Gear Mesh Research Articles

Investigation of sound and vibration behavior of cylindrical gears

As technology progresses, the demands placed on drive trains are continuously increasing. This also includes the vibration behavior and the acoustic performance of gearboxes. Especially when electric motors are used for propulsion and thus masking by an internal combustion engine or a similar driving machine vanishes, the optimization of the noise characteristics contribute as an important aspect to a successful gear design. Since the main noise originates from the characteristic power transmission process of the mating gear teeth, the transfer path of the structure-borne sound is a complex composition of gear mesh, shafts, bearings and housing. As a result, the acoustic performance depends on various influencing factors and hence a deep understanding of the dynamic interactions in a gearbox is required for optimization purposes. A suitable calculation strategy highly supports production development by identifying key influencing factors. In this context, the investigation of the dynamic behavior of a gearbox concept with respect to its acoustic performance is presented in this article.

Investigation on Tooth Surface Wear of Cycloid Drives Considering Tooth Profile Modifications

Cycloid drives are widely used in various mechanical systems due to their high reduction ratio, compact size, and high efficiency. Tooth surface wear is a major problem that affects the reliability and durability of cycloid drives. However, compared to the research on the wear of involute gears, the prediction of tooth surface wear in cycloid drives is relatively limited and less extensive. To fill this gap, the theoretical wear model of the tooth surface of cycloid-pin gear pairs is proposed based on the Hertz contact theory and Archard’s formula, with consideration of tooth profile modifications. Firstly, the loaded tooth contact analysis model is established to determine the relative sliding velocity and tooth contact stress. Secondly, the calculation steps of single tooth surface wear are presented within one gear mesh cycle. With this, the effects of the tooth profile modifications, the operating conditions such as output torque, input speed, and the assembly eccentricity on the wear depth within one gear mesh cycle are investigated. This study gives a deeper understanding of the tooth surface wear mechanisms of cycloid drives and could be employed to assist gear design and to improve the wear resistance.

A spectral kurtosis based blind deconvolution approach for spur gear fault diagnosis

Unanticipated background noises often convolute fault information in the gearboxes’ vibration response. The Blind Deconvolution strategy has been extensively applied for fault-impulse enhancement to aid gear fault detection. The existing deconvolution strategies involve designing an optimum filter applied in the time domain. Gear tooth wear leads to the excitation of Gear Mesh Frequency harmonics. Hence, spectral analysis is typically used for gearbox fault detection. As such, feature enhancement in the order domain is more practical than existing blind deconvolution approaches. This study proposes a Spectral Kurtosis-based blind deconvolution strategy with filtering done in the order domain, to aid gear fault detection. Experimental analyses show 109.76% and 64.48% better performance for constant and real-world speed operation, respectively, for the proposed method to aid spectral analysis-based fault detection.

An Improved Coupled Dynamic Modeling for Exploring Gearbox Vibrations Considering Local Defects

Gearbox is a key part in machinery, in which gear, shaft and bearing operate together to transmit motion and power. The wide usage and high failure rate of gearbox make it attract much attention on its health monitoring and fault diagnosis. Dynamic modeling can study the mechanism under different faults and provide theoretical foundation for fault detection. However, current commonly used gear dynamic model usually neglects the influence of bearing and shaft, resulting in incomplete understanding on gearbox fault diagnosis especially under the effect of local defects on gear and shaft. To address this problem, an improved gear-shaft-bearing-housing dynamic model is proposed to reveal the vibration mechanism and responses considering shaft whirling and gear local defects. Firstly, an eighteen degree-of-freedom gearbox dynamic model is proposed, taking into account the interaction among gear, bearing and shaft. Secondly, the dynamic model is iteratively solved. Then, vibration responses are expounded and analyzed considering gear spalling and shaft crack. Numerical results show that the gear mesh frequency and its harmonics have higher amplitude through the spectrum. Vibration RMS and the shaft rotating frequency increase with the spalling size and shaft crack angle in general. An experiment is designed to verify the rationality of the proposed gearbox model. Lastly, comprehensive analysis under different spalling size and shaft crack angle are analyzed. Results show that when spalling size and crack angle is lager, RMS and the amplitude of shaft rotating frequency will not increase linearly. The dynamic model can accurately simulate the vibration of gear transmission system, which is helpful to gearbox fault diagnosis.

