Method Of Multibody Systems Research Articles

A novel method for the dynamic modeling of Stewart parallel mechanism

This paper presents a new scenario for the dynamic modeling of Stewart parallel mechanism based on transfer matrix method for linear multibody systems (linear MSTMM). The mechanism is modeled as a flexible multibody system, where the platform is rigid while the legs are flexible. All the element transfer equations are re-written in the same inertial coordinate system, which significantly simplifies the deduction of the system overall transfer equation. The vibration characteristics are computed by solving homogeneous linear algebraic equations, and then the augmented eigenvector and body dynamics equation are adopted to derive the state space representation by combining modal superposition method. Without deducing system global dynamics equation, the proposed scenario is easy to formulate, systematic to apply, and can model the legs as flexible bodies without spatial discretization. Then, Hankel model reduction and LQR control are employed to demonstrate how to make use of the derived state space representation. A numerical study is performed to validate the presented method. Although the system considered in this work is Stewart parallel mechanism, the scenario is general and can be used for other linear time invariant multibody systems.

Research on precision of modular machine tool based on computer aided multi-body system method

Modularity of machine tool, an engineering technology that deals with cost-effective and quick reaction to all the market changes, is urgently needed in the modern manufacturing companies. However, a general accuracy analytical method of modular machine tool is seldom concerned. The basic module error of the machine tool is synthesized by the theory of computer aided multi-body system, a universal accuracy model for modular machine tools has been established. The developed mathematical model is used to calculate and predict the resultant position error at the tool–workpiece interface for error compensation. Results show the method based on the computer aided multi-body system only depends on the motion of module and fits for rapid modeling of computer technology, and error factors such as thermal expansion and deforming under loads can be involved in the analysis processing except the geometric error.

Free Vibration Modeling and Computation of Reinforced Thermoplastic Pipe (RTP) Conveying Fluid in Off/Inshore Industry Applications

Reinforced Thermoplastic Pipe (RTP) is a composite material flexible pipe. Due to RTP superior behavior, it encouraged the industry for using to offshore and inshore applications. Marine risers and cross-country pipelines resting on elastic medium are slender flexible structures conveying fluid and exhibit complex dynamic behaviors. Therefore, it requires accurate dynamic modeling for prediction the vibration characteristics. Transfer Matrix Method for Multibody Systems (MSTMM) is one of the sophisticated methods that can be used efficiently to model large systems and calculate its vibration characteristics and dynamic responses. The size of matrices in MSTMM remains small regardless of the number of elements in the model. Having smaller matrix sizes helps to have less computational expense leading to a faster answer. Based on the MSTMM advantages and Euler-Bernoulli linear theory, transfer matrix of the pipe in both offshore and inshore industry applications is built-up for vibration analysis. Recursive eigenvalue search algorithm is used to determine the system frequencies. Numerical examples are performed to validate with those published in the open literature.

Flapwise Vibration Computations of Coupled Helicopter Rotor/Fuselage: Application of Multibody System Dynamics

Natural vibration characteristics of rotating blades are of fundamental importance from the viewpoint of maneuvering, blade life, vibration levels, aeroelastic, and stability. Helicopters may have serious resonant vibration problems when the excitation frequencies are equal to some multiple of the rotational speed. To ensure that conditions susceptible to resonance do not exist within the range of operating speeds, it is necessary that the natural frequencies and mode shapes be determined accurately. On one hand, as the complexity of multibody systems and the methods used for their design and control increases, the need for more elegant formulations of the equations of motion becomes an issue of paramount importance. On the other hand, although processor speed has increased dramatically over the last decade, development of computationally efficient algorithms is still a major issue in multibody dynamics. The transfer matrix method for multibody systems (MSTMM) accounts for both aspects. Based on many advantages of MSTMM in studying multibody system dynamics, a scenario of dynamics coupling between the flexible twin blade rotor and flexible fuselage of a typical helicopter model is proposed. The dynamical model of the coupled system, its topological figure, the overall transfer equation, and the characteristics equation are developed. The flapwise vibrations characteristics are carried out to obtain uncoupled/coupled twin blade/fuselage system natural modes and frequencies as a function of rotor speed. Examples are performed to validate with those published in the literature and produced by Workbench ANSYS.

