The harsh environments of underground mines pose significant challenges for acquiring clear images from operational conveyor belts, thereby hindering accurate foreign object detection and threatening mining safety. In this study, a novel image enhancement technique is proposed to improve the clarity and quality of the collected images. The approach begins by converting images from RGB to HSV color space. The illumination component (V) is then estimated and corrected via a modified weighted distribution adaptive gamma correction (AGCWD) Subsequently, adaptive BM3D (ABM3D) filtering is applied to reduce noise while preserving details. After reducing the color cast through color correction, the S-channel is adjusted based on the contrast stretching algorithm to enhance the image saturation and contrast, and the image is finally transferred back to RGB space. Finally, the MSRCR algorithm is integrated to perform global color correction. Experimental results demonstrate that the proposed method effectively enhances brightness, mitigates uneven illumination, and avoids color distortion, making it highly suitable for enhancing images of foreign objects on underground coal transportation belts. Meanwhile, our proposed method shows significant improvement in several performance metrics such as information entropy and average gradient, which is compared with adaptive histogram equalization with restricted contrast, MSR and MSRCR image enhancement algorithms. Specifically, the information entropy increased by 16.94

Elliptical gears are widely used in the fields of aerospace and automation equipment due to their excellent variable speed characteristics and compact structure. To reveal the control mechanism of phase angle on the motion characteristics of two-stage elliptical gear transmission system (TSEGTS) and improve its stability under variable speed loading, this paper proposes a modeling method that integrates two-dimensional tooth profile envelope method and image processing technology to extract tooth profile and analyze system motion characteristics. By introducing the fluctuation coefficient as a stability indicator, the system studied the effects of phase angle, input speed, and load torque on angular velocity, angular acceleration, and torque. The results indicate that the phase angle has a significant periodic modulation effect on the motion characteristics of the system. The angular velocity and acceleration of intermediate shaft B and output shaft C, as well as the torque of output shaft C, exhibit a distribution with 90 degrees as the axis of symmetry within the range of 0 degrees-180 degrees. The average torque fluctuation coefficients of input shaft A and intermediate shaft B in the range of 0 degrees-90 degrees are 4.02 and 3.03, respectively, which are significantly higher than the 3.46 and 1.99 coefficients in the range of 90 degrees-180 degrees. As the input speed increases from 5 pi to 20 pi rad/s, the torque fluctuation coefficients of shafts A, B, and C increase from 2.87, 1.37, and 0.53 to 22.54, 14.19, and 8.43, respectively. When the load torque increases from 2 to 8 Nm, the fluctuation coefficients of the three axes decrease from 11.33, 7.12, and 4.22 to 3.51, 1.91, and 1.05, respectively. The increase in load torque effectively suppresses fluctuations and improves meshing stability. The experimental and simulation results are consistent, verifying the effectiveness of the model. The research results can provide theoretical basis for parameter optimization and dynamic performance control of TSEGTS.

Gas-bearing-supported gear–rotor systems are widely used in precision measurement equipment, where vibration performance is critically influenced by the bearing support characteristics. In this study, a nonlinear dynamic model of a gear–rotor system supported by gas bearings is established, in which the bending–torsional coupling effect and the bearing support stiffness are explicitly taken into account. Based on isothermal compressible gas lubrication theory, the Reynolds equation is solved using a finite difference scheme to obtain the gas film pressure distribution of the gas bearing. The influences of rotational speed from 500 to 1500 r·min−1 and gas film clearance from 7 to 11 μm on the gas film pressure characteristics and the equivalent support stiffness are investigated. The equivalent stiffness is subsequently incorporated into the dynamic equations of the gear–rotor system to analyze its vibration responses. The results show that increasing rotational speed significantly enhances the gas film pressure and enlarges the high-pressure region along the circumferential direction due to strengthened hydrodynamic effects. In contrast, an increase in gas film clearance leads to a pronounced reduction in pressure magnitude and load-carrying capacity, resulting in a nonlinear decrease in the equivalent support stiffness. Dynamic analysis indicates that rotational speed plays a dominant role in the vibration behavior of the gas-bearing-supported gear–rotor system, while variations in gas bearing stiffness substantially affect the vibration response characteristics.

