Multibody Code Research Articles

A novel approach for longitudinal train dynamics simulations with multibody codes

The paper describes a novel approach to include longitudinal train dynamics within multibody codes by means of a dummy user force element. The latter solves the ordinary differential equations describing longitudinal train dynamics through the definition of additional dynamic states, and it calculates the in-train forces, which have a strong effect on the running safety of railway vehicles. The novel strategy allows to evaluate longitudinal train dynamics and multibody dynamics within the same computational framework, thus solving the dynamic states of both problems with the same numerical integrator. The method is first validated in simulation scenarios of an international benchmarking activity against traditional approaches and then it is applied to evaluate the dynamic safety of an emergency braking operation of a European freight train. With respect to developing multibody models with one body per vehicle in the train consist, the novel approach can be up to four times faster. Moreover, the novel method proves to be faster by up to one order of magnitude when compared to co-simulation strategies, whose accuracy is strongly related to a proper tuning of the communication rate.

Multibody Models Generated from Natural Language

AbstractComputational models are conventionally created with input data, script files, programming interfaces, or graphical user interfaces. This paper explores the potential of expanding model generation, with a focus on multibody system dynamics. In particular, we investigate the ability of Large Language Model (LLM), to generate models from natural language. Our experimental findings indicate that LLM, some of them having been trained on our multibody code Exudyn, surpass the mere replication of existing code examples. The results demonstrate that LLM have a basic understanding of kinematics and dynamics, and that they can transfer this knowledge into a programming interface. Although our tests reveal that complex cases regularly result in programming or modeling errors, we found that LLM can successfully generate correct multibody simulation models from natural-language descriptions for simpler cases, often on the first attempt (zero-shot).After a basic introduction into the functionality of LLM, our Python code, and the test setups, we provide a summarized evaluation for a series of examples with increasing complexity. We start with a single mass oscillator, both in SciPy as well as in Exudyn, and include varied inputs and statistical analysis to highlight the robustness of our approach. Thereafter, systems with mass points, constraints, and rigid bodies are evaluated. In particular, we show that in-context learning can levitate basic knowledge of a multibody code into a zero-shot correct output.

Velocity Level Approximation of Pressure Field Contact Patches

Pressure Field Contact (PFC) was recently introduced as a method for detailed modeling of contact interface regions at rates much faster than elasticity-theory models, while at the same time predicting essential trends and capturing rich contact behavior. The PFC model was designed to work in conjunction with error-controlled integration at the acceleration level. Therefore a vast majority of existing multibody codes using solvers at the velocity level cannot incorporate PFC in its original form. In this work we introduce a discrete in time approximation of PFC making it suitable for use with existing velocity-level time steppers and enabling execution at real-time rates. We evaluate the accuracy and performance gains of our approach and demonstrate its effectiveness in simulating relevant manipulation tasks. The method is available in open source as part of Drake's Hydroelastic Contact model.

Efficient Discrete Element Modeling of Particle Dampers

Particle dampers’ dissipative characteristics can be difficult to predict because of their highly non-linear behavior. The application of such devices in deformable vibrating systems can require extensive experimental and numerical analyses; therefore, improving the efficiency when simulating particle dampers would help in this regard. Two techniques often proposed to speed up the simulation, namely the adoption of a simplified frictional moment and the reduction of the contact stiffness, are considered; their effect on the simulation run-time, on the ability of the particle bed to sustain shear deformation, and on the prediction of the dissipation performance is investigated for different numerical case studies. The reduction in contact stiffness is studied in relation to the maximum overlap between particles, as well as the contacts’ duration. These numerical simulations are carried out over a wide range of motion regimes, frequencies, and amplitude levels. Experimental results are considered as well. All the simulations are performed using a GPU-based discrete element simulation tool coupled with the multi-body code MBDyn; the results and execution time are compared with those of other solvers.

Multibody Computer Model of the Entire Equine Forelimb Simulates Forces Causing Catastrophic Fractures of the Carpus during a Traditional Race.

