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Keywords = rigid-flexible multi-body dynamic theory

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24 pages, 5233 KB  
Article
Research on Inertial Force Balance and Optimization of V-Type High-Pressure Air Compressors for Ships
by Jun Feng, Huiqing Zou, Jing Liu and Xiaohan Jia
Machines 2026, 14(4), 436; https://doi.org/10.3390/machines14040436 - 14 Apr 2026
Viewed by 778
Abstract
To address the vibration and noise issues induced by inertial forces in marine V-type air compressors during operation, this study systematically investigates inertial force balancing and optimization. Based on dynamic analysis, analytical expressions for the first- and second-order reciprocating inertial forces and the [...] Read more.
To address the vibration and noise issues induced by inertial forces in marine V-type air compressors during operation, this study systematically investigates inertial force balancing and optimization. Based on dynamic analysis, analytical expressions for the first- and second-order reciprocating inertial forces and the rotating inertial force under unbalanced conditions are precisely derived. Considering the characteristics of a V-type air compressor with a V-angle of γ = 60°, the synthesis model of the first-order reciprocating inertial force is modified. The positive–negative rotating wheel system method is employed for preliminary balancing design, and the rigid–flexible coupling dynamics theory is innovatively introduced to construct a high-precision multi-body dynamics model that accounts for the flexible deformation of the crankshaft and connecting rod. Through joint simulation using ANSYS (2024R1) and Adams (2024.2), the dynamic responses of the pure rigid-body model and the rigid–flexible coupling model are compared to determine the optimal balancing configuration. The Adams/Insight module is utilized to perform multi-objective optimization of the balance iron mass. Results indicate that the rigid–flexible coupling model more accurately reflects the dynamic characteristics of the air compressor compared to the pure rigid-body model, significantly enhancing simulation accuracy. The optimized balance iron configuration effectively suppresses system vibration, with the peak X-direction bearing reaction force decreasing from 3750 N to 3610 N (a reduction of 3.7%), the vibration intensity reducing by 45.3%, and the radiated noise sound power level decreasing by 7.45%. This study provides a systematic theoretical approach and technical pathway for vibration and noise reduction, as well as for structural reliability design of marine air compressors. Full article
(This article belongs to the Special Issue High-Performance Compressor Design, Model Analysis and Application)
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23 pages, 10702 KB  
Article
A Versatile SPH Approach for Modelling Very Flexible and Modularized Floating Structures in Moored Configurations
by Rafail Ioannou, Vasiliki Stratigaki, Eva Loukogeorgaki and Peter Troch
J. Mar. Sci. Eng. 2025, 13(12), 2283; https://doi.org/10.3390/jmse13122283 - 30 Nov 2025
Cited by 1 | Viewed by 1218
Abstract
A variety of Offshore Floating Photovoltaics (OFPVs) applications rely on the capacity of their floating support structures displacing in the shape of surface waves to reduce extreme wave-induced loads exerted on their floating-mooring system. This wave-adaptive displacement behaviour is typically realized through two [...] Read more.
