Cable installation simulation by using a multibody dynamic model

A major concern when installing the cables into the underground conduit is minimizing the tensile forces exerted on the cables as they are pulled. This knowledge makes it possible to avoid over conservative design practices and to achieve substantial saving during construction. A general computing algorithm of predicting the tensile force of the cable pulled through the underground conduit with an arbitrary configuration is presented in this paper, which is based on multibody system dynamic formulation. The presented multibody dynamic model for this problem consists of the cable, the underground conduit, and the interaction between the cable and the conduit. In this paper, the cable is modeled by the finite cable element based on an absolute nodal coordinate formulation. The interaction between the cable and the underground conduit is described by the Hertz contact theory. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed method for estimating the cable tension.     

Comment on spanning trees for multibody dynamic simulation

The results of [1] are generalized to accept an arbitrary search method for the construction of a spanning tree of the mechanical system graph.     

Symbolic multibody methods for real-time simulation of railway vehicles

In this work, recently developed state-of-the-art symbolic multibody methods are tested to accurately model a complex railway vehicle. The model is generated using a symbolic implementation of the principle of virtual power. Creep forces are modeled using a direct symbolic implementation of the standard linear Kalker model. No simplifications, such as base parameter reduction, partial-linearization or lookup tables for contact kinematics, are used. An Implicit–Explicit integration scheme is proposed to efficiently deal with the stiff creep dynamics. Real-time performance is achieved: the CPU time required for a very robust \(1~\text{ms}\) integration time step is 203 μs.     

基于多体力学的车辆动力学控制系统仿真及优化

利用多体分析软件ADAMS建立了多自由度汽车整车多体动力学仿真模型,并进一步简化为15自由度非线性模型,结合2自由度线性模型建立PID控制策略,进行了冰面单周正弦工况下的汽车操纵稳定性仿真试验研究,采用自适应模拟退火算法与非线性序列二次规划法相结合的组合优化方法对控制系统的控制参数进行了分析和优化.结果表明,该控制方法能够大幅度提高车辆的操纵稳定性和安全性,能够适应复杂的路面和行驶工况,取得了良好的效果.     

Performance of automatic differentiation tools in the dynamic simulation of multibody systems

Within the multibody systems literature, few attempts have been made to use automatic differentiation for solving forward multibody dynamics and evaluating its computational efficiency. The most relevant implementations are found in the sensitivity analysis field, but they rarely address automatic differentiation issues in depth. This paper presents a thorough analysis of automatic differentiation tools in the time integration of multibody systems. To that end, a penalty formulation is implemented. First, open-chain generalized positions and velocities are computed recursively, while using Cartesian coordinates to define local geometry. Second, the equations of motion are implicitly integrated by using the trapezoidal rule and a Newton–Raphson iteration. Third, velocity and acceleration projections are carried out to enforce kinematic constraints. For the computation of Newton–Raphson’s tangent matrix, instead of using numerical or analytical differentiation, automatic differentiation is implemented here. Specifically, the source-to-source transformation tool ADIC2 and the operator overloading tool ADOL-C are employed, in both dense and sparse modes. The theoretical approach is backed with the numerical analysis of a 1-DOF spatial four-bar mechanism, three different configurations of a 15-DOF multiple four-bar linkage, and a 16-DOF coach maneuver. Numerical and automatic differentiation are compared in terms of their computational efficiency and accuracy. Overall, we provide a global perspective of the efficiency of automatic differentiation in the field of multibody system dynamics.     

Parameter identification of damping models in multibody dynamic simulation of mechanical systems

To reduce vibration and noise, a damping mechanism is often required in mechanical systems. Many types of dampers are currently used. In this paper, several typical damping models, i.e., structural damping, frictional damping, and viscoelastic damping, are illustrated, and their parameters are identified for multibody dynamic simulation. Linear damping, widely adopted for structural damping, is applied to beam deflection. Quadratic damping including air resistance is applied to plate deflection. To model stick phenomenon in mechanical dampers, a STV (stick-transition velocity) model was first introduced. To identify parameters, an optimization process is applied to the damping parameters. A new MSTV (modified stick-transition velocity) model is proposed for a friction damper. A modified Kelvin–Voight model is suggested for a rubber bushing model used in vehicle dynamics, and its parameters are identified. A modified Bouc–Wen model is also proposed; it includes the hysteretic behavior of an elastomer, and optimized results with parameter identification are compared to test results.     

