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Gear tooth profile deviations are usually inevitable due to the application of intentional tooth profile modification, the existence of undesired gear manufacturing errors and the tooth surface defects during operation, and they have been demonstrated to have significant effect on the vibration and noise level of gear transmissions. How to calculate the gear mesh forces accurately is crucial for gear dynamic simulation, especially in the presence of gear tooth profile deviations that will complicate the interactions at the gear mesh interface. This paper presents a spur gear dynamic model where the detailed deformations of individual teeth are considered, including the tooth flexible deformations, gear body deformations, the local teeth contact deflections, and the tooth deformations due to its neighboring loaded tooth. This dynamic model is validated by experimental test results with and without tooth tip reliefs. Then, the optimization of the tooth tip relief is performed. Finally, it is compared with three traditional dynamic models to reveal their discrepancies and applicability which could supply theoretical guidance for selection of gear dynamic models.

The traction motor is the power source of the locomotive. If the surface waviness occurs on the races of the motor bearing, it will cause abnormal vibration and noise, accelerate fatigue and wear, and seriously affect the stability and safety of the traction power transmission. In this paper, an excitation model coupling the time-varying displacement and contact stiffness excitations is adopted to investigate the effect of the surface waviness of the motor bearing on the traction motor under the excitation from the locomotive-track coupled system. The detailed mechanical power transmission path and the internal/external excitations (e.g., wheel–rail interaction, gear mesh, and internal interactions of the rolling bearing) of the locomotive are comprehensively considered to provide accurate dynamic loads for the traction motor. Effects of the wavenumber and amplitude of the surface waviness on the traction motor and its neighbor components of the locomotive are investigated. The results indicate that controlling the amplitude of the waviness and avoiding the wavenumber being an integer multiple of the number of the rollers are helpful for reducing the abnormal vibration and noise of the traction motor.

For railway locomotive, its motor bearing is one of the key components, which is likely to be damaged due to the intensified vibration conditions caused by the wheel-rail interaction and gear mesh....

Development of railway transportation capabilities towards high-power, high-speed and heavy axle-load makes the dynamic interactions between the electric drive subsystem and the mechanical subsyste...

Development of railway locomotive towards high-speed and high-power has a higher requirement on traction motor bearing under the intensified wheel–rail interactions since the dynamic performance of...

Wheel flat can cause a large impact between the wheel and rail and excites a forced vibration in the locomotive and track structure systems. The working conditions and fatigue life of the motor bearings are significantly affected by the intensified wheel–rail interaction via the transmission path of the gear mesh. In this study, a fatigue life prediction method of the traction motor bearings in a locomotive is proposed. Based on the L−P theory or ISO 281 combined with the Miner linear damage theory and vehicle–track coupled dynamics, the irregular loads induced by the track random irregularity and gear mesh are considered in this proposed method. It can greatly increase the accuracy of predictions compared with the traditional prediction models of a rolling bearing life whose bearing loads are assumed to be constant. The results indicate that the periodic impact forces and larger mesh forces caused by the wheel flat will reduce the fatigue life of the motor bearings, especially when the flat length is larger than 30 mm. Using this method, the effects of the flat length and relatively constant velocity of the locomotive are analyzed. The proposed method can provide a theoretical basis to guarantee safe and reliable working for motor bearings.

Rotor eccentricity is a common fault in traction motors that directly affects the stability of the locomotive system. A locomotive-track coupled spatial dynamics model with traction power transmissions was established by considering the effect of rotor eccentricity in this study. The time-varying gear mesh forces, nonlinear wheel-rail contact forces, internal interactions between the components of the motor bearing, and dynamic forces induced by the rotor eccentricity, namely centrifugal force of the rotor, rotor-motor rub-impact force, and unbalanced magnetic pull (UMP), were comprehensively considered in the proposed model. The results indicated that rotor eccentricity affects the vibrations of the traction motor significantly. Additionally, the working condition of motor bearings was deteriorated by the rotor eccentricity, which was reflected by the increase in contact forces between the roller and races. The load region of the non-driving end bearing varies with the angular position of the rotor under the effect of rotor eccentricity. The proposed dynamics model will contribute in understanding and controlling the nonlinear dynamic behavior of locomotive traction motors.

