最新刊期
卷 50 ， 期 3 ， 2026
- 摘要：ObjectiveThe differential planetary roller screw mechanism is a new type of transmission mechanism in which the screw thread is meshed with the roller ring groove, as well as the mesh between the roller ring groove and the nut ring groove. The bearing characteristics of a new type of five-stage differential planetary roller screw mechanism was investigated.MethodsThe analysis model was established and the bearing characteristics were analyzed based on the finite element method. Besides, the influence of different design parameters on the bearing characteristics was analyzed. Finally, the modification design was carried out.ResultsThe results show that the stress, the load and strain of the ring groove of the contact section between the roller and the nut are larger than those of the contact section between the roller and the screw. The maximum values of stress, ring groove load and strain in the two sections of the contact between the roller and the screw are located at the leftmost end of the meshing contact. The maximum values of stress and strain in the three sections of the contact between the roller and the nut are located at the rightmost end of the meshing contacts. It is proved that there is an uneven load distribution in the differential planetary roller screw mechanism. The relevant design parameters of the ring groove teeth have an important influence on the load distribution. When the tooth surface arc radius is 1.5 mm, the angle of the ring groove teeth is 50° and the chamfer radius of the ring groove teeth is 0.02 mm, the load of the ring groove teeth in the contact section between the roller and the screw is the most uniform. When the tooth crest modification amount is 0.63 mm or the tooth root modification amount is 0.84 mm, the bearing and stress distribution of the ring groove teeth in the contact section between the roller and the screw are uniform. The modification design effectively improves the uneven bearing of the roller ring groove teeth, which is beneficial to prolong the service life of the differential planetary roller screw mechanism.关键词：Differential planetary roller screw mechanism;Finite element method;Bearing characteristic analysis;Design parameter;Modification design275|106|0更新时间：2026-05-27
- 摘要：ObjectiveAddressing the issue of difference in the evaluation of tooth root bending strength for spiral bevel gears based on the strength verification benchmarks in Aviation Industry Standard of China (HB for short), International Organization for Standardization (ISO) standard, and American Gear Manufacturers Association (AGMA) standard, a comparative analysis was conducted to derive the optimal strategy for the design of spiral bevel gear.MethodsFirstly, based on the foundational mathematical models of each standard, the essential differences among the three standards were analyzed. Secondly, the influence parameters and their corresponding influence mechanisms of bending stress and strength safety factors obtained from the three standards were investigated from a theoretical perspective. Finally, through case analysis, the influence law of stress results and differences in strength calculation results obtained from the three standards were further explored.ResultsThe results show that ISO standard and HB use the 30° tangent method to determine the dangerous section and select the load point at the top of the tooth for calculation, while AGMA standard uses the parabolic method to determine the dangerous section and select the load point at the dangerous points for calculation. Compared with the 30° tangent method, the chord tooth thickness and bending moment arm obtained by the parabola method are more accurate, so the tooth form coefficient and stress correction coefficient obtained by the two methods are slightly different. According to the correction coefficients and their corresponding calculation formula, because the geometric coefficient
- 摘要：ObjectiveAiming at the problems of severe tooth surface wear and gluing failure in the planetary reducers of baling equipment under heavy loads, the maximum sliding rate and its influencing factors in a 3K-I planetary gear train with center distance errors were investigated to enhance transmission performance and prolong service life by optimizing the modification coefficients.MethodsFirstly, based on the gear meshing principle, the calculation formulas for the maximum sliding rate of the planetary gear train with center distance errors were derived. Secondly, the control variable method was used to analyze the specific influence of the modification coefficient and tooth number ratio on the maximum sliding rate. Thirdly, based on the equal sliding rate principle and combined with constraints such as undercutting and contact ratio, an optimization model using the weighted average method was constructed, aiming to minimize the sum of the sliding rate differences among gear pairs. Finally, nonlinear constrained optimization was solved using the fmincon command in Matlab, and different optimization schemes, such as taking the center distance error as a design variable, were comparatively analyzed.ResultsThe results show that the modification coefficient is the dominant factor affecting the maximum sliding rate. The comparative analysis reveals that the scheme treating the center distance error as an optimization design variable is the most reasonable. Within the given error range of [-0.1, 0.1] mm, this scheme significantly reduces both the maximum sliding rates and their differences among the gear pairs. Specifically, the sliding rate differences of the three gear pairs are decreased by 19.6%, 90.9%, and 96.1%, respectively. This effectively improves the sliding balance of the tooth surfaces and provides a reference for the design of planetary gear trains.