Chain Vibration and Dynamic Stress in Three-Dimensional Multibody Tracked Vehicles

A three-dimensional computational finite element procedure for the vibration and dynamic stress analysis of the track link chains of off-road vehicles is presented in this paper. The numerical procedure developed in this investigation integrates classical constrained multibody dynamics methods with finite element capabilities. The nonlinear equations of motion of the three-dimensional tracked vehicle model in which the track link s are considered flexible bodies, are obtained using the floating frame of reference formulation. Three-dimensional contact force models are used to describe the interaction of the track chain links with the vehicle components and the ground. The dynamic equations of motion are first presented in terms of a coupled set of reference and elastic coordinates of the track links. Assuming that the structural flexibility of the track links does not have a significant effect on their overall rigid body motion as well as the vehicle dynamics, a partially linearized set of differential equations of motion of the track links is obtained. The equations associated with the rigid body motion are used to predict the generalized contact, inertia, and constraint forces associated with the deformation degrees of freedom of the track links. These forces are introduced to the track link flexibility equations which are used to calculate the deformations of the links resulting from the vehicle motion. A detailed three-dimensional finite element model of the track link is developed and utilized to predict the natural frequencies and mode shapes. The terms that represent the rigid body inertia, centrifugal and Coriolis forces in the equations of motion associated with the elastic coordinates of the track link are described in detail. A computational procedure for determining the generalized constraint forces associated with the elastic coordinates of the deformable chain links is presented. The finite element model is then used to determine the deformations of the track links resulting from the contact, inertia, and constraint forces. The results of the dynamic stress analysis of the track links are presented and the differences between these results and the results obtained by using the static stress analysis are demonstrated.     

Global modes for the reduction of flexible multibody systems

Multibody System Dynamics - Modeling a flexible multibody system employing the floating frame of reference formulation (FFRF) requires significant computational resources when the flexible...     

First order sensitivity analysis of flexible multibody systems using absolute nodal coordinate formulation

Design sensitivity analysis of flexible multibody systems is important in optimizing the performance of mechanical systems. The choice of coordinates to describe the motion of multibody systems has a great influence on the efficiency and accuracy of both the dynamic and sensitivity analysis. In the flexible multibody system dynamics, both the floating frame of reference formulation (FFRF) and absolute nodal coordinate formulation (ANCF) are frequently utilized to describe flexibility, however, only the former has been used in design sensitivity analysis. In this article, ANCF, which has been recently developed and focuses on modeling of beams and plates in large deformation problems, is extended into design sensitivity analysis of flexible multibody systems. The Motion equations of a constrained flexible multibody system are expressed as a set of index-3 differential algebraic equations (DAEs), in which the element elastic forces are defined using nonlinear strain-displacement relations. Both the direct differentiation method and adjoint variable method are performed to do sensitivity analysis and the related dynamic and sensitivity equations are integrated with HHT-I3 algorithm. In this paper, a new method to deduce system sensitivity equations is proposed. With this approach, the system sensitivity equations are constructed by assembling the element sensitivity equations with the help of invariant matrices, which results in the advantage that the complex symbolic differentiation of the dynamic equations is avoided when the flexible multibody system model is changed. Besides that, the dynamic and sensitivity equations formed with the proposed method can be efficiently integrated using HHT-I3 method, which makes the efficiency of the direct differentiation method comparable to that of the adjoint variable method when the number of design variables is not extremely large. All these improvements greatly enhance the application value of the direct differentiation method in the engineering optimization of the ANCF-based flexible multibody systems.     

Reanalysis-based fast solution algorithm for flexible multi-body system dynamic analysis with floating frame of reference formulation

Multibody System Dynamics - In order to improve the computational efficiency of flexible multi-body system dynamic analysis with floating frame of reference formulation (FFRF), a reanalysis-based...     

