The thin-walled spiral bevel gear system in aviation transmission systems is particularly vulnerable to resonance failure. Conventional system dynamics modeling approaches often lack the fidelity to accurately represent the dynamic behaviors arising from such thin-walled structural configurations. To address this limitation, this paper proposes a hybrid modeling method(HMM) for the dynamic characteristic analysis of thin-walled bevel gear systems which enables the characterization of traveling wave resonance (TWR), incorporates the Goodman curve and the Smith-Watson-Topper (SWT) parameter method for resonance failure identification, and validates the accuracy of the proposed modeling approach through dynamic experiment. The findings indicate that the traveling wave characteristics are manifested solely through the the gear body node. Distinct peak responses of the forward and backward traveling waves are observed at frequencies of fm-mfs and fm + mfs, respectively. Furthermore, the amplitude of axial vibration significantly exceeds that of radial vibration.The fatigue limit stress obtained via the SWT parameter method is conservative, demonstrating higher predictive efficacy for nodal diameters resonance failures dominated by bending. Dynamic experiments identify TWR speeds and corresponding frequencies with a maximum error of 5%, while the predicted vibration stress remains within a 15% deviation margin. The proposed HMM demonstrates high accuracy, providing a reliable analytical framework for resonance testing and identification in aerospace thin-walled spiral bevel gear systems.

Rotating machinery RUL prediction is a cornerstone of industrial prognostic and health management, where Transformer-based models have emerged as state-of-the-art approaches due to their superior long-range temporal dependency modeling capabilities. However, the inherent quadratic computational complexity of global self-attention imposes prohibitive memory and latency costs for long industrial time-series, while fixed attention architectures fail to adapt to the heterogeneous feature dynamics across equipment degradation stages. Here we present a lightweight convolutional Transformer framework that integrates a degradation-aware dynamic chunked self-attention mechanism to resolve the fundamental trade-off between prediction accuracy and computational efficiency. The dynamic chunked self-attention mechanism partitions input sequences into adaptive chunks and restricts attention computation within chunks, reducing complexity from O(n2) to linear O(nk) while preserving global dependency modeling via a lightweight cross-chunk interaction module. Uniquely, the framework employs a data-driven degradation stage perception system that dynamically adjusts chunk size and attention fusion weights based on real-time signal statistics, enabling optimal resource allocation across healthy, slow degradation, rapid degradation and severe degradation phases. Extensive validation on NASA C-MAPSS and XJTU-SY bearing datasets shows that the proposed method consistently outperforms the baseline ConvFormer, achieving substantially lower RMSE and S-score while significantly reducing model parameters and computational cost. This work establishes a high-precision, resource-efficient paradigm for industrial prognostics, enabling real-time RUL prediction on resource-constrained edge devices.

Diaphragm couplings are widely used in connecting all shaft systems because of their good axial and angular misalignment compensation ability. With the development of composite material technology, many metal parts use composite materials instead. Based on ABAQUS finite element simulation software, this paper establishes a finite element model of composite diaphragm coupling and simulates the static stiffness characteristics of it and metal diaphragm coupling to compare its compensation ability; and analyzes the influence of lay-up order and lay-up angle on the compensation ability. Finally, carbon fiber-reinforced epoxy resin prepreg is used to prepare composite diaphragm test pieces by hot pressing process, and an axial tensile test is carried out to verify the accuracy of the simulation results. The results show that under the same size conditions, the axial, angular, and radial compensation ability of composite diaphragm couplings is better than that of metal diaphragm couplings; the use of 0 °, ±45 °, 90 ° multi-angle layup can significantly improve the compensation ability, but the layup order has little effect on the compensation ability of composite materials. The results of the study are of great significance for the application of composite materials in couplings.