Use of penalty formulations in dynamic simulation and analysis of redundantly constrained multibody systems

The determination of particular reaction forces in the analysis of redundantly constrained multibody systems requires the consideration of the stiffness distribution in the system. This can be achieved by modeling the components of the mechanical system as flexible bodies. An alternative to this, which we will discuss in this paper, is the use of penalty factors already present in augmented Lagrangian formulations as a way of introducing the structural properties of the physical system into the model. Natural coordinates and the kinematic constraints required to ensure rigid body behavior are particularly convenient for this. In this paper, scaled penalty factors in an index-3 augmented Lagrangian formulation are employed, together with modeling in natural coordinates, to represent the structural properties of redundantly constrained multibody systems. Forward dynamic simulations for two examples are used to illustrate the material. Results showed that scaled penalty factors can be used as a simple and efficient way to accurately determine the constraint forces in the presence of redundant constraints.     

A criterion on inclusion of stress stiffening effects in flexible multibody dynamic system simulation

This paper presents a criterion on inclusion of stress stiffening effects in dynamic simulation of flexible multibody systems. The proposed criterion examines numerically the eigenvalue variation of the total modal stiffness matrix that is a combination of the modal stress stiffness matrix and the conventional linear modal stiffness matrix prior to actual dynamic simulation. If the variation is sufficiently large for any flexible body in the multibody system, then stress stiffening effects must be included in dynamic simulation of flexible multibody systems for accurate prediction of dynamic behavior. Since the criterion uses the most general stress stiffness matrix contributed from applied and constraint reaction loads as well as from a system of 12 inertial loads, this criterion is applicable to any general flexible multibody dynamic system. Several numerical results are presented to show the effectiveness of the proposed criterion.     

移动通信车辆动态组网抗干扰效能评估仿真

针对传统的评估方法非移动通信车辆动态组网抗干扰效能评估不准确的问题,提出基于最大离差法与支持向量机法相互结合的移动通信车辆动态组网抗干扰效能评估方法,在分析移动通信车辆动态组网结构及评估指标的基础上,对移动通信车辆动态组网信息进行预处理,增加信息的准确度;引入基于最大离差法与支持向量机法相互结合,建立移动通信车辆动态组网抗干扰效能评估模型,实现抗干扰效能的评估。实验结果证明,采用改进的评估方法时,其评估相对误差较小,抗干扰效能评估性能好,具有一定的优势。     

Dynamics simulation of multibody chains on a transputer system

The paper describes the implementation on a transputer system of a novel parallel algorithm for dynamics simulation of a multibody chain. The algorithm is formulated at a level of parallelism which is natural for the problem but is essentially unavailable to other simulation dynamics algorithms. The experimental results demonstrate that one can improve efficiency of computation by exploiting this level of parallelism. However, analysis of the performance shows that the serial component of the resulting parallel algorithm grows to be a large fraction of the total parallel execution time and therefore limits the speedup that can be achieved with this approach.     

Dynamic simulation of crankshaft multibody systems

General multibody system approaches are often not sufficient for specific situations in applications to yield an efficient and accurate solution. We concentrate on the simulation of the crankshaft dynamics which is characterized by flexible bodies and force laws describing the interaction between the bodies. The use of the floating frame of reference approach in our model leads to an index-2 DAE system. The algebraic constraints originate from the reference conditions and the normalization equation for the quaternions. For the time integration of this system, two aspects have to be taken into account: firstly, for efficiency exploiting the structure of the system and using parallelization. Secondly, consistent initial values also with respect to a related index-3 system have to be computed in order to compute missing initial velocities and to reduce transient phenomena. The work of C.B. Drab, J.R. Haslinger, and R.U. Pfau is supported by the “Bundesministerium für Wirtschaft und Arbeit” and by the government of Upper Austria within the framework “Industrielle Kompetenzzentren und Netzwerke”.     

复杂环境下车辆动力模型计算机仿真与研究

TORQUE是一种基于三维图形库OPENGL的仿真引擎。本文通过三维建模软件的引入,实现了仿真系统场景的构建,分析了STL模型的存储特点,设计并实现了STL模型的读入和优化处理,提高了整个系统的三维图形模拟效果和运行效率。借助于多体受力分析工具ADAM,以复杂环境下的行驶车辆为研究对象,构建了受力模型和运动方程,较为客观的描述了机车的运行规律,并分析了各个因素对车辆行驶安全性的影响,为驾驶人员提供了参考,对提高机车行驶安全具有一定的促进作用。     

Optimization of flexible components of multibody systems via equivalent static loads

An optimization methodology that iteratively links the results of multibody dynamics and structural analysis software to an optimization method is presented to design flexible multibody systems under dynamic loading conditions. In particular, rigid multibody dynamic analysis is utilized to calculate dynamic loads of a multibody system and a structural optimization algorithm using equivalent static loads transformed from the dynamic loads are used to design the flexible components in the multibody dynamic system. The equivalent static loads, which are derived from equations of motion, are used as multiple loading conditions of linear structural optimization. A simple example is solved to verify the proposed methodology and the pelvis part of the biped humanoid, a complex multibody system which consists of many bodies and joints, is redesigned using the proposed methodology.     