关键词：Planetary gear train;Center distance error;Maximum sliding rate;Modification coefficient85|31|0更新时间：2026-05-27
- 摘要：ObjectiveAiming at the unclear correlation between tooth thickness, cumulative pitch deviations and hysteresis error of single-tooth meshing harmonic gears, the distribution law and key influencing factors of hysteresis error were revealed, providing a reference for the optimization of harmonic gear transmission accuracy.MethodsFirstly, discrete point data of the tooth profiles of the circular spline and flexspline were obtained by an image measuring instrument, and cumulative pitch deviation and tooth thickness deviation were extracted to provide accurate basic data for modeling. Secondly, a geometric model of hysteresis error for single-tooth meshing was constructed based on the deviation data, and transmission error expressions for forward and reverse rotations were derived to establish the correlation mechanism between deviations and hysteresis error. Then, hysteresis errors under single-wave and double-wave transmissions were calculated through left and right meshing angle errors to compare the transmission characteristics of different wave numbers. Finally, combined with the balancing effect of meshing zones, the smoothing effect of multi-wave transmission on output end error was analyzed to clarify the advantages of multi-wave transmission.ResultsThe results show that the hysteresis error of harmonic gears is negatively correlated with the tooth thickness deviation of the fixed gear and positively correlated with the tooth space width deviation. Compared with single-wave transmission, the amplitude of hysteresis error of double-wave transmission is reduced by 32.2%, the amplitudes of left and right meshing angle errors are reduced by 23.1% and 34.3% respectively, the envelope diagram of the curve has higher consistency, and the transmission stability is significantly improved.关键词：Projected tooth profile;Single tooth engaging;Hysteresis error;Tooth thickness deviation;Cumulative pitch deviation97|31|0更新时间：2026-05-27
- 摘要：ObjectiveScholars at home and abroad have conducted research on the dynamic characteristics of gears under different modification coefficients. However, the influence of the dual variables of radial modification coefficient and load on the stress variation law of differential bevel gears remains unclear. Based on the existing research foundation, the variation law of equivalent stress of differential planetary gear pairs under different radial modification coefficients and different load conditions was mainly explored, and the modal analysis of differential bevel gears was also carried out.MethodsFirstly, with the radial modification coefficient as the independent variable, separate configurations of positive and negative radial modifications were created for the planetary gear and side gear. Secondly, taking the torque applied to the side gear as the independent variable, three types of torques were imposed on the boundary conditions of the planetary gear and side gear models with different radial modification coefficients. Finally, non-linear contact analysis elements were employed to conduct contact and mechanical performance analyses and solve for the stress distribution of the gears.ResultsThe results indicate that the maximum stress position of the bevel gears during meshing occurs at the gear roots. Under different torque loadings, as the radial modification coefficient x1 of the planetary gear increases from 0.1 to 0.2, the maximum stress at the tooth root decreases, while the average stress along the meshing line increases. When the radial modification coefficient x2 of the side gear decreases from -0.1 to -0.2, the maximum stress at the tooth root of the gear increases, and so does the average stress along the meshing line. The modal analysis results of the planetary gear and side gear in the differential show that as the positive and negative modification coefficients increase, the maximum natural frequency and maximum spatial displacement of both the side gear and planetary gear gradually increase.关键词：Bevel gear;Numerical analysis;Modal analysis;Radial modification coefficient155|269|0更新时间：2026-05-27