Projectile impact damages could chang the mass distribution and stiffness characteristics of the tail drive shaft. However, the effect mechanisms of its effect on mass distribution and stiffness characteristics are unclear. Hence, this paper conducts research on the projectile impact damage of the helicopter tail drive shaft and its effect on mass distribution and stiffness characteristics. The finite element simulation model of the projectile impact damage is established, and the stiffness simulation model is further proposed. The residual velocity, projectile impact duration, and projectile impact damage morphology have been analysed in detail. The effect of projectile impact damage on mass loss, centre of mass displacement, stiffness reduction, stiffness asymmetry, and cross stiffness is evaluated. The projectile impact experiment bench is established. The maximum error between the experimental incidence velocity and the ideal incidence velocity is 3.4%. The projectile impact damage morphology obtained from the experiment is larger than the simulated damage, with a maximum error of 26.5%, because the armour and lead sheath expand the damage area. Experimental results effectively validated the accuracy of the finite element simulation model of the projectile impact damage. This paper provides important theoretical guidance and technical support for the helicopters' survival ability.

Ship limiters must not only possess high impact stiffness to withstand explosive forces but also exhibit sufficient static and dynamic stiffness and damping characteristics to resist periodic ocean loads. Based on phenomenological theory and the generalized Maxwell model, this paper establishes hyperelastic and viscoelastic constitutive models for metal-rubber and nitrile rubber composite materials. After determining material parameters, a high-precision simulation model for the vertical and transverse/longitudinal directions of the limiter was developed, accounting for its complex structure, material properties, nonlinear components, and intricate contact relationships. Using this model, the influence of geometric parameters of annular rubber components and bushings on the triaxial properties of these critical limiters was analyzed. These findings provide direct theoretical support for multi-objective co-design of limiters targeting impact resistance and vibration damping performance.

PurposeTo accurately identify the role of oil film in the contact heat transfer of ball-raceway and thoroughly characterize the bearing heating, this paper aims to discuss the impact of lubricating oil film on the thermal contact transfer of bearing ball-raceway, and accordingly presents a novel comprehensive contact heat transfer model coupling the thermal dissipation of oil film and the relative motions of bearing ball-oil film-raceway as well.Design/methodology/approachThe Hertz contact of ball-raceway was first analyzed, and how the relative motions between the oil film, bearing ball and raceway affect the thermal dissipation of oil film also was discussed. The oil film thermal exchanges induced by the rolling and spin of bearing balls accordingly were modeled. To further integrate the heat conduction inside oil film, a novel heat transfer network of bearing oil film was constructed, and its thermal equivalent resistance was derived. A novel comprehensive thermal contact transfer model of ball-raceway with the Hertz contact and oil film impacts next was proposed, by which an improved bearing thermal network under oil-air two-phase separation was planned. In the meantime, this newly proposed bearing model, for proving the above findings, was used to arrange a thermal grid for the selected motorized spindle. The thermal changes with or no oil film effect were both simulated. The corresponding numerical results under different operation conditions were also contrasted with the corresponding test values for validation.FindingsThis paper explores the lubrication oil film effect on the contact heat transfer of bearing ball-raceway. The results indicate that the bearing heating is partly influenced by the oil film. For a more precise thermal forecasting, it needs to be factored.Originality/valueThe oil film impacts on the thermal transmission of ball-raceway are discussed in detail and assessed separately, and accordingly a novel equivalent thermal grid of oil film is presented. A comprehensive thermal contact transfer model, meanwhile, is constructed for the first time to thoroughly characterize the thermal contact transfer of ball-raceway.

The traveling wave resonance (TWR) of thin-walled bevel gears in the aviation field continues to pose a significant threat to the overall system’s operational health. Despite extensive research on TWR, the method for determining critical dynamic stress for additional vibration reduction measures remains unclear, and a comprehensive method for predicting the damping effects of supplementary dampers is still lacking. This paper proposes a method for determining the allowable dynamic stress and establishes a single modal forced response (SMFR) model to predict the vibration damping effects of the ring damper. First, the allowable dynamic stress is determined by combining the gear material’s fatigue life curve with the Goodman curve. Using the SMFR model and experimental results, the modal damping ratio and resonance dynamic stress (RDS) at different points can be obtained. The frictional energy dissipation of the ring damper is analyzed to refine the SMFR model, considering the influence of structural parameters of the damper. Additionally, the damping effect is evaluated, accounting for wear between the damper and the gear, providing a solid foundation for the damper’s design. A series of tests, including continuous speed-up tests and speed hold-rise tests, are conducted to identify the TWR speed points and RDS within the working speed range. The dynamic stress reduction within the ring damper is then obtained through both the SMFR model and experimental data. The results show a maximum RDS reduction of over 60 %, with a dynamic stress prediction error of less than 13 %, thus confirming the effectiveness of the proposed model.