Simple SummaryPalios are traditional horseraces held in the main square of few Italian cities. Due to peculiar features of such circuits, adapted to the square architecture and thus characterized by tight curves and unconventional footing surface, horses involved are at particular risk of accidents. Prevention of catastrophic musculoskeletal injuries is a significant issue and matter of debate during these events. In particular, the negotiation of the curves in the city circuits is a significative concern. An experiment was set up to build a model of entire forelimb at the point of failure in the context of a turn comparable to that in a Palio circuit. The model was informed by live data and the output compared to post-mortem findings obtained from a horse that sustained a catastrophic fracture of the carpus during this competition. The objective of this study is to determine the magnitude and distribution of internal forces generated across the carpus under which the catastrophic injury has occurred and describe related post-mortem findings.A catastrophic fracture of the radial carpal bone experienced by a racehorse during a Palio race was analyzed. Computational modelling of the carpal joint at the point of failure informed by live data was generated using a multibody code for dynamics simulation. The circuit design in a turn, the speed of the animal and the surface characteristics were considered in the model. A macroscopic examination of the cartilage, micro-CT and histology were performed on the radio-carpal joint of the limb that sustained the fracture. The model predicted the points of contact forces generated at the level of the radio-carpal joint where the fracture occurred. Articular surfaces of the distal radius, together with the proximal articular surface of small carpal bones, exhibited diffuse wear lines, erosions of the articular cartilage and subchondral bone exposure. Even though the data in this study originated from a single fracture and further work will be required to validate this approach, this study highlights the potential correlation between elevated impact forces generated at the level of contact surfaces of the carpal joint during a turn and cartilage breakdown in the absence of pre-existing pathology. Computer modelling resulted in a useful tool to inversely calculate internal forces generated during specific conditions that cannot be reproduced in-vivo because of ethical concerns.

Wheel-rail contact models in the presence of switches and crossings

The development and implementation of wheel-rail contact models in multibody codes are two active research topics, aiming at improving the accuracy of numerical results and computational efficiency of the dynamics analysis. However, the realism of numerical results is challenged when considering switches and crossings (S&C), where the most adverse wheel-rail contact conditions occur. This paper presents a benchmark study where the performance of the multibody codes MUBODyn, VOCO and VI-Rail are assessed using three case scenarios that involve typical contact conditions observed in S&C. A focused description of the relevant methods to determine the wheel-rail contact forces is presented for each software. The three scenarios considered in this work have been designed to represent typical challenging contact conditions observed in S&C, i.e. conformal contact, contact with a sharp edge, and impact loads. The scenarios proposed in this work are fully described, making them easily reproducible. The agreement between results is discussed in the framework of the methods implemented in each code. This work highlights the impact of wheel-rail contact methods on the results as well as on the computational efficiency of the multibody codes.

Analysis of electric scooter user kinematics after a crash against SUV.

The article presents the results of the analysis of electric scooter user kinematics after a crash against a vehicle. The share of electric scooters (e-scooters) in urban traffic has been growing in recent years. The number of road accidents involving e-scooters is also increasing. However, the safety situation of electric scooter users is insufficiently researched in terms of kinematics and injury outcomes. The article presents the importance of this problem based on an in-depth literature analysis of e-scooter-related types of accidents, injuries percentages, and helmet use. Subsequently, four accident scenarios were designed and simulated using two numerical codes–LS-DYNA for handling finite element (FE) code (the vehicle and scooter model) and MADYMO for multibody code (dummy model). Scenario one is a side bonnet crash that simulates an accident when the scooter drives into the side-front of the vehicle. The second and the third simulation is a side B-pillar crash, which was divided into two dummy’s positions: the squat and up-right. The fourth simulation is a frontal impact. For each scenario, subsequent frames describing the dummy movement are presented. The after-impact kinematics for various scenarios were analyzed and discussed. The plots of the dummy’s head linear acceleration and its magnitude for the analyzed scenarios were provided. As the study is devoted to increasing riders safety in this means of transportation, the potential directions for further research were indicated.

The Motion Formalism for Flexible Multibody Systems

Abstract This paper describes a finite element approach to the analysis of flexible multibody systems. It is based on the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) recognizes that these are members of the special Euclidean group thereby coupling their displacement and rotation components, and (3) resolves all tensors components in local frames. The goal of this review paper is not to provide an in-depth derivation of all the elements found in typical multibody codes but rather to demonstrate how the motion formalism (1) provides a theoretical framework that unifies the formulation of all structural elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, and (4) prevents the occurrence of singularities.

