Flexible Multibody Dynamics Research Articles

A peridynamics approach to flexible multibody dynamics for fracture analysis of mechanical systems

The classical theory of continuum mechanics is formulated using partial differential equations (PDEs) that fail to describe structural discontinuities, such as cracks. This limitation motivated the development of peridynamics, reformulating the classical PDEs into integral-differential equations. In this theory, each material point interacts with its neighbours inside a characteristic length-scale through bond-interaction forces. However, while peridynamics can simulate complex multi-physics phenomena, its integration in the study of mechanical systems is still limited. This work presents a methodology that incorporates a peridynamics formulation into a planar multibody dynamics (MBD) formulation to allow the integration of flexible structures described by peridynamics into mechanical systems. A flexible body is described by a collection of point masses, in analogy with the meshless collocation scheme commonly used for peridynamics discretisations. Each point mass interacts with other point masses through nonlinear forces governed by a bond-based peridynamics (BBPD) formulation. The virtual bodies methodology enables the definition of kinematic joints connecting the flexible body with the neighbouring bodies. The implementation of the methodology proposed is illustrated using various mechanisms with different levels of complexity. Notched plates subjected to different loading conditions are compared with the results presented in the literature of the peridynamics field. The deformations of a flexible slider-crank mechanism compare well with the results obtained using a classical flexible MBD formulation. Additionally, three scenarios involving a rotating pendulum illustrate how the methodology proposed allows simulating impact scenarios. The results demonstrate how this methodology is capable to successfully simulate highly nonlinear phenomena, including crack propagation, in a multibody framework.

Designing customized temporomandibular fossa prosthesis based on envelope surface of condyle movement: validation via in silico musculoskeletal simulation.

Objective: This study presents an innovative articular fossa prosthesis generated by the envelope surface of condyle movement, and compares its mandible movements, muscle activities, and joint reaction forces with two temporomandibular joint (TMJ) prostheses using multibody musculoskeletal simulation. Methods: A healthy 23-year-old female was recruited for this study. Cone-beam computed tomographic (CBCT) was performed to reconstruct the mandibular bone geometry. A customized TMJ fossa prosthesis was designed based on the subject-specific envelope surface of condyle movement (ESCM). Mandibular kinematics and jaw-closing muscle electromyography (EMG) were simultaneously recorded during maximum jaw opening-closing movements. To validate our prosthesis design, a mandibular musculoskeletal model was established using flexible multibody dynamics and the obtained kinematics and EMG data. The Biomet fossa prosthesis and the ellipsoidal fossa prosthesis designed by imitating the lower limb prostheses were used for comparison. Simulations were performed to analyze the effects of different fossa prostheses on jaw opening-closing motions, mandibular muscle activation, and contact forces. Results: The maximum opening displacement for the envelope-based fossa prosthesis was greater than those for Biomet and ellipsoidal prostheses (36mm, 35mm, and 33mm, respectively). The mandibular musculoskeletal model with ellipsoidal prosthesis led to dislocation near maximal jaw opening. Compared to Biomet, the envelope-based fossa reduced the digastric and lateral pterygoid activation at maximal jaw opening. It also reduced the maximal resistance to condylar sliding on the intact side by 63.2N. Conclusion: A customized TMJ fossa prosthesis was successfully developed using the ESCM concept. Our study of musculoskeletal multibody modeling has highlighted its advantages and potential. The artificial fossa design successfully achieved a wider condylar range of motion. It also reduced the activation of jaw opening muscles on the affected side and resistance on the intact side. This study showed that an ESCM-based approach may be useful for optimizing TMJ fossa prostheses design.

