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Keywords = flexible ring model

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20 pages, 1382 KB  
Article
Capacity Optimization Configuration of a Highway Ring Multi-Microgrid System Considering the Coordination of Fixed and Mobile Energy Storage
by Lulu Wang, Jinsong Wang, Yabin Wang, Feng Lin, Xianran Zhu, Chengyu Jiang and Ruifeng Shi
Sustainability 2026, 18(2), 629; https://doi.org/10.3390/su18020629 - 7 Jan 2026
Viewed by 207
Abstract
To mitigate the mismatch between fluctuating renewable generation and load demand in highway service area multi-microgrid systems, this paper develops a day-ahead capacity optimization model based on the coordinated operation of fixed and mobile energy storage. A ring-structured multi-microgrid architecture is established, incorporating [...] Read more.
To mitigate the mismatch between fluctuating renewable generation and load demand in highway service area multi-microgrid systems, this paper develops a day-ahead capacity optimization model based on the coordinated operation of fixed and mobile energy storage. A ring-structured multi-microgrid architecture is established, incorporating a “one-to-many” interaction mode of mobile storage stations. A coordinated control strategy is then proposed to enable flexible power dispatch and resource sharing among microgrids. The objective function minimizes both investment and operating costs of energy storage on a day-ahead timescale, and the model is solved using an optimization approach. Case study results demonstrate that introducing mobile energy storage significantly reduces the required capacity of local fixed storage, enhances energy interconnection among microgrids, and improves overall storage utilization and system economy. Full article
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36 pages, 4951 KB  
Review
A Comprehensive Review on the Mechanics of Cyclodextrin-Based Slide-Ring Polymers
by D. M. Li, Longyu Wei, Luxi Chen, Bingchang Zhao and Heyang Wei
Polymers 2026, 18(1), 37; https://doi.org/10.3390/polym18010037 - 23 Dec 2025
Viewed by 424
Abstract
The widespread application of polymer soft materials in cutting-edge fields such as flexible electronics and biomedicine has placed higher demands on their mechanical properties. Traditional chemically cross-linked or physically cross-linked polymers each have inherent limitations. In contrast, slide-ring polymers (SRPs), also known as [...] Read more.
The widespread application of polymer soft materials in cutting-edge fields such as flexible electronics and biomedicine has placed higher demands on their mechanical properties. Traditional chemically cross-linked or physically cross-linked polymers each have inherent limitations. In contrast, slide-ring polymers (SRPs), also known as sliding cross-linked polymers or topologically cross-linked polymers, effectively distribute chain tension through their slip-cross-link characteristics, thereby exhibiting remarkable toughness, elongation at break, and low hysteresis. Among them, cyclodextrin (CD) has emerged as an ideal building block, such as the CD-based rotaxane/polyrotaxane/pseudortaxane/polypseudortaxane, for constructing SRPs due to its unique cavity structure and ease of modification, enabling diverse regulation of material structure and function through molecular design. Currently, the preparation strategies for cross-linking are relatively well established. However, existing research on the physical and mechanical behavior of SRPs—particularly their responses and damage mechanisms under complex loading conditions—remains unsystematic. Furthermore, establishing a cross-scale correlation mechanism from molecular design to macroscopic performance remains a key challenge. This review systematically summarizes recent advances in the mechanics of cyclodextrin-based sliding cross-linked polymers (CD-based SRPs) focusing on the molecular design and network structures, physical and mechanical behaviors and properties, deformation mechanism and theoretical models, and simulation and prediction, to provide clear guidance for future development of these materials. Full article
(This article belongs to the Special Issue Mechanics of Polymer-Based Soft Materials)
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18 pages, 5967 KB  
Article
Effect of Rotational Speed Fluctuation Parameters on Dynamic Characteristics of Angular Contact Ball Bearings
by Haibin He, Jun Feng, Zuoxiang Zhu, Jinmei Guo and Guohu Luo
Symmetry 2025, 17(10), 1761; https://doi.org/10.3390/sym17101761 - 18 Oct 2025
Viewed by 517
Abstract
The fluctuation in the rotational speed of the inner ring can lead to significant instability in the motion of both the inner ring and the cage of rolling bearings. This instability seriously impacts the operational performance and service life of the bearings. In [...] Read more.
