Multibody Research Articles

Application of Laminate Theory to Plate Elements Based on Absolute Nodal Coordinate Formulation

Abstract Laminated plates have a wide range of applications in engineering, and their flexibility becomes increasingly significant with the development of lightweighting technology. The absolute nodal coordinate formulation (ANCF) has emerged as a promising approach for modeling flexible multibody dynamics. However, researches on thick laminated plates with shear deformation for multi-flexible systems remains limited. To investigate the application of ANCF plate elements for laminated plates, this article introduces a new laminated plate element that considers shear deformation. We utilize the fully parameterized ANCF plate element to analyze laminated composite structures, focusing specifically on their layers in the thickness direction. By employing a structural mechanics approach, the study achieves a uniform stiffness matrix that can adapt to laminated plates with shear deformation and can be pre-computed in advance. Additionally, a summary of a thin laminated plate element is provided for comparison. Both plate elements are composed by layers, and their elastic forces and Jacobian matrices are derived using first-order shear theory and Kirchhoff's theory, respectively. The effectiveness and accuracy of the proposed elements are validated through a series of benchmark problems encompassing modal, static, and dynamic investigations. The study thoroughly analyzes the results compared with the commercial finite element method software ABAQUS and analytical approach. The findings demonstrate that the methods effectively address laminated plates.

Numerical investigation of bucket wear and excavation performance with non-spherical materials

Wear significantly affects equipment performance at mining sites, especially when excavating materials with diverse shapes, leading to increased bucket wear and reduced service life. This work combines the co-simulation of multibody dynamics and discrete element method with the Archard wear model to investigate the dynamic interactions between the bucket and non-spherical materials, and the impact of bucket wear on excavation performance. The results indicate that wear is evident on the bottom surface, side surface, and teeth of the bucket throughout the working cycle. The wear patterns observed for different teeth vary, highlighting the importance of maintenance for the middle and side teeth. Compared to spherical particles, ellipsoidal ones cause greater excavating resistance, bucket wear, and hydraulic fluctuations. As wear intensifies, the teeth become blunt, and the bottom surface exhibits unevenness, resulting in reduced payload and increased resistance and hydraulic power. Proposed wear mitigation strategies can help uphold satisfactory operating performance.

Avalanche dynamics in nonconservative water droplet

The self-organized criticality (SOC) exhibits excellent performance in describing the dynamic features of multi-body systems in nature. It is usually considered that conservative law is a necessary condition for the existence of SOC. However, mass or energy dissipation typically exists in the process from self-organization to a critical state in natural systems such as earthquakes and air pollution, namely, non-conservation. At present, few physical experiments have systematically explored the SOC behavior in a non-conservative system, compared to numerical simulations. This study is the first to design a non-conservative sandpile experiment using water droplets. Based on this experiment, the dynamic evolution process of avalanches in a non-conservative system has been analyzed. The results show that the avalanche size of water droplets follows a power-law distribution, as the water mass decays with time. This phenomenon obeys the rules of scale-free distribution, which is consistent with SOC behavior. Moreover, the waiting time of water droplets avalanche follows a stretched exponential distribution. These results suggest that SOC behavior still exists in non-conservative multi-body systems, which is affected by the decay coefficient. We then explore the mechanism by which the decay coefficient affects the transition of the system to a critical state in the non-conservative sandpile model (NBTW). We find that only when the decay coefficient is small do the inequality measures, Gini coefficient g and Kolkata index k, exhibit nearly universal values, similar to the mechanism of the system transitioning to a critical state in the traditional BTW model. When the decay coefficient is large, the NBTW model shows scaling-limited effects and the scaling exponent of avalanche size increases with the decay coefficient. Furthermore, we use the NBTW model to study how the decay coefficient influences the scaling exponent of avalanche size. We find that the NBTW model can effectively explain the variability of scaling exponents observed in different SOC systems and establish a quantitative relationship between the mass decay coefficient and the avalanche size scaling exponent. This study provides new insight into SOC behavior in non-conservative systems in nature.

Numerical Modeling and Analysis of Pendant Installation Method Dynamics Using Absolute Nodal Coordinate Formulation

Accurately simulating the deployment process of coupled systems in deep-sea environments remains a significant challenge. This study employs the Absolute Nodal Coordinate Formulation (ANCF) to dynamically model and analyze multi-body systems based on the Pendant Installation Method (PIM). Utilizing the principle of energy conversion, this study calculates the stiffness, generalized elastic forces, mass matrices, and Morison equation, formulating a motion equation for the dynamic coupling of nonlinear time-domain forces in cables during pendulum deployment, which is numerically solved using the implicit generalized-α method. By comparing the simulation results of this model with those from the catenary theory model, the advanced modeling capabilities of this model are validated. Lastly, the sensitivity of the multi-body system under various boundary conditions is analyzed. The results indicate that deployment operations are more effective in environments with strong ocean currents. Furthermore, upon comparing the impacts of structural mass and deployment depth on the system, it was found that deployment depth has a more significant effect. Consequently, the findings of this study provide a scientific basis for formulating subsequent optimization strategies.