Aeroelastic Analysis Considering the Coupling Effect Between the Reference and Elastic Displacements in Flexible Multibody Dynamics

Aeroelastic Analysis Considering the Coupling Effect Between the Reference and Elastic Displacements in Flexible Multibody Dynamics

Response analysis and effect evaluation of dynamic stabilization for ballasted track

Dynamic stabilization is a process of the railway lines that are newly built must go through before it is put into operation. This study investigates the characteristics of stabilizing operation on ballasted track and proposes methods for detecting and evaluating the state of the ballast bed in an attempt to improve the operation quality. Firstly, the influence mechanism of stabilization on the migration of ballast particles and the settlement of track panel from the macro and micro perspectives through the method of visual non-contact measurement by video images were demonstrated. A three-dimensional simulation model which the first wheelset of the tamping and stabilizing vehicle - ballasted track was established using the discrete element method and multi-flexible body dynamics coupling algorithm, and the logistic mathematical model for sleeper displacement and support stiffness of ballast bed was constructed. Furthermore, an innovative non-contact method for measuring the support stiffness of ballast bed under complex scenes was proposed. Results show that the ballast particles on the slope of the ballast bed are rearranged and gradually compacted by a movement mode of “vertical as the main direction and horizontal as the auxiliary” during the stabilizing operation. As the number of stabilizing operations increases, the settlement of the track panel gradually decreases, with a maximum attenuation amplitude of 44.9%. Comprehensively, the track panel achieves reasonable load distribution after the second stabilizing operation, and achieves the best effect with the relative growth rate of the two-point stiffness being 49.5%. Significantly, this study provides key theoretical basis for the scientific stabilizing operation and evaluation of ballast bed status of railway lines that are newly built.

Optimized Design and Experiment of a Self-Covering Furrow Opener for an Automatic Sweet Potato Seedling Transplanting Machine

The yield and quality of sweet potatoes are significantly influenced by the transplantation posture of sweet potato seedlings. The performance of the sweet potato seedling transplanting opener directly affects the transplantation posture of sweet potato seedlings. In order to improve the yield and quality of sweet potatoes, this study proposes a joint simulation method based on discrete element and flexible multi body dynamics (DEM-FMBD), which optimizes the structure of a self-covering soil opener. By exploring the influence of self-covering soil trenchers on the planting depth and posture of sweet potato seedlings during horizontal transplantation, it was determined that the influencing factors of the experiment were wing spacing, soil reflux height, and soil reflux length. Based on the DEM-FMBD coupling simulation platform, single factor, and quadratic rotation orthogonal experiments were carried out. According to the results of the simulation test, the effect of the interaction of test factors on planting depth and planting attitude was analyzed by the response surface method. Finally, the optimal structural parameter combination was obtained by a multi-objective optimization method: the spacing of the wings was 58 mm, the height of the soil backflow port was 71 mm, and the length of the soil backflow port was 163 mm; thus, the quality of transplanting is improved effectively. This study provides the method and theory reference for the study of sweet potato transplanting.

Development, analysis, and verification of an intelligent auxiliary beekeeping device mounted on a crawler transporter

The transportation of beehives poses a significant challenge in the beekeeping industry. To address the manual handling practices prevalent in the beekeeping industry and enhance the automation level, this study attempts the design and development of a mobile auxiliary beekeeping device mounted on a caterpillar vehicle for beehive transportation. Specifically, the design of the auxiliary device was completed in SolidWorks with the notion of the cylindrical mechanical arm. Subsequently, a dynamic model of the simulated environment is constructed using RecurDyn, facilitating the determination of the torque requirements for each joint based on the dynamic model. Furthermore, the multi-flexible body dynamics analysis is utilized to conduct a flexible analysis of the auxiliary beekeeping device’s three principal components and the maximum beehive weight, which can be safely transported, is estimated through simulation analysis. Particularly, field experiments involve the use of strain gauges to measure the stress exerted on the components of the auxiliary beekeeping device during actual beehive transportation. Additionally, it incorporates the errors and precision associated with each joint, and the planar positioning accuracy result. Meanwhile, the maximum torque required for the joints, which is about 5 N·m was determined by simulation results, affirming that the selected drive motors can meet the operational requirements. Through simulation, it is determined that the auxiliary device can handle a maximum beehive weight of 126 kg, approximately three times the weight of the standard beehives (40 kg) utilized in beekeeping farms. This ensured that the auxiliary device poses no risk of overturning during the beehive transportation. In addition, the stress levels at crucial locations are ascertained through on-site strain experiments. Interestingly, the auxiliary support part (57.68 MPa) and the spindle connection (58.8 MPa) experienced the highest stress levels; and the stress levels in the telescopic rod and lower support part remained below 5 MPa. In particular, these stress levels fall within the permissible range of the materials employed (200 MPa), which ensures the auxiliary device’s safe utilization. An evaluation of each joint’s operational accuracy showed that the planar positioning accuracy result of joint 1 and joint 2 is 9.65 mm for 50% CEP and 23.55 mm for 95% CEP, respectively. Furthermore, the highest final error was exhibited by the vertical extension joint (11.48 mm), indicating that the auxiliary device can successfully accomplish the beehive transportation tasks within beekeeping farms. Overall, this research provides a solid foundation for the subsequent development of automated beehive handling devices.