The fluctuation in the rotational speed of the inner ring can lead to significant instability in the motion of both the inner ring and the cage of rolling bearings. This instability seriously impacts the operational performance and service life of the bearings. In this paper, a nonlinear dynamic model of a fully flexible angular contact ball bearing was established by comprehensively considering various nonlinear factors, including elastic contact relationships, internal collisions, friction, and clearance. The dynamic characteristics of the inner ring and cage under sinusoidal rotational speed fluctuations were studied. The effects of amplitude and frequency of rotational speed fluctuation of the inner ring on the motion stability of the inner ring and cage were analyzed. The results show that a greater the fluctuation amplitude leads to a higher the fluctuation amplitude in the cage’s rotational speed curve, while a higher fluctuation frequency correlates with an increased frequency in the cage’s rotational speed curve. These results indicate that increases in both the amplitude and frequency of rotational speed fluctuations result in more pronounced oscillations of the inner ring. The validity of the model was confirmed by comparing the LS-DYNA results with the analytical results and experimental results. The research findings can provide a theoretical foundation for enhancing motion stability and optimizing design of the bearings. Full article
(This article belongs to the Section Engineering and Materials)
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16 pages, 7056 KB  
Article
Molecular Dynamics Simulation Reveals the Mechanism of Substrate Recognition by Lignin-Degrading Enzymes
by Xue Ma, Xueting Cao, Zhenyu Ma, Jingyi Zhu, Letian Yang, Min Xiao and Xukai Jiang
Int. J. Mol. Sci. 2025, 26(19), 9378; https://doi.org/10.3390/ijms26199378 - 25 Sep 2025
Viewed by 950
Abstract
Lignin, the most abundant aromatic biopolymer, represents a key renewable feedstock for sustainable biorefineries, yet its structural complexity poses a formidable challenge for enzymatic degradation. While ligninolytic enzymes such as laccases (LACs), lignin peroxidases (LiPs), and manganese peroxidases (MnPs) exhibit remarkable catalytic versatility, [...] Read more.
Lignin, the most abundant aromatic biopolymer, represents a key renewable feedstock for sustainable biorefineries, yet its structural complexity poses a formidable challenge for enzymatic degradation. While ligninolytic enzymes such as laccases (LACs), lignin peroxidases (LiPs), and manganese peroxidases (MnPs) exhibit remarkable catalytic versatility, the molecular mechanisms underlying their ability to balance substrate specificity and structural flexibility remain unresolved. Here, we employed all-atom molecular dynamics (MD) simulations and virtual mutagenesis to dissect the dynamic interactions between these enzymes and lignin model compound (β-O-4-linked H-type dimers). Our simulations revealed a dual recognition mechanism in which polar residues (such as Asp, Glu, Arg and His) formed hydrogen bonds with hydroxyl and keto groups near catalytic cleavage sites, ensuring precise alignment for bond scission, while aromatic residues stabilized diverse lignin conformations via hydrophobic interactions with conserved aromatic rings. Conformational dynamics of active-site residues enabled adaptive adjustments to substrate heterogeneity, reconciling enzymatic specificity with structural promiscuity. Virtual mutation experiments further demonstrated that aromatic residues were indispensable for binding stability, whereas polar residues dictated cleavage-site selectivity. These findings provide atomic-scale insights into the catalytic mechanism of ligninolytic enzymes, with implications in the rational design of superior biocatalyst for lignin biorefineries. Full article
(This article belongs to the Special Issue Molecular Dynamics Simulations of Protein Structures)
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21 pages, 20900 KB  
Article
Balancing Accuracy and Efficiency in Wire-Rope Isolator Modeling: A Simplified Beam-Element Framework
by Claudia Marin-Artieda
Vibration 2025, 8(3), 55; https://doi.org/10.3390/vibration8030055 - 22 Sep 2025
Viewed by 910
Abstract
Wire-rope isolators (WRIs) are widely used in vibration and seismic protection due to their multidirectional flexibility and amplitude-dependent hysteretic damping. However, their complex nonlinear behavior, especially under inclined and combined-mode loading, poses challenges for predictive modeling. This study presents a simplified finite-element modeling [...] Read more.
