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.     

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.     

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.     

履带车辆路面激励响应的简化计算

为了快速计算履带车辆在路面不平度激励下的动力学响应,基于合理假设采用理论力学方法建立了某履带车辆的简化动力学模型,用ADAMS 软件建立了同种工况下的履带车辆动力学模型,并把两种模型的求解结果进行了对比,验证了简化模型的合理性. 研究结果为基于简化模型的动力学方程对车辆悬挂系统进行优化和逆动力学分析奠定了基础.     

Longitudinal dynamics of a tracked vehicle: Simulation and experiment

In recent years virtual dynamic system simulation has become very important in the design and development stage, as new strategies can be examined without expensive measurements and with reduced time. This paper describes the development of a simulation model for transient analysis of the longitudinal dynamics of a heavy tracked vehicle. The driving inputs for this simulation model are obtained from a powertrain model. The main elements of the powertrain include the engine, Torque Converter (TC), transmission and drivetrain. Here the engine is modeled based on the engine maps from steady-state experiments. The TC is modeled based on its characteristic map from experiments. A fairly simple transmission model is used which is based on static gear ratios assuming small shift times. The final drivetrain model however includes the rotational dynamics of the sprocket. The simulation model developed is validated by comparing the predicted values with the measured data from experiments. The results have demonstrated that the developed model is able to predict fairly accurately the acceleration and braking performance of the heavy tracked vehicle on both soft and hard terrain.     

Experimental study of a tracked mobile robot’s mobility performance

This paper proposes an experimental method of predicting the traction performance of a small tracked mobile robot. Firstly, a track-terrain interaction model based on terramechanics is built. Then, an experimental platform of the tracked robot is established, on which the measurement methods of the parameters that influencing the accuracy of the prediction model are introduced and the data post-processing are improved, including drawbar pull, slip ratio, sinkage, track deformation and so on. Based on the experimental data, several key terrain parameters are identified. With the tracked robot platform, the drawbar pull-slip ratio relationship is tested, and the effects on drawbar pull considering different kinds of terrain and the influence of the grousers are analyzed as well. The research results provide a reference for the experimental study on the traction performance of small tracked robots.     

基于逆动力学分析的路面不平度测试研究

通过分析一个简化的履带车辆单扭力轴-负重轮力学模型,建立了扭力轴扭转角与路面不平度的联系方程,基于该方程可以由路面不平度求出扭力轴扭转角,如已知扭转角则可以通过逆动力学分析得到路面不平度.数值算例结合ADAMS仿真结果验证了该方法用于路面不平度测试的可行性.     

On the numerical solution of tracked vehicle dynamic equations

In this investigation, the solution of the nonlinear dynamic equations of the multibody tracked vehicle systems are obtained using different procedures. In the first technique, which is based on the augmented formulation that employes the absolute Cartesian coordinates and Lagrange multipliers, the generalized coordinate partitioning of the constraint Jacobian matrix is used to determine the independent coordinates and the associated independent differential equations. An iterative Newton-Raphson algorithm is used to solve the nonlinear constraint equations for the dependent variables. The numerical problems encountered when one set of independent coordinates is used during the simulation of large scale tracked vehicle systems are demonstrated and their relationship to the track dynamics is discussed. The second approach employed in this investigation is the velocity transformation technique. One of the versions of this technique is discussed in this paper and the numerical problems that arise from the use of inconsistent system of kinematic equations are reported. In the velocity transformation technique, the tracked vehicle system is assumed to consist of two kinematically decoupled subsystems; the first subsystem consists of the chassis, the rollers, the sprocket and the idler, while the second subsystem consists of the track which is represented as a closed kinematic chain that consists of rigid links connected by revolute joints. It is demonstrated that the use of one set of recursive equations leads to numerical difficulties because of the change in the track configuration. Singular configurations can be avoided by repeated changes in the recursive equations. The sensitivity of the predictor-corrector multistep numerical integration schemes to the method of formulating the state equations is demonstrated. The numerical results presented in this investigation are obtained using a planner tracked vehicle model that consists of fifty four rigid bodies.     

Ride dynamics mathematical model for a single station representation of tracked vehicle

Tracked vehicles are exposed to severe ride environment due to dynamic terrain-vehicle interactions. Hence it is essential to understand the vibration levels transmitted to the vehicle, as it negotiates different types of terrains at different speeds. The present study is focused on the development of single station representation of tracked vehicles with trailing arm hydro-gas suspension systems, simulating the ride dynamics. The kinematics of hydro-gas suspension system have been derived in order to determine the non-linear stiffness characteristics at various charging pressures. Then, incorporating the actual suspension kinematics, non-linear governing equations of motion have been derived for the sprung and unsprung masses and solved by coding in Matlab. Effect of suspension non-linear dynamics on the single station ride vibrations have been analyzed and validated with a multi-body dynamics model developed using MSC.ADAMS. The above mathematical models would help in estimating the ride vibration levels of the tracked vehicle, negotiating different types of terrains at various speeds and also enable the designers to fine-tune the suspension characteristics such that the ride vibrations are within acceptable limits. The mathematical ride model would also assist in development of non-linear ride vibration model of full tracked vehicle and estimate the sprung mass dynamics.     

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.     