As the prompt development of modern railway transportation towards high-speed and high load-capacity, the high-power locomotive is urgently required. Under this situation, the wheel–rail dynamic interaction is becoming more and more intensified which will deteriorate the vibration condition of the key elements of locomotive, such as the gear transmissions. Once gear failures are present, such as gear tooth crack or breakage, it is likely to threaten the operation safety of the locomotive. Thus, deep insight into the fault features of the locomotive gear transmission is urgently necessary for prevention of the induced disastrous consequences. This paper is concentrated on the fault vibration feature extraction of a locomotive in presence of gear tooth root crack under the complicated dynamic excitations from both the gear transmissions and the nonlinear wheel–rail interactions. The locomotive–track coupled dynamics model considering the dynamic effect of the mechanical power transmission path is employed, and the time-varying mesh stiffness of the gear pair with tooth root crack fault and the rail geometric irregularities are then incorporated into the dynamics model to obtain the vibration responses. Then, angular synchronous average technique is proposed to enhance the fault vibration features, and the statistical indicators extracted in frequency domain are developed to reveal the evolution law for the crack propagation scenarios along crack depth or tooth width. The analyzed results indicate that the angular synchronous average technique could effectively reveal the fault vibration feature, and the M8A in the selected statistical indicators is most sensitive to the tooth crack propagation in frequency domain.

Time-varying contact line and mesh stiffness are important parameters for dynamic investigation of helical gear pair with profile modification; however, the calculation methods of the time-varying mesh with high accuracy and high efficiency are also very limited currently. A new mesh stiffness calculation method for helical gear pairs with profile modification is proposed. The new method is conducted by cutting the helical gear tooth into slices to obtain the change of the contact line and the time-varying mesh stiffness with considering the change of each slice's engagement performance introduced by the profile modification. Then, the mesh stiffness of the assumed three different modification cases is calculated by using the proposed method. The calculated results indicate that the proposed method can be used to calculate the mesh stiffness of helical gear pairs, especially of those with tooth profile modification.

The axle box bearing is a critical component to support the vehicle and reduce the friction effect between the wheelset and the axle box. As one of the major failure modes, the localized defect in the outer race of the axle box bearing is a great threat to the operation safety of railway vehicles. Therefore, it is helpful to investigate the dynamic features of locomotive with effect of a localized defect of axle box bearing so as for better understanding of the bearing fault mechanism. In this paper, a locomotive-track coupled dynamics model with traction transmissions is proposed where the dynamics sub-model of the axle box rolling bearing is included. And the impact effect between the roller and the defect region is described as the time-varying displacement excitation and the time-varying contact stiffness excitation of the fault bearing. The results show that the passing frequency of roller and its harmonics of the vertical acceleration vibration of the axle box could be good indicators for the diagnosis of this localized defect, even if the fault feature could not be observed in the time history signals under the wheel-rail interaction. This work can provide some guidance for the early localized defect detection and diagnosis for the axle box bearing.

The dynamics of spiral bevel gears have gained increasing importance due to concerns relating to noise and durability. This is because the mesh force acting on the gear teeth is amplified under dynamic conditions, potentially reducing the fatigue life of the gears. Furthermore, a sizable dynamic force can be transmitted to the housing, inducing structure-born gear whine. The elasticity of the bearings can influence the dynamics of spiral bevel gears. In this article, the finite element formulation of a spiral bevel geared rotor dynamic system is applied to investigate the influence of bearing elasticity on the dynamics of spiral bevel gears. The designs and configurations of rear axles are modeled and analyzed for real-world applications, to gain an enhanced practical understanding of the effect of bearing stiffness on spiral bevel gear dynamics.

