Multi-body Dynamics Simulation Research Articles

Validation of a new road and contact model for vehicle–soft soil terrain interaction through an elaborate modelling of the FED-Alpha vehicle

Employing multibody dynamic simulations with semi-empirical tyre models is widely recognised as a cost-effective approach. A recent development introduces a novel road and tyre–soil contact model that is not only swift and memory-efficient but also addresses limitations in classical semi-empirical models. This study conducts a thorough validation of the new road and contact model by creating a detailed multibody model of the four-wheeled vehicle, Fuel Efficiency Demonstrator – Alpha, integral to NATO’s Next-Generation reference mobility model. The comprehensive model encompasses the chassis, suspension, tyres, engine, transmission and various other components. Through simulations of various driving scenarios, accounting for complex terrain geometries, spatially varying soil properties and multi-pass phenomena, the model’s performance is evaluated. The simulation results are compared with physical measurements, providing a detailed assessment of the tyre–soil model’s predictive accuracy for wheeled vehicle mobility on deformable terrains.

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.

Railway Track Irregularity Estimation Using Car Body Vibration: A Data-Driven Approach for Regional Railway

Track and preventive maintenance are necessary for the safe and comfortable operation of railways. Track displacement measured by track inspection vehicles or trolleys has been primarily used for track management. Thus, vibration data measured in in-service vehicles have not been extensively used for track management. In this study, we propose a new technique for estimating track irregularities from measured car body vibration for track management. The correlation between track irregularity and car body vibration was analysed using a multibody dynamics simulation of travelling rail vehicles. Gaussian process regression (GPR) was applied to the track irregularity and car body vibration data obtained from the simulation, and a method was proposed to estimate the track irregularities from the constructed regression model. The longitudinal-level, alignment, and cross-level irregularities were estimated from the measured car body vibrations and travelling speeds on a regional railway, and the results were compared with the actual track irregularity data. The results showed that the proposed method is applicable for track irregularity management in regional railways.

Rapid and precise calibration of soil microparameters for high-fidelity discrete element models in vehicle mobility simulation

In the realm of numerical simulations concerning vehicle mobility, the establishment of a high-fidelity soil discrete element model often necessitates substantial parameter adjustments to align with the mechanical responses of actual soil. In pursuit of a rapid and precise calibration of the microparameters of the soil model, this paper describes an approach rooted in machine learning surrogate models. This method calibrates the corresponding discrete element microparameters based on the macroscopic Mohr–Coulomb parameters derived from actual soil direct shear tests. The distinct contribution lies in the creation of a dataset that bridges the soil microparameters and macroparameters through simulated direct shear tests, which serves as training data for machine learning algorithms. Additionally, an adaptive particle swarm optimization neural network algorithm is proposed to represent the nonlinear relationships among parameters within the dataset, thus achieving intelligent calibration. To verify the reliability of the proposed soil calibration model in the context of vehicle mobility simulations, a co-simulation is conducted using a vehicle multibody dynamics simulation model and the calibrated soil model, with validation conducted across multiple criteria.

Multibody Dynamics and Terramechanics-based modeling and simulation of Quarter-Car with Suspension

Abstract While tires only compress when acted upon by a load in on-road scenarios, in off-road conditions, on the other hand, the tires not only undergo compression but also sinkage into the ground, in a manner that depends on the terrain. The tire-ground contact, in turn, affects the forces acting on the suspension system. Hence, it is necessary to study the vertical dynamic response of a system in off-road conditions by accounting for the terramechanics phenomenon (tire-terrain interface). The forces acting at the tire and terrain interface in off-road conditions have been studied in terramechanics separately; however, their integration with multibody systems is relatively less explored. In this paper, a multibody dynamic-based modeling and simulation of a quarter car with a linear spring-damper suspension system for off-road vehicles is presented. The generalized external forces are obtained using the Bekker-Wong based soil pressure-sinkage approach for two different kind of multibody systems interacting with sandy loam terrain. This model is integrated with the Tangent Space Ordinary Differential Equations of the quarter car and suspension system and solved using numerical integration techniques. Thus, by accounting for the terramechanics in the multibody system, the technique provides a more realistic response of the system in off-road scenarios.

