Multi-body Dynamic Model Research Articles

Enhanced robust adaptive flight control for a convertible VTOL UAV

In this paper, we propose less conservative formulations for candidate controllers of robust adaptive mixing control (RAMC) strategies. The RAMCs are employed to solve the trajectory tracking problem throughout the full flight envelope, with guaranteed stability, of a convertible plane (CP) vertical take-off and landing (VTOL) unmanned aerial vehicle (UAV). Initially, the multi-body nonlinear dynamic model of the CP VTOL UAV is obtained using the Euler–Lagrange formalism, from which a linear parameter-varying (LPV) model is derived to be used in the design of the RAMC candidate controllers. The new formulations of the candidate controllers are proposed considering two approaches: a (i) Parallel Distributed Compensation (PDC); and (ii) a parameter-dependent Lyapunov function. Hardware-In-the-Loop (HIL) experiments are performed in a high-fidelity flight simulator to verify the fulfillment of real-time constraints, ensuring a computationally lightweight control strategy ready for implementation in a low-cost embedded computational system.

The use of an artificial neural network for assessing tone perception in electric powertrain noise, vibration and harshness

The transition from internal combustion engines to electric powertrains brings new challenges for the Noise, Vibration, and Harshness (NVH) analysis of these vehicles. The tonal nature of the electromagnetic excitations and of the gear meshing mechanism are reflected in the radiated noise of electric powertrains, often leading drivers and passengers to rate the noise from electric vehicles with an increased nuisance even if they are quieter than internal combustion driven powertrains. In this paper, a flexible multi-body dynamics model is developed to calculate the vibration and forces transmitted from the bearings to the housing of an electric powertrain. Acceleration, force and sound spectra data are used to train an artificial neural network to assess the prominence of tones in the noise based on the results of the structural simulation. The results show it is possible to identify psychoacoustic metrics from the multibody dynamics simulation alone. With this new approach, it is feasible to quickly investigate how changes in the powertrain will affect the tonal perception of the noise without the need of new acoustic simulations and experiments. For the tonal perception analysis, the Prominence Ratio is used as a metric. This framework of combining multibody dynamics simulation with initial acoustic data and neural networks can be also applied to different NVH metrics as appropriate.

A Rigid-Flexible Coupling Dynamic Model for Robotic Manta with Flexible Pectoral Fins

The manta ray, exemplifying an agile swimming mode identified as the median and paired fin (MPF) mode, inspired the development of underwater robots. Robotic manta typically comprises a central rigid body and flexible pectoral fins. Flexible fins provide excellent maneuverability. However, due to the complexity of material mechanics and hydrodynamics, its dynamics are rarely studied, which is crucial for the advanced control of robotic manta (such as trajectory tracking, obstacle avoidance, etc.). In this paper, we develop a multibody dynamic model for our novel manta robot by introducing a pseudo-rigid body (PRB) model to consider passive deformation in the spanwise direction of the pectoral fins while avoiding intricate modeling. In addressing the rigid-flexible coupling dynamics between flexible fins and the actuation mechanism, we employ a sequential coupling technique commonly used in fluid-structure interaction (FSI) problems. Numerical examples are provided to validate the MPF mode and demonstrate the effectiveness of the dynamic model. We show that our model performs well in the rigid-flexible coupling analysis of the manta robot. In addition to the straight-swimming scenario, we elucidate the viability of tailoring turning gaits through systematic variations in input parameters. Moreover, compared with finite element and CFD methods, the PRB method has high computational efficiency in rigid-flexible coupling problems. Its potential for real-time computation opens up possibilities for future model-based control.