As critical transmission components in aero-engines, hard-tooth-surface involute helical cylindrical gears require precise control of surface morphology to ensure high-quality manufacturing with minimized subsurface damage. The complexity of form grinding processes arises from intricate wheel-workpiece spatial kinematics and heterogeneous local contact geometries, which challenge the prediction of chip formation mechanisms and resultant surface topography. This study presents a numerical calculation model to characterize surface morphology in helical gear form grinding. By analyzing localized contact conditions and geometric mapping relationships, the abrasive grain trajectories were mathematically formulated through a spatial helical motion model. The helical tooth surface was discretized to calculate undeformed chip thickness along the normal direction, enabling the reconstruction of three-dimensional surface morphology. Experimental validation using manufactured specimens confirmed the accuracy of the model, with further investigation revealing non-uniform surface distribution characteristics. Key findings demonstrate that surface roughness along the involute profile increases with rolling angle, exhibiting negative correlation with wheel speed, while positively correlating with feed rate and grinding depth. The proposed model provides a theoretical foundation for optimizing helical gear grinding parameters and enhancing in-service performance through surface integrity control.

Thin-walled spiral bevel gears in aviation applications exhibit increased susceptibility to resonance due to their reduced structural stiffness, posing considerable risks to transmission system integrity. Traditional dynamic modeling methods struggle to capture the critical dynamic characteristics introduced by thin-walled structures. To overcome this limitation, this study develops a hybrid dynamic model (HDM) of thin-walled spiral bevel gears system that integrates the gear pair, shaft assembly, and housing structure. This model facilitates the assessment of dynamic properties at critical monitoring locations, enables the characterization of traveling wave resonance (TWR) phenomena, and analyzes the vibration response at web measurement points under different resonance conditions. The proposed model has been rigorously validated through dynamic response experiments. The results indicate that the gyroscopic effect is the primary factor inducing TWR in the gear, which is only observable at the gear nodes. Forward and backward traveling waves exhibit distinct peak responses at frequencies of fm-mfs and fm+mfs, respectively. The resonance speeds and corresponding frequencies are determined by dynamic sweep tests with a maximum error of 5%, and the vibration stresses exhibit deviations within 15%. These findings consistently confirm the model's accuracy. The proposed model demonstrates high precision and provides a reliable analytical framework for resonance testing and identification in aviation thin-walled spiral bevel gear systems.

This study addresses the dual challenges of transcritical and self-excited vibrations in helicopter supercritical tail drive shafts by proposing and validating a novel piezoelectric-actuated limiting ring. A comprehensive dynamic model of the supercritical shaft system, incorporating a floating spline coupling and a limiting ring, is established. This high-fidelity model characterizes the stiffness and friction torque of the spline, along with the rub-impact and stick–slip dry friction characteristics of the limiting ring components. Numerical calculations based on this model reveal that while passive limiting rings effectively suppress transcritical vibrations, they inherently face a contradiction: reducing clearance to suppress self-excited vibrations significantly intensifies impact during transcritical passage, widening the critical region and compromising safe operation. To overcome this limitation, the core innovation lies in an active adjustment strategy for the limiting ring’s preload force, leveraging piezoelectric actuation. This strategy dynamically applies a smaller preload during critical speed passage to minimize impact and rapidly traverse the critical region, then adjusts to a larger preload in the stable operating regime to efficiently suppress self-excited vibrations. Both theoretical analysis and numerical simulations demonstrate the significant potential of this active limiting ring in simultaneously achieving safe transcritical passage and effective self-excited vibration suppression. Finally, experimental validation using a specially designed supercritical shafting test rig confirms the accuracy of the established dynamic model. Crucially, the experiments validate the engineering feasibility and effectiveness of the proposed piezoelectric-actuated limiting ring, offering a promising, novel solution for advanced vibration control in helicopter tail drive shaft systems.