TRAFFIC VIDEO-BASED MOVING VEHICLE DETECTION AND TRACKING IN THE COMPLEX ENVIRONMENT

Moving vehicle detection and tracking is the key technology in the intelligent traffic monitoring system. For the shortcomings and deficiencies of the frame-subtraction method, a novel Marr wavelet, kernel-based background modeling method and a background subtraction method based on binary discrete wavelet transforms (BDWT) are introduced. The background model keeps a sample of intensity values for each pixel in the image and uses this sample to estimate the probability density function of the pixel intensity. The density function is estimated using a new Marr wavelet kernel density estimation technique. The background and current frame are transformed by BDWT, and moving vehicles are detected in the binary discrete wavelet transforms domain. For the shortages of RGB (Red, Green, Blue) or HSV (Hue, Saturation, Value) color space-based vehicle shadow segmentation algorithms, shadow segmentation algorithm based on YCbCr color space and edge detection is proposed. The original data of the shadow according to the characteristics of the YCbCr space is chosen, and then, combined with edge detection, the shape and location of the vehicle region is determined. An automatic particle filtering algorithm is used to track the vehicle after detection and obtaining the center of the object. An actual road test shows that the algorithm can effectively remove the influence of pedestrians and cyclists in the complex environment, and can track the moving vehicle exactly. The algorithm with better robustness has a practical value in the field of intelligent traffic monitoring.     

自适应神经模糊推理结合PID控制的并联机器人控制方法

针对6自由度液压驱动并联机器人的精确控制问题,提出一种结合自适应神经模糊推理系统(ANFIS)和比例积分微分(PID)控制的机器人控制方法。首先,利用浮动坐标系描述法(FFRF)来模拟机器人柔性组件,并构建并联机器人的拉格朗日动力学模型。然后,根据模糊推理中的模糊规则来自适应调整PID控制器参数。最后,利用神经自适应学习算法使模糊逻辑能计算隶属度函数参数,从而使模糊推理系统能追踪给定的输入和输出数据。将该控制器与传统PID控制器、模糊PID控制器进行比较,结果表明,ANFIS自整定PID控制器大大减小了末端器位移误差,能很好的控制并联机器人末端机械手的运动。     

On the use of absolute interface coordinates in the floating frame of reference formulation for flexible multibody dynamics

In this work a new formulation for flexible multibody systems is presented based on the floating frame formulation. In this method, the absolute interface coordinates are used as degrees of freedom. To this end, a coordinate transformation is established from the absolute floating frame coordinates and the local interface coordinates to the absolute interface coordinates. This is done by assuming linear theory of elasticity for a body’s local elastic deformation and by using the Craig–Bampton interface modes as local shape functions. In order to put this new method into perspective, relevant relations between inertial frame, corotational frame and floating frame formulations are explained. As such, this work provides a clear overview of how these three well-known and apparently different flexible multibody methods are related. An advantage of the method presented in this work is that the resulting equations of motion are of the differential rather than the differential-algebraic type. At the same time, it is possible to use well-developed model order reduction techniques on the flexible bodies locally. Hence, the method can be employed to construct superelements from arbitrarily shaped three dimensional elastic bodies, which can be used in a flexible multibody dynamics simulation. The method is validated by simulating the static and dynamic behavior of a number of flexible systems.     

自动分割及跟踪视频运动对象的一种实现方法

随着MPEG-4压缩标准的制定,分割及跟踪视频运动对象的研究显得极其重要。在MPEG-4视频编码标准中,为了实现基于视频内容的交互功能,其视频序列的每一帧由视频对象面（VOP）来表示。为了生成视频对象面,需要对视频序列中的运动对象进行有效的分割;并跟踪运动对象随时间的变化,为此提出并实现了一种用于分割及跟踪视频运动对象的时空联合方法。该方法首先采用连续帧间差的4次统计量假设检验,确定运动对象的位置,自动地分离出运动区域与背景区域;在运动区域内,采用数学形态学的分水线算法来精确地提取运动对象的轮廓;最后,将提取到的运动对象作为模板,对后续的视频序列,用Hausdorff距离度量,来跟踪并提取后续帧中运动对象。实验结果表明,该方法能有效地分割和跟踪视频运动对象,且能有效减少计算复杂度,其调整参数也较少。     