Wire-rope isolators (WRIs) are widely used in vibration and seismic protection due to their multidirectional flexibility and amplitude-dependent hysteretic damping. However, their complex nonlinear behavior, especially under inclined and combined-mode loading, poses challenges for predictive modeling. This study presents a simplified finite-element modeling framework using constant-property Timoshenko beam elements with tuned Rayleigh damping to simulate WRI behavior across various configurations. Benchmark validation against analytical ring deformation confirmed the model’s ability to capture geometric nonlinearities. The framework was extended to five WRI types, with effective cross-sectional properties calibrated against vendor-supplied quasi-static data. Dynamic simulations under sinusoidal excitation demonstrated strong agreement with experimental force-displacement loops in pure modes and showed moderate accuracy (within 29%) in inclined configurations. System-level validation using a rocking-control platform with four inclined WRIs showed that the model reliably predicts global stiffness and energy dissipation under base accelerations. While the model does not capture localized nonlinearities such as pinched hysteresis due to interstrand friction, it offers a computationally efficient tool for engineering design. The proposed method enables rapid evaluation of WRI performance in complex scenarios, supporting broader integration into performance-based seismic mitigation strategies. Full article
(This article belongs to the Special Issue Nonlinear Vibration of Mechanical Systems)
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28 pages, 4648 KB  
Article
Allosteric Control Overcomes Steric Limitations for Neutralizing Antibodies Targeting Conserved Binding Epitopes of the SARS-CoV-2 Spike Protein: Exploring the Intersection of Binding, Allostery, and Immune Escape with a Multimodal Computational Approach
by Mohammed Alshahrani, Vedant Parikh, Brandon Foley and Gennady Verkhivker
Biomolecules 2025, 15(9), 1340; https://doi.org/10.3390/biom15091340 - 18 Sep 2025
Viewed by 1314
Abstract
Understanding the atomistic basis of multi-layer mechanisms employed by broadly reactive neutralizing antibodies of the SARS-CoV-2 spike protein without directly blocking receptor engagement remains an important challenge in coronavirus immunology. Class 4 antibodies represent an intriguing case: they target a deeply conserved, cryptic [...] Read more.
Understanding the atomistic basis of multi-layer mechanisms employed by broadly reactive neutralizing antibodies of the SARS-CoV-2 spike protein without directly blocking receptor engagement remains an important challenge in coronavirus immunology. Class 4 antibodies represent an intriguing case: they target a deeply conserved, cryptic epitope on the receptor-binding domain yet exhibit variable neutralization potency across subgroups F1 (CR3022, EY6A, COVA1-16), F2 (DH1047), and F3 (S2X259). The molecular basis for this variability is not fully understood. Here, we employed a multi-modal computational approach integrating atomistic and coarse-grained molecular dynamics simulations, binding free energy calculations, mutational scanning, and dynamic network analysis to elucidate how these antibodies engage the receptor-binding domain (RBD) of the SARS-CoV-2 spike protein and influence its function. Our results reveal that neutralization efficacy arises from the interplay of direct interfacial interactions and allosteric effects. Group F1 antibodies (CR3022, EY6A, COVA1-16) primarily operate via classic allostery, modulating flexibility in RBD loop regions to indirectly interfere with the ACE2 receptor binding through long-range effects. Group F2 antibody DH1047 represents an intermediate mechanism, combining partial steric hindrance—through engagement of ACE2-critical residues T376, R408, V503, and Y508—with significant allosteric influence, facilitated by localized communication pathways linking the epitope to the receptor