Crack detection of a modified high contact ratio gear

For the purpose of vibration-based fault detection and to avoid gear failure consequences it is necessary to investigate the possibility of early fault detection. A reduction in the gear time-varying mesh stiffness (TVMS) due to the existence of a crack can be used to detect and evaluate tooth damage. The reduction in TVMS has an impact on the system’s dynamic response signal, and then the used fault detection indicators are affected. The current article sheds light on the fault detection possibility of high contact ratio (HCR) gears as compared to those standard ones of low contact ratio (LCR). The influence of modifying the gear tooth addendum dimension for obtaining a high contact ratio on the possibility of early fault detection is studied. Twenty different crack cases are examined by using both the LCR and HCR design cases. For every crack case, the mesh stiffness is evaluated and introduced to the used gear dynamic model for obtaining the system’s dynamic response. The TVMS evaluation is presented for both the LCR and HCR gear cases. Four fault detection indicators, namely the RMS, kurtosis, peak value and crest factor are applied as different measures to enhance the research outcome. The results show that the studied indicators will have less increase when the crack size increases in the HCR design than in the LCR one. Therefore, the HCR design will be less sensitive or more difficult to detect from the fault detection perspective. Lowering the amount of signal noise is applied to the HCR case to examine the impact on enhancing the obtained indicators. The four applied indicators show different behaviours with reducing noise.

The Non-Linear Excitation Load-Sharing Method of a High-Powered Nuclear Planetary Gear Train

The paper primarily employs the 3D calculation method of the helical gear-meshing line and meshing position, in addition to the traditional method of the gear-meshing stiffness calculation. This analysis and correction of load-sharing are beneficial for improving the assembly process of high-powered critical equipment. The dynamic models of rigid–flexible coupling, velocity–torque, and the meshing force of planetary gear trains in nuclear power plants are established based on the principles of gear dynamic characteristics. Based on an analysis of the vibration characteristics of a planetary gear train, a load-sharing method for the planetary gear train is proposed. This uniform load-sharing method is explored under different modification values to provide a reference for load-sharing research on high-powered key equipment. In this paper, a dynamic simulation analysis of the gearbox system is conducted, using virtual prototype software to study the load-sharing performance of the planetary gear system. Furthermore, via a vibration frequency analysis of the gear mesh force, the causes of planetary gear train vibration are discussed, particularly their impact on planetary load. This provides a basis for the assembly process of a nuclear power circulation pump gearbox, ensuring that the gearbox for the circulation pump has a longer life that meets the 40-year service life requirement, and provides a foundation for the study of planetary load characteristics.

Optimization Method of Design Parameters of Hypoid Gears With Low Sliding Ratio

Abstract To reduce the wear, an optimization method of hypoid gears with the objective of minimizing the pinion sliding ratio is proposed. First, the sliding ratio model of the hypoid gear is established on the basis of the spatial gear meshing theory. Furthermore, the influence of design parameters on the sliding ratio and the relative sliding velocity is discussed, and the analysis results show that the parameters, especially the spiral angle and the pressure angle, have the most significant influence on the sliding ratio of the pinion. Additionally, the optimization model of hypoid gears is established, and the optimization objective is to minimize the sum of the absolute sliding ratios of 34 meshing points on the pinion tooth surfaces. Through comparison before and after optimization, it is found that the maximum drops of the sliding ratios for the pinion drive and coast side are 68.6% and 29.58%, respectively. Finally, the results of the running temperature tests demonstrate that the temperature of the optimized gear pair is significantly reduced and that the proposed method is effective.

Crowned spur gears for constant mesh stiffness: A conceptual approach

Flank line crowning is a gear surface geometry modification that can be applied as a measure to accommodate contact imperfections along the gear teeth facewidth, that are a consequence of misalignment from either geometric defects or elastic deflection. Due to flank line crowning, the contact stiffness between the teeth of an ideal spur gear changes, thus modifying the gear mesh stiffness. Gear mesh stiffness fluctuations are one of the main driving factors behind gear performance, such as transmission error, dynamic overload and overall system vibration. Regardless of manufacturing feasibility, a set of analytical equations, derived from the classical elliptical contact theory is presented aiming to find the flank line crowning values along the path of contact that eliminate gear mesh stiffness fluctuations. This is achieved by transforming the shape of single teeth pair mesh stiffness through the contact stiffness, making it similar to the shape of the load sharing. A direct method to find the load sharing of spur gears with flank line crowning is also presented.