Reliability analysis of 50000 kN hydraulic support test bench under shrinkage test conditions

The large mining-height hydraulic support test-bed serves as a crucial tool for heavy hydraulic support factory inspections and type testing. With the successful development of the ZY29000/45/100D hydraulic support, the need for a large high-mining hydraulic support test-bed has become evident. This paper combines the theory of rigid-flexible coupling in virtual prototypes and ADAMS multi-body dynamic simulation technology to analyze the strength of the 50,000 kN hydraulic support test-bed. ANSYS classic modules were employed to address the flexibility of key components within the test-bed. The fatigue life of the test-bed was analyzed using NSOFT software, the von Mises yield criterion, and the Goodman modified curve. The S-N curve of material parameters for the test-bed components was used to conduct a shrinkage test. The results indicate that the lowest position is the most vulnerable during the shrinkage test. Among the key components, the stress on the pin bearing is 356.6 MPa, which is 167.9 %, 123.3 %, and 41.6 % higher than that of the pillar, movable beam, and base, respectively. The fatigue life of the base under low, medium, and high shrinkage conditions is1.1×107, 4.0×108, and 1.7×108, with damage values of 8.8×10-8, 2.5×10-9, and 5.7×10-9, respectively. The base’s life under low shrinkage conditions is the shortest, followed by that under high shrinkage conditions. These research findings provide technical guidance and an optimization foundation for the successful development of a 50000 kN hydraulic support test-bed. They also offer a new method and approach for analyzing and predicting the fatigue life of key components in large-scale industrial and mining equipment operating under complex conditions, with promising practical applications.

Design optimization of a snowboard performing an ollie

The ollie, a fundamental manoeuver in snowboarding, serves as a basis for various tricks requiring high altitude and extended airtime. The maximum ollie height depends on the snowboard’s geometry and structural characteristics. In this study, the influence of these properties is investigated with a flexible multibody dynamics simulation, where the snowboard is modeled by geometrically non-linear finite elements, snow contact is considered by a penetration depth and velocity proportional normal force and ollie motion is achieved by imposing measured loads to the bindings. To maximize the height, a genetic optimization procedure is presented, which yields substantial improvements. Optimizing the camber line and the bending stiffness distribution yields enhanced performance. Less damping as well as lighter boards lead to higher jumps, no noteworthy correlation between axial stiffness and damping distribution and jump height was found, and the strain energy stored in the board during takeoff is a useful indicator for estimating ollie heights. Nevertheless, further investigations should take a more advanced and realistic rider interaction into account.

Virtual Prototyping of the RM Active Grid®: a DEM-MBD Study

Numerical simulation is an established tool to improve knowledge of complex systems and to accelerate the development of new prototypes. In this contribution, the patented Active Grid® made by the company RM RUBBLE MASTER HMH GmbH is examined.In an initial step, representative system parameters (spring properties) are found via a multibody dynamic simulation; at this point, without particles acting on the system components. After that, the virtually defined Active Grid® system is loaded with particles in order to include the interaction effects of various bulk materials acting on the system’s mechanical components. For this purpose, a DEM-MBD co-simulation, extending the discrete element method (DEM) towards multibody dynamics (MBD) simulation, is performed, accounting for the bulk materials via DEM and the interacting system components via MBD. This bi-directional co-simulation enables the consideration of interactions between the bulk materials (the particles) and the driven spring-damper system (the moving system components).With this virtual prototype of the Active Grid®, performance benefits and characteristics in terms of screening efficiency for different material types and varying drive speeds are analysed. The overall aim is to achieve a scalable DEM-MBD model that allows virtual prototyping and, especially, optimisation for future system developments.

Research on non-linear dynamic simulation model of feeding system

Abstract The automatic gun feeding system is an important mechanism for achieving continuous shooting, but due to its complex structure, there is a lot of contact during firing, and its reliability is lower. To improve the reliability of the feeding system and its dynamic characteristics, a multi rigid body dynamic simulation model of the feeding system considering contact nonlinearity was established based on nonlinear dynamics theory. The dynamic characteristics of the feeding system were analyzed for single and continuous firing. The research results indicate that the presence of contact nonlinearity increases the interaction forces between components and also increases the uncertainty of component motion.

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.

Improving the energy efficiency and riding comfort of high-speed trains across slopes by the optimized suspension control

As the link between cities, the high-speed train (HST) not only effectively enhances national and regional accessibility, but also induces much energy consumption. On the other hand, passengers have a higher requirement for riding comfort of HST than before. Considering the impacts of slope gradient on energy consumption and vertical carbody acceleration, this paper optimizes the scale factor of the damper controller depending on the running condition to juggle the energy efficiency and riding comfort when HST is across slopes. Firstly, the multibody dynamics simulation model of HST is established to evaluate the energy consumed by motion resistances and carbody vibrations. Then the Skyhook control strategy is applied to the secondary vertical damper of the vehicle model. The effects of vehicle speed, slope gradient, and scale factor of the Skyhook controller on energy saving and vertical carbody acceleration of HST are investigated. Based on the simulation results, the Gaussian process regression model is established to predict the vehicle performance and describe the bi-objective optimization problem. It is demonstrated that the optimized Skyhook control system can at most save energy consumed by motion resistances by 8.52 % or reduce vertical carbody acceleration by 37.14 % without sacrificing the other target. Finally, a comprehensive feasibility and economic analysis of the proposed control system is carried out to promote its practical implementation.