Non-smooth numerical solution for Coulomb friction, rolling and spinning resistance of spheres applied to flexible multibody system dynamics

Non-smooth numerical solution for Coulomb friction, rolling and spinning resistance of spheres applied to flexible multibody system dynamics

Strongly coupled fluid–structure interaction analysis of aquatic flapping wings based on flexible multibody dynamics and the modified unsteady vortex lattice method

Because of their superior efficiency and low detectability compared to conventional submarine-shaped vehicles, bionic underwater vehicles such as Mantabot are playing increasingly important roles in ocean exploration. However, current research on manta-inspired robots is limited to structural design and pure hydrodynamics analysis of pectoral fin performance, with other aspects such as hydroelasticity and optimal design of flapping wings rarely addressed. This work presents a novel method for analyzing aquatic flapping wings by coupling flexible multibody dynamics with a modified unsteady vortex lattice method. The flexible multibody system is solved by using the absolute nodal coordinate formulation, and the conventional unsteady vortex lattice method is modified to accommodate dynamic stall. Compactly supported radial basis functions are used to transfer the hydroelastic forces and structural displacements across the interface meshes while satisfying global energy conservation, and a predictor–corrector method is used to stabilize the iteration procedure. Three different experiments are used to validate the flexible multibody dynamics solver, the modified unsteady vortex lattice solver, and the proposed fluid–structure interaction framework, respectively. Finally, the hydroelastic framework is demonstrated for a fin-like wing, and how flexibility and movement affect the flapping wing dynamics is examined. Numerical examples show that reducing the structural stiffness of the aquatic flapping wing within a certain range improves the propulsive efficiency but also reduces the thrust coefficient, and how the stiffness distribution affects the thrust and propulsive efficiency remains consistent over a range of the Strouhal number.

Lubrication failure analysis of camshaft bearings in V6 diesel engine

This contribution investigates the lubrication characteristics and failure causes of camshaft bearings belong to a V6 diesel engine. Numerical simulation based on the theory of elastohydrodynamic lubrication and flexible multibody dynamics is performed to analyse the lubrication characteristics of camshaft bearings. The results reveal that lubrication performance of different bearings of camshaft shows great differences. For a certain bearing, the mixed lubrication state and elastohydrodynamic lubrication state alternately occur in one engine cycle. The duration of mixed lubrication varies greatly in different bearings. For the bearing closest to the timing drive gear, the total pressure is dominated by the asperity contact pressure, and the predicted safety factors of the asperity contact pressure, hydrodynamic pressure and oil film thickness are less than 1, which means that this bearing will have lubrication failure.

