Multibody System Dynamics Research Articles

Research progress in multi-body system dynamics modeling in stomatology

The stomatognathic system is an organic combination of bone, dentition, joints, masticatory muscles and innervation nerves. It is an organ system for the human body to perform mastication, speech, swallowing and other important functions. Due to the complex anatomical structure of stomatognathic system and ethical limitations, it is difficult to directly measure the movement and force by using the biomechanical experimental methods. Multi-body system dynamics is an important tool to study the kinetics and force of a multi-body system, which consists of several objects with relative motion. We can use the method of multi-body system dynamics simulation in engineering to study the movement, soft tissue deformation and force transfer of this complex stomatognathic system. This paper briefly introduces the history and application methods of multi-body system dynamics and the commonly used modeling methods. The application and research progress of multi-body system dynamics modeling methods in the field of stomatology was emphatically summarized, development prospects of current research and difficulties were put forward.

Dynamic Response of 15 MW Floating Wind Turbine With Non-Redundant and Redundant Mooring Systems Under Extreme and Accidental Conditions

AbstractThis work focuses on examining the dynamic behavior of large floating offshore wind turbine (FOWT) exposed to extreme (wind and wave with 50-year return period) and accidental (mooring line breakage) loadings. The FOWT considered is 15 MW reference turbine supported on semi-submersible platform stationed using catenary moorings. As the mooring configuration greatly affects the response of FOWT, two different mooring configurations namely non-redundant (three-line) and redundant (six-line) systems were studied and compared. The coupled multi-body dynamic system was solved using Openfast. When simulating the mooring line failure, both the operating and extreme loading conditions were considered. Failure of one mooring was considered at a time. The response of the coupled system due to breakage of the mooring indicates high displacements in surge and sway directions in comparison to the intact system especially for the non-redundant mooring system. Furthermore, change in platform yaw angle and increased tension in the other intact mooring lines were observed. The findings from this study will be helpful in accidental limit state design and preventing failure of similar large FOWT systems. In addition, insights into using non-redundant and redundant mooring configurations for such large structures with respect to extreme and accidental loadings were also discussed.

The simulation of the rigid-flexible coupling model of the tank firing on the move based on fully flexible body modeling method

Generally, the rigid-flexible coupling model based on the modal reduction method cannot realize the contact between the rigid body and the flexible body. Based on the multi-body systems dynamics and fully flexible body modeling method, the rigid-flexible coupling dynamics model of the tank gun system was constructed. Then by combining with the PID control model, the mechanical/control co-simulation model of the tank gun on the move was constructed. The influences of the control system and vehicle speed on the muzzle vibration during the shooting process were respectively analyzed. It has been shown that the control system model can effectively simulate the response characteristics of the muzzle during the move of the tank. Under the same road surface and the same control law, the frequency and amplitude of the muzzle angular displacement in the low frequency range increase with the increase of the vehicle speed. The constructed model and the simulation results are of great significance to the analysis and optimization of the shooting accuracy of the tank gun on the move.

Optimal Control of Dielectric Elastomer Actuated Multibody Dynamical Systems.

In this work, a simulation model for the optimal control of dielectric elastomer actuated flexible multibody dynamics systems is presented. The dielectric elastomer actuator (DEA) behaves like a flexible artificial muscle in soft robotics. It is modeled as an electromechanically coupled geometrically exact beam, where the electric charges serve as control variables. The DEA-beam is integrated as an actuator into multibody systems consisting of rigid and flexible components. The model also represents contact interaction via unilateral constraints between the beam actuator and, for example, a rigid body during the grasping process of a soft robot. With a mathematically concise and physically representative formulation, a reduced free energy function is developed for the electromechanically coupled beam. In the optimal control problem, an objective function is minimized while the electromechanically coupled dynamic balance equations for the multibody system have to be fulfilled together with the complementarity conditions for the contact and boundary conditions. The optimal control problem is solved via a direct transcription method, transforming it into a constrained nonlinear optimization problem. The electromechanically coupled geometrically exact beam is firstly semidiscretized with one-dimensional finite elements and then the multibody dynamics is temporally discretized with a variational integrator leading to the discrete Euler-Lagrange equations, which are further reduced with the null space projection. The discrete Euler-Lagrange equations and the boundary conditions serve as equality constraints, whereas the contact constraints are treated as inequality constraints in the optimization of the discretized objective. The constrained optimization problem is solved using the Interior Point Optimizer solver. The effectiveness of the developed model is demonstrated by three numerical examples, including a cantilever beam, a soft robotic worm, and a soft robotic grasper.