Study on Friction Characteristics of ADC12-POM Gear Pair

In a transmission system, the cooperative utilization of metal small gears and plastic large gears not only significantly reduced the system weight and noise levels, but also harmonized strength and longevity between the gears of varying sizes. Nevertheless, the existing research on metal-plastic friction remains insufficient. This study focused on the ADC12-POM gear pair, conducted sliding friction tests between polyoxymethylene (POM) plastic balls of different diameters and ADC12 metal plates using a self-made reciprocating friction and wear testing machine. The friction coefficients between the ADC12-POM sliding pairs were evaluated under different load and velocity conditions, and subsequent nonlinear regression analysis using the IBM SPSS software yielded an initial calculation model for the friction coefficients at the contact surfaces of the ADC12-POM gear pair. By analyzing the Engagement characteristics of gears, we calculated the variations in curvature radius, relative sliding velocity, and load distribution coefficient during the Engagement process. This enabled us to establish a computational model for determining the tooth surface friction coefficient of the ADC12-POM gear pair. Furthermore, we derived the relationship between Engagement efficiency and the friction coefficient and conducted experimental investigations to assess the efficiency of gear Engagement. The deviation between the theoretically calculated Engagement efficiency and the experimental results was approximately 2%, thereby confirming the feasibility of the friction coefficient calculation model.

Robust deep learning-based fault detection of planetary gearbox using enhanced health data map under domain shift problem

Abstract The conventional deep learning-based fault diagnosis approach faces challenges under the domain shift problem, where the model encounters different working conditions from the ones it was trained on. This challenge is particularly pronounced in the diagnosis of planetary gearboxes due to the complicated vibrations they generate, which can vary significantly based on the system characteristics of the gearbox. To solve this challenge, this paper proposes a robust deep learning-based fault-detection approach for planetary gearboxes by utilizing an enhanced health data map (HDMap). Although there is an HDMap method that visually expresses the vibration signal of the planetary gearbox according to the gear meshing position, it is greatly influenced by machine operating conditions. In this study, domain-specific features from the HDMap are further removed, while the fault-related features are enhanced. Autoencoder-based residual analysis and digital image-processing techniques are employed to address the domain-shift problem. The performance of the proposed method was validated under significant domain-shift problem conditions, as demonstrated by studying two gearbox test rigs with different configurations operated under stationary and non-stationary operating conditions. Validation accuracy was measured in all 12 possible domain-shift scenarios. The proposed method achieved robust fault detection accuracy, outperforming prior methods in most cases.

Characteristics in hard conformal EHL line contacts

PurposeInternal gearings are commonly used in transmissions due to their advantages like high-power density. To ensure high efficiency, load-carrying capacity and good noise behavior, a profound knowledge of the local gear mesh is essential. The tooth contact of internal gears relates to a convex and concave surface that form a conformal contact. This is in contrast to external gears, where two convex surfaces form a contraformal contact. This paper aims at a better understanding of conformal contacts under elastohydrodynamic lubrication (EHL) to improve the design of internal gearings.Design/methodology/approachAn existing numerical EHL model is used for studying the characteristic properties of a hard conformal EHL line contact. A hard contraformal EHL line contact is studied as reference. Non-Newtonian fluid behavior and thermal effects are considered. By taking into account the local contact conformity and kinematics, the effects and relevance of the curvature of the lubricant gap and micro-slip are analyzed. In a parameter study, scale effects of the contact radii on film thickness, temperature rise and friction are examined.FindingsThe curvature of the lubricant gap and effects of micro-slip are small in hard conformal EHL line contacts. For high micro-slip, it can be neglected. Hence, the modeling of conformal contacts using an equivalent geometry of the contact problem is reasonable. The parameter study shows beneficial tribological aspects of the conformal contact compared to the contraformal contact. Higher film thickness and lower fluid coefficient of friction are observed for conformal contacts, which can be attributed to lower pressures for the case of the same external normal force, or to a higher contact temperature rise for the case of equivalent contact pressure.Originality/valueDespite its widespread existence, the local geometry and kinematics in hard conformal EHL line contacts like in internal gearings have been rarely studied. The findings help for a better understanding of local contact characteristics and its relevance. The quantified scale effects help to improve the efficiency and load-carrying capacity of machine elements with hard conformal EHL contacts, like internal gearings.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-12-2022-0366/

Meshing impact analysis of the gear and rack of the pumping machine based on the SPH–FEM coupling method

This paper explores the feasibility of using the coupled smooth particle hydrodynamics–finite element method (SPH–FEM) to study the gear rack and meshing impact problem. Firstly, a numerical model containing both SPH and FEM units is established, and its accuracy is verified. Then, the principle of gear rack meshing impact is analyzed from the perspective of impact dynamics theory, and the formula of maximum meshing impact force is derived. Finally, the meshing impact process of the rack and pinion is simulated using the coupled SPH–FEM method, and experiments are designed to verify it. The analysis results show that the SPH–FEM coupling method can simulate the meshing impact behavior of the gear mechanism more accurately. On the other hand, the severity of the impact in each operating section was obtained. It is also found that the impact stress has reached the material's tensile limit, revealing the mechanism of tooth surface wear caused by the impact. The results of the study provide a choice of research methods for gear mechanism meshing impact and also provide some reference for gear rack tooth shape optimization.