- 摘要：ObjectiveAiming at the lack of efficiency parameter optimization design and simulation verification for the 3K-H type (type 5310) self-locking planetary gear train, an efficiency maximization design method was proposed to develop a gear train structure with both reliable self-locking characteristics and high forward transmission efficiency, providing a reference for related engineering applications.MethodsFirstly, a parameter-efficiency maximization model was established, the relation between efficiency and the transmission ratio of the converted gear train with different power flows was derived, and a parameter-efficiency curve was drawn to lay a foundation for efficiency optimization. Secondly, under the condition of satisfying self-locking, the transmission ratio of the converted gear train corresponding to the maximum efficiency was determined, and the gear tooth parameters were designed considering the constraints of module and pitch circle diameter. Finally, dynamic simulation was carried out using Adams software, and the effectiveness of the design scheme was verified by combining theoretical calculations.ResultsThe reverse transmission efficiency of the designed gear train is less than 0, achieving reliable self-locking; the forward transmission design efficiency reaches 0.506, and the simulation efficiency is 0.481. The theoretical calculation results are highly consistent with the simulation results, verifying the feasibility and effectiveness of the design method.关键词：3K-H;Planetary gear train;Efficiency parameter;Self-locking;Transmission ratio method91|38|0更新时间：2026-05-27
- 摘要：ObjectiveThe failure of transmission gears in imported and aged equipment due to tooth flank wear often leads to premature scrapping of the entire machine, as original design data is frequently unavailable for repair or replacement. To address this issue, a method for reverse-engineering the design parameters of involute spur gears with unilateral tooth flank wear based on visual inspection was proposed.MethodsFirstly, a high-precision visual inspection system was used to obtain the end face tooth profile images of the gear. Based on the principle of the gear structure, the tooth profile feature point sequences were effectively extracted and segmented. Then, the geometric characteristics of the involute tooth flank were utilized to accurately identify the worn tooth flank, which was then reconstructed using the standard tooth flank from the unworn side to obtain the original design tooth flank. Finally, the design parameters of the gear were solved by using the structural dimensions of the reconstructed involute spur gear tooth profile.ResultsThe test results show that the gear modulus and pressure angle obtained by the proposed method are consistent with the theoretical values, and the absolute errors of the profile shift coefficient and other basic parameters are all less than 0.035 mm, meeting the requirements of manufacturing precision. In addition, the proposed method has the advantages of non-contact, simple operation, stable detection results, and being less affected by the degree of gear wear.关键词：Worn gear;Feature extraction;Tooth flank reconstruction;Parameter inversion34|25|0更新时间：2026-05-27
- 摘要：ObjectiveBecause gears perform circumferential rotational motion, the topological optimization design of the gear body requires consideration of rotational symmetry. Different rotational symmetry orders may influence the results of the gear body’s topological optimization design. However, no definitive conclusions have yet been established regarding which order of rotational symmetry produces the most optimal results in topological optimization. In this regard, the influence of rotational symmetry order on the results of the gear’s topological optimization design was investigated.MethodsThe output shaft gear of a specified reducer was selected as the research object. Stress analysis and modal analysis were performed on the gear without topological optimization design using the finite element simulation software Abaqus, resulting in the stress state and the natural vibration characteristics during gear meshing. The gear was then subjected to topological optimization design by the variable density method. Subsequently, stress analysis and modal analysis were conducted on the topologically optimized gear. Additionally, the influence of different rotational symmetry orders on the results of the gear’s topological optimization was systematically analyzed.ResultsThe finite element simulation results indicate that the rotational symmetry order influences the distribution of the topology-optimized regions of the gear, but has a slight effect on the volume reduction fraction of topology optimization. For the gears designed with different rotational symmetry orders, no yielding occurs under meshing stress. However, modal analysis results reveal significant variations in the natural vibration characteristics. When the rotational symmetry order is set to 6, the topology-optimized gear not only avoids yielding under meshing stress, but also exhibits the largest frequency difference between its natural vibration frequency and the meshing frequency, which can effectively avoid resonance during gear meshing.关键词：Gear;Topology optimization;Rotational symmetry order;Modal analysis45|27|0更新时间：2026-05-27
Structural Design and Parameter Optimization