Viscous Vortex Particle Method Coupling with Computational Structural Dynamics for Rotor Comprehensive Analysis

A panel/vortex particle hybrid method is coupled with a computational structure dynamics code to predict helicopter rotor loads. The rotor blade surfaces and near wakes are modeled by the panel method, while the far wake is modeled by resorting to the vortex particles method. A fast summation method is introduced to accelerate the evolution of particle–particle-induced velocity and its derivative as well as panel–particle interactions. The developed vortex particle method code is coupled with the multibody code MBDyn to predict the rotor airloads. Numerical validations are carried, out and the results are compared with the experiments and simulation results in the literature.

Flutter study of flapwise bend-twist coupled composite wind turbine blades

Bending-twisting coupling induced in big composite wind turbine blades is one of the passive control mechanisms which is exploited to mitigate loads incurred due to deformation of the blades. In the present study, flutter characteristics of bend-twist coupled blades, designed for load alleviation in wind turbine systems, are investigated by time-domain analysis. For this purpose, a baseline full GFRP blade, a bend-twist coupled full GFRP blade, and a hybrid GFRP and CFRP bend-twist coupled blade is designed for load reduction purpose for a 5 MW wind turbine model that is set up in the wind turbine multi-body dynamic code PHATAS. For the study of flutter characteristics of the blades, an over-speed analysis of the wind turbine system is performed without using any blade control and applying slowly increasing wind velocity. A detailed procedure of obtaining the flutter wind and rotational speeds from the time responses of the rotational speed of the rotor, flapwise and torsional deformation of the blade tip, and angle of attack and lift coefficient of the tip section of the blade is explained. Results show that flutter wind and rotational speeds of bend-twist coupled blades are lower than the flutter wind and rotational speeds of the baseline blade mainly due to the kinematic coupling between the bending and torsional deformation in bend-twist coupled blades.

Development and validation of a simplified automotive steering dynamic model

This paper describes an innovative analytic/numerical method for modeling steering systems for automotive applications. Starting from a detailed literature analysis and pushed by vehicle manufacturers’ needs, a simplified steering dynamic model, characterized by few parameters, has been identified. It guarantees both the replication of the dynamic behavior of real systems, generally represented through more complex multibody models, and the reduction of the simulation time of the entire vehicle system, making it suitable for dedicated numerical computing environments, such as the, so-called, explicit multibody codes. Moreover, particular emphasis has been place on the correct evaluation of the influence of friction on steering system dynamics.

The nodal-based floating frame of reference formulation with modal reduction

In a recent paper of the authors, a novel nodal-based floating frame of reference formulation (FFRF) for solid finite elements has been proposed. The nodal-based approach bypasses the unhandy inertia shape integrals ab initio, i.e. they neither arise in the derivation nor in the final equations of motion, leading to a surprisingly simple derivation and computer implementation without a lumped mass approximation, which is conventionally employed within commercial multibody codes. However, the nodal-based FFRF has so far been presented without modal reduction, which is usually required for efficient simulations. Hence, the aim of this follow-up paper is to bring the nodal-based FFRF into a suitable form, which allows the incorporation of modal reduction techniques to reduce the overall system size down to the number of modes included in the reduction basis, which further reduces the computational complexity significantly. Moreover, this exhibits a way to calculate the so-called FFRF invariants, which are constant “ingredients” required to set up the FFRF mass matrix and quadratic velocity vector, without integrals and without a lumped mass approximation.

Grousers Effect in Tracked Vehicle Multibody Dynamics with Deformable Terrain Contact Model

In this work, a multibody model of a small size farming tracked vehicle is shown. Detailed models of each track were coupled with the rigid body model of the vehicle. To describe the interaction between the track and the ground in case of deformable soil, custom defined forces were applied on each link of the track model. Their definition derived from deformable soil mechanics equations implemented with a specifically designed routine within the multibody code. According to the proposed model, it is assumed that the main terrain deformation is concentrated around the vehicle tracks elements. The custom defined forces included also the effects of the track grousers which strongly affect the traction availability for the vehicle. A passive soil failure model was considered to describe the terrain behaviour subjected to the grousers action. A so developed model in a multibody code can investigate vehicle performance and limit operating conditions related to the vehicle and soil characteristics. In this work, particular attention was focused on the results in terms of traction force, slip and sinkage on different types of terrain. Tests performed in the multibody environment show how the proposed model is able to obtain tractive performance similar to equivalent analytical solutions and how the grousers improve the availability of tractive force for certain type of soil characteristics.

