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.     

Dynamic analysis of turning performance of 4WD-4WS tractor on paved road

In this research, using a 4-wheel-driven, 4-wheel-steered tractor, two experiments and a computer simulation about its turning on paved ground are described. One experiment is on the relation between the wheel turning angle and the steering angle, and the other is a turning experiment to determine the path traced by the vehicle and to check the simulation. The computer simulation with equations of motion was conducted, and some effects, for example of the running speed, on the yaw angular velocity and on the side slip angle of the center of gravity of the tested tractor were analysed.     

The problems of multi-axle vehicle drives

The multi-axle drive provides for maximum traction of the vehicle. However, this mode of driving, apart from the complicated design of the driving mechanism, is connected with major problems due to the so-called kinematic discrepancy encountered by a vehicle under operation. In certain conditions, the kinematic discrepancy results in the phenomenon of so-called circulating power which causes, first of all, additional loading on the drive system, then increased energy loss and tyre wear and, in the case of an articulated frame-steer vehicle, the substantial growth of steering resistance.The paper reviews some examples of results of the studies on wheel slips, load on the drive system, and on the 4-wheel-drive articulated frame-steer vehicle's steering gear. The author also discusses a new concept for determining kinematic discrepancy. The suggested equations, when applying the present mathematical models which express the dependence of a tyre's slip rate on longitudinal forces, permit to solve the statically undeterminable problem concerning the distribution of the wheel's longitudinal forces in any multi-axle vehicle.     

Behaviour of tyres driven in soft ground with side slip

A six-component measuring device has been developed, with which forces and moments can be measured on a braked or driven yawing wheel in yielding ground, both in the field and in a test bin. Experimental results on tyres running at a side slip angle are discussed and plotted to show the variety of effects of driving force, slip, side-force and side slip angle. It is shown that with an increasing driving-force at constant slip angle the side-force is considerably reduced. In an approximately calculation, by means of linearized equations of motion of a rear-wheel-drive and a four-wheel-drive vehicle, the behaviour on side slopes and on curves has been studied.As a result it follows that the interaction of the side-force and the driving-force affects markedly the motion of the vehicle. With the four-wheel-drive vehicle on a curve, the radius of curvature and, on the slope, the yaw angle of the vehicle are less than with rear-wheel-drive vehicles.     

Numerical simulation of a 4WD–4WS tractor turning in a rice field

For the steady-state circular turning of a 4WD–4WS (4 wheel driven–4 wheel steered) tractor in a rice field, a numerical simulation was achieved. Equations of motion of this tractor were developed in a vehicle fixed x–y coordinate system. By comparing the calculated and measured results of acting forces on the tractor tires, this simulation was evaluated. Then, the characteristic parameters of the turning vehicle, which are the side slip angle and the yaw angular velocity of the vehicle center of gravity, were simulated in several combinations of the steering wheel angle and the forward speed. Also the same simulation applied to a 4WD–2WS tractor which had the same body as the 4WD–4WS tractor. The simulated results showed a clear difference of turnability between 4WS and 2WS. ©     

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.     

Design and development of a new transformable wheel used in amphibious all-terrain vehicles (A-ATV)

Conventional ground-wheeled vehicles usually have poor trafficability, low efficiency, a large amount of energy consumption and possible failure when driving on soft terrain. To solve this problem, this paper presents a new design of transformable wheels for use in an amphibious all-terrain vehicle. The wheel has two extreme working statuses: unfolded walking-wheel and folded rigid wheel. Furthermore, the kinematic characteristics of the transformable wheel were studied using a kinematic method. When the wheel is unfolded at walking-wheel status, the displacement, velocity and acceleration of the wheel with different slip rates were analyzed. The stress condition is studied by using a classic soil mechanics method when the transformable wheel is driven on soft terrain. The relationship among wheel traction, wheel parameters and soil deformation under the stress were obtained. The results show that both the wheel traction and trafficability can be improved by using the proposed transformable wheel. Finally, a finite element model is established based on the vehicle terramechanics, and the interaction result between the transformable wheel and elastic–plastic soil is simulated when the transformable wheel is driven at different unfold angles. The simulation results are consistent with the theoretical analysis, which verifies the applicability and effectiveness of the transformable wheel developed in this paper.     

