Flexible Multibody Dynamics Research Articles

Optimal design of a variable-twist proprotor incorporating shape memory alloy hybrid composites

The tiltrotor blades, or proprotor, act as a rotor in the helicopter mode and a propeller in the airplane mode. The helicopter mode generally requires relatively a low built-in twist angle, whereas in the airplane mode, a high built-in twist is desired. Meeting these rather conflicting requirements make the tiltrotor design a challenging task. This paper explores an optimal design of a variable-twist proprotor that changes the built-in twist in an adaptive manner by using the shape memory alloy hybrid composite (SMAHC). The optimum design problem attempts to find the cross-section internal layout that maximizes the twist actuation of the variable-twist proprotor while satisfying a series of design constraints. An optimum design framework is constructed in the current work by combining various analysis and design tools, such as an active composite cross-sectional analysis, a nonlinear flexible multibody dynamics analysis, a 3-D strain analysis, and a gradient-based optimizer. The MATLAB is used to integrate and synthesize the individual tools. A static tip twist is chosen as an objective function that should be maximized for the best performance. The optimum results exhibit that the twist actuation of the variable-twist proprotor can be maximized while satisfying all the prescribed design constraints.

Efficient balancing-based MOR for large-scale second-order systems

Large-scale structure dynamics models arise in all areas where vibrational analysis is performed, ranging from control of machine tools to microsystems simulation. To reduce computational and resource demands and be able to compute solutions and controls in acceptable, that is, applicable, time frames, model order reduction (MOR) is applied. Classically modal truncation is used for this task. The reduced-order models (ROMs) generated are often relatively large and often need manual modification by the addition of certain technically motivated modes. That means they are at least partially heuristic and cannot be generated fully automatic. Here, we will consider the application of fully automatic balancing-based MOR techniques. Our main focus will be on presenting a way to efficiently compute the ROM exploiting the sparsity and second-order structure of the finite element method (FEM) semi-discretization, following a reduction technique originally presented in [V. Chahlaoui, K.A. Gallivan, A. Vandendorpe, and P. Van Dooren, Model reduction of second-order system, in Dimension Reduction of Large-Scale Systems, P. Benner, V. Mehrmann, and D. Sorensen, eds., Lecture Notes in Computer Science and Engineering, Vol. 45, Springer Verlag, Berlin, 2005, pp. 149–172], [Y. Chahlaoui, D. Lemonnier, A. Vandendorpe, and P. Van Dooren, Second-order balanced truncation, Linear Algebra Appl. 415 (2006), pp. 373–384], [T. Reis and T. Stykel, Balanced truncation model reduction of second-order systems, Math. Comput. Model. Dyn. Syst. 14 (2008), pp. 391–406] and [J. Fehr, P. Eberhard, and M. Lehner, Improving the Reduction Process in Flexible Multibody Dynamics by the Use of 2nd Order Position Gramian Matrices, Proceedings ENOC, St. Petersburg, Russia, 2008]. Large-scale sparse solvers for the underlying matrix equations solved in the balancing process are adapted to the second-order structure of the equations and the suitability of our approach is demonstrated for two practical examples.

Validation of comprehensive dynamics analysis predictions for a rotor in descending flight

PurposeThe purpose of this paper is to evaluate the prediction capability of comprehensive structural dynamics (CSD) analysis codes for the higher harmonic control aeroacoustic rotor test (HART) II data.Design/methodology/approachA nonlinear flexible multibody dynamics analysis code DYMORE, as well as the comprehensive analytical model of rotorcraft aerodynamics and dynamics (CAMRAD) II, are used to perform the task. The predicted results on rotating free vibration analysis, airloads, blade elastic motions, and structural moments are correlated with the measured data for the baseline, minimum noise, and minimum vibration cases.FindingsThe DYMORE analysis results with a free wake model show a good performance in capturing blade vortex interaction peaks in the prediction of section normal forces but apparently with a phase shift problem. The high‐frequency behavior in the airloads signal does not affect much on the aeroelastic response and structural moments of the rotor.Originality/valueThe present approach uses two separate CSD codes to systematically validate the HART II data. The accuracy of each code on structural dynamic aspects of HART II rotor is assessed using a consistent set of inputs. The effects of blade tip deflections on the interaction of blades and their trailed vortices leading to a reduced noise emission are also investigated.

