Aeroelastic Effects in Multibody Dynamics

To enable a realistic assessment of the aeroelastic phenomena of aircraft, a simultaneous application of computational fluid dynamics (CFD), computational structural mechanics and flight mechanics has to be performed. Each discipline has developed powerful specialized tools which have to be adapted for multidisciplinary applications. The combination of CFD and elastic multibody systems is well suited for the simulation of a range of aircraft applications, especially for aircraft ground dynamics. Approaches to a coupling of elastic multibody systems and computational fluid dynamics have been performed using close coupling, that is a modal approach, and loose coupling, that is by co-simulation. In the article the applied programs and the coupling methods are presented. Advantages and limits of using multibody simulation as compared to the direct use of FEA methods for the representation of structural dynamics are discussed. Results of coupled steady and unsteady simulations are presented. Finally, an approach to the aeroelastic trim problem is shown.     

基于ADAMS的装载机多体动力学研究

采用虚拟样机设计技术建立装载机模型，考虑到轮胎与工作机构的相互影响，对装载机的上坡过程进行纵向稳定性分析，模拟不同的坡度下装载机的上坡能力，得出最大坡度时装载机可能出现的运动现象；并对此做出了分析，结果表明与物理样机实测情况基本一致。     

General Purpose Vehicle System Dynamics Software Based on Multibody Formalisms

SUMMARY

This paper pursues two objectives: Firstly, to review the state-of-the-art of general purpose vehicle system dynamics software and secondly, to describe two representatives, the program MEDYNA and the program NEWEUL. The general modeling requirements for vehicle dynamics software, the multibody system approach and a comparative discussion of multibody software are given. The two programs NEWEUL and MEDYNA are described with respect to modeling options, computational methods, software engineering as well as their interfaces to other software. The applicability of these programs is demonstrated on two selected examples, one from road vehicle problems and the other from wheel/rail dynamics. It is concluded that general purpose software based on multibody formalisms will play the same role for mechanical systems, especially vehicle systems, as finite element methods play for elastic structures.     

General Purpose Vehicle System Dynamics Software Based on Multibody Formalisms

This paper pursues two objectives: Firstly, to review the state-of-the-art of general purpose vehicle system dynamics software and secondly, to describe two representatives, the program MEDYNA and the program NEWEUL. The general modeling requirements for vehicle dynamics software, the multibody system approach and a comparative discussion of multibody software are given. The two programs NEWEUL and MEDYNA are described with respect to modeling options, computational methods, software engineering as well as their interfaces to other software. The applicability of these programs is demonstrated on two selected examples, one from road vehicle problems and the other from wheel/rail dynamics. It is concluded that general purpose software based on multibody formalisms will play the same role for mechanical systems, especially vehicle systems, as finite element methods play for elastic structures.     

基于多体动力学的柴油机曲轴疲劳寿命分析

为分析4100QBZL柴油机曲轴的疲劳寿命,建立该曲柄连杆机构的刚柔耦合多体动力学模型,将多组试验测量的缸内压力作为驱动力,进行耦合仿真得到曲轴在柔性体模型下的主轴颈、连杆轴颈负荷仿真结果,并根据载荷结果对曲轴进行静强度校核。最后结合由多体动力学软件得到的载荷谱与有限元分析所得的曲轴在各个工况下的应力应变分析结果,以及通过材料的各项属性拟合出的S-N曲线,对曲轴进行了疲劳寿命预测。结果表明:曲轴的静强度及疲劳寿命均达到了工程设计要求,曲轴最危险部位的寿命次数也达到了1013以上,认为曲轴不会发生疲劳破坏。     

基于多体动力学的车辆悬架控制臂载荷谱混合分布外推研究

试验场强化路载荷谱外推全寿命载荷谱是汽车构件疲劳耐久性能评判准确性的关键因素,针对参数法外推单分布估计的局限性,引入混合分布估计描述载荷谱多峰或复杂分布的综合特征。基于试验场强化路实车测试,应用多体动力学与有限元联合仿真,提取控制臂危险点应力谱;分别应用单分布和混合分布法解算应力谱拟合优度,以此为据选取应力谱最优均值、幅值概率密度并将应力谱循环外推至10⁶次,应用FKM平均应力修正法编制8级应力谱,依据Miner准则分别从载荷幅值分布、损伤分布以及总损伤量等方面对单分布与混合分布外推应力谱进行综合分析。研究结果表明：应用拟合优度能较好评估两分布对应力谱均、幅值拟合程度,混合分布拟合效果优于单分布,拟合优度均为98%,对应力谱分布特征描述更为精确,可为外推提供较真实的载荷分布概率密度,从而提高外推载荷谱精度;比较应用2种分布拟合的外推载荷谱,损伤分布趋势相近,中级载荷损伤占比高,单分布外推载荷谱总损伤量为6.3×10^-4,大于混合分布外推载荷谱总损伤为5×10^-4,寿命预测偏于保守,导致耐久性设计裕度较大,应用混合分布外推能提高耐久性评估与轻量化设计精度。     

