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Copyright of Bearing is the property of Bearing Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In a gear transmission, power losses come from a variety of sources, classified as load-dependent and no-load-dependent losses. No-load-dependent losses are the ones that remain constant regardless of the applied load, such as losses due to drag in rolling element bearings, seals, churning and/or windage for gears. Load-dependent losses include friction losses due to sliding and rolling between gear teeth. These losses are particularly important in some gear transmissions because of their direct impact on overall efficiency and thermal behaviour. Consequently, knowledge of the friction coefficient associated to this loss is of major interest for optimising gears (geometry, surface finish, lubrication, etc.). In this article, a new method is proposed for predicting the mechanical efficiency losses associated with the mean coefficient of friction for pairs of cylindrical gears. It is based on a model developed previously to estimate the instantaneous tooth friction along the plane of action in gears. This model takes into account the lubricant shear and the friction on contacting asperities. The proposed mean friction coefficient is deduced from the instantaneous friction coefficient using specific calculations, particularly at the pitch point. To verify the method, the estimated results are compared with those in the literature calculated for gears and operating conditions common on FZG test rigs. [ABSTRACT FROM AUTHOR]

High-speed gears are crucial transmission components found in airplanes and other systems, and they are maintained primarily through oil injection. However, due to their high operating speeds and the influence of oil injection settings, gear surface lubrication efficacy is frequently insufficient, compromising the transmission system's precision, durability, and safety. Currently, the parameter choices for oil injection in high-speed gears mostly rely on empirical judgment, which results in significant time and resource expenses. This study focuses on one pair of internal meshing gears within a specific aircraft gearbox, establishing an oil injection lubrication model for high-speed internal meshing gears using the computational fluid dynamics (CFD) approach. This research provides insights and references for optimizing oil injection parameters and improving lubrication efficiency in high-speed internal meshing gear systems by examining the dynamic characteristics of internal meshing wind resistance in addition to the effects of injection tube position, angle, and speed on lubrication performance. [ABSTRACT FROM AUTHOR]

Presently, robots have widespread application in mechanical processes, automation, healthcare, food processing, etc., where the motion of robots majorly depends on the precise gear transmission and type of gear to be used. The primary aspect considerated in redesigning of the sun and planet gear mechanism are the pressure angle and face width of the gears. Static and dynamic analyses of the redesigned planetary gear are performed using ANSYS 2021 R1. To ensure accuracy of the analysis, a mesh-independent study was carried out to obtain an optimal element size. The static analysis results reveal the total deformation and Von-Mises stress occurring in the planet gear due to the rotation of the sun gear. The secondary objective of this study is to compare the natural frequencies obtained from the numerical modal analysis for two different types of material: 20CrNi2Mo alloy steel and titanium alloy. In a nut shell, the findings of this research provide a foundation for understanding the sun and planetary gear system's static and modal responses for its improved efficiency. [ABSTRACT FROM AUTHOR]

Due to recent technological advances, preciseness in gear transmission has evolved into an essential goal, in which vibration is one of the critical issues. This study demonstrated an experimental platform for a proposed construction model on the spur gear pair, in which damping particles were filled into six through-cavities in gear bodies to verify decreases in vibration. The experimental design involved variable control of input rotational speed, filling ratio, particle size, and material to investigate the damping particles' behavior. Subsequently, operating both ADAMS and EDEM software established a reliable two-way coupling analysis model. The results confirmed that the filling damping particles effectively reduced system vibration, and both simulation and experimental tests demonstrated a consistent impact. In addition, the damping particle behavior indicated that high rotational speed was more effective in vibration reduction, and increased filling ratio decreased radial vibration. Increases in particle diameter only contributed slightly to vibration reduction. Moreover, although density increase significantly reduced vibration, bead elasticity did not impact vibration. Finally, the dynamic behavior of damping particles with the greatest reduction impact was achieved by applying a soft lead bead in a 5-mm diameter, 48% filling ratio, and the system working at a rotational speed of 600 rpm. [ABSTRACT FROM AUTHOR]

• A comprehensive vertical dynamics model of the electric vehicle considering the integrated powertrain system is proposed. • The limitations of traditional vertical dynamics model of electric vehicle in the high frequency range are revealed. • The effects of mounting stiffness and damping on the vibration of chassis and integrated powertrain system are explored. • A multi-objective optimization model is designed to minimize the vibration of chassis and integrated powertrain system. Integrated powertrain system, mainly composed of driving motor and reducer, is one of the excitation sources to electric vehicle vibration but is limited in coupling with the vertical vehicle dynamic in the existing research, which restricts the reliability of dynamics investigation of vehicle and integrated powertrain system. This work proposes a novel vertical dynamic model of the electric vehicle considering the integrated powertrain system, enabling the way to access the coupled vibration among the chassis, unsprung mass, and integrated powertrain system. The road irregularity, unbalanced magnetic pull, and gear mesh excitation are developed and are further applied to the novel vehicle dynamic model with ten degrees of freedom (DOFs). Then, the dynamic response between the novel model and traditional one is compared. Further, the effects of the stiffness and damping of suspension and mounting on the vibration of chassis and integrated powertrain system are explored by numerical calculation. Finally, a multi-objective optimization model is proposed and is driven by the dragonfly algorithm to minimize the vibration of chassis and integrated powertrain system. The research results shown that there will be present the new complex dynamic characteristics with considering the excitation from the integrated powertrain system. The suspension and mounting parameters have the nonlinear effects on the vehicle vibration. And the system vibration can be globally optimized with the optimization algorithm. [ABSTRACT FROM AUTHOR]