Research on MFBD Modeling Method for a Gantry Machining Center Beam Components

In modern machining processes, Gantry Machining Center is one of the most important machine tools. Moreover, beam components directly relate to the overall performance. From multi-body simulation (MBS) and finite element analysis (FEA) respectively, the paper discusses current state of the multi-body dynamics modelling of the machine tool components in domestic and overseas. In this paper, We adopt a method, the multi-flexible body dynamics(MFBD) modeling method for machine tool transmission components (linear guidance and ball screw drives) in software Recurdyn, to create the conditions for MFBD simulation analysis of the beam components system. Much more, it provides a way of MFBD modelling for machine tools components in both the high-speed and high-performance.

Coupling Analysis of Dynamics and Oil Film Lubrication on Rotor - Floating Bush Bearing System

A coupling calculation method using dynamics and lubrication for a rotor and floating bush bearing system has been developed to predict self-excited oscillations and unbalance oscillations using a flexible multibody dynamics technique with hydrodynamic lubrication theory. Based on experimental results using a floating bush bearing, an accurate and numerically efficient lubrication model is proposed to calculate the hydrodynamic force, the bush rotating speed and the temperature of the oil film. In the multibody dynamics analysis, the rotor was modeled using the finite element method to include bending elasticity and the gyroscopic effect. The bearing bush was modeled by a rigid body. The coupling analysis between the rotordynamics and the oil film force of the bearing was performed by an in-house flexible multibody dynamics solver. Subsequently, the detailed mechanism of the rotor oscillation and the influence of some design parameters were investigated by numerical simulations and experiments.

Coupled Analysis of Piston Mechanism and Lubrication (Numerical Calculation of Piston Skirt Friction)

In this study, we have developed a coupled analysis method of piston dynamics and lubrication. The kinematic motion and structural vibration are calculated by the flexible multibody dynamics theory developed in the former study. The mixed lubrication film between the piston skirt and the cylinder bore is numerically modeled as a force element. The hydrodynamic pressure and the friction force in fluid lubrication region on this interface are solved by a finite difference method. The contact pressure and the friction force by solid contact are calculated by the statistic asperity contact model. This mixed lubrication model is validated by a reciprocating friction tester. Then, we apply this method to the estimation of the friction force measured by a floating liner type friction tester at firing condition, and clarify the contributions of hydrodynamic and solid contact on the friction force.

329 B-spline要素の柔軟マルチポディダイナミクスへの応用に関する研究

329 B-spline要素の柔軟マルチポディダイナミクスへの応用に関する研究

Investigation of a theoretical problem in spacecraft dynamics

Recent study to solve the problems of flexible multi-body dynamics mainly depends on the numerical, quantitative methods and almost no one involves in the analytical discussion. It is unfavorable to understand profoundly the essence of nonlinear mechanics of the system and to predict the feature of overall dynamics of system. Therefore, it is the need to study theoretical analysis of flexible multi-body system. The research of this paper carries out to adapt this need. The theoretical problem is discussed which is coming with the projection of the vector equations in a suitable moving coordinate system. Then some important results are obtained. The important results show that not only the theoretical analysis of flexible multi-body system has been necessary, but also it has provided reference for the modeling of flexible multi-body system.

Dynamics of variable-length tethers with application to tethered satellite deployment

The dynamics of variable-length tethers are studied using a flexible multibody dynamics method. The governing equations of the tethers are derived using a new, hybrid Eulerian and Lagrangian framework, by which the mass flow at a boundary of a tether and the length variation of a tether element are accounted for. The variable-length tether element based on the absolute nodal coordinate formulation is developed to simulate the deployment of satellite tethers. The coupled dynamic equations of tethers and satellites are obtained using the Lagrangian multiplier method. Several tethered satellite systems involving large displacements, rotations, and deformations are numerically simulated, where the tethers are released from several meters to about 1 km. A control strategy is proposed to avoid slackness of the tethers during deployment. The accuracy of the modeling and solution procedures was validated on an elevator model.

A flexible approach to the simulation of hybrid multibody systems

AbstractThe present works deals with the incorporation of both flexible beam and shell structures into the realm of flexible multibody dynamics. Geometrically exact beam formulations based on classical Simo‐Reissner kinematics are suitable for modelling beam‐type flexible components in the context of finite‐deformation multibody dynamics. So geometrically exact shell formulations are based on Reissner‐Mindlin kinematics.In [2], a flexible framework for dealing with flexible structural elements in a multibody context is described. A specific isoparametric finite element discretization of a shell formulation leads to semi‐discrete equations of motions assuming the form of differential‐algebraic equations (DAEs). A compatible isoparametric formulation of beams has already been developed in [1].The uniform DAE framework makes possible the incorporation of alternative finite element formulations. In addition to that, various time‐stepping schemes such as energy‐momentum methods or variational integrators can be applied. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling and Dynamic Analysis for Rigid-Flexible Coupling Nonlinear Floating Raft Vibration Isolation System

To analyze the influence of the nonlinearity of the floating raft vibration isolation system, the theory of flexible multibody dynamics was used here to model the rigid-flexible coupling nonlinear floating raft vibration isolation system. The dynamical characteristics of the model were studied with ADAMS software and some typical nonlinear phenomena, such as subharmonics, superharmonics and attractor coexistence, were observed through time domain analysis.

