Flexible Multibody Simulation Research Articles

Practical Design Guidelines for Topology Optimization of Flexible Mechanisms: A Comparison between Weakly Coupled Methods

Industrial robots are complex systems, as they require the integration of several sub-assemblies to perform accurate operations. Moreover, they may experience remarkable dynamic actions due to high kinematic requirements, which are necessary to obtain reduced cycle times. The dynamic design of industrial robots can therefore be demanding, since the single structural component can induce an impact both in the design phase (development strategy and computational time) and at the machine level (global stiffness and natural frequencies). To this end, the present paper proposes first a topology optimization procedure based on the Equivalent Static Loads (ESL) method that integrates flexible multibody simulation outputs. The same procedure also foresees an intermediate static reduction to reduce and to precisely define the application points of the ESL. Secondly, an optimization procedure based on the Quasi-Static Loads (QSL) method integrating flexible multibody simulation outputs is proposed as well. The objective is to carry out a comparison between the two methods and consequently evaluate the benefits and drawbacks of the two. In the end, practical guidelines regarding the selection and application of the two methods are also provided to the reader.

An Approximation-Based Design Optimization Approach to Eigenfrequency Assignment for Flexible Multibody Systems

The use of flexible multibody simulation has increased significantly over recent years due to the increasingly lightweight nature of mechanical systems. The prominence of lightweight engineering design in mechanical systems is driven by the desire to require less energy in operation and to reach higher speeds. However, flexible lightweight systems are prone to vibration, which can affect reliability and overall system performance. Whether such issues are critical depends largely on the system eigenfrequencies, which should be correctly assigned by the proper choice of the inertial and elastic properties of the system. In this paper, an eigenfrequency assignment method for flexible multibody systems is proposed. This relies on a parametric modal model which is a Taylor expansion approximation of the eigenfrequencies in the neighborhood of a configuration of choice. Eigenfrequency assignment is recast as a quadratic programming problem which can be solved with low computational effort. The method is validated by assigning the lowest eigenfrequency of a two-bar linkage by properly adding point masses. The obtained results indicate that the proposed method can effectively assign the desired eigenfrequency.

Flexible multibody impact simulations based on the isogeometric analysis approach

Usually detailed impact simulations are based on isoparametric finite element models. For the inclusion in multibody dynamics simulation, e.g., in the framework of the floating frame of reference, a previous model reduction is necessary. A precise representation of the geometry is essential for modeling the dynamics of the impact. However, isoparametric finite elements involve the discretization of the geometry. This work tests isogeometric analysis (IGA) models as an alternative approach in the context of impact simulations in flexible multibody systems. Therefore, the adaption of the flexible multibody system procedure to include IGA models is detailed. The use of nonuniform rational basis splines (NURBS) allows the exact representation of the geometry. The degrees of freedom of the flexible body are afterwards reduced to save computation time in the multibody simulation. To capture precise deformations and stresses in the area of contact as well as elastodynamic effects, a large number of global shape functions is required. As test examples, the impact of an elastic sphere on a rigid surface and the impact of a long elastic rod are simulated and compared to reference solutions.

Validation of the Time-Domain Boundary Element Method in Acoustics regarding Flexible Multibody Simulations and Acoustic Measurements

With flexible multibody simulation, the dynamical behaviour of vehicle components as well as entire systems can be simulated in an efficient way. In addition to structural vibrations, noise emissions play an important role in terms of comfort in the vehicle industry. While the dynamics of the structures can be simulated directly in the time-domain, the sound radiation is usually calculated in the frequency-domain. This process enables an efficient investigation of steady-state operating conditions but not of transient operating conditions. The time-domain Boundary Element Method (TD-BEM) in acoustics allows to determine the sound pressure directly in the time-domain, without complicated transformation from the frequency-domain. Existing work concentrates on stability criteria and general theoretical applicability. The validation on real test cases with measurement results, however, has rarely been focused. On this work, we aim to close this gap between theory and practical applications with the help of real housing structures and test cases. In order to set up an acoustic validation, meaningful measurements need to be combined with validated structural simulations that match the physical world with regard to the sound radiation as closely as possible. Therefore, several test set-ups are used to measure the real dynamic and acoustic behaviour in an anechoic chamber with multiple accelerometers, a laser vibrometer, various microphones and a sound intensity PU probe. Based on these measurements, multibody and BE-models are created, representing the same scenarios with numerical methods. Derived from the simulated surface accelerations, the acoustic radiation is calculated in the time-domain. Comparisons at a simple oval-shaped housing show that the method generates very promising results. The mean deviation between the measured and simulated sound pressure levels (time-domain) is less than 1 dB and the frequency spectra show a high quantitative correlation as well.