A skid steering model with track pad flexibility

The paper describes a model for predicting the skid-steering performance of tracked vehicles that allows for the flexibility of the track pads. It thus accounts for the reductions in friction moment that are observed as the radius of the turn is increased. The pad model computes a compound slip function and takes account of the shear stiffness of the pad and the limiting friction between the pad and the ground. Vehicle dimensions and the equations of motion are entered into a Microsoft Excel spreadsheet. The equations are solved using the Excel Solver routine. This avoids the need for specialised software or programming skills. It also gives good insight into the mechanics of steering and the factors affecting performance. Predicted sprocket torques for a Jaguar vehicle turning at different radii show good agreement with experimental measurements. The steering performance of an example six axle 24 tonne vehicle is computed and compared with that using the early Merritt/Steeds model that ignored track pad flexibility. The flexible pad model generally shows the vehicle to be slightly oversteer, whereas the Merritt/Steeds model predicts the vehicle to be understeer. At higher speeds the maximum cornering acceleration is likely to be limited by available power at the sprockets. Altering the static weight distribution of the vehicle shows that a forward weight distribution tends to cause a more oversteer response with reduced limiting lateral acceleration. With a rearward weight distribution, the vehicle response tends towards neutral to slight understeer. This is in contrast to Ackerman steered wheeled vehicles with pneumatic tyres where moving the CG forward tends to a more understeer response. Using the concept of static margin as applied to wheeled vehicles, it is suggested that a uniform or slightly forward weight distribution would make tracked vehicles less sensitive to external disturbances (cambered roads for example).     

A method of optimal wheel torque determination for independent wheel drive vehicles

A method of optimal wheel torque determination for electric motor vehicles is presented. Electric motor vehicles are increasing with the rise of public interest in environmental protection. In the case of vehicles driven by controllable motors on each individual wheel, the determination of the wheel torque is an essential factor for efficient driving. In this research, a method of optimal torque determination has been formulated by using the variational principle to minimize frictional work done by the tires with the ground contact. Optimal torque on each wheel for a four-wheel vehicle was numerically obtained by solving the equations under several driving conditions. The result of the numerical simulation is useful as a guide to control the motor torque of electric vehicles for efficient driving.     

The effect of velocity on rigid wheel performance

A simulation model to predict the effect of velocity on rigid-wheel performance for off-road terrain was examined. The soil–wheel simulation model is based on determining the forces acting on a wheel in steady state conditions. The stress distribution at the interface was analyzed from the instantaneous equilibrium between wheel and soil elements. The soil was presented by its reaction to penetration and shear. The simulation model describes the effect of wheel velocity on the soil–wheel interaction performances such as: wheel sinkage, wheel slip, net tractive ratio, gross traction ratio, tractive efficiency and motion resistance ratio. Simulation results from several soil-wheel configurations corroborate that the effect of velocity should be considered. It was found that wheel performance such as net tractive ratio and tractive efficiency, increases with increasing velocity. Both, relative wheel sinkage and relative free rolling wheel force ratio, decrease as velocity increases. The suggested model improves the performance prediction of off-road operating vehicles and can be used for applications such as controlling and improving off-road vehicle performance.     

一种车辆模型辅助的MEMS-SINS导航方法

针对城市环境中GNSS因遮挡导致MEMS-SINS精度快速降低的问题,在车辆运动学约束的基础上,结合四通道ABS轮速传感器和方向盘转角信息,提出一种新的适用于陆地车辆的MEMS-SINS导航方法。该方法通过分析车辆转弯和运动约束特性,构建角速度和加速度观测量,从而实现基于模型辅助的MEMS误差在线补偿;其次,ABS轮速信息与非完整约束条件结合可额外增加三维车体速度观测量,进一步维持卫星失效时组合滤波器的量测更新。跑车实验表明,在GNSS信号频繁丢失甚至长时间无法定位时,低精度MEMS惯性器件引起的快速误差积累得到有效抑制,与经典车体约束结合里程计算法相比,航向精度提高约70%,位置、速度精度也有相应的提高,验证了算法的有效性。     

Measurement of forces acting on 4WD-4WS tractor tires during steady-state circular turning on a paved road

Measuring method and measured results of vertical, longitudinal and lateral forces, which act on tires of a four-wheel drive and four-wheel steering (4WD-4WS) agricultural tractor, are presented in this paper as well as those of longitudinal and lateral slip of the tires. These results were measured during steady-state circular turning, in which a fixed steering wheel angle and a constant running speed were kept, on a paved road. The measurement was also done for a four-wheel drive and two-wheel steering (4WD-2WS) state, disconnecting a rear steering link and fixing the steering angles of the rear tires of the 4WD-4WS tractor to zero. Through the analysis of the results, some turning characteristics of the 4WD-4WS tractor were obtained. A tight corner braking phenomenon was clearly found in the case of 2WS. The 4WS system supplied more efficient turning than the 2WS system. Results obtained from the computer simulation agreed well with the experimental results except in the case of a low speed turn and as to thrusts of tires.     

