Aiming at the rotor shaft of the common axis reverse transmission system, the optimization design of the transmission system structure was studied. By response surface optimization method, a response surface optimization model based on the finite element simulation analysis software ANSYS workbench was established. According to the fitted response surface model, the structure optimization design of the inner and outer rotor shafts was carried out. Taking a set of inner and outer rotor shafts as an example, effectiveness of optimization of the rotor shaft structure of a common axis reverse transmission system based on response surface method is verified.

This paper presents a PID-based feedback control strategy for the smart spring vibration-reduction system (SSVRS), which is intended to suppress transverse vibrations in rotating machinery caused by mass imbalance. A transfer function model of the SSVRS is first established to systematically design the controller. This model allows the distinct modulation of the system's damping, stiffness, and mass characteristics by the proportional, integral, and derivative parameters to be analyzed in detail. Based on this analysis, a novel feedback control strategy is proposed which dynamically selects and combines PID components according to real-time vibration states, achieving adaptive and effective suppression. Comprehensive simulations demonstrate the performance of the strategy: the peak vibration response under swept excitation is reduced by 66.1%, while under impulse loading, displacement offset decreases by 30% and recovery time is reduced by 70%. Experimental validation on a rotating machinery test rig confirms a 51.0% reduction in the resonance peak, thus substantiating the practical effectiveness of the proposed approach and its superior vibration suppression capability.

This paper addresses the lack of proper design methods and the current status of being in the engineering imitation stage in the research of viscoelastic dampers for supporting helicopter tail drive shafting by proposing a systematic optimal design approach. First, a dynamic model of the tail drive shaft coupled with a viscoelastic damper is created using the finite element method. The influence of different viscoelastic dampers on the vibration characteristics of the tail drive shaft during the transcritical process and at supercritical stable speeds is studied, after which a test bench is constructed for verification. Next, the impact of the material and structural parameters of the viscoelastic dampers on the vibration characteristics of the tail drive shaft is investigated, and the parameters with the most significant impact are identified. Finally, a surrogate model is created using back-propagation (BP) neural network, with the key parameters of the viscoelastic damper as the input and the maximum displacement amplitude of the tail drive shaft during the transcritical process as well as the displacement amplitude at supercritical stable speeds as the output. Furthermore, the optimal design of the viscoelastic damper is conducted based on the NSGA-II genetic algorithm to minimize the displacement amplitude of the tail drive shaft. Test results show that the optimized viscoelastic damper achieves a 29.05

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.

This study addresses the severe vibration in multi-span shaft systems during acceleration beyond critical speeds, which limits overall performance. It investigates the effectiveness of a smart spring support for vibration suppression and establishes a corresponding dynamic model. First, a simulation model of the smart spring support was established based on its working principle, considering different combination states of its basic and supplementary supports. The correlation between its dynamic stiffness, damping coefficient, and main influencing factors was analyzed, leading to the development of corresponding response surface models. Subsequently, a dynamic model of the multi-span shaft system integrated with the smart spring support was built using the finite element method to reveal the vibration-damping mechanism under different support states. Finally, experimental tests were conducted to study the system's vibration characteristics. The correlation between the dynamic stiffness, damping coefficient of the smart spring support and their key influencing factors was determined, and their response surface models were successfully constructed. The vibration-damping mechanism of the system under various support combinations was elucidated. Experimental results confirmed that the established dynamic model accurately reflects the actual vibration behavior of the system. The smart spring support effectively suppresses vibration in multi-span shaft systems and enhances their operational performance when crossing critical speeds. The proposed dynamic modeling method is accurate and reliable, providing an effective tool for the analysis and design of vibration control in such systems.

Shipborne helicopters use a folding device to fold the tail pylon, thereby reducing the required deck footprint. However, maneuvering flight leads to the aggravation of misalignment in the folding device, affecting the operational safety of helicopters. To address this issue, a dynamic model of the foldable tail drive shaft system is established based on Lagrange's principle, comprehensively incorporating component nonlinearities, time-varying loads during maneuvering flight and misalignment excitations. Taking turning as a typical maneuvering flight condition, the vibration characteristics of the foldable tail drive shaft system are analyzed via time-domain waveforms, amplitude-frequency responses, and whirling orbits. On this basis, the study further investigates the influence mechanisms of misalignment on the system’s vibration characteristics under maneuvering flight. The results reveals that the foldable tail drive shaft system exhibits vibration pattern deviations under maneuvering flight. Misalignment errors in the folding device can induce second-order frequency vibrations, and angular misalignment contributes significantly more to vibration amplitude than parallel misalignment. The research herein reveals the interactive coupling mechanism between maneuvering loads and misalignment errors, providing a theoretical foundation for the health monitoring and dynamic design of foldable tail drive shaft systems.

