Multibody Research Articles

Ride comfort analysis of vehicle seat suspension systems: A co-simulation study

In this study, the vehicle seat suspension system installed with a semi-active magnetorheological (MR) damper is excited by the power spectral density (PSD) and its vibration control performance is evaluated using finite element analysis (FEA). The control system receives the velocity of the sprung and unsprung mass from the seat mounting locations and calculates the desired controllable damping forces available from MR damper. The effectiveness of the control systems is demonstrated by adopting ride quality evaluation method. To predict a better ride comfort and ride quality, co-simulation methodology is utilized considering the dynamic behavior of the real-world seat system. In this case, the multi-body dynamics and control system are coupled by solving the mechanical equations and the control logic. Then, the computed damping force is exchanged between the dynamics and controller in an iterative manner by passing state variables. The simulation results achieved from co-simulation methodology associated with the controller are analyzed by comparing with ISO 2631-1. The co-simulation results studied using vibration dose value (VDV), crest factor (CF) and seat effective amplitude transmissibility (SEAT) in terms of percentage improvement were found to be 44.33%, 26.66% and 17.65% respectively which were better than that for the passive suspension for a random rough road profile. Modified skyhook controller delivers superior performance for vibration suppression of the vehicle seat suspension as compared to other control policies. The application of co-simulation methodology can reduce time and cost for the development of a semi-active seat suspension system.

Research and Simulation of Kinematics and Dynamics of Tracked Support Equipment Based on Multi-Body Dynamics

Aiming at addressing the problems of low production efficiency and low safety factors in coal mines, this study designed a new type of support equipment and verified its theoretical reliability through the analysis of driving theory. The analysis was carried out through kinematics and dynamics, the position coordinates of the prototype at different times were analyzed using the RPY angles, and the spatial coordinate system of the prototype was established. Then, the position coordinates at different times could be solved by establishing the plane kinematics equations of the prototype. A 14-degree-of-freedom dynamic system model was established to reflect the longitudinal dynamic characteristics of the traveling mechanism of the prototype, and the differential equations of the traveling mechanism were established via the Lagrange dynamic equation method. Finally, the dynamic stability of the prototype under different working conditions was studied by using multi-body dynamic simulation technology. The research results show that the prototype meets the design requirements, has good reliability, realizes the mechanization, automation and high-efficiency production of coal mines, and realizes safe underground production. The research results provide effective solutions for ensuring the sustainable development of coal resources and the safe production of coal mines.

A Novel Approach to Predict the Structural Dynamics of E-Bike Drive Units by Innovative Integration of Elastic Multi-Body-Dynamics

This paper presents a novel approach to address noise, vibration, and harshness (NVH) issues in electrically assisted bicycles (e-bikes) caused by the drive unit. By investigating and optimising the structural dynamics during early product development, NVH can decisively be improved and valuable resources can be saved, emphasising its significance for enhancing riding performance. The paper offers a comprehensive analysis of the e-bike drive unit’s mechanical interactions among relevant components, culminating—to the best of our knowledge—in the development of the first high-fidelity model of an entire e-bike drive unit. The proposed model uses the principles of elastic multi body dynamics (eMBD) to elucidate the structural dynamics in dynamic-transient calculations. Comparing power spectra between measured and simulated motion variables validates the chosen model assumptions. The measurements of physical samples utilise accelerometers, contactless laser Doppler vibrometry (LDV) and various test arrangements, which are replicated in simulations and provide accessibility to measure vibrations onto rotating shafts and stationary structures. In summary, this integrated system-level approach can serve as a viable starting point for comprehending and managing the NVH behaviour of e-bikes.

Estimation of Road Roughness Based on Both the Sprung and Unsprung Response of a Moving Vehicle Over Ordinary Roads: Modeling, Experiments and Discussions

The study proposes a Kalman Filter Family-schemed algorithm to identify the vehicle’s parameters and evaluate the road roughness simultaneously, based on the response of an adapted monitoring vehicle. The vehicle is simplified as a three-dimensional multi-body system consisting of the unsprung mass of wheels and the sprung mass of the car body, connected by springs and dampers that represent the suspension system. Accelerometers and a gyroscope measure the accelerations or angular velocity of different positions of the vehicle during vibrations. The Kalman filter (KF) with unknown inputs enables the prediction of the car body’s accelerations from those of wheels. On the other hand, the Augmented KF can compute the accelerations of wheels based on the car body’s accelerations. Thus, an inner-systemic objective function incorporating the vehicle’s parameter is built between the predicted and measured accelerations and solved in an optimized manner with the Genetic Algorithm, so that an individual complicated impact test or bump test is avoided. The numerical examples carry out field tests on a 900[Formula: see text]m long standardized test road under two scenarios of with and without a bump. The road roughness estimated by these two KF methods from different measurements is used to calculate the International Roughness Index (IRI) and further the Riding Quality Index, which are compared with those directly provided by a standardized laser IRI profilometer. Accordance in between confirms the accuracy of the proposed algorithm under different scenarios. The analysis underlines the measurements from unsprung wheels that contact directly with the road enable a more accurate estimation of road roughness than those from the sprung car body. In addition, a vehicle speed lower than 40[Formula: see text]km/h can provide a better estimation of the road profiles.

