Modeling Of Flexible Multibody Systems Research Articles

Dynamic modeling of flexible multibody systems with complex geometry via finite cell method of absolute nodal coordinate formulation

Dynamic modeling of flexible multibody systems with complex geometry via finite cell method of absolute nodal coordinate formulation

A new subregion mesh method for the investigation of the elastic-plastic impact in flexible multibody systems

Impact processes between flexible bodies often lead to local stress concentration and wave propagation of high frequency. Therefore, the modeling of flexible multibody systems involving impact should consider the local plastic deformation and the strict requirements of the spatial discretization. Owing to the nonlinearity of the stiffness matrix, the reduction of the element number is extremely important. For the contact-impact problem, since different regions have different requirements regarding the element size, a new subregion mesh method is proposed to reduce the number of the unnecessary elements. A dynamic model for flexible multibody systems with elastic-plastic contact impact is established based on a floating frame of reference formulation and complete Lagrange incremental nonlinear finite-element method to investigate the effect of the elastic-plastic deformation as well as spatial discretization. Experiments on the impact between two bodies are carried out to validate the correctness of the elastic-plastic model. The proposed formulation is applied to a slider-crank system with elastic-plastic impact.

Coupled differential algebraic equations in the simulation of flexible multibody systems with hydrodynamic force elements

AbstractThe mathematical modelling of elastohydrodynamic bearings in combustion engines leads to a coupled system of (partial) differential algebraic equations, which is represented by a flexible multibody system model of the engine including crankshaft and bearing and by the Reynolds equation that describes the non‐linear effects in the fluid film. The hydrodynamic forces depend strongly on the position and the elastic deformation of crankshaft and bearing shell. We discuss the influence of the spatial discretization on accuracy and numerical effort. Since a fine spatial discretization substantially slows down the numerical solution, we propose a semi‐analytical method based on singular perturbation theory to speed‐up time integration. Numerical tests for a simplified benchmark problem illustrate the advantages of this approach. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Aspects of Symbolic Formulations in Flexible Multibody Systems

The symbolic modeling of flexible multibody systems is a challenging task. This is especially the case for complex-shaped elastic bodies, which are described by a numerical model, e.g., an FEM model. The kinematic and dynamic properties of the flexible body are in this case numerical and the elastic deformations are described with a certain number of local shape functions, which results in a large amount of data that have to be handled. Both attributes do not suggest the usage of symbolic tools to model a flexible multibody system. Nevertheless, there are several symbolic multibody codes that can treat flexible multibody systems in a very efficient way. In this paper, we present some of the modifications of the symbolic research code Neweul-M2 which are needed to support flexible bodies. On the basis of these modifications, the mentioned restrictions due to the numerical flexible bodies can be eliminated. Furthermore, it is possible to re-establish the symbolic character of the created equations of motion even in the presence of these solely numerical flexible bodies.

Parametric Flexible Multibody Model for Material Removal During Turning

This work presents a flexible multibody system model for the inside turning of thin-walled cylinders. The model accounts for the varying input and output behavior of the workpiece due to workpiece rotation and tool feed, as well as the changing workpiece dynamics due to material removal. A parametric approach is used to incorporate the effect of material removal. Hereby, a number of systems are precalculated for different machined states that are then interpolated to obtain the model for the desired machined state. As different systems typically have different vectors of degrees of freedom, a preprocessing step must be added to guarantee compatibility and thus a meaningful interpolation. In this work, two ways of obtaining a parametric model are presented that lead to similar results. The parametric model is then used to analyze stability of an inside turning operation. By taking into account the varying workpiece dynamics, an improved tool feed is suggested that would allow to greatly reduce the cycle time.

Methods & Prospects of Research on Flexible Multi-Body Dynamics

This paper summarized the research method of flexible multi-body system dynamics. Three stages of flexible multi-body system model are reviewed. The paper is especially summary on modeling method of flexible multi-body system, flexible multi-body dynamical equation numerical calculation and flexible multi-body system vibration control and so on. And the paper is looked forward to further study.

Object-oriented modelling of general flexible multibody systems

This paper presents a general approach to object-oriented modelling of flexible multibody systems, based on the floating frame of reference (FFR) formulation. The data describing a flexible body can be computed analytically, having defined its shape functions matrices, or calculated by several finite element method (FEM) packages as a result of a modal analysis. By the proposed approach, a modular model is then obtained in an object-oriented language, namely Modelica. This allows to integrate very realistic descriptions of distributed flexibility in multidomain models, with significant advantages for a variety of simulation studies. After describing the general methodology, the paper presents some simulation results, to validate the approach with respect to benchmark cases considered in the literature.