Postearthquake train operation safety assessment model based on machine learning

Abstract Assessing the seismic risk to high-speed rail systems with limited structural damage data is a challenging task. This study employs machine learning algorithms to predict the wheel–rail forces of high-speed trains operating under postearthquake conditions, particularly when infrastructure along the railway is damaged. By developing a postearthquake train operation safety assessment model, this article effectively predicts the impact of track irregularities induced by different earthquake intensities on wheel–rail interactions. The results obtained through feature selection and regression analysis using the Random Forest algorithm provide valuable insights into key safety indicators for postearthquake train operations. Compared to traditional multibody dynamic models, this approach significantly improves the efficiency of analysis and computation. An analysis of the results across multiple speed levels reveals that trains operating at 250 km/h face derailment risks when subjected to high-intensity earthquakes (PGA > 0.6 g). The proposed predictive safety assessment model demonstrates that adjusting train speeds according to seismic intensity can effectively enhance operational safety, offering critical support for postearthquake emergency recovery efforts.

Tyre lateral slip effect on off-tracking of a long combination vehicle

This paper evaluates the effect of tyre lateral slip on the off-tracking of a long combination vehicle (LCV) consisting of a semi-truck with 28-ft double trailers. A geometric model of LCV motion neglecting tyre slip and a high-order multi-body dynamic model in TruckSim® including tyre slip are developed and validated against other simulation and field test data. Tyre slip effect on off-tracking is measured by comparing the models' estimated off-tracking when the LCV netogiates 50, 75 and 100 ft (15.24, 22.86, and 30.48 m) radius curves at speeds of 1–16mph (1.6–25 km/hr). Two trailer payloads – 6000 lb/trailer and 14,500 lb/trailer – and three tyre-road friction coefficients – 0.85, 0.45 and 0.65 – were simulated. The simulation results indicate that tyre lateral slip increases – and thus off-tracking decreases – approximately to the second-order of vehicle speed for a given curve radius. It is also found that tyre lateral slip is negligible for speeds below 3–4mph (5–6 km/hr) in all simulated conditions. Additionally, as the path radius increases, tyre lateral slip and vehicle off-tracking sensitivity to vehicle speed reduce. The results suggest that for moderate speeds (>7mph (11 km/hr)), increasing vehicle payload and reducing surface friction coefficient result in an increase in tyre lateral slip that consequently reduces off-tracking.

Multibody dynamic modeling of the behavior of flexible instruments used in cervical cancer brachytherapy.

The steep radiation dose gradients in cervical cancer brachytherapy (BT) necessitate a thorough understanding of the behavior of afterloader source cables or needles in the curved channels of (patient-tailored) applicators. The purpose of this study is to develop and validate computer models to simulate: (1) BT source positions, and (2) insertion forces of needles in curved applicator channels. The methodology presented can be used to improve the knowledge of instrument behavior in current applicators and aid the development of novel (3D-printed) BT applicators. For the computer models, BT instruments were discretized in finite elements. Simulations were performed in SPACAR by formulating nodal contact force and motion input models and specifying the instruments' kinematic and dynamic properties. To evaluate the source cable model, simulated source paths in ring applicators were compared with manufacturer-measured source paths. The impact of discrepancies on the dosimetry was estimated for standard plans. To validate needle models, simulated needle insertion forces in curved channels with varying curvature, torsion, and clearance, were compared with force measurements in dedicated 3D-printed templates. Comparison of simulated with manufacturer-measured source positions showed 0.5-1.2mm median and<2.0mm maximum differences, in all but one applicator geometry. The resulting maximum relative dose differences at the lateral surface and at 5mm depth were 5.5% and 4.7%, respectively. Simulated insertion forces for BT needles in curved channels accurately resembled the forces experimentally obtained by including experimental uncertainties in the simulation. The models developed can accurately predict source positions and insertion forces in BT applicators. Insights from these models can aid novel applicator design with improved motion and force transmission of BT instruments, and contribute to the estimation of overall treatment precision. The methodology presented can be extended to study other applicator geometries, flexible instruments, and afterloading systems.

Sensitivity of Mass Geometry Parameters on E-Scooter Comfort: Design Guide.