Focusing on dynamic meshing force identification at the power-combining stage and system-level coupling assessment of a coaxial face-gear power-split and power-combining transmission, this study conducts a comprehensive investigation including tooth-surface contact analysis, rigidflexible coupled system dynamics with a discretized shaft-line, synchronous torque-speed experiments, and model-driven inverse identification of the combining-stage meshing force. First, based on established meshing theory, discretized contact representation of face-gear tooth surfaces is employed, and load-dependent meshing stiffness is derived using Hertzian contact theory. Second, a system-level dynamic framework integrating meshing interactions and a discretized output shaft is formulated to analyze vibration transmission and nodal coupling mechanisms in the multi-component drivetrain. Third, acceleration, torque, and speed responses are measured under various operating conditions, and a model-driven SVD-Kalman filtering scheme is implemented to reconstruct the dynamic meshing force at the power-combining stage from acceleration signals. Results show that the predicted acceleration spectra reproduce the dominant gear meshing frequency (GMF) and its harmonics observed experimentally, while the inversely identified meshing force remains physically consistent with measured dynamic responses. Furthermore, improved load sharing and enhanced synchronization are observed at higher rotational speeds. These findings provide theoretical and experimental insight into dynamic load distribution and coupling mechanisms in complex multi-branch transmissions.

Surface topography and thermal effects strongly influence the lubrication and fatigue performance of orthogonal face gear pairs. However, the lubrication and contact fatigue characteristics of face gear pairs remain insufficiently characterised when both non-Gaussian rough surfaces and micro-scale thermal deformation induced by local temperature rise are considered. This study develops a mixed thermal elastohydrodynamic lubrication (MTEHL) model for orthogonal face gear pairs that considers the combined effect of non-Gaussian rough tooth surfaces and micro-scale thermal deformation. Geometric and kinematic parameters are obtained through tooth contact analysis (TCA). Three-dimensional non-Gaussian rough surfaces are generated using a two-dimensional digital filtering method, and a rank-compressed half space thermal deformation (RHTD) method is developed to efficiently compute micro-scale thermal deformation of the tooth surfaces. A contact fatigue model is formulated to predict relative fatigue life. Model predictions are validated against benchmark solutions, finite element analyses, and oil film thickness measurements. The results indicate that micro-scale thermal deformation of the tooth surface increases the oil film pressure during meshing of the face gear pair. Along the meshing track of the orthogonal face gear pair, the pitch point region exhibits the minimum film thickness and the highest pressure. Higher surface roughness accelerates lubrication degradation and leads to a more dispersed von Mises stress field. Increasing rotational speed intensifies the temperature rise but also thickens the lubricant film and extends relative fatigue life. The proposed framework provides an effective tool for analysing lubrication characteristics and contact fatigue of orthogonal face gear pairs under multiphysics coupling conditions.

To systematically clarify the migration and evolution mechanisms of metallic particles in the solid-liquid-gas three-phase flow field of a helicopter intermediate reducer under splash lubrication, this study innovatively develops a three-phase numerical model based on the CFD-DPM framework, and establishes a high-precision oil-churning visualization test rig for experimental validation via high-speed imaging technology. Under the baseline operating condition (gear rotational speed of 1500 r/min, dimensionless oil immersion depth lambda(h) = 6.78), the effects of multiple hydrodynamic forces (gravity, pressure gradient force, virtual mass force, Magnus lift, and Saffman lift) on particle trajectories and dynamic responses are comprehensively evaluated. Meanwhile, comparative analyses are conducted to quantify the regulatory effects of particle density (intrinsic property variation) and initial release location (meshing region, spallation region, sidewall/bottom) on migration behavior. Numerical results reveal that the pressure gradient force and virtual mass force dominate macroscopic particle transport: the former prolongs the quasi-steady stage by 40%-50%, while the latter accelerates particle velocity decay to near-zero within 0.3-0.5 s. In contrast, the Saffman lift and Magnus lift play secondary roles, mainly inducing high-frequency velocity fluctuations (velocity perturbation amplitude <= 15% for Saffman lift) and exhibiting strong medium dependence (Magnus lift doubles particle migration distance in the gas phase but is negligible in the oil phase). Increasing particle inertia significantly weakens flow-following capability, and the particle velocity response intensity follows the order: meshing region > spallation region > sidewall/bottom. Visualization experiments verify a complete particle transport cycle inside the gearbox (extrusion from the meshing region-airborne flight-wall collision-gravity-driven return), which is in good agreement with numerical predictions. Further experimental results show that increasing the rotational speed from 100 to 400 r/min significantly enhances oil splash height and particle adhesion on the top and side walls. At a high immersion depth (lambda(h) = 11.86), intense turbulent splashing leads to global dispersion of the oil-particle mixture; at a low immersion depth (lambda(h) = 1.70), particle motion is dominated by local entrainment with weak wall retention. Additionally, as the particle volume fraction increases from 0.1%, 0.5%, 1.0%, the oil-particle mixture exhibits a pronounced thickening effect, suppressing oil splashing and enhancing particle deposition. These findings provide robust theoretical support and technical guidance for the optimization of splash lubrication design and reliability assessment of helicopter transmission systems.