ObjectiveAiming at the struts, the key components for the installation and support of helicopter main reducers, the research progress of conventional struts and intelligent struts is analyzed in combination with the development trend of strut structures. [Analyses] The mounting and support layouts of helicopter main reducers are divided into flange type, strut type and other structural forms. The structural characteristics and application scope of each layout are summarized and analyzed. Combined with typical aircraft cases, the application status of different mounting and support layouts in conventional single-rotor and coaxial twin-rotor helicopters is concluded. [Outlooks] The collaborative optimization of lightweight materials and intelligent algorithms is proposed as the key approach to improve the dynamic performance of the support system in the future.

Under high-speed operating conditions, spiral bevel gears may experience a severe failure mode, namely, rapid crack propagation induced by traveling-wave resonance, eventually leading to fracture. Traveling-wave resonance is typically accompanied by intense axial vibrations and is characterized by its sudden onset and high destructiveness. With the development of modern aerospace engineering trending toward lightweight design, the gear web in transmission systems has been increasingly designed thinner. Although this effectively reduces weight, it also significantly decreases axial bending stiffness, making spiral bevel gears more susceptible to traveling-wave resonance during high-speed operation. Therefore, predicting the occurrence of traveling-wave resonance and investigating the resonance responses under different crack states are of great importance for fault prevention. In this study, modal analysis is first conducted to obtain the natural frequencies of the spiral bevel gear. Subsequently, a finite element model for traveling-wave resonance of the spiral bevel gear is established using an explicit dynamic method. The modal characteristics, natural frequency variations, and vibration response changes of the spiral bevel gear in both healthy and cracked conditions with different crack severities are calculated and analyzed. The results provide important theoretical support for early crack fault warning and health monitoring of spiral bevel gears.

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.

Transmission shaft systems are widely used in aviation and maritime fields, and their dynamic behaviours will be changed due to the deformed compatibility of misalignment compensation components caused by the installation platform deformation. At present, the dynamic behaviours of the transmission shaft system with deformed compatibility are still unclear. Therefore, this study focuses on the deformed compatibility of misalignment compensation components and their effect on the dynamic characteristics of the transmission shaft system. We established the parameterized mathematical model for deformed compatibility of the transmission shaft system, developed the FE (finite element) simulation models of the stiffness of the spline joint and diaphragm group, and derived the equation of motion for the transmission shaft system with deformed compatibility. We conducted a detailed evaluation of the effects of different support position deformations on the deformed compatibility angle and the stiffness changes of the spline joint and diaphragm group. Then we further analyzed the displacement response, axis trajectory, frequency spectrum, and amplitude frequency characteristics of the transmission shaft system with deformed compatibility. The experiment rig for the transmission shaft system was developed. The results of the comprehensive experiment were in excellent agreement with the theoretical calculation results, which verified the validity of the research results in this paper. The stiffness changes of the spline joint and diaphragm group, the misalignment force of diaphragm groups, gear meshing excitation force, transmission shaft imbalance excitation, and gravity are considered comprehensively in this paper. This study can provide a theoretical basis for the forward dynamic design of transmission shaft systems.

The folding technology applied to the helicopter tail horizontal shaft system enables more naval helicopters to be accommodated on aircraft carriers. Based on the structural features of the tail horizontal shaft system with a crown gear coupling, this paper develops a dynamic model to investigate the vibration characteristics of the system incorporating the folding device. The model captures the coupling between the crown gears and the helical spline. Unlike conventional simplified models, it explicitly accounts for the geometric relationship between the shaft folding joint and the tail frame hinge. Using the Lagrange equation, the nonlinear microscopic Coulomb friction at the tooth meshing interface is converted into a macroscopic equivalent viscous damping matrix, improving the computational efficiency of the vibration analysis. Three-dimensional finite element simulations are conducted to examine the dynamic characteristics of the system, including critical speed and amplitude-frequency response, and the results are cross-validated. The findings show that the proposed model accurately represents the dynamic amplification effect in the resonance region, with a peak error within 6.1%. This work provides a theoretical basis for the structural optimization and vibration control of next-generation folding transmission systems.