E-scooter vibrations are a problem recently studied. Theoretical models based on dynamic simulations and also real measurements have confirmed the high impact of e-scooter vibrations on driver comfort and health. Some authors recommend improving e-scooter damping systems, including tyres. However, it has not been suggested nor has any research been published studying how to improve e-scooter frame design for reducing driver vibrations and improving comfort. In this paper, we have modelled a real e-scooter to have a reference. Then, we have developed a multibody dynamic model for running dynamic simulations studying the influence of mass geometry parameters of the e-scooter frame (mass, centre of gravity and inertia moment). Acceleration results have been analysed based on the UNE-2631 standard for obtaining comfort values. Based on results, a qualitative e-scooter frame design guide for mitigating vibrations and increasing the comfort of e-scooter driver has been developed. Some application cases have been running on the multibody dynamic simulation model, finding improvements of comfort levels higher than 9% in comparison with the e-scooter reference model. The dynamic model has been qualitatively validated from real measurements. In addition, a basic sensor proposal and comfort colour scale is proposed for giving feedback to e-scooter drivers.

Prediction of knee biomechanics with different tibial component malrotations after total knee arthroplasty: conventional machine learning vs. deep learning.

The precise alignment of tibiofemoral components in total knee arthroplasty is a crucial factor in enhancing the longevity and functionality of the knee. However, it is a substantial challenge to quickly predict the biomechanical response to malrotation of tibiofemoral components after total knee arthroplasty using musculoskeletal multibody dynamics models. The objective of the present study was to conduct a comparative analysis between a deep learning method and four conventional machine learning methods for predicting knee biomechanics with different tibial component malrotation during a walking gait after total knee arthroplasty. First, the knee contact forces and kinematics with different tibial component malrotation in the range of ±5° in the three directions of anterior/posterior slope, internal/external rotation, and varus/valgus rotation during a walking gait after total knee arthroplasty were calculated based on the developed musculoskeletal multibody dynamics model. Subsequently, deep learning and four conventional machine learning methods were developed using the above 343 sets of biomechanical data as the dataset. Finally, the results predicted by the deep learning method were compared to the results predicted by four conventional machine learning methods. The findings indicated that the deep learning method was more accurate than four conventional machine learning methods in predicting knee contact forces and kinematics with different tibial component malrotation during a walking gait after total knee arthroplasty. The deep learning method developed in this study enabled quickly determine the biomechanical response with different tibial component malrotation during a walking gait after total knee arthroplasty. The proposed method offered surgeons and surgical robots the ability to establish a calibration safety zone, which was essential for achieving precise alignment in both preoperative surgical planning and intraoperative robotic-assisted surgical navigation.

Research on traction guidance cooperative control of virtual track train based on path-tracking and articulation hinge forces optimisation

Virtual track train (VTT) is a new urban public transportation system that adopts rubber wheel and rail transit management mode. Its characteristics of all-wheel-driving all-axle-steering (AWDAAS) enable this multi-articulated vehicle to run along the target path (virtual track) with high precision. This paper proposes a new traction guidance cooperative control strategy aiming at path-tracking and hinge forces optimisation. Firstly, the vehicle dynamics model is established using the two-step method, which mainly includes the centre of gravity (CG) forces model between the wheel steering angles, torques and the generalised forces at every unit. Secondly, the vehicle multi-body dynamics model is built with the CG generalised forces as the control input and carries on the concrete modelling for the three-unit six-axle AWDAAS-VTT. This modelling method can satisfy the rapid expansion and reconstruction according to the different marshalling numbers and axles. Then the hinge forces are analysed and expressed quantitatively by vehicle state and control inputs. A traction guidance cooperative control strategy based on a hierarchical framework is proposed, which has mainly three parts: the cooperative distribution of path-tracking and longitudinal speed targets, the CG generalised forces calculation of every unit based on improved model predictive control (MPC) and Stanley algorithm, and the control allocation (CA) of wheel torque and angle. The control strategy is verified by Co-simulation. The results show that the proposed control strategy can achieve excellent tracking accuracy and effectively reduce hinge forces. In addition, the vehicle under cooperative control also has excellent curve passing stability and continuous curve adaptability. The control strategy has high robustness under different running speeds, curve radii and payloads. Even under the extreme condition of passing through the R20 m curve at 14 m/s, the maximum tracking error is less than 0.035 m.

