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Keywords = gear transmission system

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21 pages, 8352 KiB  
Article
Research on Vibration Characteristics of Electric Drive Systems Based on Open-Phase Self-Fault-Tolerant Control
by Wenyu Bai, Yun Kuang, Zhizhong Xu, Yawen Wang and Xia Hua
Appl. Sci. 2025, 15(15), 8707; https://doi.org/10.3390/app15158707 - 6 Aug 2025
Abstract
This paper presents an electromechanical coupling model integrating an equivalent magnetic network (EMN) model of a dual three-phase permanent magnet synchronous motor (DTP-PMSM) with the dynamic model of a helical planetary gear transmission system. Using this model, this study analyzes the dynamic characteristics [...] Read more.
This paper presents an electromechanical coupling model integrating an equivalent magnetic network (EMN) model of a dual three-phase permanent magnet synchronous motor (DTP-PMSM) with the dynamic model of a helical planetary gear transmission system. Using this model, this study analyzes the dynamic characteristics of an electric drive system, specifically motor phase current, electromagnetic torque, and gear meshing force, under self-fault-tolerant control strategies. Simulation and experimental results demonstrate that the self-fault-tolerant control strategy enables rapid fault tolerance during open-phase faults, significantly reducing system fault recovery time. Meanwhile, compared to the open-phase faults conditions, the self-fault-tolerant control effectively suppresses most harmonic components within the system; only the second harmonic amplitude of the electromagnetic torque exhibited an increase. This harmonic disturbance propagates to the gear system through electromechanical coupling, synchronously amplifying the second harmonic amplitude in the gear system’s vibration response. This study demonstrates that self-fault-tolerant control strategies significantly enhance the dynamic response performance of the electric drive system under open-phase faults conditions. Furthermore, this study also investigates the electromechanical coupling mechanism through which harmonics generated by this strategy affect the gear system’s dynamic response, providing theoretical support for co-optimization electromechanical coupling design and fault-tolerant control in high-reliability electric drive transmission systems. Full article
(This article belongs to the Section Mechanical Engineering)
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30 pages, 9435 KiB  
Article
Intelligent Fault Warning Method for Wind Turbine Gear Transmission System Driven by Digital Twin and Multi-Source Data Fusion
by Tiantian Xu, Xuedong Zhang and Wenlei Sun
Appl. Sci. 2025, 15(15), 8655; https://doi.org/10.3390/app15158655 - 5 Aug 2025
Viewed by 1
Abstract
To meet the demands for real-time and accurate fault warning of wind turbine gear transmission systems, this study proposes an innovative intelligent warning method based on the integration of digital twin and multi-source data fusion. A digital twin system architecture is developed, comprising [...] Read more.
To meet the demands for real-time and accurate fault warning of wind turbine gear transmission systems, this study proposes an innovative intelligent warning method based on the integration of digital twin and multi-source data fusion. A digital twin system architecture is developed, comprising a high-precision geometric model and a dynamic mechanism model, enabling real-time interaction and data fusion between the physical transmission system and its virtual model. At the algorithmic level, a CNN-LSTM-Attention fault prediction model is proposed, which innovatively integrates the spatial feature extraction capabilities of a convolutional neural network (CNN), the temporal modeling advantages of long short-term memory (LSTM), and the key information-focusing characteristics of an attention mechanism. Experimental validation shows that this model outperforms traditional methods in prediction accuracy. Specifically, it achieves average improvements of 0.3945, 0.546 and 0.061 in Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and R-squared (R2) metrics, respectively. Building on the above findings, a monitoring and early warning platform for the wind turbine transmission system was developed, integrating digital twin visualization with intelligent prediction functions. This platform enables a fully intelligent process from data acquisition and status evaluation to fault warning, providing an innovative solution for the predictive maintenance of wind turbines. Full article
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13 pages, 4747 KiB  
Article
Biodegradable Polyalphaolefins for Gear Lubrication in Electrical Drives: Aging and Wetting
by Kevin Holderied, Joachim Albrecht, Elisabeth Distler, Katharina Weber and Nahed El Mahallawy
Lubricants 2025, 13(8), 347; https://doi.org/10.3390/lubricants13080347 - 4 Aug 2025
Viewed by 86
Abstract
Electric propulsion requires engines and transmission systems that run at higher speeds compared to combustion engines. For improving sustainability and environmental protection, biodegradable oils are suggested for the lubrication of high-speed gears that require particularly quick wetting of the steel surfaces. Newly developed [...] Read more.