ProcDef: Local‐to‐global Deformation for Skeleton‐free Character Animation

Animations of characters with flexible bodies such as jellyfish, snails, and, hearts are difficult to design using traditional skeleton‐based approaches. A standard approach is keyframing, but adjusting the shape of the flexible body for each key frame is tedious. In addition, the character cannot dynamically adjust its motion to respond to the environment or user input. This paper introduces a new procedural deformation framework (ProcDef) for designing and driving animations of such flexible objects. Our approach is to synthesize global motions procedurally by integrating local deformations. ProcDef provides an efficient design scheme for local deformation patterns; the user can control the orientation and magnitude of local deformations as well as the propagation of deformation signals by specifying line charts and volumetric fields. We also present a fast and robust deformation algorithm based on shape‐matching dynamics and show some example animations to illustrate the feasibility of our framework.     

Modeling and simulation of structural components in recursive closed-loop multibody systems

Passenger cars, transit buses, railroad vehicles, off-highway trucks, earth moving equipment and construction machinery contain structural and light-fabrications (SALF) components that are prone to excessive vibration due to rough terrains and work-cycle loads’ excitations. SALF components are typically modeled as flexible components in the multibody system allowing the analysts to predict elastic deformation and hence the stress levels under different loading conditions. Including SALF component in the multibody system typically generates closed-kinematic loops. This paper presents an approach for integrating SALF modeling capabilities as a flexible body in a general-purpose multibody dynamics solver that is based on joint-coordinates formulation with the ability to handle closed-kinematic loops. The spatial algebra notation is employed in deriving the spatial multibody dynamics equations of motion. The system kinematic topology matrix is used to project the Cartesian quantities into the joint subspace, leading to a condensed set of nonlinear equations with minimum number of generalized coordinates. The proposed flexible body formulation utilizes the component mode synthesis approach to reduce the large number of finite element degrees of freedom to a small set of generalized modal coordinates. The resulting reduced flexible body model has two main characteristics: the stiffness matrix is constant while the mass matrix depends on the elastic modal coordinates. A consistent set of pre-computed inertia shape integrals are identified and used to update the modal mass matrix at each time step. The implementation of the component mode synthesis approach in a closed-loop recursive multibody formulation is presented. The kinematic equations are modified to include the effect of the flexible body modal elastic coordinates. Also, modified constraint equations that include the effect of flexibility at the joint connections and the necessary details of the Jacobian matrix are presented. Baumgarte stabilization approach is used to stabilize the constraint equations without using iterative schemes. A sample results for flexible body impeded in a closed system will be presented to demonstrate the above mentioned approach.     

On the influence of model reduction techniques in topology optimization of flexible multibody systems using the floating frame of reference approach

Employing the floating frame of reference formulation in the topology optimization of dynamically loaded components of flexible multibody systems seems to be a natural choice. In this formulation the deformation of flexible bodies is approximated by global shape functions, which are commonly obtained from finite element models using model reduction techniques. For topology optimization these finite element models can be parameterized using the solid isotropic material with penalization (SIMP) approach. However, little is known about the interplay of model reduction and SIMP parameterization. Also securing the model reduction quality despite major changes of the design during the optimization has not been addressed yet. Thus, using the examples of a flexible frame and a slider-crank mechanism this work discusses the proper choice of the model reduction technique in the topology optimization of flexible multibody systems.     

Online prediction model for wheel wear considering track flexibility

The objective of this study is to develop a new online model for wheel wear that takes into account the track flexibility. The proposed model consists of two parts that interact with each other, namely, (a) a locomotive/track coupled dynamics model considering the track flexibility, which is validated by field measurement results, and (b) a model for the wear estimation. The wheel wear prediction model can be employed in online solutions rather than in post-processing. The effect of including the track flexibility on the wear estimation is investigated by comparing the results with those obtained for a rigid track. Moreover, the effect of the wheel profile updating strategy on the wheel wear is also examined. The simulation results indicate that the track flexibility cannot be neglected for the wheel wear prediction. The wear predicted with the rigid track model is generally larger than that predicted with the flexible track model. The strategy of maintaining unchanged wheel profiles during the dynamic simulation coincides with the online updating strategy in terms of the predicted wear.     

