Non-inertial multi-DOF dynamic modeling and experimental analysis of marine gear systems subjected to wave-induced motions

Abstract Large excavators are critical assets in large-scale mining operations, relying on gearboxes to transmit mechanical energy during lifting and digging activities. Gear tooth failures in these systems lead to high maintenance costs and unplanned downtime, constituting a significant operational challenge. Understanding the root causes of such failures is essential for improving reliability and performance, as gear durability is governed by the interaction between metallurgical characteristics, heat treatment conditions, and operational stresses. In this study, premature fractures of gear teeth in an excavator gearbox were investigated through a multiparametric analysis. Chemical composition was determined by optical emission spectroscopy, confirming compliance with DIN 18CrNiMo 7-6 steel. Optical and scanning electron microscopy revealed the presence of retained austenite, untempered martensite, and cementite along grain boundaries, as well as multiple fatigue crack initiation sites and characteristic propagation striations. Microhardness profiling indicated heterogeneous case-hardened layers with the coexistence of martensitic and retained austenitic phases, while field vibration measurements demonstrated operational stress levels exceeding recommended limits, thereby accelerating fatigue crack propagation. Despite the chemical composition meeting material specifications, the root cause of failure was attributed to excessive retained austenite resulting from insufficient carbon potential during the carburizing process. Under cyclic loading, the retained austenite transformed into martensite, promoting material embrittlement and intensifying high cycle fatigue crack propagation until catastrophic failure occurred. These findings highlight the critical interplay between microstructure, heat treatment, and operational conditions, underscoring the need to optimize carbon potential, carburizing parameters, and vibration control to enhance the reliability of gear systems used in mining applications.

To enhance the smoothness, quietness, and reliability of traction gear transmissions in high-speed electric multiple units operating under uncertain conditions, this study introduces an innovative arc cylindrical gear system along with a robust optimization strategy for gear modification. Center distance error and material elastic modulus are selected as key disturbance factors, and their uncertainty distributions are modeled using fuzzy interval theory and the optimal level-cut method. A robust optimization model is developed with the maximum profile modification amount, modification length, and arc tooth line radius as design variables to analyze the correlation between modification parameters and noise generation. The model aims to minimize radiated noise while satisfying noise reliability constraints, and the optimal robust modification scheme is obtained using a genetic algorithm. The results indicate that the optimized gear design achieves a 63.7% reduction in transmission error, a 48.4% decrease in maximum contact stress at the meshing-out position, and a 16.3% drop in radiated noise, while maintaining a robust reliability index R s of 98.02% across the full range of disturbance parameters. This study offers theoretical guidance and practical strategies for achieving robust and reliable design of traction gears in next-generation high-speed trains.

Deep-sea gear transmission systems encounter critical lubrication challenges arising from the synergistic coupling of extreme hydrostatic pressure and cryogenic temperatures. These environmental stressors induce exponential viscosity escalation in lubricants, precipitating severe fluidity degradation, elevated startup resistance, and lubrication starvation. Concurrently, seawater intrusion triggers lubricant emulsification, additive deactivation, and electrochemical corrosion at meshing interfaces, collectively escalating the risk of catastrophic lubrication failure and compromising long-term operational reliability. This study systematically elucidates the lubrication degradation mechanisms inherent to deep-sea environments and proposes targeted mitigation strategies. Through comprehensive characterization of deep-sea environmental parameters and their impact on lubricant rheological behavior, we critically evaluate the applicability and inherent limitations of conventional Thermal Elasto-Hydrodynamic Lubrication (TEHL) theory under extreme conditions. Our analysis reveals that established TEHL frameworks necessitate substantial modification to accurately capture pressure-viscosity-temperature coupling phenomena and seawater contamination kinetics. Meshing interface texturing, as an effective anti-friction and wear-mitigation strategy, is investigated to delineate its mechanistic pathways for enhancing lubricant film formation and tribological performance under starved lubrication regimes. Key findings demonstrate that optimized micro-texture architectures can effectively compensate for viscosity-induced fluidity deficits and attenuate the deleterious effects of seawater ingress. Critical knowledge gaps are identified, and future research trajectories are charted: (i) multiphysics coupling models integrating thermo-hydrodynamic, chemo-physical, and mechanical degradation processes; (ii) synergistic texture-coating design paradigms; (iii) high-pressure low-temperature experimental validation protocols; and (iv) engineering implementation frameworks for deep-sea gear transmission systems. This review establishes theoretical foundations and provides technical guidelines for robust lubrication design and long-term operational stability of deep-sea transmission equipment.