Electric propulsion requires engines and transmission systems that run at higher speeds compared to combustion engines. For improving sustainability and environmental protection, biodegradable oils are suggested for the lubrication of high-speed gears that require particularly quick wetting of the steel surfaces. Newly developed promising candidates include short-chained polyalphaolefins. In the present work, a study on the applicability of such oil is presented and discussed with respect to different aging levels based on biodegradable properties. It focuses on the wettability of metallic surfaces investigated through time-resolved contact angle measurements. Carbon steels with different carbon contents and microstructures are selected as the most commonly used materials for gears. Effects of steel composition, surface roughness and oil oxidation are studied. The results show that in most cases, the application of biodegradable polyalphaolefins is not critical; however, a combination of steels with inhomogeneous microstructure, high surface roughness and aged oil can be critical because of limited wetting. Full article
(This article belongs to the Special Issue Tribology of Electric Vehicles)
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31 pages, 5480 KiB  
Review
Solid Core Magnetic Gear Systems: A Comprehensive Review of Topologies, Core Materials, and Emerging Applications
by Serkan Sezen, Kadir Yilmaz, Serkan Aktas, Murat Ayaz and Taner Dindar
Appl. Sci. 2025, 15(15), 8560; https://doi.org/10.3390/app15158560 - 1 Aug 2025
Viewed by 293
Abstract
Magnetic gears (MGs) are attracting increasing attention in power transmission systems due to their contactless operation principles, low frictional losses, and high efficiency. However, the broad application potential of these technologies requires a comprehensive evaluation of engineering parameters, such as material selection, energy [...] Read more.
Magnetic gears (MGs) are attracting increasing attention in power transmission systems due to their contactless operation principles, low frictional losses, and high efficiency. However, the broad application potential of these technologies requires a comprehensive evaluation of engineering parameters, such as material selection, energy efficiency, and structural design. This review focuses solely on solid-core magnetic gear systems designed using laminated electrical steels, soft magnetic composites (SMCs), and high-saturation alloys. This review systematically examines the topological diversity, torque transmission principles, and the impact of various core materials, such as electrical steels, soft magnetic composites (SMCs), and cobalt-based alloys, on the performance of magnetic gear systems. Literature-based comparative analyses are structured around topological classifications, evaluation of material properties, and performance analyses based on losses. Additionally, the study highlights that aligning material properties with appropriate manufacturing methods, such as powder metallurgy, wire electrical discharge machining (EDM), and precision casting, is essential for the practical scalability of magnetic gear systems. The findings reveal that coaxial magnetic gears (CMGs) offer a favorable balance between high torque density and compactness, while soft magnetic composites provide significant advantages in loss reduction, particularly at high frequencies. Additionally, application trends in fields such as renewable energy, electric vehicles (EVs), aerospace, and robotics are highlighted. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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20 pages, 4809 KiB  
Article
Design of a Bidirectional Veneer Defect Repair Method Based on Parametric Modeling and Multi-Objective Optimization
by Xingchen Ding, Jiuqing Liu, Xin Sun, Hao Chang, Jie Yan, Chengwen Sun and Chunmei Yang
Technologies 2025, 13(8), 324; https://doi.org/10.3390/technologies13080324 - 31 Jul 2025
Viewed by 230
Abstract
Repairing veneer defects is the key to ensuring the quality of plywood. In order to improve the maintenance quality and material utilization efficiency during the maintenance process, this paper proposes a bidirectional maintenance method based on gear rack transmission and its related equipment. [...] Read more.