An improved dynamic modeling of a multibody system with spherical joints

A dynamic modeling of multibody systems having spherical joints is reported in this work. In general, three intersecting orthogonal revolute joints are substituted for a spherical joint with vanishing lengths of intermediate links between the revolute joints. This procedure increases sizes of associated matrices in the equations of motion, thus increasing computational burden of an algorithm used for dynamic simulation and control. In the proposed methodology, Euler parameters, which are typically used for representation of a rigid-body orientation in three-dimensional Cartesian space, are employed to represent the orientation of a spherical joint that connects a link to its previous one providing three-degree-of-freedom motion capability. For the dynamic modeling, the concept of the Decoupled Natural Orthogonal Complement (DeNOC) matrices is utilized. It is shown in this work that the representation of spherical joints motion using Euler parameters avoids the unnecessary introduction of the intermediate links, thereby no increase in the sizes of the associated matrices with the dynamic equations of motion. To confirm the efficiency of the proposed representation, it is illustrated with the dynamic modeling of a spatial four-bar Revolute-Spherical–Spherical-Revolute (RSSR) mechanism, where the CPU time of the dynamic modeling based on proposed methodology is compared with that based on the revolute joints substitution. Finally, it is explained how a complex suspension and steering linkage can be modeled using the proposed concept of Euler parameters to represent a spherical joint.     

Subsystem synthesis method with approximate function approach for a real-time multibody vehicle model

This paper presents the subsystem synthesis method with approximate function approach for a real-time multibody vehicle dynamics model. In the subsystem synthesis method, equations of motion for the car body of a vehicle and the equations of motion for suspension subsystems are formed separately for efficient computation. Joint coordinates are used to construct suspension subsystem equations of motion. Since these joint coordinates must satisfy the loop closure constraint equations that represent suspension linkage kinematics, they are not all independent. Using the generalized coordinate partitioning method, suspension subsystem equations of motion can be represented only in terms of independent generalized coordinates. To represent dependent coordinates as a function of independent coordinates in the generalized coordinate partitioning method, expensive numerical approaches, such as the Newton–Raphson method, must be applied. For real-time computation of the multibody vehicle model, an approximate function approach is proposed to express the dependent coordinates as polynomial functions of the independent coordinates within the framework of the subsystem synthesis method. Different orders of candidate polynomial functions are investigated for solution accuracy. Efficiency of the proposed method has been studied theoretically by counting arithmetic operators. By measuring actual CPU times of the simulations with a quarter car and a full car model, efficiency of the proposed method has also been investigated.     

刚性轮—土壤相互作用的多体动力学仿真研究*

车轮与松软地面相互作用的研究对越野车辆的设计、性能评价和行驶操作等至关重要。提出了一种新的多体系统大规模接触碰撞理论与地面力学理论相结合的车轮土壤相互作用仿真方法。基于自行开发的多体动力学仿真软件研制了车轮土壤相互作用模块并构建了单轮土槽多体仿真模型。对相同实验条件下得到的仿真与实验结果的对比分析表明,该仿真算法具有较高的工程实用性。     

Off-line identification of dynamic loads

This paper considers off-line identification of spatial and temporal characteristics of a dynamic load, and is focused on the case of a limited number of sensors. Both elastic and elasto-plastic structural behaviours are taken into account. The identification is performed off-line, based on optimisation of modelled local structural responses, and—in the case of limited number of sensors—identifies an observationally equivalent load, which in a given sense optimally approximates the actual load. Compared to previous researches this approach allows to identify general dynamic loads of unknown locations, including multiple impacts and moving loads, and gives more insight into the identification process by distinguishing between the reconstructible and unreconstructible load components. Additionally, the problem of optimum sensor location is discussed. The author gratefully acknowledges the financial support of the Polish Research Projects DIADYN (PBZ-KBN-105/T10/2003) and MAT-INT (PBZ-KBN-115/T08/2004). Parts of this paper will be used in a coming book “Smart Technologies for Safety Engineering” to be published by John Wiley & Sons in 2008.     

动力学系统实时仿真数值方法研究

从6个方面概述动力学系统实时仿真数值方法的一些最近的研究进展，内容包括：产时仿真快速混合算法、实时并行Rosenbrock算法、实时并行组合算法、微分代数系统的实时算法与实时并行算法、实时间断处理并行算法以及一些并行算法的效率分析等。给出构造实时仿真算法新的思想和方法，同时也涉及一些有关问题的讨论。