Tooth Spalling Research Articles

Improved mesh stiffness model of spur gear considering spalling defect influenced by surface roughness under EHL condition

Gear tooth spalling is a typical tooth surface defects in gear transmission. The accurate calculation of the time-varying mesh stiffness of the gear pair with spalling defect under mixed elastohydrodynamic lubrication (EHL) plays an important role in tooth damage prediction and fault feature analysis. In this work, an improved time-varying mesh stiffness (TVMS) model of spalling faulty gear in mixed EHL line contact considering the coupled effect of rough surface topography is established. The proposed model considers the combined effect of spalling defect, surface roughness topography, and lubrication on the contact characteristics of the meshing interface to obtain a revised contact stiffness, which is further used to determine the comprehensive TVMS. The cylindrical contact coefficient for curved meshing interface with spalling fault is derived and incorporated into the statistical micro-contact Greenwood and Williamson model (GW model) to obtain the asperity contact stiffness. The revised contact stiffness at the rough faulty gear interface is obtained from the parallel action of the asperity contact stiffness and oil film stiffness under load-sharing concept. The dynamic responses of the gear system are analyzed using the established mesh stiffness model through the six degrees of freedom translational-torsional dynamic model, in which the dynamic meshing force is calculated iteratively using the transit surface topography and geometrical parameters along the line of contact instead of a quasi-static meshing force. Effects of multi-parameters as surface roughness, spalling fault size, and lubricant on the mesh characteristics and dynamic responses of the gear system are further investigated and discussed.

Dynamical modeling and characteristics analysis of tooth spalling in gear system with weight reduction structure

Focusing on gear transmission systems having thin web and hole structures for energy saving and weight reduction, this work aims to propose an effective method for dynamical modeling and characteristics identification of spalling in lightweight gear systems. A novel three-dimensional (3D) spalling morphology modeling method is developed by the optical scanner. Subsequently, an analytical-finite element (AFE) model is established to calculate the mesh stiffness with weight reduction structures and spalled teeth. Additionally, the discrete tooth surfaces from coordinate measuring machines (CMMs) are used to calculate the no-load static transmission error (NLSTE). A rigid-flexible coupling dynamic model is introduced into the gear-rotor-bearing system considering the lightweight rotor and friction characteristics. The effects of spalling fault levels, the number and distribution form of spalled teeth on dynamic characteristics of the lightweight gear system are investigated. The numerical and experimental results demonstrate the existence of coupling modulation between spalling and holes, but it can still be identified by time and frequency domain characteristics. The proposed model and analysis results provide important references for identifying spalling in lightweight gear systems.

Dynamic Characteristics and Fault Mechanism of the Gear Tooth Spalling in Railway Vehicles under Traction Conditions

Gear tooth spalling is one of the inevitable fault modes in the long-term service of the traction transmission system of railway vehicles, which can worsen the dynamic load of the rotating mechanical system and reduce the operating quality. Therefore, it is necessary to study its fault mechanism to guide fault diagnosis scientifically. This paper established a planar railway vehicle model with a traction transmission system and an analytical time-varying meshing stiffness (TVMS) model of the spalling spur gear. Then, it analyzed the dynamic characteristics under traction conditions. The research found that the spalling length and depth affect the amplitude of the TVMS at the defect, while the width affects the range of the TVMS loss. The crest factor is the best evaluation indicator in ideal low-noise environments due to its sensitivity and linearity, but it is not good in strong-noise environments. Similarly, a time–frequency analysis tool cannot significantly detect the sideband characteristics that are excited by spalling. After high-pass filtering, the root mean square and variance exhibit excellent classification and vehicle speed independence in strong-noise environments. This research achievement can provide adequate theoretical support for feature selection and making strategies for fault diagnosis of railway vehicle gear systems.