An efficient parallel algorithm for flexible multibody systems based on domain decomposition method

Recently, a large number of lightweight flexible structures are successfully used in the field of aerospace industry, intelligent robot and 3D printing. Because of the increasing flexibility of elastic components, some large scale mechanical systems will perform typical rigid-flexible coupled dynamic characteristic. Previous studies have indicated that the traditional modeling methods of the flexible multibody system based on the assumptions of small rotations and small deformation, such as the floating frame of reference method, can not lead to correct results for the dynamic response of those large deformation structures. Under the framework of Isogeometric analysis, the basis functions of the NURBS are employed to discretize the displacement field of elastic components with large deformation. Based on the large deformation theory of the continuum mechanics, the geometrical nonlinearity of planar structures undergoing the overall motion and large deformation is accurately taken into account. In order to improve the computational efficiency, some efficient formulations to calculate the elastic force and the tangent stiffness matrix are proposed via the invariant matrix method. Furthermore, based on the finite element tearing and interconnecting (FETI) method, an efficient parallel algorithm is presented to deal with the dynamic equations of motion for flexible multibody systems. First, the governing partial differential equations of multibody systems are transformed into a set of nonlinear algebraic equations after spatial and time discretization. Then, the preconditioned conjugate gradient method is exploited to solve the linearization equation in parallel. Compared with the existing parallel direct methods for flexible multibody systems, the proposed method can improve the computational efficiency significantly. Finally, several numerical examples are given to validate the effectiveness of the proposed parallel algorithm, including the complexity, the speed-up ratio and the scalability.

Visualized simulation and design method of mechanical system dynamics based on transfer matrix method for multibody systems

The transfer matrix method for multibody systems is a new method with very high computational speed developed in recent 20 years for studying multibody system dynamics. By combining transfer matrix...

Influence of model order reduction methods on dynamical–optical simulations

In this work, the influence of model order reduction (MOR) methods on optical aberrations is analyzed within a dynamical–optical simulation of a high precision optomechanical system. Therefore, an integrated modeling process and new methods have to be introduced for the computation and investigation of the overall dynamical–optical behavior. For instance, this optical system can be a telescope optic or a lithographic objective. In order to derive a simplified mechanical model for transient time simulations with low computational cost, the method of elastic multibody systems in combination with MOR methods can be used. For this, software tools and interfaces are defined and created. Furthermore, mechanical and optical simulation models are derived and implemented. With these, on the one hand, the mechanical sensitivity can be investigated for arbitrary external excitations and on the other hand, the related optical behavior can be predicted. In order to clarify these methods, academic examples are chosen and the influences of the MOR methods and simulation strategies are analyzed. Finally, the systems are investigated with respect to the mechanical–optical frequency responses, and in conclusion, some recommendations for the application of reduction methods are given.

Active Vibration Control Design Method Based on Transfer Matrix Method for Multibody Systems

AbstractThe efficient vibration control of complex multibody systems is an important issue in engineering design and has drawn substantial attention in the field of multibody system dynamics and co...

Dynamic modeling of sail mounted hydroplanes system- Part I: Modal characteristics from a transfer matrix method

Hydroelastic stability and vibration analysis of full-scale fairwater planes system/or bow planes system mounted on the sail (bridge)/or main body can be quite complex. With the aim of addressing these problems, the present paper, Part I of a two part work, focuses on two aspects: (i) modeling and computation of the natural vibration characteristics of the entire assembly system utilizing and comparing two approaches, based on a finite element commercial software ANSYS and a recently developed Transfer Matrix Method of Multibody systems (MSTMM). Results show the latter technique is computationally accurate and efficient. It is also shown that an equivalent model consisting of one hydroplane with a torsional spring under specified boundary conditions may capture the dynamics behavior of the whole system; and (ii) implementing an equivalent model and MSTMM to obtain in-vacuum uncoupled pure bending and torsional frequencies. Such a treatment of the problem enables one to get a better understanding of the various parameters involved in the linear/nonlinear hydroelastic problem from a two degrees-of-freedom (2-DOF) reduced order model.