A spectral self-focusing fault diagnosis method for automotive transmissions under gear-shifting conditions

Transmissions are core components of automobiles in adjusting the speed. The time-varying operation conditions, particularly the frequent gear shifting, present significant challenges for condition monitoring and fault locating of transmissions. At present, most existing studies primarily focus on the issues arising from time-varying speed, but they do not consider the challenges introduced by gear shifting. Gear shifting changes the meshing gear pairs within the transmission, causing the monitoring indicator amplitude fluctuates greatly. Consequently, the indicator fails to reflect the overall degradation trend of the transmission. To address this problem, this paper proposes a fault diagnosis method for automotive transmissions with the consideration of gear shifting. Our contributions are as follows: Firstly, we propose a spectral variation sparsity indicator (SVSI) based on the order spectrum at each gear position. Secondly, we fuse SVSI from different gear positions and create a comprehensive indicator called weighted health indicator (WHI). Finally, a diagnosis method based on SVSI and WHI is proposed for automotive transmissions under gear-shifting conditions. The effectiveness of the proposed method is validated using datasets from four automotive transmissions. The results demonstrate that our method is capable of detecting faults prior to inspection and accurately identifying faulty gears. Moreover, the performance of WHI is compared with several existing indicators. The results demonstrate that WHI exhibits stronger correlation, monotonicity, and robustness. This indicates that WHI is able to effectively mitigate the influence of gear shifting, thereby better reflecting the overall degradation trend of the transmission. Consequently, our proposed method significantly contributes to the field of condition monitoring and fault locating for automotive transmissions.

Measuring instantaneous angular speed using a gear wheel as material measure to detect pitting damage during an endurance test

Gearbox condition monitoring is mostly carried out using accelerometers at the housing. The long transfer path interferes with the information on damaged gears. Therefore, new technologies such as measuring the instantaneous angular speed (IAS) are gaining interest. But these require constructive changes in the power-transmitting elements. Therefore, this contribution uses magnetoresistive (MR) sensors and a minimally invasive integration approach to measure IAS. Three sensor classes are integrated: accelerometers at the gearbox housing, MR sensors, which use a gear wheel as a material measure and MR sensors, which use an encoder magnet at the end of the shaft. These sensor concepts are introduced by Koch et al. 2022 [1] and applied to a 3-stage bevel helical gearbox in this contribution. The first results are on artificial tooth flank damage. Therefore, this contribution focuses on real fatigue pitting damage.A back-to-back test stand is set up for the endurance test. The tests are carried out with an overload load at a constant speed to generate fatigue pitting damage. The results are evaluated in the frequency domain by exploring the gear mesh frequency (GMF) and sidebands modulated with the shaft frequency of the damaged pinion. Results show that with all sensor concepts, the damages can be detected. Influences when using a gear wheel as a material measure are described for one measurement concept. A feature to compare the damage-specific information over the endurance test is introduced and the influence of the transfer path is evaluated through analysis of the relative rise of damage-specific amplitudes.

Gear evaluation deviations-based crucial geometric error identification of five-axis CNC gear form grinding process

The gear form grinding accuracy is significantly affected by crucial geometric errors. The gear form grinding process is a special line contact forming method. There are exclusive evaluation standards for gear grinding accuracy. While the existing sensitivity analysis for spatial point errors cannot meet the final gear report requirements. Hence, a novel method for analysis of geometric error influence on the key gear evaluation deviations (GED) is proposed. First, the actual digital tooth surface considering geometric errors and gear form grinding mechanism was constructed according to the homogeneous transformation matrix (HTM) and multi-body system theory (MBS). Second, the GED of the digital tooth surface was gained according to the modified gear meshing equations. Third, the analytic mapping relationship between the GED and machine tool geometric errors was first established. Then, the crucial geometric errors affecting the GED were identified based on a proposed Morris method. Finally, the identification results were compared to the existing publications, and the compensation discussions of crucial errors were demonstrated to validate the advantages of the proposed method. It can be found that the compensation results of GED-oriented key errors are better than those of the traditional methods, which is beneficial to the improvement of evaluation reports.