Research on Dynamic Characteristics of 750KW Wind Turbine Flexible Blades

It is necessary and fitting to use flexible multibody dynamics method to study the wind turbine blades. Because the characteristics of the blades will directly affect the whole wind turbine’s, and the results by using flexible multibody method are to agree with reality. Considering the anisotropic composite blades, it established the flexible blades model and rigid-flexible wind rotor model of the 750KW wind turbine by the software of ANSYS and ADAMS. Then fit the loads which are computed from BLADE to the wind rotor, analyze the dynamic characteristics of the rotor. It gets the dynamic features of the flexible blades and the rigid blades’ as a comparison, which will be useful to research on WTGS, and will supply reference data to blade trouble analysis and optimization design.

Correlation study of a rotor in descending flight using DYMORE with a freewake model

In this work, the Blade Vortex Interaction (BVI) airloads characteristic for a rotor in descending flight condition is investigated using a nonlinear flexible multibody dynamics analysis code DYMORE. A free vortex wake model is incorporated into the comprehensive analysis system and improvement of airloads prediction as well as collective and cyclic pitch control settings is obtained over the finite-state dynamic inflow model that is adopted in the conventional DYMORE analysis. The three test conditions in the HART (Higher harmonic control Aeroacoustic Rotor Test) II are considered to illustrate the present investigation. It is found that the BVI airloads characteristic is significantly influenced by the higher harmonic pitch control inputs. The influence of BVI oscillatory peaks along with the miss-distance between the blade and the vortices is studied in detail to identify the mechanism of reducing noise and vibration in the HART II experiment.

중량물의 동적 거동에 미치는 크레인 붐(boom)의 탄성 영향 분석

In this paper, in order to analyze the dynamic response of a floating crane when it lifts a heavy cargo, the boom of the floating crane is considered as an elastic beam. The boom is divided into elements based on finite element formulation and the floating frame of reference formulation and nodal coordinates are employed to model the boom as a flexible body. As an extension of the previous study, in order to consider spatial motion in waves, the coupled equations of motions of the 6 degree of freedom (DOF) floating crane and 6 DOF cargo are developed based on the flexible multibody system dynamics. The 3 dimensional deformation of the elastic boom is considered with 18 DOF. The dynamic simulation of the floating crane and the cargo is performed under regular wave conditions with various cargo weights. Finally, the effects of the elastic boom on lifting cargo are discussed by comparing the simulation results between the elastic boom and a rigid boom.

Erratum to: New efficient method for dynamic modeling and simulation of flexible multibody systems moving in plane

Efficient, precise dynamic analysis for general flexible multibody systems has become a research focus in the field of flexible multibody dynamics. In this paper, the finite element method and component mode synthesis are introduced to describe the deformations of the flexible components, and the dynamic equations of flexible bodies moving in plane are deduced. By combining the discrete time transfer matrix method of multibody system with these dynamic equations of flexible component, the transfer equations and transfer matrices of flexible bodies moving in plane are developed. Finally, a high-efficient dynamic modeling method and its algorithm are presented for high-speed computation of general flexible multibody dynamics. Compared with the ordinary dynamics methods, the proposed method combines the strengths of the transfer matrix method and finite element method. It does not need the global dynamic equations of system and has the low order of system matrix and high computational efficiency. This method can be applied to solve the dynamics problems of flexible multibody systems containing irregularly shaped flexible components. It has advantages for dynamic design of complex flexible multibody systems. Formulations as well as a numerical example of a multi-rigid-flexible-body system containing irregularly shaped flexible components are given to validate the method.