Modeling and Simulation of Heavy-Lift Tethered Multicopter Considering Mechanical Properties of Electric Power Cable

In case of a fire at a high-rise building which is densely populated, an extension ladder is used to rescue people who have yet to evacuate to a safe place away from the fire, whereas those who are stranded at a height that is unreachable with the ladder should be promptly saved with different rescue methods. In this case, an application of the tethered flight system capable of receiving power over a power cable from the ground to a multicopter may guarantee effective execution of the rescue plan at the scene where fire is raging without any restrictions of the flight time. This article identified restrictions that should be considered in the design of a multicopter capable of tethered flight aimed to rescue stranded people at an inaccessible location with an extension ladder at a fire-ravaged high-rise building and assessed its feasibility. A power cable capable of providing dozens of kilowatts of electricity should be installed to enable the implementation of the rescue mission using the tethered multicopter. A flexible multi-body dynamics modeling and simulation with viscoelastic characteristics and heavy weight of power cable were carried out to evaluate the effects of such cable of the tethered flight system on the dynamic characteristics of the multicopter. The results indicate that as for a heavy-lift tethered multicopter designed to be utilized for rescue operations, the properties of the power cable, such as weight, rigidity and length, have a major impact on the position and attitude control performance.

A noninvasive system‐level model order reduction scheme for flexible multibody simulation

AbstractThis paper presents a novel system‐level model order reduction scheme for flexible multibody simulation, namely the system‐level affine projection (SLAP). Contrary to existing system‐level model order reduction approaches for multibody systems simulation, this methodology allows to obtain a constant reduced order basis which can be obtained in a noninvasive fashion with respect to the original flexible multibody model. It is shown that this scheme enables an automatic joint constraint elimination which can be obtained at low computational cost through exploitation of the component level modes typically employed in flexible multibody simulation. The equations of motion are derived such that the computational cost of the resulting SLAP model is independent of the original model size. This approach results in a set of ordinary differential equations with a constant mass matrix and nonlinear internal forces. This structure makes the resulting model suitable for a range of estimation, control, and design applications. The proposed approach is validated numerically on a flexible four‐bar mechanism and shows good accuracy for a very low‐order SLAP model.

Gravity compensation system of mesh antennas for in-orbit prediction of deployment dynamics

Large deployable mesh antennas are central components of high gain satellites that are used for gathering electromagnetic signals. Deploying such antennas in-orbit is a delicate and precise process, and any failure in their unfolding can result in satellite malfunction. Thus, on-ground experiments have been used to attempt to predict the in-orbit deployment performance of mesh antennas. However, Earth's gravitational field presents a great obstacle in achieving this goal, and how best to design a gravity compensation system for the flexible webs of mesh antennas remains unclear despite various proposed gravity compensation techniques. In this paper, we attempt to address this problem via flexible multibody simulations. The results first reveal that, if the webs are not offloaded at all, the weight of the webs causes the driving forces of the motors and the bending moments of the truss members obtained during on-ground tests to deviate from those experienced by the antenna in-orbit. To counteract this problem, two different gravity suspension systems for the webs of mesh antennas were designed and evaluated. In particular, the different numbers and positions of the suspension nodes were investigated. The results show that no matter which of the two proposed designs is adopted, the number and location of suspension nodes should be carefully selected to achieve well-behaved compensation performance. Furthermore, the proposed modeling and analysis methods can also be applied to other flexible mechanical systems requiring gravity compensation.