- 摘要：ObjectiveAiming at the excessive vibration of the traction gear transmission system of urban rail vehicles and the problems of long operation time and slow convergence speed in optimization design, a multi-objective optimization method based on a combined surrogate model was proposed to achieve precise improvement of system vibration characteristics and enhancement of optimization efficiency.MethodsFirstly, a lumped parameter method was used to establish the electromechanical coupling dynamic model of the system, and vibration response data were obtained to provide a foundation for subsequent optimization. Secondly, with structural parameters as inputs and vibration responses as outputs, a combined surrogate model integrating Kriging, radial basis function method (RBF) and polynomial response surface was constructed to quickly map the relation between parameters and vibration. Finally, taking bearing support stiffness and damping as optimization variables, the Pareto solution set was solved based on the non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) to minimize vibration acceleration.ResultsAfter optimization, the root mean square value of the system’s vibration acceleration is reduced by an average of 24%, with the root mean square value of the vertical vibration acceleration of the large gear decreasing by 38.4%; the optimization efficiency is increased by 97%, and the calculation time is shortened from 16 days to 10 min. The vibration suppression effect was stable at different rotational speeds, and the gear bearing capacity is not affected, providing a reference for the optimal design of the traction transmission system of urban rail vehicles.关键词：Urban rail vehicle;Electromechanical coupling;Vibration response;Surrogate model;Multi-objective optimization95|145|0更新时间：2026-05-27
- 摘要：ObjectiveIn order to accurately calculate the dynamic characteristics of the multi-stage gear transmission of a loader and the influence of gearbox structure flexibility on dynamic response, an efficient numerical calculation method for dynamic response considering the flexibility of the casing was proposed.MethodsFirstly, considering the stiffness and error excitation of the gear transmission system, a multi-degree-of-freedom dynamic model of the multi-stage gear transmission system with bending-torsion coupling was established using the concentrated mass method. Secondly, using finite element software and Romax software, a finite element model of the gearbox was established. Finally, based on the substructure method, a coupled dynamic equation for the gearbox and transmission system was constructed, which added a new degree of freedom for the gearbox condensation point on the basis of the transmission system dynamic equation. The dynamic meshing force and bearing support reaction could be obtained by using the Runge-Kutta method.ResultsThe results show that the influence of gearbox flexibility on the transmission system is related to the position of the gear pair and working conditions. At low speeds and light loads condition, the influence of gearbox flexibility on the dynamic meshing force in the transmission system is relatively small. Due to the direct contact between the bearing and the gearbox, the influence of the gearbox on the transmission system is attenuating from the bearing to the gear pair. Therefore, the influence of the gearbox flexibility on the bearing support reaction is greater than that on the gear meshing force. Therefore, in order to accurately predict the vibration noise of high-speed and heavy-duty complex transmissions, the flexibility of the gearbox can’t be ignored.关键词：Gearbox;Box flexibility;Gear system dynamic;Dynamic response;Gear meshing force37|22|0更新时间：2026-05-27
- 摘要：ObjectiveAiming at the problem of finding an accurate time-varying mesh stiffness solution for helical gears, a helical gear mesh stiffness calculation method based on axial force and slicing was proposed.MethodsEach lamellar gear was simplified as a variable-section cantilever beam, and a stiffness improved algorithm was proposed by adding a new axial bending potential energy through force analysis and further modifying the existing potential-energy-based method for calculating helical gear meshing stiffness. The feasibility of the improved algorithm was verified by comparing and analyzing with the finite element method and the slice method. On this basis, the effects of parameters such as helix angle, pressure angle, tooth number and tooth width on the meshing stiffness were investigated.ResultsThe results show that the traditional potential energy method is only applicable to helical gears with small helix angles, while the improved algorithm applies to arbitrary helical gears. The smoother the gearing performance is at increasing the helix angle. The pressure angle has less effect on the mean value of time-varying meshing stiffness. The tooth width has a large influence, which is approximately linear. When the center distance is certain, the change of the number of teeth has a smaller influence on the mean value, and the fluctuation value of the meshing stiffness is smaller when the number of teeth is larger. The fluctuation value is the smallest when the axial overlap is close to an integer.关键词：Helical gear;Time-varying meshing stiffness;Potential energy method;Axial component of force;Axial bending stiffness43|68|0更新时间：2026-05-27
