Complex Multibody Systems Research Articles

Impact-induced vibration in complex flexible multi-body systems: numerical and experimental investigation of press machines

This article is concerned with the numerical and experimental investigations of impact-induced vibrations in highly non-linear complex multibody system applications. In order to accurately model the impact response of such complex systems, a computational procedure based on the integration of finite element and multibody system algorithms is used. This procedure, which employs the finite element floating frame of reference formulation, allows for defining arbitrary joint constraint and forcing functions, for accurately capturing the coupling between the rigid body motion and the elastic deformation, and for modeling the impact forces between rigid and flexible bodies in the multibody system model. The system equations of motion are developed using the augmented Lagrangian formulation that allows for the use of sparse matrix techniques. The algorithm used in this study ensures that the kinematic constraint equations are satisfied at the position, velocity, and acceleration levels. The impact-induced vibration of a highly non-linear press machine is numerically and experimentally examined in this study. In order to accurately model the dynamic behavior of such a press machine, it is necessary to model the transfer feeder elastic deformations resulting from the impulsive impact forces. The deformations of the transfer press system as well as those of its frame are modeled in this investigation using the floating frame of reference formulation that allows for effectively reducing the number of degrees of freedom by filtering out very high-frequency modes of vibration using component mode synthesis techniques. The formulations of several relative angle and angular velocity kinematic constraints that are required to model this multibody system are developed in order to model transfer feeder complex rotational components. The numerical results obtained using the three-dimensional multibody system transfer press model developed in this study are validated using experimental results.

The Research on Model Updating Technology of Complex Multibody System Virtual Prototyping

In this paper, the concept and application of virtual prototype technology are simply introduced, and analyses the veracity program in course of complex multi-body system simulation. The rigid-flexible couple virtual prototype model of complex multi-body system including collision is built, and the veracity of virtual prototype simulation is evaluated combining limited test data. Updating some typical system parameters by sensitivity method and perturbation method, it makes the simulation results have better consistency with test results, and improves the simulation precision of virtual prototype model.

325 マルチボディシステムのリカーシブ動力学計算法の高速化

Multibody dynamics have a wide range of applications including automobiles, railways, robots, rotating machinery, and so on. In order to conduct dynamics simulation of complex multibody systems, efficient forward dynamics algorithms are needed. The most basic and conventional algorithms have O(N^3) complexities where N is the number of degrees of freedom, due to the explicit computation of inverse of the inertia matrix, while Schiehlen proposed an elegant algorithm with O(N^2) complexity based on a representation through recursive formulation of kinematic and dynamic relationships. In this paper, we develop a new algorithm for further acceleration of the forward dynamics computation by modifying the Schiehlen's method. The algorithm achieves O(N) complexity and has the short and compact description that leads to easy maintainability of the program.

New Approach to the Modeling of Complex Multibody Dynamical Systems

In this paper, a general method for modeling complex multibody systems is presented. The method utilizes recent results in analytical dynamics adapted to general complex multibody systems. The term complex is employed to denote those multibody systems whose equations of motion are highly nonlinear, nonautonomous, and possibly yield motions at multiple time and distance scales. These types of problems can easily become difficult to analyze because of the complexity of the equations of motion, which may grow rapidly as the number of component bodies in the multibody system increases. The approach considered herein simplifies the effort required in modeling general multibody systems by explicitly developing closed form expressions in terms of any desirable number of generalized coordinates that may appropriately describe the configuration of the multibody system. Furthermore, the approach is simple in implementation because it poses no restrictions on the total number and nature of modeling constraints used to construct the equations of motion of the multibody system. Conceptually, the method relies on a simple three-step procedure. It utilizes the Udwadia–Phohomsiri equation, which describes the explicit equations of motion for constrained mechanical systems with singular mass matrices. The simplicity of the method and its accuracy is illustrated by modeling a multibody spacecraft system.

Research on Control and Experiment of a New Lunar Rover

Because of the complexity of the lunar environment,the lunar rover,as a complex multi-body system,has many characteristics in its dynamics behavior and its control.The analysis is more difficult than that of simple system.The mathematical models of lunar rover control,such as dynamics,motion constraints and kinematics,are presented in this paper.The harmonious control is explained by the sample of running across a ravine.For imitation of the lunar gravitational circumstances,a single wheel test device based on gas lubrication was designed.The range of the kinematic and dynamic parameters of each wheel can be determined by that device.

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.

Control of Single Wheel Robots (Xu, Y. and Ou, Y.; 2005)

The book deals with a particular type of robot consisting of a single wheel with a mechanism inside suspended from the axle providing a means for driving the wheel and containing a spinning flywheel that can be tilted to provide balance and steering. A practical robotics engineer will probably regard the single wheeled robot as an interesting academic problem, but not necessarily worthy of the extensive study necessary to follow the developments detailed in the book. The real interest in the book lies in the careful analysis of the dynamics of a complex multibody system as well as in the control of an unstable system.