Handling Actuator Saturation as Underactuation: Case Study With Acroboter Service Robot

Model-based control methods such as inverse dynamics control and computed torque control encounter difficulties if actuator saturation occurs. However, saturation is a common phenomenon in robotics leading to significant nonlinearity in system behavior. In this study, the saturation of the actuator torques is considered as a temporary reduction of the number of independent control inputs. The reduction of the number of actuators leads to an underactuated control problem which typically involves the handling of differential algebraic equation systems. The saturated system may become especially complex when intricate combinations of the actuator saturations appear. A servoconstraint-based inverse dynamics control method for underactuated multibody systems is applied for the treatment of actuator torque saturation. In case of human-friendly robots, the problem of saturation cannot be avoided on the level of trajectory planning because unexpected human perturbations may take place, which result in such abrupt changes in the desired trajectory that lead to saturation at some actuators. A case study for the service robot Acroboter shows the applicability of the proposed approach.

Distributed parallel computing of the recursive eigenvalue search in the context of transfer matrix method for multibody systems

The modeling and solving a transcendental eigenvalue problem are important issues in the transfer matrix method for linear multibody systems. Based on the recursive eigenvalue search algorithm for transfer matrix method for linear multibody system, the distributed parallel approach for assembling overall transfer matrix and searching eigenvalues is proposed. This is achieved based on Message Parallel Interface. The influence of the CPU core number as well as the distributed network environment on the final computational time is analyzed through numerical examples of both a non-uniform beam and a multiple launch rocket system. The results indicate that the computational time is significantly reduced by the proposed parallel computing method, so that the computational efficiency on optimization and design of complex multibody systems can be improved.

Riccati Transfer Matrix Method for Linear Tree Multibody Systems

The Riccati transfer matrix method (RTMM) improves the numerical stability of analyzing chain multibody systems with the transfer matrix method for multibody systems (MSTMM). However, for linear tree multibody systems, the recursive relations of the Riccati transfer matrices, especially those for elements with multiple input ends, have not been established yet. Thus, an RTMM formulism for general linear tree multibody systems is formulated based on the transformation of transfer equations and geometrical equations of such elements. The steady-state response under harmonic excitation of a linear tree multibody system is taken as an example and obtained by the proposed method. Comparison with the finite-element method (FEM) validates the proposed method and a numerical example demonstrates that the proposed method has a better numerical stability than the normal MSTMM.

A unified approach for treating linear multibody systems involving flexible beams

Over the last decades, various strategies have been proposed to exactly treat linear multibody systems composed of multibody system elements and flexible beams. Mostly they involve advanced calculus and are devoted to a specific system topology. On the other hand, general multibody system approaches have been developed where, however, elastic bodies can be treated only approximately. The transfer matrix method for multibody systems (MSTMM) combines both advantages: it may account for any general multibody system structure and treat beams exactly. This is achieved by introducing new connection elements in the transfer matrix method which allow to set up the overall algebraic transfer equations easily and to determine vibration frequencies by solving minimization problems. The proposed approach will be demonstrated for several beam/body examples taken from specialized literature.

Dynamic response multiobjective optimization of road vehicle ride quality—A computational multibody system approach

Computational multibody system (MBS) method is a practical technique utilized for modeling, simulation, and optimization of mechanical systems. In the methodology of computational multibody system, equations of motion are derived, formulated, and solved through a systematic, generalized, and well-structured computational-mathematical approach. In this paper, the computational multibody system formulation, based on the appended Lagrangian method, is implemented to establish the governing equations of ride dynamics for a nonlinear ride model that represents a versatile half-car two-track model of a road vehicle. The input to the system is a simulated road surface model based on the ISO road surface classification. The solution of the equation of motion is obtained using the direct integration approach along with constraint violation elimination and control techniques. Following the simulation, a time-domain multiobjective design optimization procedure is performed to improve the ride quality of the model. The ride quality comprises both ride comfort and ride safety. The optimization considers relevant objective functions including vibration isolation, suspension travel, road holding, and force index. The results of work show that the proposed method could acceptably estimate the optimal values of design variables for specific road classes and vehicle driving speeds. The simulation-based ride quality optimization performed here could facilitate improvement of suspension and tyre.

Comparison of two model order reduction methods for elastic multibody systems with moving loads

In this paper, two different model order reduction approaches for elastic multibody systems with moving loads are considered. The first approach is based on a parametric formulation of the input an...