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Study on the meshing surface temperature field of polymer gears under different operating conditions
摘要：ObjectivePolymer gears are widely used due to their lightweight, corrosion resistance, and noise reduction properties. However, their thermal behavior during meshing under complex operating conditions remains insufficiently understood. This study aims to investigate the specific effects of operating conditions and surface roughness on the maximum pressure and temperature rise of the gear tooth surface by coupling thermo-viscoelastic theory with a gear dynamic contact model to provide a basis for design and performance evaluation.MethodsA thermo-viscoelastic contact model for polymer gears was established. By adjusting operating conditions and incorporating surface roughness factors, simulations were conducted to evaluate the influence of gear rotational speed, load, and surface topography parameters (specifically wavelength and amplitude) on the maximum tooth surface pressure and temperature rise.ResultsThe results indicate that gear speed and load significantly affect the maximum temperature rise of the tooth surface. Surface topography exhibits distinct regulatory effects on the meshing pressure and temperature: wavelength shows a negative correlation with pressure, while amplitude shows a positive correlation. The developed model effectively simulates the distribution of pressure and surface temperature under various surface conditions, which is of great significance for optimizing the design and service performance of polymer gears.关键词：Polymer gear;Thermo-viscoelastic coupling effect;Gear dynamic performance;Surface roughness26|26|0更新时间：2026-05-27 - 摘要：ObjectiveTemperature is a key factor affecting the service performance of plastic gear. In order to predict the maximum steady-state temperature of gear meshing under dry operation conditions, the research method of temperature distribution on the tooth surface of curved plastic gear with small modulus was put forward, and the influence of different speed and load on the maximum steady-state temperature of gear meshing was analyzed.MethodsThe finite element numerical model of the temperature field of the gear was established based on the precise three-dimensional model of the polyoxymethylene (POM) material temperature-modulus effect combined with the curve configuration of the small modulus gear. The meshing temperature test of curved configuration POM gear pair under dry operation condition was carried out, and the test results were compared with the finite element results to verify the accuracy of the prediction model.ResultsThe results show that the temperature difference of the tooth body is large under dry operation conditions, the maximum temperature distribution is in the middle of the meshing zone of the single tooth on the first contact trace of the curved gear configuration,and the maximum steady-state temperature difference of gear pair meshing and the steady-state temperature difference of the master-slave drive wheel test gradually increase with the increase of speed and load. The test results are in good agreement with the model prediction results, and the maximum error between the maximum steady-state temperature of the tooth body and the test results is no more than 6.35%. The study can provide support for the long-term service application design of small-modulus plastic gear based on curve configuration.关键词：Curve configuration;Plastic gear;Small module;Dry running;Steady-state temperature field22|20|0更新时间：2026-05-27
- 摘要：ObjectiveWith the increasing demand for the load-bearing capacity and service life of face gear transmission systems in the industrial field, a design method for face gear pair transmission based on equiangular spiral tooth profile was proposed to further enhance the load-bearing performance of face gear transmission.MethodsThe formation principle of the tooth surface of face gear with equiangular spiral was studied, and the discrete model of the tooth surface of face gear with equiangular spiral was derived by solving the meshing parameters of the meshing inlet point, meshing outlet point, the top point of the inner tooth profile and the root point of the outer tooth profile. The correctness of the tooth surface model was verified by using the numerical computation examples. The key characteristic parameters such as principal curvature, sliding rate and pressure angle of face gear with equiangular spiral were analyzed to prove that the tooth profile of face gear which are conjugated through the tooth profile of cylindrical gear are still equiangular spiral. The theoretical analytical model for the contact stress and bending stress of face gear was derived, and the accuracy of the theoretical model was verified through simulation.ResultsThe simulation results show that the stress of equiangular spiral face gear is significantly smaller than that of involute face gear. It is concluded that the load bearing capacity of equiangular spiral face gear is significantly higher than that of involute face gear. This study provides a new design idea for improving the load bearing capacity of face gear transmission.关键词：Equiangular spiral;Face gear;Line contact;Load bearing capacity23|23|0更新时间：2026-05-27