This article investigates the multiphysics coupling mechanism among Dynamic Thermal Elastohydrodynamic Lubrication (DTEHL), Load Tooth Contact Analysis (LTCA), and system dynamics in a Closed Differential Herringbone Gear Transmission System (CDHGTS). Based on gear meshing theory, ring gear flexibility, and rough surface contact, a dynamic contact lubrication model is developed using thermoelastic fluid dynamic lubrication theory. A gear heat transfer model integrating heat transfer and flexible deformation is established to capture dynamic thermal variations at each ring gear node. By coupling the DTEHL model, heat transfer model, and LTCA model, a nonlinear dynamic model incorporating flexible-tribo coupling is constructed. The nonlinear dynamic response of the CDHGTS under DTEHL conditions is analyzed, focusing on the influence of ring gear flexibility on system vibration. Furthermore, nonlinear dynamic behavior induced by ring gear flexibility, friction coefficient, and damping coefficient is examined. The proposed model is validated through bench vibration experiments. The study refines dynamic modeling and analysis methods for herringbone gears, offering theoretical guidance for evaluating the impact of coupled engineering factors on gear dynamics.

Non-circular planetary gear systems exhibit significant time-varying transmission characteristics, which can easily trigger complex nonlinear dynamic responses during operation, adversely affecting vibration stability. This paper develops a 36-degree-of-freedom bending-torsional coupling nonlinear dynamic model for 4-6 order non-circular planetary gear systems, incorporating multiple excitation factors, including time-varying mesh stiffness (TVMS), meshing damping, backlash, friction, and comprehensive transmission error. A TVMS calculation method applicable to both internal and external meshing pairs is proposed based on curvature radius theory. The system's nonlinear dynamic equations are solved numerically using the Runge-Kutta method. Nonlinear dynamic analyses, including bifurcation diagrams, time histories, phase diagrams, and Poincare sections, were employed to systematically investigate the influence of key parameters-rotational speed, eccentricity, damping, and backlash on the system response. Multiscale methods were further used to examine their effects on main resonance characteristics. Quantitative results show that the system transitions from periodic motion to 2-periodic and chaotic states as rotational speed increases, with peak vibration amplitudes rising from 1.12 m/s 2 to over 5.6 m/s 2 across tested speeds. Eccentricity critically affects dynamic behavior: under identical speed conditions, the external meshing pair enters a quasi-periodic state at an eccentricity of 0.22, earlier than the internal pair at 0.32. Increasing tooth flank clearance can trigger chaotic responses, whereas enhancing system damping reduces peak amplitudes by up to 32%45%, significantly improving operational stability at medium to high speeds. Finally, a prototype test platform was established to validate the model. Experimental results and theoretical predictions show good agreement, peak to peak comparison has good consistency, confirming that the model effectively captures the system's main dynamic behavior. These findings elucidate the unique nonlinear dynamics of non-circular planetary gear systems, providing a quantifiable theoretical basis for structural optimization and engineering applications.