Many industrial machines inevitably suffer from external impacts which can change the meshing state of gears and thus affect the vibration characteristics of the gear transmission system. Previous studies mostly directly applied external impact excitation to the gear pair, with few considering the gear–shaft-bearing system. In reality, external impact excitation first acts on the bearing ends and then is transmitted to the gear ends through the transmission shaft. Therefore, the paper established a bending–torsion coupled dynamic model of the gear–shaft-bearing transmission system, taking into account external impacts, gear eccentricity, time-varying meshing stiffness, transmission error, shafts elastic deformation and nonlinear reactions forces. The vibration characteristics of the bending–torsion coupled gear–shaft-bearing transmission system under external impacts were analyzed in the time and frequency domains. Additionally, the effects of impact load amplitude and impact duration on gear vibration characteristics were investigated. External impacts instantaneously amplified the vibrational energy of the gear pair, which promotes the generation of impact components and increases the vibration acceleration signal amplitude in the time domain. Distinct sidebands emerge in the frequency domain, with meshing impacts intensified during gear operation. Furthermore, as the impact load amplitude increases and the impact duration is shortened, the vibration characteristics of the gear transmission system become more pronounced. The findings provide important theoretical insights and practical engineering significance for improving the reliability and service life of gear transmission systems.

Accurate fault diagnosis of gear transmission systems is crucial for ensuring mechanical reliability and preventing catastrophic failures. However, existing research predominantly focuses on single-gear crack faults, often overlooking the complex coupling effects when cracks occur simultaneously on meshing gears in practical engineering scenarios. To address this research gap, a multi-degree-of-freedom dynamic model incorporating time-varying mesh stiffness under normal, single-crack, and coupled-crack conditions is established. Experimental validation is conducted based on an FZG closed test rig for power flow. The results indicate that the mesh stiffness under coupled-crack conditions is generally lower than that under single-crack conditions. In the time-domain vibration response, the periodic impact amplitudes induced by coupled cracks are significantly amplified, with the impact period jointly influenced by the rotational speeds of both the driving and driven gears. According to frequency-domain analysis, coupled cracks result in a notable increase in harmonic peaks of the mesh frequency, enhanced sideband amplitudes, and a modulation period that is between the rotational frequencies of the driving and driven gears. The simulation results from the dynamic model show high consistency with the experimental signals in terms of time-frequency characteristic trends and time-domain indicators such as the crest factor, thereby validating the effectiveness of the dynamic model. This study elucidates the unique influence mechanism of coupled cracks on the dynamic behavior of gear systems and can provide theoretical guidance for the accurate diagnosis and condition assessment of multi-tooth faults in subsequent research.

Concentric magnetic gears (CMGs) offer significant advantages for electric vehicle drivetrains, including contactless torque transmission, high efficiency, and built-in overload protection. Despite these benefits, commercial viability is stalled by a heavy dependence on rare-earth permanent magnets (REPMs), which raises serious concerns about cost, supply chain security, and sustainability. This review critically examines strategies to mitigate this reliance. Analysis of recent topological innovations shows that while torque density has improved, the fundamental dependence on REPMs remains unchanged. Furthermore, direct reduction strategies, including system integration, material substitution, topological optimization, passive conductors, and complete electrification, often result in considerable performance trade-offs. Consequently, hybrid excitation is identified as a key paradigm shift. The core contribution of this review is the development of a clear taxonomy distinguishing “auxiliary electromagnetic integrations” for added functionality and “true hybrid excitation,” where windings act as a co-primary source of magnetic flux. The study concludes that true hybrid excitation is the most strategic yet underexplored research area, uniquely enabling features such as variable gear ratios, overload resilience, and the capability to directly replace REPM volume. Therefore, focused research on true hybrid-excited CMGs is presented as the essential path toward developing sustainable, high-performance, next-generation magnetic gearing systems.