interface. Group F3 antibody S2X259 achieves potent neutralization through a synergistic mechanism involving direct competition with ACE2 and localized allosteric stabilization, albeit with potentially increased escape vulnerability. Dynamic network analysis identified a conserved “allosteric ring” within the RBD core that serves as a structural scaffold for long-range signal propagation, with antibody-specific extensions modulating communication to the ACE2 interface. These findings support a model where Class 4 neutralization strategies evolve through the refinement of peripheral allosteric connections rather than epitope redesign. This study establishes a robust computational framework for understanding the atomistic basis of neutralization activity and immune escape for Class 4 antibodies, highlighting how the interplay of binding energetics, conformational dynamics, and allosteric modulation governs their effectiveness against SARS-CoV-2. Full article
(This article belongs to the Special Issue Protein Biophysics)
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20 pages, 4448 KB  
Article
AFSS Wide-Frequency Reconfigurable Design and Electromagnetic Characterization Research
by Lei Gong, Xinru Tian, Ge Zhang, Xuan Liu, Shigeng Song, Jian Song, Haoyang Liu, Liguo Wang and Zhiqiang Yang
Electronics 2025, 14(18), 3628; https://doi.org/10.3390/electronics14183628 - 12 Sep 2025
Viewed by 720
Abstract
In order to solve the dynamic adaptation problem of the working frequency band of the FSS in the complex electromagnetic environment and further expand the frequency tuning range, a reconfigurable AFSS unit model based on PIN and varactor diodes are designed, which can [...] Read more.
In order to solve the dynamic adaptation problem of the working frequency band of the FSS in the complex electromagnetic environment and further expand the frequency tuning range, a reconfigurable AFSS unit model based on PIN and varactor diodes are designed, which can achieve the insertion loss below−1 dB in the wide frequency range of 10.2–15.2 GHz, meet the working-band switching, and allow for flexibly adjusting the working frequency point. In order to verify the accuracy of the design method, a square-ring aperture and notched patch-coupling structure that can exhibit broadband transmission response in the X-Ku band is first proposed based on the equivalent circuit model topology. A numerical simulation and a processing test of the structure are carried out. The measured data are in good agreement with the simulation results. After optimizing the unit structure, different capacitance values and resistance values are added to the diodes in the numerical simulation to control the equivalent PIN diode switch and the capacitance change in the varactor diodes. According to the equivalent circuit model and the electric-field intensity distribution, the AFSS regulation mechanism of the loaded diodes is explored. In this paper, through numerical simulation optimizations and experimental verification, the design method and performance optimization strategy of frequency-tunable FSS in the working range of 2–18 GHz are systematically studied, which provides theoretical support for the design of electromagnetic functional devices in the new generation of communication, radar, and electronic warfare systems. Full article
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25 pages, 4353 KB  
Article
Adaptive Gradient Loading Mechanism of Ball–Column Composite Bearings Considering Collar Deformation
by Guanjie Li, Yongcun Cui, Hedong Wei, Zhiwen Yang and Yanguang Ni
Machines 2025, 13(9), 785; https://doi.org/10.3390/machines13090785 - 1 Sep 2025
Viewed by 666
Abstract
To address the issue of uneven load and premature failure in ball–column composite bearings caused by ring deformation, this study develops a mechanical analysis model, considering ring deformation based on flexible ring theory and rolling bearing design. It systematically examines radial deflection of [...] Read more.
