Multi-body Simulation Model Research Articles

Analysis of the degradation in transmission accuracy of RV reducers considering the wear clearance between cycloidal wheels and pinwheels

To accurately determine the transmission accuracy degradation pattern of Rotate Vector (RV) reducers due to wear, a predictive method is proposed that simultaneously considers the initial clearance and wear clearance between the cycloid wheel and the pinwheel. The initial clearance is derived from a comprehensive gear system analysis, considering assembly errors, manufacturing errors and modifications. Building on this, the wear depth of the cycloid wheel tooth profile is numerically simulated using Archard's wear theory, revealing the wear distribution pattern under various operating conditions. A Gaussian regression model is used to predict the maximum wear amount for different operational durations. Based on the predicted wear amount, a multi-body dynamic simulation model incorporating wear clearance was established to analyze the transmission error under varying clearance conditions. Results indicate that the wear depth along the tooth profile initially increases and then decreases. The depth and region of wear along the tooth profile gradually increase with load and output speed, with the impact of load on the wear region being greater than that of output speed. Under the initial clearance condition, the maximum transmission error is 22.91″. As the wear clearance increases, transmission accuracy declines sharply. When the cumulative wear clearance reaches 0.2 mm, the transmission error exceeds the allowable backlash limit. This study provides a theoretical reference for predicting accuracy degradation and guides the manufacturing design of RV reducers.

Optimisation of the hammer throw using parameterised synthetic motion kinematics in a multi‐body simulation

AbstractHammer throwing is a motorically demanding sport in which the execution of the movement significantly influences the result, that is the throwing distance. There are many approaches for supporting technical training that are based on measurement technology and image capturing. The accelerations and locus curves of the athlete and hammer are recorded and compared. In this article, these methods are supplemented by a multi‐body simulation (MBS) of the hammer throw. The kinematics of the hand movement is described using a parameterized synthetic trajectory. Scalar parameters in the approach allow the trajectory to be modified. With a MBS model of the wire cable and the hammer, the movement of the hammer can be determined by numerical time integration from the hand's trajectory. As a result the final throwing distance after free flight phase can be analyzed. Due to the complex spatial motion of the hammer during the acceleration phase only heuristic methods can be used to optimize the maximum throwing distance. In a final step the optimized movement can be used to improve the athlete's training.

Optimization of the cruising speed for high-speed trains to reduce energy consumed by motion resistances

As one of the effective measures to reduce energy consumption of high-speed railway, train operation control has gained much attention because of its cost-effectiveness. Conventional approaches to eco-driving generally rely on single-mass train models and lack a thorough investigation into the vehicle cruising process, which can overlook real-world operation conditions and hinder further improvements in energy efficiency. To address these issues, this paper proposes a comprehensive framework for optimizing the cruising speed of high-speed trains (HSTs) based on track conditions to reduce energy consumed by motion resistances (ECMR). Firstly, a multibody dynamics simulation model of the HST is developed and validated to accurately evaluate ECMR under a range of operation scenarios. Simulation results show that the impact of speed on ECMR varies considerably according to track characteristics. Subsequently, a neural network is constructed to derive the regressive relationship between operation conditions and ECMR. On this basis, an optimization model for the cruising speed under different track conditions is formulated to minimize the ECMR of a railway segment with a given operation time. Finally, the effectiveness of the model is validated through case studies, which demonstrate that ECMR can be reduced by up to 27.85% compared to traditional control strategies. The proposed optimization method can be integrated with current train speed profiles to further enhance energy efficiency. This framework has broad applicability for addressing engineering problems related to train operation optimization.

Open wedge high tibial osteotomy alters patellofemoral joint kinematics: A multibody simulation study.

