Flexible Body Dynamics Research Articles

Dynamics of weighted flexible ribbons in a uniform flow

This study explores the dynamics of flexible ribbons with an added weight $G$ at the tail in uniform flow, considering key parameters like inflow Reynolds number ( $Re_u$ ), mass ratio ( $M_t$ ) and aspect ratio ( ${A{\kern-4pt}R}$ ). For two-dimensional ribbons, a simplified theoretical model accurately predicts equilibrium configurations and forces. Inspired by Barois & De Langre (J. Fluid Mech., vol. 735, 2013, R2), we introduce an important control parameter ( $C_G$ ) that effectively collapses normalized forces and angle data. Vortex-induced vibration is observed, and Strouhal number ( $St$ ) scaling laws with $C_G$ are identified. In three-dimensional scenarios, the model effectively predicts lift, but its accuracy in predicting drag is limited to situations with small $Re_u$ values. The flow along the side edges mitigates pressure differences, thereby suppressing vibration and uplift, particularly noticeable in the case of narrow ribbons. This study offers new insights into the dynamics of flexible bodies in uniform flow.

Modeling and stability analysis of a tethered asteroid probe system based on multi flexible body dynamics

Modeling and stability analysis of a tethered asteroid probe system based on multi flexible body dynamics

Elucidation on step-out phenomenon of magnetic strain wave gear by multi flexible body dynamics and displacement measurement

Elucidation on step-out phenomenon of magnetic strain wave gear by multi flexible body dynamics and displacement measurement

Analysis and construction of the coal and rock cutting state identification system in coal mine intelligent mining

The recognition of cutting state of coal-rock is the key technology to realize “unmanned” mining in coal face. In order to realized real-time perception and accurate judgment of coal-rock cutting state information, this paper combined the field test sampling, construction technology of complex coal seam, virtual prototype technology, bidirectional coupling technology, data processing theory, image fusion method, and deep learning theory to carry out multi domain deep fusion experimental research on multi-source heterogeneous data of coal and rock cutting state. The typical complex coal seam containing gangue, inclusion, and minor fault in Yangcun mine of Yanzhou mining area was taken as the engineering object. The high-precision three-dimensional simulation model of the complex coal seam that can update and replace particles was constructed. Based on the simulation results of Discrete Element Method-Multi Flexible Body Dynamics (DEM-MFBD), the one-dimensional original vibration acceleration signals of the key components of the shearer cutting part were determined, including spiral drum, rocker arm shell, and square head. After transforming one-dimensional original signal data into two-dimensional time–frequency images by Short-time Fourier Transform, morphological wavelet image fusion technology was used to realize the effective fusion of characteristic information of spiral drum, rocker arm shell, and square head under different working conditions. Based on the deep learning theory, the DCGAN-RFCNN (Deep Convolutional Generative Adversarial Networks-Random Forest Convolutional Neural Networks) coal and rock cutting state recognition network model was constructed. Combining convolution neural network with random forest recognition classifier, RFCNN coal and rock cutting state recognition classification model was constructed, and the recognition network model was trained to obtain the model recognition results. Through the comparative experimental analysis of the RFCNN network model with different recognition network models and different synthetic sample numbers in the recognition network, the effectiveness of the recognition network model was verified. The results show that: When synthetic samples are not included in each working condition in the RFCNN model, the average recognition rate is 90.641%. With the increase of the number of synthetic samples, the recognition rate of coal and rock cutting state increases. When the number of synthetic samples added to each working condition reaches 5000, the recognition effect is the best, and the average recognition rate reaches 98.344%, which verifies the superiority of enriching the data set by using the improved DCGAN network. Also, the RFCNN outperformed the other variants: it obtained higher recognition accuracy by 25.085, 21.925 and 19.337%, respectively, over SVW, CNN, and AlexNet. Also, the experimental platform of shearer cutting coal and rock was built, where the coal and rock cutting state recognition network was trained and tested based on the migration learning theory. Through the statistical test results, the accuracy of coal and rock cutting state recognition is 98.64%, which realizes the accurate recognition of coal and rock cutting state.

