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Keywords = load-deformation coordination

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20 pages, 2785 KB  
Article
Dynamic Posture Programming for Robotic Milling Based on Cutting Force Directional Stiffness Performance
by Yuhang Gao, Tianyang Qiu, Ci Song, Senjie Ma, Zhibing Liu, Zhiqiang Liang and Xibin Wang
Machines 2025, 13(9), 822; https://doi.org/10.3390/machines13090822 (registering DOI) - 6 Sep 2025
Abstract
Robotic milling offers significant advantages for machining large aerospace components due to its low cost and high flexibility. However, compared to computerized numerical control (CNC) machine tools, robot systems exhibit lower stiffness, leading to force-induced deformation during milling process that significantly compromises path [...] Read more.
Robotic milling offers significant advantages for machining large aerospace components due to its low cost and high flexibility. However, compared to computerized numerical control (CNC) machine tools, robot systems exhibit lower stiffness, leading to force-induced deformation during milling process that significantly compromises path accuracy. This study proposed a dynamic robot posture programming method to enhance the stiffness for aluminum alloy milling task. Firstly, a milling force prediction model is established and validated under multiple postures and various milling parameters, confirming its stability and reliability. Secondly, a robot stiffness model is developed by combining system stiffness and milling forces within the milling coordinate system to formulate an optimization index representing stiffness performance in the actual load direction. Finally, considering the constraints of joint limit, singular position and joint motion smoothness and so on, the robot posture in the milling trajectory is dynamically programmed, and the joint angle sequence with the optimal average stiffness from any cutter location (CL) point to the end of the trajectory is obtained. Under the assumption that positioning errors were effectively compensated, the experimental results demonstrated that the proposed method can control both axial and radial machining errors within 0.1 mm at discrete points. For the specific milling trajectory, compared to the single-step optimization algorithm starting from the initial optimal posture, the proposed method reduced the axial error by 12.23% and the radial error by 8.61%. Full article
(This article belongs to the Section Advanced Manufacturing)
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12 pages, 4654 KB  
Article
In Situ TEM Investigation of Dislocation-Mediated Deformation in Eutectic Fe36Ni18Mn33Al13 Alloy
by Fanling Meng, Jiaqi Zhu, Heyi Wang, Jiayi Li and Yang Lu
Crystals 2025, 15(9), 792; https://doi.org/10.3390/cryst15090792 - 5 Sep 2025
Abstract
Eutectic FeNiMnAl multi-principal element alloys exhibit exceptional strength–ductility synergy, yet their dynamic deformation mechanisms remain poorly characterized. This study employs in situ transmission electron microscopy to investigate dislocation-mediated plasticity in Fe36Ni18Mn33Al13—a lamellar FCC/B2 alloy with [...] Read more.
Eutectic FeNiMnAl multi-principal element alloys exhibit exceptional strength–ductility synergy, yet their dynamic deformation mechanisms remain poorly characterized. This study employs in situ transmission electron microscopy to investigate dislocation-mediated plasticity in Fe36Ni18Mn33Al13—a lamellar FCC/B2 alloy with balanced properties. Real-time observations under tensile loading (at a strain rate of 0.1 μm/s, with a resolution of ~2 nm) reveal coordinated dislocation planar glide, cross-slip at obstacles, and pile-up formation at phase boundaries. Planar slip bands dominate early deformation, while cross-slip facilitates barrier bypass and strain homogenization. The coarse microstructure of Fe36Ni18Mn33Al13 promotes extensive dislocation storage, reducing strength but enhancing ductility compared to finer FeNiMnAl variants. 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
Viewed by 208
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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30 pages, 5867 KB  
Article
Theoretical and Experimental Investigation on Motion Error and Force-Induced Error of Machine Tools in the Gear Rolling Process
by Ziyong Ma, Yungao Zhu, Zilong Wang, Qingyuan Hu and Wei Yang
Appl. Sci. 2025, 15(17), 9524; https://doi.org/10.3390/app15179524 - 29 Aug 2025
Viewed by 170
Abstract
Cylindrical gears are used extensively due to their significant advantages including high efficiency, high load-bearing capacity, and long lifespan. However, the machining accuracy of cylindrical gears is significantly affected by motion errors and force-induced errors of machine tools. In this study, a motion [...] Read more.