A Multi-Body Space-Coupled Motion Simulation for A Deep-Sea Tethered Remotely Operated Vehicle

A multi-body coupled dynamic model is developed to simulate the motion of a Tethered Remotely Operated Vehicle (TROV) system. A strong nonlinear coupling motion between umbilical tether and ROV is discussed. The movement of ROV is considered as six-degrees of freedom. The lumped mass model is applied and an averaged tangential vector technique is included in the three-dimensional dynamic response equations of the cable-segments. The model can simulate the three-dimensional transient coupled motion of the complex multi-body system in typical ship maneuvering conditions and can be used in either a towing problem or a tethered underwater vehicle problem. Simulation results are seen to fit well with the experiment.

Linear Dynamic Modeling of Spacecraft With Various Flexible Appendages

We present here a method and some tools developed to build linear models of multi-body systems for space applications (typically satellites). The multi-body system is composed of a main body (hub) fitted with rigid and flexible appendages (solar panels, antennas, propellant tanks, …etc). Each appendage can be connected to the hub by a cantilever joint or a pivot joint. More generally, our method can be applied to any open mechanical chain. In our approach, the rigid six degrees of freedom (d.o.f) (three translational and three rotational) are treated all together. That is very convenient to build linear models of complex multi-body systems. Then, the dynamics model used to design AOCS, i.e. the model between forces and torques (applied on the hub) and angular and linear position and velocity of the hub, can be derived very easily. This model can be interpreted using block diagram representation.

Port-based Simulation of Flexible Multi-body Systems

This paper is devoted to simulation aspects of complex multi-body systems resulting from the interconnection of rigid and flexible links. This work is the natural complement of Macchelli et al. [2006, 2007a], in which only the mathematical modeling aspects of such kind of devices have been discussed. This paper tries to show how the port Hamiltonian framework can be instrumental also for the easy implementation of efficient simulations if proper packages able to deal with the a-causality of port-based modeling techniques are used. In fact, once the main components (i.e. rigid and flexible links and kinematic pairs) have been created, the complete model just follows by port interconnection in a plug-and-play fashion. Then, it is the simulation engine that solves the causality of the overall scheme and generate the simulation code. The main steps are illustrated in detail with an example.

A fast contraction mapping for solving multibody systems

AbstractThe simulation of complex multibody systems with contacts and friction requires a fast and robust solver for complementarity problems. This work presents an efficient method which can solve large cone‐complementarity problems by means of a fixed point iteration. Our method performs like a contractive mapping, providing a monotonic approximation to the exact solution. The algorithm features high computational performance even if thousands of unilateral constraints are added to the system. Also, this scheme fits well in a real‐time simulation context because it can be terminated prematurely. As a benchmark for testing the method in challenging situations, we propose the simulation of the granular flow in a fourth‐generation bebble‐bed nuclear reactor, including 150'000 rigid bodies and more than a million of constraint multipliers. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Experiment on Dynamics of the Hybrid Polishing Kinematics Machine Tool with Clearance Based on the Flexible Multi-Body Systems

This paper develops a novel five DOF hybrid polishing kinematics machine tool in order to obtain more stable machining result in the elastic polishing on the free-form surfaces. Because the machine tool is a complex multi-body system that comprises many close-loop structures, jointing clearance becomes the important influence factor to its moving stability. The unified rigid multi-body and flexible multi-body dynamics equation of for the parallel mechanism of hybrid polishing kinematics machine tool is respectively built, which considers the influence of joint with clearance and applies the kinematics model of Newton second state. The result of analysis shows that the moving stability of the hybrid polishing kinematics machine tool is reduced due to the existing jointing clearance. However, the interior flexibility of the mechanism can reduce the shock effect of collision in the part of motion pair. It can improve the working stability of mechanism.

Equilibrium analysis of multibody dynamic systems using genetic algorithm in comparison with constrained and unconstrained optimization techniques

The present paper describes a set of procedures for the solution of nonlinear equilibrium problems in complex multibody systems. To find the equilibrium position of the system, six different optimization algorithms are used to minimize the total potential energy (TPE) of the system and compared with respect to accuracy and efficiency. A computer program is developed to evaluate the equality constraints and objective function of a general multibody dynamic system to find the equilibrium condition. It is seen that the indirect methods have better results and converge faster. Also it is shown that the genetic algorithm (GA) results in a global optimum while the other methods converge to a local optimum.

A simplified force-based method for the linearization and sensitivity analysis of complex manipulation systems

In this paper a method is proposed to efficiently linearize the geometry of complex multibody systems by exploiting the kinetostatic dualism, i.e. formulating the linearization in terms of the force transmission. In this setting, an algorithm is introduced by which one can perform the linearization of the transmission behavior from any number of geometric parameters to the motion of a six-degree-of-freedom end-effector by applying six unit loads to the end-effector and determining internal forces. Moreover, applications in first-order error analysis, calculation of the stiffness matrix, and calibration of manipulators are proposed. Examples of both serial and fully parallel manipulators are presented.