Spline wear threatens the reliability of mechanical transmission systems, but conventional monitoring fails to reconcile heterogeneous data, capture dynamic degradation, or delineate hierarchical states. Here we present a geometric deep learning framework for multisensor fusion: vibration (macroscopic dynamics) and acoustic emission (AE, microscopic damage) signals are encoded as symmetric positive definite (SPD) matrices to form a Riemannian manifold. Log-Euclidean metrics and Riemannian means mitigate cross-modal misalignment, while an attention-based graph neural network (GATConv) fuses features to learn spatiotemporal dependencies. Fused representations are embedded into Poincare ball space-leveraging hyperbolic geometry's exponential volume growth to enhance hierarchical wear separability-with unsupervised clustering and temporal mapping enabling time-resolved monitoring. On industrial datasets (slewing bearing, spline wear), the framework consistently outperforms mainstream methods by achieving effective cross-modal alignment, superior clustering quality, and accurate full-cycle wear tracking. This work establishes a geometric deep learning paradigm for mechanical health monitoring, advancing predictive maintenance in critical engineering systems.

Substructures not only affect the heat conduction and contact heat transfer of spindle units, but also impact the radiation and convection heat dissipations, which were extensively studied. More and more integrated structural details for higher thermal forecasting precision raise the complexity of prediction models significantly. This will inevitably result in a contradiction between the accuracy and efficiency of thermal assessment. Considering the high real-time and deep integration requirements of CNC (Computer Numerical Control) machining systems, to perform a dimension pre reduction of complex models and then reconstruct a lightweight and precise thermal grid is an ideal solution to the current challenge. This paper aims at developing a simplification approach of complex thermal grids to assess the spindle heating truly and efficiently, and meanwhile providing an effective way in the prediction accuracy gap improvement of thermal network modeling. For this, a typical spindle unit was selected as an analysis object. The sub structures of its bearings and their external constraints were first simplified and abstracted, and then the full heat network of a typical feature unit (hollow cylinder) was planned. The heat transfer capacity evaluation function with structural constraint was subsequently constructed. By it, the roles of axial heat dissipation, radiation and convection as well in temperature reduction were discussed in detail, which provides a strong theoretical base for next thermal model simplification. The thermal equivalent resistance on a hollow cylinder was accordingly proposed, and a novel dimension reduction approach of thermal networks was constructed. Next, a novel spindle thermal prediction network with radiation heat transfer was planned. It, as a typical application, also was employed to explain the dimension reduction in detail. In this process, we employed the oil-air separation and heat transfer equivalence to further improve the latest multi-node mode of bearings, and meanwhile the double counting on the convective heat transfer of oil-air also was avoided. Finally, the above-proposed work was validated by experiments and contrast. The temperature predictions based on the current and newly developed models with no heat radiation, meanwhile, were performed and compared with the simplified grid for further verification. Both comparative analysis and test verification indicate that the thermal forecasting is more lightweight with high accuracy. This dimension pre reduction way evidently also benefits improving the forecasting precision shortcoming effectively because there is no worry about the complexity of the developed thermal assessment networks by employing it. These above contrast researches, in the meantime, also prove our developed spindle heating forecasting grid model considering the thermal radiation effect.