To elucidate the energy dissipation mechanism of a Standard straight bevel gear transmission system under splash lubrication, this article proposes a churning power loss prediction model tailored to such systems. This model decomposes the total power loss into three parts, namely circumferential resistance, end face stirring, and extrusion loss in the meshing area, and combines the control volume method with the bevel gear slicing method to achieve an engineering approximate quasi analytical model of stirring power loss. A transparent visualization test rig for churning power loss was developed, and systematic experiments were conducted over a range of rotational speeds (1,000-4,000 r/min), the dimensionless immersion depth (defined as the ratio between oil level and gear pitch radius) (0.5-1.5), and lubricant dynamic viscosities (0.0085-0.21228 Pa & centerdot;s). The results show that, as the speed increases from 1,000 r/min to 4,000 r/min, the total churning power loss rises from 135 W to 5524 W; meanwhile, the proportion of end-face drag loss decreases from 51.6% to 38.7%, whereas the contribution of squeeze loss in the meshing region increases from 48.2% to 61.3%. At 2,000 r/min, when the dimensionless immersion depth increases from 0.5 to 1.5, the total power loss increases from 283 W to 1559 W, and the share of mesh-region squeeze loss rises from 44.5% to 58%, becoming the dominant dissipation component. Under high-speed conditions of 4,000 r/min and dimensionless immersion depth of 1.0, increasing the lubricant viscosity from 0.0085 to 0.21228 Pa & centerdot;s causes the total power loss to increase from 774 W to 8176 W, with the dominant loss mechanism gradually transitioning from viscous shear to hydrodynamic squeeze. The theoretical predictions and experimental data trends are roughly consistent, confirming the accuracy and applicability of the proposed model under a wide range of operating conditions, and providing a quantitative basis for energy optimization of high-performance bevel gear transmission systems.

Asymmetric pitch deviation (APD) is an inevitable manufacturing deviation in herringbone gear pairs, and existing research literature has not yet conducted in-depth exploration into the effects of APD on the load distribution, multi-origin excitation, and vibration behaviors of herringbone gear throughout the entire tooth meshing cycle (ETMC). Moreover, the objective functions of existing optimization models are mostly set to multi-origin excitation and vibration acceleration, lacking an optimization design method that can balance the load uniformity performance and vibration performance of the ETMC. To solve these problems, a tooth contact analysis (TCA) model, an enhanced loaded tooth contact analysis (LTCA) model, and a meshing impact force (MIF) model for herringbone gear were first established. The load distribution coefficient (LDC), load distribution, comprehensive meshing stiffness (CMS), axial displacement (AD), comprehensive meshing error (CME), and MIF of the ETMC were obtained. A dynamic model for herringbone gear system considering the multi-origin excitation of the ETMC was constructed, with the corresponding parameters involved in the model calculated systematically. A general expression for tooth surface modification (TSM) was derived, and a mathematical model for the collaborative optimization design of load uniformity and vibration of herringbone gear was established. The variation laws in multi-origin excitation and vibration behaviors of the ETMC under different asymmetric pitch deviations (APDs) were revealed, and the vibration characteristics of the ETMC before and after TSM were compared. The correctness and effectiveness of the proposed method were experimentally verified. This research provides support for the load uniformity and vibration reduction design of herringbone gear.

Increasing the Cu content is an important approach to enhancing the strength of Al-Cu alloys, but the widening of the solidification temperature range leads to deterioration in the casting performance of the alloy, significantly limiting its application. This work investigates the effect of Sc content on the microstructure and mechanical properties of Al-Cu-Mg-Mn-Ti alloys with high Cu content. The results show that the solidification path of the Al-8.5Cu-0.3Mg-0.35Mn-0.2Ti-xSc alloy changes when the Sc content reaches 0.37%. When the Sc content is less than 0.37%, the primary phase is α-Al, whereas when the Sc content is greater than 0.37%, the primary phase is Al3Sc. As the Sc content increases to 0.4%, the grain size of the alloy first decreases and then increases, with the smallest grain size occurring at a Sc addition of 0.3 wt.%. Accordingly, the tensile strength of the alloy at both room temperature and high temperature reaches the highest when the Sc content is 0.3 wt.%. Specifically, the alloy's tensile strength at room temperature reaches 327.2 MPa, an increase of 14.0% compared to the alloy without Sc, and the alloy's tensile strength reaches 103 MPa at 350 °C, an increase of 24.5% compared to the alloy without Sc. It is speculated that when Sc is added to the Al-Cu melt, it refines the grains by forming Al3Sc heterogeneous nucleation cores, and it may also form Sc-containing precipitates with higher temperature resistance, which boosts the alloy's strength.