Multibody formalism for real-time application using natural coordinates and modified state space

The paper describes the multibody formalism based on natural coordinates and modified state space that is suitable for real-time applications. The complex multibody systems include closed loops and thus result into DAE equations. Their simulation then usually requires iterative stabilization. The described multibody formalism has two important properties making it suitable for real-time applications. Firstly, it provides the stable solution of DAE equations for multibody systems with kinematical loops without necessity of iterations. Secondly, it consists of system matrices with simple expressions (constant, linear or quadratic terms) for their elements and thus it is very suitable for massive parallelization. The resulting computational complexity is growing only linearly with the number of DOFs despite any occurrence of kinematical loops and it is about 5 times smaller than the recursive multibody formalisms.

Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics

We present the new, general, explicit form of the equations of motion for constrained mechanical systems applicable to systems with singular mass matrices. The systems may have holonomic and/or non-holonomic constraints, which may or may not satisfy D'Alembert's principle at each instant of time. The equation provides new insights into the behaviour of constrained motion and opens up new ways of modelling complex multi-body systems. Examples are provided and applications of the equation to such systems are illustrated.

Equations of Motion for Constrained Multibody Systems and their Control

This paper presents some recent advances in the dynamics and control of constrained multibody systems. The constraints considered need not satisfy the D’Alembert principle and therefore the results are of general applicability. They show that, in the presence of constraints, the constraint force acting on the multibody system can always be viewed as made up of the sum of two components whose explicit form is provided. The first of these components consists of the constraint force that would have existed were all the constraints ideal; the second is caused by the nonideal nature of the constraints, and though it needs specification by the mechanician who is modeling the specific system at hand, it has a specific form. The general equations of motion obtained herein provide new insights into the simplicity with which Nature seems to operate. They point toward the development of new and novel approaches for the exact control of complex multibody nonlinear systems.

Two implementations of IRK integrators for real‐time multibody dynamics

AbstractRecently, several authors have proposed the use of implicit Runge–Kutta (IRK) integrators for the dynamics of multibody systems. On the other hand, Newmark‐type or structural integrators have shown to be appropriate when real‐time performance is demanded in that field. Therefore, the following question arises: might the IRK integrators be suitable for real‐time purposes? And, provided the answer is positive: might they be preferable to the Newmark‐type family?This paper reports an investigation which has been conducted by the authors in order to get insight into the two questions formulated above. Since, based on previous experiences, it can be suspected that the performance of the integrators may be dependent on the type of dynamic formulation applied, the following three formulations have been considered for the study: a global penalty formulation in dependent natural co‐ordinates (many constraints), a topological semi‐recursive penalty formulation in dependent relative co‐ordinates (few constraints), and a topological semi‐recursive formulation in independent relative co‐ordinates (no constraints).As representative of the IRK family, a two‐stage SDIRK integrator has been selected due to its low associated computational burden, while, on the side of the structural integrators, the trapezoidal rule has been chosen. Two alternative implementations have been proposed to combine the dynamic formulations and the SDIRK integrator.A very demanding maneuver of the whole model of a vehicle has been simulated through all the possible combinations dynamic‐formulation/integrator, for different time‐steps. Conclusions have been drawn based on the obtained results, which provide some practical criteria for those interested in achieving real‐time performance for large and complex multibody systems. Copyright © 2005 John Wiley & Sons, Ltd.

Dynamic Simulation of Multibody Systems Using a New State-Time Methodology

This paper presents a new methodology demonstrating the feasibility and advantages of a state-time formulation for dynamic simulation of complex multibody systems which shows potential advantages for exploiting massively parallel computing resources. This formulation allows time to be discretized and parameterized so that it can be treated as a variable in a manner similar to the system state variables. As a consequence of such a state-time discretization scheme, the system of governing equations yields to a set of loosely coupled linear-quadratic algebraic equations that is well-suited in structure for some families of nonlinear algebraic equations solvers. The goal of this work is to develop efficient multibody dynamics algorithm that is extremely scalable and better able to fully exploit anticipated immensely parallel computing machines (tera flop, peta flop and beyond) made available to it.

Stability Analysis of Complex Multibody Systems

The linearized stability analysis of dynamical systems modeled using finite element-based multibody formulations is addressed in this paper. The use of classical methods for stability analysis of these systems, such as the characteristic exponent method or Floquet theory, results in computationally prohibitive costs. Since comprehensive multibody models are “virtual prototypes” of actual systems, the applicability to numerical models of the stability analysis tools that are used in experimental settings is investigated in this work. Various experimental tools for stability analysis are reviewed. It is proved that Prony’s method, generally regarded as a curve-fitting method, is equivalent, and sometimes identical, to Floquet theory and to the partial Floquet method. This observation gives Prony’s method a sound theoretical footing, and considerably improves the robustness of its predictions when applied to comprehensive models of complex multibody systems. Numerical and experimental applications are presented to demonstrate the efficiency of the proposed procedure.