Modeling and transient analysis of a gear transmission system with flexible casing during maneuvering flight

Fault dynamic characteristics analysis of gear transmission systems considering bearing nonlinearity

Nonlinear dynamic characteristics investigation of helicopter high-power gear transmission system

Vibration analysis of lightweight spur gear system considering flexibility

Dynamic response analysis of helical gear systems considering periodic surface waviness deviation

Research on dynamic characteristics of gear systems with coupled cracks

Modeling and vibration characteristics analysis of flexible spiral bevel gear system

Gear systems operate under high mechanical and tribological loads, making their surfaces vulnerable to wear and fatigue. Improving surface durability requires finishing processes that improve near-surface properties and extend service life. Since machine hammer peening (MHP) offers such potential, this study investigates its influence on the performance of case-hardened spur gears and evaluates its suitability as an alternative to shot peening as a conventional finishing method. Analog specimens with simplified geometries were treated using various MHP parameters to identify effective process settings. These optimized settings were then applied to real spur gears to assess performance under practical conditions. The experiments showed that MHP can significantly modify surface integrity, achieving surface roughness reductions of up to 55%, surface hardness increases of up to 30%, and compressive residual stresses exceeding −1400 MPa with stability to depths of 200 µm. These modifications resulted in improved wear and fatigue performance, with increases in load cycle number in the tooth flank up to 99% and an increase in load amplitude in the tooth root of more than 5%. For comparison, specimens were also treated with shot peening. Although MHP induced stronger surface integrity modifications, shot peening achieved higher overall load-carrying capacity because several critical areas could not be fully accessed by MHP, limiting its effectiveness. Overall, MHP shows promise as a finishing process, but its full potential depends on overcoming accessibility limitations in complex gear geometries.

As the primary power transmission conduits, aircraft hydraulic pipelines are critical for actuating flight control surfaces and landing gear systems. Accurate in situ strain evaluation of these pipelines is essential, as installation-induced pre-loads directly compromise fatigue life and sealing performance, threatening overall system reliability. However, such evaluation is frequently hindered by the perspective distortions and limited depth of field inherent in conventional imaging systems. To overcome these metrological limitations, this study presents a novel virtual telecentric camera array system designed for high-precision, non-contact strain measurement. Unlike traditional pinhole models, the proposed system leverages a catadioptric setup with planar mirrors to create a virtual four-eye telecentric array from a single physical lens, ensuring constant magnification within the depth of field. A comprehensive simulation framework was established to rigorously compare the reprojection errors and scale accuracies between telecentric and pinhole projection models, quantitatively demonstrating the superior stability of the telecentric approach. Furthermore, a dedicated calibration strategy for non-overlapping telecentric fields of view was developed and validated. Experimental results from pipeline installation tests indicate a high concordance with strain gauge data, confirming that the proposed telecentric system effectively mitigates parallax errors and provides a robust solution for static and quasi-static micro-scale deformation monitoring in complex assembly environments.

With engineering architecture being shifted to meet the requirements of sustainable development, the need for optimized design solutions places precise engineering methods at the core of the contemporary industrial transition toward data-driven strategies. A timely conversion to lightweight components in drivetrain systems has led to the prominent use of high-strength polymer gears, establishing them as a critical point of interest in the field of power transmission. However, as the conversion to polymer gears relies on expensive and time-consuming laboratory testing, there is a standstill in evaluating the structural properties specific to polymer gear design. In addition, one of the major concerns in the development of polymer-based gear drives is linked with their operational performance and dynamic response under fault conditions influenced by surface wear. To address these difficulties, a framework for surface wear prediction is developed, enabling precise design optimization for specific drivetrain requirements. Computations of wear progression over multiple duty cycles are built upon the mathematical background of Archard’s wear theory, while internal changes in gear contact pressure distribution are constructed on Winkler’s surface model. The framework provides an innovative support for polymer gear systems, as it imports the three-dimensional (3D) scanning data of gear geometry, therefore enabling the analysis of actual flank surfaces with designated surface modifications and manufacturing errors. The framework’s effectiveness, confirmed by experimental validation, demonstrates a superior estimation of contact parameters and overall performance compared to traditional design methods, highlighting scalable solutions that contribute to ongoing industrial engineering objectives.