Recent Progress in the Physical Principles of Dynamic Ground Self-Righting.

Animals and robots must self-right on the ground after overturning. Biology research has described various strategies and motor patterns in many species. Robotics research has devised many strategies. However, we do not well understand the physical principles of how the need to generate mechanical energy to overcome the potential energy barrier governs behavioral strategies and 3D body rotations given the morphology. Here, I review progress on this which I led studying cockroaches self-righting on level, flat, solid, low-friction ground, by integrating biology experiments, robotic modeling, and physics modeling. Animal experiments using three species (Madagascar hissing, American, and discoid cockroaches) found that ground self-righting is strenuous and often requires multiple attempts to succeed. Two species (American and discoid cockroaches) often self-right dynamically, using kinetic energy to overcome the barrier. All three species use and often stochastically transition across diverse strategies. In these strategies, propelling motions are often accompanied by perturbing motions. All three species often display complex yet stereotyped body rotation. They all roll more in successful attempts than in failed ones, which lowers the barrier, as revealed by a simplistic 3D potential energy landscape of a rigid body self-righting. Experiments of an initial robot self-righting via rotation about a fixed axis revealed that the longer and faster appendages push, the more mechanical energy can be gained to overcome the barrier. However, the cockroaches rarely achieve this. To further understand the physical principles of strenuous ground self-righting, we focused on the discoid cockroach's leg-assisted winged self-righting. In this strategy, wings propel against the ground to pitch the body up but are unable to overcome the highest pitch barrier. Meanwhile, legs flail in the air to perturb the body sideways to self-right via rolling. Experiments using a refined robot and an evolving 3D potential energy landscape revealed that, although wing propelling cannot generate sufficient kinetic energy to overcome the highest pitch barrier, it reduces the barrier to allow small kinetic energy from the perturbing legs to probabilistically overcome the barrier to self-right via rolling. Thus, only by combining propelling and perturbing can self-righting be achieved when it is so strenuous; this physical constraint leads to the stereotyped body rotation. Finally, multi-body dynamics simulation and template modeling revealed that the animal's substantial randomness in wing and leg motions helps it, by chance, to find good coordination, which accumulates more mechanical energy to overcome the barrier, thus increasing the likelihood of self-righting.

Smartphone videos-driven musculoskeletal multibody dynamics modelling workflow to estimate the lower limb joint contact forces and ground reaction forces.

The estimation of joint contact forces in musculoskeletal multibody dynamics models typically requires the use of expensive and time-consuming technologies, such as reflective marker-based motion capture (Mocap) system. In this study, we aim to propose a more accessible and cost-effective solution that utilizes the dual smartphone videos (SPV)-driven musculoskeletal multibody dynamics modeling workflow to estimate the lower limb mechanics. Twelve participants were recruited to collect marker trajectory data, force plate data, and motion videos during walking and running. The smartphone videos were initially analyzed using the OpenCap platform to identify key joint points and anatomical markers. The markers were used as inputs for the musculoskeletal multibody dynamics model to calculate the lower limb joint kinematics, joint contact forces, and ground reaction forces, which were then evaluated by the Mocap-based workflow. The root mean square error (RMSE), mean absolute deviation (MAD), and Pearson correlation coefficient (ρ) were adopted to evaluate the results. Excellent or strong Pearson correlations were observed in most lower limb joint angles (ρ = 0.74 ~ 0.94). The averaged MADs and RMSEs for the joint angles were 1.93 ~ 6.56° and 2.14 ~ 7.08°, respectively. Excellent or strong Pearson correlations were observed in most lower limb joint contact forces and ground reaction forces (ρ = 0.78 ~ 0.92). The averaged MADs and RMSEs for the joint lower limb joint contact forces were 0.18 ~ 1.07 bodyweight (BW) and 0.28 ~ 1.32 BW, respectively. Overall, the proposed smartphone video-driven musculoskeletal multibody dynamics simulation workflow demonstrated reliable accuracy in predicting lower limb mechanics and ground reaction forces, which has the potential to expedite gait dynamics analysis in a clinical setting.