Changes in lower limb alignment after open-wedge high tibial osteotomy (owHTO) influence joint kinematics. The aim of this study was to investigate the morphological and kinematic changes of the knee joint, in particular the patellofemoral joint, using a multibody simulation model. OwHTO with an open tibial wedge of 6-12 mm (1 mm intervals) was virtually performed on each of 13 three-dimensional (3D) computer-aideddesign models (CAD models) derived from computer tomography scans of full-leg cadaver specimens. For each owHTO, an individual biomechanical simulation model was built and knee flexion from 5° to 100° was simulated using a multibody simulation model of the native knee. Morphologic and alignment parameters as well as tibiofemoral and patellofemoral kinematic parameters were evaluated. Almost linear changes in tibial tuberosity trochlea groove(TT-TG) (0.42 mm/1 mm wedge height) were observed which led to pathological values (TT-TG > 20 mm) in 3 out of 13 knees. Furthermore, a 6 mm increase in osteotomy wedge height increased lateral patellofemoral rotation by 0.8° (range: 0.39° to 1.11°) and led to a lateral patellar translation of 0.8 mm (range: 0.37-3.11 mm) on average. Additionally, valgisation led to a medial translation of the tibia and a decrease in the degree of tibial internal rotation during knee flexion of approximately 0.3°/1 mm increase in osteotomy wedge height. The increase in TT-TG and the biomechanical effects observed influence patellofemoral tracking, which may increase retropatellar pressure and are potential risk factors for the development of anterior knee pain.

Investigation of Nonlinear Effects in the Tower Structure of Wind Turbines and Their Influence on System Behavior

In multibody simulation (MBS) software, large structural components such as the tower are often modeled as flexible bodies using the Craig-Bampton method. While being very computationally efficient, nonlinear effects cannot be modelled in this way. The flange connections between the segments of tubular steel towers are one such source of nonlinearity. The magnitude of this nonlinearity increases with damages at the flanges as flange gaping becomes more common. The nonlinearities in the flanges lead to a changing stiffness and hence changing eigenfrequencies of the structure as a function of its deformation. In this paper, a nonlinear model of a tower with and without damages is being developed and validated based on an FEM model. The model is assembled from linear flexible bodies linked with nonlinear rotatory springs. The damages considered are broken bolts as well as axially symmetric angular flange gaps. It is shown that the MBS model closely emulates the FEM model including all nonlinear effects. The nonlinear tower model is incorporated into an existing MBS model of a commercial wind turbine in the 4 MW range. The eigenfrequencies of the full turbine model are being calculated using the build-in eigenvalue solver in Simpack. The results show a small but measurable decrease in eigenfrequencies compared to the linearized model, which scales with the extend of the damage.

Real-time multibody simulation of vehicle wheel suspensions of different topologies with elastokinematic properties

AbstractDriving simulators are becoming increasingly important in vehicle development, as they allow test drivers to evaluate the driving characteristics of a vehicle at an early stage of the development process. Vehicle dynamics models used for such real-time applications are usually simplified to achieve sufficiently low computation times, especially with respect to the elastokinematic properties of the wheel suspension. This contribution introduces a real-time capable multibody simulation model for wheel suspensions taking into account their elastokinematics. The underlying data model allows the parametrization of different suspension topologies. Linear-implicit integration methods enable real-time capable integration of the underlying numerically stiff equation of motion without major model simplifications. It is shown how the computational effort of linear-implicit integration can be reduced by explicitly taking the suspension topology into account. A versatile process for the analytical online-linearization of the equation of motion of arbitrary suspension topologies is presented. Both a double wishbone and a multilink suspension are simulated with very high accuracy in real-time on a standard PC.