A variety of Offshore Floating Photovoltaics (OFPVs) applications rely on the capacity of their floating support structures displacing in the shape of surface waves to reduce extreme wave-induced loads exerted on their floating-mooring system. This wave-adaptive displacement behaviour is typically realized through two principal design approaches, either by employing slender and continuously deformable structures composed of highly elastic materials or by decomposing the structure into multiple floating rigid pontoons interconnected via flexible connectors. The hydrodynamic behaviour of these structures is commonly analyzed in the literature using potential flow theory, to characterize wave loading, whereas in order to deploy such OFPV prototypes in realistic marine environments, a high-fidelity numerical fluid–structure interaction model is required. Thus, a versatile three-dimensional numerical scheme is herein presented that is capable of handling non-linear fluid-flexible structure interactions for Very Flexible Floating Structures (VFFSs): Multibody Dynamics (MBD) for modularized floating structures and floating-mooring line interactions. In the present study, this is achieved by employing the Smoothed Particles Hydrodynamics (SPH) fluid model of DualSPHysics, coupled both with the MBD module of Project Chrono and the MoorDyn+ lumped-mass mooring model. The SPH-MBD coupling enables modelling of large and geometrically non-linear displacements of VFFS within an Applied Element Method (AEM) plate formulation, as well as rigid body dynamics of modularized configurations. Meanwhile, the SPH-MoorDyn+ captures the fully coupled three-dimensional response of floating-mooring and floating-floating dynamics, as it is employed to model both moorings and flexible interconnectors between bodies. The coupled SPH-based numerical scheme is herein validated against physical experiments, capturing the hydroelastic response of VFFS, rigid body hydrodynamics, mooring line dynamics, and flexible connector behaviour under wave loading. The demonstrated numerical methodology represents the first validated Computational Fluid Dynamics (CFD) application of moored VFFS in three-dimensional domains, while its robustness is further confirmed using modular floating systems, enabling OFPV engineers to comparatively assess these two types of wave-adaptive designs in a unified numerical framework. Full article
(This article belongs to the Section Ocean Engineering)
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18 pages, 3076 KB  
Article
Study on Mooring Design and Hydrodynamic Performance of Floating Offshore Wind Turbines with CFRP Mooring Lines
by Yaqiang Yang, Riwei Xi, Mingxin Li, Jianzhe Shi, Yongzheng Li, Xin Wang, Wentao Shang and Hongming Li
Buildings 2025, 15(20), 3734; https://doi.org/10.3390/buildings15203734 - 16 Oct 2025
Cited by 5 | Viewed by 2045
Abstract
To address the issues of traditional mooring lines, such as high self-weight, low strength, and poor durability, Carbon-Fiber-Reinforced Polymer (CFRP) was investigated as a material for mooring lines of offshore floating wind turbines, aiming to achieve high performance, lightweight design, and long service [...] Read more.
To address the issues of traditional mooring lines, such as high self-weight, low strength, and poor durability, Carbon-Fiber-Reinforced Polymer (CFRP) was investigated as a material for mooring lines of offshore floating wind turbines, aiming to achieve high performance, lightweight design, and long service life for mooring systems. Based on a “chain–cable–chain” configuration, a CFRP mooring line design is proposed in this study. Taking a 5 MW offshore floating wind turbine as the research object, the dynamic performance of offshore floating wind turbines with steel chains, steel cables, polyester ropes, and CFRP mooring lines under combined wind, wave, and current loads was compared and analyzed to demonstrate the feasibility of applying CFRP mooring lines by combining the potential flow theory and the rigid–flexible coupling multi-body model. The research results indicate that, compared to traditional mooring systems such as steel chains, steel cables, and polyester ropes, (1) under static water, the CFRP mooring system exhibits a larger static water free decay response and longer free decay duration; (2) under operating sea conditions, the motion response and mooring tension of the offshore floating wind turbine with CFRP mooring lines are smaller than those with steel cables and steel chains but greater than those with polyester ropes; and (3) under extreme sea conditions, the motion responses of the offshore floating wind turbine with CFRP mooring lines are smaller than those with steel wire ropes and steel chains but close to the displacement responses of the polyester rope system, while the increase in mooring tension is relatively moderate and the safety factor is the highest. Full article
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34 pages, 6658 KB  
Article
Computational Method for Dynamic Analysis of Multibody Systems with Deformable Elements
by Sorin Dumitru, Nicolae Dumitru, Cristian Copilusi and Adrian Sorin Rosca
Mathematics 2025, 13(17), 2797; https://doi.org/10.3390/math13172797 - 31 Aug 2025
Cited by 1 | Viewed by 1400
Abstract
The dynamics of mechanical systems with fast motions and dynamic loads are strongly influenced by the deformability of kinematic elements. The finite element method and the superposition of rigid body motion with deformable body motion allow us to determine a new structure for [...] Read more.
