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.

The composite tail drive shaft of the helicopter offers the advantages of high power density, excellent vibration damping characteristics, and superior energy absorption properties. However, it is vulnerable to ballistic impact threats under operational conditions. In this study, ballistic impact tests and finite element modeling were employed to assess and analyze the ballistic impact damage of the composite tail drive shaft. To simulate the intra-laminar high-velocity impact damage behavior of composites, a dynamic damage model was developed based on continuum damage mechanics and 3D-Hashin criterion. The cohesive zone model was used to characterize the inter-laminar damage initiation and propagation of composites. Additionally, to account for the strengthening effects caused by high strain rates, the strain rate correlation coefficients were introduced to modify the constitutive model. The bullet's residual velocity, the impact process, and the damage morphology of composites obtained from numerical simulations and impact tests demonstrate a high degree of consistency, effectively validating the reliability of the simulation model. Subsequently, using the validated simulation model, the detailed impact damage process and failure characteristics under different typical impact conditions were analyzed and compared. Delamination, matrix tensile damage, and fiber tensile damage were identified as the dominant failure modes, with edge impacts causing more severe damage than central impacts. Furthermore, the effects of offset distance and incident angle on the ballistic impact damage were investigated, revealing significant non-monotonic effects on material removal volume and the bullet's residual velocity.

Dynamic performances of floating splines are directly related to the safe operation of helicopter transmission systems. The dynamic behaviour analysis of floating splines should comprehensively consider the coupling effects of O-rings, locating surfaces, and misalignment. Currently, this type of spline dynamic model is not yet available. Considering the locating surface rub-impact, misalignment, vibration displacement, this study modeled the meshing state of spline teeth and reserved clearance of locating surfaces, simplified O-rings into mechanical Voigt models, and then proposed a general floating spline dynamic model. By coupling the floating spline to the spline-rotor system, the equation of motion for the spline-rotor system is obtained, whose accuracy was verified through dynamic experiments on the spline-rotor system dynamic experimental rig. Detailed effect mechanisms of locating surfaces, O-rings, misalignment, and vibration displacement on the spline-rotor system were revealed. The floating spline dynamic model proposed in this paper can accurately determine whether locating surfaces are rub-impact or not, which can provide theoretical basis for the dynamic design of floating splines and related rotor 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.

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.

ObjectiveThe encased differential planetary gear train of a coaxial helicopter consists of numerous components with varying failure probabilities. Identifying weak components and potential failure modes is critical for implementing targeted measures, such as structural optimization or material substitution, to enhance the system's service life and reliability.MethodsFirstly, a comprehensive risk assessment model was developed by integrating fuzzy set theory with the technique for order preference by similarity to ideal solution (TOPSIS). Secondly, trapezoidal fuzzy numbers were utilized to construct a robust fuzzy evaluation matrix, and a hybrid weighting scheme combining the analytic hierarchy process (AHP) and the entropy weight method was implemented to determine objective and subjective index weights. Finally, an expert scoring framework was established, and a ranking index was calculated for each component to prioritize failure risks.ResultsThe analysis results demonstrate that among the gear components, the sun gear of the differential stage exhibits the highest risk index, identifying it as the weakest part of the system. The primary failure modes are determined to be tooth surface wear and tooth root cracks. The evaluation results provide clear technical guidance for the structural optimization and material replacement of this gear train.

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.

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.

To clear the effect mechanism of self-excited vibration instability on the supercritical tail drive shaft system (STDSS), this paper established the finite element dynamic model of the STDSS, studied the self-excited vibration mechanism, and revealed the effect mechanism of key parameters on self-excited vibration. Results show that the negative damping generated by the larger spline tooth surface friction is greater than the system damping at supercritical speed, leading to self-excited vibration of the system in supercritical conditions. It causes the system to maintain a larger vibration amplitude even after passed the critical speed. At the same time, the system’s response includes the rotational frequency component and the self-excited vibration component near the first critical speed. The degree of self-excited vibration has a direct ratio to the spline teeth number, the spline tooth friction coefficient, the shaft inner diameter, and an inverse ratio to the shaft outer diameter. When there is no O-ring sealing ring, the self-excited vibration amplitude significantly increases, and the unstable speed significantly decreases, which has a significant damping effect. The critical speed and unstable speed of the system are different due to the effect of the shaft material.