To clarify nonlinear instability in the coaxial orthogonal face gear power-split and confluence transmission system, this study develops a 21-degree-of-freedom multi-backlash bending-torsion coupled dynamic model based on the lumped parameter method. The model incorporates piecewise backlash nonlinearity, time-varying mesh stiffness and tooth surface friction, and is solved using a nondimensional variable-step fourth-order Runge–Kutta scheme. Combined with bifurcation diagrams, Lyapunov exponents and other analytical methods, the influence laws of rotational speed, tooth backlash, damping coefficient and friction coefficient on the bifurcation evolution and chaos of the transmission system were revealed. The results show that increasing backlash from 0 to 50 μm expands the sensitive resonance region by about 37

Study on the effects of backlash, friction, and rotational speed on the nonlinear bifurcation characteristics of Non-Orthogonal Misaligned Face Gear Power Split-Flow Transmission System (NOMFGPSFTS), aiming to provide theoretical basis and technical guidance for improving power to weight ratio, prolonging service life, and ensuring the reliability of the power transmission mechanism of innovative helicopters, ships and automobiles. An 11 degree of freedom (DOF), bending, torsion and axis coupling nonlinear dynamic model is established by using the lumped mass method. The model uses Load Tooth Contact Analysis(LTCA) method to calculate the meshing stiffness of Non-Orthogonal Misaligned Face Gear (NOMFG), and combines the key nonlinear elements, including gear tooth surface friction, backlash, support stiffness and transmission error, to facilitate an accurate representation of the system dynamics. The system's dynamic differential equations are solved using the RungeKutta algorithm, and the system's nonlinear characteristics are demonstrated through time domain diagrams, Fast Fourier Transform (FFT) spectrograms, phase plane diagrams, Poincare maps and Maximum Lyapunov Exponent diagrams. Bifurcation diagrams are used to further reveal the effects of backlash, rotational speed, and friction coefficient on the system's nonlinear behavior. The study finds that with the increase of dimensionless backlash, the system transits from periodic-1 motion to chaotic motion, and may evolve into periodic-2 motion, showing obvious nonlinear vibrations. With the increase of rotating speed, the system transits from periodic-2 motion to chaotic motion, and finally realizes periodic-1 motion. With the increase of friction coefficient, the chaotic region of the system decreases. Finally, the correctness of the theoretical model is verified by experiments, which provides a theoretical basis for the stability study of the system.

Most of the existing dynamic models of herringbone gear assume that the three major internal excitations, namely, the comprehensive mesh stiffness (CMS), the comprehensive mesh error (CME), and the meshing impact force (MIF), are the same at each meshing period. However, due to the inevitable asymmetric pitch deviation in the machining and installation process, the three internal excitations are coupled with each other and vary in a long period. In addition, since the driving gear usually adopts an axially floating support, this in turn gives rise to a unique axial displacement (AD) excitation of the herringbone gear. Firstly, an improved loaded tooth contact analysis (LTCA) model of herringbone gear with asymmetric pitch deviation is established, and the coupling relationship between multi-source excitation is explored. Secondly, a nonlinear dynamic model of herringbone gear with asymmetric pitch deviation is proposed, and the above multi-source excitation is introduced into the model to study the effects of load, speed, and asymmetric MIF on the long period three-dimensional (3-D) vibration characteristics of herringbone gear. Finally, the correctness of the theoretical simulation results is verified by experiments. The proposed novel method can predict the 3-D vibration characteristics of herringbone gear more realistically and effectively.