Fault feature analysis and detection of progressive localized gear tooth pitting and spalling

Fault feature analysis of gear tooth spalling plays a vital role in gear fault diagnosis. Understanding how fault features evolve as a fault progresses is key to fault severity assessment. Due to the complicated nature of gear meshing, fault features and their development as the fault severity progresses remain mostly unknown. The assessment of fault severity is generally based on the hypothesis that ‘the more severe the fault, the stronger the fault symptom’, an assumption that has not been experimentally validated. This paper provides a comprehensive, experimental analysis of the evolution of fault vibration features of a gear transmission with progressive localized gear tooth spalling. The effects of rotational speed on the vibration features of the gear transmission are analysed. Changes in fault features (e.g. periodic impulses and sideband phenomena) under different fault severity levels and speed conditions are compared. Results indicate that the number, amplitude and distribution of sidebands increase nonlinearly as the fault progresses. Based on feature analysis, a new health indicator of the mean of the nth order peaks is proposed to detect progressive localized tooth spalling. Results indicate that the proposed indicator shows very good performance for tracking the severity of progressive tooth spalling under different speed conditions.

An improved model for dynamic characteristics analysis of high-contact-ratio spur gears considering localised tooth spall defect

Tooth spall defects are one of the most common types of gear failures. The impact of the bottom features of the tooth spall on the dynamic properties of high-contact-ratio spur (HCRS) gears is investigated in this work. Considering the load sharing ratio, coupling structure effects, and nonlinear contact stiffness, a hybrid model was developed for evaluating the mesh stiffness of the HCRS gear, and a torsional dynamic model of the HCRS gear pair was built. The dynamic transmission errors and dynamic meshing forces are acquired by solving the above model; based on the dynamic responses of the healthy HCRS gear, the dynamic characteristics of two different spalled gear systems were compared. The results revealed that the proposed mesh stiffness model is effective within 5% calculation errors. The bottom shape of the tooth spall has important effects on the mesh stiffness but limited influence on the gear dynamic response. This study is expected to provide a theoretical foundation for future research on spall defect diagnosis in gear transmission devices.

Effect of localised tooth spall defect on dynamic performance of a high-contact-ratio spur gear system

This study considers the tooth spall morphology and establishes a kinetic model of a high contact ratio gear pair system with an ellipsoid tooth spall defect. The mesh stiffness of the spalled gear system is evaluated using the potential energy method. To obtain the accurate dynamic response, the friction force was incorporated into the gear kinetic model. The dynamic transmission error and dynamic meshing force under different rotational speeds are acquired by the proposed model. The dynamics of a healthy gear system and spalled gear system was compared. The results reveal that the presence of the tooth spall defect alters the motion state of the system, making it prone to instability. The study provides a theoretical foundation for future research on spall defect diagnosis of gear transmission devices.

Dynamic Analysis of a High-Contact-Ratio Spur Gear System with Localized Spalling and Experimental Validation

The dynamic characteristics and tooth spalling fault features are studied for the high-contact-ratio spur gear bearing system. The bending torsional dynamic model is proposed in this study for the gear bearing system with an ellipsoid spalling fault. This model also considers time-varying meshing stiffness, tooth friction, fractal gear backlash, and comprehensive transmission error. The meshing stiffness of the system is evaluated using the potential energy method. The bifurcation diagram, time-domain waveform, Poincaré map, phase map, frequency spectrum, and related three-dimensional map are used as tools to analyze the system’s dynamic response qualitatively. The results reveal that the system’s motion with ellipsoid tooth spalling defect exhibits rich dynamic behavior. The response of the proposed dynamic model is consistent with experimental results in the frequency domain. Therefore, the developed dynamic model can predict the system’s vibration behavior with localized spalling fault. Hence, it could also provide a theoretical foundation for future spall defect diagnosis of the gear transmission system.

A new analytical model for evaluating the time-varying mesh stiffness of helical gears in healthy and spalling cases

Accurately evaluating the time-varying mesh stiffness (TVMS) of a mating gear pair is one of the most important aspects in gear vibration dynamic simulation. Existing work on estimating TVMS of helical gears with tooth spalls generally assumes the defects are in flat bottom shape which deviates from the spalling features as observed in curved bottom shape in practice. The cliff like spalling feature results in inaccurate calculation of TVMS of helical gears with such spalls. This paper proposes an advanced method to evaluate the TVMS of helical gears with tooth spalls with curved-bottom features. In the proposed method, the gear tooth is sliced along the center line of tooth spall in order to easily evaluate the equivalent cross-section area and area moments of inertia of the gear tooth which enables the proposed method adapts to tooth spall(s) with curved-bottom features in arbitrary position, angle and size. The proposed method corrects the foundation stiffness errors of existing methods and takes the influence of axial mesh forces into consideration. Its effectiveness on modelling tooth spalls with curved-bottom features for helical gears is validated by FEM (finite element method).