- 摘要：ObjectiveRoller enveloping toroidal worm drives are widely used in computer numerical control (CNC) turntables but face challenges such as high error sensitivity and difficult installation. To solve these problems, a non-backlash end-face roller enveloping worm drive pair was proposed, achieving zero backlash by using one side for motion transmission and the other for clearance elimination.MethodsFirstly, based on spatial meshing theory and differential geometry, the mathematical model of the non-backlash end-face roller enveloping worm drive was established. Secondly, mathematical expressions for meshing performance, including the meshing equation, contact lines, tooth surface equations, induced normal curvature, lubrication angle, and relative entrainment velocity, were derived. Finally, the influence of geometric parameters on meshing performance was analyzed using Matlab software.ResultsThe results indicate that the theoretical meshing teeth of the proposed drive pair are 5 pairs, providing high load-carrying capacity. The lubrication angles of three or more pairs of meshing teeth are approximately 85°, indicating excellent lubrication performance. The induced normal curvatures of these teeth are below 0.25 mm-1, suggesting a good fit of the conjugate tooth surfaces. This design provides a reliable basis for the development of high-precision CNC transmission systems.关键词：End-face roller;Enveloping worm;Non-backlash meshing;Meshing performance （编辑：李立）25|24|0更新时间：2026-05-27
- 摘要：ObjectiveTo study the effect of tooth surface micromorphology on gear contact and operating conditions, the wear rate and dynamic response characteristics of anisotropic 3D rough tooth surface were investigated.MethodsFirstly, an anisotropic 3D microscopic rough gear surfaces were established based on fractal geometry theory. Secondly, the non-uniform wear of these microscopic rough gear surfaces under different rotational speeds and operating durations was calculated according to Archard’s theory. The wear depth of the gear surfaces was combined with gear dimensional parameters to solve for the time-varying meshing stiffness and backlash during the worn gear meshing, and they were used as internal excitation input parameters for the dynamic model of the gear transmission system. Lastly, the variable step-size Runge-Kutta algorithm was employed to solve the dynamic differential equations, thereby obtaining the dynamic response characteristics of the gear transmission system.ResultsThe results indicate that, with the same tooth surface roughness, as the rotational speed and operating duration of the gears increase, the wear depth of the tooth surface and the tooth side clearance gradually increase, while the time-varying meshing stiffness gradually decreases. In gear transmission systems considering the micromorphology of tooth surfaces, the gear transmission system exhibits abundant dynamic response characteristics as the rotational speed changes. As the operating duration increases, the dynamic transmission error of the gear transmission system enlarges. The overall dynamic response of the system tends from periodic motion state to chaotic motion state, manifesting as chaotic vibrations, which are detrimental to the system’s smooth operation. The gear transmission system transitions from chaotic motion state to relatively stable periodic motion state when the torque or rotational speed of worn gears in a chaotic motion state changes.关键词：3D rough tooth surface;Wear;Time-varying meshing stiffness;Backlash;Dynamic response characteristic46|22|0更新时间：2026-05-27
- 摘要：ObjectiveTo address the interference and blocking phenomena caused by large axial displacement in crossed beveloid gear pairs, a new transmission type involving a beveloid gear and an involute cylindrical gear with a low crossed shaft angle was proposed. This research aims to enhance the reliability and stability of the gear system.MethodsFirstly, based on the spatial gear meshing theory, a mathematical model of the working pitch cone-pitch cylinder for this gear pair was established. Secondly, a geometric design method was developed to obtain the necessary design and installation parameters. Finally, a loaded tooth contact model was created using the finite element method to investigate the influences of load, pitch cone angle, and helix angle on contact patterns, transmission errors, and tooth root stresses.ResultsThe results indicate that the contact pattern area, transmission error, and tooth root bending stress all increase with increasing load. An increase in the pitch cone angle of the beveloid gear leads to a reduction in the contact pattern area and an increase in both transmission error and tooth root stress. Conversely, increasing the helix angle of the beveloid gear enlarges the contact pattern area while decreasing the peak-to-peak value of the transmission error and the tooth root stress. These findings provide a basis for the precision design and performance optimization of low-crossed-shaft-angle gear transmissions.关键词：Low crossed shaft angle;Beveloid gear and involute cylindrical gear transmission;Working pitch cone-pitch cylinder;Meshing characteristic;Crossed axis70|120|0更新时间：2026-05-27