Repairing veneer defects is the key to ensuring the quality of plywood. In order to improve the maintenance quality and material utilization efficiency during the maintenance process, this paper proposes a bidirectional maintenance method based on gear rack transmission and its related equipment. Based on the working principle, a geometric relationship model was established, which combines the structural parameters of the mold, punch, and gear system. Simultaneously, it solves the problem of motion attitude analysis of conjugate tooth profiles under non-standard meshing conditions, aiming to establish a constraint relationship between stamping motion and structural design parameters. On this basis, a constrained optimization model was developed by integrating multi-objective optimization theory to maximize maintenance efficiency. The NSGA-III algorithm is used to solve the model and obtain the Pareto front solution set. Subsequently, three optimal parameter configurations were selected for simulation analysis and experimental platform construction. The simulation and experimental results indicate that the veneer repair time ranges from 0.6 to 1.8 seconds, depending on the stamping speed. A reduction of 28 mm in die height decreases the repair time by approximately 0.1 seconds, resulting in an efficiency improvement of about 14%. The experimental results confirm the effectiveness of the proposed method in repairing veneer defects. Vibration measurements further verify the system’s stable operation under parametric modeling and optimization design. The main vibration response occurs during the meshing and disengagement phases between the gear and rack. Full article
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22 pages, 4262 KiB  
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 239
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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16 pages, 4737 KiB  
Article
An Influence Analysis of the Bearing Waviness on the Vibrations of a Flexible Gear
by Shenlong Li, Yajun Xu, Ruikun Pang and Jing Liu
Machines 2025, 13(8), 661; https://doi.org/10.3390/machines13080661 - 28 Jul 2025
Viewed by 186
Abstract
Roller bearing manufacturing errors have been proven to be critical factors affecting the vibrations of gear systems. Waviness is one main form of manufacturing error affecting the operational performance and life of bearings. However, most previous studies did not completely incorporate the effects [...] Read more.
Roller bearing manufacturing errors have been proven to be critical factors affecting the vibrations of gear systems. Waviness is one main form of manufacturing error affecting the operational performance and life of bearings. However, most previous studies did not completely incorporate the effects of the uneven bearing waviness on the flexible gear system vibrations. To characterize the contribution of the uneven bearing waviness on the vibrations of the gear system, a gear transmission system dynamics model considering shaft flexibility was established. The evenness sinusoidal waviness model (SWM) and uneven sinusoidal waviness model considering the time-varying contact (SWMS) were compared. The influences of the time-varying gear meshing stiffness excitations and flexibilities of shafts on the vibrations of the gear system were considered. A dynamic model was established, and the vibrations of the flexible gear system with the SWM and SWMS were compared. The vibrations induced by different amplitudes and orders of bearing waviness were analyzed. Note that the waviness of the bearing has a great influence on the system vibrations. The vibrations of the flexible gear system intensified with the increase in the bearing waviness order and amplitude. The vibrations from the gear system with the SWMS were bigger than those of the SWM. This paper introduces an alternative dynamic modeling model enabling the vibration analysis of the flexible gear system with evenness and uneven bearing waviness. Full article
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23 pages, 9638 KiB  
Article
A Study on the Influence Mechanism of the Oil Injection Distance on the Oil Film Distribution Characteristics of the Gear Meshing Zone
by Wentao Zhao, Lin Li and Gaoan Zheng
Machines 2025, 13(7), 606; https://doi.org/10.3390/machines13070606 - 14 Jul 2025
Viewed by 309
Abstract
Under the trend of lightweight and high-efficiency development in industrial equipment, precise regulation of lubrication in gear reducers is a key breakthrough for enhancing transmission system efficiency and reliability. This study establishes a three-dimensional numerical model for high-speed gear jet lubrication using computational [...] Read more.
Under the trend of lightweight and high-efficiency development in industrial equipment, precise regulation of lubrication in gear reducers is a key breakthrough for enhancing transmission system efficiency and reliability. This study establishes a three-dimensional numerical model for high-speed gear jet lubrication using computational fluid dynamics (CFD) and dynamic mesh technology. By implementing the volume of fluid (VOF) multiphase flow model and the standard k-ω turbulence model, the study simulates the dynamic distribution of lubricant in gear meshing zones and analyzes critical parameters such as the oil volume fraction, eddy viscosity, and turbulent kinetic energy. The results show that reducing the oil injection distance significantly enhances lubricant coverage and continuity: as the injection distance increases from 4.8 mm to 24 mm, the lubricant shifts from discrete droplets to a dense wedge-shaped film, mitigating lubrication failure risks from secondary atomization and energy loss. The optimized injection distance also improves the spatial stability of eddy viscosity and suppresses excessive dissipation of turbulent kinetic energy, enhancing both the shear-load capacity and thermal management. Dynamic data from monitoring point P show that reducing the injection distance stabilizes lubricant velocity and promotes more consistent oil film formation and heat transfer. Through multiphysics simulations and parametric analysis, this study elucidates the interaction between geometric parameters and hydrodynamic behaviors in jet lubrication systems. The findings provide quantitative evaluation methods for structural optimization and energy control in gear lubrication systems, offering theoretical insights for thermal management and reliability enhancement in high-speed transmission. These results contribute to the lightweight design and sustainable development of industrial equipment. Full article
(This article belongs to the Section Friction and Tribology)
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20 pages, 5652 KiB  
Article
Capacitive Sensing of Solid Debris in Used Lubricant of Transmission System: Multivariate Statistics Classification Approach
by Surapol Raadnui and Sontinan Intasonti
Lubricants 2025, 13(7), 304; https://doi.org/10.3390/lubricants13070304 - 14 Jul 2025
Viewed by 353
Abstract
The quantification of solid debris in used lubricating oil is essential for assessing transmission system wear and optimizing maintenance strategies. This study introduces a low-cost capacitive proximity sensor for monitoring total solid particle contamination in lubricants, with a focus on ferrous (Fe), non-ferrous [...] Read more.