This paper aimed to investigate the effect of the lateral stiffness of secondary suspensions on the stability capacity and running safety of heavy-haul locomotives during braking based on the dynamic model and the field braking tests. The dynamic model of heavy-haul locomotives included two double-unit locomotives and five coupler systems. Simulation results indicate that the increasing of the lateral stiffness of secondary suspensions can improve the stability capacity and running safety of heavy-haul locomotives. Then, the field braking experiments were conducted to validate the dynamic model. Comparing the experiment results of different locomotives, the coupler and carbody yaw angles are respectively decreased by 31.8 and 29.5%, which is consistent with the simulation results. It is worthy to be noted that lateral vibration behaviour of the carbody increases with the increasing of the lateral stiffness of secondary suspensions. For the improved locomotive, the main frequency of lateral acceleration is 1…2Hz. However, the main frequency of lateral acceleration is 0.5…1Hz in the original locomotive tests. Moreover, the high-frequency vibration is increased, especially in 10…12.5Hz. According to the simulation and experiment results, the reasonable lateral stiffness of secondary suspensions is 400kN/m for the test locomotive.

Three kinds of gear mesh stiffness calculation models are developed for spur gear transmission system in this paper, namely, the dynamic model of gear transmission system based on the analytical mesh stiffness calculation by “slice method”, the gear transmission system dynamic model based on SIMPACK 225 force element, and the finite element dynamic model of gear transmission system. Based on these dynamic models, the mesh force and dynamic transmission error for the high speed and the low speed operation conditions are analyzed, respectively. The research results indicate that the results obtained by the three dynamic models are in good agreement with each other for both low and high speed operation conditions. The dynamic transmission error calculated by gear transmission system dynamic model based on mesh stiffness calculation with “slice method” are much closer to the results obtained by the finite element dynamic model. Consequently, considering the computation accuracy and computation time, the gear transmission system dynamic model based on the mesh stiffness calculated by “slice method” could be better applied to analyze the dynamic performance of gear transmission system considering the trade off between the computational accuracy and the efficiency.

Gear tooth root crack is a typical fault of gear transmissions and it threatens the operation safety of gear systems. Therefore, precise detection of the tooth root crack is of a great significance for the prevention of serious safety accidents. As one of the commonly used methods, vibration-based detection has drawn great attentions. However, the mapping relationship between the vibrations and the severity of tooth root crack has not been established well, especially for the crack with non-uniform distribution due to the complexity of its dynamic modelling. To address this problem, an improved gear dynamics model considering non-uniform distribution of the gear tooth root crack fault is established in this paper by using the ‘slice method’. Compared with the traditional methods, the advantage of the proposed model is that it enables the accurate modelling of the non-uniform dynamic mesh forces along tooth width that will further excite the support bearings. Then, the dynamic simulation of the gear transmission with non-uniform tooth root crack is performed. The results indicate that the improved model can reveal the vibration characteristics of the gear transmission due to the extra roll and yaw motions caused by the non-uniform tooth root crack. In addition, the correlation between the vibration and the crack size and location is quantified. This study could provide theoretical reference for quantitative detection and diagnosis of gear tooth root crack.

Two improved analytical calculation models of gear tooth fillet-foundation stiffness are proposed for spur gears with tooth root crack. The proposed two models are capable of taking tooth root crack into account in the calculation of gear tooth fillet-foundation stiffness. For Model-1, the reduction of gear tooth fillet-foundation stiffness is assumed to be the production of the stiffness under healthy condition and the ratio of the crack length to the tooth thickness along the potential crack path. While in Model-2, the stiffness of the gear tooth fillet-foundation is calculated by updating related geometrical parameters in the traditional calculation formulas for the healthy gears according to the variation of the load carrying zone due to tooth root crack. The two calculation models for calculating the tooth fillet-foundation stiffness of cracked gears are verified by the finite element method (FEM). The results show that model-1 has a relatively poor accuracy for large crack cases when the position of applied force is close to the tooth root, while model-2 has a higher accuracy for both small and large crack length. The proposed models can be employed to improve the accuracy of gear mesh stiffness calculation and assist gear faults detection and diagnosis.