Due to factors such as eccentric load and error, the gear will produce cracks and pitting corrosion and other failure modes, resulting in the change of the dynamic characteristics of the two-stage herringbone gear transmission system (TSHBGTS), which will have a serious impact on the stability of the operation of the high-torque engine. To investigate the impact of crack-pitting coupling on the vibration characteristics of the TVMS, a dynamic model with 48 degrees of freedom was developed. This model considers various factors such as errors, time-varying meshing stiffness (TVMS), torsional stiffness, support stiffness, tooth friction, and repulsion slot variations. The potential energy method is employed to calculate the TVMS for each herringbone gear pair in the system, accounting for the effects of crack-pitting coupling and changes in the retractor slot parameter. The dynamic model is solved using the Runge–Kutta numerical integration method, enabling the analysis of the system’s time-domain and frequency-domain responses under varying degrees of crack-pitting coupling. The vibration testing explores how different degrees of crack-pitting coupling affect the system’s time-frequency response characteristics. The results reveal that the system’s stiffness decreases with an increasing degree of crack-pitting coupling, initially dominated by pitting and eventually by crack influence. The time-domain response characteristics exhibit shock behavior that varies with the meshing cycle, becoming more pronounced with increased crack-pitting coupling. Additionally, the frequency-domain response is characterized by side frequency signals near the octave frequency, indicative of crack-pitting coupling effects. This behavior exacerbates as the crack-pitting coupling intensifies, leading to deteriorating vibration stability. Comparative analysis of test and theoretical data demonstrates consistency in trends, affirming the model’s accuracy. The research results are of great significance for the dynamic stability and quality evaluation of TVMS.

To investigate the vibration characteristics of the herringbone gear planetary transmission system (HGPTS) with crack-pitting coupling factors, a 55-DOF bending-torsion-axle-pendulum (BTAP) coupled dynamics model of the drive system is established. This model accounts for the effects of errors, time-varying mesh stiffness (TVMS), torsional stiffness, support stiffness, and retract groove. In the model, the TVMS of the sun and planetary herringbone gear pair is calculated, considering crack-pitting coupling using the potential energy method and the slicing method. The dynamics model is solved using the Runge-Kutta numerical integration method, yielding the time-domain and frequency-domain responses of the drive system under different degrees of crack-pitting coupling. The analysis focuses on the vibration response of the system due to changes in crack-pitting coupling. Additionally, vibration tests are performed to assess the impact of different crack-pitting parameters on the system's time-frequency response characteristics. The results show that the time-domain response of the system, influenced by crack-pitting coupling, is characterized by periodic impact behavior, which becomes more pronounced as the degree of crack-pitting coupling increases. In the frequency domain, the system's response exhibits failure frequency phenomena, with noticeable side-frequency signals near the octave frequency. These signals worsen as crack-pitting coupling increases, leading to a deterioration in the vibration stability of the system. A comparison between experimental data and theoretical results shows good consistency, validating the correctness of the model. This research provides a theoretical foundation for fault diagnosis as well as the operation and maintenance of the system.

To reveal the influence of cracks on the dynamic characteristics of a two-stage planetary gear transmission system (TSPGTS), a nonlinear dynamic model with 30-DOF in bending and torsion was constructed, taking into account parameters of different crack degrees (depth, angle, length), as well as factors such as error, time-varying meshing stiffness (TVMS), and damping. In the model, the TVMS model of components with cracks was established using the potential energy method. By incorporating the crack factor into the model, time domain, frequency domain, phase diagram, and Poincare diagram characterizing the dynamic load characteristics were obtained, as well as the curve of dynamic load-sharing characteristics changing with cracks. The influence of different crack degrees on the displacement vibration and dynamic load characteristics of the system was analyzed, and vibration testing experiments were conducted on the system with planetary gear cracks. The results indicate that when the gear contains cracks, it will lead to a decrease in the stiffness of the system, when cracks appear on the II-stage planetary gear, the system will experience impact components with intervals of the rotation period of the II-stage planetary gear, and obvious sidebands will appear near the meshing frequency doubling. These situations will become more pronounced as the degree of cracks intensifies. As the degree of cracks in the II-stage planetary gear increases, the dynamic load-sharing characteristics of the TSPGTS will first improve and then deteriorate, and as the degree of cracks increases, the external and internal dynamic load coefficients continue to increase. Through experiments, the influence of normal gears and cracked gears on system vibration changes was compared and analyzed, and the theoretical results were in good agreement with experimental results, verifying the correctness of the theoretical model. This provides a theoretical basis for fault diagnosis and reliability research of the system.