A study of mechanism-data hybrid-driven method for multibody system via physics-informed neural network

A study of mechanism-data hybrid-driven method for multibody system via physics-informed neural network

Modeling and simulation framework for missile launch dynamics in a rigid-flexible multibody system with slider-guide clearance

Modeling and simulation framework for missile launch dynamics in a rigid-flexible multibody system with slider-guide clearance

Parameter identification of vibratory conveying systems including statistical part behavior

This work presents a complete workflow for the parameter identification of an MBS model representing a vibratory conveying system. First, the MBS model built within the multibody dynamics tool HOTINT is shown. Essential components, such as contact modeling and adaptive time step control, are explained in detail. The model includes a considerable amount of parameters that need to be identified. Altough, this model is fully deterministic, the complex contact dynamics can cause major effect on results by minor parameter variations. Thus, parameter variations usually show statistical variance, which is characteristic for real conveying processes too. For parameter identification it is important to detect parameters that significantly correlate with results. A method that allows to distinguish significant and non-significant parameters is presented. The application to the multibody system shows that stiffness, restitution and sliding friction of the contact model are the essential parameters. Next, the parameter identification is discussed with particular attention to multimodal distributions, that can occur in conveying systems. Furthermore, the integration of statistics into the deterministic simulation model is discussed. In order to demonstrate the applicability of the proposed methods, a parameter identification is performed based on measurement data of a single part on a real conveying system in the development site of STIWA Automation GmbH. Finally, the validity of the fully parametrized simulation model is shown by investigating geometric adjustments of the conveyor. In order to further verify the identified set of parameters, a conveying process with multiple parts is analyzed and compared in measurement and simulation.

Comparative Study on the Performances of a Hinged Flap-Type Wave Energy Converter Considering Both Fixed and Floating Bases

The dynamical modeling and power optimization of floating wind–wave platforms, especially in regard to configurations based on constrained floating multi-body systems, lack in-depth systematic investigation. In this study, a floating wind-flap platform consisting of a flap-type wave energy converter and a floating offshore wind turbine is solved in the frequency domain considering the mechanical and hydrodynamic couplings of floating multi-body geometries and a model that suits the constraints of the hinge connection, which can accurately calculate the frequency domain dynamic response of the flap-type WEC. The results are compared with bottom-fixed flap-type wave energy converters in the absence of coupling with a floating wind platform. Moreover, combined with traditional optimization methods of power take-off systems for wave energy conversion, an optimization method is developed to suit the requirements of floating wind-flap platform configurations. The results are drawn for a specific operation site in the South China Sea, whereas a sensitivity analysis of the parameters is performed. It is found that the floating wind-flap platform has better wave energy absorption performance in the low-frequency range than the bottom-fixed flap-type wave energy converter; the average power generation in the low-frequency range can increase by up to 150 kW, mainly due to constructive hydrodynamic interactions, though it significantly fluctuates from the sea waves’ frequency range to the high-frequency range. Based on spectral analysis, operational results are drawn for irregular sea states, and the expected power for both types of flap-type WECs is around 30 kW, which points to a similar wave energy absorption performance when comparing the bottom-fixed flap with the flap within the hybrid configuration.

Riding safety prediction of a high-speed train running on transition zone under foundation settlement

The settlement of piers and subgrade bending deformation are widely recognized as common issues in the transition zones of high-speed railway bridges. This study aims to investigate the settlement behavior within these transition zones and its impact on the dynamic interaction between trains and the track. To achieve this, a vehicle-track-transition zone mapping relationship model is developed to analyze both the settlement behavior and the resulting dynamic response characteristics. The study employs the finite element method and multi-body dynamics to construct the simulation model. Settlement effects are simulated using the Newton-Raphson iterative method, with the additional rail deformation caused by foundation settlement serving as the excitation for the vehicle-track-transition zone dynamic interaction system. In the numerical analysis, the dynamic effects of three key factors—train speed, transition zone length, and the amplitude of foundation settlement—are examined based on the performance of the vehicle-track-transition zone interaction. The time-frequency technique is utilized to comprehensively reveal and clarify the spatial-frequency characteristics of system responses influenced by settlement excitation. Moreover, the relationship between the safety-based settlement threshold and these three factors is calibrated.