Cylindrical gears are used extensively due to their significant advantages including high efficiency, high load-bearing capacity, and long lifespan. However, the machining accuracy of cylindrical gears is significantly affected by motion errors and force-induced errors of machine tools. In this study, a motion error model of the machine tools was established based on multi-body system theory and homogeneous coordinate transformation method, quantifying the contributions and variation patterns of 12 key errors in the A and B-axes to workpiece geometric errors. Then, by using the stiffness analytical model and the spatial meshing theory, the influence of the force-induced elastic deformation of the shaft of rolling wheel and the springback of the workpiece tooth flank on the geometric error was revealed. Finally, taking the through rolling of a spur cylindrical gear with a module of 1.75 mm, a pressure angle of 20°, and 46 teeth as an example, the force-induced elastic deformation model of the shaft was verified by the rolling tests. Results show that for 40CrNiMo steel, the total profile deviation, total helix deviation, and single pitch deviation in the X-direction caused by rolling forces are 32.48 μm, 32.13 μm, and 32.13 μm, respectively, with a maximum contact rebound is δc = 28.27 μm. The relative error between theoretical and measured X-direction spindle deformation is 8.26%. This study provides theoretical foundation and experimental support for improving the precision of rolling process. Full article
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19 pages, 12652 KB  
Article
Automated Arch Profile Extraction from Point Clouds and Its Application in Arch Bridge Construction Monitoring
by Xiaojun Wei, Yang Liu, Xianglong Zuo, Jiwei Zhong, Yihua Yuan, Yafei Wang, Cheng Li and Yang Zou
Buildings 2025, 15(16), 2912; https://doi.org/10.3390/buildings15162912 - 17 Aug 2025
Viewed by 376
Abstract
Accurate extraction of the arch profile, the key spatial geometric parameter of the core load-bearing component in arch bridges, is crucial for construction process control and for achieving the designed final bridge configuration. To overcome the limitations of existing methods—geometric information loss, sensitivity [...] Read more.
Accurate extraction of the arch profile, the key spatial geometric parameter of the core load-bearing component in arch bridges, is crucial for construction process control and for achieving the designed final bridge configuration. To overcome the limitations of existing methods—geometric information loss, sensitivity to noise, and inefficiency—when extracting continuous, precise profiles from point clouds of complex spatially curved arch ribs, this paper proposes a multi-step point cloud processing workflow. The approach integrates geometric feature constraints specific to arch bridges to enable automated, high-precision extraction of the arch profile during construction. The approach comprises three steps. First, arch point cloud subset partitioning: the primitive arch point cloud is efficiently divided using parameters from down-sampling arch point cloud data. Second, component segmentation: a Random Sample Consensus (RANSAC) algorithm, optimized with cylindrical geometric constraints, is then employed to precisely segment the point cloud of individual arch tube components from each subset point cloud. Third, arch profile extraction: the geometric invariance of the bottom edge of each arch tube is leveraged to identify feature points via local coordinate system transformation and longitudinal constraints. These feature points are then spliced together to reconstruct the complete arch profile. The proposed method is employed in multiple construction stages of a concrete-filled steel tubular (CFST) arch bridge and quantifies the vertical deformation between adjacent stages. Compared with Total Station (TS) measurements, the average error ranged from 0.24 mm to 4.13 mm, with an overall average error of 2.105 mm, demonstrating accuracy and reliability. Full article
(This article belongs to the Section Construction Management, and Computers & Digitization)
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21 pages, 3166 KB  
Article
Structure/Aerodynamic Nonlinear Dynamic Simulation Analysis of Long, Flexible Blade of Wind Turbine
by Xiangqian Zhu, Siming Yang, Zhiqiang Yang, Chang Cai, Lei Zhang, Qing’an Li and Jin-Hwan Choi
Energies 2025, 18(16), 4362; https://doi.org/10.3390/en18164362 - 15 Aug 2025
Viewed by 371
Abstract
To meet the requirements of geometric nonlinear modeling and bending–torsion coupling analysis of long, flexible offshore blades, this paper develops a high-precision engineering simplified model based on the Absolute Nodal Coordinate Formulation (ANCF). The model considers nonlinear variations in linear density, stiffness, and [...] Read more.