The gear components are among the core fundamental parts of wind turbine gearboxes, and their operating condition significantly affects the performance of the gearbox transmission chain and even the entire wind turbine. This article derives the calculation method for the time-varying mesh stiffness (TVMS) of cracked herringbone gears based on the slice method. Additionally, a dynamic model with multiple degrees of freedom, considering factors such as relief grooves and errors, is established for the cracked herringbone gear planetary system (HGPS) with a bending-torsion-axis pendulum (BTAP) based on the lumped parameter method. The vibration curves of the system with varying cracks are obtained by solving the model using the Runge-Kutta method. Furthermore, a test rig is set up, and vibration tests are conducted. The results show that when cracks appear in the sun gear, the TVMS of the meshing pairs, both inside and outside the system, decreases. As the crack worsens, the fluctuation of the TVMS diminishes. Cracks induce periodic impact behaviors in the system, with an impact time of the fault cycle of T = 0.012 s. Significant sidebands appear near the mesh harmonic frequency, fm = 750 Hz, and the vibration trajectory of the gear becomes chaotic. As the cracks intensify, the vibration of the system becomes more pronounced. Experimental results are consistent with the theoretical results, verifying the accuracy of the established model and the feasibility of the simulation.

To explore the impact of gear floating on the system's nonlinear dynamic characteristics, a gear floating model was developed based on the concept of gear floating. A nonlinear dynamic model, bending-torsional-axial-pendular (BTAP), has been developed for a coaxial reverse closed differential herringbone gear transmission system (CRCDHGTS), accounting for gear floating. This model considers factors such as gear floating backlash, tooth surface friction, gyroscopic effects, time-varying meshing stiffness (TVMS), meshing damping, and dynamic meshing parameters. A calculation model for the floating backlash and floating TVMS of a herringbone gear system was derived, and the nonlinear dynamic response of the gear system was solved using the Runge–Kutta method. The influence of input speed, initial backlash, gear float value, and system transmission error on the nonlinear dynamic vibration characteristics is analyzed using various diagrams, including bifurcation diagrams, maximum Lyapunov exponent (MLE) plots, time history diagrams, frequency diagrams, phase diagrams, and Poincaré section diagrams. The research reveals that gear floating diminishes the chaotic motion behavior of the system under different excitation factors, thereby improving the system's global bifurcation characteristics. The developed BTAP coupled nonlinear dynamic model provides more accurate numerical solutions compared to models with fixed meshing parameters, rendering it more suitable for analyzing the system's dynamic characteristics. Analysis of the gear floating value indicates an optimal range of 0–20 μm and 34–43 μm for generating periodic motion, with floating values around 10–20 μm demonstrating better performance in mitigating the negative effects of initial backlash and transmission error.

The inevitable elastic deformation and vibration displacement of components can cause gear mesh misalignment (MM) in gear systems, thereby affecting the actual contact state of gear pairs and system dynamic performance. A novel three-dimensional (3D) dynamic gear contact model is proposed in this study for determining the 3D dynamic contact state of gear pairs considering system flexibility. By combining the loaded tooth contact analysis (LTCA) model with the MM calculation approach proposed in our published work, a proxy model for dynamic mesh excitations of gear pairs with system flexibility is developed for improving the solution efficiency. An efficient solution method of the proposed dynamic gear contact model is established through coupling the proxy model of dynamic mesh excitations and Newmark numerical integration method. It is conducted in-depth research on the influences of input speed, shaft parameters and gear installation position on dynamic MM and dynamic contact stress (CS), dynamic composite mesh stiffness (CMS) and dynamic composite mesh error (CME), as well as dynamic mesh force (DMF) and dynamic transmission error (DTE) of gear pairs.