In response to the requirements for modern high-speed helicopters, including high-torque capacity, significant angular misalignment compensation, and lightweight design, this paper proposes an integrated composite drive shaft design method incorporating a variable-thickness membrane disk. Firstly, Draw on existing mature ply schemes to undertake the new drive shaft design. Subsequently, by comparing the angular compensation capabilities of rectangular, circular, tapered, and trapezoidal membrane disk configurations, the optimal configuration is selected. The specific dimensional parameters of this configuration are then determined using a co-simulation optimization approach integrating ABAQUS and Isight. On this basis, guided by the principle of equal stress distribution on the membrane disk surface under extreme working conditions, a variable-thickness disk profile is designed by adopting a stepwise discrete ply-drop-off methodology from the inner to the outer region, ensuring the continuity of the primary fibers. Furthermore, finite element analysis is performed to evaluate the strength and modal characteristics of the integrated drive shaft. Experimental validation of its modal and stiffness properties is conducted, and the close agreement between the experimental results and theoretical analyses confirms the effectiveness and feasibility of the proposed design method. The findings of this study can provide a theoretical foundation for the design of drive shafts for high-speed helicopters.

The ballistic impact identification method for the helicopter Tail Drive Shaft System(TDSS) isn't yet comprehensive, which affects helicopter flight safety. This paper proposes a ballistic impact identification method for the TDSS based on vibration response analysis. Based on the Johnson-Cook constitutive model and failure criteria, the ballistic impact finite element simulation model is established, which is verified by the ballistic impact experiment of the Tail Drive Shaft(TDS). Considering the ballistic impact excitation force, the dynamic model of the TDSS with ballistic impact is established, which is verified by finite element commercial software. If a bullet hits the TDS, the bending vibration displacement increases sharply at a certain moment and then significantly increases but remains stable. Meanwhile, the critical speed component appears in the frequency-domain response of bending vibration, and then the speed component significantly increases but remains stable. What's more, the axis trajectory exhibits a sudden, large-scale, and irregular whirling motion at a certain moment, followed by a significant increase but remains stable.Furthermore, if the axial vibration response is small, the bullet core shooting should be considered vertically or at a small incident angle, otherwise, it should be considered at a large incident angle.

In the research on the coupling vibration mechanism of the bearing installation misalignment and rub-impact, the existing research hasn’t considered the change in the rub-impact clearance caused by bearing installation misalignment, resulting in its incomplete understanding. Therefore, considering the change in the rub-impact clearance and the six degrees of freedom (6-DOF) rub-impact excitation force, the coupling geometric model of the bearing installation misalignment and rub-impact is first proposed. The dynamic model of the supercritical shaft system with the bearing installation misalignment and rub-impact is established, and then first reveals the coupling vibration mechanism of the bearing installation misalignment and rub-impact. The established supercritical shaft system dynamic experiment bench verifies the dynamic model. The research results indicate that the bearing installation misalignment would reduce the rub-impact clearance, increase the rub-impact force, lead to a larger rub-impact range, may even cause the backward whirling phenomenon, and thus weaken the vibration reduction performance of the dry friction damper. The bearing installation misalignment causes the axis trajectory to deviate with a deflection angle approximately equal to the arctangent value of the vertical misalignment and the horizontal misalignment in the rub-impact state, which can be used to analyze the form of the bearing installation misalignment. The vibration mechanism revealed in this paper can provide theoretical support for the dynamic design of supercritical shaft systems.