The quantification of solid debris in used lubricating oil is essential for assessing transmission system wear and optimizing maintenance strategies. This study introduces a low-cost capacitive proximity sensor for monitoring total solid particle contamination in lubricants, with a focus on ferrous (Fe), non-ferrous (Al), and non-metallic (SiO2) debris. Controlled tests were performed using five mixing ratios of large-to-small particles (100:0, 75:25, 50:50, 25:75, and 0:100) at a fixed debris mass of 0.5 g per 25 mL of SAE 85W-140 automotive gear oil. Cubic regression analysis yielded high predictive accuracy, with average R2 values of 0.994 for Fe, 0.943 for Al, and 0.992 for SiO2. Further dimensionality reduction using Principal Component Analysis (PCA), along with Linear Discriminant Analysis (LDA) of multivariate statistical analysis, effectively classifies debris types and enhances interpretability. These results demonstrate the potential of capacitive sensing as an offline, non-invasive alternative to traditional techniques for wear debris monitoring in transmission systems. These results confirm the potential of capacitive sensing, supported by statistical modeling, as a non-invasive, cost-effective technique for offline classification and monitoring of wear debris in transmission systems. Full article
(This article belongs to the Special Issue Tribological Research on Transmission Systems)
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16 pages, 3015 KiB  
Article
Energy Efficiency Analysis of Hydraulic Excavators’ Swing Drive Transmission
by Vesna Jovanović, Dragoslav Janošević, Dragan Marinković, Nikola Petrović and Boban Nikolić
Machines 2025, 13(7), 596; https://doi.org/10.3390/machines13070596 - 10 Jul 2025
Viewed by 280
Abstract
The paper provides an analysis of the energy efficiency of the swing drive system of hydraulic excavators, which integrally includes a hydraulic motor and a planetary reducer. The indicator of the drive’s energy efficiency is determined based on the efficiency of the hydraulic [...] Read more.
The paper provides an analysis of the energy efficiency of the swing drive system of hydraulic excavators, which integrally includes a hydraulic motor and a planetary reducer. The indicator of the drive’s energy efficiency is determined based on the efficiency of the hydraulic motor and the planetary reducer. The efficiency of the hydraulic motor is defined as a function of the specific flow, pressure, and the number of revolutions of the hydraulic motor. The efficiency of the reducer is determined using structural analysis of planetary gearboxes and the moment method. As an example, the results of a comparative analysis of the energy efficiency of the swing drive of a tracked hydraulic excavator, weighing 16,000 kg and having a bucket volume of 0.6 m3, are presented. From the set of possible generated variant solutions of the drive, obtained through the synthesis process based on the required torque and platform rotation speed, two extreme drive variants were selected for the analysis. In the first configuration, a hydraulic motor characterized by a low specific flow is combined with a three-stage reduction gear featuring a higher overall transmission ratio, whereas the second configuration integrates a high-specific-flow hydraulic motor with a two-stage reduction gear of a lower transmission ratio. The obtained results of the comparative analysis of the drive’s energy efficiency are presented depending on the change in the required torque and the rotational speed of the platform. Full article
(This article belongs to the Special Issue Components of Hydrostatic Drive Systems)
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21 pages, 3800 KiB  
Article
Development of Technical Diagnostics for Lubrication in Gear Modules for Advanced Robotic Applications
by Silvia Maláková, Ľubomír Ilečko, Tibor Krenicky and Marian Dzimko
Appl. Sci. 2025, 15(13), 7431; https://doi.org/10.3390/app15137431 - 2 Jul 2025
Viewed by 213
Abstract
The paper focuses on the experimental investigation of the impact of filtration and tribological parameters on the reliability, service life, and functional characteristics of gear mechanisms used in robotics. The primary objective was to analyze the importance of lubricant cleanliness in robotic transmission [...] Read more.