Traction or braking operations are usually applied to trains or locomotives for acceleration, speed adjustment, and stopping. During these operations, gear transmission equipment plays a very significant role in the delivery of traction or electrical braking power. Failures of the gear transmissions are likely to cause power loses and even threaten the operation safety of the train. Its dynamic performance is closely related to the normal operation and service safety of the entire train, especially under some emergency braking conditions. In this paper, a locomotive–track coupled vertical–longitudinal dynamics model is employed with considering the dynamic action from the gear transmissions. This dynamics model enables the detailed analysis and more practical simulation on the characteristics of power transmission path, namely motor–gear transmission–wheelset–longitudinal motion of locomotive, especially for traction or braking conditions. Multi-excitation sources, such as time-varying mesh stiffn...

This paper aims to improve car body stability performance by optimising locomotive parameters when coupler jack-knifing occurs during braking. In order to prevent car body instability behaviour caused by coupler jack-knifing, a multi-locomotive simulation model and a series of field braking tests are developed to analyse the influence of the secondary suspension and the secondary lateral stopper on the car body stability performance during braking. According to simulation and test results, increasing secondary lateral stiffness contributes to limit car body yaw angle during braking. However, it seriously affects the dynamic performance of the locomotive. For the secondary lateral stopper, its lateral stiffness and free clearance have a significant influence on improving the car body stability capacity, and have less effect on the dynamic performance of the locomotive. An optimised measure was proposed and adopted on the test locomotive. For the optimised locomotive, the lateral stiffness of second...

Locomotive is used to drag trailers to move or supply the braking forces to slow the running speed of a train. The electromagnetic torque of the motor is always transmitted by the gear transmission system to the wheelset for generation of the tractive or braking forces at the wheel–rail contact interface. Consequently, gear transmission system is significant for power delivery of a locomotive. This paper develops a comprehensive locomotive–track vertical-longitudinal coupled dynamics model with dynamic effect of gear transmissions. This dynamics model enables considering the coupling interactions between the gear transmission motion, the vertical and the longitudinal motions of the vehicle, and the vertical vibration of the track structure. In this study, some complicated dynamic excitations, such as the gear time-varying mesh stiffness, nonlinear gear tooth backlash, the nonlinear wheel–rail normal contact force and creep force, and the rail vertical geometrical irregularity, are considered. Then, the dynamic responses of the locomotive under the tractive conditions are demonstrated by numerical simulations based on the established dynamics model and by experimental test. The developed dynamics model is validated by the good agreement between the experimental and the theoretical results. The calculated results reveal that the gear transmission system has strong dynamic interactions with the wheel–rail contact interface including both the vertical and the longitudinal motions, and it has negligible effect on the vibrations of the bogie frame and carbody.

Wheel wear is a fundamental problem for railway vehicles. The unequal wear rate of the two wheels of a wheelset results in the wheel diameter difference (WDD). The WDD and wheel wear not only affect the dynamic performances of rail vehicles, but also increase the maintenance cost. This paper presents an investigation of the effect of the WDD on tread wear for freight wagons based on extensive field measurements and numerical simulations. The evolution laws of the WDD and tread wear of 4 freight wagons are first analyzed based on the monitoring data in an operation period of 200,000 km. A freight wagon dynamics model considering wheel-rail non-Hertzian contact is then established to study the influence of the WDD on the wheel tread wear of a freight wagon. The correlation analysis of wheel tread wear and the WDD is conducted based on the field test data. The results show that the initial WDD significantly affects the shapes and stress distributions of wheel-rail contact patches. The WDD can lead to the asymmetric wear of the two wheels of a wheelset, which conversely aggravates the WDD in return.

