Modeling Of 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

Deployment Simulation of Foldable Membranes Using Absolute Nodal Coordinate Formulation and Validation

It has become a trend to use foldable membranes to construct large spacecraft structures such as solar sails, antennas, and drag sails with the advantages of being lightweight and having high packing efficiency. To enhance the existing numerical simulation of membrane deployment, the nonlinear behavior of the crease is finely described based on experiments and integrated into the numerical model via the principle of virtual work. Specifically, a foldable membrane is modeled as a multibody system (MBS) based on the absolute nodal coordinate formulation (ANCF), where the flexible facet is meshed with both ANCF triangular and quadrilateral thin shell elements and the crease is treated as a virtual torsional spring with special constraints along the fold line. The MBS modeling method is validated via the deployment experiment of a Z-folding membrane. The deployment of a four-unit Miura-ori membrane is further analyzed to show the capability of the approach in modeling foldable membranes with complicated configurations. Good agreement is obtained on the membrane-deformed configurations between the simulation and experiment. Additionally, the driving force at the corners is obtained. This research is expected to provide a more accurate simulation to facilitate the design and optimization of the space deployable membrane structure.

Inertial Parameter Identification for Closed-Loop Mechanisms: Adaptation of Linear Regression for Coordinate Partitioning

Abstract This study investigates the use of linear-regression-based identification in rigid multibody system applications. A multibody system model, originally described with differential-algebraic equations (DAE), is transformed into a set of ordinary differential equations using coordinate partitioning. This allows the identification framework (where the system is described with ordinary differential equations) to be applied to rigid multibody systems described with nonminimal coordinates. The methodology is demonstrated via numerical and experimental validation on a slider–crank mechanism. The results show that the presented methodology is capable of accurately identifying the system's inertial parameters even with a short motion trajectory used for training. The presented linear-regression-based identification approach opens new opportunities to develop more accurate multibody models. The resulting updated multibody models can be considered especially useful for state-estimation and the control of multibody systems.

Dynamic vibration absorber for the mitigation of potential wheel polygonization at trams

Polygonal wheels are a widespread problem in the railway industry. Oscillation phenomena appearing at the wheelset may provide an environment where the wheel polygonization is promoted essentially. The flexibility of the wheelset was highlighted as an important influence on these phenomena in curves with a small radius of curvature at trams in recent studies. A dynamic vibration absorber applied on the wheelset may reduce oscillations at the wheelset significantly and is studied as a potential mitigation measure of wheel polygonization. A basic system model, representing a wheelset with non-driven independently rotating wheels, is used to investigate the mechanism and performance of this passive remedy. Influences of different parameter combinations of the absorber are discussed systematically. The efficiency of the dynamic vibration absorber is analysed further with a more detailed multibody system model of a two-axle tram bogie. Results reveal that an adequately tuned absorber might significantly reduce the possible development and further evolution of predominant polygonal orders. Additionally, basic guidelines for the design of the dynamic vibration absorber applied at the wheelset are pointed out.

Development of a head-weighted injury criterion for evaluation of multiple types of AIS 4+ injuries for vulnerable road users

Vulnerable Road users (VRUs) often suffer multiple fatal head injury types simultaneously in road accidents. In this study, a head-weighted injury criterion (HWIC4) was proposed for assessing the risk of head AIS 4+ injuries considering multiple injury types. Firstly, the kinematic characteristics of VRUs in the 50 in-depth accidents were reconstructed by using multi-body system models, and head injuries were reconstructed using eight head kinematic-based injury criteria and eight brain tissue injury criteria via the THUMS (Ver. 4.0.2) head finite element model. The predictive capability of each injury criterion to predict head AIS 4+ injuries was assessed and four better predictors (HIC15, angular acceleration, coup pressure, and maximum principal strain) were selected. The different head injury types and the weighting parameters for each injury type were taken into account in the development of HWIC4. Finally, the effectiveness and evaluation of HWIC4 for head AIS 4+ injury was validated based on the area under of receiver operating characteristic (AUROC) curve and reconstruction results from 10 additional selected accident cases. The results showed that HWIC4 has a good predictive capability for head AIS 4+ injuries with an AUROC of 0.983, which means that HWIC4 is superior and more reliable than a single head injury criterion. This knowledge further improves the capability of head injury criteria to predict head AIS 4+ injuries.