Spatial Dynamics of Multibody Tracked Vehicles Part I: Spatial Equations of Motion

In this paper, the nonlinear dynamic equations of motion of the three dimensional multibody tracked vehicle systems are developed, taking into consideration the degrees of freedom of the track chains. To avoid the solution of a system of differential and algebraic equations, the recursive kinematic equations of the vehicle are expressed in terms of the independent joint coordinates. In order to take advantage of sparse matrix algorithms, the independent differential equations of the three dimensional tracked vehicles are obtained using the velocity transformation method. The Newton-Euler equations of the vehicle components are defined and used to obtain a sparse matrix structure for the system dynamic equations which are represented in terms of a set of redundant coordinates and the joint forces. The acceleration solution obtained by solving this system of equations is used to define the independent joint accelerations. The use of the recursive equations eliminates the need of using the iterative Newton-Raphson algorithm currently used in the augmented multibody formulations. The numerical difficulties that result from the use of such augmented formulations in the dynamic simulations of complex tracked vehicles are demonstrated. In this investigation, the tracked vehicle system is assumed to consist of three kinematically decoupled subsystems. The first subsystem consists of the chassis, the rollers, the sprockets, and the idlers, while the second and third subsystems consist of the tracks which are modeled as closed kinematic chains that consist of rigid links connected by revolute joints. The singular configurations of the closed kinematic chains of the tracks are also avoided by using a penalty function approach that defines the constraint forces at selected secondary joints of the tracks. The kinematic relationships of the rollers, idlers, and sprockets are expressed in terms of the coordinates of the chassis and the independent joint degrees of freedom, while the kinematic equations of the track links of a track chain are expressed in terms of the coordinates of a selected base link on the chain as well as the independent joint degrees of freedom. Singularities of the transformations of the base bodies are avoided by using Euler parameters. The nonlinear three dimensional contact forces that describe the interaction between the vehicle components as well as the results of the numerical simulations are presented in the second part of this paper.     

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.     

整车转弯制动控制仿真研究

转弯制动是汽车行驶中的常见工况。为了研究在该工况下对汽车控制时的各项性能，建立了整车非线性多体动力学模型．仿真分析了样车的操纵稳定性、平顺性和制动性能；利用ADAMS与MATLAB联合仿真技术，针对汽车在转弯制动的工况下的动态特性，对前轮转向和悬架采取联合控制，仿真结果表明所采用的模糊PID控制方法能较好地改进汽车的行驶性能。     

Flexible Bodies in Multibody System Codes

SUMMARY

Multibody codes are'efficient tools to simulate nonlinear dynamic behaviour of rigid and flexible multibody systems undergoing large overall motions overlaid by small elastic deformation. This paper gives an overview of common approaches for the equations of motion of flexible body models and presents a general way to prepare the required data including geometric stiffening terms. In particularly, for the nodal approach the data are derived using standard results of a finite element analysis of the body. The computation of coefficient matrices describing the equations of motion is done outside the finite element code by matrix manipulations only. The data are stored in a standardised object-oriented structure. Consequently, the data set is independent of the formulation of the multibody system code.     

A Report on the State-of-Affairs on “Application of Multibody Computer Codes to Vehicle System Dynamics”

SUMMARY

This report gives a preview to a state-of-the-art paper and a special session which are devoted to the problem of the applicability of multibody computer codes to vehicle system dynamics. These activities were initiated at the 11th IAVSD Symposium 1989 in Kingston, CAN, followed by a workshop in Herbertov, CSR, and to be reported at the 12th IAVSD Symposium in Lyon, 1991. The concluding documentation will be a special issue of the VSD journal. The status of this report is what has been achieved up to May 1991.     

Flexible Bodies in Multibody System Codes

Multibody codes are'efficient tools to simulate nonlinear dynamic behaviour of rigid and flexible multibody systems undergoing large overall motions overlaid by small elastic deformation. This paper gives an overview of common approaches for the equations of motion of flexible body models and presents a general way to prepare the required data including geometric stiffening terms. In particularly, for the nodal approach the data are derived using standard results of a finite element analysis of the body. The computation of coefficient matrices describing the equations of motion is done outside the finite element code by matrix manipulations only. The data are stored in a standardised object-oriented structure. Consequently, the data set is independent of the formulation of the multibody system code.     