The isolation system, which protects the gas turbine by isolating the impact from the ship's hull when the ship is impacted, consists of a steel frame and isolation elements. A rate-dependent generalized Prandtl-Ishlinskii model is proposed and the mechanical models of the isolation elements are developed, which are verified by impact tests and found to have a maximum error of 3.05 % in relative displacement and 9.75 % in acceleration. The steel frame is discretized into multiple Timoshenko beam cells, and a stiffness matrix establishment method for spatial rigid-flexible coupling unit is proposed to establish the dynamics model of the isolation system. The maximum error in the natural frequency of the steel frame is found to be 8.44 % by comparing with the simulation results, and the maximum error in the natural frequency of the steel frame-gas turbine system is found to be -10.62 %. The impact dynamics calculations are completed based on the pseudo-force method, and the influence of the isolation elements arrangement on the isolation performance is analyzed in conjunction with the energy transfer between modes. The isolation system has the highest energy share for the 7th, 8th, and 11th order modes, and it does affect the energy share of each order mode when changing the number, position, and spacing of the isolation elements.

Compared to conventional helicopters, high-speed helicopters demonstrate higher maneuverability, leading to increased maneuvering loads on transmission system. The supercritical drive shaft in these helicopters, duo to its extended span and high flexibility, is susceptible to exhibit complex dynamic behaviors during maneuvering flight, potentially leading to severe vibrations and even abnormal operation. To investigate these behaviors, the dynamic model of the supercritical drive shaft system equipped with a dry friction damper in coaxial high-speed helicopters (CHH) under maneuvering flight is established based on the Lagrange's principle. Considering the flight characteristics of CHH, the vibration characteristics of the supercritical drive shaft system in both transition and airplane modes are revealed through time history diagram, bifurcation diagram, Poincare maps and whirling orbits, with a specific focus on the responses during serpentine and dolphin jump maneuvers. The results indicate that the supercritical drive shaft system exhibits complex dynamic behaviors, such as non-synchronous vibrations, bifurcations, asymmetrical vibrations and jumping phenomena, when subjected to maneuvering flight in conjunction with the effects of the dry friction damper. The effects of the maneuvering parameters on the transient responses are further revealed, including the turning radius of serpentine maneuver and the climbing height of dolphin jump maneuver. Through this investigation into the nonlinear vibration characteristics of supercritical drive shaft system under maneuvering flight, the study of this paper can offer some insights for the dynamic design of transmission systems in high-speed helicopters with high maneuverability and agility.

The supercritical drive shaft is becoming increasingly popular in helicopter transmission system. Dry friction dampers are specially employed to ensure the supercritical shafts crossing the critical speed safely. Due to design tolerances, manufacturing errors and time-varying factors, the parameters of the damper are inherently uncertain, affecting the safety performance of the rotor system. This paper incorporates these parameter uncertainties to investigate the dynamic response uncertainties of a supercritical shaft and dry friction damper system, which is characterized by its high dimensionality and nonlinear behaviors of rub-impact and dry friction. The nonintrusive Polynomial Chaos Expansion (PCE) is adopted to achieve the propagation of uncertainties in the rotorsystem. To achieve efficient uncertainty quantification for this high-dimensional nonlinear system, a double-layer dimensionality reduction algorithm combining modal superposition with sparse grid technique has been applied. In the computational workflow, the inner layer uses modal superposition and the outer layer uses sparse grid techniques. The stochastic dynamic response of the rotorsystem is analyzed considering the uncertainty of five design parameters of the damper. Furthermore, as a post-processing of the PCE coefficients, the Sobol global sensitivity analysis is conveniently conducted. The influence of individual parameters or groups of parameters on the dynamic response is studied. A multi-objective optimization design for the key parameters is then carried out based on the established PCE model. The dynamic model and optimization design method are verified by experiments. The results will benefit uncertainty quantification analysis of high-dimensional nonlinear rotorsystem.

The marine damper is a crucial component for vibration isolation and shock resistance. In this study, a parametric finite element model of the damper is established and validated through experiments. Dynamic and shock excitations are applied to the damper, and a comprehensive dataset is generated. A random forest regression model is employed to build the surrogate model, with Bayesian optimisation used for hyperparameter tuning. The maximum acceleration and maximum relative displacement are set as the optimisation objectives, while the static displacement and natural frequency serve as constraints. A genetic algorithm is then applied to optimise the structural parameters of the damper, and the results are validated through simulations. The optimisation results indicate that the surrogate model based on random forest regression achieves a coefficient of determination above 0.9 for all predicted indicators. Additionally, two sets of highly effective optimisation results are obtained, with prediction errors within +/- 5%.

