Spatial Dynamics of Multibody Tracked Vehicles Part II: Contact Forces and Simulation Results

In this part of the paper, three dimensional computational capabilities, that includes significant details, are developed for the nonlinear dynamic analysis of large scale spatial tracked vehicles. Three dimensional nonlinear contact force models that describe the interaction between the track links and the vehicle components such as the rollers, sprockets, and idlers as well as the interaction between the track links and the ground are developed and used to define the generalized contact forces associated with the vehicle generalized coordinates. Tangential friction and contact forces are developed in order to maintain the stability of the track motion and avoid the slippage of the track or its rotation as a rigid body. Body and surface coordinate systems are introduced in order to define the spatial contact conditions. The nonlinear equations of motion of the tracked vehicle are solved using the velocity transformation procedure developed in the first part of this paper. This procedure is used in order to obtain a minimum set of differential equations, and avoid the use of the iterative Newton-Raphson algorithm. A computer simulation of a tracked vehicle that consists of one hundred and six bodies and has one hundred and sixteen degrees of freedom is presented in order to demonstrate the use of the formulations presented in this study.     

Dynamics of Tracked Vehicles

This paper provides a brief review of the state-of-the-art of tracked vehicle dynamics, including mobility over soft terrain, ride dynamics over rough surfaces and manoeuvrability. It is found that considerable progress has been made in the development of analytical frameworks for evaluating and predicting tracked vehicle mobility over soft terrain, taking into account the characteristics of terrain response to normal and shear loading. Certain computer simulation models for tracked vehicle mobility have been gaining increasingly wide acceptance by industry and governmental agencies in product development and in procurement. It is also found that most of the research on tracked vehicle ride dynamics and manoeuvrability is confined to operations on rigid surfaces. To achieve a realistic evaluation and prediction of the dynamic behaviour of tracked vehicles in the field, the key is to have a better understanding of terrain response to dynamic vehicular loading, including its dynamic stiffness and damping. Challenges that face vehicle dynamicists in this emerging field are identified.     

Dynamics of Tracked Vehicles

SUMMARY

This paper provides a brief review of the state-of-the-art of tracked vehicle dynamics, including mobility over soft terrain, ride dynamics over rough surfaces and manoeuvrability. It is found that considerable progress has been made in the development of analytical frameworks for evaluating and predicting tracked vehicle mobility over soft terrain, taking into account the characteristics of terrain response to normal and shear loading. Certain computer simulation models for tracked vehicle mobility have been gaining increasingly wide acceptance by industry and governmental agencies in product development and in procurement. It is also found that most of the research on tracked vehicle ride dynamics and manoeuvrability is confined to operations on rigid surfaces. To achieve a realistic evaluation and prediction of the dynamic behaviour of tracked vehicles in the field, the key is to have a better understanding of terrain response to dynamic vehicular loading, including its dynamic stiffness and damping. Challenges that face vehicle dynamicists in this emerging field are identified.     

Ride Dynamics of High-Speed Tracked Vehicles: Simulation with Field Validation

SUMMARY

Ride dynamic behaviour of a typical high-speed tracked vehicle, such as a conventional military armoured personnel carrier (APC) negotiating rough off-road terrains, is studied through computer simulations and field tests. A comprehensive ride dynamic simulation model is developed, assuming constant forward vehicle speed and non-deformable terrain profile. The ride model includes dynamic track load and wheel/track-terrain interaction. Dynamic track load is modeled in view of track belt stretching and initial track tension, whereas an equivalent damper and continuous radial spring formulation is employed to model wheel/track-terrain interaction. Field testing of a APC subjected to discrete half round obstacles of various radii, a sinusoidal course, a random course, and a Belgian Pave\ is carried out for various vehicle configurations and speeds. Computer simulation results are validated against field measured results. The comparison of measured and predicted results shows generally good agreement.     

Simulation of Multibody Vehicles Moving over Elastic Guideways1

SUMMARY

This paper describes the present state of a general purpose computer program for calculating the dynamic response of vehicles travelling over guideways which may be elastic.

The linearized state-equations of motion for general multibody vehicles are constructed automatically by the program, these equations are supplemented by the equations for the active subsystems. Finally, the vehicle system equations are combined with the modal equations for elastic guideways and the complete set of coupled equations is solved simultaneously by numerical integration.     

Simulation of Multibody Vehicles Moving over Elastic Guideways1

This paper describes the present state of a general purpose computer program for calculating the dynamic response of vehicles travelling over guideways which may be elastic.

The linearized state-equations of motion for general multibody vehicles are constructed automatically by the program, these equations are supplemented by the equations for the active subsystems. Finally, the vehicle system equations are combined with the modal equations for elastic guideways and the complete set of coupled equations is solved simultaneously by numerical integration.     

Two-Dimensional Motion of Four-Wheel Vehicles

This paper deals with two-dimensional motion of vehicles. Since the general four-wheel vehicle model is statically indeterminate, the motion of vehicles has been analyzed by replacing the vehicle with the equivalent two-wheel one proposed by E. Marquard. Because this approximation is based on the axisymmetry of vehicles, it causes significant errors in the general case. To improve the accuracy of the analysis of vehicle motion, a four-wheel model is suggested. In this model, it is assumed that the chassis remains in a flat plane during motion. By introducing this condition, the motion of the vehicle can be analyzed. Several results from the four-wheel model and the equivalent two-wheel model are shown for comparison, and the vehicle trajectories with time are discussed.     