Terramechanics Models for Tracked Vehicle Terrain Interaction Analysis A Review

Efficient manoeuvrability of off-road tracked vehicles such as military tanks and rovers is essential in ensuring the success of military/extra-terrestrial operations. To achieve this, in-depth research on vehicle-terrain interaction is crucial. This manuscript deals with reviewing the ways to study terramechanics viz. theoretical, empirical, and field tests, and proposing the merits and demerits of each method. Under the theoretical approach, empirical, numerical, and semi-empirical methods are discussed. Under the empirical approach, the method based onthe vehicle cone index for tracked and wheeled vehicles is discussed. Under the numerical approach, advantages and disadvantages of Finite Element Method (FEM) and Discrete Element Method (DEM) are discussed. Semi-empirical method, based upon a combination of the best features of numerical and empirical approaches discusses terrain response to normal repetitive loads and shear repetitive loads for tracked as well as wheeled vehicles. Pressure sinkage relationship for terrains at various loading conditions and shear stress displacement relationship for different terrains obtained through penetration and shear tests are discussed to determine the vehicle’s mobility parameters under a semi-empirical approach. Further, the Super element model, multi-body simulation model, and ride and cornering vibration model are discussed under computer simulation models. A detailed review of various models customized towards tracked vehicle-terrain interaction discussed in this manuscript helps the authors set up a laboratory for terramechanics at DIAT. Preliminary analysis along with conceptual design of the experimental setup is also discussed. In a nutshell, this paper attempts to summarize the research that has been carried out in the field of tracked vehicle-terrain inter action comprising of VCI, MMP, FEM, DEM, Super element model, Multibody technique, and Semi-empirical methods helping the authors to establish a laboratory of terramechanics for their M. Tech. program on Armament and Combat Vehicles at DIAT Pune.

Evaluation of Ground Pressure, Bearing Capacity, and Sinkage in Rigid-Flexible Tracked Vehicles on Characterized Terrain in Laboratory Conditions.

Trafficability gives tracked vehicles adaptability, stability, and propulsion for various purposes, including deep-sea research in rough terrain. Terrain characteristics affect tracked vehicle mobility. This paper investigates the soil mechanical interaction dynamics between rubber-tracked vehicles and sedimental soils through controlled laboratory-simulated experiments. Focusing on Bentonite and Diatom sedimental soils, which possess distinct shear properties from typical land soils, the study employs innovative user-written subroutines to characterize mechanical models linked to the RecurDyn simulation environment. The experiment is centered around a dual-tracked crawler, which in itself represents a fully independent vehicle. A new three-dimensional multi-body dynamic simulation model of the tracked vehicle is developed, integrating the moist terrain's mechanical model. Simulations assess the vehicle's trafficability and performance, revealing optimal slip ratios for maximum traction force. Additionally, a mathematical model evaluates the vehicle's tractive trafficability based on slip ratio and primary design parameters. The study offers valuable insights and a practical simulation modeling approach for assessing trafficability, predicting locomotion, optimizing design, and controlling the motion of tracked vehicles across diverse moist terrain conditions. The focus is on the critical factors influencing the mobility of tracked vehicles, precisely the sinkage speed and its relationship with pressure. The study introduces a rubber-tracked vehicle, pressure, and moisture sensors to monitor pressure sinkage and moisture, evaluating cohesive soils (Bentonite/Diatom) in combination with sand and gravel mixtures. Findings reveal that higher moisture content in Bentonite correlates with increased track slippage and sinkage, contrasting with Diatom's notable compaction and sinkage characteristics. This research enhances precision in terrain assessment, improves tracked vehicle design, and advances terrain mechanics comprehension for off-road exploration, offering valuable insights for vehicle design practices and exploration endeavors.

Dynamic Performance Optimization of Monorail Rapid Transit Formation Vehicles Based on Improved Artificial Potential Field Algorithm

This paper presents a new type of monorail rapid transit vehicle, which can operate in formation. In order to optimize the dynamic performance of the formation vehic-les when passing through the small radius curve, this paper first analyzes the structure of the new monorail rapid transit vehicle, and establishes the vehicle dynamic model and multi-body dynamics simulation model. Then the improved artificial potential field algorithm is used to build the formation vehicle operation controller. Finally, the dynamic performance evaluation index of the new mono-rail rapid transit formation vehicle is formulated, and the formation vehicle passing through the small radius curve scene is simulated. The simulation results show that the controller of the formation vehicle with dynamic optimi-zation control can effectively optimize the load transfer coefficient of running wheels, unbalanced centrifugal acce-leration and roll angle of vehicle body when passing thro-ugh the curve. Through this control method, the dynamic performance of formation vehicles passing through small radius curve lines can be optimized.