Instability during Stepping and Distance between the Center of Mass and the Minimal Moment Axis: Effect of Age and Speed

The goal of this study was to analyze instability during stepping at different speeds in young and older adults. To this aim, the anteroposterior and the mediolateral distances between the body center of mass (COM) and the minimum moment axis (MMA) were computed. A total of 15 young adults (25 y.o. [19–29]) and 15 older adults (68.7 y.o. [63–77]) volunteered for this study. For the computation of the distances, a complete biomechanical protocol combining two force platforms and a 3D motion capture analysis system was setup. The subjects were equipped with 47 reflective markers and were modeled as a frictionless multibody system with 19 segments, 18 joints and 42 degrees of freedom. They were asked to perform a series of stepping tasks at fast and spontaneous speeds. The stepping was divided into five phases, with successive swing and double-stance phases. Greater instability was observed during the swing phases. The distances reveal a significant higher instability at fast speed for both groups (p < 0.001) for all the phases compared with spontaneous speeds. The anteroposterior distance was significantly greater for older adults, highlighting greater instability compared to young adults, while no differences were observed for the mediolateral distance all along the five phases, suggesting higher risks of backward and forward falls during stepping.

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

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

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

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

Susceptibility Modeling of a Rubber Track for Lightweight Mobile Robots

The elastic-damping properties of the rubber track structure can have a significant impact on the running gear performance of lightweight mobile robots. Taking these properties into account is particularly important for modeling obstacle negotiation and estimating the robot’s driving force. The article presents track susceptibility identification using both static and dynamic tests. The experimental results were used to validate the multi-body dynamics model of the rubber track for three modeling methods and for three track link number model variants. The methods and variants were compared by the accuracy of the susceptibility parameters obtained using them. The impact of the modeling methods on the track bending resistance simulations was also checked.

Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems

A dynamic iteration scheme for linear differential-algebraic port-Hamiltonian systems based on Lions–Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no stability conditions are required. The developed iteration scheme is even new for linear port-Hamiltonian systems governed by ODEs. The obtained algorithm is applied to a multibody system and an electrical network.

A CPU parallelized coupling framework for constrained flexible multibody system and granular matter based on contact-graph

This paper proposes a coupling model for simulating the interaction between particles and the flexible multibody system. The flexible rods are described using the Absolute Nodal Coordinate Formulation, and various types of contacts, including particle-particle, particle-rod, particle-rigid body contacts, and contacts within multibody objects, are considered. The contact detection is improved by combining space partitioning techniques and the bounding box method. A data structure based on a contact graph is introduced to store the contact relationships efficiently. The discrete element system and multibody system are coupled through serial time integration, with data exchanges at the program level. Numerical examples demonstrate the validity of the proposed model. Moreover, the model is applied to simulate the asteroid soil sampling with flexible brush sampler, showing good agreement with experimental data. The analysis of engineering examples provides insights for sampler design, and show the model's engineering value.

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

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

An Analytical Method for Sensitivity Analysis of Rigid Multibody System Dynamics Using Projective Geometric Algebra

Abstract The analytical sensitivity analysis, i.e., the analytical first-order partial derivatives of dynamical equations, is one key to improving descent-based optimization methods for motion planning and control of robots. This paper proposes an efficient algorithm that recursively evaluates the analytic gradient of the dynamical equations of a multibody system. The theory of projective geometric algebra (PGA) is used to generate the algorithm. It provides a systemic and geometrically intuitive interpretation for the multibody system dynamics, and the resulting algorithm is highly efficient, with concise formula. The algorithm is first applied to the open-chain system and extended for the cases when kinematic loops are contained. The runtime varying with respect to the degree-of-freedom (DOF) of the system is analyzed. The results are compared with that obtained from the algorithm based on spatial vector algebra (SVA) using open-source matlab codes. A 2DOF serial robot, a 3DOF robot with a kinematic loop and the PUMA560 robot are used for the validation of the minimum-effort motion planning, and it is verified that the proposed algorithm improves the efficiency.