Modeling De-Coring Tools with Coupled Multibody Simulation and Finite Element Analysis

De-coring is an essential process in the casting process chain, determining the quality and cost of production. In this study, a coupled multibody system (MBS) and finite element modeling (FEM) technique is presented to study the mechanical loads during the de-coring process. The removal of cast-in sand cores from the inner regions of the cast part by de-coring or knocking out is a complex process with dynamic loads. Currently, the process relies upon empirical knowledge and tests. Inorganic sand cores pose additional challenges in the success of the de-coring process. Increasing complexity in geometry and stringent environmental regulations compel a predictive process in the earlier stages of design. Predicting the process’ success is challenged by the dynamic non-linearities of the system. The dynamic characteristics and the interaction between hammer and casting were studied here for the first time using an industrial-based test rig, and a novel modeling approach was formulated. The results of the developed model are in good compliance with the experiments. The methodology presented in this study can be used to include a varying number of hammers and loads. The proposed approach presents the possibility to discretize the process and qualitatively assess the process parameters for optimization.

Multibody system dynamics modelling and simulation of a high-speed train for its suspension optimization

Multibody system (MBS) dynamics modelling and simulation of high-speed train system is essential and meaningful in the context of train dynamics research and product design. In this work, MBS modelling of a CRH high-speed train is carried out, in the modelling process, nonlinear geometry of wheel-rail contact, nonlinear characteristics of the suspensions and nonlinear railroad irregularities are fully considered. With the obtained MBS model, simulation is performed and demonstrates that critical speed of the CRH train is 378 km/h, vertical ride comfort of the CRH train is in “Excellent” level and lateral ride comfort is in “Good” level, in addition, RMS derailment coefficient of the train is less than 0.5 which means curving performance of the train is good. Agreement of simulation result with actual test or running data validates the established MBS model, thus, the MBS model developed in this study is accurate and would be useful in the next step vibration analysis and suspension optimization of the CRH train.

Effect of an inter-vehicle damper on the dynamics of a high-speed train

It is meaningful to understand the effect of inter-vehicle damper and its parameters on high-speed train dynamics in the context of train inter-vehicle suspension design or optimization. In this study, Multi-body System (MBS) dynamics modelling of a high-speed CRH train with inter-vehicle damper is firstly carried out, in which a simplified-parametric model was proposed and validated to depict damping characteristics of the damper. Simulation results using the MBS model show that inter-vehicle damper devised in high-speed train can obviously reduce lateral vibrations at the connecting passage of adjacent compartments without increasing the wheelset lateral shift force and derailment coefficient, thus it can improve overal ride comfort of the CRH train. In addition, inter-vehicle damper can resist severe lateral shocks and guarantee safety when two high-speed trains pass each other. The developed MBS model of the CRH train is an accurate and useful platform, the obtained results in this study are also valuable in following vibration analysis and inter-vehicle suspension optimization of the CRH train.

Assessing the dynamic behavior of multiconnected offshore floating photovoltaic systems under combined wave-wind loads: A comprehensive numerical analysis

Floating photovoltaic (FPV) systems have garnered considerable interest due to their numerous benefits. However, the mechanical design of these systems remains underexplored in existing literatures, necessitating further investigation before they can be commercially deployed in ocean environments. In this study, a novel modular offshore FPV solution was proposed, and numerical modeling and hydrodynamic coupling analysis of multi-body FPV systems were conducted to assess the relative behavior of multi-connected FPV modules under combined wave-wind conditions. Initially, the multi-connected system was modeled, taking into account fixed and hinged connection boundary conditions (BC). Utilizing frequency-domain analysis, the hydrodynamic coefficients essential for time-domain analysis were derived. Subsequently, the overall hydrodynamic performance and behavioral characteristics of various FPV platform types were evaluated. In addition, the strength of connectors under extreme conditions were assessed. Lastly, we compared the motion responses of the multi-body platform under different connection BCs and wave headings. It has been proven that the joint of the hinged connector will generate additional moments, which will affect the dynamic response of the platform as an excitation load. Moreover, the connector's structural responses were mainly dominated by the motion response of the FPV platforms. Furthermore, for the multi-body FPV systems, 0° wave heading should be avoided for installation to reduce the motion responses and structural responses. This study provides valuable insights into the mechanical design of FPV systems for ocean deployment.

