interaction model is introduced; this constitutive model relates the traction exerted on the track by soil to the slip velocity and sinkage of the track. The model is based upon available soil plasticity theories and furnishes mechanics-based interpretation of Bekker's empirical relations. For planar motion the proposed model reduces to the existing equations of motion by introducing kinematic constraints on the vertical translation, pitching and rolling degrees-of-freedom.