Reconstruction of a Car-Running Pedestrian Accident Based on a Humanoid Robot Method.

Due to the characteristics of multibody (MB) and finite element (FE) digital human body models (HBMs), the reconstruction of running pedestrians (RPs) remains a major challenge in traffic accidents (TAs) and new innovative methods are needed. This study presents a novel approach for reconstructing moving pedestrian TAs based on a humanoid robot method to improve the accuracy of analyzing dynamic vehicle-pedestrian collision accidents. Firstly, we applied the theory of humanoid robots to the corresponding joints and centroids of the TNO HBM and implemented the pedestrian running process. Secondly, we used rigid-flexible coupling HBMs to build pedestrians, which can not only simulate running but also analyze human injuries. Then, we validated the feasibility of the RP reconstruction method by comparing the simulated dynamics with the pedestrian in the accident. Next, we extracted the velocity and posture of the pedestrian at the moment of collision and further validated the modeling method through a comparison of human injuries and forensic autopsy results. Finally, by comparing two other cases, we can conclude that there are relative errors in both the pedestrian injury results and the rest position. This comparative analysis is helpful for understanding the differences in injury characteristics between the running pedestrian and the other two cases in TAs.

Influence of Variable Height of Piers on the Dynamic Characteristics of High-Speed Train–Track–Bridge Coupled Systems in Mountainous Areas

With the increase in the occupancy ratio of bridges and the speed of trains, the probability of trains being located on bridges during earthquakes increases, and the risk of derailment increases. To investigate the influence of unequal-height piers on the dynamic response of high-speed railway train bridge systems, a seismic action model of high-speed train–track–bridge dynamic systems was established based on the in-house code using the finite element method and multi-body dynamics method. It is found that (1) compared to equal-height piers, the peak lateral dynamic response of unequal-height piers (with gradually increasing pier heights) decreases, while the peak vertical dynamic response increases; (2) the peak lateral dynamic response of unequal-height piers (with a steep increase in pier height) increases sharply, while the peak vertical dynamic response decreases; and (3) the safety indicators of equal-height piers are significantly superior to the two unequal-height pier operating conditions.

Influence of axis misalignments in stepped planetary gear stages on the excitation behavior—test rig development and simulative analysis

AbstractOne challenge in the design of automotive gearboxes is the combination of high power density, high efficiency and low noise emission. With the electrification of the powertrain, the requirements in terms of noise emission and efficiency increase additionally. Stepped planetary gear stages are a potential topology to solve the current challenges in gearbox technology. Current research shows the pronounced misalignment behavior of planetary gear stages, especially with manufacturing or assembly deviations. However, the effects of dynamic misalignment behavior on tooth contacts in stepped planetary gear stages have not been adequately investigated. This paper presents a test rig that allows the investigation of the excitation and displacement behavior of stepped planetary gear stages taking into account adjustable axis misalignments. The axis misalignment of the stepped planetary shafts is introduced with eccentric bushings in this test rig concept. To evaluate the excitation and displacement behavior the transmission error and the displacements of different components can be measured. The test rig is modeled in the dynamic multibody simulation. The tooth contact is modeled using the force module GearForce6D. The axis misalignment is varied in the simulation model and the influence on the excitation and displacement behavior is evaluated. The simulation results show that planet pin position errors have the highest influence on the sun trajectory and the load sharing. The misalignments occurring in the tooth contacts due to inclination and skew of the stepped planetary shaft lead to higher tooth flank pressures and an increase in the total transmission error.

Motion Primitive Approach to Spacecraft Trajectory Design in a Multi-body System

The increasing number and variety of spacecraft that are expected to operate within cislunar space and other multi-body gravitational environments throughout the solar system necessitates the continued development of strategies for rapid trajectory design and design space exploration. In the field of robotics, similar needs have been addressed using motion primitives that capture the fundamental building blocks of motion and are used to rapidly construct complex paths. Inspired by this concept, this paper leverages motion primitives to construct a framework for rapid and informed spacecraft trajectory design in a multi-body gravitational system. First, motion primitives of fundamental solutions, e.g., selected periodic orbits and their stable and unstable manifolds, are generated via clustering to form a discrete summary of segments of the phase space. Graphs of motion primitives are then constructed and searched to produce primitive sequences that form candidate initial guesses for transfers of distinct geometries. Continuous transfers are computed from each initial guess using multi-objective constrained optimization and collocation. This approach is demonstrated by constructing an array of geometrically distinct transfers between libration point orbits in the Earth-Moon circular restricted three-body problem with impulsive maneuvers.