Copyright of FME Transactions is the property of University of Belgrade, Faculty of Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

With the development of the gear transmission system towards complexity, multiple transmission types and high reliability, it becomes more and more important to assign the reliability of the gear transmission system quickly and accurately. In this study, aiming at the problems of incomplete consideration factors, inconsistent range of changes in different allocation methods for the same parameter, and inconvenient digital software development in existing reliability allocation methods, an improved advisory group on reliability of electronic equipment (AGREE) allocation method is proposed, the scoring allocation method is extended, and the digital characteristics of reliability allocation method are discussed. The basic reliability model and task reliability model of the complex gear transmission system are established, and the traversal algorithm of the automatic reliability model generation is studied. A digital platform for rapid reliability allocation of fixed axle gear train, planetary gear train and hybrid gear train is developed. Four independent modules, namely input module, calculation module, result display module and output module, are designed. The accuracy of the calculation results of the software is verified by comparing with the results of examples. The parametric modeling and the automatic generation of the example report for the reliability allocation of the gear transmission system are realized, and the accuracy and efficiency of the reliability allocation model are raised.

In this work, a dynamic model considering time-varying mesh stiffness and backlash was proposed and a test rig was built to investigate the vibration behavior of the idle gear set in a gerotor pump. The effects of input shaft speed, torque fluctuation, and gear tooth backlash on the dynamic performance of gerotor pump were analyzed according to the numerical and experimental results. Results demonstrate that when the torque fluctuation is neglected, the dynamic transmission error of drive gear is dominated by the first three mesh harmonic components; however, the RMS values of vibration acceleration have high frequency characteristics. When the torque fluctuation is considered, the dynamic responses of gerotor pump are modulated by the torque fluctuation. The effect of tooth backlash on the dynamic performance of gerotor pump is limited and mostly depended on the torque fluctuation condition. The gerotor pump noise is dominated by the low frequency component around the mesh frequency. The vibration energy can be divided into two parts in the frequency domain. In the low frequency band, the vibration energy is caused by the mechanical vibration. However, in the high frequency band, the cavitation phenomena may cause the concentration of the vibration energy and resonant of pump structure. [ABSTRACT FROM AUTHOR]

The existence of backlash causes de-meshing and reverse impact in the gear system, and the influence of the working lubrication conditions of the gear on the dynamics is ignored. This study focused on the impact of the coupling characteristics of gear system based on the multi-meshing state model and the gear lubrication model on the evolution of nonlinear dynamic behavior. Firstly, the transition of the meshing state was considered, and the time-varying parameters such as contact radius, load distribution ratio, meshing stiffness, entrainment speed, and slip-to-roll ratio were analyzed under meshing and reverse impact conditions. Then, the elastohydrodynamic lubrication model of the gear was analyzed, the coupling effect between the lubrication model and the gear system was reflected by two factors. One was the comprehensive meshing stiffness obtained by coupling the gear meshing stiffness and the lubricating oil film stiffness, and the other was the lubrication state transition of the system determined by the oil film thickness. Further, the gear dynamics model considering the above factors was established, and the influence of the coupling characteristics of lubrication and gear systems on the dynamic behavior was analyzed on the torque–speed parameter plane. The research results have theoretical guiding significance for the parameter selection, optimization design of gear system and the optimization of meshing characteristics. [ABSTRACT FROM AUTHOR]

Gear transmission holds paramount significance for intricate mechanical systems. However, when the size of the driving gear is miniaturized to less than 50 microns, both manufacturing and control meet challenges. Here, a magneticdriven micro-gear pair (MMGP) and its manipulation strategy are proposed. The MMGP is composed of two micro-gears fabricated by the two-photon polymerization (TPP) and its manipulation strategy depends on the gear engagement. The driving gear is processed with a magnetic photoresist and can rotate stably with a rapid rotation response (<100 ms) under the control of an external magnetic field. The driven gear can be driven by the driving gear through the meshing relationship of the gear teeth. As a proof of concept, number counters and the delivery of drugs are achieved by specially designed MMGPs. This development establishes a pivotal foundation for micro-gear transmission in complex intelligent systems, microfluid operation, and biological manipulation. [ABSTRACT FROM AUTHOR]

This article deals with the research and analysis of electric motors and their matched transmission systems within the context of a versatile electric mini-tractor designed for tasks such as street cleaning, urban park maintenance, and transportation of small loads. The primary objective of the research is to assess the strengths and weaknesses of several electric motor and transmission combinations designed to meet the specific operational demands of the tractor. As the driveline has to provide substantial torque while maintaining optimal operating conditions and avoiding overheating, a series of experiments were conducted, covering various electric motor configurations operating within the 60V range, with power outputs ranging from 1000 to 1500 watts and including multiple gearbox variations. A comparative analysis was performed to assess the advantages and disadvantages of direct chain drive transmission solutions without a differential on a rigid axle, in contrast to a sealed motor-gearbox unit featuring differential and semi-axles. The results of this research were used for mathematical comparison of the driveline solutions, enabling the detection of optimally matched transmission and motor solutions. The experiments also covered the identification of energy-efficient solutions and optimal design parameters for an electric tractor explicitly designed for continuous operation exceeding 10 hours, with cargo capacity exceeding 500 kg, high off-road maneuverability, and a service life exceeding 5000 hours. The dynamic tests carried out during the research have provided valuable insight into the relation of the overall power efficiency of the vehicle to the weight and transmission ratio variations.