Real-Time Simulation of Ground Vehicles on Deformable Terrain

Abstract Sophisticated modeling and simulation, based on rigid and flexible multibody dynamics, are nowadays a standard procedure in the design and analysis of vehicle systems and are widely adopted for on-road driving. Off-road driving for both terrestrial wheeled and tracked vehicles, as well as wheeled and legged robots and rovers for extra-terrestrial exploration pose additional modeling and simulation challenges, a primary one being that of the vehicle–terrain interaction, modeling of deformable terrain, and terramechanics in general. Techniques for modeling deformable terrain span an entire range varying in complexity, representation accuracy, and ensuing computational effort. While formulations such as fully resolved granular dynamics, continuum representation of granular material, or finite element can provide a high level of accuracy, they do so at a significant cost, even when the implementation leverages parallel computing and/or hardware accelerators. Real-time or faster than real-time terramechanics is a highly desired capability (in applications such as training of autonomous vehicles and robotic systems) or critical capability (in applications such as human-in-the-loop or hardware-in-the-loop). We present a real-time capable deformable soil implementation, extended from the soil contact model (SCM) developed at the German Aerospace Center which in turn can be viewed as a generalization of the Bekker-Wong and Janosi-Hanamoto semi-empirical models for soil interaction with arbitrary three-dimensional shapes and arbitrary contact patches. This SCM implementation is available, alongside more computationally intensive deformable soil representations, in the open-source multiphysics package Chrono. We describe the overall implementation and the features of the Chrono SCM model, the efficient underlying data structures, the current multicore parallelization aspects, and its scalability properties for concurrent simulation of multiple vehicles on deformable terrain.

Rigid-flexible coupling multi-body dynamics modeling of a semi-submersible floating offshore wind turbine

A 14-degree-of-freedom (14-DOF) flexible multibody dynamics model is developed and verified for a semi-submersible floating offshore wind turbine (FOWT). The model considers the coupled dynamics of the platform, tower, nacelle, blades, and mooring subjected to external wind and wave loads. The platform is simplified as a rigid body connected to the seabed by the mooring system. The tower and blade are modeled as flexible cantilever beams. The energy method is used to derive the governing equations of motion, where the kinetic energy, potential energy, and work done by external wind-wave forces are all deduced in a global coordinate system. The 5-MW baseline semi-submersible FOWT is used to verify the derived model against the results simulated from FAST developed by the US National Renewable Energy Laboratory (NREL) at two scenarios: free decay state and different wind-wave load cases. Results show that the established FOWT model can well reflect the vibration characteristics of FAST model. The application of the model to the control of platform pitch with a tuned mass damper is studied. The simplified model could provide a low-order method for the structural dynamics analysis and advanced vibration control design for the multi-body components of the semi-submersible FOWT in the future.

Dynamic analysis of a deep-towed seismic system based on a flexible multi-body dynamics frame

A deep-towed seismic system is an effective tool for exploring minerals in strata. Because the exploration accuracy is closely related to the towing depth and array cable shape, a computational framework based on the flexible multi-body dynamics system is proposed to analyze the dynamic characteristics of the deep-towed seismic system caused by the mothership motion and sea current. The towing cable and seismic array cable are modeled using the absolute nodal coordinate formulation (ANCF), and several classical towing cases are designed to systematically analyze the influences of the mothership motion and current. The results indicate that the axial motion of the mothership along the towing cable is approximately rigidly transmitted, and the phase difference is related to the curvature distribution of the towing cable. In addition, currents parallel to the towing speed significantly change the towing depth. These dynamic characteristics can inform the design of array cable arrangements and control algorithms.

Proposal of strain wave gear actuated by magnetic force

Lower limb exoskeletons with actuators aids disabled individuals in walking. However, the exoskeleton weight is greater than that of conventional medical devices such as orthoses and walking frames. In this study, we propose a novel strain wave gear for light exoskeletons, which is 50% lighter than conventional commercial strain wave gears. This gear uses magnets and yokes, rather than mechanical elements. The thin-walled elastic cylinder is deformed by the magnetic force in the gear, and the torque is transmitted by tooth engagements. The maximum torque was calculated to be 10.5 Nm using flexible multibody dynamics analyses with a magnetic force database. The outcome was efficient in development of lightweight machines.

