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.     

Practical method of reducing turning motion resistance of tracked vehicles

A practical method of reducing the resistance of a tracked vehicle to turning or steering motion is discussed. The torque of the sprocket shaft for driving the crawler was measured and used to evaluate how the resistance varied compared with the existing method to turning. There are two ways of reducing the turning resistance by decreasing the contact area of track; one is to decrease the width of the braked track and the other is to shorten its contact length during turning or steering motion. The former is practically impossible to control, but the latter is comparatively easy to do, even under that condition. Applying this mechanism, the resistant force (evaluated by measuring the driving torque of the sprocket shaft) could be reduced about 20% when the contact length of the braked track was shortened to form a small pivot area at its center. It was also reduced more than 50% when the contact length of both tracks was shortened to a pivot during turning motion.     

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.     

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.     

Finite-time optimal formation tracking control of vehicles in horizontal plane

This paper studies the problem of finite-time optimal formation tracking for planar vehicles which are considered as rigid bodies, under the condition that the tracking time is given according to task requirements in advance. By using Pontryagin’s maximum principle (PMP) on a Lie group, an optimal control law is designed for vehicles with holonomic dynamics to track a desired reference trajectory at the given tracking time in the manner of rigid formation which is also specified by task requirements. Simultaneously, a corresponding cost function is considered and guaranteed to be optimal. Then, the above mentioned result of tracking is extended to the case of multi-vehicle systems with a directed-tree communication topology. Furthermore, some conditions are proposed to ensure the adjoint orbits of vehicles to be non-holonomic. Finally, the numerical simulations are provided to illustrate the effectiveness of the theoretical results.     

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.     

Dynamic motion of a conical frustum over a rough horizontal plane

An analytical and numerical study of the dynamic motion of a conical frustum over a planar surface is presented resulting to a non-linear system of ordinary differential equations. Wobbling and rocking components of motion are discussed in detail concluding that, in general, the former component dominates the latter. For small inclination angles an asymptotic approximation of the angular velocities is possible, revealing the main characteristics of wobbling motion and its differences from rocking. Connection is made of the analysis with the behavior of the ancient classical columns, whose three dimensional dynamic response challenges the accuracy of the two dimensional models, usually applied in practice. The consideration of such discrete-blocky systems can benefit from the present study, through qualitative results and benchmarks for more complicated numerical methods, like the Distinct Element Method.     

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.     

Steady motion of a rigid disk of finite thickness on a horizontal plane

The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady-state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of ground and it is shown that the possible steady motion of a disk is either on a straight line or in a circle. Oscillations about steady state are discussed and conditions for stable motion established. The bifurcations of steady motions on a smooth surface are also considered.     

An application of pattern mapping to plane motion

A new, highly automated method for measuring plane motion, pattern mapping, has been developed for rigidbody motion and strain analysis. Pattern mapping employs image processing and syntactic pattern recognition principles to recognize a known pattern before and after motion. In this paper, the Lagrangian definition of motion was used to map points in the two images, and the map was used to determine plane motion. Full-image analysis is thoroughly demonstrated.     

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 motion of a sphere with weak nutation on a rough horizontal plane

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Computer aided analysis of the effects of design parameters on the performance of tracked vehicles

This paper describes the application of a computer simulation model, known as NTVPM-85, to the evaluation of the effects of design parameters on the performance of tracked vehicles over various types of terrain. It demonstrates that the computer simulation model is a useful tool for the vehicle designer and the user in the evaluation of competing designs and in the examination of the effects on performance of design modifications and terrain conditions.     

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.     

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.     

The residual effects of tracked vehicles on soil surface properties

Differences in soil surface properties were measured on soil cores collected from within tracks and adjacent undisturbed areas. The passage of tracks resulted in an increase in bulk density, a reduction in saturated hydraulic conductivity and an increase in cone penetrometer resistance. Laboratory direct-shear tests showed in-track soil was stronger than out-of-track samples. The saturated hydraulic conductivity of in-track soil cores increased with an increasing number of wetting and draining cycles, whereas out-of-track samples showed little change. Implications for erosion, vegetation regeneration and management strategies for off-road vehicle areas are discussed, with some speculation as to the rate of recovery of impacted areas.