The dynamics of mechanical systems with fast motions and dynamic loads are strongly influenced by the deformability of kinematic elements. The finite element method and the superposition of rigid body motion with deformable body motion allow us to determine a new structure for the matrices that define the mechanical system equations of motion. Meshing the kinematic elements into finite elements causes the unknowns of the problem to no longer be displacement functions but rather nodal displacements. These displacements are considered as a linear combination of modal shapes and modal coordinates. This method is applied to a drive mechanism of an internal combustion engine with three pistons mounted in line. The system is driven by the pressure exerted by the gas on the piston head, which was experimentally determined. The longitudinal and transversal deformations of the connecting rod are determined, including the nodal displacements. These results were verified through virtual prototyping on the 3D model, using multibody system theory and the finite element method. The recorded differences are mainly explained by the type, size, and shape of the used finite elements. Experimental analysis allows us to determine the connecting rod kinematic and dynamic parameters as functions of time and frequency variation. The developed method is flexible and can be easily adapted to systems with fast motions in which, during operation, impact forces appear in joints for various reasons. Full article
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23 pages, 7958 KB  
Article
Modeling and Dynamic Characteristic Analysis of a Rigid–Flexible Coupling Multi-Stage Gear Transmission System for High-Power-Density Diesel Engines
by Chenkun Yi, Huihua Feng, Ziqing Zhu, Peirong Ren, Zhongwei Zhang and Qidi Zhou
Machines 2025, 13(5), 416; https://doi.org/10.3390/machines13050416 - 15 May 2025
Cited by 4 | Viewed by 2040
Abstract
To investigate the mechanisms of unexpected failures in a multi-stage gear transmission system under a relatively low load, a rigid–flexible coupled multi-body dynamics model with 10 spur gears and 12 helical gears is established. The dynamic condensation theory is applied to improve computational [...] Read more.
To investigate the mechanisms of unexpected failures in a multi-stage gear transmission system under a relatively low load, a rigid–flexible coupled multi-body dynamics model with 10 spur gears and 12 helical gears is established. The dynamic condensation theory is applied to improve computational efficiency. The construction of this model incorporates critical nonlinear factors, ensuring high precision and reliability. Based on the proposed model, four critical dynamic parameters, including acceleration, mesh stiffness, dynamic transmission error, and vibration displacement, are analyzed. This research systematically reveals the nonlinear dynamic mechanism under the multi-gear coupling effect. The spectrum of the gears exhibits prominent low-frequency peaks at 320 Hz and 750 Hz. Notably, alternate load-dominated gears show a shift in prominent low-frequency peaks. The phenomenon of marked oscillations in mesh stiffness suggests a potential risk of localized weakening in the system’s load-carrying capacity. Critically, alternating torques induce periodic double-tooth contact regions in the gear at specific time points (0.115 s and 0.137 s), which are identified as critical factors leading to gear transmission system failures. The variation characteristics of the dynamic transmission error (DTE) demonstrate that the DTE is strongly correlated with the meshing state. The analysis of vibration displacement further indicates that the alternating external loads are the dominant excitation source of vibrations, noise, and failures in the gear transmission system. Full article
(This article belongs to the Section Machine Design and Theory)
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29 pages, 2350 KB  
Article
Dynamics Modeling and Motion Evaluation of a Near-Ground Tethered Balloon Cable System under Severe Wind Environments
by Zhenhua Lai, Mao Tang, Xiaojin Hu, Xin Shu, Weicheng Huang and Yongjun Pan
Actuators 2024, 13(10), 402; https://doi.org/10.3390/act13100402 - 5 Oct 2024
Cited by 5 | Viewed by 3366
Abstract
Weather survival poses a significant challenge for the utilization of tethered balloons. The dynamic modeling of tethered balloon systems presents challenges due to the flexible nature of the cables and the intricate nature of gust forces. The present study introduces a new approach [...] Read more.
Weather survival poses a significant challenge for the utilization of tethered balloons. The dynamic modeling of tethered balloon systems presents challenges due to the flexible nature of the cables and the intricate nature of gust forces. The present study introduces a new approach for modeling near-ground tethered balloon systems, which enables the analysis of their dynamic responses and performance evaluation under complex boundary conditions. First, finite cylindrical rigid bodies that are joined together by bushing forces to describe the dynamics of the tethered cable. The properties of the flexible cables under severe bending and translation can be illustrated by the dynamics model. Second, a three-dimensional dynamics model based on the multibody dynamics theory is created to deal with the interaction of the tethered balloon system and flexible cables. The dynamic responses of the tethered balloon system under challenging operating conditions are investigated, focusing on the number of cable segments and the place and direction of gust wind impacts. This model allows for precise assessment and optimization of the system’s overall performance to improve weather resistance. The results show that compared to computational fluid dynamics (CFDs) methods, the multibody system dynamics-based balloon model improved the solution time by 80%, with a pitch angle deviation of only 0.0016°. Moreover, the bushing model effectively reduced cable force and enabled accurate reflection of the system’s motion characteristics. Full article
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17 pages, 8370 KB  
Article
The Effect of Cycloid Gear Wear on the Transmission Accuracy of the RV Reducer
by Yourui Tao, Huishan Liu, Miaojie Wu, Nanxian Zheng and Jiaxing Pei
Machines 2024, 12(8), 511; https://doi.org/10.3390/machines12080511 - 29 Jul 2024
Cited by 16 | Viewed by 3666
Abstract
The cycloid gear wear of RV reducers leads to the degradation of the industrial robots’ transmission accuracy, but the degradation law with respect to the wear volume is still unclear. In this paper, a method for determining transmission error (TE) through a combination [...] Read more.