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.

Multibody Simulation Model as Part of Digital Twin Architecture: Stewart Platform Example

Multibody Simulation Model as Part of Digital Twin Architecture: Stewart Platform Example

Study on Lateral Vibration of Tail Coach for High-Speed Train under Unsteady Aerodynamic Loads

As the speed of high-speed trains increases, the vehicle’s lateral stability steadily deteriorates. There have been observations of abnormal vibrations in the tail car, particularly on certain sections of the railway line. This study built a high-speed train aerodynamic simulation model for a three-car consist, and a multibody dynamics simulation model for an eight-car consist based on numerical simulations of train aerodynamics and multibody dynamics. It investigated both steady and unsteady aerodynamic loads, flow field characteristics, and the dynamic performance of vehicles under varied aerodynamic loads at 400 km/h. The results indicate that the aerodynamic loads generated during high-speed train operation exhibit highly unsteady characteristics. Steady aerodynamic loads have a relatively minor impact on the vehicle’s dynamic performance, whereas unsteady loads exert a more significant influence. Under unsteady aerodynamic forces, the tail car experiences severe lateral vibrations. The lateral stability index, displacement, velocity, and acceleration of the tail car under unsteady conditions were measured at 2.26, 7.54 mm, and 0.53 m/s2, respectively. These values represent increases of over 17.71%, 148.84%, and 111.24%, respectively, compared to the steady loads. Large oscillation amplitudes result in more significant lateral displacements and accelerations of the vehicle. This phenomenon is a crucial factor contributing to the “tail swing” effect observed in high-speed trains. This study emphasizes the importance of considering unsteady aerodynamic effects in assessing the lateral stability of high-speed trains and highlights the significance of mitigating the adverse impacts of such dynamic responses, particularly in the tail car.

A transfer learning-based method for marine machinery diagnosis with small samples in noisy environments

The operating conditions of marine machinery are demanding, and their operational state significantly affects the safety of marine structures. Detecting faults is crucial for machinery health management and necessitates a highly precise diagnostic method. In this paper, we propose a fault diagnosis framework that employs transfer learning and dynamics simulation. A denoising convolutional autoencoder is used to reduce noise when monitoring vibration data in marine environments. To address the challenge of limited sample sizes in marine machinery fault data, a multibody dynamics simulation model is developed to acquire data under fault conditions. The fault features are extracted using a convolutional neural network model. Parameter transfer is applied to enhance the accuracy of fault diagnosis. The effectiveness and applicability of the framework are demonstrated through a case study of a bearing fault dataset.

Investigation of dynamic gauge widening in small radius curves and its impact on lateral wheel-rail contact forces

In this paper, the lateral interaction between a rail vehicle and the track is investigated during cases of an occurrence of dynamic gauge widening. This is composed of the nominal track gauge, wear of the rail profiles and track widening due to wheel-rail forces on sections of curved track. A multibody simulation model is used to investigate the various influencing parameters. This model not only analyses the single rail’s lateral displacement but also tilting. Furthermore, the simulation of rail pads with adjustable stiffnesses is enabled. The resulting different contact points between the wheel and rail are represented, affecting the wheel-rail contact forces. The results reveal that changes in contact geometry caused by rail tilting depend strongly on the specific wheel and rail profiles. This is illustrated by comparing a new rail profile with a heavily worn rail profile. Particular attention is also paid to the distinction between leading and trailing wheelsets. Finally, the model is validated using measured wheel-rail forces and rail head movement, as measured on the track. A better understanding of dynamic track widening can improve the running behaviour of the wheelset on small radius curves, help protect against derailment and reduce wear on the wheel and rail.