SignificanceAiming at the strict requirements for lubrication performance of face gear transmission in helicopter transmission systems, as well as the problems that the analysis system of tooth surface contact-lubrication coupling characteristics in existing research needs to be improved and the engineering application technical path is not clear, the research progress of face gear lubrication technology was systematically sorted out, and the core technical direction and development trend were clarified. [Analysis] Firstly, the research context of face gear lubrication technology for helicopter transmission scenarios was sorted out, and the core research boundary of this field was defined; secondly, the core technology of tooth surface contact characteristic analysis of face gear was disassembled to provide key input parameters for lubrication characteristic analysis; thirdly, the analysis methods and research results of tooth surface lubrication characteristics of face gears were summarized to clarify the key influencing factors of lubrication performance; finally, combined with the engineering requirements of helicopter transmission, the future key development directions of this field were prospected.

To address the prominent vibration challenges posed by the lightweight design of aviation thin-walled bevel gear systems, this paper presents a systematic investigation into multi source excitation coupling modeling and dynamic characteristics analysis. Fully accounting for the structural characteristics of thin-walled spiral bevel gears, the flexibility of the gear body is incorporated through segmented modeling approach. A hybrid dynamic model is subsequently developed which comprehensively accounts for the multi source excitation effects arising from bearing supports, pitch deviations, and unbalance excitations. It is capable not only of predicting the overall system vibration response but also of capturing vibration characteristics of the gear body, such as traveling wave resonance. This study analyzes the modulation effects of multiple excitations on vibration spectral components, reveals the variation patterns of bearing dynamic contact forces and the amplitudes of various frequency components with respect to unbalance magnitude and rotational speed, and the distinctive characteristics of traveling wave resonance in thin-walled bevel gears are also elucidated. Experimental comparisons demonstrate that the proposed model can accurately simulate the multi-source excitation coupling vibration characteristics of the system, and exhibits good predictive capability, particularly for traveling wave resonance. This study provides a theoretical basis for establishing vibration limits and identifying resonance failure modes in aviation transmission systems.

SignificanceOriented to the supporting and mounting struts of helicopter final drive, the technical development status of periodic and intelligent struts was explored based on the evolution trend of strut structure. [Analysis] Firstly, the layout configurations for mounting and supporting of the helicopter final drive was introduced. Secondly, the structural characteristics and applicable scopes of each mounting and supporting layout were summarized and analyzed. Finally, combined with typical aircraft cases, the application status of various mounting and supporting layouts in conventional single-rotor helicopters and coaxial twin-rotor helicopters was concluded. [Prospect] It is proposed that the collaborative optimization of lightweight materials and intelligent algorithms will serve as a vital approach to improve the dynamic performance of support systems in the future.

The folding device significantly reduces the deck footprint of shipborne helicopters. However, the coupling between its inherent structural nonlinearities and maneuver-induced loads intensifies vibrations in the tail horizontal shaft system. To address this issue, we develop a dynamic model of the foldable tail horizontal shaft system that simultaneously accounts for both component nonlinearities and time-varying loads during maneuvering flight. Using this model, we analyze the dynamic characteristics of the folding device under turning conditions and further investigate how component stiffness influences system behavior. The results reveal that as component stiffness decreases, the amplitude–frequency response of the folding device exhibits pronounced second-order harmonics, increasing the likelihood of resonance within the shaft system. This study elucidates the coupled interaction between maneuver-induced loads and structural nonlinearities in the folding device, thereby providing a theoretical foundation for health monitoring and dynamic design of foldable tail horizontal shaft system.

The supercritical drive shaft system is widely used in the aviation field. It may experience self-excited vibration, misalignment, and rub-impact during operation, which could change the system's dynamic behavior and stability. However, the coupling effect of the law of the three is not clear at present. To address this issue, the dynamic equation of the supercritical drive shaft system considering self-excited vibration, misalignment, and rub-impact is obtained, and the stability analysis is derived. The misalignment decreases the rub-impact amplitude and increases the rub-impact range due to the reduced reserve gap caused by the misalignment. The three can undergo coupling when the lubrication state of the spline tooth surface is relatively poor and the misalignment is large. The coupling effect of misalignment and rub-impact excites the unstable region that appears near the critical speed, and this effect would be weakened by the spline damping introduced by the spline tooth friction. The methods and conclusions presented in this paper provide a technical approach for further optimization of supercritical shaft systems.