Energy-absorbing limitations of hard hat safety helmets in mitigating trauma from falling objects

The aim of the study was to analyze the effectiveness of hard hat helmets in mitigating head injuries from high-energy falling objects through a real-world case study, advanced numerical simulations and an uncertainty study. The study aims to answer the following research questions: (a) to what extent would the use of the protective helmet limit the kinetic energy of the falling construction prop, (b) whether the hard hat helmet would be damaged, and if so, to what extent, according to the helmet standards? A fatal construction accident involving a falling prop impact on the victim’s head was reconstructed using multi-body dynamics simulations and finite element analysis (FEA) based on uncertainty-based determination of initial conditions. The study quantified the impact energy, helmet damage and its energy-absorbing capabilities, and potential injury reduction compared to scenarios without a helmet. While the helmet absorbed significant energy (245% of the standard requirement) and reduced the Head Injury Criterion by 8–11%, the high impact energy ultimately proved fatal. This study highlights the limitations of hard hat helmets in extreme scenarios with high kinetic energy impacts. While helmets offer valuable protection, unrealistic expectations should not be placed on their ability to prevent all head injuries. The study not only enhances our understanding of the biomechanics of head injuries in such incidents but also provides practical implications for safety protocols and regulations.

Numerical Simulation and Bench Test of Crawler-Type Cotton Time-Delay Hole-Forming Device Based on RecurDyn-EDEM Coupling

In view of the challenges faced by cotton dibbler in Xinjiang under high-speed operation, a novel crawler-type delayed hole-forming device has been designed to address the seed throwing and floating issues in high-speed cotton dibbling in Xinjiang, enhancing the duck bill’s performance. This mechanism increases the sowing speed to 6 km/h by extending the duck bill horizontally. Utilizing agronomic principles, the mechanism’s layout and key components were optimized for efficient hole-forming. DEM and multi-body dynamics simulations were employed to analyze the motion, focusing on the fixed the tilt angle of the duck bill (A), the depth of the duck bill hole-forming into the soil (B), and the angle of rotation of the moving duck bill (C) as factors affecting hole dimensions (longitudinal length of hole Y1 and hole-forming depth of cotton seed hole Y2). Quadratic regression test using RecurDyn-EDEM coupling identified optimal parameter settings for maximum hole-forming performance. When A was 2.4°, B was 42.4 mm, and C was 30.5°, the performance of the hole-forming was the best. Under the optimal parameter combination, the bench verification test was carried out. The error between the bench verification results and the simulation results is small, indicating that the model has high accuracy. The average opening time of the duck bill at a speed of 6 km/h is 0.45 s, which is much longer than the time required for cotton seeds to fall from the duck bill (0.11 s). It meets the requirements of high-speed cotton planting in China and facilitating advancements high-speed planter technology.

World Modeling for Autonomous Wheel Loaders

This paper presents a method for learning world models for wheel loaders performing automatic loading actions on a pile of soil. Data-driven models were learned to output the resulting pile state, loaded mass, time, and work for a single loading cycle given inputs that include a heightmap of the initial pile shape and action parameters for an automatic bucket-filling controller. Long-horizon planning of sequential loading in a dynamically changing environment is thus enabled as repeated model inference. The models, consisting of deep neural networks, were trained on data from a 3D multibody dynamics simulation of over 10,000 random loading actions in gravel piles of different shapes. The accuracy and inference time for predicting the loading performance and the resulting pile state were, on average, 95% in 1.2 ms and 97% in 4.5 ms, respectively. Long-horizon predictions were found feasible over 40 sequential loading actions.

Improved Multi-Body Dynamic Simulation of Landing Gear Drop Test Incorporating Structural Flexibility and Bearing Contact

The investigation of multi-body dynamics (MBD) modeling for landing gear drop tests is a hot topic in the realm of landing gear design. The current results were primarily focused on the multi-rigid body simulation or a simple multi-flexible body simulation, with little regard for the correctness of longitudinal loads and their experimental confirmation, particularly wheel–axle loads. Based on a genuine oleo-pneumatic landing gear drop test of a large civil aircraft, enhanced multi-body dynamics simulation research is carried out, considering the structural flexibility and bearing support by adopting flexible multi-bodies modeling and rigid-flex coupling contacts. When compared to the test data, which purposefully measured the longitudinal wheel–axle loads, the simulation results show that the loads, shock absorber compression, and shock absorber inner pressures are all within good agreement. Furthermore, the influence of structural stiffness and bearing contact was investigated by adjusting the model settings to confirm their importance.