Including Blade Elasticity into Frequency-Domain Propeller Whirl Flutter Analysis

Whirl flutter as an aeroelastic instability can be a limiting factor in the design and certification of turboprop aircraft configurations, especially for the engine suspension. Whirl flutter prediction for these configurations is currently done in the frequency domain using rigid propeller aerodynamic derivatives. Blade flexibility is neglected in this process, although it is known to have an impact on whirl flutter predictions. This paper uses frequency-domain transfer matrices for the propeller hub loads identified from a time-domain multibody simulation model of an isolated turboprop propeller and included into a frequency-domain flutter analysis to study the impact of blade elasticity on propeller whirl flutter. Results demonstrate a significantly stabilizing effect of blade elasticity on propeller whirl flutter due to a reduction of the destabilizing pitch-yaw cross-coupling moment. The method demonstrated in this paper is applicable to arbitrary time-domain propeller models and compatible with standard frequency-domain flutter processes, allowing for increased fidelity in the flutter prediction process.

The influence of journal bearings on the gearbox dynamics of a 5 MW wind turbine drivetrain

In recent years, journal bearings have been replacing roller bearings in wind turbine gearboxes, as they are believed to provide higher reliability compared with roller bearings. However, replacing roller bearings with journal bearings can drastically change the gearbox dynamics. Journal bearings have complex dynamics at different operating speeds, and, as a wind turbine operates at various speeds, it is vital to analyze the gearbox dynamics for the entire speed range. This contribution presents the dynamic response of a wind turbine gearbox when the roller bearings of the high-speed shaft are replaced with journal bearings. This is done by performing a comparative case study using a detailed multibody simulation (MBS) model of a 5 MW reference wind turbine drivetrain. A dynamic model of the journal bearings, developed in Simulink, is dynamically coupled with the 5 MW drivetrain MBS model using co-simulation. The simulation results for the gearbox vibration as well as gear forces are compared with the simulation results of the drivetrain model with roller bearings. The findings from this work will help in clarifying the advantages (or disadvantages) of using journal bearings instead of roller bearings in wind turbine gearboxes.

Predicting Friction of Tapered Roller Bearings with Detailed Multi-Body Simulation Models

In the presented work, a parametric multibody simulation model is presented that is capable of predicting the friction torque and kinematics of tapered roller bearings. For a highly accurate prediction of bearing friction, consideration of solid and lubricant friction is mandatory. For tapered roller bearings in particular, the friction in the contact between the rolling element and raceway is of importance. Friction forces in the contact between the rolling element end face and inner ring rib as well as roller cage pocket contacts are also considered in the model. A large number of tests were carried out to validate the model in terms of the simulated frictional torque. Influencing variables such as speed, axial load, radial load, and temperature were investigated. The simulation results show good agreement with the measured friction torque, which confirms that the model is well suited to predict frictional torques and therefore the kinematics of tapered roller bearings.

Machine learning-based rail corrugation recognition: a metro vehicle response and noise perspective.

Rail corrugation is a common problemin metro lines, and its efficient recognition is always an issue worth studying. To recognize the wavelength and amplitude of rail corrugation, a particle probabilistic neural network (PPNN) algorithm is developed. The PPNN is incorporated with the particle swarm optimization algorithm and the probabilistic neural network. On the basis ofthe above, the in-vehicle noise characteristics measured in the field are used to recognize normal rail wavelengths of 30 and 50 mm. A stepwise moving window search algorithm suitable for selecting features with a fixed order was developed to select in-vehicle noise features. Sound pressure levels at 400, 500, 630 and 800 Hz of in-vehicle noise are fed into the PPNN, and the average accuracy can reach 96.43%. The bogie acceleration characteristics calculated by the multi-body dynamics simulation model are used to recognize normal rail amplitudes of 0.1 and 0.2 mm. The bogie acceleration is decomposed by the complete ensemble empirical mode decomposition with adaptive noise, and a reconstructional signal is obtained. The energy entropy of the reconstructional signal is fed into the PPNN, and the average accuracy can reach 95.40%. This article is part of the theme issue 'Artificial intelligence in failure analysis of transportation infrastructure and materials'.