The cycloid gear wear of RV reducers leads to the degradation of the industrial robots’ transmission accuracy, but the degradation law with respect to the wear volume is still unclear. In this paper, a method for determining transmission error (TE) through a combination of numerical and simulation analysis is proposed. The wear model of cycloid gear was ascertained based on the theory of Archard. Then, the full rigid body and rigid–flexible coupling model of RV reducers were established using the multibody dynamics theory. Finally, the static transmission error (STE) and dynamic transmission error (DTE) were investigated. The results show that as working hours increase, the cycloid gear wear volume increases, and transmission accuracy deteriorates, but the rate tends to slow down. Full article
(This article belongs to the Special Issue Design and Manufacturing for Lightweight Components and Structures)
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19 pages, 5716 KB  
Article
Reconstruction of a Car–Running Pedestrian Accident Based on a Humanoid Robot Method
by Qian Wang, Bo Wei, Zheng Wei, Shang Gao, Xianlong Jin and Peizhong Yang
Sensors 2023, 23(18), 7882; https://doi.org/10.3390/s23187882 - 14 Sep 2023
Cited by 2 | Viewed by 3484
Abstract
Due to the characteristics of multibody (MB) and finite element (FE) digital human body models (HBMs), the reconstruction of running pedestrians (RPs) remains a major challenge in traffic accidents (TAs) and new innovative methods are needed. This study presents a novel approach for [...] Read more.
Due to the characteristics of multibody (MB) and finite element (FE) digital human body models (HBMs), the reconstruction of running pedestrians (RPs) remains a major challenge in traffic accidents (TAs) and new innovative methods are needed. This study presents a novel approach for reconstructing moving pedestrian TAs based on a humanoid robot method to improve the accuracy of analyzing dynamic vehicle–pedestrian collision accidents. Firstly, we applied the theory of humanoid robots to the corresponding joints and centroids of the TNO HBM and implemented the pedestrian running process. Secondly, we used rigid–flexible coupling HBMs to build pedestrians, which can not only simulate running but also analyze human injuries. Then, we validated the feasibility of the RP reconstruction method by comparing the simulated dynamics with the pedestrian in the accident. Next, we extracted the velocity and posture of the pedestrian at the moment of collision and further validated the modeling method through a comparison of human injuries and forensic autopsy results. Finally, by comparing two other cases, we can conclude that there are relative errors in both the pedestrian injury results and the rest position. This comparative analysis is helpful for understanding the differences in injury characteristics between the running pedestrian and the other two cases in TAs. Full article
(This article belongs to the Section Sensors and Robotics)
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21 pages, 3951 KB  
Article
Numerical Prediction on the Dynamic Response of a Helical Floating Vertical Axis Wind Turbine Based on an Aero-Hydro-Mooring-Control Coupled Model
by Yan Li, Liqin Liu, Ying Guo and Wanru Deng
Energies 2022, 15(10), 3726; https://doi.org/10.3390/en15103726 - 19 May 2022
Cited by 11 | Viewed by 3197
Abstract
Considering the aero-hydro-mooring-control coupled performance of a floating Vertical Axis Wind Turbine (VAWT), the numerical model of the floating helical VAWT system is established, and the fully coupled simulation program of the floating helical VAWT is developed. The aerodynamic load of the wind [...] Read more.