A Two-Dimensional Corotational Beam Formulation Based on the Local Frame of Special Euclidean Group SE(2)

AbstractThe corotational frame method is widely used in the simulation of flexible multibody dynamics. Its core idea is to separate the rigid motion from the flexible deformation so that it can make fully exploit a large number of excellent local finite elements. The essence of the conventional corotational frame method is the projection relationship between the element frame and the global frame. This paper explores another coordinate projection method for two-dimensional (2D) corotational beam element. The projection relationship between the element frame and the local frame in the framework of Lie algebra se(2) has been proposed. Based on the description of SE(2), the formulation of corotational beam element and integration algorithm is presented. The local frame description greatly reduces the nonlinearity of the formula by eliminating the effect of the rigid body motion on the projection matrix, internal force and inertial force. Several examples of large deformation and large rotation are performed, and it is found that the step-size convergence and iterative efficiency of SE(2) description are improved compared with R3 description. Moreover, some examples are used given to verify that the frame invariance brought by SE(2) is valuable for improving computing efficiency. The presented transformation method can easily extend to other 2D elements.

Grid-Stamping on a Polygon Model for Implementing Arbitrary-Shaped Boundary Conditions in a Moving Particle Semi-Implicit Method

This study proposes a new wall boundary condition for the grid-stamping on a polygon (G-StoP) model, which enables a simpler and more efficient handling of boundary surfaces of arbitrarily complex-shaped bodies represented using polygons (or meshes). For example, computer-aided design surface data can be used to analyze flow using a particle-based fluid-solver moving particle semi-implicit method. For coupling simulations of fluid–multibody dynamics, the Pusan-National-University-modified MPS method is improved, and the coupling analysis is performed using RecurDyn, a commercial software package for multibody (or flexible multibody) dynamics. To confirm the applicability of the developed G-StoP model, hydrostatic pressure simulations are conducted in a rectangular tank at various corner angles. Then, the hydrostatic pressure results are compared with previously proposed polygonal wall boundary model results and theoretical solutions. That is, in the case with a corner angle of 30°, it was confirmed that the relative error to the experiment of the polygon model was 11.3%, while that of the G-StoP model was 1.3%. This demonstrates that the proposed G-StoP model is exceptional for numerical stability and robustness even when it is difficult to secure information on neighboring particles as the corner angle of the object becomes small. In addition, the G-StoP model was applied to dam breaking, subaerial landslide tsunami, and wine sloshing problems, and its accuracy and applicability were tested through comparison with experimental and other simulation results. As a result, it was shown that the present simulation results were much closer to the experiments than other simulations.

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.

A fluid–structure interaction model for large wind turbines based on flexible multibody dynamics and actuator line method

With higher demand of affordable electricity and rapid development of wind turbine technology, scale of wind turbines has been upsizing. As a consequence, blades grow longer and slender. Large geometrically nonlinear deformation and vibration of the blades lead to more challenges in the structural design. In the aerodynamic analysis, traditional blade element momentum theory cannot predict the complicated behavior of these modern blades while fully resolved Navier–Stokes equation methods cost much time modeling and refinement. To overcome these challenges, this paper proposes a new numerical method to analyze turbine aeroelastic performance and fluid–structure interaction based on flexible multibody dynamics and large eddy simulation with anisotropic actuator line method. By comparing the results with various existing numerical methods, we show that the newly proposed method can effectively predict the performance of the wind turbine, such as deformation and power output. We find that blade flexibility poses noticeable impact on the performance of large scale turbines in normal working conditions. The location of nascent vortex is postponed by blade deflection. The max difference between rigid and flexible blades in downstream velocity distributions reaches 10% and occurs at a radial distance around 0.55D. The new method also takes the fluid–structure coupling effect and momentum interaction into consideration and eliminates the non-physical oscillations caused by uncoupled methods. Also, blades deflection and vibration are found to accelerate momentum exchange, which facilitates the wake recovery process. Furthermore,compared to the rigid-blade model, the turbulent kinetic energy obtained by the newly developed flexible-blade model is higher in the low-frequency region, in which large-scale vortices develop and the turbulent mixing effect is strong. This paper is expected to provide a framework for researchers and technology developers to design or estimate the performance of modern large wind turbines.