Experimental‐based study of gear vibration characteristics incorporating the fractal topography of tooth surface

AbstractMicroscopic roughness is inevitable on the gear meshing surface, which is also a key parameter affecting the dynamic response. The surface roughness exhibits self‐affine characteristics across multiscales. To explore the influence of surface fractal topography on the vibration amplitude of the gear system under different rotational speeds and loads, an experimental setup of spur gear transmission is devised. The fractal dimension and fractal roughness of the meshing surface are calculated by the power spectral density method. The relationships between gear response and fractal parameters are revealed experimentally. Results indicate that a rougher tooth surface, that is, a smaller fractal dimension or larger fractal roughness, corresponds to an intense vibration amplitude. The sensitivity of dynamic response to the tooth surface topography varies at different rotational speeds and loads. Under low speed and light load conditions, the fractal dimension and fractal roughness have a more obvious influence on the dynamic response of the gear transmission system. With the increase of speed and load, the macroworking conditions gradually become the main factor attributed to vibration amplitude.

Kalorimetrische Messung der Ver- zahnungsverlustleistung im Bereich hoher Umfangsgeschwindigkeiten

Gear damage, e.g. scuffing, reacts sensitively to the local dissipation of frictional heat during a full gear mesh. Several empirical friction models have been established in relevant literature. These can be used to calculate the gear friction locally or averaged over a mesh. For calibration purpose, experimental data from twin disc machines with stationary contact conditions are mostly used. However, the assignment of the model as well as the consideration of topographical, rheological and geometrical effects is often subject to uncertainties. In this paper, a method is presented to measure the power losses of high-speed spur gears up to vt = 100 m/s. The measurement principle uses the calorimetric properties of the circulating lubricant. The implementation of the measurement setup in a highspeed gear test rig reduces thermal interferences from sealings and bearings. Analysis regarding the measurement quality show that the measurement method delivers reproducible results with a high measurement resolution over a wide range of operating conditions.

Research on time-varying meshing stiffness of wind turbine gearbox considering tooth surface wear

The time-varying meshing stiffness (TVMS) is an important element of the gear system. In this paper, the TVMS of each gear set of a wind turbine gearbox is calculated based on the principle of potential energy method, where wear is the most likely failure in the operation of a wind turbine gearbox. Therefore, the Archard wear model is brought into it, and theoretically the analytical formula of stiffness considering tooth wear is derived, and the time-varying wear depth is deduced as the natural wind speed keeps changing and the input torque of the wind turbine gearbox keeps changing. The interrelationship between gear tooth wear and meshing pressure angle and number of meshes is studied in depth, and the TVMS of each gear set under wear is calculated using the modified tooth profile model. The results show that the tooth profile wear depth is related to the gear meshing angle, and the tooth profile wear depth becomes larger as the number of meshes increases, thus reducing the TVMS of the wind turbine, and the TVMS shows irregular fluctuations under time-varying wear.

Experimental and Simulation Analysis on Windage Power Loss of Herringbone Gear Pair

Abstract This paper presents a novel windage power loss (WPL) measurement method for the meshing herringbone gear pair. First, the WPL test rig of the herringbone gear pair is put up, and then the measurement sequence of WPL is described. Second, the WPL of different gear pairs is tested and the influence of operation speed, design parameters on the WPL of meshing gear pairs is studied. Finally, the WPL simulation analysis of meshing gear pair is carried out. The generation mechanism of WPL is analyzed and the WPL of each meshing gear pair at different rotational speeds is obtained, which verifies the accuracy of the presented WPL measurement method. The research on the measurement method of WPL can provide support for the optimization design of the high-speed gear pair.

Vibration response mechanism of fixed-shaft gear train with cracks based on rigid-flexible coupling dynamics and signal convolution model

Affected by external flexible transfer path of fixed-shaft gear train, internal gear meshing vibration signals that representing the healthy state of gear will convolve with modal information of gearbox housing and become much more complicated. Moreover, gear crack fault features of fixed-shaft gear train are relatively weak and complex, which are difficult to diagnose. Therefore, to reveal the origination mechanism of crack fault, a rigid-flexible coupling dynamics model of fixed-shaft gear train with full consideration of flexible housing is firstly established, then a signal convolution model is proposed to solve housing vibration response signal by combining internal excitation and external transfer path. Thereinto, as internal influence factor, time-varying meshing stiffness that drives excitation forces is used to reflect excitation characteristics under normal and crack state; as external influence factor, flexible transfer path that includes modal characteristics of gearbox housing is calculated by finite-element-method. Through the established models, modulation sideband features of housing vibration response signals are selected as crack fault indicator. Corresponding vibration response mechanism is revealed clearly under normal and different crack degrees in simulations. Experimental results keep good consistency at crack fault features with simulation signals and verify the effectiveness of the proposed models.