The coal washing and processing industry generates substantial quantities of coal gangue, which exerts significant impacts on soil and groundwater environments. Activating the reactivity of inert coal gangue to achieve comprehensive utilization in the field of cementitious materials holds considerable importance. This study investigates a method that synergistically utilizes thermal activation and mechanical activation to enhance the reactivity of coal gangue. The approach aims to reduce the temperature required for thermal activation while effectively stimulating the reactive properties. Furthermore, the mechanisms underlying the thermal–mechanical synergistic activation and its hydration characteristics are thoroughly examined. Experimental results demonstrate that thermo-mechanical synergistic activation, in comparison to sole thermal activation at 950 °C, enhances reaction activity by 28.3%, improves mechanical properties by 27.4%, reduces setting time by 65 min, and significantly optimizes flow performance. The XRD, FT-IR, and TG-DTG analyses demonstrate that the interlayer hydrogen bonds of kaolinite are disrupted during the thermal activation stage, resulting in the formation of amorphous and highly reactive metakaolinite. Subsequent mechanical activation after thermal treatment significantly reduces particle size, further breaks the interlayer hydrogen bonds of kaolinite, and leads to the complete disintegration of the lattice framework. This process markedly enhances the degree of amorphization and thoroughly disrupts the long-range ordered crystalline structure of the kaolinite mineral phase in coal gangue. Concurrently, the d002 interplanar spacing of kaolinite expands by 0.155 Å, leading to an increase in reactivity. SEM-EDS analysis reveals that C-S-H gel is embedded within the mortar matrix, with a reduction in calcium hydroxide content and Ca/Si ratio, and an increase in Al/Si ratio in coal gangue mortar. This confirms that the thermo-mechanical synergistic activation introduces highly reactive Ca2+ and Al3+ from coal gangue into the secondary hydration reaction, resulting in the formation of a gel structure characterized by high stability and enhanced durability.

As a typical type of spatial crossed-axis gear transmission,face gears,with significant advantages such as light weight,compact volume,low transmission noise,high load-carrying capacity and stable operation,were successfully applied in helicopter transmission systems and exhibited excellent transmission performance.Lubrication was identified as a key link to ensure the reliable operation of face gear transmission systems.It could not only effectively suppress tooth surface friction and wear and further enhance the load-carrying capacity of the system,but also reduce noise and vibration during transmission,improve transmission efficiency and prolong the service life of equipment.Firstly,the research progress of face gear lubrication technology for helicopter transmission scenarios was systematically summarized in this paper.Secondly,two core technical directions,namely the analysis of face gear tooth contact characteristics and the analysis of tooth surface lubrication characteristics,were focused on sorting out.then, on this basis,the future development trends of this field were further prospected.Finally,the specific contents of the prospect included the design of high-efficiency lubrication and dry operation of face gears,the accurate measurement of tooth surface oil film thickness and online monitoring technology.

The reducer housing will experience the vibration produced by the gear meshing in the encased differential planetary train. Determining the vibration receiving structure of vibration transmission and analyzing the sensitivity of its parameters can enable researchers to control the parameters with high sensitivity. In this paper, the time-varying meshing stiffness and error equivalent displacement generated during gear meshing are used as intrinsic excitations to systematically analyse the vibration-receiving structure of the encased differential planetary gear to reveal its dynamic characteristics and vibration response mechanism. The state equation of the encased differential planetary train is then used to create the first-order trajectory sensitivity model. The first-order trajectory sensitivity function amplitude is defined as the first sensitivity indicator S1, and the sensitivity change corresponding to the increase in the percentage of the parameter is defined as the peak sensitivity indicator S2 and the mean sensitivity indicator S3, respectively. Based on this, the sensitivity histograms of each parameter concerning the response of the vibration receiving mechanism under the three indicators are obtained. The results show that the sensitivity index of the system mesh damping parameter is much larger compared with the mesh stiffness parameter when the parameter unit value is changed, the peak sensitivity index and the mean sensitivity index have high similarity when the parameter percentage is changed.