Improving the dynamic stability of a workpiece dominated turning process using an adaptronic tool holder

In this contribution, inside turning of a thin-walled cylinder is investigated in simulation. Self-excited vibrations can arise due to repeated cutting of the same surface, that lead to instability. A flexible multibody system model of the system is the basis for a subsequent analysis of the stability of the process. Stability analysis is done using an approximation as a time-discrete system via the semi-discretization method. An adaptronic turning chisel comprising a piezo actuator and sensors is then used in combination with different control concepts to improve the stability of the process. The effectiveness of the different strategies is compared based on the influence on the stability charts. A classic H∞ controller based on a model of the coupled system of workpiece and tool can only yield some improvements, when an additional measurement of the workpiece displacement is added. Incorporating knowledge on the cutting process coupling workpiece and tool using a gain scheduled H∞ controller allows further improvements. However, robustness with respect to model uncertainties, notably concerning the force law, remains an issue.

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.

Active Vibration Control for a Machine Tool With Parallel Kinematics and Adaptronic Actuator

The use of adaptronic components opens up interesting new possibilities for modern machine tools such as parallel kinematics. In this paper, two active vibration control concepts are designed for an adaptronic component of a parallel kinematic machine tool. The machine tool is modeled as a flexible multibody system model including a nonlinear flatness-based position control. Both the combination of a frequency shaped linear quadratic regulator with an active damping concept in a high authority control/low authority control approach and the H2 optimal control with gain scheduling show a high potential in the simulation to significantly increase the disturbance rejection or the tracking performance of the machine tool.

An adaptronic approach to active vibration control of machine tools with parallel kinematics

In recent years, more and more lightweight components are used in machine tools in order to provide advantages in highly dynamic applications because of their reduced mass. One major drawback of these lightweight systems is their sensitivity to structural vibrations which are induced by high jerks during fast positioning and the machining process itself. Moreover, in case of parallel kinematic structures, the dynamic response depends nonlinearly on the actual pose of the mechanism in the workspace. In this paper, a concept for active vibration control for a machine tool with planar parallel kinematics is presented. For this purpose, an adaptronic rod has been developed and integrated into the existing machine tool. The unit consists of a high-power lead–zirconate–titanate piezo stack actuator, which is able to induce forces in longitudinal direction of the rod, and various sensors so that different control concepts from the field of active vibration control can be implemented and tested. Based on a flexible multibody system model of the machine tool, a hierarchical controller consisting of an integrated force feedback as low authority Control combined with a frequency-shaped linear quadratic regulator has been designed. The experimental results presented here demonstrate the ability of the chosen approach to clearly suppress the first dominating resonance without loss of performance in the low frequency range, which is often a serious problem of active damping concepts.

Nonlinear Position Control of a Scissor‐like Kinematics with Elastic Bodies

AbstractParallel kinematics such as the described machine tools with scissor‐like kinematics present as nonlinear mechanical and strongly coupled systems with flexible bodies new challenges in the design and control of machine tools. Linear and independently controlled drives become infeasible due to the parallel setup, machine vibrations become important because lightweight designs are used. Advanced nonlinear and multi‐variable control methods show the potential to significantly increase the system performance. Furthermore, flexible multibody system models are a powerful tool for the controller design and evaluation in simulations. In this paper, a rigid as well as a flexible multibody system model of a test machine with scissorlike kinematics is developed. Experimental results with the machine prove that the developed nonlinear flatness‐based position controller is able to reduce the trajectory error significantly and that is is possible to achieve an adequate system performance with a nonlinear algorithm in a standard control setup for machine tools. Simulation results with the flexible multibody system further accentuate the need for additional measures such as active vibration damping if flexibilities and process forces are present in the system. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dynamic Modelling of Mechatronic Multibody Systems With Symbolic Computing and Linear Graph Theory

The application of linear graph theory to the modelling of flexible multibody systems is described. When combined with symbolic computing methods, linear graph theory leads to efficient dynamic models that facilitate real-time simulation of systems of rigid bodies and flexible beams. The natural extension of linear graphs to the modelling of mechatronic multibody systems is presented, along with a recently-developed theory for building complex system models from models of individual subsystems.

Computational strategies for flexible multibody systems

The status and some recent developments in computational modeling of flexible multibody systems are summarized. Discussion focuses on a number of aspects of flexible multibody dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies. The characteristics of the three types of reference frames used in modeling flexible multibody systems, namely, floating frame, corotational frame, and inertial frame, are compared. Future directions of research are identified. These include new applications such as micro- and nano-mechanical systems; techniques and strategies for increasing the fidelity and computational efficiency of the models; and tools that can improve the design process of flexible multibody systems. This review article cites 877 references.

Non-linear dynamics of flexible multibody systems

In this work we set to examine several important issues pertinent to currently very active research area of the finite element modeling of flexible multibody system dynamics. To that end, we first briefly introduce three different model problems in non-linear dynamics of flexible 3D solid, a rigid body and 3D geometrically exact beam, which covers the vast majority of representative models for the particular components of a multibody system. The finite element semi-discretization for these models is presented along with the time-discretization performed by the mid-point scheme. In extending the proposed methodology to modeling of flexible multibody systems, we also present how to build a systematic representation of any kind of joint connecting two multibody components, a typical case of holonomic contraint, as a linear superposition of elementary constraints. We also indicate by a chosen model of rolling contact, an example of non-holonomic constraint, that the latter can also be included within the proposed framework. An important aspect regarding the reduction of computational cost while retaining the consistency of the model is also addressed in terms of systematic use of the rigid component hypothesis, mass lumping and the appropriate application of the explicit–implicit time-integration scheme to the problem on hand. Several numerical simulations dealing with non-linear dynamics of flexible multibody systems undergoing large overall motion are presented to further illustrate the potential of presented methodology. Closing remarks are given to summarize the recent achievements and point out several directions for future research.