Accurate and lightweight evaluation on heat transfer is an essential step for realistically simulating the manufacturing process and efficiently regulating the service accuracy and life of spindles. Segmentation modeling without sacrificing accuracy is a simple and practical solution. A precise separation coefficient is essential to accurately divide a spindle into front and rear halves and then model them separately. To the best of the authors' knowledge, spindle segmentation modeling has not been extensively studied despite it being widely employed in spindle heating evaluation. This lack of research can be attributed to the failure to provide a sufficient theoretical basis and quantitative support for the employed segmentation coefficients. This paper presents a semi-empirical segmentation factor based on the response surface and assesses spindle heating efficiently and precisely for the first time. The effects of various operating settings on the spindle thermal figure and its peak area variation are first tested and discussed experimentally, and the response surface method is employed for identifying the axial spindle peak temperature location. Segmentation coefficients are formulated with integrated spindle structure features, and subsequently, a thermal network of the half spindle is designed to predict spindle heating; the numerical results are compared with the corresponding experimental results for proving our work. In this process, a more lightweight and accurate semi-empirical thermal grid of bearings based on gray-box and oil-air two-phase heat transfer separation was employed for developing a simpler model and a higher thermal forecasting efficiency. The prediction precisions of the current partition coefficients were introduced for contrast and verification. The result confirm that thermal forecasting deviation can be reduced to nearly 5% with the proposed factors. Further, the prediction efficiency is enhanced by more than 70% when using the proposed factors compared to that when simulating the entire spindle thermal network.

Floating spline couplings, crucial for aviation transmission systems, are susceptible to self-excited vibration (SEV) due to friction, especially under lubricant loss conditions. However, research on spline-connected rotor systems under complex maneuvering flight, a critical operational environment, remains largely unexplored. This study establishes a comprehensive dynamic model of a helicopter spline-connected shaft system operating under maneuvering flight, integrating nonlinear spline stiffness and friction torque models. The developed model is thoroughly validated against experimental data from a spline-coupled test rig and through comparisons with reference results. The shaft system's dynamic responses across three distinct maneuvers are analyzed to investigate how maneuvering parameters influence SEV. The findings reveal that maneuvering flight profoundly influences SEV, inducing shifts in vibration trajectories and strong bending vibrations that progressively intensify with decreasing turning radius and increasing climb height. Additionally, increased spline transmissible torque, observed during more aggressive maneuvers, augmented SEV. Analysis of spline meshing forces consistently showed an uneven load distribution within the coupling during dynamic maneuvers. Furthermore, it is found that a reduction in turning radius perturbed the shaft's vibration, causing the self-excited vibration to gradually diminish and ultimately disappear without reoccurring. This offers a novel insight: a strong maneuver perturbation could potentially force the shaft system out of severe SEV. While further validation is needed, this concept presents a promising direction for self-excited vibration mitigation strategies.

To conduct in-depth research on the fatigue life of coaxial reverse twin rotating rotor shafts, a model of the coaxial reverse twin rotor shaft is established. Based on static analysis, the stresses under different loads are examined. Using the equivalent stress-based multi-axial safety life assessment method, the normal and shear stress components of the danger point are extracted after simulation, and the stress amplitude and average stress are calculated. A four-parameter S-N curve equation is used to predict the number of cycles of the inner and outer rotor shafts under a specific load condition; the average S-N curve is adjusted using a life reduction system and strength reduction coefficient to yield a safe S-N curve. By repeatedly iterating the Miner linear cumulative damage theory, the high cycle fatigue load of the rotor shaft is calculated, along with its fatigue cycle number. The predicted lifespan value is 6.40 × 106. Experimental technology research on the rotor shaft is conducted, utilizing a hydraulic loading test bench to gather rotor shaft strain data, which verifies the reliability of the simulation model and settings. The relative error between the test values and simulation values of various sections under different loads is within 15

In the modeling and analysis of herringbone star gear train (HSGT), the differences in dynamic parameters and loads on both sides of the herringbone gears are usually ignored, which seriously impairs the system load-sharing performance. In this paper, the component modal synthesis method is used to solve the condensation model of the casing and the carrier. A herringbone gear meshing model with tooth surface modification and uneven meshing deformation is proposed, which accurately characterizes the dynamic load distribution of helical gears on both sides. Then, a rigid-flexible coupled dynamic model of HSGT is constructed. The effects of differentiated support stiffness on both sides and modification parameters on the offset load are analyzed, and multi-objective optimization of the dynamic performance of HSGT is carried out. A star gearbox test bench is built to test the improvement effect of differentiated modification parameters on offset load. This study provides guidance for the structural and modification design of HSGT, and improves the system load-sharing performance and vibration characteristics.