Two-Dimensional Motion of Four-Wheel Vehicles

This paper deals with two-dimensional motion of vehicles. Since the general four-wheel vehicle model is statically indeterminate, the motion of vehicles has been analyzed by replacing the vehicle with the equivalent two-wheel one proposed by E. Marquard. Because this approximation is based on the axisymmetry of vehicles, it causes significant errors in the general case. To improve the accuracy of the analysis of vehicle motion, a four-wheel model is suggested. In this model, it is assumed that the chassis remains in a flat plane during motion. By introducing this condition, the motion of the vehicle can be analyzed. Several results from the four-wheel model and the equivalent two-wheel model are shown for comparison, and the vehicle trajectories with time are discussed.     

A Track-Wheel-Terrain Interaction Model for Dynamic Simulation of Tracked Vehicles

A mathematical model of track-wheel-terrain interaction is presented that supports the dynamic simulation of tracked vehicles. This model combines approximate and known constitutive laws for terrain response with a new representation for the track segment. The resulting track-wheel-terrain model allows the computation of the track tension and the normal and shear forces at the track-terrain interface as the track negotiates terrain of arbitrary profile. A key feature of this model is the uniform treatment of contact between the track and the roadwheels and the track and the terrain. Treating both contact problems in the same manner significantly simplifies the problem formulation and also reduces difficulties in computing points of track-wheel and track-terrain separation. The model takes the form of a two-point nonlinear boundary value problem that accounts for tension variations along the track (due to the non-uniformly distributed normal pressure and traction), track extensibility, and geometrically large (nonlinear) track deflections. Solutions are obtained using a finite element formulation. Both the model and the solution method are formulated for implementation within a multibody dynamics code for simulating full vehicles. Several examples illustrate the capabilities of the proposed model.     

Analytical Wheel Models for Ride Dynamic Simulation of Off-road Tracked Vehicles

This paper outlines various analytical approaches of varying complexities to model the wheel in the ride dynamic formulation of off-road tracked vehicles. In addition to a proposed model, four analytical models available in the literature are compared to study their effectiveness in modeling the wheel/track-terrain interaction for ride dynamic evaluation of typical high mobility tracked vehicles. The ride dynamic model used in this study describes the bounce-pitch plane motion of an armoured personnel carrier (Ml 13 APC) traversing over an arbitrary rigid terrain profile at constant speed. The ride dynamic response of the tracked vehicle is evaluated with different wheel models, and compared against field-measured ride data. The relative performance of different wheel models are assessed based on the accuracy of response prediction and associated computational time. The proposed wheel model is found to perform very well in comparison, and is equally applicable for the case of wheeled vehicles.     

Roll Dynamics of Commercial Vehicles

An analytical model is developed here for studying the roll dynamics of commercial vehicles. Large displacements and rotations are accounted for in this nonlinear model so that it can be used for the study of roll dynamics well beyond the limits of wheel lift-off. The model is used to illustrate some of the dynamic phenomena in vehicle rollover, especially the interactive coupling between the roll and the vertical modes of motion. The influence of suspension backlash on rollover resistance is demonstrated, and the phenomenon of roll motion resonance is illustrated to suggest new means for evaluating vehicle rollover sensitivity.     

Non-Linear Dynamics of Railway Vehicles

The theoretical development of the lateral dynamics of railway vehicles has made rapid strides in recent years and many of the instabilities arising from the geometry of the wheel-rail interface and the forces acting in the contact area are now understood. In addition methods of analysis of curving and dynamic response to track irregularities have been developed and validated by experiment. This paper reviews the present status of equations of motion, limit cycle solutions for hunting oscillations and the relationship of stability to behaviour in curves.     

Dynamics of Actively Guided Vehicles

SUMMARY

In spite of considerable interest in active controls for a wide variety of road and rail vehicles comparatively little work has been carried out on the dynamics of actively guided vehicles in which steering is carried out in response to signals from a controller seeking to follow a given path or track. Drawing from the relevant fields of guided rubber tyred vehicles, rail vehicles and mobile robots the common basis of the dynamics of active guidance is discussed,and this simple theoretical framework is then followed by a review of work in this field. Attention is restricted to wheeled vehicles.     

Adaptation of a General Multibody Dynamical Formalism to Dynamic Simulation of Terrestrial Vehicles

The development of general Eulerian dynamic formalisms for the digital simulation of multi-body systems is reviewed. The formalism of Robertson/Wittenburg is generalized to systems whose configuration includes closed loops, thereby adapting it to the dynamic simulation of terrestrial vehicles.     

The Dynamics of Single Track Vehicles

SUMMARY

The paper contains a brief review of the more subjective aspects of the steering behaviour of single track vehicles, a review of the more significant published work in the field, and an assessment of the current state of understanding and likely ways in which further progress can be made

Attention is drawn to the many areas of agreement between theory and practice and to some areas of disagreement. The greatest need now seems to be for the incorporation of more complex tyre models into vehicle handling models.