Power Compensation Strategy and Experiment of Large Seedling Tree Planter Based on Energy Storage Flywheel

The intermittent hole-digging tree-planting machine shows a periodic short-time peak load law in planting operation, and the operation process is “idling” for small loads most of the time, leading to large torque fluctuations in the transmission system, unscientific power matching, and high energy consumption. To solve the above problems, this article proposes to use a series of energy-saving flywheels in the transmission system of the tree planting machine. On the premise of obtaining holes that meet the target young tree planting requirements, the optimal power compensation strategy for the flywheel system of the tree planting machine is studied to reduce torque fluctuations in the power transmission system, use smaller power drive units, and save energy. Firstly, the nonlinear multi-body dynamics simulation model of soil cutting by the hole-digging component is established. The boundary and contact conditions are set to simulate the power consumption of the hole-digging component at three rotating speeds. Based on the simulation results, the flywheel power compensation strategy is discussed, and the torque fluctuation of the flywheel balance system is analyzed. The results showed that the higher the speed, the greater the power consumption. The power value suddenly increased from 17.82 kW (1.28 s) to 27.93 kW (1.43 s) when the speed was 220 r/min. Then, the power value rapidly decreased, and the power consumption presented a short-term peak feature. The transmission system’s maximum input power is determined as 17.82 kW according to the various simulated power consumption characteristics. The part exceeding the power consumption is compensated by the energy storage flywheel. The total compensation energy was 2382.5 J. After the flywheel system was involved, the maximum output power of the tractor power output shaft decreased by 36.2%, and the peak torque decreased from 445.7 N·m to 285.1 N·m. The power consumption obtained from the field test and simulation was similar, but the energy required to overcome peak load was jointly provided by the flywheel and the engine. The actual input power of the power output shaft during the energy release period of the flywheel system was 18.51 kW when the rotating speed of the hole-digging component was 220 r/min, and the relative error with the simulation value was 2.43%. The measured actual speed reduction of the flywheel system was 8.9%. After installing an energy storage flywheel in the transmission system of the tree planting machine, the output power of the power unit can be stabilized. Tree planting machines can be equipped with smaller power units, which can reduce energy consumption and exhaust emissions.

A Simple, Efficient Method for an Automatic Adjustment of the Lumbar Curvature Alignment in an MBS Model of the Spine

In many fields of spinal health care, efforts have been made to offer individualized products and therapy tailored to the patient. Therefore, the prevailing alignment of the spine must be considered, which varies from person to person and depends on the movement and loading situation. With the help of patient-specific simulation models of the spine, the geometrical parameters in a specific body position can be analyzed, and the load situation of the spinal structures during dynamic processes can be assessed. However, to enable the future usability of such simulation models in medical reality, as many patient-specific conditions as possible need to be considered. Another critical requirement is that simulation models must be quickly and easily created for use in clinical routine. Building new or adapting existing spine multibody simulation (MBS) models is time-consuming due to their complex structure. To overcome this limitation, we developed a simple, efficient method by which to automatically adjust the lumbar curvature orientation of the spine model. The method extracts a new 3D lordosis curve from patient-specific data in the preprocessing step. Then the vertebrae and all linked spinal structures of an existing spinal simulation model are transformed so that the lumbar lordosis follows the curve obtained in the first part of the method. To validate the proposed approach, three independent experts measured the Cobb angle in the source and the generated spine alignments. We calculated a mean absolute error of 1.29° between the generated samples and the corresponded ground truth. Furthermore, the minor deviation in the root mean square error (RMSE) of 0.0012 m2 between the areas under the alignment curves in the original and target lordosis curvatures indicated the accuracy of the proposed method. The proposed method demonstrated that a new patient-specific simulation model can be generated in a short time from any suitable data source.