Wear is the main failure form in the gear transmission process. The increased wear will increase the non-linear backlash of the gear teeth, reduce the transmission accuracy and increase the impact force of the tooth surface, which will lead to aggravated vibration of the gear transmission system, and impose great impact on the gear transmission performance and the stable operation of the equipment. In order to solve the above problems, a method for predicting the wear amount in the gear transmission process under complex working conditions is proposed. The gear wear state is identified and determined based on the formal wear index. Through in-depth analysis of the gear wear mechanism, a typical gear wear process curve is drawn based on this, the gear transmission friction torque value is calculated, and a mathematical model of the gear wear amount is built; then the known gear state values are input into the construction model, the predicted gear wear amount is obtained, and the prediction of gear wear amount is realized. The experimental results show that under three complex working conditions, the prediction simulation data proposed in this study is closer to the actual parameters, which fully verifies that the prediction accuracy of the wear amount is higher.

High-speed gears are crucial transmission components found in airplanes and other systems, and they are maintained primarily through oil injection. However, due to their high operating speeds and the influence of oil injection settings, gear surface lubrication efficacy is frequently insufficient, compromising the transmission system’s precision, durability, and safety. Currently, the parameter choices for oil injection in high-speed gears mostly rely on empirical judgment, which results in significant time and resource expenses. This study focuses on one pair of internal meshing gears within a specific aircraft gearbox, establishing an oil injection lubrication model for high-speed internal meshing gears using the computational fluid dynamics (CFD) approach. This research provides insights and references for optimizing oil injection parameters and improving lubrication efficiency in high-speed internal meshing gear systems by examining the dynamic characteristics of internal meshing wind resistance in addition to the effects of injection tube position, angle, and speed on lubrication performance.

Gear surface wear will inevitably occur under the complicated excitations in a locomotive. The continuous accumulated wear would induce the deterioration of the meshing state of the gear pair and it affects the stability of operation and shorten the service life of components. Therefore, it is the premise of fault maintenance to accurately grasp the evolution law of wear and its effect on the components' vibrations. However, there is little work on the wear calculation of the gear pain in a locomotive considering the complicated excitations. To fill this gap, a locomotive-track spatially coupled dynamics model with the discrete gear model is employed in this paper, which combines with the typical Archard's wear calculation equation. The calculation method of load distribution of discrete tooth slices under misalignment is proposed. The time-varying mesh stiffness, track irregularity, and time-varying wear coefficient are comprehensively taken into account. In addition, the developed wear depth, deemed as a kind of profile error, is taken into account in the dynamic transmission error (DTE). The results indicate that the accumulated wear depth of the driving gear is more severe than that of the driven gear. There is an apparent difference in wear distribution for different discrete slices along the tooth width under misalignment. In addition, the developed cumulative wear depth could exert a vital influence on the dynamic performance of components in the vehicle system. This study can provide a theoretical guideline for service life prediction and structural design. [ABSTRACT FROM AUTHOR]

Gear is the core component of mechanical transmission system, and pitting and wear are its main failure forms. In order to solve the problem that the time-varying meshing stiffness and dynamic characteristics of double involute gear are unknown when pitting failure occurs. The meshing stiffness of double involute gear with pitting corrosion was calculated by using the percentage of contact line method, and the correctness of the algorithm was verified through finite element method. Firstly, the different erosion conditions were categorized and the influence of different number of pitting on the contact line length was analyzed. Then, based on the method of the percentage of contact line, the ratio relationship between tooth load and tooth deformation was used to solve the meshing stiffness of gear at different points of erosion. The correctness of the algorithm was verified by finite element method, and the influence of pitting on meshing stiffness of double involute gear and ordinary involute gear was compared and analyzed. Finally, the flexible multi-body dynamic models of the two gears were established, and the dynamic characteristics of the two gears under different corrosion conditions were analyzed based on the impulse function method. The research results show that, under the same working conditions, with the deepening of pitting corrosion, the meshing stiffness of both types of gears continuously decreases, while the dynamic meshing force and vibration angle acceleration amplitude increase. Among them, the maximum meshing force of double involute gear is 1. 24 × 105 N, and the maximum angular acceleration is 2. 66 × 106 °/ s². Comparing with ordinary involute gear, the meshing stiffness of double involute gear under the influence of pitting corrosion is more stable, the acceleration amplitude fluctuates more gently, and it has better impact resistance and power transmission stability. [ABSTRACT FROM AUTHOR]

The gear transmission in high-speed trains is crucial for transmitting the traction torque. Its dynamic characteristics impact the system's reliability and safety. Additionally, the gear transmission and its support bearings can be affected by wheel-rail interactions, particularly on curves with larger centrifugal forces. To address this, a spatial vehicle-track coupled dynamics model that considers the complete power transmission path and mechanical structure of the gear transmission is proposed. The model considers factors such as time-varying mesh stiffness, dynamic transmission error (DTE), time-varying support stiffness, and internal interactions of the gearcase bearing. Results indicate that when a high-speed train passes through a curve, the derailment coefficient and lateral force of the wheelset are less on the right curve due to the lateral component of the mesh force, but the opposite occurs on the left curve. The centrifugal effect affects the contributions of the lateral and vertical motions of the gear pair, which are balanced by the torsional motions of the components in the power transmission path. Additionally, the internal interactions between the rolling elements and races are intensified due to track irregularity and gear engagement, but the centrifugal effect of the pinion can be ignored. [ABSTRACT FROM AUTHOR]