Rigid-flexible coupling modelling and dynamic performance analysis of novel flexible road wheel

A novel flexible road wheel with hub-hinge-ring combined structure is introduced to improve the buffer damping performance and lightweight level of tracked vehicles. To balance computational efficiency and precision, an advanced rigid-flexible coupled model of the flexible road wheel is established using a hybrid modelling method combining finite element method and multi-body dynamics. The reliability and accuracy of the established rigid-flexible coupled model are verified by wheel static loading experiment. The modal flexible body of the elastic outer ring is developed by modified Craig-Bampton method and the simulated results are in good agreement with the experimental data. Based on the verified rigid-flexible coupled model, the dynamic characteristics of the flexible road wheel under typical operation conditions were investigated. The simulation results show that when the motion state changes, the elastic outer ring will produce a hysteretic angle with respect to the hub, delaying the transmission of torque. The system parameters have a greater effect on the vertical vibration of the flexible road wheel. The higher the vehicle speed, the more vibration will be caused, and the increase in the load and number of hinge groups will reduce the vibration. The research results provide reference for structure optimization of flexible road wheel and lay a foundation for flexible multi-body dynamic simulation of tracked vehicles with flexible road wheels.

Multifidelity Modeling of Deployable Wings: Multibody Dynamic Simulation and Wind Tunnel Experiment

Slender deployable wings have attracted interest for use in Mars, Titan, and high-altitude flights. Such wings are composed of multiple bodies connected by hinge joints and can be deployed or folded spanwise during flight. A deployment simulation model is required for their design. This paper proposes a multifidelity multibody modeling method that uses a new asymmetrically gradient-deficient absolute nodal coordinate beam element. The proposed method addresses the drawbacks of conventional elements, namely, numerical locking and the need for a large number of generalized coordinates, by exploiting a structural characteristic of a slender wing. It enables computationally efficient low-fidelity rigid multibody simulation and more realistic high-fidelity flexible multibody simulation, both accomplished using a consistent modeling process and the same simulation program architecture. Additionally, the low-fidelity and high-fidelity models can be coupled with an aerodynamic model using a consistent coupling methodology. To validate the proposed modeling method, wing deployment experiments were performed in a wind tunnel at the Institute of Fluid Science, Tohoku University. The simulation results obtained using the proposed modeling method were found to be in good agreement with those of the wind tunnel experiments, even when the wings experienced large geometrically nonlinear deformations.

An efficient formulation for flexible multibody dynamics using a condensation of deformation coordinates

This paper introduces a more efficient formulation for flexible multibody dynamics based on the floating frame of reference formulation (FFRF). A two-step condensation method is proposed. The first condensation involves coordinate reduction using a modal transformation, from nodal coordinates to modal coordinates, in the context of model order reduction (MOR). The second condensation involves re-fabrication of the equations of motion using a dynamic condensation of the deformation modal coordinates obtained from the first condensation. In the first condensation, constraint modes are corrected by condensation of the truncated modes that represent the effects of residual flexibility. As a result, the first condensation offers a more accurate deformation field in the reduced order model, which consequently leads to a more accurate flexible multibody simulation. In the second condensation, the equations of motion of a flexible multibody are once more reduced to the equations of motion in terms of absolute coordinates for the body reference frames. In this way, the proposed method deals with smaller sized equations of motion than in the conventional FFRF, where they are represented in terms of both absolute coordinates and deformation modal coordinates. The effect of the first condensation was verified using a benchmark example of a slider–crank mechanism with a flexible connecting rod. The efficiency of the proposed condensation method was also investigated using a computational complexity analysis with an $n$ -flexible body pendulum.