Dynamic modelling and experimental validation of a dynamic track stabiliser vehicle–track spatially coupling dynamics system

A dynamic track stabiliser vehicle is an unconventional vehicle for maintaining the quality of ballasted tracks, and its dynamic performance has a significant impact on its working efficiency. For the first time, this paper proposes a comprehensive dynamic track stabiliser vehicle–track coupled vertical and lateral multi-body dynamics model based on classical vehicle–track coupling dynamics theory. In this model, detailed attention is given to the vertical, lateral, roll, yaw, and pitch motions of the components, including the vehicle body, bogies, wheelsets and stabilisers. The Shen–Hedrick–Elkins theory is employed to describe non-linear wheel–rail contact relationships between the bogie wheelsets and the rails, and three various methodologies are adopted to address complicated wheel–rail interaction problems between the stabiliser wheelsets and the rails. This comprehensive multi-body dynamics model enables a detailed investigation of the dynamic performance of the system under complex excitations, such as the lateral excitation of the stabilisers and vertical downward pressure exerted by hydraulic cylinders, especially the dynamic response of the stabilisers in the vibration environment of the complete vehicle. The dynamics model was fully validated by comparing its results with time- and frequency-domain data obtained from field tests. The results indicate that the model is capable of being used for analysis of the dynamic performance of dynamic track stabiliser vehicles.

Simulating Noise, Vibration, and Harshness Advances in Electric Vehicle Powertrains: Strategies and Challenges

This study examines the management of noise, vibration, and harshness (NVH) in electric vehicle (EV) powertrains, considering the challenges of the automotive industry’s transition to electric drivetrains. The growing popularity of electric vehicles brings new NVH challenges as the lack of internal combustion engine noise makes drivetrain noise more prominent. The key to managing NVH in electric vehicle powertrains is understanding the noise from electric motors, inverters, and gear systems. Noise from electric motors, mainly resulting from electromagnetic forces and high-frequency noise generated by inverters, significantly impacts overall NVH performance. This article details sources of mechanical noise and vibration, including gear defects in gear systems and shaft imbalances. The methods presented in the publication include simulation and modeling techniques that help identify and solve NVH difficulties. Tools like multi-body dynamics, the finite element method, and multi-domain simulation are crucial for understanding the dynamic behavior of complex systems. With the support of simulations, engineers can predict noise and vibration challenges and develop effective solutions during the design phase. This study emphasizes the importance of a system-level approach in NVH management, where the entire drivetrain is modeled and analyzed together, not just individual components.

Fast-Activated Minimal Gated Unit: Lightweight Processing and Feature Recognition for Multiple Mechanical Impact Signals.

Multiple dynamic impact signals are widely used in a variety of engineering scenarios and are difficult to identify accurately and quickly due to the signal adhesion phenomenon caused by nonlinear interference. To address this problem, an intelligent algorithm combining wavelet transforms with lightweight neural networks is proposed. First, the features of multiple impact signals are analyzed by establishing a transfer model for multiple impacts in multibody dynamical systems, and interference is suppressed using wavelet transformation. Second, a lightweight neural network, i.e., fast-activated minimal gated unit (FMGU), is elaborated for multiple impact signals, which can reduce computational complexity and improve real-time performance. Third, the experimental results show that the proposed method maintains excellent feature recognition results compared to gate recurrent unit (GRU) and long short-term memory (LSTM) networks under all test datasets with varying impact speeds, while its metrics for computational complexity are 50% lower than those of the GRU and LSTM. Therefore, the proposed method is of great practical value for weak hardware application platforms that require the accurate identification of multiple dynamic impact signals in real time.

Analysis and optimization of vibration characteristics of gyratory crusher based on DEM-MBD and PSO

Dynamic analysis and optimization can improve the stability of gyratory crushers. In this research, a multibody dynamic (MBD) model of a gyratory crusher was built for motion simulation, and the discrete element method (DEM) was applied to describe ore breakage numerically. Specifically, both the stiffness and damping parameters were defined for vibration analysis. A bonding particle model (BPM) was used to extract the distributed breaking force. Then, actual production data was taken to determine the value ranges of key parameters in the established DEM-MBD co-simulation system such as the self-rotation friction coefficient of the mantle, stiffness and damping of the base. Furthermore, the influence of the horizontal stiffness and damping parameters on the vibration of the gyratory crusher was analyzed using the co-simulation results. A dynamic performance prediction model of the gyratory crusher was established using the kriging interpolation method. Finally, based on the prediction model, the particle swarm optimization (PSO) algorithm was applied for the multi-objective optimization of the gyratory crusher. The simulation results indicate that mantle movement is influenced by the horizontal stiffness and damping parameters, which became more complex with the extension of breaking time. The interaction between the stiffness coefficient and the damping coefficient in the Z direction significantly influences productivity. Additionally, horizontal vibrations are significantly affected by the damping coefficient in the Z direction. After optimization, the productivity increased by 10.96 %, the root mean square (RMS) value of the vibration velocity in the X direction decreased by 21.12 %, and that in the Z direction decreased by 4.21 %.