Parameter Identification on Flexible Multibody Models Using the Adjoint Variable Method and Flexible Natural Coordinate Formulation

Abstract This work proposes a methodology for in situ parameter identification using system-level measurements of (flexible) multibody systems, opposed to dedicated component-level identification. The sensitivity information employed for the optimization is obtained using the adjoint variable method (AVM). This method has the advantage of obtaining sensitivity information at a computational cost independent of the amount of model parameters. The underlying flexible multibody formulation employed is a novel approach called the flexible natural coordinates formulation (FNCF). This formulation combines the advantageous properties of the floating frame of reference formulation (FFRF) and the generalized component mode synthesis (GCMS) methods and results in a constant mass and stiffness matrix with quadratic constraint equations. This work shows how the specific structure of equations obtained through FNCF drastically reduces the complexity of the AVM as the simulation derivatives can be readily obtained and are of limited order. The proposed approach has been implemented in an in-house object-oriented matlab multibody code. The methodology is illustrated by identifying 13 model parameters of a MacPherson suspension model, in situ and using system-level measurements.

A Solution to Remove Railway Track Discontinuities at Spiral Junctions

To design railway track layouts, engineers use tangent and circle segments. To maintain curvature and bank angle continuities between flat straight lines, with zero curvature, and banked circles, they use spiral segments where curvature and bank angle vary linearly as function of distance. This method meets the behavior of track engineers for which curvature and super-elevation are the main data used to lay the groundwork. However, it demonstrates dynamical drawbacks at both ends of spirals where bank angle and curvature derivatives would be discontinuous. Several unsuccessful attempts have been made to change spirals definition to alleviate this issue. In reality, track engineers smoothen the theoretical layout at the junctions, but there is no analytical definition for that although it is necessary track data at least for simulation codes. Smoothing portions are called ‘doucines’ but the maps of railway lines do not mention these unknown data and railway numerical codes ignore them, thus having to deal with subsequent dynamical perturbations which are avoided by doucines in reality. This paper proposes an analytical definition of practical doucines which does not modify actual theoretical method for designing lines. It also describes a method for programming it in railway codes. It uses trigonometric functions, sine and cosine which are simple to integrate to get at first the track orientation and then the X-Y coordinates of the layout line. In addition to doucine definitions, usable as well in practice as for all multibody codes, the paper shows how it can be implemented into the specific French calculation method, which uses an imaginary space, developed at first for calculating the dynamics of TGV. After modifying the author’s Ocrecym code according to the proposed doucine method, dynamical simulations of a light trailer coach, running over curved lines with and without doucines are presented to demonstrate the effectiveness of proposed solution.

Numerical stability of co-simulation approaches to evaluate wheel profile evolution due to wear

ABSTRACTWear simulation for railway wheel profiles is a complex problem which requires dynamics simulation of the vehicle on a long track and detailed analyses of the contact forces, which have to adopt non-linear methods to simulate the material behaviour. Since the dynamics of the vehicle and the behaviour of the material evolve differently, it is possible to use different codes to solve the problems. Furthermore, when thousands of kilometres are needed to produce wear, the profile wear is usually virtually amplified using wear multipliers to reduce computing time. This process can produce numerical instability if the multipliers and profile update intervals are not chosen appropriately. In this paper, the Simpack multibody code is used to simulate vehicle dynamics and to calculate the wear removed on a reference track, then the MATLAB code is used to smooth the profile and define the update intervals.