Floating splines are widely used in helicopter tail transmission systems due to their simplicity, reliability, and high specific power. However, long-term operation leads to lubrication degradation, which increases tooth surface friction and may even introduce self-excited vibrations, thereby affecting system stability. To address this issue, a self-excited vibration suppression method for a supercritical spline-shaft system based on a piezo-actuated smart dry friction damper is proposed. The proposed method integrates piezoelectric actuation control into the conventional dry friction damper of the helicopter transmission shaft system. A dynamic model of the supercritical shaft system incorporating a floating spline and a dry friction damper is established, and numerical simulations are conducted to reveal the self-excited vibration characteristics. The coupled dynamic response is further derived to verify the feasibility of suppressing self-excited vibration through the damper. Finally, the structural design and control strategy of the piezo-actuated smart dry friction damper are presented. The findings provide new insights and theoretical references for vibration control and damper design of spline-shaft systems in helicopter.

Gears are commonly utilized in marine transmission systems because of their fast rotational speed and heavy load, which can readily create traveling wave resonance. Adding a damping ring to the gear to reduce vibration is an efficient way to improve the vibration performance of gears. The damping ring is inserted into a groove that has been opened inside the wheel rim to create friction and energy consumption. Based on the energy method, equivalent parameter models of the damping ring are established, the structure is simplified into amplitude-dependent equivalent parameters, and amplitude frequency response analysis under steady-state response is conducted. Analyze the vibration reduction effect of the damping ring under different influencing factors. Study how the geometric parameters of the damping ring affect the vibration performance. Optimize the damping ring's structural characteristics to achieve the optimal contact pressure under diametral pitch vibration, and determine the damping ring parameters with the best vibration reduction effect. The results indicate that the optimized damping ring has a resonance stress reduction ratio of about 50

Additional loads introduced by maneuvering flight of shipborne helicopters can readily couple with the folding device and excite abnormal vibrations of the foldable tail horizontal shaft system. To address this issue, this study develops a dynamic model of the foldable tail horizontal shaft system under maneuvering flight, where the airframe motion parameters are consistently transformed into additional loads. Two representative maneuvers, Eagle Strike and Zigzag Evasion, are then considered to investigate the dynamic characteristics. The results show that maneuvering flight induces a deviation in the vibration response and introduces pronounced low frequency components. Parametric analysis indicates that increasing the flight altitude from 50 m to 150 m changes the whirling orbits amplitude by 0.9%, whereas increasing the flight speed from 45 m/s to 55 m/s increases the orbit amplitude by 35.7%, demonstrating that speed has a more pronounced amplification effect on bending vibration responses. Steady state bench modal and operational tests further validate the model credibility, with a maximum error of 1.6% for the first two critical speeds and a peak response deviation of 8.6% in the operational test. These findings provide a theoretical basis for vibration assessment, structural optimization, and the extraction of monitoring indicators for the foldable tail horizontal shaft system under maneuvering flight.

Composite drive shafts, characterized by lightweight, high specific strength, design flexibility, and fatigue resistance, have been widely used in aerospace, marine, and rail transportation drive systems. This paper presents the design of an integrally molded composite drive shaft benchmarked against an aluminum alloy counterpart, with particular focus on structural optimization of the flange bolt connection region and the shaft-tubeflange transition zone. Finite element models with various bushing configurations and dimensions were constructed using ABAQUS for the bolted joint analysis. Additional models were developed for the shaft tube-flange transition region and the transition fillet. Strength verification and mechanical performance analysis were conducted using the Tsai-Wu and Hashin failure criteria to identify the optimal engineering solution. Furthermore, a finite element model of the integrally molded composite drive shaft was established to analyze torsional strength, bending stiffness, torsional stiffness, and natural frequencies, with simulation accuracy validated through experimental testing. The results indicate that the designed integrally molded composite drive shaft is 10% lighter than the original aluminum alloy version and withstood a static torsion test of 35,000 N m without failure. Notably, the flanged bushing effectively enhances the torsional strength of the flange, and the transition zone design alleviates stress concentration. This study provides a theoretical basis for lightweight design of integrally molded composite drive shafts.