Identification of abnormal loads between carbody and hanging equipment of high speed train using inverse method

ABSTRACT The ability to effectively identify abnormal loads caused by hanging equipment local resonance problems is important for assessing the structural integrity of railway vehicles. The structural dynamics inverse problems analysis method is presented to minimise resonance effects and equipment-underframe interactions at different structural frequencies. A mathematical model of the structure forward and inverse dynamics is developed to simulate such interactions based on multibody system dynamics and finite elements theory. The Euler-Bernoulli beam model is also used to simulate the flexible carbody integrated with the inverse approach to compare the effects of reconstructed loads utilised by the optimised regularisation algorithm. The vehicle rolling vibration rig test is made to verify the identification effects. The results are found to be in good agreement with the predictions of the mathematical model using the measured acceleration and demonstrated the effectiveness and non-destructive test applicability.

High-fidelity modeling of dynamic origami folding using Absolute Nodal Coordinate Formulation (ANCF)

Origami has evolved into a framework for creating engineering systems at vastly different scales: from large deployable airframes to architected materials to small DNA machines. These emerging applications require us to develop high-fidelity models that can simulate and examine folding-induced mechanical responses, especially those involving significant facet rotation, non-uniform deformation, and complex dynamics. To this end, this study formulates and experimentally validates a new origami mechanics model based on Absolute Nodal Coordinate Formulation (ANCF), which has unique advantages for predicting the nonlinear dynamics of multibody systems with large rotation and deformation. This new model treats origami facets as ANCF thin plate elements rotating around compliant creases. Moreover, Torsional Spring Damper Actuator (TSDA) connectors are developed to represent crease folding. After careful calibration with experimentally measured constitutive material properties, this study provides the first reported quantitative agreement between simulation predictions and experiment results involving complex and non-uniform facet deformation and transient dynamic responses. Therefore, this model can help deepen our knowledge of folding-induced mechanics and dynamics, fostering future applications for origami.

Non-linear consensus dynamics on temporal hypergraphs with random noisy higher-order interactions

AbstractComplex networks encoding the topological architecture of real-world complex systems have recently been undergoing a fundamental transition beyond pairwise interactions described by dyadic connections among nodes. Higher-order structures such as hypergraphs and simplicial complexes have been utilized to model group interactions for varied networked systems from brain, society, to biological and physical systems. In this article, we investigate the consensus dynamics over temporal hypergraphs featuring non-linear modulating functions, time-dependent topology and random perturbations. Based upon analytical tools in matrix, hypergraph, stochastic process and real analysis, we establish the sufficient conditions for all nodes in the network to reach consensus in the sense of almost sure convergence and $\mathscr{L}^2$ convergence. The rate of consensus and the moments of the equilibrium have been determined. Our results offer a theoretical foundation for the recent series of numerical studies and physical observations in the multi-body non-linear dynamical systems.

Absolute coordinate formulation and generalized component mode synthesis with rigid body coordinates

The dynamics of linearly-elastic multibody (MB) systems is conventionally modeled via the floating frame of reference formulation (FFRF); however, its equations of motion (EOMs) involve significantly more nonlinear terms and quantities than alternative formulations, such as the absolute coordinate formulation (ACF) and generalized component mode synthesis (GCMS). This large number of operations required makes computer implementations of the FFRF laborious as well as error-prone and introduces more complexity in general. These issues associated with the FFRF, and the fact that the formulations are mathematically equivalent as shown by the authors, render the ACF and its relatives appealing alternatives due to their simplistic equation structures. To make these alternatives even more appealing, this contribution proposes an improved ACF and GCMS, which (i) reduces the nonlinearity in the EOMs compared to their standard versions and (ii) eliminates the necessity to calculate the rigid body (RB) motion from the global nodal displacement field to obtain the flexible part of the degrees of freedom (DOFs) and the rotation matrix. The proposed EOMs feature a constant mass matrix, a corotated stiffness matrix in the flexible part, and a “small” nonlinear stiffness matrix in the RB rotation part. Moreover, attaching the moving reference frame to the center of mass of the underlying rigid body and employing linearized Tisserand and rotation matrix constraints eliminates coupling terms within the mass matrix and yields implementation-friendly EOMs to analyze the dynamics of linear-elastic flexible MB systems.