Hydrodynamic analysis of a floating platform coupled with an array of oscillating bodies

In this paper, based on multi-body dynamics and beam bending theory, a frequency-domain model is developed to investigate the hydrodynamic performance of a hybrid floating platform (HFP). The HFP investigated here is characterized by hydroelasticity and complex interconnection conditions. The constraint matrix is derived to handle the couple response of an elastic platform and an array of rigid bodies, representing wave energy converters. The hydroelasticity and coupled dynamics of the floating platform in waves and the wave power extraction performance is analyzed. The numerical results reveal that the platform deformations have a significant impact on the relative pitch response between the buoy array and the platform. Neglecting hydroelasticity leads to an overestimation of the hydrodynamic efficiency of the buoy array when 0.4 < λ/L < 1.0, as demonstrated in our calculations. Influence of key parameters such as spacing and incident wave angle is examined numerically. As a result of these investigations, suggestions are identified for an improved design of such kind of multi-use floating platform.

Current and Future Trends in Tribological Research

The paper provides a commentary on the theme of “Current and Future Trends in Tribological Research: Fundamentals and Applications”, which is a special feature issue commemorating the 10th anniversary of the journal, Lubricants. A historical discourse is provided regarding various aspects of tribology as a multi-disciplinary subject that interacts in an inter-disciplinary manner with many other subjects: multi-body dynamics, thermofluids and heat transfer, contact mechanics, surface science, chemistry, rheology, data science, and biology, to name but a few. Such interactions lead to many important topics including propulsion with different sources of energy, mitigating emissions, palliation of friction, enhancing durability and sustainability, optimization through detailed analysis, and the use of artificial intelligence. Additionally, issues concerning kinetics at various physical scales (from macroscale to microscale onto mesoscale and nanoscale) affecting the kinematics of contacts are discussed. The broad range of considered applications includes vehicular powertrains, rotor bearings, electrical machines, mammalian endo-articular joints, nanobiological attachment/detachment, and locomotion. Current state-of-the-art tribological research is highlighted within a multi-physics, multi-scale framework, an approach not hitherto reported in the open literature.

Research on Variable-Swept Hybrid Aerial Underwater Vehicle Plunge-Diving Control Based on Adaptive Dynamic Surface Control

The variation in aerodynamic parameters during the process of a variable sweepback hybrid aerial underwater vehicle (HAUV) affects flight stability. During the air–water trans-media locomotion, there are medium mutations and solid–liquid gas coupling phenomena, resulting in the complex dynamic process of HAUV. To ensure stable control during the trans-media process of a variable sweepback vehicle, this study proposes a neural-network-based adaptive dynamic surface control method for aircraft flight-path angle. This method aims to establish an effective control model for the entire process of air to media transition, in response to the characteristics of uncertainty and external disturbances in the process of variable backsweeping in the air and media transition. By utilizing the multibody dynamics method, the dynamic equations for variable-swept vehicles are established and transformed into a rigorous feedback system with model uncertainty. The adaptive dynamic surface method in this paper introduces a first-order filter, which overcomes the “differential explosion” problem in traditional backstepping control design through differential filtering; the unknown parameters present in the model are estimated online through adaptive laws, and the uncertain parts of the system are overcome through nonlinear damping items. By analyzing Lyapunov stability, the semi-global stability of the required closed-loop system can be obtained, and adjusting the controller parameters can make the tracking error infinitely small. Numerical simulations are conducted to illustrate the tracking control of flight-path angles for different plunge-diving angle rates and strategy of ingress. The results show that HAUV with variable-swept configuration with different strategy has a great effect on the stability of plunge-diving locomotion; the designed controller can effectively track the target trajectory and has a certain degree of robustness and adaptability.

L1 Adaptive Control Based on Dynamic Inversion for Morphing Aircraft

Morphing aircraft are able to keep optimal performance in diverse flight conditions. However, the change in geometry always leads to challenges in the design of flight controllers. In this paper, a new method for designing a flight controller for variable-sweep morphing aircraft is presented—dynamic inversion combined with L1 adaptive control. Firstly, the dynamics of the vehicle is analyzed and a six degrees of freedom (6DOF) nonlinear dynamics model based on multibody dynamics theory is established. Secondly, nonlinear dynamic inversion (NDI) and incremental nonlinear dynamic inversion (INDI) are then employed to realize decoupling control. Thirdly, linear quadratic regulator (LQR) technique and L1 adaptive control are adopted to design the adaptive controller in order to improve robustness to uncertainties and ensure the control accuracy. Finally, extensive simulation experiments are performed, wherein the demonstrated results indicate that the proposed method overcomes the drawbacks of conventional methods and realizes an improvement in control performance.