To address the issue of uneven load and premature failure in ball–column composite bearings caused by ring deformation, this study develops a mechanical analysis model, considering ring deformation based on flexible ring theory and rolling bearing design. It systematically examines radial deflection of the ring and how key parameters affect load distribution and stress. The results demonstrate that the elastic deformation of the collar redistributes the load, reduces the roller column’s load-carrying efficiency, and disrupts the optimal load distribution mode. Increasing the number of loaded rolling elements significantly improves the load uniformity, reduces the peak contact stress, and enhances the overall load-carrying performance. By optimizing the clearance matching across three bearings rows, a load-adaptive gradient bearing mechanism is realized by dynamically transferring, 70–90% of the heavy-load optimal distribution. These findings address the domestic research gaps and offer theoretical support for the performance prediction and optimal design of integrated ball–column composite bearings. Full article
(This article belongs to the Section Machine Design and Theory)
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27 pages, 7925 KB  
Article
Development and Verification of a Centrifugal Pump Rotor Model Based on Integrated Multibody Dynamics in the ADAMS Environment
by Madina Isametova, Rollan Nussipali, Gulbarshyn Smailova, Layla Sabirova, Arailym Tursynbayeva, Laila Sagatova, Denis Tkachenko and Nazym Saidinbayeva
Appl. Sci. 2025, 15(16), 9132; https://doi.org/10.3390/app15169132 - 19 Aug 2025
Viewed by 1467
Abstract
This study proposes a novel computational method, employing the integral dynamics of multibody systems to simulate the transverse vibrations of the rotor in a cantilever-type centrifugal pump. This method was applied to the kinematic assembly of the rotor and its supports, with the [...] Read more.
This study proposes a novel computational method, employing the integral dynamics of multibody systems to simulate the transverse vibrations of the rotor in a cantilever-type centrifugal pump. This method was applied to the kinematic assembly of the rotor and its supports, with the latter modeled as springs possessing stiffness and damping properties equivalent to those of real bearings supporting the shaft in an actual design. To investigate transverse vibrations within the system, three key observation points were defined—at the locations of the left and right bearings, as well as at the rotor’s center of mass—to allow for a thorough dynamic analysis. Additionally, the influence of motor rotational speed and the impeller’s eccentricity on the transverse vibrations of the supports and the shaft was examined. The results have revealed that transverse vibrations significantly affect the system’s dynamics at lower rotational speeds, leading to the classification of the shaft as flexible. As the rotational speed increases, the system exhibits enhanced dynamic stability. Furthermore, it was found that for impellers with a diameter less than 300 mm, the unbalanced forces are negligible and can be disregarded in pump design. To reduce vibration levels, an elastic damping ring was selected and incorporated into the system. This novel method provides an effective tool for analyzing the transverse vibrations of centrifugal pump rotors and for optimizing vibration mitigation strategies. Full article
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25 pages, 8879 KB  
Article
Sector-Based Perimeter Reconstruction for Tree Diameter Estimation Using 3D LiDAR Point Clouds
by Wonjune Kim, Hyun-Sik Son and Su-Yong An
Remote Sens. 2025, 17(16), 2880; https://doi.org/10.3390/rs17162880 - 18 Aug 2025
Viewed by 1217
Abstract
Accurate estimation of tree diameter at breast height (DBH) from LiDAR point clouds is essential for forest inventory, biomass assessment, and ecological monitoring. This paper presents a perimeter-based DBH estimation framework that achieves competitive accuracy against geometric fitting methods across three datasets. The [...] Read more.