To meet the requirements of geometric nonlinear modeling and bending–torsion coupling analysis of long, flexible offshore blades, this paper develops a high-precision engineering simplified model based on the Absolute Nodal Coordinate Formulation (ANCF). The model considers nonlinear variations in linear density, stiffness, and aerodynamic center along the blade span and enables efficient computation of 3D nonlinear deformation using 1D beam elements. Material and structural function equations are established based on actual 2D airfoil sections, and the chord vector is obtained from leading and trailing edge coordinates to calculate the angle of attack and aerodynamic loads. Torsional stiffness data defined at the shear center is corrected to the mass center using the axis shift theorem, ensuring a unified principal axis model. The proposed model is employed to simulate the dynamic behavior of wind turbine blades under both shutdown and operating conditions, and the results are compared to those obtained from the commercial software Bladed. Under shutdown conditions, the blade tip deformation error in the y-direction remains within 5% when subjected only to gravity, and within 8% when wind loads are applied perpendicular to the rotor plane. Under operating conditions, although simplified aerodynamic calculations, structural nonlinearity, and material property deviations introduce greater discrepancies, the x-direction deformation error remains within 15% across different wind speeds. These results confirm that the model maintains reasonable accuracy in capturing blade deformation characteristics and can provide useful support for early-stage dynamic analysis. Full article
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22 pages, 4262 KB  
Article
Tribo-Dynamics of Dual-Star Planetary Gear Systems: Modeling, Analysis, and Experiments
by Jiayu Zheng, Yonggang Xiang, Changzhao Liu, Yixin Wang and Zonghai Mou
Sensors 2025, 25(15), 4709; https://doi.org/10.3390/s25154709 - 30 Jul 2025
Viewed by 380
Abstract
To address the unclear coupling mechanism between thermal elastohydrodynamic lubrication (TEHL) and dynamic behaviors in planetary gear systems, a novel tribo-dynamic model for dual-star planetary gears considering TEHL effects is proposed. In this model, a TEHL surrogate model is first established to determine [...] Read more.
To address the unclear coupling mechanism between thermal elastohydrodynamic lubrication (TEHL) and dynamic behaviors in planetary gear systems, a novel tribo-dynamic model for dual-star planetary gears considering TEHL effects is proposed. In this model, a TEHL surrogate model is first established to determine the oil film thickness and sliding friction force along the tooth meshing line. Subsequently, the dynamic model of the dual-star planetary gear transmission system is developed through coordinate transformations of the dual-star gear train. Finally, by integrating lubrication effects into both time-varying mesh stiffness and time-varying backlash, a tribo-dynamic model for the dual-star planetary gear transmission system is established. The study reveals that the lubricant film thickness is positively correlated with relative sliding velocity but negatively correlated with unit line load. Under high-speed conditions, a thickened oil film induces premature meshing contact, leading to meshing impacts. In contrast, under high-torque conditions, tooth deformation dominates meshing force fluctuations while lubrication influence diminishes. By establishing a test bench for the planetary gear transmission system, the obtained simulation conclusions are verified. This research provides theoretical and experimental support for the design of high-reliability planetary gear systems. Full article
(This article belongs to the Special Issue Feature Papers in Physical Sensors 2025)
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34 pages, 5960 KB  
Article
Motor Temperature Observer for Four-Mass Thermal Model Based Rolling Mills
by Boris M. Loginov, Stanislav S. Voronin, Roman A. Lisovskiy, Vadim R. Khramshin and Liudmila V. Radionova
Sensors 2025, 25(14), 4458; https://doi.org/10.3390/s25144458 - 17 Jul 2025
Viewed by 365
Abstract
Thermal control in rolling mills motors is gaining importance as more and more hard-to-deform steel grades are rolled. The capabilities of diagnostics monitoring also expand as digital IIoT-based technologies are adopted. Electrical drives in modern rolling mills are based on synchronous motors with [...] Read more.