The global dynamics of a herringbone planetary gear system under stochastic excitations are analyzed, Specifically, excitation parameters following a normal distribution are generated via the Box-Muller transformation, while the Largest Lyapunov Exponent (LLE) and cell mapping spatial discretization are jointly applied to the system’s global analysis. The results show that periodic subdomains are intricately nested at the boundaries of the chaotic subdomain and with the higher-periodic enclosed by the lower-periodic in the parametric solution domain, quasi-periodic motion occurs in the sun gear speed range of [5200, 6000] r/min. In addition, lower periodic subdomains (e.g. P1 and P2) typically exhibit regular borders, increasing the damping ratio above 0.15 or reducing the backlash below 0.08 can weaken the vibration response, meanwhile, a P13 basin of attraction is validated at the [0, 0] state cell. Stochasticity induces chaos to erode periodic subdomains across their boundaries and with numerous scattered chaotic cells evolving into the P2 and P1 regions, enhancing the stochasticity of damping ratio or backlash significantly impairs high-speed vibration stability, and stochasticity acting on backlash more easily induces scattered chaotic cell distribution in the state space. These findings could help optimize the dynamic parameter design of gear systems and thereby mitigate their vibrations.

When wheels roll on the ground, they move forward via the contact friction. This propulsion mechanism is also frequently used to create artificial microswimmers in viscous liquid environment. In such cases hydrodynamic lubrication at the contact point greatly reduces the driving forces, nevertheless forward motion can be still remarkable under rapid rotation. Interestingly, here we demonstrate that when rolling in viscoelastic fluids, a roller can slide backwards even though its rotational direction suggests forward motion. These fluids exhibit along sheared flow lines a non-zero elastic tension due to the stretch of the viscoelastic media. When the roller rolls on a surface within such fluid, a rear-front flow-field asymmetry develops, which leads to a net backward viscoelastic stress that forces the roller to slide backwards. In addition, the viscoelastic flow field results in an effective attraction between the roller and the surface. This allows the assembling of a microscale gearing system which transmit motion from a rotating colloid to a much larger object. Our findings opens up new directions for the fabrication of micro scale actuation systems relevant for active matter design and cargo delivery in complex liquid environment.

The overall transmission error and phase difference between the internal and external gear meshing pairs in planetary gear trains (PGTs) play crucial roles in vibration reduction design. However, these factors have received limited attention in existing studies concerning the dynamics and tooth profile modification of PGTs. In this paper, a shifted spur planetary gear system is employed as a case study. The formulation for calculating the phase difference of both internal and external meshing pairs is derived. Furthermore, a new time-varying meshing stiffness model incorporating the phase difference is proposed based on Tooth Contact Analysis (TCA) and Loaded Tooth Contact Analysis (LTCA). The calculation method for the overall transmission error considering the phase difference is provided. An optimization method for tooth profile modification is developed to minimize the fluctuation amplitude of the overall transmission error, and applied to a shifted spur planetary gear system. Utilizing the time-varying meshing stiffness and phase differences of both internal and external meshing pairs, a dynamic model of the planetary transmission system is established. Dynamic simulations based on this model confirm the effectiveness of the proposed profile modification strategy, demonstrating a significant reduction in the vibration acceleration of the sun gear. In summary, optimizing the tooth profile to suppress fluctuations in overall transmission error enhances the vibration reduction performance of planetary transmission systems.