In order to study the meshing efficiency of the gear pair under the actual working conditions, the force and kinematics of the contact surface of the gear pair are analyzed, the lubrication state of the gear pair is judged by combining the theory of elastohydrodynamic lubrication, and the relationship between the elastohydrodynamic lubrication and the mixed lubrication state is established. The mathematical model of the dynamic friction factor is used to obtain the friction factor of the gear pair at different meshing positions along the meshing line. From the point of view of force, the calculation formula of gear pair meshing efficiency is deduced, and the dynamic sliding friction factor is introduced to obtain the result of gear pair meshing efficiency that conforms to the actual working conditions. Combined with the simulation analysis software, the influence of the transmission ratio and the number of pinion teeth on the sliding friction factor and the meshing efficiency of the gear pair is analyzed. The results show that the calculation method of the gear pair meshing efficiency based on dynamic sliding friction factor is in good agreement with the actual working conditions, which has certain guiding significance for gear transmission design.

Wheel polygonization intensifies the dynamic interaction between wheel and rail and reduces the service life of the locomotive and the rail system. The dynamic performance of the drive and transmission system (DATS) directly affects the wheel-rail interaction and further affects the wheel polygonization. In this study, a rigid-flexible locomotive coupled dynamics model of an HX locomotive is established. The DATS and the flexible characteristics of the wheelset are both considered. The calculation model of the wheel polygonal wear is established based on the local tangential contact distribution algorithm FaStrip and the USFD wear function. Effects of the DATS on the wheel-rail dynamic response and wheel polygonal wear are investigated. Evolution of the wear depth is studied under the different running speeds and the wheel profile initial states. The results indicate that the torsional vibration response of the DATS plays a significant role in promoting the development of the wheel polygonization. The more serious wear damage of the wheelset on the non-gear side (NGS) is both reflected in the actual service process and the numerically calculated results, which validates the established dynamics model and calculation method. This study could provide helpful reference for further understanding on the wheel polygonization phenomenon. [ABSTRACT FROM AUTHOR]

Scuffing is one of the most typical damage forms in the gear transmission of agricultural machinery. The fast bursting speed and serious damage degree should be strictly avoided in the conditions of the low lubrication and extreme loading during the gear service. This study aims to improve the scuffing resistance load carrying performance in the transmission gears of agricultural machinery under severe lubrication, variable speed, and heavy-duty conditions. The surface coating strengthening was applied to the meshed tooth surface. A mathematical model was established for the relationship between the contact properties of coatings and gears, as well as the scuffing load capacity. The gear meshing, tribology, and thermodynamics were also utilized in this case. The finite element model of plane strain was selected to explore the influence of elastic modulus ratio between coating and substrate on the stress field distribution. Anti-scuffing gear coatings were achieved to clarify the effect of tooth surface frictional coefficient on oil film thickness and transient contact temperature, according to the calculation in ISO/TS 6336-22. Then, the carbon films were prepared by low-temperature plasma enhanced chemical vapor deposition technology. Surfaces of standard steel balls were coated with the tungsten containing ta-C and a-C:H coatings. Tribological properties of coating materials were evaluated using the four-ball method. A series of experiments of scuffing resistance were performed on the two coated gears in the FZG (Forschungsstelle für Zahnräder und Getriebesysteme) transmission test rig. The results showed that the carbon film friction pairs had the better running-in performance, compared with the uncoated components. The a-C:H coating presented the higher sp² C-C bond content than ta-C, resulting in a lower frictional coefficient. Also, the scuffing resistance capacity increased by 2 FZG loading stages in the ta-C coating, while at least 4 loading stages were found in the a-C:H coating one. In the process of engagement, the ta-C coating was peeled off, and then the peeled coating particles were pressed into, adhered to the contact surface, or discharged from the scratched surface, thus forming abrasive wear between the tooth surfaces, and finally the gear steel substrate was completely exposed. Furthermore, the failure mode was changed from abrasive wear to adhesive wear with the increase of frictional temperature. The surface material was subject to adhesive tearing. Moreover, both uncoated and ta-C coated tooth surfaces showed the significant competitive relationship between the thermal scuffing and micro pitting damage, which was mainly determined by the oil film thickness and contact temperature. In addition, the concave plastic deformation near the driving wheel pitch line was found on both surfaces. The a-C:H coating showed the conventional fatigue wear with the smooth and flat wear trace, where the tooth surface coating had the high integrity without outstanding damage. Theoretical analysis and experimental data were combined to enhance the gear scuffing resistance capacity. Although the frictional coefficient was low, the ta-C coating was more prone to the coating peeling and interface damage, due to the high elastic modulus ratio between coating and substrate. By contrast, a-C:H coating shared the relatively low elastic modulus ratio. The interface stress was smaller and more difficult to peeling, and the frictional coefficient was smaller, resulting in a relatively thicker oil film thickness and lower transient contact temperature on the tooth surface. The achievements demonstrated that the a-C:H coating exhibited the excellent scuffing resistance load carrying performance suitable for gear transmission. The finding can lay the foundation for the application of coating strengthening technology in the high-performance agricultural machinery gears, even the other transmission systems with harsh service conditions. [ABSTRACT FROM AUTHOR]