Error-Controlled Model Reduction in Flexible Multibody Dynamics

One important issue for the simulation of flexible multibody systems is the quality controlled reduction in the flexible bodies degrees of freedom. In this work, the procedure is based on knowledge about the error induced by model reduction. For modal reduction, no error bound is available. For Gramian matrix based reduction methods, analytical error bounds can be developed. However, due to numerical reasons, the dominant eigenvectors of the Gramian matrix have to be approximated. Within this paper, two different methods are presented for this purpose. For moment matching methods, the development of a priori error bounds is still an active field of research. In this paper, an error estimator based on a new second order adaptive global Arnoldi algorithm is introduced and further assists the user in the reduction process. We evaluate and compare those methods by reducing the flexible degrees of freedom of a rack used for active vibration damping of a scanning tunneling microscope.

Variational Integrators and Energy-Momentum Schemes for Flexible Multibody Dynamics

This work contains a comparison between variational integrators and energy-momentum schemes for flexible multibody dynamics. In this connection, a specific “rotationless” formulation of flexible multibody dynamics is employed. Flexible components such as continuum bodies and geometrically exact beams and shells are discretized in space by using nonlinear finite element methods. The motion of the resulting discrete systems are governed by a uniform set of differential-algebraic equations (DAEs). This makes possible the application and comparison of previously developed structure-preserving methods for the numerical integration of the DAEs. In particular, we apply a specific variational integrator and an energy-momentum scheme. The performance of both integrators is assessed in the context of three representative numerical examples.

붐(Boom)의 탄성을 고려한 해상크레인의 비선형 정적/동적 거동을 위한 수치 해석

해상크레인은 크레인을 탑재한 선박으로서, 조선소에서 대형 블록이나 구조물의 탑재 및 해상 운송 작업에 사용된다. 본 논문에서는 해상크레인과 중량물의 전후 동요(Surge), 상하 동요(Heave), 종 동요(Pitch)에 대한 정적/동적 거동을 분석하였다. 이 때, 유연 다물체계 동역학을 적용하여 해상크레인의 붐(boom)을 탄성으로 고려하였으며, 플로팅 프레임(floating frame)과 노드 좌표(nodal coordinates)를 사용하였다. 질량 행렬, 탄성 강성 행렬, 2 차 속도 벡터, 일반화 좌표 방향으로 작용하는 외력 등을 고려하여 모든 운동이 연성된 비선형 운동 방정식을 구성하였다. 외력으로는 비선형 유체정역학 힘, 선형화된 유체동역학 힘, wire rope 힘, 계류력이 고려되었다. 수치 해석을 위해 Hilber-Hughes-Taylor 방법을 비선형 운동방정식에 적용하였다. 정적 거동 분석을 통한 정적 평형 자세를 고려한 경우와 고려하지 않은 경우에 대해 결과를 비교하였으며, 수치 해석 방법에 대한 정적/동적 거동 분석 결과를 비교하였다.

ADVANCES IN THE ABSOLUTE NODAL COORDINATE METHOD FOR THE FLEXIBLE MULTIBODY DYNAMICS

Firstly,the research background of the multibody system dynamics theory is presented and shortcomings of the conventional methods for investigating flexible multibody dynamics are illustrated.Secondly, the advances in the absolute nodal coordinate method for the flexible multibody dynamics research over the last ten years are systematically reviewed in terms of the following four aspects,i.e.the advances in the element researches,the numerical algorithm researches,the researches on the dynamics of multibody systems with nonlinear materials and the researches of corresponding applications.Finally,key topics for further research are pointed out.

Fatigue analysis of the main frame of over head transportation vehicles using flexible multibody dynamics

The industrial over head transportation vehicle is a guided railway vehicle that is attached overhead and transports cargo, hoisting it up and down from the factory ceiling. The vehicle is widely used in many industries, such as automobile and liquid crystal display (LCD), because it can carry freight very safely and quickly to destinations. This kind of freight transportation usually operates for several months to a few years, carrying large amounts of products. Accidently, the vehicle often fails during operation because of a part’s plastic deformation from large loads. Furthermore, periodic dynamic loads cause fatigue accumulation, which leads to OHT failure. This failure is directly connected to significant economic loss during mass production processes. Therefore, the prediction of fatigue life for the important parts becomes an important task. In this study, the fatigue life of an OHT main frame was calculated and predicted by using a flexible multibody dynamic model. The development of a flexible multibody dynamic model and the procedure of fatigue life prediction were presented. To predict the fatigue lives of parts of interest, the prediction procedure required three kinds of data: Dynamic stress time history from a dynamic analysis, material properties of the parts, and stress-life curves of the parts. Using a finite element model and a multibody model, a flexible multibody model was developed. To ensure the reliability of the model, displacement and strain measurement tests were conducted. After verification of the reliability, the fatigue life of the main frame was predicted.