Dynamic Performance and Mesh Characteristics
- 摘要：ObjectiveThe fault diagnosis method for gearboxes based on intelligent optimization algorithms and deep neural networks has gradually become a research hotspot, but there are still many problems. To address the challenges of fault feature extraction and low diagnostic accuracy for gearboxes under strong noise environments, a novel gearbox fault diagnosis method was proposed based on a fusion-enhanced dung beetle optimization (FDBO) algorithm, the Informer model, and the efficient channel attention network (ECANet) module.MethodsFirstly, to overcome the limitations of the conventional dung beetle optimization (DBO) algorithm, such as insufficient global search capability and tendency to fall into local optima, a fusion strategy integrating Fuch chaotic mapping combined with inverse learning, an adaptive step size strategy, convex lens imaging, and a stochastic differential mutation strategy was introduced, significantly enhancing the algorithm’s global search performance. Secondly, benefiting from its excellent long-term time series processing capability, the Informer model was enabled to efficiently extract global features and local features from sequence data; especially for fault signals involving long-term dependencies, the model was able to demonstrate extremely high classification performance. Thirdly, an ECANet module was incorporated into the encoder of the Informer model to perform channel-wise adaptive calibration of extracted features, enhancing the model’s attention to critical features, strengthening feature representation, and reducing noise interference. Finally, the FDBO algorithm was employed to optimize multiple hyperparameters of the Informer-ECANet model, determining the optimal parameter combination to improve the diagnostic accuracy and generalization capability of the model.ResultsTest results demonstrate that the proposed method achieves an accuracy of 100% under noise-free conditions, and maintains a high accuracy of 94.4% even when subjected to Gaussian white noise at a -6 dB signal-to-noise ratio, thereby validating the superior performance and robustness of the model. This study provides an effective intelligent approach for gearbox fault diagnosis under challenging noisy environment.关键词：Fusion-enhanced dung beetle optimization algorithm;Informer model;ECANet module;Stochastic differential variation strategy36|20|0更新时间：2026-05-27
- 摘要：ObjectiveDue to the complex structure of planetary gearboxes, fault features are difficult to extract, and traditional methods rely heavily on professional expertise. To solve these problems, a fault diagnosis method integrating beluga whale optimization (BWO) algorithm optimized variational mode decomposition (VMD), multi-scale permutation entropy (MPE), and extreme learning machine (ELM) was proposed.MethodsFirstly, the BWO algorithm was employed to optimize the decomposition layers K and penalty factor α of VMD using the minimum envelope entropy as the objective function to achieve adaptive signal decomposition. Secondly, the MPE algorithm was used to compute the non-linear features of the intrinsic mode function (IMF) components, and a feature vector consisting of five time-domain indexes was constructed. Finally, the vectors were fed into the ELM for training and diagnosis. Comparative tests were conducted on a planetary gearbox test bench under four working conditions.ResultsThe testing results show that the overall accuracy of the proposed method reaches 97.92%, which is significantly higher than that of EMD-ELM and optimized VMD-SVM models. The findings verify that the BWO-VMD effectively improves signal de-noising and adaptive decomposition. This research provides a reliable basis for the health monitoring and precision design of planetary gearboxes.关键词：Planetary gearbox;Variational mode decomposition;Beluga whale optimization;Multi-scale permutation entropy;Extreme learning machine;Fault diagnosis33|23|0更新时间：2026-05-27