Neuro-musculoskeletal flexible multibody simulation yields a framework for efficient bone failure risk assessment

Fragility fractures are a major socioeconomic problem. A non-invasive, computationally-efficient method for the identification of fracture risk scenarios under the representation of neuro-musculoskeletal dynamics does not exist. We introduce a computational workflow that integrates modally-reduced, quantitative CT-based finite-element models into neuro-musculoskeletal flexible multibody simulation (NfMBS) for early bone fracture risk assessment. Our workflow quantifies the bone strength via the osteogenic stresses and strains that arise due to the physiological-like loading of the bone under the representation of patient-specific neuro-musculoskeletal dynamics. This allows for non-invasive, computationally-efficient dynamic analysis over the enormous parameter space of fracture risk scenarios, while requiring only sparse clinical data. Experimental validation on a fresh human femur specimen together with femur strength computations that were consistent with literature findings provide confidence in the workflow: The simulation of an entire squat took only 38 s CPU-time. Owing to the loss (16% cortical, 33% trabecular) of bone mineral density (BMD), the strain measure that is associated with bone fracture increased by 31.4%; and yielded an elevated risk of a femoral hip fracture. Our novel workflow could offer clinicians with decision-making guidance by enabling the first combined in-silico analysis tool using NfMBS and BMD measurements for optimized bone fracture risk assessment.

Preconditioning strategies for linear dependent generalized component modes in 3D flexible multibody dynamics

The trend away from physical towards virtual prototyping as well as increasing industrial demands require advanced simulation tools for dynamical systems. Virtually all engineering systems are assemblies and are associated with stresses, noise and vibrations; therefore, flexible multibody simulations are inevitable for accurate predictions. However, real-world finite element models contain millions of degrees of freedom that cannot be reasonably handled without model reduction techniques. Generalized component mode synthesis is a promising tool for flexible 3D multibody systems, since the generalized component modes not only represent the deformation modes in any possible orientation, but also rigid body motion, which preserves a linear configuration space, yielding a constant mass matrix, a co-rotated but constant stiffness matrix, no quadratic velocity vector and a simple structure of the equations of motion. In this novel framework, the displacement is approximated by a linear combination of generalized component modes generated from vibration eigenmodes, undeformed nodal coordinates and the Cartesian base vectors. The emerging system matrices may be ill-conditioned and may introduce significant numerical errors, because of linearly dependent generalized component modes and due to different orders of magnitude of their Euclidean norm. However, this issue has not received much attention in the open literature despite its importance. Hence, the current contribution sheds light on this problem and derives preprocessing procedures to convert ill-conditioned into well-conditioned problems, which shall improve the formulation’s applicability. The new findings are illustrated by numerical experiments of simple bodies and a crankshaft.

From multiscale modeling to design of synchronization mechanisms in mesh antennas

Flexible multibody simulation is supposed to be a promising method for studying the deployment dynamics of large mesh antennas and assisting the design of the related crucial mechanisms. However, fulfilling a full-scale deployment simulation of a mesh antenna is so challenging that it can be rarely found in the literature. In our opinion, the bottleneck of modeling some mesh antennas is dealing with the multiscale physics mainly sourced from the cable-pulley systems that are frequently used to transfer forces for long distance range. A traditional model of a cable-pulley is based on contact method, which involves fine cable mesh, a large amount of contact detection, and small time step for numerical integration, resulting in low calculation efficiency. To cope with this difficulty, we proposed a novel and efficient multiscale method to handle the cable-pulley systems. The basic idea is avoiding the contact detection by separating a cable into two segments: non-contact and contact segments, according to which part of the cable is in contact with the pulley. The non-contact segment is meshed with variable-length elements based on the arbitrary Lagrangian–Eulerian (ALE) formulation. The contact segment is considered an invisible segment to constrain the variable-length cable element on the pulley; its border is dynamically located by the relative configuration between the pulley and the cable. The accuracy and efficiency of the proposed method were confirmed by a numerical example. Then, it was used to evaluate, compare and design the synchronization mechanism in a kind of mesh antenna. The obtained results can directly guide the actual design of mesh antennas, and the proposed multiscale method can be applied to simulating other similar mechanical systems.