Machine learning based condition monitoring for gear transmission systems using data generated by optimal multibody dynamics models

Condition monitoring (CM) of mechanical systems such as gear transmissions can be performed with vibration measurements and processing of the recorded signals for identification of possible faults. The accuracy and robustness of a CM application depends among others on the availability of data for different health states which typically requires complete experimental measurements. The presented work contains a novel CM scheme using a Convolutional Neural Network (CNN) trained by data generated through numerical simulations of a Multibody Dynamics (MBD) system. The goal is to perform damage identification on different health states by exploiting simulated instead or experimental responses for supervised health state classification. First, a MBD model corresponding to the real system is developed and optimized using experimental measurements of the healthy mechanical structure. Then, data is generated by the MBD model using an uncertainty simulation repetitive load case algorithm to account for various model parameters inaccuracies. The simulated data is used after to train a supervised CNN classifier which is finally validated on vibration measurements of the physical system. The classifier is shown to be capable of generalizing to the experimental damages, proving therefore the potential of the model-based proposed framework for CM. The presented methodology may find application in cases where experimental measurements are difficult or nearly impossible to acquire. CM was performed on the benchmark gear transmission systems for different rotation speeds and the limitations are discussed.

Trajectory-tracking control from a multibody system dynamics perspective

The development of modern mechatronic systems is often driven by the desire for more efficiency and accuracy. These requirements not only result in more complex system designs, but also in the simultaneous development of improved control strategies. Therefore, control of multibody systems is an active field of research. This contribution gives an overview of recent control-related research from the perspective of the multibody dynamics community. A literature review of the research activity in the journal Multibody System Dynamics is given. Afterwards, the framework of servo-constraints is reviewed, since it is a powerful tool for the computation of a feedforward controller and it is directly developed in the multibody system dynamics community. Thereby, solution strategies for all possible system types, such as differentially flat systems, minimum phase and non-minimum phase systems are discussed. Selected experimental and simulation results are shown to support the theoretical results.

A framework for establishing constraint Jacobian matrices of planar rigid-flexible-multibody systems

<abstract> <p>Constraint violation correction is an important research topic in solving multibody system dynamics. For a multibody system dynamics method which derives acceleration equations in a recursive manner and avoids overall dynamics equations, a fast and accurate solution to the violation problem is paramount. The direct correction method is favored due to its simplicity, high accuracy and low computational cost. This method directly supplements the constraint equations and performs corrections, making it an effective solution for addressing violation problems. However, calculating the significant Jacobian matrices for this method using dynamics equations can be challenging, especially for complex multibody systems. This paper presents a programmatic framework for deriving Jacobian matrices of planar rigid-flexible-multibody systems in a simple semi-analytic form along two paths separated by a secondary joint. The approach is verified by comparing constraint violation errors with and without the constraint violation correction in numerical examples. Moreover, the proposed method's computational speed is compared with that of the direct differential solution, verifying its efficiency. The straightforward, highly programmable and universal approach provides a new idea for programming large-scale dynamics software and extends the application of dynamics methods focused on deriving acceleration equations.</p> </abstract>

Итерационный метод решения систем линейных алгебраических уравнений с положительно полуопределенными матрицами системы

The normal pseudo-solution for perturbed linear algebraic equations systems with positive sem-idefinite matrices finding problem is considered. This problem is actual for numerical simulation process of a multibody systems dynamics taking into account additional constraints on its motion. The problem is solved by the iterative quasi-Newtonian method based on the SR1-formula for quadratic functions minimum finding. The main algorithm properties are proved. An one mechanical system dynamics study example is given, which shows the method efficiency.