Considering the aero-hydro-mooring-control coupled performance of a floating Vertical Axis Wind Turbine (VAWT), the numerical model of the floating helical VAWT system is established, and the fully coupled simulation program of the floating helical VAWT is developed. The aerodynamic load of the wind turbine system is calculated using the unsteady BEM model, and the hydrodynamic load is calculated using the 3D potential theory. The floating foundation is considered as a rigid body, and the blades and tower are considered as flexible bodies. Based on the Kane method of a multi-body system, the dynamic responses of the VAWT could be solved in the time domain. A variable speed control model considering efficiency and load is established to match the rotating speed with the wind speed, and it could maintain the target output power under the influence of turbulent wind and large-scale movement of the floating foundation. The control strategy of limiting the target speed change rate and low-pass filtering is adopted to ensure the rapid regulation of the wind turbine under low wind speed conditions and stable regulation under high wind speed conditions. Full article
(This article belongs to the Special Issue Offshore Floating Wind Farms)
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13 pages, 10808 KB  
Article
Railway Wheel Flat Detection System Based on a Parallelogram Mechanism
by Run Gao, Qixin He and Qibo Feng
Sensors 2019, 19(16), 3614; https://doi.org/10.3390/s19163614 - 20 Aug 2019
Cited by 23 | Viewed by 7464
Abstract
Wheel flats are a key fault in railway systems, which can bring great harm to vehicle operation safety. At present, most wheel flat detection methods use qualitative detection and do not meet practical demands. In this paper, we used a railway wheel flat [...] Read more.
Wheel flats are a key fault in railway systems, which can bring great harm to vehicle operation safety. At present, most wheel flat detection methods use qualitative detection and do not meet practical demands. In this paper, we used a railway wheel flat measurement method based on a parallelogram mechanism to detect wheel flats dynamically and quantitatively. Based on our experiments, we found that system performance was influenced by the train speed. When the train speed was higher than a certain threshold, the wheel impact force would cause vibration of the measuring mechanism and affect the detection accuracy. Since the measuring system was installed at the on-site entrance of the train garage, to meet the speed requirement, a three-dimensional simulation model was established, which was based on the rigid-flexible coupled multibody dynamics theory. The speed threshold of the measuring mechanism increased by the reasonable selection of the damping coefficients of the hydraulic damper, the measuring positions, and the downward displacements of the measuring ruler. Finally, we applied the selected model parameters to the parallelogram mechanism, where field measurements showed that the experimental results were consistent with the simulation results. Full article
(This article belongs to the Section Physical Sensors)
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11 pages, 1282 KB  
Article
Multibody Dynamic Stress Simulation of Rigid-Flexible Shovel Crawler Shoes
by Samuel Frimpong and Magesh Thiruvengadam
Minerals 2016, 6(3), 61; https://doi.org/10.3390/min6030061 - 25 Jun 2016
Cited by 4 | Viewed by 8686
Abstract
Electric shovels are used in surface mining operations to achieve economic production capacities. The capital investments and operating costs associated with the shovels deployed in the Athabasca oil sands formation are high due to the abrasive conditions. The shovel crawler shoes interact with [...] Read more.
Electric shovels are used in surface mining operations to achieve economic production capacities. The capital investments and operating costs associated with the shovels deployed in the Athabasca oil sands formation are high due to the abrasive conditions. The shovel crawler shoes interact with sharp and abrasive sand particles, and, thus, are subjected to high transient dynamic stresses. These high stresses cause wear and tear leading to crack initiation, propagation and premature fatigue failure. The objective of this paper is to develop a model to characterize the crawler stresses and deformation for the P&H 4100C BOSS during propel and loading using rigid-flexible multi-body dynamic theory. A 3-D virtual prototype model of the rigid-flexible crawler track assembly and its interactions with oil sand formation is simulated to capture the model dynamics within multibody dynamics software MSC ADAMS. The modal and stress shapes and modal loads due to machine weight for each flexible crawler shoes are generated from finite element analysis (FEA). The modal coordinates from the simulation are combined with mode and stress shapes using modal superposition method to calculate real-time stresses and deformation of flexible crawler shoes. The results show a maximum von Mises stress value of 170 MPa occurring in the driving crawler shoe during the propel motion. This study provides a foundation for the subsequent fatigue life analysis of crawler shoes for extending crawler service life. Full article
(This article belongs to the Special Issue Frontiers of Surface Mining Research)
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