The Pretension Design of Cable Mesh considering the Large Deformation of Ring Truss

The conventional pretension design of cable mesh usually takes the ring truss as a rigid body or assumes small deformation. This method needs to be more accurate in designing super large aperture antennas. A cable mesh design method considering the large deformation of the ring truss is proposed in this paper based on the flexible multibody dynamics (FMD) and the force density method (FDM). With this method, the significant range deviation of the boundary points’ position of the ring truss under the tension of the external area of the cable mesh after the completion of the pretension design can be predicted with high accuracy. After the ring truss and cable mesh surface are assembled stably, there is only a minimal deviation between the actual mesh surface and the theoretical mesh surface of the antenna, and there is only a minimal deviation between the genuine mesh pretension and the design pretension. The above calculation method is verified by numerical simulation, and the simulation results show that the technique can be applied to the mesh pretension design of a super large aperture ring deployable antenna.

Influence of clearance and structural coupling parameters on shimmy stability of landing gear

AbstractThere are many factors causing the shimmy of the aircraft landing gear and structural clearance of landing gear is a typical factor. Some aircraft in service or operation did not shimmy before, but suddenly appeared after a period of use. To solve the problem of clearance shimmy during the service of a certain aircraft, we established a dynamic model of rotating gear with clearance based on the flexible multi-body dynamics model of landing gear and L-N contact theory. We defined different types of clearance and established a mechanical model of aircraft pendulum vibration considering the clearance of landing gear structure for dynamic simulation, and studied the effects of different clearance types, clearance size of motion pair and different clearance positions on the stability of pendulum. The results show that the axial clearance has little effect on the shimmy performance of landing gear; the radial clearance has a certain effect on the shimmy performance of medium speed running, which slightly improves the shimmy damping required by medium speed running; the rotational clearance affects the shimmy performance of the nose landing gear by affecting the force transmission of structural components. The required shimmy damping coefficient increases at low speed and decreases at high speed. The main reason for the return clearance is that during the return, the shimmy damper does not work, which leads to the decrease of the shimmy damping performance and the increase of the required shimmy damping coefficient in the whole speed range. Meanwhile, the structural clearance will increase the shimmy frequency of the nose landing gear. By analysing the yaw angle of the nose landing gear and the time domain curve of the yaw angle of the yaw damper, we can determine which structure of the landing gear and which type of clearance is the cause of the yaw. Finally, the coupling effect caused by the main structural parameters of the landing gear in “gap shimmy” was analysed according to different mechanical stability distances and strut stiffness of the nose landing gear, providing reference for aircraft anti-shimmy design, nose landing gear fault diagnosis and nose landing gear maintenance support.

A semi-analytical approach to sensitivity analysis with flexible multibody dynamics of a morphing forward wing section

In the present paper, semi-analytical design sensitivity analysis of a morphing forward wing section modeled as a flexible multibody system is developed. The flexible multibody dynamics model consists of a flexible external wing skin and an actuation mechanism with rigid bodies. The floating frame of reference formulation is used for the formulation of the equations of motion, while time integration is carried out with the generalized-alpha method and Newton–Raphson iterations for the nonlinear analysis. These steps are considered in both the primal analysis and the developed efficient design sensitivity analysis. The calculation of the design sensitivities is based on direct differentiation and carried out with a semi-analytical approach. The responses of interest include the deviations of the wing profile from the targeted morphed geometry and the resulting stresses in the wing skin. The design variables considered in this work are geometric parameters, material parameters and loading parameters. The calculations with the shown method provide reliable and accurate results combined with high computational efficiency. The visualization of the computed sensitivity values gives an easy interpretation of the sensitivities and facilitates the understanding of the design engineer on how to change the design variables to improve the design of the system. The introduced sensitivity analysis enables future investigations, including the application of the method to gradient-based design optimization and uncertainty analysis.