Study on the symmetries and conserved quantities of flexible mechanical multibody dynamics

<abstract> <p>In this paper, in order to provides a powerful new tool for quantitative and qualitative analysis of dynamics properties in flexible mechanical multibody systems, the symmetry theory and numerical algorithms for preserving structure in modern analytical mechanics is introduced into flexible multibody dynamics. First, taking the hub-beam systems as an example, the original nonlinear partial differential-integral equations of the system dynamics model are discretized into the finite-dimensional Lagrange equations by using the assumed modal method. Second, the group analysis theory is introduced and the criterion equations and the corresponding conserved quantities of Noether symmetries are given according to the invariance principle, which provide an effective way for analytic integral theory of dynamic equations. Finally, a conserved quantity-preserving numerical algorithm is constructed by coordinates incremental discrete gradient, which makes full use of the invariance of conserved quantity to eliminate the error consumption for a long time. The simulation results show that the deeper mechanical laws and motion characteristics of flexible mechanical multibody systems dynamics can be obtained with the help of symmetries and conserved quantities, which can provide reference for more precise dynamic optimization design and advanced control of systems.</p> </abstract>

A unified framework for corotational flexible multibody system dynamics formulations.

Corotational formulations play an important role for flexible multibody dynamics systems, because they reflect the nature of many technical systems undergoing arbitrarily large rigid body motions but small deformations within each body. This paper defines flexible multibody dynamics and corotational formulations in this context. Furthermore, the «ingredients» and workflow of a flexible multibody dynamics simulation are briefly addressed for the reader less familiar with the topic. This part also points to major review papers and textbooks in the field, and embeds the unified formulations in the literature. The paper's main part presents state-of-the-art corotational flexible multibody dynamics formulations in a systematic and unified way. In this formulation part, the standard integral-based floating frame of reference formulation with modal reduction and with the conventionally employed lumped mass approximation is presented, and its drawbacks highlighted. Then, the so-called nodal-based, i.e., space-wise discretized, equations of motion are presented for several up-to-date nodal-displacement-based formulations within a unified framework. This approach clearly shows the equivalence of the presented formulations, and highlights the fact that the formulations differ only in the choice of degrees of freedom. Moreover, this contribution also intends to reduce the information and complexity within the scientific literature, since this unified framework allows the derivation of these formulations with significantly less effort..

Planar multibody dynamics of floating Y-method installation system and the lowering of subsea equipment based on finite element modeling

The subsea equipment installation is a complex operation that demands a precise and reliable approach to avoid the accidental losses of lives and equipment damage. The multibody installation system is overwhelmed with the dynamic behavior and responses of the system, which signifies the importance of analysis of the Multibody Dynamic System (MBDS). The modeling of MBDS is challenging and complicated due to the interconnectivity and nonlinearity assigned to them. In this paper, the planar dynamics of a floating multibody system are attained by employing two tugboats and a payload with a contextual offshore installation scenario to be applied in a water depth of over 1500 m. The lifting operation is nine degrees of freedom (9-DOF) multibody model done with the help of two strands and three bodies having 3-DOF each. The coupled equations of motion are established by deploying the Velocity Transformation Technique. The hydrodynamic and two-strand forces are simplified as linear, while the hydrostatic and mooring forces are treated as nonlinear external loads. The numerical solution to the equations for the MBDS is obtained from the Runge Kutta Method of Fourth-Order. Furthermore, the Finite Element Modeling approach discusses the installation operation using Y-method. The results of the proposed numerical model are validated by comparing it with the numerical simulation from OrcaFlex, and the results from both models are found to be in good agreement. The findings of this study will help improve the safe and stable installation of deep-water multibody structures.

Dynamic Analysis on Stainless Steel New Generation Passenger Coach using Multibody Dynamic System

Stainless-steel passenger coaches are the most operated passenger trains in Indonesia, which are manufactured by the Indonesian railway industry, (PT. INKA), from its first launch to the last generation of trains. PT. INKA still keeps innovating to improve the performance of these trains. Nowadays, this passenger coach is being developed to reach a speed of more than 120 km/hour, while keeping the stability, ride quality index, and ride comfort index during operation. This new train would be called a stainless-steel new generation (SS-NG) passenger coach. To reach the target, one of the methods is redesigning the old bogie structure of the stainless-steel passenger coach. The purpose of this research is to design a new bogie for the SS-NG passenger coach and analyze its dynamics during operation at high-speed using multibody simulation. The result was then compared to the existing passenger coach (SS-2018) which was structured by the old bogie one. Sperling’s method was utilized for evaluating the ride comfort index of all designed trains. As a result, the SS-NG with a new bogie design showed stable operation and gave an acceptable ride comfort index based on Sperling’s method even though travels at 240 Km/h in speed. The results will be important for improving the performance of any train, especially the SS-NG passenger coach which will be fabricated by PT. INKA.