Thermal control in rolling mills motors is gaining importance as more and more hard-to-deform steel grades are rolled. The capabilities of diagnostics monitoring also expand as digital IIoT-based technologies are adopted. Electrical drives in modern rolling mills are based on synchronous motors with frequency regulation. Such motors are expensive, while their reliability impacts the metallurgical plant output. Hence, developing the on-line temperature monitoring systems for such motors is extremely urgent. This paper presents a solution applying to synchronous motors of the upper and lower rolls in the horizontal roll stand of plate mill 5000. The installed capacity of each motor is 12 MW. According to the digitalization tendency, on-line monitoring systems should be based on digital shadows (coordinate observers) that are similar to digital twins, widely introduced at metallurgical plants. Modern reliability requirements set the continuous temperature monitoring for stator and rotor windings and iron core. This article is the first to describe a method for calculating thermal loads based on the data sets created during rolling. The authors have developed a thermal state observer based on four-mass model of motor heating built using the Simscape Thermal Models library domains that is part of the MATLAB Simulink. Virtual adjustment of the observer and of the thermal model was performed using hardware-in-the-loop (HIL) simulation. The authors have validated the results by comparing the observer’s values with the actual values measured at control points. The discrete masses heating was studied during the rolling cycle. The stator and rotor winding temperature was analysed at different periods. The authors have concluded that the motors of the upper and lower rolls are in a satisfactory condition. The results of the study conducted generally develop the idea of using object-oriented digital shadows for the industrial electrical equipment. The authors have introduced technologies that improve the reliability of the rolling mills electrical drives which accounts for the innovative development in metallurgy. The authors have also provided recommendations on expanded industrial applications of the research results. Full article
(This article belongs to the Section Industrial Sensors)
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23 pages, 3551 KB  
Article
The Influence of Soft Soil, Pile–Raft Foundation and Bamboo on the Bearing Characteristics of Reinforced Concrete (RC) Structure
by Zhibin Zhong, Xiaotong He, Shangheng Huang, Chao Ma, Baoxian Liu, Zhile Shu, Yineng Wang, Kai Cui and Lining Zheng
Buildings 2025, 15(13), 2302; https://doi.org/10.3390/buildings15132302 - 30 Jun 2025
Viewed by 580
Abstract
Pile–raft foundations are widely used in soft soil engineering due to their good integrity and high stiffness. However, traditional design methods independently design pile–raft foundations and superstructures, ignoring their interaction. This leads to significant deviations from actual conditions when the superstructure height increases, [...] Read more.
Pile–raft foundations are widely used in soft soil engineering due to their good integrity and high stiffness. However, traditional design methods independently design pile–raft foundations and superstructures, ignoring their interaction. This leads to significant deviations from actual conditions when the superstructure height increases, resulting in excessive costs and adverse effects on building stability. This study experimentally investigates the interaction characteristics of pile–raft foundations and superstructures in soft soil under different working conditions using a 1:10 geometric similarity model. The superstructure is a cast-in-place frame structure (beams, columns, and slabs) with bamboo skeletons with the same cross-sectional area as the piles and rafts, cast with concrete. The piles in the foundation use rectangular bamboo strips (side length ~0.2 cm) instead of steel bars, with M1.5 mortar replacing C30 concrete. The raft is also made of similar materials. The results show that the soil settlement significantly increases under the combined action of the pile–raft and superstructure with increasing load. The superstructure stiffness constrains foundation deformation, enhances bearing capacity, and controls differential settlement. The pile top reaction force exhibits a logarithmic relationship with the number of floors, coordinating the pile bearing performance. Designers should consider the superstructure’s constraint of the foundation deformation and strengthen the flexural capacity of inner pile tops and bottom columns for safety and economy. Full article
(This article belongs to the Section Building Structures)
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31 pages, 7677 KB  
Article
Mechanical Performance and Interfacial Bonding Mechanism of High-Performance ECC in Steel-Concrete Composite Link Slab in Simply Supported Bridges
by Chengquan Wang, Rongyang Liu, Kangyu Wang, Yuhan Liang and Yingjie Ning
Buildings 2025, 15(13), 2277; https://doi.org/10.3390/buildings15132277 - 28 Jun 2025
Viewed by 478
Abstract
This paper proposes a steel-ECC ordinary concrete composite continuous bridge deck structure to address the cracking problem of simply supported beam bridge deck continuity. Through theoretical and experimental research, a high-performance ECC material was developed. The ECC material has a compressive strength of [...] Read more.