Modeling and robust adaptive iterative learning control of a vehicle‐based flexible manipulator with uncertainties

In this brief, this paper deals with a robust adaptive iterative learning control (ILC) problem for a flexible manipulator attached to a moving vehicle with uncertainties. To begin with, considering the infinite dimensionality of the flexible distributed parameter system, a coupled ordinary differential equation and partial differential equation model is established without any discretization. Then, it is followed by a presentation of an adaptive ILC strategy, which can drive the vehicle and joint to the desired positions based on a proportional‐derivative feedback structure with unmodeled dynamics and external disturbances. The deformation of the flexible manipulator can also be suppressed simultaneously under the proposed control laws. By using Lyapunov's direct method, the stability of the closed‐loop system is demonstrated. The simulation results are provided to illustrate the effectiveness of the proposed control laws.     

Effect of tangent track buckle on vehicle derailment

In order to investigate the effect of a tangent track buckle on the dynamic derailment of a railway vehicle, a coupled vehicle/track dynamics model is developed, in which the vehicle is modeled as a 35 D.O.F. multibody system and the track is modeled as a 3-layer discrete elastic support model. Rails are assumed to be Timoshenko beams supported by discrete sleepers, and the effects of vertical and lateral motions and rolling of the rail on the wheel/rail creepages are taken into account. The sleepers are treated as Euler beams on elastic foundation for the vertical vibration, while as lumped masses in the lateral direction. A moving sleeper support model is developed to simulate the effect of the periodical discrete sleepers on the vehicle/track interaction. The vehicle and the track are coupled by wheel/rail contacts whereas the normal forces and the creep forces are calculated using the Hertzian contact theory and the nonlinear creep theory by Shen et al., respectively. The equations of motion of the coupled vehicle/track system are solved by means of an explicit integration method. A tangent track buckle is simulated with a cosine function, which describes the misalignment of the track with different lengths due to its buckling. In the analysis the effects of the buckle wavelength and amplitude and of the vehicle speed on the dynamic behavior of the coupled vehicle/track system are considered. The present paper analyzes in detail the conventional derailment coefficients which include the ratio of the wheel/rail lateral force to the vertical force, the wheel load reduction, and the new criteria indicating the wheel/rail contact point traces and the wheel rise with respect to the rail. These criteria are simultaneously used to evaluate the risk of derailment of the whole vehicle. The numerical results obtained indicate that the track misalignment caused by the buckle and the vehicle speed have a great influence on the whole vehicle running safety when the vehicle passes through the buckled tangent track.     

Simulation of Deployment of a Flexible Solar Array

The deployment of a solar array is simulated three-dimensionally using the multibody program SIMPACK. The analyses are performed for 500 real-time seconds, which contain the three deployment phases, (I) jump-out, (II) steering phase and (III) deployed phase. The goal of the simulations is to check the influence of the flexibility of the solar array on the solar generator motions during these three phases against results obtained by a rigid body model simulation.The modelling of flexible bodies is based on the widely used method of floating frame of reference formulation applying global shape functions (Ritz method). The preparation of a proper set of shape functions to represent the flexibility of the yoke and the six solar panels is one of the main objectives of thispaper. For each of the components, eigenmodes and static modes forvarious boundary conditions are computed using the finite elementprogram NASTRAN.For a good convergence of the Ritz approximation with a smallnumber of shape functions, the shape functions are selected usingmodal participation factors, that are computed for various load casesprior to the time simulations. The load cases are obtained, for example,by a rigid body simulation of the deployment phases. The proposed methodof shape function selection using modal participation factors isdemonstrated by examples.     