A framework for practically effective creation of postprocessors for 5-axis CNC machines with all possible configurations and working mechanisms

The 5-axis CNC (Computer Numerical Control) machining plays an important role in manufacturing, especially in making parts of complex shapes such as turbine or propeller blades. However, there are always challenges of generating 5-axis CNC machining programs when working with different 5-axis CNC machines of various structures; and 5-axis CNC programs must be automatically generated by CNC postprocessors which calculate the inverse kinematics and convert the Cutter Location data to the CNC programs that are used for operating 5-axis CNC machines. Since the family of 5-axis CNC machines has a wide spectrum of machine configurations, with hundreds of mechanisms of 5 degrees of freedom, it is therefore practically challenging for engineers and CNC machine operators to create CNC postprocessors for specific 5-axis CNC machines. It is more challenging to create CNC postprocessors if engineers or CNC operators do not have strong backgrounds and professional skills in mathematical modeling and kinematics of machines. This paper presents a universal and intuitive framework and practical guidance to create CNC postprocessors for all 5-axis CNC machines, with the focus on a novel mathematical formulation of inverse kinematics of three main groups of 5-axis CNC machines. The case studies of creating CNC postprocessors with the commercially available 5-axis CNC machines were successfully demonstrated, in which the simulation scenarios and experiments were implemented to verify the created CNC postprocessors. The proposed frameworks and guides for generating CNC postprocessors can be conveniently and effectively applied in industrial practices, without the required strong backgrounds and skills for engineers or CNC operators in mathematical modeling and kinematics of machines, especially mathematical modeling of multibody systems.

Model reduction for constrained mechanical systems via spectral submanifolds

Dynamical systems are often subject to algebraic constraints in conjunction with their governing ordinary differential equations. In particular, multibody systems are commonly subject to configuration constraints that define kinematic compatibility between the motion of different bodies. A full-scale numerical simulation of such constrained problems is challenging, making reduced-order models (ROMs) of paramount importance. In this work, we show how to use spectral submanifolds (SSMs) to construct rigorous ROMs for mechanical systems with configuration constraints. These SSM-based ROMs enable the direct extraction of backbone curves and forced response curves and facilitate efficient bifurcation analysis. We demonstrate the effectiveness of this SSM-based reduction procedure on several examples of varying complexity, including nonlinear finite-element models of multibody systems. We also provide an open-source implementation of the proposed method that also contains all details of our numerical examples.

Satellite Dynamics Toolbox Library: a tool to model multi-body space systems for robust control synthesis and analysis

The level of maturity reached by robust control theory techniques nowadays contributes to a considerable minimization of the development time of an end-to-end control design of a spacecraft system. The advantage offered by this framework is twofold: all system uncertainties can be included from the very beginning of the design process; the validation and Verification (V&V) process is improved by fast detection of worst-case configurations that could escape to a classical sample-based Monte Carlo simulation campaign. Before proceeding to the control synthesis and analysis, a proper uncertain plant model has to be available in order to push these techniques to their limits of performance. In this spirit, the Satellite Dynamics Toolbox Library (SDTlib) offers many features to model a spacecraft system in a multi-body fashion on SIMULINK. Parametric models can be easily built in a Linear Fractional Transformation (LFT) form by including uncertainties and varying parameters with minimal number of repetitions. Uncertain Linear Time Invariant (LTI) and uncertain Linear Parameter-Varying (LPV) controllers can then be synthesized and analyzed in a straightforward way. The authors present in this article a tutorial, that can be downloaded at https://nextcloud.isae. fr/index.php/s/XDfRfHntejHTmmp, to show how to deal with an end-to-end robust design of a spacecraft mission and to provide to researchers a benchmark to test their own algorithms.