A multibody simulation study of alpine ski vibrations caused by random slope roughness

In alpine skiing an athlete's performance or injury mechanisms are strongly influenced by ski vibrations. Ski vibrations are mainly caused by irregularities of the ski-snow interaction (e.g. ripplets and disturbances of the slope, friction between ski and snow). With respect to the ski-snow interaction ski vibrations were not yet considered in computer simulation studies. During this study a planar multibody simulation model of a mono-skier has been developed to investigate transversal vibrations of unedged skis during schussing in the fall line over rough (random) ski slopes. The skis are modelled as dynamic Euler-Bernoulli beams and are incorporated as flexible beams into a multibody skier model. The interaction between skis and snow is modelled by a Kelvin-Voigt constitutive equation for the snow penetration force. The random ripplets and disturbances of the slope are described by random fields, which are generated based on real data obtained from measuring a public ski slope surface with a high resolution laser scanner. By the Monte Carlo simulation method a sequence of runs over random slope surfaces is performed and the ski vibrations of the ski shovel are analysed. The results show that the irregularities on a ski slope contribute considerably to the vibration of a ski and the performance of a skier. Thus, they have to be considered in multibody simulation models of alpine skiing. The developed simulation model will support the understanding of ski vibrations and their causes to improve the run time and to prevent injuries in alpine skiing. The presented simulation model can also be applied to find optimal material parameters to reduce ski vibrations during schussing. This work combines a flexible multibody simulation model and random fields. The implementation of random fields in multibody simulation models admits a more realistic investigation of the mechanical behaviour of complex systems due to random spatial uncertainties in input parameters.

On the study of Rigid Body Inertia

In the classical finite element literature beams and plates are not considered as isoparametric elements since infinitesimal rotations are used as nodal coordinates. As a consequence, exact modeling of an arbitrary rigid body displacement cannot be obtained, and rigid body motion does not lead to zero strain. In order to circumvent this problem in flexible multibody simulations, an intermediate element coordinate system, which has an origin rigidly attached to the origin of the deformable body coordinate system and has axes which are parallel to the axes of the element coordinate system in the undeformed configuration was introduced. The correct equations of motion, however, can be obtained if the coordinates are defined in terms of global slopes. Using this new definition of the element coordinates, an absolute nodal coordinate formulation that leads to a constant mass matrix for the element can be developed. Using this formulation, in which no infinitesimal or finite rotations are used as nodal coordinates, beam and plate elements can be treated as isoparametric elements. G M T Detect language Afrikaans Albanian Arabic Armenian Azerbaijani Basque Belarusian Bengali Bosnian Bulgarian Catalan Cebuano Chichewa Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Esperanto Estonian Filipino Finnish French Galician Georgian German Greek Gujarati Haitian Creole Hausa Hebrew Hindi Hmong Hungarian Icelandic Igbo Indonesian Irish Italian Japanese Javanese Kannada Kazakh Khmer Korean Lao Latin Latvian Lithuanian Macedonian Malagasy Malay Malayalam Maltese Maori Marathi Mongolian Myanmar (Burmese) Nepali Norwegian Persian Polish Portuguese Punjabi Romanian Russian Serbian Sesotho Sinhala Slovak Slovenian Somali Spanish Sundanese Swahili Swedish Tajik Tamil Telugu Thai Turkish Ukrainian Urdu Uzbek Vietnamese Welsh Yiddish Yoruba Zulu Afrikaans Albanian Arabic Armenian Azerbaijani Basque Belarusian Bengali Bosnian Bulgarian Catalan Cebuano Chichewa Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Esperanto Estonian Filipino Finnish French Galician Georgian German Greek Gujarati Haitian Creole Hausa Hebrew Hindi Hmong Hungarian Icelandic Igbo Indonesian Irish Italian Japanese Javanese Kannada Kazakh Khmer Korean Lao Latin Latvian Lithuanian Macedonian Malagasy Malay Malayalam Maltese Maori Marathi Mongolian Myanmar (Burmese) Nepali Norwegian Persian Polish Portuguese Punjabi Romanian Russian Serbian Sesotho Sinhala Slovak Slovenian Somali Spanish Sundanese Swahili Swedish Tajik Tamil Telugu Thai Turkish Ukrainian Urdu Uzbek Vietnamese Welsh Yiddish Yoruba Zulu Text-to-speech function is limited to 200 characters Options : History : Feedback : Donate Close