To study the nonlinear dynamic characteristics of the electric drive transmission system of clean propulsion vehicles, a rotor-bearing system consisting of dual-stage meshing gear pairs and multiple loaded bearings was established. The influence of time-varying meshing stiffness, tooth side clearance, bearing clearance, and other factors were considered. A multi-degree of freedom vibration differential of the system was established equation, to analyze the vibration characteristics of various parts of the transmission system under different parameters. Using time-domain diagrams, poincaré cross-sections, bifurcation diagrams, and other images to study the vibration of gears. In addition, the primary resonance stability equation of the system is derived and its stability under different conditions is analyzed using meshing damping, stiffness, and load as variables. The results show that as the rotational speed increases, the first stage gear of the system undergoes the "single cycle-bifurcation-chaos-bifurcation-single cycle" vibration process, while the second stage gear undergoes two such processes. The instability intervals can be obtained as [3092,4859] and [8098,10896] r/min, [2797,3533] and [9423,14135] r/min respectively. Avoiding these speed ranges helps to improve the stability and safety of automotive motion. [ABSTRACT FROM AUTHOR]

How to effectively extract weak fault features of planetary gears under strong background noise is a difficult problem that needs to be solved in the field of planetary gear fault diagnosis. For the nonlinear and non-stationary vibration signals of planetary gears, in order to improve the accuracy of fault diagnosis, a planetary gear fault diagnosis method optimized by genetic algorithm-optimized long-short-term memory network (GA-LSTM) and ensemble empirical mode decomposition (EEMD) was proposed. First, the vibration signals of four types of planetary gear faults were collected in the experiment, and the original vibration signal of the planetary gear was decomposed into six intrinsic mode function (IMF) components by using EEMD method, which was used as the feature components for further processing. Then, the hyperparameters of the LSTM network were optimized using the genetic algorithm (GA) to improve the accuracy of fault type identification. Finally, the feature components were inputted into the trained GA-LSTM model, the network model was used as the final classifier to diagnose and identify the faults of the planetary gears. By comparing the unoptimized network and artificially adding noise to the original signal to simulate the actual engineering signal, the validity and effectiveness of the method based on EEMD and GA-LSTM algorithms were verified effectiveness. The research results show that the trained network achieves a loss rate of less than 2%, and has good stability. The fault classification accuracy of the GA-LSTM method reaches 94.17%. Comparing with the non-optimized network, the verification accuracy of the GA-LSTM model is found to be higher than that of the LTSM, which shows better timing performance on all components; even when identifying engineering signals with added noise, high fault diagnosis accuracy can also be maintained, which shows its superiority in planetary gear fault diagnosis. This study has certain theoretical guidance and reference value in improving the fault diagnosis ability of mechanical transmission equipment. [ABSTRACT FROM AUTHOR]

The positive characteristics observed in terms of compact structural sizes and high torque-transmitting capacities have allowed co-rotating twin-screw (CRTS) gear transmissions to be extensively applied to instances requiring small central distances and large power densities. In this study, a multi-objective optimization model for the quick determination of structural parameters of the CRTS gear transmission system is proposed based on the heuristic search and non-dominant sorting genetic algorithm. Results reveal that the optimized scheme with 17 design variables and 18 constrained parameters can be achieved with this model. The system reduces mass by 7.74 % from the original mass of 199.06 kg, while the safety factor variance of the transmission system decreases by 29.3 %. This method applies to other transmission systems with different structures and thus provides general theoretical support for modern gear transmission optimizations. [ABSTRACT FROM AUTHOR]

The reliability research of mechanical system mainly includes reliability design, distribution, modeling, analysis and evaluation.Only by establishing a correct and reasonable model and adopting the correct analysis method can accurate reliability evaluation results be obtained.In order to solve the problems of large computation and time consuming in reliability modeling of complex system, a digital analysis method for fast reliability modeling of gear transmission system was proposed. Firstly, a system reliability model considering the load dependence of each part was established, the reliability mathematical model was used to solve the reliability of the gear transmission parts, and the reliability relationship model was used to characterize the relationship between the whole system, subsystem and parts. The digital platform for rapid modeling of gear transmission system reliability was designed, enabling it to achieve reliability modeling and reliability rapid analysis for any gear transmission system. Secondly, the automatic generation method of reliability model and case report was discussed by the digital technology, the traversal method of gear transmission system reliability digital modeling was studied, the parametric input module, the numerical solution module and the automatic result output module were developed, and three common gear transmission system cases were solidified. Finally, the power branch gear transmission system was taken as an example for reliability modeling and digital analysis, and the analytical calculation results were compared with the software simulation results. The results show that the error between analytical calculation results and software simulation results is only 0.016%, which verifies the correctness and efficiency of the proposed reliability modeling digital analysis method and software. At the same time, this method has the functions of saving loading examples, automatically generating reliability model block diagram and quickly calculating system reliability, which provides a digital platform for the reliability modeling and reliability rapid design of gear transmission system. [ABSTRACT FROM AUTHOR]