Fault Feature Analysis of Gear Tooth Spalling Based on Dynamic Simulation and Experiments.

Gear dynamics analysis based on time-varying meshing stiffness (TMS) is an important means to understand the gear fault mechanism. Based on Jones bearing theory, a bearing statics model was established and introduced into a gear system. The lateral–torsion coupling vibration model of the gear shaft was built by using a Timoshenko beam element. The lumped parameter method was used to build the dynamic model of a gear pair. The dynamic model of a spur gear system was formed by integrating the component model mentioned above. The influence of rectangular and elliptical spalling on TMS was analyzed by the potential energy method (PEM). The fault feature of tooth spalling was studied by dynamic simulation and verified by experiments. It is found that the gear system will produce a periodic shock response owing to the periodic change of the number of meshing gear teeth. Due to the contact loss and the decrease of TMS, a stronger shock response will be generated when the spalling area is engaged. In the spectrum, some sidebands will appear in the resonance region. The results can provide a theoretical guide for the health monitoring and diagnosis of gear systems.

Failure dynamic modelling and analysis of planetary gearbox considering gear tooth spalling

The spalling mechanism and influence of fault evolution are studied for the gear system of wind turbine by analyzing the dynamic responses.The lateral-torsional dynamic model is proposed in this paper for multistage gear system with gear spalling fault, which considers the influences of nonlinear factors such as tooth friction, sun gear support, time-varying mesh stiffness, gear backlash and comprehensive mesh error.Based on the improved energy method, a calculation model of gear spalling fault is performed to analyze the effect of fault on the time-varying mesh stiffness. At the same time, the bifurcation diagram, time series, phase trajectory, Poincaré map, spectrum diagram and related three-dimensional diagramsare used as tools to qualitatively analyze the dynamic response of gear system. The results show that the fault characteristic frequency of sun gear is sensitive at low excitation frequency, which indicates that it is suitable for fault detection. In addition, the dynamic behavior of the system becomes more complex as the spalling becomes deeper.

Analysis of time-varying meshing stiffness of helical gear pair with tooth surface spalling

Time-varying meshing stiffness (TVMS) provides significant information about the health of gear systems. Tooth spalling will change the TVMS. Considering the contact state of gear pair, the purpose of this study is to investigate the influence of tooth surface spalling on the TVMS of helical gears. Firstly, the meshing stiffness analysis algorithm of helical gear pair with tooth surface spalling is proposed, based on the potential energy method, slicing method and numerical integration formula. Then the influence of different spalling parameters on the TVMS of helical gear pair is analysed by considering spalling length, width and the oblique cylinder bottom shape. Finally, the results show that the contact line falls into the defect area, the spalling has the most significant effect on the stiffness. The influence of oblique cylinder shape at the bottom of spalling is mainly affected after the contact line passes through the spalling area. This study improve the theoretical basis for spalling fault of helical geared mesh.

Dynamic Characteristics of a Gear System with Double-Teeth Spalling Fault and Its Fault Feature Analysis

Tooth spalling is one of the most destructive surface failure models of the gear faults. Previous studies have mainly concentrated on the spalling damage of a single gear tooth, but the spalling distributed over double teeth, which usually occurs in practical engineering problems, is rarely reported. To remedy this deficiency, this paper constructs a new dynamical model of a gear system with double-teeth spalling fault and validates this model with various experimental tests. The dynamic characteristics of gear systems are obtained by considering the excitations induced by the number of spalling teeth, and the relative position of two faulty teeth. Moreover, to ensure the accuracy of dynamic model verification results and reduce the difficulty of fault feature analysis, a novel parameter-adaptive variational mode decomposition (VMD) method based on the ant lion optimization (ALO) is proposed to eliminate the background noise from the experimental signal. First, the ALO is used for the self-selection of the decomposition number K and the penalty factor â of the VMD. Then, the raw signal is decomposed into a set of Intrinsic Mode Functions (IMFs) by applying the ALO-VMD, and the IMFs whose effective weight kurtosis (EWK) is greater than zero are selected as the reconstructed signal. Combined with envelope spectrum analysis, the de-nosing ability of the proposed method is compared with that of the method known as particle swarm optimization-based variational mode decomposition (PSO-VMD), the fixed-parameter VMD, the empirical mode decomposition (EMD), and the local mean decomposition (LMD), respectively. The results indicate that the proposed dynamic model and background elimination method can provide a theoretical basis for spalling defect diagnosis of gear systems.