This paper proposes a steel-ECC ordinary concrete composite continuous bridge deck structure to address the cracking problem of simply supported beam bridge deck continuity. Through theoretical and experimental research, a high-performance ECC material was developed. The ECC material has a compressive strength of 57.58 MPa, a tensile strain capacity of 4.44%, and significantly enhanced bending deformation ability. Bonding tests showed that the bond strength of the ECC-reinforcing bar interface reaches 22.84 MPa when the anchorage length is 5d, and the splitting strength of the ECC-concrete interface is 3.58 MPa after 4–5 mm chipping treatment, with clear water moistening being the optimal interface treatment method. Full-scale tests indicated that under 1.5 times the design load, the crack width of the ECC bridge deck continuity structure is ≤0.12 mm, the maximum deflection is only 5.345 mm, and the interface slip is reduced by 42%, achieving a unified control of multiple cracks and coordinated deformation. The research results provide a new material system and interface design standards for seamless bridge design. Full article
(This article belongs to the Special Issue Research on Building Foundations and Underground Engineering)
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20 pages, 10249 KB  
Article
The Effect of Cementation on Microstructural Evolution and Particle Characteristics of Calcareous Sand Under Triaxial Loading
by Wanying Wang, Jiepeng Huang, Degao Chen, Qingzi Luo and Bingxiang Yuan
Buildings 2025, 15(12), 2041; https://doi.org/10.3390/buildings15122041 - 13 Jun 2025
Viewed by 503
Abstract
Calcareous sands are widely distributed across the South China Sea’s continental shelf and coastlines. Understanding their mechanical behavior and microstructural evolution under cementation is critical for coastal engineering applications. While previous studies have investigated cemented calcareous sands, the comparative analyses of particle breakage [...] Read more.
Calcareous sands are widely distributed across the South China Sea’s continental shelf and coastlines. Understanding their mechanical behavior and microstructural evolution under cementation is critical for coastal engineering applications. While previous studies have investigated cemented calcareous sands, the comparative analyses of particle breakage and microstructural characteristics between cemented and pure sands remain limited. This study combines triaxial compression tests with X-ray CT scanning and Digital Volume Correlation analysis to systematically examine both material types. Pre- and post-loading CT scans enabled the detailed tracking of microstructural transformations. Results demonstrate that cemented specimens exhibit higher strength–stiffness properties with strain-softening behavior compared to pure sand under 200 kPa confining pressures. A quantitative analysis revealed greater particle breakage in cemented sand, while pure sand showed more pronounced increases in particle sphericity and the aspect ratio during deformation, accompanied by reduced porosity variation along specimen height (coefficient of variation decreased from 15.2% to 12.8% for pure sand. Microstructural analysis indicated moderate increases in pore sphericity and reduced anisotropy in both materials. Fractal dimension analysis demonstrated more significant structural reorganization in cemented sands. Both materials exhibited increases in key morphological parameters, including the throat equivalent radius, channel length, pore equivalent radius, and coordination number, with changes being more substantial in cemented sands. Within shear band regions, cemented sands displayed marked reductions in pore and throat quantities. These findings elucidate fundamental relationships between cementation effects and micro–macro mechanical responses, providing theoretical support for geotechnical applications involving calcareous sands. Full article
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24 pages, 4655 KB  
Article
Effect of Bearing Support Parameters on the Radial and Angular Deformation of Rotor Shaft Gear Based on CRDRS Support Configuration with Intermediate Bearing Support
by Xiaojie Yuan, Xiaoyu Che, Rupeng Zhu and Weifang Chen
Machines 2025, 13(6), 513; https://doi.org/10.3390/machines13060513 - 12 Jun 2025
Viewed by 1299
Abstract
The rotor shaft is a critical component responsible for transmitting engine power to the helicopter’s rotor. Deformation of the rotor shaft can affect the meshing performance of the output stage gears in the main gearbox, thereby affecting load transfer efficiency. By adjusting the [...] Read more.