Vector form intrinsic finite element method for planar multibody systems with multiple clearance joints

A new computational methodology is presented for the dynamic analysis of multibody systems with multiple clearance joints by vector form intrinsic finite element method. A joint model is developed to simulate the motion of ideal and clearance joints for multibody systems. The dynamic behaviour of a four-bar mechanism with three clearance joints in continuous contact mode is analysed. The results show that the dynamic performance of the mechanism with three clearance joints in continuous contact mode is not similar to that with ideal joints and is fluctuating and affected by the clearance size of the joints and input crank speed.

A new version of transfer matrix method for multibody systems

In order to avoid the global dynamics equations and increase the computational efficiency for multibody system dynamics (MSD), the transfer matrix method of multibody system (MSTMM) has been developed and applied very widely in research and engineering in recent 20 years. It differs from ordinary methods in multibody system dynamics with respect to the feature that there is no need for a global dynamics equation, and it uses low-order matrices for high computational efficiency. For linear systems, MSTMM is exact even if continuous elements like beams are involved. The discrete time MSTMM, however, has to use local linearization. In order to release the method from such approximations, a new version of MSTMM is presented in this paper where translational and angular accelerations, on the one hand, and internal forces and moments, on the other hand, are used as state variables. Already linear relationships among these quantities are utilized, which results in new element transfer matrices and algorithms making the study of multibody systems as simple as the study of single bodies. The proposed approach also allows combining MSTMM with any general numerical integration procedure. Some numerical examples of MSD are given to demonstrate the proposed method.

Analysis of the response of a reinforced concrete shear wall structure during earthquakes using the transfer matrix method of multibody systems

Although reinforced concrete shear wall structures are widely used in high-rise buildings, the methods used to analyze the seismic response of such a structure during an earthquake generally have low calculation efficiencies. In this article, the transfer matrix method of multibody systems is first established as a mechanical model of a regular reinforced concrete shear wall structure with both bifurcated and closed transfer paths to analyze the seismic responses of structures. By separating the shear wall legs, establishing a state vector relationship between the two endpoints of the coupling beams, and combining all state vectors of the inputs or outputs of each shear wall leg, the total transfer between shear wall legs is realized, and the overall transfer equation and overall transfer matrix of a shear wall structure are obtained. Applying the transfer matrix method of multibody systems, a 15-story shear wall structure is used as an engineering example to analyze seismic responses for frequent and rare earthquakes using MATLAB software. The findings show that the transfer matrix method of multibody systems provides similar results to ANSYS but that the transfer matrix method of multibody systems greatly increases calculation efficiency while maintaining accuracy.

On the equivalent static load method for flexible multibody systems described with a nonlinear finite element formalism

SummaryThe equivalent static load (ESL) method is a powerful approach to solve dynamic response structural optimization problems. The method transforms the dynamic response optimization into a static response optimization under multiple load cases. The ESL cases are defined based on the transient analysis response whereupon all the standard techniques of static response optimization can be used. In the last decade, the ESL method has been applied to perform the structural optimization of flexible components of mechanical systems modeled as multibody systems (MBS). The ESL evaluation strongly depends on the adopted formulation to describe the MBS and has been initially derived based on a floating frame of reference formulation. In this paper, we propose a method to derive the ESL adapted to a nonlinear finite element approach based on a Lie group formalism for two main reasons. Firstly, the finite element approach is completely general to analyze complex MBS and is suitable to perform more advanced optimization problems like topology optimization. Secondly, the selected Lie group formalism leads to a formulation of the equations of motion in the local frame, which turns out to be a strong practical advantage for the ESL evaluation. Examples are provided to validate the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

An Approach Regarding Windshield Wiper Mechanism Design

This research presents the use of a computer oriented numerical approach in the characterization of a parallelogram mechanism used on automobile windscreen wipers. The aim is to perform a kinetostatic analysis for obtaining through numerical simulations the joint reaction forces for a parameterized mechanism. Based on a combination between classical methods and computer simulations using Multi-body System method, the friction forces between wipers blades and windshield will be evaluated. The obtained results add new contributions on automobile windshield wiper mechanism design and analysis.