Design and Dynamic Analysis of a 2 Dual Axes Solar Tracking Mechanism

This paper describes the implementation of general multibody system dynamics on sun tracker mechanism. In this study, a dual axes solar tracking mechanism designed within the scope of a project to obtain an efficient electrical energy from solar rays is examined. Dynamic and kinematic calculations of the moving and joint places in the mechanism were made. This study is important as the use of an efficient solar tracker is very useful in military, industrial and residential areas. Free Body Diagrams of all the elements or limbs that make up the sun tracker mechanism have been drawn. Thus, dynamic and kinematic values at elements points were calculated. The proposed dynamics model of the mechanism offers an accurate and fast method to analyze the dynamics of the mechanism knowing that there is no suchwork available for sun tracker. Also, 3D tracker elements were drawn and planned in Solid Work program. The simulation gives a clear idea about energy parameters for different link lengths of the mechanism over a linear displacement.

Determination of the critical defect and fatigue life of high-speed railway axles under variable amplitude loads

High-speed railway axles are suffered from extremely complex variable amplitude (VA) loads during operation. However, in the design codes and operation maintenance of railway axles, most of them are based on the equivalent constant amplitude (CA) load spectrum to perform the fatigue resistance design by using the traditional nominal stress method, and carry out the routine inspection based on running experiments and data. In this paper, an innovative time-domain stepwise fatigue assessment (TSFA) approach has been introduced to include the influence of VA loads on the accumulated damage and fatigue crack propagation. Based on this procedure, the fatigue load spectrum from the multi-body system (MBS) dynamics simulation was integrated into the fatigue damage and remaining lifetime assessment of the axles. The calculation indicates that the safe lifetime of the powered and non-powered axles under the time-domain loading is considerably larger than the design value, which shows that the axle could safely operate until they are retired. However, for an original crack with the morphology ratio of 0.6 propagating to 45.0 mm, the lifetime of the powered and non-powered axle is sharply reduced to 1.32, and 2.07 years, respectively. Compared with the classical nominal stress method, the newly-developed TSFA procedure could produce a more conservative but practical result.

Real-time multi-body co-simulation model of a veneer peeling lathe

ABSTRACT This paper introduces a real-time co-simulation model for the prediction of the dynamics behavior of a veneer peeling lathe machine. The real-time co-simulation model introduced is described in the framework of multi-body system dynamics. It makes use of a co-simulation procedure in which a semi-recursive multi-body approach is combined with a detailed contact description. In the employed closed-loop semi-recursive method, the constraint conditions are carried out in the system motion differential equations via the augmented Lagrangian method. A contact procedure is presented to describe the contact between the wooden log and the cutting blade and the support rollers. The results obtained by the co-simulation are compared against those experimentally measured through a peeling lathe machine in operation and an approximate finite element model of the peeling process. According to the numerical results, it is concluded that the real-time simulation model can predict dynamic performance of the complicated system of a veneer peeling lathe in real-time. Solvability of equations of motion makes the introduced model suitable to be utilized in a number of product process purposes such as marketing, training and product development projects.

Optimal Greedy Control in Reinforcement Learning.

We consider the problem of dimensionality reduction of state space in the variational approach to the optimal control problem, in particular, in the reinforcement learning method. The control problem is described by differential algebraic equations consisting of nonlinear differential equations and algebraic constraint equations interconnected with Lagrange multipliers. The proposed method is based on changing the Lagrange multipliers of one subset based on the Lagrange multipliers of another subset. We present examples of the application of the proposed method in robotics and vibration isolation in transport vehicles. The method is implemented in FRUND-a multibody system dynamics software package.