Implementation of a non-Hertzian contact model for railway dynamic application

The development of wheel–rail contact models is an active topic of railway research with the dual objective of improving the accuracy of multibody simulations and reducing its computational effort. This paper extends the online Hertzian contact model, proposed by Pombo et al. (Veh. Syst. Dyn. 45: 165–189, 2007) to propose a non-Hertzian contact model. The new methodology presented here includes the following steps: (i) search of the points of contact; (ii) identification of the undeformed distance function; (iii) evaluation of the contact patch; (iv) calculation of the normal and tangential contact forces; (v) application of the contact forces in the multibody vehicle model. Among several contact models available in the literature, this non-Hertzian contact approach uses the Kik–Piotrowski model for the normal contact force, while the tangential forces are obtained from the interpolation of the available Kalker Book of Tables for non-Hertzian (KBTNH) contact. With the purpose to demonstrate the proper implementation and selection of parameters that define this new model, several contact analysis and dynamic simulations are performed in which the wheel S1002 and the rail UIC50 are considered. First, the contact analyses that determine the contact condition of different wheel–rail interactions serve to assess the accuracy of the Hertzian and non-Hertzian models with respect to the software of reference CONTACT. Second, the Hertzian and non-Hertzian models are utilised to perform dynamic simulations of a wheelset, a bogie and a vehicle running in tangent and curved tracks. In short, this work provides, not only a complete description of the implementation of a non-Hertzian contact model in a multibody code, but also suggests for the proper selection of the parameters that promote better accuracy and optimal computational efficiency.

A Novel Analytical Method to Calculate Wheel-Rail Tangential Forces and Validation on a Scaled Roller-Rig

The study of railway dynamic strongly depends on the estimation of the tangential forces acting between wheel and rail. Simulation of the dynamical behaviour of railway vehicles is often performed using multibody codes, and the calculation of the contact forces must be efficient and accurate, even if the contact problem is strongly nonlinear. Therefore, the contact problem is still of great interest for researchers. This work proposes an analytical and efficient algorithm to calculate wheel-rail tangential forces. The proposed method is compared with the most commonly used algorithms under different conditions. In addition, experimental tests are performed on a scaled prototype on roller-rig to demonstrate that the method can be easily adjusted using experimental results. The benefit of the proposed method is to provide an analytical and fast solution, able to obtain accurate results and to allow corrections based on empirical evidence.

Multibody simulation of a tracked vehicle with deformable ground contact model

In this paper, the realisation of a multibody model of a tracked machine is described. A new compact modelling of the tracks–soil interaction is presented and soil mechanics laws for terrain response are implemented. Tracked vehicles can be used in different fields such as agriculture, military and construction. The conditions of the terrain on which they operate may vary a lot, in terms of soil composition, slope and roughness. For this reason, performance of tracked vehicles is difficult to predict without a great number of field tests. The model is developed in a multibody code that makes it possible to investigate its dynamic and kinematic behaviour in several operating conditions. A specific routine is implemented in the multibody model in order to simulate the behaviour of the tracked vehicle on deformable terrains. The main hypothesis of this paper is that the terrain deformation could be in a narrow zone affected by the vehicle. Thus, the deformation of the soil is kinematically correlated to the vehicle. Soil mechanics equations are implemented on each track portion and solved only for track links in contact with the soil. The latter is modelled as a rigid body and terrain stress or deformation are not directly computed, thus simplifying solution and terrain modelling despite obtaining coherent results in terms of vehicle traction force, slip and sinkage. Results are reported pointing out performance of the tracked machine on different ground conditions.

A parametric analysis of a controlled deployable space manipulator for capturing a non-cooperative flexible satellite

In the near future robotic systems will be playing an increasingly important role in space applications such as repairing, refueling, re-orbiting spacecraft and cleaning up the increasing amount of space debris. Space Manipulator Systems (SMSs) are robotic systems made of a bus (which has its own actuators such as thrusters and reaction wheels) equipped with one or more deployable arms. The present paper focuses on the issue of maintaining a stable first contact between the arms terminal parts (i.e. the end-effectors) and a non-cooperative target satellite, before the actual grasp is performed. The selected approach is a modified version of the Impedance Control algorithm in which the end-effector is controlled in order to make it behave like a mass-spring-damper system regardless of the reaction motion of the base, so to absorb the impact energy. The effects of non-modeled dynamics in control determination such as the structural flexibility of the manipulator and the target satellite are considered as well, and their impact on control effectiveness is analyzed. The performance of the proposed control architecture and a parametric analysis are studied by means of a co-simulation involving the MSC Adams multibody code (for describing the dynamics of the space robot and target) together with Simulink (for the determination of the control actions). The results show that the first contact phase of the grasping operation of a large satellite requires careful tuning of the control gains and a proper selection of the end-effector dimensions; otherwise, the large geometric and inertia characteristics of the target could lead to a failure with serious consequences. Both successful and underperforming cases are presented and commented in the paper.