At present, domestic and foreign scholars have conducted research on the dynamic characteristics of gear rotor coupling systems, but none of the above studies have considered the composite fault state of planetary gears and rotors. Therefore, taking a single stage planetary gearbox as an example, a dynamic model of the planetary gear rotor coupling system with rotor eccentricity and root crack faults was constructed, to simulation analyze and experimentally study the vibration response characteristics of the planetary gear rotor coupling system under composite fault conditions. Aiming at the problem of multi-source coupling vibration and composite fault diagnosis in planetary gear transmission systems, a single stage planetary gearbox was executed by dynamic modeling, dynamic characteristics analysis and experimental analysis. Firstly, considering time-varying meshing stiffness, support stiffness, damping, gyroscopic effect, and transmission shaft flexibility, the lumped parameter method and Timoshenko beam theory was used to establish a dynamic model of a planetary gear-rotor coupling system with shaft eccentricity root crack composite fault. Then, the influence of different faults on the dynamic characteristics of the system was analyzed by numerical analysis using time waves, frequency spectrum, axis center orbit and phase diagram. The influence of the root crack propagation of the sun gear on the vibration response characteristics of the system under eccentric state was studied. Finally, the accuracy of the dynamic model was verified by different crack fault experiment. The results show that the influence of eccentricity on meshing vibration is significant and can not be ignored in the analysis of fault characteristics of planetary gear trains. Under the influence of eccentric-crack coupling, the vibration response of the system is composed of unbalanced vibration, normal meshing vibration and fault impact vibration. In the spectrum, there are rotational frequency fr, meshing harmonic kfm and complex sideband component kfm±fr、kfm±fr±nfsc. With the increase of crack degree, the modulation phenomenon is more obvious.The research results can provide a theoretical basis for the compound fault diagnosis of planetary gear-rotor system. [ABSTRACT FROM AUTHOR]

When the static analysis and genetic algorithm were combined to design and optimize the reducer, the inertia force caused by acceleration was not considered for the wheel-side reducer which bears large torque in transmission. Aiming at the problem of weak strength of the secondary gear group of the original main gear group of the electric driven rescue wheel side reducer, the gear of the second gear set of the main reducer was designed and optimized, and the problem of weak strength of the second gear set of the original reducer was solved. Firstly, the 3D modeling design of main wheel reducer was carried out according to the basic data of the main wheel reducer, and then the corresponding constraint conditions were added to the designed model for transient dynamics simulation analysis. It was found that the strength of the two-stage gear group was weak. Then, the Monte Carlo algorithm was used in coordination with macro and micro-optimization to optimize the data of the two stage gear parameters, such as helix angle, pressure angle and normal surface modulus. Finally, the two-stage gear group of the reducer was modeled and simulated with the obtained optimization data, and the reliability of the optimization was determined by the simulation analysis results. The results show that the linear transmission error of gear in the second gear set of the reducer is reduced by 59.38%, and the maximum stress at the root is reduced by 14.3% after optimization. The contact impression, contact load and maximum contact stress at the root are optimized, and the service life of gear is improved as a whole. [ABSTRACT FROM AUTHOR]

The tooth surface friction has an important impact on the tooth surface contact stress and the tooth surface contact fatigue life. In the estimation of the contact fatigue life of the tooth surface, the influence of the friction force of the tooth surface is often ignored, which is not conducive to the accurate prediction of the contact fatigue life of the tooth surface. In order to accurately predict the contact fatigue life of the tooth surface, the R-S-N curves are fitted based on the three-parameter Weibull distribution and the nominal stress method according to the tooth surface contact fatigue test data of 18CrNiMo7-6 gear material. By calculating the contact stress on the tooth surface, the time-varying friction factor is introduced, and the influence of the time-varying friction factor on the contact fatigue life of the tooth surface is analyzed. Finally, the tooth surface contact fatigue test is used to verify the validity. The results show that the contact fatigue limit of tooth surface estimated by the traditional nominal stress method is large due to the influence of the time-varying friction factor, and the influence of the friction factor on contact fatigue life of tooth surfaces decreases with the increase of stress.

Aiming at the problems of high damage rate and loss rate of the existing safflower harvesting equipment, this study designed a rotary cutting safflower harvesting end effector by combining the growth characteristics and mechanical properties. Through force analysis of the cutting tool, the key factors, which affects the harvesting performance, were clarified to be the blade inclination and the knife shaft speed. The Fluent software was used to analyze the flow field of the harvesting chamber, which aims to determine the appropriate wind speed. To improve the working performance of the rotary cutting safflower harvesting end effector, a three-factor, threelevel orthogonal test was carried out with the blade inclination, knife shaft speed and wind speed as the influencing factors, and with the recovery rate, damage rate and loss rate as the response indexes. A regression model for the three-factor interaction was developed and optimized based on the results of the Box-Behnken test. The optimal parameter combination is: the blade inclination is 15°, the knife shaft speed is 1570, and the wind speed is 6 m/s. A test of the optimization results showed that the recovery rate was 91.47%, the damage rate was 7.51%, and the loss rate was 4.67%. This study can provide theoretical basis and technical reference for the mechanized harvesting of safflower. [ABSTRACT FROM AUTHOR]