Fast flexible multibody dynamic analysis of machine tools using modal state space models

Digital twins of machine tools are widely used for the validation and optimization of part programs. However, implementing flexible body dynamics in digital twins is challenging due to low computational efficiency. This study presents a flexible multibody dynamic model of a machine tool using modal state space representation of a finite element model. Simulation using the model is twice as fast as actual machining, enabling vibration analysis of flexible body machines in parallel with the machining process. Experiments using a horizontal machine tool confirm that the model predicts residual vibration under various acceleration conditions with an average accuracy of 88%.

Dynamic response of a coal rock caving impact tail beam for hydraulic support

Based on the two-way coupling technology of Discrete Element Method-Multi Flexible Body Dynamics (EDM-FMBD), a virtual caving coal wall is established by using the discrete element software, EDEM. The rigid flexible coupling model of the tail beam of caving supports is established by using multibody dynamics software, RecurDyn. The stiffness of the oil cylinder is calculated by using the solid–liquid spring coupling theory and is replaced by a spring. By simulating the process of a coal rock collapse impacting the tail beam, the dynamic signal from the coal rock collapse impacting the tail beam to crushing in the coal caving stage of the comprehensive caving working face is studied, and the test is carried out underground. The angular acceleration at the hinge point of the tail beam is the largest and shows a variation pattern of "large at both ends and small in the middle". The definition of a "low amplitude band" on the surface of the tail beam is proposed. The force signal at the hinge point of the front link is the strongest and is the best measurement point for the force sensor; the angular acceleration signal at the hinge point of the tail beam is the strongest and it is the best measurement point for the angular acceleration sensor. The results have practical implications for the identification of the coal gangue and the adaptive control of support for integrated top coal mining.

New Design of Hy-Vo Chain Based on the Ultra-Small Rolling Radius

To improve the system meshing performance and the chain stability, a totally new type Hy-Vo chain with an ultra-small rolling radius is proposed in this research. According to the rolling theory of the rocker pin, the design method and the meshing system for the new Hy-Vo chain are proposed. Based on the analysis model of polygonal action, by calculating a specific example, it is proved that the variable pitch characteristic of the new Hy-Vo chain is controllable. Through comparing the system center distance fluctuations for the new and the classical Hy-Vo chain, it is shown that both the system fluctuation difference and the system running deviation are all smaller for the new Hy-Vo chain. Combined with the analysis of Multi Flexible Body Dynamics (MFBD), for the new Hy-Vo chain plate and the rocker pin, the stress distribution is more uniform, and the chain life is longer. As a result, the new Hy-Vo chain with the ultra-small rolling radius has a better meshing performance and fatigue resistance, as well as better process economy. Moreover, the new design proposed in this paper is not only a novel structure for the Hy-Vo chain drive, but it also reveals the meshing mechanism and the controllable variable pitch characteristic.

Study On Dynamic Characteristics of a Repulsion Mechanism in Superconducting Fault Current Limiter

The objective of the paper is to study the dynamic characteristics of a repulsion mechanism applied in superconducting fault current limiter (SFCL). A novel fully coupled simulation was established, which involved modules of the flexible-body dynamics, the external circuits, motion equations, multi-body dynamics, transient electromagnetic fields and fatigue analysis. The dynamic characteristics including the velocity, the displacement curve, discharging current, Lorentz force, the stress and strain of each dynamic transmission part in the opening process, was calculated. The vulnerable parts were focused and their fatigue life was calculated. The deviation about discharging current and displacement curve of the fully-coupled simulation was experimentally validated to be less than 8%. Stress concentration positions of the vulnerable parts recommended by the simulation results are the same as fatigue failure positions in the experimental results, which verified the accuracy of the fully coupled simulation.

Advances in dynamic modeling and simulation of soft machines

Soft machines are a sort of mechanical systems mainly composed of soft materials and soft structures. Its soft compliance enables motion of large deformation, which results in a series of functionalities that traditional machines are not capable to achieve and the possibility to interact closely with humans. Therefore, soft machines are not only important complement to artificial machines but also a fascinating branch in future development of advanced machines. Mechanical modeling and analysis offer essential ways to designing and manufacturing soft machines. Dynamic modeling and simulation become increasingly effective and necessary for systematic design and motion control. This paper reviews and analyzes advances in dynamic modeling and simulation of soft machines. First, recent developments are overviewed from five aspects, namely kinematics, modeling of soft material, contact dynamics of flexible bodies, efficient computation of transient dynamics, and dynamic control. Second, problems and challenges are discussed. Several balances in the research of dynamics of soft machines are proposed. Third, potential directions in future research are predicted according to the current developments and challenges. Summary and prospects on dynamics and control of soft machines are given.