Development of longitudinal vibration isolator between carbody and bogie for railway vehicle (Study on characteristics of the device by multi-body dynamics model)

Development of longitudinal vibration isolator between carbody and bogie for railway vehicle (Study on characteristics of the device by multi-body dynamics model)

Noise analysis of interior structure under powertrain excitation

To accurately identify the structural noise problem caused by vibration in the cockpit, an experimental study was conducted on a certain type of SUV under uniform acceleration conditions. Based on the planning of the multi-body system dynamics model, a transfer path model with secondary contributions is constructed, and the load is identified using the single degree of freedom model and multi-frequency bandwidth model under the OPAX method based on this path. The results indicate that the second-order vibration of the powertrain is transmitted to the entire suspension system through the X direction of the right suspension. The second-order vibration of the suspension system is then transmitted to the Z direction of the right rear bolt of the subframe, causing the entire subframe vibration and ultimately reaching the target point. This structural path has the greatest impact on the interior noise of the vehicle. This path research method can more accurately determine the main excitation points that cause interior noise problems on a certain path and better understand the overall energy transfer characteristics along the transmission path.

A Reinforcement-Learning-based Parameter Tuning Methodology for Traction Control in the Holistic Railway Digital Twin System

Holistic railway digital twin systems can optimize railway performance by merging diverse models and data for monitoring, diagnostics, and prognostics. In such systems, traction control is critical to safe and efficient train operations. However, due to the dynamic and non-linear railway operations, achieving the optimal parameter configuration for traction control algorithms remains complex. Conventional approaches to parameter tuning often rely on experience-based manual adjustments or simple optimization algorithms, failing to capture the intricate interplay between various parameters and their impact on overall system performance. To address this, we present a novel methodology that leverages deep rein- forcement learning (RL) techniques to autonomously fine-tune traction control parameters within the holistic railway digital twin system. The core idea involves modeling the traction control in a co-simulation of a well-built multibody dynamic model and a traction controller. Through iterative learning, the RL agent refines its policy, converging toward parameter configurations that enhance both operational efficiency and safety. The RL- based tuning methodology shows significant traction control improvement over conventional methods. The RL-based methodology showcases its adaptability to varying conditions, which is essential for modern railway systems that operate in dynamic and unpredictable environments.

Dynamic Modeling and Combination Analysis of Plunger Valve Considering Both Flow and Actuator

The plunger valve has an important role in a large compressor system as its operating characteristics directly affect the aerodynamic boundary condition of the compressor equipment. In this study, dynamic modeling and analysis method of the plunger valve are proposed for an accurate control of the system. By considering the interaction between the dynamic flow in the valve and actuator action, a lumped parameter model for the fluid–structure interaction force and multibody dynamic model of the actuator are developed based on intrinsic correlation parameters. A combination analysis to simultaneously predict valve flow and actuator dynamic characteristics is proposed. The predicted results are in a good agreement with experimental data, which validates the proposed model and analysis method. The analysis results show that the coupling effect between the valve flow and actuator is significant and has an important role in valve control, particularly when the valve opening is smaller. Compared to the experimental data and computational fluid dynamics results, the presented methods are accurate for valve control and effective for prediction of flow rate.

Estimation of Cervical Spinal Loading and Internal Motion at Adjacent Segments after C5–C6 Fusion Using a Musculoskeletal Multi-Body Dynamics Model during the Head Flexion–Extension Movement

Cervical spinal fusion is the standard of care for treating intractable spinal diseases. However, frequent adjacent segment disease (ASD) has recently drawn a great deal of attention among clinicians and researchers. At present, the etiology of ASD remains controversial. The investigation of cervical spine biomechanics after fusion may contribute to understanding the causes of ASD. In the present study, a cervical spinal musculoskeletal fusion model, with multi-body dynamics method, was established. Dynamic head flexion–extension movements were simulated for both a fusion subject and a normal subject. The cervical spinal loading pattern, load sharing ratios, and translations of instant centers of the rotation at adjacent segments were then predicted. The average intervertebral compressive forces, shear forces, and facet joint forces against the intervertebral angle were also obtained. By comparison, some obvious differences in cervical spinal loading patterns were found between the fusion subject and the normal subject. Fusion surgery would alter the postoperative biomechanical surrounding of the cervical spine, especially the adjacent segments. These changes might affect the intervertebral disc-bearing capacity, and even weaken the physiological structure. From a purely biomechanical perspective, the cervical spinal fusion model can contribute to comprehending the etiology of ASD after spinal fusion.