Finite Element Analysis for Time Varying Mesh Stiffness behavior of different shapes of spalling

Time Varying gear mesh stiffness is the variation of stiffness for the one contact period of a gear pair. Spalling on gear tooth is one of the most common defects in gear transmission. The loss of surface materials due to tooth spall reduces the Time-Varying Mesh Stiffness (TVMS) of the gear pair. The time varying mesh stiffness is the change in mesh stiffness for a gear pair in one contact period. The evaluation of the TVMS of the pair of gear tooth under gear tooth spalling conditions may be useful in finding its dynamic behavior or instant change in TVMS behavior may be the signal of fault developed. The potential energy method is used for analytical calculation of time varying mesh stiffness of the gear. The tooth spall may be of any shape and in this paper we have assumed the spall to be circular, triangular and elliptical and conducted analytical calculation to find TVMS and compare with healthy gear pair. The same gear pair with three shape of spall and modelled and verified through finite element analysis. The data may be used for further analysis. Also a number of shape may be modelled in future.

Dynamics responses analysis in frequency domain of helical gear pair under multi-fault conditions

This work aims to investigate dynamic characteristics of a helical gear pair under multiple faults condition, through model-based dynamic analysis. Two kinds of faults, tooth spalling and local breakages are considered. Firstly, influences of each kind of fault on meshing stiffness of gear pair with one or more faulted teeth were revealed. Then an 8 degree of freedom lumped-parameter model was developed to obtain dynamic responses. Furthermore, frequency spectrum analysis of the responses was conducted and compared with those under healthy condition. Results indicate that spalling or local breakage introduce different affects into mesh stiffness, and consequently displacement & velocity amplitudes of pinion appear with different waveforms, especially for the case only tooth breakages happen. This work could provide useful instructions for fault detection diagnosis of geared transmissions under multiple fault conditions.

Comparison of meshing characteristics of helical gears with spalling fault using analytical and finite-element methods

Abstract This paper investigates the effect of a gear tooth spalling in a helical gear. An analytical model was developed to study the effect of the damage to the time-varying mesh stiffness, contact stress and tooth root fillet stress. In order to validate the efficiency and the accuracy of the proposed method, a finite element method is presented for simulation, such to compare the mesh stiffness and stresses obtained from the analytical method under different spalling variables, including the spalling lengths, widths, axial positions (in the direction of face width) and tooth orientation positions (from dedendum to addendum). The results show that the proposed analytical method has higher computation efficiency than the finite element method, and the mesh stiffness obtained from two methods shows a good agreement. However, some errors exist between the time-varying mesh stiffness and stresses obtained by the two methods, but change laws of the tooth root stress and contact stress obtained from the two methods are similar. This is because the effects of flank-tip contact and spalling edge contact are considered in the finite element method, which makes the results more accurate than the results obtained by the proposed analytical method.

A shape-independent approach to modelling gear tooth spalls for time varying mesh stiffness evaluation of a spur gear pair

Abstract Accurately evaluating the gear mesh stiffness with tooth fault(s) plays an important role in gear dynamic simulations. Common approaches to evaluating the gear TVMS with spall assume a specific geometry (rectangular, round, elliptical, V-shape etc.) to approximate the features of the spall. The accuracy of geometry-based methods on modeling gear tooth spall depends on how close the utilized geometry is to the actual shape of the spall. In practice, gear tooth spalls often occur in very irregular shapes and may also have randomly distributed features under multi-spall conditions. Due to shape irregularities and uncertainties in their distribution, it is often difficult to apply existing methods to accurately evaluate gear TVMS with spalls as observed in practice. To address these shortcomings, this paper proposes a shape-independent method to model tooth spall(s) based on defect ratios instead of a specific geometry. The proposed method is applicable to tooth spalls of various sizes, shapes, numbers and distribution conditions, and thus is capable of modeling any kind of tooth spall. A powerful advantage of the proposed method is that to change the type of spall being modelled, only the functions of the defect ratios need to be modified rather than the entire algorithm. Therefore, the proposed method is general in nature and much easier to implement in practice. The effectiveness of the proposed shape-independent approach to modelling different kinds of tooth spalls is validated by finite element results.