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.     

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.     

A method of torque control for independent wheel drive vehicles on rough terrain

Our previous research has revealed that, for vehicles with independently driven wheels, a torque distribution based on the ratio of the vertical load of each wheel to the total vehicle load is efficient for driving on flat ground. In this research, this method of torque distribution was extended to electric off-road vehicles driving on rough ground. In order to examine the driving efficiency of these vehicles, a numerical vehicle model was constructed in the pitch plane. Simulations using the numerical vehicle model on rough ground were conducted with a proposed torque distribution and control method. The numerical results from these simulations were compared with those of a conventional vehicle to evaluate the driving efficiency and trafficability on ground with various profiles. A comparison between the simulations demonstrated that the proposed method of torque distribution to the front and rear wheels based on the ratio of the vertical load is efficient for driving on rough ground.     

Estimation of net traction for differential-steered wheeled robots

We present a method for estimating the net traction and resistive wheel torques for a suspensionless, differential-steered robot on rigid or deformable terrain. The method, based on extended Kalman-Bucy filtering (EKBF), determines time histories of net traction and resistive wheel torques and wheel slips during steady or transient maneuvers. This method assumes good knowledge of the vehicle dynamics and treats the unknown forces and moments due to terrain response as random variables to be estimated. A proprioceptive sensor suite renders a subset of the unknown forces and associated wheel slip and slip angles observable. This methodology decouples semi-empirical terramechanics models from the net effect of the vehicle-terrain interaction, namely the net traction developed by the vehicle on the terrain. By collecting sensor data and processing data off-line, force-slip characteristics are identified irrespective of the underlying terramechanics. These characteristics can in turn support development or validation of terramechanics models for the vehicle-terrain system. For autonomous robots, real-time estimates of force-slip characteristics can provide setpoints for traction and steering control, increasing vehicle performance, speed, and maneuverability. Finally, force-slip estimation is the first step in identifying terrain parameters during normal maneuvering. The methodology is demonstrated through both simulation and physical testing using a 13-kg robot.     

Numerical analysis to predict turning characteristics of rigid suspension tracked vehicle

Numerical analysis was developed to calculate the steering properties of a rigid suspension tracked vehicle turning on soft terrain. The developed numerical analysis is based on a method to solve a set of non-linear equations. To verify the numerical analysis, an experiment on a model-tracked vehicle turning with a steering ratio of 1.6 on a loose sandy terrain was carried out. The comparison between measured and calculated values shows that the numerical analysis can predict sinkage, slip ratios and turning radius within an error amount of 15%.     

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.     

Development of a vehicle to study the tractive performance of integrated steering-drive systems

This paper describes a test-bed vehicle for studying the integration of the steering system of a wheeled vehicle with the drive system. The vehicle was produced in order to determine whether such an integrated system is practical; to investigate tractive performance compared to other steering-drive systems; and to determine under which conditions such a system has better performance. The integrated steering-drive system of the test-bed vehicle uses a computer to co-ordinate the independently driven wheel speeds of the drive system (which is also the primary steering system) with the steer angles of the non-driven steerable wheels to produce a beneficial secondary steering effect. The secondary steering system assists the primary steering system when side forces act on the vehicle, while producing minimal conflict. This concept can be applied to agricultural vehicles such as tractors, harvesters, mowers, sprayers and self-propelled windrowers. The test-bed vehicle is able to be configured for the following steering-drive systems types: open differential drive with steerable wheels, independent drive wheels with castors, locked differential drive with steerable wheels and a computer integrated steering-drive system. The capacity of the test-bed vehicle to be configured as described is a significant advantage when measuring tractive performance, as the results obtained will be more valid due to the vehicle parameters being the same.