The heavy haul coupler/buffer system equipped with arc surfaces on the coupler tail and the follower is widely applied to connect the locomotives and wagons. As one of the most important parameters, arc surfaces friction coefficient plays a key role in coupler instability, which threatens the safety of trains. To investigate the effect of arc surfaces friction coefficient on coupler stability, a simulation model adopting the latest modelling methods is established and field tests employing the locomotives equipped with different friction coefficients are conducted. The results show that the friction coefficient of arc surfaces can affect the coupler yaw angle remarkably. Increasing the friction coefficient can improve the coupler stability. However, under severe compressive force condition, the increased friction coefficient can be reduced quickly, which calls for further attention.

This paper aims to study the effect of the secondary lateral stopper on the compressed stability of the couplers in order to improve the running safety of the heavy-haul locomotives. The influence mechanism of the secondary lateral stopper on the compressed stability of the couplers is theoretically analyzed. To verify the effect of the secondary lateral stopper, both the simulation and the field braking tests are conducted. The multi-body dynamic model consists of two eight-axle locomotives, one dummy of freight vehicle and four detailed connected couplers. The field braking tests are conducted on the tangent line using three eight-axle locomotives. The results indicate that decreasing the free clearance and increasing the stiffness of the secondary lateral stopper both have a positive effect. However, when the free clearance decreases from 20 mm to 10 mm, there is no remarkable decrease in the yaw angles of the coupler and the car body, and the maximum lateral force of the wheelset is still out of the standard in the simulation. When the stiffness of the secondary lateral stopper increases by five times, the yaw angles of the coupler and the car body are reduced significantly and the running safety of the locomotives is also enhanced.

A gear transmission system is a key element in a locomotive for the transmission of traction or braking forces between the motor and the wheel–rail interface. Its dynamic performance has a direct effect on the operational reliability of the locomotive and its components. This paper proposes a comprehensive locomotive–track coupled vertical dynamics model, in which the locomotive is driven by axle-hung motors. In this coupled dynamics model, the dynamic interactions between the gear transmission system and the other components, e.g. motor and wheelset, are considered based on the detailed analysis of its structural properties and working mechanism. Thus, the mechanical transmission system for power delivery from the motor to the wheelset via gear transmission is coupled with a traditional locomotive–track dynamics system via the wheel–rail contact interface and the gear mesh interface. This developed dynamics model enables investigations of the dynamic performance of the entire dynamics system unde...

Gear tooth crack is likely to happen when a gear transmission train is working under excessive and/or long-term dynamic loads. Its appearance will reduce the effective tooth thickness for load carrying, and thus cause a reduction in mesh stiffness and influence the dynamic responses of the gear transmission system, which enables the possibility for gear fault detection from variations of the dynamic features. Accurate mesh stiffness calculation is required for improving the prediction accuracy of the dynamic features with respect to the tooth crack fault. In this paper, an analytical mesh stiffness calculation model for non-uniformly distributed tooth root crack along tooth width is proposed based on previous studies. It enables a good prediction on the mesh stiffness for a spur gear pair with both incipient and larger tooth cracks. This method is verified by comparisons with other analytical models and finite element model (FEM) in previous papers. Finally, a dynamic model of a gear transmission train is developed to simulate the dynamic responses when cracks with different dimensions are seeded in a gear tooth, which could reveal the effect of the tooth root crack on the dynamic responses of the gear transmission system. The results indicate that both the mesh stiffness and the dynamic response results show that the proposed analytical model is an alternative method for mesh stiffness calculation of cracked spur gear pairs with a good accuracy for both small and large cracks.

Prevention of train from derailment is the most important issue for the railway system. Keeping derailed vehicle close to the track centreline is beneficial to minimise the severe consequences associated with derailments. In this paper, the post-derailment safety measures are studied based on low-speed derailment tests. Post-derailment devices can prevent deviation of the train from the rail by catching the rail, and they are mounted under the axle box. Considering the different structures of vehicles, both trailer and motor vehicles are equipped with the safety device and then separately used in low-speed derailment tests. In derailment tests, two kinds of track, namely the CRTS-I slab ballastless track and the CRTS-II bi-block sleeper ballastless track, are adopted to investigate the effect of the track types on the derailment. In addition, the derailment speed and the weight of the derailed vehicle are also taken into account in derailment tests. The test results indicate that the post-derailme...