Accurate estimation of tree diameter at breast height (DBH) from LiDAR point clouds is essential for forest inventory, biomass assessment, and ecological monitoring. This paper presents a perimeter-based DBH estimation framework that achieves competitive accuracy against geometric fitting methods across three datasets. The proposed approach partitions the trunk cross-section into angular sectors and employs Gaussian Mixture Models (GMMs) to identify representative boundary points in each sector, weighted by radial proximity and statistical confidence. To handle occlusion and partial scans, missing sectors are reconstructed using symmetry-aware proxy generation. The final perimeter is modeled via either convex hull or B-spline interpolation, from which DBH is derived. Extensive experiments were conducted on two public TreeScope datasets and a custom mobile LiDAR dataset. Compared to the Density-Based Clustering Ring Extraction (DBCRE) baseline, our method reduced RMSE by 22.7% on UCM-0523M (from 2.60 to 2.01 cm), 34.3% on VAT-0723M (from 3.50 to 2.30 cm), and 29.6% on the Custom Dataset (from 2.16 to 1.52 cm). Ablation studies confirmed the individual and synergistic contributions of GMM clustering, radial consistency filtering, and proxy synthesis. Overall, the method provides a flexible alternative that reduces dependence on strict geometric assumptions, offering improved DBH estimation performance with moderate occlusion and incomplete, uneven boundary coverage. Full article
(This article belongs to the Section Forest Remote Sensing)
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16 pages, 8118 KB  
Article
The Influence of Long-Term Service on the Mechanical Properties and Energy Dissipation Capacity of Flexible Anti-Collision Rings
by Junhong Zhou, Jia Lu, Wei Jiang, Ang Li, Hancong Shao, Zixiao Huang, Fei Wang and Qiuwei Yang
Coatings 2025, 15(8), 880; https://doi.org/10.3390/coatings15080880 - 27 Jul 2025
Viewed by 588
Abstract
This study investigates the long-term performance of flexible anti-collision rings after 12 years of service on the Xiangshan Port Highway Bridge. Stepwise loading–unloading tests at multiple loading rates (0.8–80 mm/s) were performed on the anti-collision rings, with full-field strain measurement via digital image [...] Read more.
This study investigates the long-term performance of flexible anti-collision rings after 12 years of service on the Xiangshan Port Highway Bridge. Stepwise loading–unloading tests at multiple loading rates (0.8–80 mm/s) were performed on the anti-collision rings, with full-field strain measurement via digital image correlation (DIC) technology. The results show that: The mechanical response of the anti-collision ring shows significant asymmetric tension–compression, with the tensile peak force being 6.8 times that of compression. A modified Johnson–Cook model was developed to accurately characterize the tension–compression force–displacement behavior across varying strain rates (0.001–0.1 s−1). The DIC full-field strain analysis reveals that the clamping fixture significantly influences the tensile deformation mode of the anti-collision ring by constraining its inner wall movement, thereby altering strain distribution patterns. Despite exhibiting a corrosion gradient from severe underwater degradation to minimal surface weathering, all tested rings demonstrated consistent mechanical performance, verifying the robust protective capability of the rubber coating in marine service conditions. Full article
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18 pages, 5269 KB  
Article
Analysis of Flexible Bearing Load Under Various Torque Conditions
by Nanxian Zheng, Jia Wang, Miaojie Wu, Huishan Liu and Yourui Tao
Machines 2025, 13(7), 627; https://doi.org/10.3390/machines13070627 - 21 Jul 2025
Viewed by 682
Abstract
This paper aims to develop a model for calculating the ball load of the thin-walled flexible bearing (FB) in a harmonic drive under various external torque conditions. The effect of the flexspline (FS) on the FB ball load is considered, and the equivalent [...] Read more.
This paper aims to develop a model for calculating the ball load of the thin-walled flexible bearing (FB) in a harmonic drive under various external torque conditions. The effect of the flexspline (FS) on the FB ball load is considered, and the equivalent ring is improved to calculate the ball load of the FB. Then, the accuracy of the proposed model in calculating the ball load is verified using a finite element analysis model. Finally, a fitting formula is obtained to rapidly evaluate the FB ball load via the geometrical parameters of the FB and the FS under various external torques. The results show that the FB ball load is mainly affected by the FB maximum radial deformation under low external torque. When subjected to heavy external torque, the maximum ball load is mainly affected by the FS’s geometric parameters. Full article
(This article belongs to the Special Issue Design and Manufacturing for Lightweight Components and Structures)
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14 pages, 23403 KB  
Article
Flexibly Reconfigurable Kerr Micro-Comb Based on Cascaded Si3N4 Micro-Ring Filters
by Jieyu Yang, Guang Chen, Lidan Lu, Jianzhen Ou, Chao Mei, Yingjie Xu, Wenbo Bo, Peng Wang, Xinyi Li and Lianqing Zhu
Photonics 2025, 12(7), 661; https://doi.org/10.3390/photonics12070661 - 30 Jun 2025
Viewed by 994
Abstract
In recent years, micro-combs, due to their compact structure and high efficiency, have proven to be a practical solution for optical sources. In this paper, an approach to flexibly modulating micro-combs is proposed, and a simulation platform based on Si3N4 [...] Read more.