Effect of prosthetic joint line installation height errors on insert wear in unicompartmental knee arthroplasty

The clinical performance and failure issues are significantly influenced by prosthetic malposition in unicompartmental knee arthroplasty (UKA). Uncertainty exists about the impact of the prosthetic joint line height in UKA on tibial insert wear. In this study, we combined the UKA musculoskeletal multibody dynamics model, finite element model and wear model to investigate the effects of seven joint line height cases of fixed UKA implant on postoperative insert contact mechanics, cumulative sliding distance, linear wear depth and volumetric wear. As the elevation of the joint line height in UKA, the medial contact force and the joint anterior-posterior translation during swing phase were increased, and further the maximum von Mises stress, contact stress, linear wear depth, cumulative sliding distance, and the volumetric wear also were increased. Furthermore, the wear area of the insert gradually shifted from the middle region to the rear. Compared to 0 mm joint line height, the maximum linear wear depth and volumetric wear were decreased by 7.9% and 6.8% at -2 mm joint line height, and by 23.7% and 20.6% at -6 mm joint line height, the maximum linear wear depth and volumetric wear increased by 10.7% and 5.9% at +2 mm joint line height, and by 24.1% and 35.7% at +6 mm joint line height, respectively. UKA prosthetic joint line installation errors can significantly affect the wear life of the polyethylene inserted articular surfaces. Therefore, it is conservatively recommended that clinicians limit intraoperative UKA joint line height errors to -2-+2 mm.

Multi-body dynamic modelling and simulations for train crashworthiness design analysis

ABSTRACT One of the most important issues for rail passenger vehicles is on occupant safety through vehicle crashworthiness. Crashworthiness, in terms of rail vehicle designs, is the capability to dissipate the crash energy in such a controlled fashion that the overall damage is inconsequential to passenger space. A case study on a popular city passenger train has been conducted using a multi-body formulation of a three-dimensional, non-linear rigid body dynamic train model. The simulated crash scenario details a one to eight vehicle train in a front-on collision onto a fixed block. The crashworthiness is measured in terms of the degree of impact energy absorption, vehicle deceleration, and passenger injury criteria. The results showed that in a single vehicle, the crash energy management systems (CEMS) adequately compensated for the effects of impact at a crash speed of 44.5 km/h and below. At higher speeds, it is projected that the energy crush zones will need significant structural increases in both its crush length and crush force. An increase in the crush length is normally preferred over the crush force so as to maintain the longitudinal deceleration gradient within a tolerable range to ensure passenger safety. The benefits of computational modelling and simulations should not be underestimated as it allows for a thorough appreciation of a sound appreciation of the crashworthy structures and energy absorbers within any rail vehicle during the initial periods of the design process.

A data-driven suspension kinematics and compliance model considering multi-axis coupling effects

The kinematics and compliance characteristics (K&amp;C) significantly impact a vehicle’s dynamic response. While a comprehensive multibody suspension model can accurately express desired suspension K&amp;C characteristics, the complexity of the model limits its use in real-time applications. The K&amp;C characteristics are usually obtained through decoupled bench tests, whereby it is assumed that the suspension K&amp;C characteristics can be orthogonally decomposed and that the function outputs can be added up to restore the original characteristics, which may not be accurate. Therefore, in this research, a novel suspension K&amp;C simulation/test method is proposed to demonstrate the suspension characteristics under coupled force inputs. A multibody dynamic model of an air suspension is constructed and calibrated through bench tests. Then, a series of coupled tire forces with shapes of space spiral curves are applied to the multibody model to produce the coupled K&amp;C data. A novel data-driven model based on Long Short-Term Memory (LSTM) network is proposed to predict suspension K&amp;C. Finally, the proposed data-driven K&amp;C model and the decoupled K&amp;C model are compared under full vehicle simulations. The results suggest that the proposed method is more accurate than the decoupled K&amp;C model and can express the suspension hysteresis characteristics without further modification.