The rotor shaft is a critical component responsible for transmitting engine power to the helicopter’s rotor. Deformation of the rotor shaft can affect the meshing performance of the output stage gears in the main gearbox, thereby affecting load transfer efficiency. By adjusting the support parameters of the rotor shaft, deformation at critical positions can be minimized, and the meshing performance of the output stage gears can be improved. Therefore, it is imperative to investigate the influence of rotor shaft support parameters on the deformation of the rotor shaft. This paper takes coaxial reversing dual rotor shaft (CRDRS) support configuration with intermediate bearing support as object. Utilizing Timoshenko beam theory, a rotor shaft model is developed, and static equations are derived based on the Lagrange equations. The relaxation iteration method is employed for a two-level iterative solution, and the effects of bearing support positions and support stiffness on the radial and angular deformations of rotor shaft gears under two support configurations, simply supported outer rotor shaft–cantilever-supported inner rotor shaft, and simply supported outer rotor shaft–simply supported inner rotor shaft, are analyzed. The findings indicate that the radial and angular deformations of gear s1 are consistently smaller than those of gear s2 in the CRDRS system. This difference is particularly pronounced in the selection of support configuration. The bearing support position plays a dominant role in gear deformation, exhibiting a monotonic linear relationship. In contrast, although adjustments in bearing support stiffness also follow a linear pattern in influencing deformation, their impact is relatively limited. Overall, optimal design should prioritize the adjustment of bearing positions, particularly the layout of b3 relative to s2, while complementing it with coordinated modifications to the stiffness of bearings b2, b3, and b4 to effectively enhance the static characteristics of the dual-rotor shaft gears. Full article
(This article belongs to the Section Machine Design and Theory)
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25 pages, 5401 KB  
Article
Coupled Electro-Thermal FEM with Geometric Symmetry Constraints for Modular Battery Pack Design
by Yingshuai Liu, Chenxing Liu, Jianwei Tan and Guangdong Tian
Symmetry 2025, 17(6), 865; https://doi.org/10.3390/sym17060865 - 3 Jun 2025
Cited by 1 | Viewed by 507
Abstract
This study investigates the structural integrity and dynamic behavior of symmetry-optimized battery pack systems for new energy vehicles through advanced finite element analysis. It examines symmetry-optimized battery pack systems with mechanically stable and thermally adaptive potentials. Leveraging geometric symmetry principles, a high-fidelity three-dimensional [...] Read more.
This study investigates the structural integrity and dynamic behavior of symmetry-optimized battery pack systems for new energy vehicles through advanced finite element analysis. It examines symmetry-optimized battery pack systems with mechanically stable and thermally adaptive potentials. Leveraging geometric symmetry principles, a high-fidelity three-dimensional (3D) model was constructed in SolidWorks 2023 and subjected to symmetry-constrained static analysis on ANSYS Workbench 2021 R1 platform. The structural performance was systematically evaluated under three critical asymmetric loading scenarios: emergency left/right turns and braking conditions, with particular attention to symmetric stress distribution patterns. The numerical results confirmed the initial design’s compliance with mechanical requirements while revealing symmetric deformation characteristics in dominant mode shapes. Building upon symmetry-enhanced topology configuration, a novel lightweight strategy was implemented by substituting Q235 steel with ZL104 aluminum alloy. While mechanical symmetry has been widely studied, thermal gradients in battery packs can induce asymmetric expansions. For example, uneven cooling may cause localized warping in aluminum alloy shells. This multiphysics effect must be integrated into symmetry constraints to ensure true stability. Symmetric material distribution optimization reduced the mass by 19% while maintaining structural stability, as validated through comparative static and modal analyses. Notably, the symmetric eigenfrequency arrangement in optimized modules effectively avoids common vehicle excitation bands (8–12 Hz/25–35 Hz), demonstrating significant resonance risk reduction through frequency redistribution. This research establishes a symmetry-driven design paradigm that systematically coordinates structural efficiency with dynamic reliability, providing critical insights for developing next-generation battery systems with balanced performance characteristics. Full article
(This article belongs to the Section Engineering and Materials)
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22 pages, 7311 KB  
Article
Calculation of Time-Varying Mesh Stiffness of Internal Mesh Transmission and Analysis of Influencing Factors
by Jubo Li, Hengbo Zhao, Yanbo Ren and Jianjun Yang
Appl. Sci. 2025, 15(9), 4599; https://doi.org/10.3390/app15094599 - 22 Apr 2025
Viewed by 504
Abstract
Time-varying mesh stiffness (TVMS) of the internal mesh transmission is a significant source of excitation that causes vibration and noise in planetary gear systems, and is also an important parameter in dynamics analysis. Currently, the calculation of mesh stiffness for internal gear pairs [...] Read more.