桥梁表面不平顺对车-桥耦合振动系统动力效应的影响

利用模态分析法以及时变力学系统的求解方法,考虑桥面不平顺产生的随机激励,以简支梁桥为对象,计算了四自由度模型车辆-桥梁耦合系统的动力效应,讨论了不同等级桥面平整度情况下桥梁冲击系数、车辆垂直加速度、车轮对桥的作用力的变化规律。结果表明,随着不平整度系数逐渐增大,冲击系数逐渐增大;平整度较差等级的桥面,车辆垂直加速度较大,车轮对桥的作用力也较大。     

可压缩流场中气泡脉动数值模拟

在应用边界元方法对气泡动力学的研究中, 绝大多数模型是建立在不压缩势流理论基础之上, 针对可压缩流场中气泡运动特性的研究很少. 从波动方程出发, 分别在气泡运动前期和后期对波动方程进行简化, 得到气泡运动局部和全局简化方程, 采用双渐进方法对简化方程进行匹配, 提出了考虑流场可压缩性的非球状气泡运动模型. 该模型的计算结果与Prospertti 等的解析结果吻合很好, 气泡脉动最大半径和内部最大压力随气泡脉动逐渐减小. 基于该模型对比了自由场中药包爆炸考虑可压缩性与不考虑可压缩性的计算结果, 发现考虑可压缩性气泡射流速度较小, 随后基于该模型计算了刚性边界下气泡的运动特性.     

基于ED-LSTM的智能汽车神经网络横向动力学建模与控制

车辆动力学建模过程中通常会进行简化和假设, 导致模型在某些工况下无法准确反映车辆的实际动态特性, 影响控制精度甚至安全性. 鉴于此, 该文提出了一种基于数据驱动的非线性建模与控制方法, 建立了新型神经网络车辆横向动力学多步预测模型, 实现了智能汽车对参考轨迹的跟踪控制. 首先, 在分析车辆单轨模型并考虑轮胎非线性和纵向负载转移的基础上, 基于编码器?解码器结构设计神经网络横向动力学模型. 其中, 使用串行排列来扩展微分方程描述不完全的动力学信息, 隐藏层神经元学习车辆的高度非线性和强耦合特性, 进而提高模型全局计算精度. 利用所构建的数据集进行模型训练和测试, 结果表明, 相比于物理模型, 所提出的模型在不同路面附着系数条件下均具有更高的建模精度, 具有隐式预测路面摩擦条件能力. 其次, 利用提出的模型设计轨迹跟踪控制算法, 根据车辆稳态转向假设, 计算所需的前轮转向角和稳态质心侧偏角, 将稳态质心侧偏角纳入基于路径误差的转向反馈中, 实现参考轨迹跟踪控制. 最后, 使用CarSim/Simulink联合仿真及HIL实验测试进行不同工况试验的对比分析, 对所提出的基于神经网络模型的控制算法进行评价, 结果表明, 该模型能够实现智能汽车在高速下精确的跟踪控制效果, 并具有良好的横向稳定性.      

Vertical two-dimensional non-hydrostatic pressure model with single layer

The vertical two-dimensional non-hydrostatic pressure models with multiple layers can make prediction more accurate than those obtained by the hydrostatic pres-sure assumption. However, they are time-consuming and unstable, which makes them unsuitable for wider application. In this study, an efficient model with a single layer is developed. Decomposing the pressure into the hydrostatic and dynamic components and integrating the x-momentum equation from the bottom to the free surface can yield a horizontal momentum equation, in which the terms relevant to the dynamic pressure are discretized semi-implicitly. The convective terms in the vertical momentum equation are ignored, and the rest of the equation is approximated with the Keller-box scheme. The velocities expressed as the unknown dynamic pressure are substituted into the continuity equation, resulting in a tri-diagonal linear system solved by the Thomas algorithm. The validation of solitary and sinusoidal waves indicates that the present model can provide comparable results to the models with multiple layers but at much lower computation cost.     

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.     

刚-柔耦合动力学系统的建模理论研究

刚－柔耦合动力学系统的传统的混合坐标方法是零次近似方法,在建模过程中,直接套用的结构动力学的小变形假设,忽略了变形位移的高次耦合变形量．本文对柔性梁建立较零次近似更精确的高次耦合动力学模型,从连续介质力学理论出发,在变形位移中,计及横向位移引起的轴向缩短,导出变形位移的二次耦合量．用一致质量有限元方法对梁进行离散,基于Jourdain速度变分原理导出大范围运动为自由的柔性梁的刚－柔耦合动力学方程．计算了柔性重力摆的角速度和摆端点的横向变形,揭示零次近似模型和耦合模型的刚－柔耦合动力学性质的根本差异．     

On the global dynamics of chatter in the orthogonal cuttingmodel

The large-amplitude motions of a one degree-of-freedom model of orthogonal cutting are analysed. The model takes the form of a delay differential equation which is non-smooth at the instant at which the tool loses contact with the workpiece, and which is coupled to an algebraic equation that stores the profile of the cut surface whilst the tool is not in contact. This system is approximated by a smooth delay differential equation without algebraic effects which is analysed with numerical continuation software. The grazing bifurcation that defines the onset of chattering motion is thus analysed as are secondary (period-doubling, etc.) bifurcations of chattering orbits, and convergence of the bifurcation diagrams is established in the vanishing limit of the smoothing parameters. The bifurcation diagrams of the smoothed system are then compared with initial value simulations of the full non-smooth delay differential algebraic equation. These simulations mostly validate the smoothing technique and show in detail how chaotic chattering dynamics emerge from the non-smooth bifurcations of periodic orbits.