Flexible multibody dynamics using coordinate reduction improved by dynamic correction

This paper is concerned with the efficient dynamic analysis of flexible multibody systems using a robust coordinate reduction technique. Unlike conventional static correction, the formulation is derived by dynamic correction that considers the inertia effect. In this formulation, the constraint and fixed-interface normal modes, which are representative modes in the typical coordinate reduction, are corrected by considering the truncated modal effect with the residual flexibility. Therefore, the proposed method can offer a more precise reduced system without increasing the dimension, which consequently leads to a more accurate and efficient flexible multibody simulation. We implement here the proposed method under augmented formulations of the floating reference frame approach, and test its performance with numerical examples.

Dynamic Gear Wheel Simulations using Multibody Dynamics

Simulation of the gear train is an important part of the dynamic simulation of the power train of a medium speed diesel engine. In this paper, the advantages of dynamic gear wheel simulation as a part of the flexible multibody simulation of a complete power train are described. The simulation is performed using AVL EXCITE Power Unit.

Multi-body engine simulation including elastohydrodynamic lubrication for non-conformal conjunctions

The evaluation of lubricated contacts is an essential step in modern internal combustion engine simulation to estimate run-time behaviour. A thorough investigation of the occurring thin oil films is critical to estimate friction, wear, noise, vibration and harshness and the overall dynamic behaviour. The prediction of contact pressure and oil film height poses a complex task, especially in non-conformal conjunctions, such as between a cam and a follower. This paper introduces a generic algorithm to solve the elastohydrodynamic lubrication problem and integrates it into a multi-body simulation environment. A focus is put on the versatile integration of the elastohydrodynamic lubrication model into the multi-body framework to create a basis for a full engine simulation. The Reynolds equation and the film thickness equation are treated as modular decoupled systems and, therefore, allow a modular structure of the elastohydrodynamic lubrication algorithm. The method introduced here incorporates existing relaxation techniques and uses them in a decoupled elastohydrodynamic lubrication solver for flexible multi-body dynamics simulation. The contact between a cam and a follower of an internal combustion engine is used as an exemplary contact to test the derived elastohydrodynamic lubrication model. A four-cylinder full engine model with 16 valves and two flexible camshafts is investigated as an example to outline effects of an oil film lubricated cam follower conjunctions in valve train simulation.

Flexible multibody simulation using hybrid integration scheme

One issue in the dynamic simulation of flexible multibody system is poor computation efficiency, which is due to high frequency components in the solution associated with a deformable body. Standard explicit numerical methods should take very small time steps in order to satisfy the absolute stability condition for the high frequency components and, in turn, the computational efficiency deteriorates. In this study, a hybrid integration scheme is applied to solve the equations of motion of a flexible multibody system for achieving better computational efficiency. The computation times and simulation results are compared between the hybrid scheme and conventional methods. The results demonstrate that the efficiency of a flexible multibody simulation can be improved by using the hybrid scheme.

Structural optimization of multibody system components described using level set techniques

The structural optimization of the components in multibody systems is performed using a fully coupled optimization method. The design's predicted response is obtained from a flexible multibody system simulation under various service conditions. In this way, the resulting optimization process enhances most existing studies which are limited to weakly coupled (quasi-) static or frequency domain loading conditions. A level set description of the component geometry is used to formulate a generalized shape optimization problem which is solved via efficient gradient-based optimization methods. Gradients of cost and constraint functions are obtained from a sensitivity analysis which is revisited in order to facilitate its implementation and retain its computational efficiency. The optimizations of a slider-crank mechanism and a 2-dof robot are provided to exemplify the procedure.