A referenced nodal coordinate formulation

We develop a referenced nodal coordinate formulation (RNCF) to study the dynamics of flexible bodies undergoing large-distance travels and/or high-speed rotations. RNCF is similar to the absolute nodal coordinate formulation (ANCF) but is presented in a noninertia reference coordinate system (RCS). The position vector and rotation matrix of the RCS describe translational and rotational motions of the system, whereas the nodal coordinates and slopes in a structure depict its large deformations, such that the generalized coordinates with multiple scales in length and time are automatically separated. We develop a parameter-irrelevant technique to derive the rotation equations of the system, where the influences of large deformations on the rotatory inertia tensors are embodied. The derived governing equations are simple and elegant, and consistent with the governing equations for rigid bodies, the floating frame of reference method, as well as ANCF. We verify the RNCF approach by three typical examples, including the spin-up maneuver, the high speed motor, and the flexible slider-crank mechanism. The results indicate that to achieve the same accuracy, the computational cost for RNCF is much lower than that for the corresponding ANCF in high-speed rotating systems. Moreover, the electrical solar wind sail spacecraft system is formulated by RNCF, and its propulsive efficiencies with respect to the spin rates of the E-sails are studied by full-scale models with over ten thousand degrees of freedom. RNCF provides an effective way to formulate and study the dynamics of vehicles, trains, ships, aircrafts, and spacecrafts.

Grid and Polytopic LPV Modeling of Aeroelastic Aircraft for Co-design

Future aircraft tend to have increased flexibility that leads to increased aeroservoe-lastic (ASE) effects. Therefore, future aircraft control systems need active control to suppress ASE effects. Active flutter suppression can be effectively done in the linear parameter varying (LPV) framework. Control surface sizing for aircraft is traditionally done by iterations. In this approach engineering rules are used to determine the size of the control surfaces and the control laws are designed afterwards. Such method, besides being time consuming, might have further challenges in the future due to the coupling between the flexible and rigid body dynamics. Instead, ”co-design” was recently proposed. In the co-design approach parametric aircraft models are developed based on which the control surface sizing and the control design are optimized in a single step. The purpose of this paper is to create a control oriented, parametric control surface model of the mini MUTT aircraft that can be applied for co-design. The resulting control oriented LPV model needs to have sufficiently low dynamic order, which is achieved by the ”bottom-up” modeling approach. A grid based LPV model is obtained from the nonlinear model by Jacobian linearization and the Tensor Product (TP) type polytopic model is obtained from the grid based LPV model via TP model transformation. The resulting low order parametric control surface LPV models are assessed with the v-gap metric. These models can serve as the basis of simultaneous baseline/flutter suppression control synthesis and control surface sizing optimization.

Using a half-implicit integration scheme for the SPH-based solution of fluid–solid interaction problems

A Smoothed Particles Hydrodynamics (SPH) method for fluid dynamics is coupled with a rigid and deformable body dynamics solution to yield a framework for solving fluid–solid interaction (FSI) problems. The two-way, force–displacement, coupling of the fluid and solid phases is captured via boundary condition enforcing (BCE) markers. The partial differential equations governing each phase are discretized in space separately and the resulting ordinary and/or algebraic differential equations are integrated in time independently with coupling enforced via fluid–solid boundary conditions. Particular attention is paid to enforcing fluid incompressibility via a projection step that computes the pressure field as the solution of a linear system. The numerical solution leverages hybrid parallel computing: the rigid and flexible body dynamics is handled on the CPU using multiple cores; at the same time, the fluid phase is handled on the graphics processing unit (GPU). The methodology is validated against experimental data and numerical results obtained using two open-source solvers. Several case studies are reported to gauge the accuracy, efficiency, and scalability of the solver. The highlights of the proposed solution are: tight enforcement of fluid incompressibility; ability to handle coupled physics that combines fluid, rigid, and deformable bodies; ability to handle friction and contact; and, scalable implementation that simultaneously employs CPU and GPU computing.