In order to accurately evaluate the meshing characteristics and differences between the two meshing regions of nutated double-arc bevel gear pairs, the curvature and relative motion parameters that characterized the quality of gear transmission were theoretically calculated and studied. Firstly, the tooth surface mathematical equations of double circular-arc internal and external bevel gears were derived based on gear spatial meshing theory of gear meshing. Secondly, a meshing coordinate system of nutation drive was established and the meshing contact points under ideal installation conditions were obtained by using tooth contact analysis(TCA). Then, the mathematical expressions of the curvature and velocity at the contact point were derived based on differential geometry, and the contact region was determined with Hertz elastic contact theory. Finally, the principal curvature, induced normal curvature, entrainment velocity, relative sliding velocity and slide-roll ratio of the meshing gear pair were analyzed by an example. The results indicate that the induced normal curvature of the elliptic long-axis direction is close to 0, and the absolute value of the induced normal curvature of the short-axis direction is small, combining with the public law vector direction of the tooth flank, it is known that the curvature interference phenomenon doesn’t occur in the meshing process and the gear pair has good contact strength. Meanwhile, the relative sliding velocity is much smaller in value than the entrainment velocity, which is beneficial to reduce wear of tooth. The slide-roll ratio in both meshing areas approaches 0, indicating that the transmission is approximately pure rolling. The contact points and regions are located in the middle of the tooth surface and distributed along the direction of the tooth width; the finite element results are consistent with the theoretical calculations. The results of this study provide a theoretical basis for the elastohydrodynamic lubrication and wear analysis of nutated double-arc bevel gears. [ABSTRACT FROM AUTHOR]

Aiming at the problem that the nonlinearity of gearbox vibration signal made it difficult to effectively extract the damage feature, a fusion damage identification method based on dual-frequency refined composite multi-scale permutation entropy(DFRCMPE) and whale algorithm optimized support vector machine(WOA-SVM) was developed. First, the wavelet packet decomposition(WPD)was used to decompose the gearbox damage vibration signal in two layers to obtain the low-frequency and high-frequency components reflecting the gearbox damage characteristics. Then, the refined composite multi-scale permutation entropy(RCMPE) was used to analyze the two groups of frequency band components to fully extract the damage information embedded in the vibration signal, and constructed the damage characteristics. Finally, the damage features were input into the whale algorithm optimization support vector machine classification model to achieve intelligent damage identification; and the effectiveness of the fusion damage identification method based on DFRCMPE and WOA-SVM was discussed by taking the gearbox vibration signal collected in the experiment as the research object. The research results show that comparing with the feature extraction methods based on refined composite multi-scale entropy(RCMSE), refined composite multi-scale fuzzy entropy(RCMFE ), RCMPE and refined composite multi-scale dispersion entropy(RCMDE), the fusion damage identification method based on DFRCMPE and WOA-SVM has higher accuracy and stability, and the average recognition accuracy reaches 100%; this method can provide a feasible way to solve the problem of gearbox fault identification in practical applications. [ABSTRACT FROM AUTHOR]

Aiming at the problem of fault feature extraction and pattern recognition of planetary gearbox, a planetary gearbox fault diagnosis method combined honey badger algorithm(HBA) optimal improved complete ensemble empirical mode decomposition with adaptive noise(ICEEMDAN), hierarchical weighted permutation entropy(HWPE) and grey wolf algorithm(GWO) optimal support vector machine(SVM)was proposed. Firstly, HBA was used to optimize the white noise amplitude weight and noise adding times of ICEEMDAN, and HBA-ICEEMDAN decomposition was performed on the vibration signal of planetary gearbox to obtain several mode functions, and the components with larger correlation coefficients were selected for reconstruction. Then, sensitive feature values of reconstructed low noise signals were extracted by HWPE method to obtain fault feature vectors. Finally, GWO was used to optimize the penalty coefficient and kernel coefficient of SVM, and GWO-SVM multi fault classifier was trained to realize damage identification of planetary gearbox, and the experiments were carried out with the vibration data of planetary gearbox, and the effectiveness of the algorithm was verified. The research results show that the fault diagnosis method of planetary gearbox combining HBA-ICEEMDAN, HWPE and GWO-SVM can accurately identify typical single point faults and composite faults of planetary gearbox, with an identification accuracy rate of 98.15%. Comparing with other combination methods, the method has more advantages and effectiveness in fault diagnosis of planetary gearbox. [ABSTRACT FROM AUTHOR]

Aiming at the calculation of the contact characteristics and contact forms of the modified straight bevel gear pair, a loaded contact analysis method for the modified straight bevel gear pair was proposed. The calculation process of meshing characteristics of modified straight bevel gear pair was systematically expounded. Firstly, the standard tooth surface of straight bevel gear was generated based on the principle of spherical involute spreading, and the mathematical model of tooth root fillet was constructed according to the principle of tangential tooth root circle and spherical involute. Then, combining with binary quadratic polynomial, the tooth surface was modified and the corresponding discrete points were obtained. On this basis, the modified tooth surface equation was reconstructed by using spline surface construction method. After that, according to the principle of gear meshing, the tooth contact analysis was further completed, and the instantaneous conjugate contact points and the meshing traces of the whole meshing period were obtained. At last, the contact ellipse, the major and minor axes, maximum contact stress and stress distribution under load were calculated by using Hertz contact correction model, and the loading contact analysis of conjugate contact straight bevel gears was completed. The research results show that, comparing with the results of finite element, under the condition of using the calculation method of loading contact characteristics, the meshing characteristics such as contact trace and contact ellipse are consistent, and the errors of contact force and maximum contact stress are within 1% and 2%. The comparison results show that the loading contact of modified straight bevel gears can be accurately analyzed by the proposed method. [ABSTRACT FROM AUTHOR]