- 摘要：ObjectiveAiming at the problems of poor denoising effect and insufficient retention of key features when traditional denoising methods process gear crack impact signals, a denoising method (ITD-WPT) integrating intrinsic time-scale decomposition (IDT) and wavelet packet transform (WPT) was proposed to achieve efficient denoising and accurate feature retention of gear crack impact signals.MethodsFirstly, the noisy signal was decomposed into several proper rotation (PR) components by ITD, and high-frequency components containing noise were separated by identifying abnormal PR components to lay a foundation for precise denoising. Secondly, WPT was used for multi-scale decomposition of the noisy high-frequency components, and wavelet packet coefficients were extracted through refined threshold processing to achieve accurate noise suppression. Then, the wavelet packet denoised components were reconstructed, and signal reconstruction was performed using ITD combined with noise-free low-frequency components to obtain high-quality denoised signals. Finally, the method was applied to simulated cracked gear signals and test broken tooth signals, and comparative verification was conducted with classical methods such as moving average, empirical mode decomposition (EMD) and wavelet denoising.ResultsThe results show that the denoising effect of this method is significantly superior to the comparative methods: when the noise variance is 50, the signal-to-noise ratio (SNR) reaches 9.490 dB and the correlation coefficient is 0.944; when the variance is 100, the SNR is 4.012 dB and the correlation coefficient is 0.838. Moreover, it could effectively retain the impact characteristics of signals, providing a reference for the denoising of gear crack impact signals.关键词：Intrinsic time-scale decomposition;Wavelet packet transform;Gear crack;Impact signal;Noise reduction method24|21|0更新时间：2026-05-27
- 摘要：ObjectiveAiming at the multi-tooth fracture problem of the high-speed clutch gear on the input shaft of a certain type of plastic extruder, the failure mechanism was explored, the fracture cause was clarified, and a basis was provided for gear structure improvement and service life enhancement.MethodsFirstly, through macroscopic fracture morphology analysis and scanning electron microscope (SEM) characterization, the fatigue steps, fatigue striations on the fracture, and plastic extrusion/slip marks on the tooth surface were observed, and the failure mode was initially determined. Secondly, chemical composition detection and hardness testing were carried out to verify the compliance of the gear material composition, and the hardness of the tooth surface and core was tested to determine whether surface strengthening treatment had been performed. Then, the finite element method was used to establish a gear pair model, and three working conditions (normal fit, non-parallel centerlines, and misaligned centerlines) were simulated to analyze the stress distribution law of the tooth root, with emphasis on quantifying the influence of centerline misalignment on the tooth root stress amplitude. Finally, the bending stiffness check of the shafting was conducted, and the influence of insufficient shaft stiffness on the alignment of the gear pair centerlines was verified by calculating the equivalent diameter, moment of inertia of the shaft, and deflection at the gear.ResultsThe gear failure mode is fatigue fracture, with obvious fatigue striations and fatigue source areas visible on the fracture. Insufficient bending stiffness of the shaft causes the shaft deflection at the gear to exceed the allowable deflection, leading to misalignment of the gear pair centerlines. When the displacement in the Y direction of the translational degree-of-freedom is 0.01 mm, the stress amplitudes at the tooth roots of the internal and external gears reache 62.66 MPa and 62.72 MPa respectively, which accelerate the initiation and propagation of fatigue cracks. No strengthening treatment such as carburizing is performed on the gear surface, which further reduce the fatigue resistance.关键词：Plastic extruder;Gear;Fatigue fracture;Failure analysis37|28|0更新时间：2026-05-27
- 摘要：ObjectiveAiming at the main bearing with three-row roller structure for shield tunneling machines, a fatigue life calculation method considering roller profile modification was established to provide guidance for determining the modification method and degree.MethodsFirstly, through geometric analysis, the mathematical relation between roller-raceway contact deformation and the overall axial and radial displacements of the inner ring was established. Based on Palmgren's empirical formula and the force equilibrium equations of the inner ring, a load distribution model was constructed and solved to obtain the load on each roller. Secondly, the rollers were sliced equidistantly along the generatrix direction. An elastic contact model between the modified roller and the raceway was established using finite line contact theory to obtain the contact stress at each slice. Finally, according to ISO/TS 16281 standard, the roller slice loads corresponding to the basic rated dynamic load and the equivalent dynamic load of the ring were calculated respectively to determine the fatigue life of the main bearing.ResultsThe results show that the roller modification convexity significantly affects the fatigue life of the main bearing. With the increase of convexity, the fatigue life increases first and then decreases, indicating the existence of an optimal convexity that maximizes the fatigue life.关键词：Main bearing;Load distribution;Contact stress;Roller profile modification;Fatigue life;Numerical calculation36|23|0更新时间：2026-05-27
Fault Diagnosis and Failure Analysis
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