Finite element analysis of cylindrical gear with mechanical event simulation

In this paper, we present the finite element analysis of a cylindrical gear using the Autodesk Simulation Mechanical software, with mechanical event simulation (MES). MES combines the kinematic, rigid, and flexible-body dynamics with the nonlinear stress analysis. Therefore, MES can be used to simultaneously analyse mechanical events involving large deformations, nonlinear material properties, kinematic motion and the forces caused by this motion for predicting the resulting stresses. It is essential that MES can be used to define the surface contact between the teeth in contact at a given time, the analysis parameters by time steps, respectively the kinematic and kinetostatic parameters, variables defined by certain curves. We use the analysis to find the stress distribution, nodal displacements, etc. in the contact area of the two gear wheels, at different time steps of the kinematic cycle.

Further investigation on the coupling between the reference and elastic displacements in flexible body dynamics

A new semi-analytical multibody system (MBS) model derived using general nonlinear flexible body dynamics formulation is developed in this investigation. The semi-analytical model can serve as a benchmark example for testing the implementation of the finite element (FE) floating frame of reference (FFR) formulation in commercial MBS software. In particular, this new model sheds light on the important concept of the reference conditions which is fundamental in the computer implementation of the FE/FFR formulation. In order to develop the new FE/FFR semi-analytical model, the reference motion of the flexible body is expressed in terms of specified motion trajectories, allowing for developing a set of second-order ordinary differential equations (ODE's) with time-varying coefficients. The FE/FFR inertia shape integrals are evaluated and used to define the generalized forces associated with the deformation coordinates. The simplifications that result from the use of the mean-axis reference conditions are highlighted and the significance of these simplifications on the solution accuracy when using more appropriate sets of reference conditions is discussed. It is shown that if a MBS computer algorithm restricts the choice of the reference conditions to one set, the use of other reference conditions can lead to a homogeneous ODE system with time-varying coefficients which has zero solution in the case of zero initial conditions and zero external forces regardless of the flexible body reference rotation.

Steering test of mid-size bus with flexible-body dynamics model

The object of this paper is to analyze the vehicle structural vibration responses during the step steering simulation test. With computer simulations, confirming the influence from the difference between configurations of components on mid-size electrical bus and tradition one could be possible. The difference of the vibration responses between flexible multi-body model and rigid one would be discussed. Since the wheel base of mid-size bus is longer than passenger car, the deformation of vehicle body more obviously influences the output of vibration response. The operating condition in practical driving can be expressed by flexible model, and the performance prediction of vehicle can be closer to the real vehicle behavior. The difference between the flexible body simulation and rigid body simulation is 1.17%, and the flexible body model is more practical.

Durability analysis and implementation of the floating frame of reference formulation

The finite element floating frame of reference (FFR) formulation, implemented in most commercial multibody system (MBS) computer programs, is widely used in the durability analysis by a large number of industry sectors. In this paper, a single-degree of freedom system is used to derive a new analytical model from the general nonlinear FFR equations. The obtained new analytical model, which can serve as a benchmark example, is used to address fundamental issues related to the accurate, efficient, and general implementation of the FFR formulation, including the treatment of the algebraic joint constraint equations, fundamental difference between the FFR reference conditions and the structural mechanics boundary conditions, the choice of the deformation modes, handling redundant MBS constraints, effect of the MBS joints on the oscillation frequencies, and difference between fixed and moving boundary conditions. Structural mechanics boundary conditions eliminate degrees of freedom and define the system topology, while the FFR reference conditions eliminate coordinate redundancy and do not introduce any motion constraints. The paper shows analytically how the MBS joint constraint equations change the system oscillation frequencies, demonstrates the effect of using inappropriate set of reference conditions, proves there is no single set of reference conditions suited for all applications, and uses other FE methods to verify the results and support the conclusions drawn. The results obtained in this investigation show that improper selection of the reference conditions can lead to solution errors that exceed 100%, making such a solution completely unreliable in any durability investigation. General implementation of the FFR formulation will significantly contribute to increasing reliance on virtual testing, less reliance on building actual prototypes, better understanding of flexible body dynamics, and better communication between various computer-aided engineering groups.