System identification and force estimation of robotic manipulator using semirecursive multibody formulation

AbstractForce estimation in multibody dynamics relies heavily on knowing the system model with a high level of accuracy. However, in complex mechatronic systems, such as robots or mobile machinery, the values of model parameters may be only roughly estimated based on design information, such as CAD data. The errors in model parameters consequently have a direct effect on force estimation accuracy because the estimator compensates the erroneous inertia, friction, and applied forces by changing the value of estimated external force. The objective of this study is to present the workflow of system identification and state/force estimation of an open-loop multibody structure. The system identification utilizes a linear regression identification method used in robotics adapted to the multibody framework. The semirecursive multibody formulation, in particular, is studied as a formulation for both system identification and force estimation. The multibody state/force estimator is constructed using extended Kalman filter. The specific aim of this paper is to demonstrate the utilization of these per se known modeling, identification, and estimation tools to address their current lack of integration as a complete toolchain in virtual sensing of multibody systems. The methodology of the study is tested with both artificial and experimental data of Stäubli TX40 robotic manipulator. In the experimental analysis, an openly available benchmark data set was used. Artificial data were created by running an inverse dynamics analysis with inertia and friction parameters taken from literature. The results show that the multibody inertia and friction parameters can be accurately identified and the identified model can be used to produce decent estimates of external forces. The proposed multibody system identification method itself opens new opportunities in tuning the multibody models used in product development. Moreover, effective use of system identification together with state estimation helps to build more accurate estimators. When the system model is accurately identified, the capability of state estimator to observe unknown inputs, such as external forces, is significantly enhanced.

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.

Effect of AVL-based time-domain analysis on torsional vibration of engine shafting

The torsional vibration of the shaft system in hybrid car engines has a significant impact on the overall performance of the vehicle, and it is more complex in hybrid cars compared to traditional cars. Traditional methods for torsional vibration analysis of shaft systems have significant limitations and cannot handle nonlinear and transient problems. To explore the torsional vibration characteristics of hybrid vehicle shaft systems, a simplified engine shaft system torsional vibration equivalent model is innovatively constructed. In addition, a method for quickly determining the confidence level of the torsional vibration equivalent model is proposed. Additionally, the transient dynamic characteristics of a multi-body dynamics model containing a dual mass flywheel are analyzed in depth using the time-domain solver of AVL-exact PU. The results demonstrated that the simulation of 4th and 6th harmonics resonated at critical speeds of 4,195 rpm and 2,771 rpm, respectively, with angular displacement amplitudes of 0.141 deg and 0.047 deg. In fact, resonance was measured at 4,250 rpm and 3,040 rpm, with amplitudes of 0.14 deg and 0.052 deg. These two were basically consistent in key parameters. When the shaft model was started under operating conditions, the amplitudes of harmonics 1, 2, and 4 were basically consistent below 750 rpm, and there were slight differences after 750 rpm. Therefore, the AVL-based engine torsional vibration simulation model constructed has high credibility.

Model order reduction of thermal-dynamic coupled flexible multibody system with multiple varying parameters

Spacecrafts usually suffer from the thermal shock during operation, leading to large control error or even failure. At the same time, spacecrafts are often rigid-flexible coupled multibody systems with large degrees of freedom and multiple varying parameters. The real-time control and condition monitoring require effective order reduction methods. In this investigation, the displacement and temperature fields are discretized by the Absolute Node Coordinate Formulation (ANCF) to achieve unified description. The coupled thermal-dynamic reduced-order model (ROM) is established based on the Proper Orthogonal Decomposition (POD) method. For the purpose of further increase efficiency, a linearization method is introduced so that the calculation times of the elastic force can be significantly reduced. In order to predict the response of the thermal-dynamic coupled system with multiple varying parameters, the interpolation on Grassmann manifold is introduced to maintain the orthogonality of the basis. As verification and validation, three numerical examples are presented to show the feasibility and efficacy of the proposed method.

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.