The encased differential gear train features a high speed-ratio and a compact structure, enabling coaxial reverse rotation of twin rotors. However, gear cracks can reduce stability and may lead to safety incidents. Additionally, nonlinear factors complicate vibration responses, posing challenges for fault diagnosis. Therefore, investigating the nonlinear behavior and stability of the cracked system is crucial and significant. The dynamic model of the encased differential gear train is proposed and validated through an experiment, considering nonlinear factors involving timevarying mesh stiffness, tooth backlash, and comprehensive transmission error. Responses of sun gears in both stages, under healthy and cracked conditions, are analyzed using bifurcation diagrams, phase diagrams, Poincare diagrams, time series, and FFT spectra at different input speeds. Results show that the system exhibits chaotic, quasi-3-periodic, and 3 T-periodic motions with varying speeds under healthy conditions. Impacts of crack on system responses vary with input speeds, and stable motion rather than chaotic is preferable for fault diagnosis. Crack propagation destabilizes the system. Moreover, the differential stage is more sensitive to the encased-stage crack than the encased stage itself. The influence of transverse stiffness of the intermediate shaft on the system stability is also examined, indicating that the system becomes more stable with increased stiffness under both normal and fault conditions. Notably, with a 50 % increase in stiffness, the sun gear in the differential stage becomes stable under fault conditions. This study investigates crack-induced responses in this single-input, dual-output planetary gear train, providing valuable insights for mechanical design from the perspective of reliability and fault diagnosis in multi-stage gear systems.

Piezoelectric actuators (PEAs) play a key role in precision engineering, but their strong rate-dependent hysteresis affects accuracy. Existing hysteresis models fail to capture the simultaneous rotation and expansion of hysteresis at high rates. This paper proposes a modified Prandtl-Ishlinskii model in a Hammerstein-like architecture (HAMPI) aiming to model the rotation and expansion of the hysteresis at different input rates. Simulations and experiments are conducted to validate the HAMPI model across a wide range of input rates (50-500 Hz) and amplitudes (0-140 V), revealing that the proposed model has the root-mean-square error (resp. relative root-mean-square error) of 0.47 mu m (resp. 3.07%), which is lower than the results of existing hysteresis model. Additionally, a HAMPI-based feedforward controller with the inverse multiplicative structure shows that the tracking performance RMS error (resp. NRMS error) can be kept within 0.09 mu m (resp. 2.25%) when the operating frequency is below 150 Hz. Meanwhile, the displacement attenuation issue in feedforward control caused by the rate-dependent rotation of hysteresis loops is also successfully addressed by the proposed HAMPI model.

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.

With the development of aerospace technology, variable sweep wing aircraft have attracted attention for their excellent performance. Accurate analysis of their structural mechanics and multi-field coupling performance is a challenge. The research aims to analyse the structural mechanics and multi-field coupling performance of variable sweep wing aircraft. Using numerical simulation methods, the influence of four coupled fields of motion, vibration, heat, and aerodynamics on aircraft performance was comprehensively considered, with special attention paid to the two factors of contact friction coefficient and heat dissipation environment temperature. The results indicated that the overall stress distribution was relatively uniform, and no obvious stress concentration "hot-spots" were observed. In the absence of gravitational equilibrium, the contact forces of contact force numerical model (CFNM)1, CFNM2, and CFNM3 ultimately reached 3.5 x 1.63 N, 3.3 x 1.63 N/2.9 x 1.63 N. The maximum stress in a vibration environment was negatively correlated with the contact friction coefficient. When the contact friction coefficient increased from 0.8 to 1.2, the stress decreased from 191 MPa to 68 MPa. In addition, when the cooling environment temperature reached 50 degrees C the maximum stress in the structure exceeded 100, indicating that the structure no longer met the strength requirements. The results proposed a significant impact of contact friction coefficient and heat dissipation environment temperature on the structural performance of aircraft, and provided important information for improving flight safety and structural optimisation design.