A new adaptive evolutionary digital filter based on alternately evolutionary rules for fault detection of gear tooth spalling

Abstract Evolutionary digital filter (EDF) is an adaptive filter that controlled by adaptive algorithm based on the evolutionary strategies: cloning and mating. The adaptive algorithm of EDF exhibits the advantage of avoiding local optimum problems that arise from a multiple-peak performance surface of an adaptive noise cancellation (ANC) system. However, the convergence rate of the classic EDF is limited by inappropriate arrangement of evolutionary strategies and large population of individuals. In this paper, a new method referred to alternately evolutionary digital filter (AEDF) is proposed in order to solve the problem of lower convergence rate of the classic EDF. The basic concept of the proposed method is to alternately apply mating evolutionary strategy to locate the peaks in performance surface quickly and then apply cloning evolutionary strategy to get the global optimum near the peaks accurately. The convergence rate and noise cancellation performance of the proposed method is verified by both simulated signals and experimental signals. The results show that the proposed AEDF-based ANC method can effectively detect the gear tooth spalling faults in noisy environment and exhibits much faster convergence rate compared to previous methods.

Blind deconvolution based on cyclostationarity maximization and its application to fault identification

Blind deconvolution algorithms prove to be effective tools for fault identification, being able to extract excitation sources from noisy observations only. In this scenario, the present paper introduces a novel blind deconvolution method based on the generalized Rayleigh quotient and solved by means of an iterative eigenvalue decomposition algorithm. This approach not only is characterized by a weighting matrix that drives the deconvolution process, but can also be easily adapted to arbitrary criteria. Based on this framework, a novel criterion rooted on the maximization of the cyclostationarity of the excitation – as typically encountered with machine faults – is proposed and compared with other blind deconvolution methods existing in the literature. The comparisons involve both synthesized and real vibration signals, taking into account a gear tooth spall and an outer race bearing fault. The results reveal superior capability to recover impulsive cyclostationary sources with respect to other blind deconvolution methods, even in the presence of impulsive noise or under non-constant speed.

Evaluation of the time-varying mesh stiffness for gears with tooth spalls with curved-bottom features

Abstract Gear tooth spalling is one of the most common defects in gear transmission. The loss of surface materials due to tooth spall reduces the Time-Varying Mesh Stiffness (TVMS) of the gear pair, and thus modifies the vibration response of the gear transmission. The evaluation of the TVMS of the gear tooth pair under gear tooth spalling conditions plays an important role in gear dynamic simulation and the corresponding fault feature analysis. Common approaches assume that the tooth spall has a flat bottom with a constant tooth spall depth. This assumption implies an abrupt change in dent depth and cliff-like material loss. However, in practice, the flake of the surface material usually results in a gradually changing dent depth with a curve-shaped bottom. Thus, the modelling of tooth spalls with a flat bottom may result in mesh stiffness differences. To address this shortcoming, this paper proposes a curved-bottom shaped tooth spall to model the tooth spalling geometric features as observed in practice. The proposed method is constructed based on an ellipsoid geometry which is capable of varying radii in three dimensions to best fit the shape of the tooth spall. The foundation stiffness within the double tooth contact area in the proposed method is corrected and the non-linearity of Hertzian contact stiffness is considered. The effectiveness of the proposed method on modelling single and multiple tooth spalls with different shapes and severity conditions is then validated.

Influences of tooth spalling or local breakage on time-varying mesh stiffness of helical gears

Abstract Time-varying mesh stiffness (TVMS) provides important information about the health condition of geared systems. Tooth faults, like crack, pitting, spalling and breakage, will change the TVMS. This work aims to reveal the influences of tooth spalling and local breakage on the TVMS of helical gears. Firstly, an analytical model is developed to incorporate the faults by combining slicing method, discrete integral method and potential energy method. Then, parametric study is conducted. Finally, conclusions are arrived and the results indicate that length, width and location of these defects are very important parameters that need to be considered for calculating TVMS of helical gears. This study provides a theoretical basis for fault diagnosis of helical geared transmissions.