In recent years, micro-combs, due to their compact structure and high efficiency, have proven to be a practical solution for optical sources. In this paper, an approach to flexibly modulating micro-combs is proposed, and a simulation platform based on Si3N4 micro-combs with highly integrated, tunable, and reconfigurable features is built. By means of the Lugiato–Lefever equation model, the dynamic evolution process of micro-combs is analyzed, and a micro-ring resonator is designed with a free spectral range of 7.24 nm, an effective mode area of 1.0829µm2, and coherent comb lines spanning over 125 THz. Cascaded silicon nitride micro-ring filters are utilized to obtain reconfigurable modulation effects for Kerr-frequency micro-combs. Due to the significance of flexibly controlled optical sources with high-repetition rates and multiple channels for system-on-chip, our proposal has potential in photonic integrated circuit systems, such as high-density photonic computing and large-capacity optical communications, in the future. Full article
(This article belongs to the Special Issue Photonic Integrated Circuits: Techniques, Insights and Devices)
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42 pages, 13512 KB  
Article
Dynamic Characteristic Analysis of Angular Contact Ball Bearings with Two-Piece Inner Rings in Aero-Engine Main Shafts Under Unsteady-State Conditions
by Haisheng Yang, Qiang Liu and Si’er Deng
Lubricants 2025, 13(6), 249; https://doi.org/10.3390/lubricants13060249 - 30 May 2025
Cited by 1 | Viewed by 1255
Abstract
The dynamic interactions among the internal components of aero-engine main shaft bearings under unsteady-state conditions are intricate, involving clearance collisions, contact, friction, and lubrication. The dynamic characteristics of bearings significantly influence the performance and stability of mechanical systems. This study establishes a rigid–flexible [...] Read more.
The dynamic interactions among the internal components of aero-engine main shaft bearings under unsteady-state conditions are intricate, involving clearance collisions, contact, friction, and lubrication. The dynamic characteristics of bearings significantly influence the performance and stability of mechanical systems. This study establishes a rigid–flexible coupling dynamic model for angular contact ball bearings with two-piece inner rings based on Hertz contact theory and lubrication theory. It systematically analyzes the dynamic characteristics of bearings under the coupling effects of acceleration, deceleration, and impact load. This study explores the influence of various loads, bearing speeds, and groove curvature radius coefficients on the dynamic characteristics of bearings. The findings indicate that the uniform speed phase of a bearing is highly responsive to impact load, followed by the deceleration phase, while the acceleration phase shows lower sensitivity to impact load. The groove curvature radius coefficient significantly affects the contact stress between the ball and its corresponding raceway, with contact stress increasing as the groove curvature radius coefficient rises. As the axial load decreases and the radial load, bearing speed, and groove curvature radius coefficient increase, there is a rise in pocket force, guiding force, and maximum equivalent stress of the flexible cage. Impact load leads to short-term intense fluctuations in the thickness of the bearing oil film, which can be alleviated by an increase in axial load. The oil film thickness firstly increases and then decreases with respect to the groove curvature radius coefficient. Furthermore, variations in bearing speed notably influence the thickness of the bearing oil film. This study analyzes the dynamic characteristics of bearings under the coupling effects of acceleration, deceleration, and impact load, offering insights for the design and optimization of angular contact ball bearings with two-piece inner rings. Full article
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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
Cited by 1 | Viewed by 1426
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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