Particle swarm optimized fuzzy proportional-integral-derivative controller-based transverse leaf spring active suspension for vibration control

The transverse leaf spring (TLS) suspensions are a promising option for van vehicles due to their high load-carrying capacity and excellent handling stability. However, its ride comfort remains a major challenge. This paper investigates and compares the effects of semi-active and active control strategies to enhance the ride comfort of TLS suspensions. Firstly, a four-degree-of-freedom (4-DOF) half-car model and a multi-body dynamics (MBD) model of the TLS suspensions are established. The MBD model has higher accuracy and can describe the medium and high frequency characteristics of the TLS suspensions, such as the suspension offset frequency and the frequency response function of the body vertical acceleration (BVA). Therefore, based on the MBD half-car model with TLS suspensions, this paper proposes an optimal fuzzy PID active control strategy considering the left and right suspension coupling. The optimization objectives are the BVA, the left and right suspensions dynamic deflection, and the left and right wheels dynamic displacement. The integral absolute error is used as the evaluation criterion. The left and right fuzzy PID controllers’ parameters are obtained through particle swarm optimization. Simulation results demonstrate that the particle swarm optimization fuzzy PID active control strategy effectively controls the low-frequency vibration of the TLS suspensions and suppresses the medium- and high-frequency vibration characteristics compared with the traditional skyhook semi-active control strategy. This technology provides a reference for improving the ride comfort of the TLS suspensions.

Investigation on Aerodynamic Fluid–Structure Coupling Vibration of 160 km/h EMU Tail in Single-Track Tunnels

Recently, the phenomenon of tail-sustained swaying of the 160[Formula: see text]km/h EMU in single-track tunnels has gained much attention, especially for the rear-powered vehicle. This phenomenon is investigated from the perspective of aerodynamic fluid–structure coupling vibration in this study. The aerodynamics simulation model of the train in tunnels and the multi-body dynamics model of the rear-powered vehicle were respectively established through the software of XFlow and Simpack, and then the fluid–structure coupling vibration was simulated by using real-time data dynamic exchange between the two models. Moreover, the carbody’s vibration acceleration and the aerodynamic loads acting on the carbody under various wheel–rail contact geometrical conditions were discussed. Finally, the train tail swaying in field was tested, and the dominant frequencies were analyzed. The results show that the periodic aerodynamic loads and the frequency locking effect caused by the coupled vibration are the main factors for ride comfort deterioration. The violent vibration caused by fluid–structure coupling is named vortex-induced vibration (VIV) in some industries such as bridge and submarine pipeline. For the vehicle in this work, with the decrease of equivalent conicity in wheel–rail contact, the amplitude of carbody swaying increases owing to the carbody hunting, which enhances the fluid–structure coupling vibration, and further deteriorates the ride comfort. The swaying of the carbody is dominated by the vehicle hunting frequency, and the improvement of vehicle lateral stability can weaken this phenomenon.

Gear walk instability caused by brake-disc friction characteristics

A multi-body dynamic rigid-flexible coupling model of landing gear is established to study the gear walk instability caused by the friction characteristics of the brake disc. After validating the model with the experimental results, the influence of the landing gear structure and braking system parameters on gear walk is further investigated. Among the above factors, the slope of the graph for the friction coefficient of the brake disc and the relative velocity of brake stators and rotors is the most influential factor on gear walk instability. Phase trajectory analysis verifies that gear walk occurs when the coupling of multiple factors causes the system to exhibit an equivalent negative damping trend. To consider a more realistic braking case, a back propagation neural network method is employed to describe the nonlinear behavior of the friction coefficient of the brake disc. With the realistic nonlinear model of the friction coefficient, the maximum error in predicting the braking torque is less than 10% and the effect of the brake disc temperature on gear walk is performed. The results reveal that a more negative friction slope may contribute to a more severe unstable gear walk, and reducing the braking pressure is an effective approach to avoid gear walk, which provides help for future braking system design.