ANÁLISE DA CARGA ARTICULAR NOS MEMBROS INFERIORES DURANTE O BACKFLIP

ABSTRACT Introduction: Sports injuries restrict the acquisition of optimal results and represent a great threat to the athlete's physical health, lower limb injuries being the most prominent, mainly those caused by landing. Objective: Use biomechanics to analyze the joint load of the lower limbs during the landing process in the gymnastics backflip, establishing movement control and reducing the risk of lower limb injury. Methods: The male athletes of the National Gymnastics Team were selected as the research objects, and the three-dimensional backflip (BS) motion trajectory was completed after the landing process was completed, the vertical ground reaction force (VGRF) after landing and the lower limb muscle electromyography (EMG) after landing was collected, and the human multi-body system model and the landing platform model of the landing action were completed with the help of the system simulation software. Results: Statistics show that gymnasts train more intensively during competition or daily training, performing more than 200 landings per week, a factor that increases the risk of injuries during the backflip in athletes. Conclusion: The lower limb joint load of the landing action in gymnastics backflip is high, which will cause a certain risk of injury, and specific measures can be taken to control it. Level of evidence II; Therapeutic studies - investigation of treatment outcomes.

A symbolic framework to obtain mid-fidelity models of flexible multibody systems with application to horizontal-axis wind turbines

Abstract. The article presents a symbolic framework (also called computer algebra program) that is used to obtain, in symbolic mathematical form, the linear and nonlinear equations of motion of a mid-fidelity multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The shape function approach does not represent the state of the art for flexible multibody dynamics but is an effective trade-off to obtain mid-fidelity models with few degrees of freedom, taking advantage of the separation of space and time. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitates the creation and manipulation of models with various levels of complexity by adding or removing degrees of freedom. The symbolic treatment allows for analytical gradients and linearized equations of motion. The linear and nonlinear equations can be exported to Python code or dedicated software. There are multiple applications, such as time domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins. In this article, we describe the method we used to systematically generate the equations of motion of multibody systems and present the implementation of the framework using the Python package SymPy. We apply the framework to generate illustrative land-based and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. The Python implementation is provided as an open-source project.

Phase plane analysis applied to non-explicit multibody vehicle models

A new methodology for constructing stability maps (phase-plane analysis) is presented and validated for application to complex multibody vehicle models implemented in Multibody Dynamics simulation software (Adams®). Traditional methodologies are developed to be applied to explicit mathematical models. Given the complexity of some special multibody systems, particularly in vehicle dynamics, simplifications are needed to apply this stability analysis technique. The main limitation when using simplified models is the need to neglect components which could have a significant influence on the dynamic behavior of the system and therefore on its stability. In the proposed methodology it is not necessary to have access to explicit mathematical models of multibody systems. Thus, the stability map of a vehicle model can be constructed by considering highly nonlinear dynamic elements, such as tires and silent-blocks components, modeled using the nonlinear finite element technique.

Dynamic Model of a Conjugate-Surface Flexure Hinge Considering Impacts between Cylinders.

A dynamic model of a Conjugate-Surface Flexure Hinge (CSFH) has been proposed as a component for MEMS/NEMS Technology-based devices with lumped compliance. However, impacts between the conjugate surfaces have not been studied yet and, therefore, this paper attempts to fill this gap by proposing a detailed multibody system (MBS) model that includes not only rigid-body dynamics but also elastic forces, friction, and impacts. Two models based on the Lankarani-Nikravesh constitutive law are first recalled and a new model based on the contact of cylinders is proposed. All three models are complemented by the friction model proposed by Ambrosìo. Then, the non-smooth Moreau time-stepping scheme with Coulomb friction is described. The four models are compared in different scenarios and the results confirm that the proposed model outcomes comply with the most reliable models.