The paper focuses on the experimental investigation of the impact of filtration and tribological parameters on the reliability, service life, and functional characteristics of gear mechanisms used in robotics. The primary objective was to analyze the importance of lubricant cleanliness in robotic transmission modules and to assess the effectiveness of filtration as a preventive and protective measure. As part of the research, a dedicated test rig was designed and developed. Based on the measurements and analyses performed, a significant correlation was confirmed between lubricant contamination levels and degradation phenomena in transmission modules. The study also highlights a sharp increase in contamination during the initial hours of operation, emphasizing the need for early intervention and continuous monitoring. The findings have strong practical potential and are highly relevant for manufacturers of robotic systems, maintenance service providers, and operators of automated production lines. The results contribute to increased system reliability and extended service life, reduced maintenance and repair costs, and improved environmental aspects of robotic system maintenance. Full article
(This article belongs to the Special Issue Technical Diagnostics and Predictive Maintenance, 2nd Edition)
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21 pages, 5651 KiB  
Article
Design and Experimental Setup of an Innovative Tribometer Aiming to Evaluate Small Quantities of Lubricants
by Lenine Marques de Castro Silva, Adilson José de Oliveira, Aylla Maria Alencar Rocha, José Josemar de Oliveira Junior and Salete Martins Alves
Lubricants 2025, 13(7), 292; https://doi.org/10.3390/lubricants13070292 - 29 Jun 2025
Viewed by 424
Abstract
The proposed tribometer design evaluates lubricants’ lubricating and wear protection properties at the interface of a loaded set of gears. However, this tribometer configuration and testing procedure described in standard ISO 14645-1 does not limit the tribological studies of gear test rigs. This [...] Read more.
The proposed tribometer design evaluates lubricants’ lubricating and wear protection properties at the interface of a loaded set of gears. However, this tribometer configuration and testing procedure described in standard ISO 14645-1 does not limit the tribological studies of gear test rigs. This study aimed to design and manufacture a mechanical transmission test rig capable of investigating the tribological condition of a lubricated enclosed gears transmission. The methodology consisted of (i) a definition of the test rig’s requirements; (ii) downsizing the main subassemblies present in the ISO 14635-1 test rig; (iii) designing innovative subassemblies; (iv) an instrumentation and data acquisition system, and (v) setup testing. The proposed system is suitable for evaluating small quantities of lubricants, allowing the analysis of special lubricants such as nanolubricants and ionic liquids in development for gearbox applications. Also, the dynamic loading avoids interruption in the test, providing results closer to working conditions. The experimental test evaluated the lubrication ability of two different base oils simultaneously under various loading conditions. Also, monitoring vibration signals helped identify the appearance of damage on the gear surface. Full article
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22 pages, 6760 KiB  
Article
Nonlinear Dynamics of a Coupled Electromechanical Transmission
by Antonio Zippo, Moslem Molaie and Francesco Pellicano
Vibration 2025, 8(3), 34; https://doi.org/10.3390/vibration8030034 - 20 Jun 2025
Viewed by 464
Abstract
The mechanical connection between a transmission system and an electric motor gives rise to a strong interaction between their respective dynamics. In particular, the coupling between an electric motor and a nonlinear spur gear transmission significantly influences the overall dynamic behavior of the [...] Read more.