Dynamic Response Analysis of Moving Trains Passing Through the Stationary Thunderstorm Downburst Wind

The safety of the high-speed train traveling through the stationary thunderstorm downburst wind was studied. First, a thunderstorm wind test device was used to simulate the stationary thunderstorm downburst wind. Based on the rigid model pressure measurement tests, the aerodynamic forces of the train traveling along different paths through the stationary thunderstorm downburst wind were measured. The influence of the radial distance of the crossing path on the aerodynamic force coefficients of the train was investigated. On this basis, an unsteady aerodynamic model of the high-speed train crossing through the stationary thunderstorm downburst wind was established, and dynamic response analysis was carried out using the SIMPACK multibody dynamics simulation software to explore further the safety of the high-speed train crossing through the stationary thunderstorm downburst wind. The research showed that the stationary thunderstorm downburst wind field has significant spatial variation characteristics compared with the atmospheric boundary layer wind field. When the train passes through the thunderstorm downburst wind, the radial wind speed and wind yaw angle experienced by the train constantly change, and the change curve shows a symmetrical distribution. The aerodynamic force of the train will undergo sudden loading and unloading processes, and the lateral force coefficient of the train on different paths shows a “pulse-type” variation. Moreover, the lateral force coefficient increases with the increase of wind yaw angle. Under the influence of the thunderstorm downburst wind, the variation trend of the aerodynamic force coefficients of the train is consistent with that under crosswind. However, there are significant differences in the numerical values. Therefore, it is impossible to simply use the formula for calculating the aerodynamic force coefficients of the train under crosswinds to predict the aerodynamic force coefficients of the train under the thunderstorm downburst wind. While passing through the thunderstorm downburst wind, the overturning coefficient index plays a decisive role in the safety of train operations. Train rollover is the main form of train safety accidents, while derailment accidents are not easy. The numerical results obtained in this study are significant for evaluating the operational safety while moving trains traversing the stationary thunderstorm downburst wind.

Experimental Structural Safety Analysis of Front-End Loader of Agricultural Tractor

The agricultural front-end loader is an implement attached to the front of tractors to transport various agricultural materials, including soil. Since they are subjected to various loads due to the working environment, their safety analysis in consideration of actual working conditions is required. However, there are no official standardized test codes to consider various actual working environments currently. In this study, the structural safety of a front-end loader for static and fatigue failures was evaluated using new test code reflecting actual working environments. Thirty-four measurement locations were determined as the stress concentration spots of each component of the front-end loader derived through multibody dynamic simulation. The total testing time was set to 1 h, and the test time for each task was determined considering the duty percentage of the actual loader work. The measurement results showed that the maximum stress that exceeds the material’s yield strength occurred at two locations of the mount, which is the connection to the tractor body, resulting in static yielding. For tasks, the pulling and dumping exhibited the highest stress. The task that had the largest impact on fatigue damage was the dumping. The static safety factor was found to be over 1.93 and the fatigue life met the required lifespan at all measurement locations except for those exhibiting static yielding. Therefore, the most vulnerable part of the front-end loader is the mount, and it is necessary to secure the overall structural integrity by robust design for the mount.

Multi-Objective Optimization of Bogie Stability for Minimum Radius Curve of Battery Track Engineering Vehicle

A battery track engineering vehicle faces challenges such as derailment and other safety concerns when navigating an R20m minimum radius curve, primarily owing to its low vertical and horizontal stabilities. To address these issues, a methodology integrating genetic optimization algorithms with a rigid and flexible coupled multi-body dynamics simulation is proposed to optimize the primary suspensions of the bogie of the vehicle. Initially, a multi-objective optimization model combining rigid and flexible coupled multi-body dynamics of battery track engineering vehicles with a genetic optimization algorithm was formulated. Subsequently, the optimal Latin hypercube design was applied to analyze the sensitivity of vertical and horizontal stability to various suspension parameters. Finally, a non-dominated sorting genetic algorithm (NSGA-II) and an archive-based micro genetic algorithm (AMGA) were applied to optimize the primary suspensions to enhance stability. Consequently, a set of optimal suspension parameter combinations was obtained. A notable enhancement was observed in the lateral stability of the optimized battery track engineering vehicles by 23.33% and in the vertical stability by 3.5% when traversing the R20m minimum radius curve, thereby establishing a theoretical foundation for further improving the running safety of railway vehicles and resolving the shortcomings of less research on the smallest radius curve.