Aiming at the problems that the traditional fault diagnosis methods had poor diagnosis effect and poor generalization ability in the wind turbine gearbox under variable operating conditions and mixed fault conditions, a wind turbine gearbox fault diagnosis method (TL-RN-ELM) based on deep residual network (ResNet) -extreme learning machine (ELM) and transfer learning (TL) was proposed. Firstly, the principles of continuous wavelet transform (CWT), convolutional neural network (CNN), ResNet, TL and ELM were introduced. Then, the TL-RN-ELM fault diagnosis model of wind turbine gearbox was established. Finally, the bearing data set and gearbox data set were used to validate the proposed method. Data acquisition and processing were carried out from the CWRU bearing data set and the SEU gearbox data set. The original one-dimensional vibration signal was converted into two-dimensional wavelet time-frequency image using CWT, and the ResNet18 model was trained using CWRU bearing data set to generate a pre-training model. The data in the pre-training model was migrated to the SEU gearbox dataset, the module was fine-tuned, features were extracted and input into the ELM classifier, and then the classification results were compared with the other three types of models. The experiment results show that the average accuracy of TL-RN-ELM can reach 98.79% for small sample migration fault diagnosis from bearing to bearing, bearing to gear and mixed fault. Comparing with other methods, the average accuracy rate is increased by 4.73%～9.6%. The research results show that this method has good diagnostic effect and generalization ability. [ABSTRACT FROM AUTHOR]

When the gears work under high-speed and heavy-load conditions, the effects of friction and wear cannot be ignored. The gear modification can reduce gear wear and surface temperature, and has a significant effect on improving the anti-scuffing ability of gears. Thus, the heat distortion and modification of gears are studied. Based on the basic theories of gear meshing principle and gear modifying principle, the following studies have been made: a parametric model of gear thermo-mechanical coupling is established using the finite element simulation software; the steady-state heat balance equations for each face of the gear teeth are determined, and the finite element simulation software is used to automatically impose convection boundary conditions and frictional heat fluxes on each point of the gears. By solving the temperature field of the gear, the influence of gear tooth temperature change on gear deformation is analyzed, and gear modification technology is studied. The calculation formulas of elastic deformation, thermal deformation and thermo-mechanical coupling deformation are derived. The results show that the modification can reduce the gear temperature and improve the scuffing strength of the gear.

With the continuous improvement of locomotive operating speed, increasing axle load and increasing traction power, the dynamic excitation of wheel-rail interface and gear pair interface have become more and more intense, directly affecting the operational reliability or even safety of the locomotive or the train. Based on the traditional rotor dynamics and the classical vehicle-track coupled dynamics, a locomotive-track coupled spatial dynamics model is established, in which the dynamic effects from drive system are considered. Under three different combinations of excitation, namely constant mesh stiffness, time-varying mesh stiffness and track geometrical irregularity, the vibration responses of the gear transmission are simulated during the uniform and accelerated operation of the locomotive. By comparing the difference of vibration response, mesh force and dynamic transmission errors of gear pair of traction motor under different combinations of excitation, the influence of different excitation on the vibration characteristics of gear transmission is explored. The following conclusions are drawn: 1) The time-varying mesh stiffness directly affects the vertical and longitudinal vibration of the traction motor. 2) The influence of time-varying mesh stiffness and track geometrical irregularity varies at different speed stages of locomotives. 3) During the acceleration process of the locomotive, resonance phenomenon of the traction motor and gear pair can be caused at a certain speed when considering time-varying mesh stiffness. The conclusions obtained will provide certain reference significance for the selection of design parameters, evaluation of dynamic characteristics, and life prediction of locomotive drive system.

Aiming at the transmission gear system of the head main drive of large shield machines with a diameter of 16 m and in order to explore the dynamic characteristics of the multiple sources parallel drive transmission gear system (including 16 groups of power sources) under real driving conditions, an equivalent dynamic model of 68 DOF bending-torsional coupling of the main drive gear system of the large scale shield machine is established using the lumped parameter method. Considering the influence of the nonlinear factors such as time-varying meshing stiffness, gear transmission error and gear clearance, the model analyzes the time-frequency dynamic response characteristics of the transmission system under the action of multi-source driving torque in actual driving conditions. The results show that the vibration frequency of the system mainly consists of gear meshing frequency and its frequency doubling, and the maximum value of dynamic meshing force occurs at the frequency doubling of corresponding meshing frequency. The amplitude of gear vibration and its meshing force are obviously affected by the input torque fluctuation of hydraulic motors.

With the development of technology and advances in manufacturing technology, higher requirements have been placed on reducing the vibration and noise of gear transmission systems. Gear modification is one of the effective ways to reduce the noise and vibration of the gear transmission system. In this paper, finite element method is used to analyze the contact stress of gear teeth in the gear transmission process. The influence of gear modification on the gear transmission system is analyzed. The optimal modification of the gear is determined by comparing the dynamic characteristics. Considering the difference between tooth modification and profile modification, the effects of tooth modification and profile modification on gear transmission system are analyzed. It has been found that proper modification of the gear can improve the dynamic characteristics of the gear transmission system. It provides the basis for reducing vibration and noise control in gear transmission systems. [ABSTRACT FROM AUTHOR]