Time-varying mesh stiffness (TVMS) of the internal mesh transmission is a significant source of excitation that causes vibration and noise in planetary gear systems, and is also an important parameter in dynamics analysis. Currently, the calculation of mesh stiffness for internal gear pairs primarily relies on finite element simulation, and there still lacks a mesh stiffness analytical model that accounts for tooth surface nonlinear contact. Therefore, this paper proposes an analytical model for nonlinear contact mesh stiffness that comprehensively accounts for tooth surface modification and the flexibility of the ring gear. Firstly, a mesh stiffness calculation model for a sliced tooth pair was established using the potential energy method, which accounted for the influence of gear ring flexibility. Secondly, the tooth deviation ease-off diagram was derived from the modified tooth surface equations, which provided data support for the nonlinear contact analysis. On this basis, slicing element pairs that met the contact conditions were identified by combining elastic deformation with mesh clearance. The comprehensive mesh stiffness in nonlinear contact was calculated by integrating the deformation coordination equation with the principle of minimum potential energy. Finally, using a group of internal helical gear pairs as an example, the validity of the proposed method was verified through finite element simulation. The effects of load, modification amount, and face width on the TVMS and load transmission error (LTE) of an internal helical gear pair were investigated by the analytical model. The results show that the analytical model can provide a reference for the optimal design of internal gear transmission. Full article
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18 pages, 2858 KB  
Article
Analysis of Distributed Dynamic Loads Induced by the Own Mass of Manipulator Links and Their Visualization on Interactive 3D Computer Models
by Muratulla Utenov, Tarek Sobh, Yerbol Temirbekov, Saltanat Zhilkibayeva, Sarosh Patel, Dauren Baltabay and Zhadyra Zhumasheva
Robotics 2025, 14(4), 46; https://doi.org/10.3390/robotics14040046 - 7 Apr 2025
Viewed by 597
Abstract
This study proposes an approach to 3D modeling of spatial manipulators in the Maple 2023 software environment. Algorithms and program codes have been developed to create computer 3D models of manipulators controlled by generalized coordinates. The implementation of these algorithms and program codes [...] Read more.
This study proposes an approach to 3D modeling of spatial manipulators in the Maple 2023 software environment. Algorithms and program codes have been developed to create computer 3D models of manipulators controlled by generalized coordinates. The implementation of these algorithms and program codes has enabled the creation of three-dimensional computer models of manipulators with clear visual representations of links, their cross-sections, kinematic pairs, grippers, and loads, differing in structure and degrees of freedom while ensuring a comprehensive view from all spatial perspectives. During the motion of the manipulator, complex distributed dynamic loads arise in its links due to their intrinsic masses. These dynamic loads create several challenges: for instance, excessive dynamic loads or significant deformation of the links may lead to failure of the manipulator or a loss of precision in the positioning of the gripper. Such loads significantly impact the design, operation, and reliability of manipulators. The study and understanding of dynamic loads in manipulators are crucial areas in mechanics and robotics, enabling the development of more reliable and efficient systems. The Denavit–Hartenberg method was applied to control the motion of the created computer 3D models of manipulators using generalized coordinates. Using the recursive Newton–Euler equations, the necessary kinematic characteristics of the manipulator’s links were determined for calculating the distributed dynamic loads arising from the intrinsic masses of the links at each cross-section, relative to the local coordinate systems rigidly attached to the links. Algorithms and program codes were developed for controlling the motion of 3D models of manipulators, as well as for constructing visual diagrams of distributed dynamic loads in mutually perpendicular planes, formed by the principal axes of the link cross-sections and the axes passing along the longitudinal axes of the links. The implementation of these algorithms and program codes enabled the generation of distribution diagrams of all dynamic loads in all links of the moving manipulator. These diagrams visually illustrate the changes in direction and magnitude of the distributed dynamic loads in all cross-sections of the links throughout the full cycle of the manipulator’s operation. This allows for the consideration of the identified dynamic loads in the strength and stiffness calculations of the manipulator links, which is essential for the design of new innovative manipulators. Full article
(This article belongs to the Special Issue Robotics and Parallel Kinematic Machines)
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