An MLS-based cartoon deformation

We present an image deformation method driven by skeleton; it is based on MLS deformation algorithm (Schaefer et al. in SIGGRAPH, vol. 25, pp. 533–540, 2006). We improve the MLS deformation by defining a new weight function based on skeleton. Being different from the weight function based on control points, our weight function has benefited from the shape information of undeformed object and keeps deformation local, therefore our method can achieve a realistic effect. In cartoon video, we propose a new method to track the skeleton in the video, to build new origin skeleton and new target skeleton on each frame, and to apply our image deformation method to each frame and maintain spatiotemporal consistency. Results demonstrate that our method is able to decrease the effect of squeeze and use less control points.     

柔性轮对结构振动对车辆动力学性能的影响

为研究轮对柔性对车辆动力学的影响,建立高速列车轮对的有限元模型,对轮对进行自由模态分析.通过模态综合法获取柔性轮对模态信息,应用多体系统动力学理论建立柔性轮对-刚性轨道接触力学模型;建立包含高速旋转柔性轮对的车辆-轨道耦合动力学模型,研究高速列车在直线和曲线通过时轮对结构振动对车辆动力学性能的影响.结果表明:轮对的结构振动对轮轨接触点位置、蠕滑率、蠕滑力和脱轨因数等均产生较明显的影响,但是对轮重减载率影响较小,因此应采用更加精确的柔性轮轨耦合模型研究轮轨相互作用、轮轨滚动接触疲劳和轮轨噪声等.     

柔性多体系统动力学在直升机旋翼桨叶上的应用

提出了一种全新的计算旋翼桨叶动力响应的方法。以柔性多体系统动力学为基础，结合有限单元法和拉格朗日方程，推导出绕动轴转动的多柔体动力学质量矩阵，建立了直升机旋翼桨叶的动力学控制方程及其系数矩阵的解析表达式，采用Rung-Kutta法进行数值积分．分析了挥舞运动在强耦合状态下的运动规律。仿真结果表明采用此方法建立旋翼桨叶的动力学控制方程。可以更真实的反映桨叶的实际运动状态。     

Frame loads accuracy assessment of semianalytical multibody dynamic simulation methods of a recreational vehicle

The design of a vehicle frame is largely dependent on the loads applied on the suspension and heavy parts mounting points. These loads can either be estimated through full analytical multibody dynamic simulations, or from semi-analytical simulations in which tire and road sub-models are not included and external vehicle loads, recorded during field testing, are used as inputs to the wheel hubs. Several semi-analytical methods exist, with various modeling architectures, yet, it is unclear how one method over another improves frame loads prediction accuracy.

This study shows that a semi-analytical method that constrains the vehicle frame center of gravity movement along a recorded trajectory, using a control algorithm, leads to an accuracy within 1% for predicting frame loads, when compared to reference loads from a full analytical model. The control algorithm computes six degrees of freedom forces and moments applied at the vehicle center of gravity to closely follow the recorded vehicle trajectory. It is also shown that modeling the flexibility of the suspension arms and controlling wheel hub angular velocity both contribute in improving frame loads accuracy, while an acquisition frequency of 200 Hz appears to be sufficient to capture load dynamics for several maneuvers. Knowledge of these loads helps engineers perform appropriate dimensioning of vehicle structural components therefore ensuring their reliability under various driving conditions.

     

Dynamics modeling for a rigid-flexible coupling system with nonlinear deformation field

In this paper, a moving flexible beam, which incorporates the effect of the geometrically nonlinear kinematics of deformation, is investigated. Considering the second-order coupling terms of deformation in the longitudinal and transverse deflections, the exact nonlinear strain-displacement relations for a beam element are described. The shear strains formulated by the present modeling method in this paper are zero, so it is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motions. Then, considering the coupling terms of deformation in two dimensions, finite element shape functions of a beam element and Lagrange’s equations are employed for deriving the coupling dynamical formulations. The complete expression of the stiffness matrix and all coupling terms are included in the formulations. A model consisting of a rotating planar flexible beam is presented. Then the frequency and dynamical response are studied, and the differences among the zero-order model, first-order coupling model and the new present model are discussed. Numerical examples demonstrate that a ‘stiffening beam’ can be obtained, when more coupling terms of deformation are added to the longitudinal and transverse deformation field. It is shown that the traditional zero-order and first-order coupling models may not provide an exact dynamic model in some cases.