The mechanical connection between a transmission system and an electric motor gives rise to a strong interaction between their respective dynamics. In particular, the coupling between an electric motor and a nonlinear spur gear transmission significantly influences the overall dynamic behavior of the integrated system. This study presents a detailed investigation into the electromechanical coupling effects between a permanent magnet synchronous machine (PMSM) and a nonlinear spur gear transmission. To focus on these effects, three configurations are analyzed: (i) a standalone gear pair model without motor interaction, (ii) a combined gear–motor system without dynamic coupling, and (iii) a fully coupled electromechanical system where the mechanical feedback influences motor control. The dynamic interaction between the motor’s torsional vibrations and the gear transmission is captured using the derivative of the transmission error as a feedback signal, enabling a closed-loop electromechanical model. Numerical simulations highlight the critical role of this coupling in shaping system dynamics, offering insights into the stability and performance of electric drive–gear transmission systems under different operating conditions. It also underscores the limitations of traditional modeling approaches that neglect feedback effects from the mechanical subsystem. The findings contribute to a more accurate and comprehensive understanding of coupled motor–gear dynamics, which is essential for the design and control of advanced electromechanical transmission systems in high-performance applications. Full article
(This article belongs to the Special Issue Nonlinear Vibration of Mechanical Systems)
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27 pages, 4277 KiB  
Article
Probability Density Evolution and Reliability Analysis of Gear Transmission Systems Based on the Path Integration Method
by Hongchuan Cheng, Zhaoyang Shi, Guilong Fu, Yu Cui, Zhiwu Shang and Xingbao Huang
Lubricants 2025, 13(6), 275; https://doi.org/10.3390/lubricants13060275 - 19 Jun 2025
Viewed by 467
Abstract
Aimed at dealing with the problems of high reliability solution cost and low solution accuracy under random excitation, especially Gaussian white noise excitation, this paper proposes a probability density evolution and reliability analysis method for nonlinear gear transmission systems under Gaussian white noise [...] Read more.
Aimed at dealing with the problems of high reliability solution cost and low solution accuracy under random excitation, especially Gaussian white noise excitation, this paper proposes a probability density evolution and reliability analysis method for nonlinear gear transmission systems under Gaussian white noise excitation based on the path integration method. This method constructs an efficient probability density evolution framework by combining the path integration method, the Chapman–Kolmogorov equation, and the Laplace asymptotic expansion method. Based on Rice’s theory and combined with the adaptive Gauss–Legendre integration method, the transient and cumulative reliability of the system are path integration method calculated. The research results show that in the periodic response state, Gaussian white noise leads to the diffusion of probability density and peak attenuation, and the system reliability presents a two-stage attenuation characteristic. In the chaotic response state, the intrinsic dynamic instability of the system dominates the evolution of the probability density, and the reliability decreases more sharply. Verified by Monte Carlo simulation, the method proposed in this paper significantly outperforms the traditional methods in both computational efficiency and accuracy. The research reveals the coupling effect of Gaussian white noise random excitation and nonlinear dynamics, clarifies the differences in failure mechanisms of gear systems in periodic and chaotic states, and provides a theoretical basis for the dynamic reliability design and life prediction of nonlinear gear transmission systems. Full article
(This article belongs to the Special Issue Nonlinear Dynamics of Frictional Systems)
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18 pages, 3602 KiB  
Article
Modeling and Analysis of Torsional Stiffness in Rehabilitation Robot Joints Using Fractal Theory
by Shuaidong Zou, Wenjie Yan, Guanghui Xie, Renqiang Yang, Huachao Xu and Fanwei Sun
Materials 2025, 18(12), 2866; https://doi.org/10.3390/ma18122866 - 17 Jun 2025
Viewed by 309
Abstract
The torsional stiffness of rehabilitation robot joints is a critical performance determinant, significantly affecting motion accuracy, stability, and user comfort. This paper introduces an innovative traction drive mechanism that transmits torque through friction forces, overcoming mechanical impact issues of traditional gear transmissions, though [...] Read more.
The torsional stiffness of rehabilitation robot joints is a critical performance determinant, significantly affecting motion accuracy, stability, and user comfort. This paper introduces an innovative traction drive mechanism that transmits torque through friction forces, overcoming mechanical impact issues of traditional gear transmissions, though accurately modeling surface roughness effects remains challenging. Based on fractal theory, this study presents a comprehensive torsional stiffness analysis for advanced traction drive joints. Surface topography is characterized using the Weierstrass–Mandelbrot function, and a contact mechanics model accounting for elastic–plastic deformation of micro-asperities is developed to derive the tangential stiffness of individual contact pairs. Static force analysis determines load distribution, and overall joint torsional stiffness is calculated through the integration of individual contact contributions. Parametric analyses reveal that contact stiffness increases with normal load, contact length, and radius, while decreasing with the tangential load and roughness parameter. Stiffness exhibits a non-monotonic relationship with fractal dimension, reaching a maximum at intermediate values. Overall system stiffness demonstrates similar parameter dependencies, with a slight decrease under increasing output load when sufficient preload is applied. This fractal-based model enables more accurate stiffness prediction and offers valuable theoretical guidance for design optimization and performance improvement in rehabilitation robot joints. Full article
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