Detection of critical mode-shapes in flexible multibody system dynamics: The case study of a racing motorcycle

In multibody system models, body flexibility is introduced when the structure compliance is not negligible for an accurate description of the system behaviour. Flexible multibody systems provide a more detailed description of system kinematics and dynamics, introducing the effects of the body dynamics deformations.The influence of component higher frequency harmonics is often undesired during system working conditions. Therefore, in the design of a flexible multibody system the components and assembly modal properties are optimised to avoid resonances in the operating condition frequency ranges. However, in the system optimisation phase or when the system is upgraded to a new release, the least modifications would be ideally performed to optimise the system for its working conditions. In this context, there are no straightforward methods available to recognise which component mode-shapes require structural optimisation to avoid undesired dynamics behaviours.Based on an assembly-to-components modal approach, this paper proposes a method to detect the component mode-shapes responsible for undesired dynamics in the assembled multibody systems; the method is suitable for both numerical model or experimental applications. The inputs to the detection method are the components, sub-structures and assembly mode-shapes, together with the main frequencies exciting the system in operating conditions, to which operative deformations are associated. The procedure reveals the critical components and their mode-shapes requiring modifications.The detection method is conceived especially for systems requiring fast and continuous optimisation, e.g. high-performance racing vehicles, which are at least annually upgraded, or new improved releases of industrial complex machines. Firstly, the proposed method is numerically applied to the flexible multibody model of a slider–crank mechanism, detecting high-frequency vibrations in the piston stroke. Then, it is applied to a race motorcycle chassis frame to detect the critical component mode-shapes in realistic working conditions. Independent application of the procedure to numerical and experimental data of the motorcycle chassis pinpoints the same component mode-shapes as critical, on which optimisation efforts would be required.

Multibody system dynamic analysis and payload swing control of tower crane

A new payload swing control method considering the vibration of tower crane is proposed in this study. The coupling between the structural vibration and the payload swing is neglected in existing studies on tower crane swing suppression. Changes of sling length are considered as disturbances. They cause the existing methods of swing suppression method ineffectual in the actual working situation. In contrast, the structural vibration of the tower crane is taken into account in this study. At the same time, the sling length is regarded as a control variable to reduce the payload swing. A new swing suppression algorithm is proposed in conjunction with phase plane analysis method. In addition, a systematical tower crane multibody system dynamic analysis platform with changing of sling length is established to verify the effectiveness of the algorithm. The traditional finite element method is used to model the tower body and boom of tower crane while the Arbitrary Lagrange Euler Absolute Nodal Coordinate Formulation (ALE-ANCF) cable element is applied for modeling the sling. This two parts are connected with sliding joint obtaining the tower crane multibody system model. Numerical examples show that the proposed method can reduce the swing amplitude the payload effectively when considering the coupling between the structural vibration and the payload swing.

Simulation of the inherent structural irregularities of high-speed railway turnouts based on a virtual track inspection method

Track geometry parameters measured by a track recording car at a turnout are often hard to interpret due to the concomitant geometric complexity, especially for a high-speed railway turnout whose running edge is not interrupted. The virtual track inspection (VTI) method integrated with a multibody system model is proposed to reveal the longitudinal level and alignment of high-speed railway turnouts when the train passes in the main line and in the branch line. Firstly, the principle of inertial measurement and its implementation in MBS are introduced. Then, the VTI method is applied to the vehicle-turnout dynamics using a single-layered co-running track model and validated on tangent and curved tracks in the spatial and wavelength domain. Zero-phase Filters for wavelength ranges 3–25 m and 1–5 m are necessary to eliminate interference from long waves, and to better identify the switch and crossing, respectively. Finally, the effect of different track foundations is studied, including the two-layered co-running track model and the finite element model on the VTI method.

Continuum damage dynamics of a large-scale flexible multibody system comprised of composite beams

Herein, a continuum damage dynamic model of a large-scale flexible multibody system comprising composite beams is proposed based on the framework of the absolute nodal coordinate formulation. To accurately model the continuum damage dynamics of a multibody system, the Hashin criterion is adopted to describe damage initiation during dynamics. A type of nonlinear evolution law is used to characterize the value of material damage. Furthermore, a material stiffness degradation rule is introduced to describe the process of structural damage. A formulation for the damage element elastic force and its Jacobian are derived based on the second Piola–Kirchhoff stress tensor. Two dynamic numerical examples, including a deployment dynamic analysis of the spatial beam structural unit, are conducted to verify the availability and applicability of the proposed model.