Finite Element Method in Dynamics of Flexible Multibody Systems: Modeling of Holonomic Constraints and Energy Conserving Integration Schemes

In this work we discuss an application of the finite elementmethod to modeling of flexible multibody systems employing geometricallyexact structural elements. Two different approaches to handleconstraints, one based on the Lagrange multiplier procedure and anotherbased on the use of release degrees of freedom, are examined in detail.The energy conserving time stepping scheme, which is proved to be wellsuited for integrating stiff differential equations, gouverning themotion of a single flexible link is appropriately modified and extendedto nonlinear dynamics of multibody systems.

Bond-graph modelling of flexible robots: the residual flexibility

An accurate modelling of flexible multibody systems is not a simple task because the flexible phenomena involve complex models which, at times, cannot be used in simulation and control. The object of this paper is to present some bond-graph modelling procedures of a flexible slender beam which can have relatively large planar displacements. The model can then be incorporated into the model of a multibody system with rigid beams.

Rayleigh-Ritz based substructure synthesis for flexible multibody systems

This paper is concerned with the modeling of flexible multibody systems by a Rayleigh-Ritz based substructure synthesis method, so that certain advantages can be accrued by using the variational approach to derive the eigenvalue problem. As with the classical Rayleigh-Ritz method, if the admissible functions used to represent the motion of the substructures are not chosen properly, convergence can suffer. This paper presents a new substructure synthesis method with superior convergence characteristics achieved by representing the motion by means of a recently developed class of functions, namely, the class of quasi-compari son functions. This improved convergence is shown to be related to improved approximation of both the differential equations and the natural boundary conditions. The theory is demonstrated by means of a numerical example. I. Introduction T HIS investigation is concerned with the modeling of flexible multibody systems. Many structures, such as fixedwing aircraft, helicopters, flexible spacecraft, flexible robots, etc., can be modeled as assemblages of interacting flexible bodies. A method proposed by Hurty1'2 in the early 1960s, and known as component-mode synthesis, consists of modeling the motion of the individual substructures, referred to as components, by means of He uses three types of modes to represent the motion of a substructure: rigid-body modes, constraint modes, and normal modes. To define constraint modes, Hurty divides the constraints into two classes, statically determinate and redundant. The constraint modes are equal in number to the number of redundant constraints and are defined by producing a unit displacement on each redundant constraint in turn, with all other constraints fixed. The normal modes represent the modes of vibration of the components with all constraints fixed. An approach by Craig and Hampton3 differs from that of Hurty 1'2 mainly in the selection of the component modes. Indeed, Craig and Hampton suggest two types of component modes: boundary modes providing for displacements and rotations at points along the substructure boundaries, and related to the constraint modes of Hurty, and substructure modes corresponding to completely restrained boundaries. The substructures modeled individually in Refs. 1-3 are made to act together as a single structure by eliminating the redundant generalized coordinates arising from the fact that displacements at points common to two adjacent substructures are included twice in the overall problem formulation, once for each substructure. The elimination process is based on the use of constraint equations resulting from the enforcement of compatibility conditions, which amounts to saying that the displacement of a boundary point shared by two substructures is the same. In another approach to the problem, proposed by

Force and Position Control of Industrial Robots for Manufacturing Purposes

In this paper contrary to the majority of conventional position control algorithms for industrial robots (IR) which are based on rigid multi-body system models a more realistic control concept will be presented that refers to a flexible multi-body system model It provides a much better disturbance behaviour because the deflection of each joint and its time derivative are additionally considered in the closed-loop algorithm. Further improvement can be achieved by a feedforward compensation. Disturbing effects of nonlinear slip-stick friction can be compensated by the injection of high-frequency “dithering”. Moreover superimposed force control algorithms for the automatic tactile edge and surface scanning of work pieces by means of a force/torque wrist sensor will be proposed.

On the Dynamics and Control of a Flexible Industrial Robot

There are several advanced manufacturing tasks like the highly accurate cutting of geometrically difficult metal surfaces which have not yet been solved in the past by means of industrial robots because of their flexible properties mainly, caused by elasticity, plasticity or backlash within the gears. In this paper contrary to the majority of conventional position control algorithms which are based on rigid multibody system models, an alternative control concept is proposed that refers to a more realistic flexible multi-body system model. It provides both a better tracking and disturbance behaviour because not only the servo motor position but also the deflection of each joint and its time derivatives are considered in the closed-loop algorithm. Disturbing nonlinear effects of slip-stick friction can be compensated by the injection of high-frequency “dithering”. The performance quality of the proposed control concept which has been implemented on a microcomputer system will be thoroughly investigated.