Launch vehicle design and GNC sizing with ASTOS

The European Space Agency (ESA) is currently involved in several activities related to launch vehicle designs (Future Launcher Preparatory Program, Ariane 6, VEGA evolutions, etc.). Within these activities, ESA has identified the importance of developing a simulation infrastructure capable of supporting the multi-disciplinary design and preliminary guidance navigation and control (GNC) design of different launch vehicle configurations. Astos Solutions has developed the multi-disciplinary optimization and launcher GNC simulation and sizing tool (LGSST) under ESA contract. The functionality is integrated in the Analysis, Simulation and Trajectory Optimization Software for space applications (ASTOS) and is intended to be used from the early design phases up to phase B1 activities. ASTOS shall enable the user to perform detailed vehicle design tasks and assessment of GNC systems, covering all aspects of rapid configuration and scenario management, sizing of stages, trajectory-dependent estimation of structural masses, rigid and flexible body dynamics, navigation, guidance and control, worst case analysis, launch safety analysis, performance analysis, and reporting.

Electrical contact resistance and wear of a dynamically excited metal–graphite brush

The wear and contact resistance of sliding contacts are typically researched with a pin-on-disk experiment that prevents dynamic excitation. However, in electrical machines, the brush clearance enables dynamic excitation, resulting in flexible body dynamics. To research the wear and contact resistance during dynamical excitation, an in-situ experimental approach is introduced here, with the influences of rotational speed, electrical current, and temperature being assessed. This research shows that a small wear rate and contact resistance are possible at 10,000 and 5000 RPM if the electrical current is higher than 3 A. It was also found that the contact resistance decreased with an increased ambient temperature, electrical current, and rotating speed, whereas the wear rate increased with the rotating speed at low current density and low ambient temperature.

Nonlinear dynamics of a cable–pulley system using the absolute nodal coordinate formulation

It is reasonable to develop models and to investigate the dynamic behaviour of systems composed of cables since cable vibration can have an important effect on the motion of these mechanical systems. This paper deals with the application of the nonlinear formulation for flexible body dynamics called the absolute nodal coordinate formulation (ANCF). It is used for modelling the systems composed of cables, pulleys, other rigid bodies and a motor with prescribed motion. The ANCF was chosen as a suitable approach, which that can allow to consider a detailed interaction of the cable and the pulley with its nonlinear dynamical behaviour. The ANCF uses absolute positions of nodes (reference vectors) and slopes (reference vector derivations) as a set of nodal coordinates. An in-house modelling tool in the MATLAB system was created based on the proposed modelling methodology and two case studies were performed. A simple system containing a pulley and a cable with two attached bodies was used in order to test the simulation tool based on the proposed modelling methodology with respect to different parameters. A more complex mechanical system composed of a driven weight joined with a motor by a cable led over a pulley was numerically and also experimentally investigated. The comparison of obtained numerical and experimental results shows sufficient agreement and proves that the proposed modelling approach can be used for dynamic analyses of such systems.

Research on dynamic modeling and electromagnetic force centering of piston/piston rod system for labyrinth piston compressor

Inside labyrinth piston compressor, the piston/piston rod system is main moving part. They suffer from very large periodically varying loads caused by gas force and inertia force. This may result in the piston rod’s bending and vibration. Therefore, the piston is always running eccentrically inside cylinder. It is difficult to calculate and predict the piston’s eccentricity accurately by the traditional analytical method. However, an accurate radial clearance between the piston and the cylinder wall must be calculated in the early design of the labyrinth piston compressor. Thus, this article proposes a new numerical method of studying the piston’s dynamic behavior, which is based on flexible body dynamics and finite element method. The method overall considers the piston rod’s characteristics of bending and vibration, effect of the radial clearance between the piston rod and the guide bearing, as well as crosshead and slideway. Through the model, the piston’s radial eccentric path can be better predicted. In addition, this article also introduces a new idea for realizing piston/piston rod system’s centering and utilizing an electromagnetic guiding system instead of traditional mechanical structure. The new centering technology will simplify greatly the inner structure of the compressor by removing the guide bearing. We have designed theoretically the structure of an electromagnetic guiding system and built its control model. Simulation verifies the effectiveness of this method, and good control result is obtained.