Design of a Stroke Dependent Damper for the Front Axle Suspension of a Truck Using Multibody System Dynamics and Numerical Optimization

Summary A stroke dependent damper is designed for the front axle suspension of a truck. The damper supplies extra damping for inward deflections rising above 4 cm. In this way the damper should reduce extreme suspension deflections without deteriorating the comfort of the truck. But the question is which stroke dependent damping curve yields the best compromise between suspension deflection working space and comfort. Therefore an optimization problem is defined to minimize the maximum inward suspension deflection subject to constraints on the chassis acceleration for three typical road undulations. The optimization problem is solved using sequential linear programming (SLP) and multibody dynamics simulation software. Several optimization runs have been carried out for a small two degree of freedom vehicle model and a large full-scale model of the truck semi-trailer combination. The results show that the stroke dependent damping can reduce large deflections at incidental road disturbances, but that the optimum stroke dependent damping curve is related to the acceleration bound. By means of vehicle model simulation and numerical optimization we have been able to quantify this trade-off between suspension deflection working space and truck comfort.     

Modeling and Analysis of Nonlinear Multibody Systems

SUMMARY

The method of multibody systems is introduced for the modeling of nonlinear vehicle systems. The equations of motion and the equations of reaction are found. For the dynamical analysis a classification of nonlinear phenomena is presented using objective and subjective criteria. As an illustrative example the dynamical behaviour of a four-body pendulum is investigated.     

Symbolic-numerical Solution of Multibody Systems with Closed Loops

For multibody systems with closed kinematic Loops a set of ordinary differential equations and decoupled algebraic equations is formulated which can be solved with explicit multistep integration algorithms. This is achieved by introducing a minimal set of generalized coordinates being specified during numerical integration. For avoiding restart of the integration algorithm after changing these variables transformation relationships are given. Velocity and acceleration constraints are satisfied exactly, position constraints are fulfilled approximately by a dynamic invariant projection onto the constraint manifold. The method is demonstrated by an application to a five-point wheel suspension.     

Symbolic-numerical Solution of Multibody Systems with Closed Loops

SUMMARY

For multibody systems with closed kinematic Loops a set of ordinary differential equations and decoupled algebraic equations is formulated which can be solved with explicit multistep integration algorithms. This is achieved by introducing a minimal set of generalized coordinates being specified during numerical integration. For avoiding restart of the integration algorithm after changing these variables transformation relationships are given. Velocity and acceleration constraints are satisfied exactly, position constraints are fulfilled approximately by a dynamic invariant projection onto the constraint manifold. The method is demonstrated by an application to a five-point wheel suspension.     

桥梁气弹响应分析的时域气动模型

为了解决传统桥梁气弹响应分析方法因非定常不可压流CFD计算量巨大而导致的效率低下问题,提出一种桥梁气弹响应分析的新方法。该方法采用频域特性可调的广谱指数脉冲时间序列强迫桥梁断面运动,并通过CFD计算得到作用在桥梁断面上的气动力,然后由桥梁断面的运动位移和气动力时程,通过系统识别建立起桥梁绕流系统的时域离散时间气动模型。最后以具有扭转自由度的薄平板在初始位移激励下的运动为例,进行了振动响应计算和气弹全过程分析。研究结果表明:该方法能显著提高桥梁气弹响应分析的计算效率。     

Overview of Coupling of Multibody and Control Engineering Tools

The role of Computer Aided Engineering in vehicle development has been significantly increased during the last decade. Specialised simulation tools became very complex, however, growing demands on complexity and particularly interdisciplinarity of vehicles and their simulation models have led to a number of approaches trying either to develop multidisciplinary simulation tools or to connect various specialised simulation tools by interfaces. This paper addresses some aspects of interconnection of the specialised simulation tools as one possibility for simulating complex mechatronic vehicle systems. It classifies the interfaces between specialised software packages in general, mentions some historical development of the interfacing and further discusses the examples of the implemented couplings between the Multibody System codes and Computer Aided Control Engineering tools. Finally, the performance of selected interfaces is compared on an example simulation of a controlled vehicle suspension.     

Multibody dynamics modelling of the freight train bogie system

Previous work in the railway technology laboratory at Virginia Polytechnic Institute and State University (Virginia Tech) focused on better capturing the dynamics of the friction wedge, modelled using three-dimensional rigid body dynamics with unilateral contact conditions. The current study extends the previous work to a half-bogie model treated as an application of multibody dynamics with unilateral contact to model the friction wedge interactions with the bolster and the sideframe. The half-bogie model was derived using MATLAB and functions as a three dimensional, dynamic, and multibody dynamics model comprised of four rigid bodies: a bolster, two friction wedges, and a sideframe assembly. This expanded model allows each wedge four degrees of freedom: vertical displacement, longitudinal displacement (between the bolster and sideframe), pitch (rotation around the lateral axis), and yaw (rotation around the vertical axis). The bolster and the sideframe are constrained to have only the vertical degree of freedom. The geometry of these bodies can be adjusted for various simulation scenarios. The bolster can be initialised with a pre-defined yaw (rotation around the vertical axis) and the sideframe may be initialised with a pre-defined pitch/toe (rotation around the lateral axis). The results of the multibody dynamics in half-bogie model simulation are shown in comparison with results from NUCARS^®, an industry standard in train-modelling software, for similar inputs.