This paper presents a method to study the vertical dynamic characteristics of a heavy-haul locomotive in curve. A quasi-static analysis model based on the static force equilibrium relationship is established to investigate the load bearing characteristics of suspension system when the locomotive runs through the curve. Then a locomotive–track coupled dynamics model is used to analyse the dynamic characteristics of wheel load in curves. Finally, a field test in curve is carried out to validate the simulated results. The theoretical analysis results indicate that due to the different twist shapes of track on the entry and exit transition curves, for some specific position in the suspension system or wheel arrangements, the corresponding vertical load along the curve length presents an asymmetry about the section of circular curve. The asymmetry is predominantly caused by the Superelevation Angle Differences (SADs) between car body, bogie frames and wheelsets. A distinct phenomenon is that the outer wheel–rail vertical load of the first axle increases when the locomotive enters the transition curve and then reduces when it exits. These results are expected to provide theoretical guidance to the design of the heavy-haul railways. It is suggested that the asymmetric characteristics of the wheel loads can be improved by some measures, such as adopting a low vertical stiffness in the secondary suspension and increasing the transition curve length. First published online 04 May 2016

Time-varying mesh stiffness and gear transmission errors are the major excitations to gear dynamics system. How to calculate them more accurately and efficiently has attracted much attention worldwide for a long period. Especially consideration of the gear body structure coupling effect and the tooth profile error will make interactions between the tooth pairs in mesh more complicated so that traditional analytical methods could not applicable any more. In this paper, a comprehensive and general analytical gear mesh model is proposed by considering all the deformations including the teeth deformation, teeth contact deformation, fillet-foundation deformation, and gear body structure coupling effect, as well as tooth profile deviations. The calculation formulas for the mesh stiffness, load sharing ratio and static transmission error are derived, and the corresponding efficient solving method is also proposed. Based on the proposed model, the influencing mechanism of the gear body structure coupling effect on the total mesh stiffness is revealed. The proposed mesh stiffness calculation model is proven to be more general and comprehensive since the traditional analytical models are the special cases of the proposed model.

Dynamic interactions between wheel and rail are becoming more intensified under the development of locomotive towards high-speed, heavy-haul and high-power directions, which are more likely to cause failures in gear transmission system of high-power heavy-haul electric locomotive. The dynamic impact of the locomotive gear transmission system becomes more drastic, especially for the extreme operation conditions, such as traction/braking process. Gear fault diagnosis under unsteady conditions has always been a hot and difficult research spot, and revealing of the gear fault vibration characteristics under the transient conditions is the premise and basis for effective fault detection and diagnosis. In order to reveal the gear fault vibration characteristics of railway locomotive dynamics system, a spatial dynamic model of a heavy-haul electric locomotive considering the dynamic coupling effect of gear transmission system is proposed based on the multibody dynamics theory in this paper. Then the dynamic responses of the locomotive under transient condition are obtained by considering the complicated excitations induced by the wheel-rail nonlinear contact, gear mesh and tooth root crack. The time-frequency analysis and angular synchronous average method are adopted to investigate the fault vibration feature of the tooth root crack. Finally, the distribution and variation of vibration characteristics of the gear tooth root crack fault evolution are revealed by condition indicators such as the Crest Factor (CF), Kurtosis (K), Fourth Order Figure of Merit (FM4), M6A, and M8A. The results indicate that: (1) the time-frequency analysis results of vibration acceleration of wheelset and bogie frame and dynamic mesh force could reflect the fundamental mesh frequency and its harmonics, however, only the vertical and longitudinal vibration acceleration of the wheelset and the gear dynamic mesh force could reflect the fault vibration characteristics in time-frequency analysis results; (2) the FM4, M6A and M8A values of locomotive system vibration signal could effectively reflect the crack propagation on the dynamic features of the locomotive system after being processed by angular synchronous averaging method.

Vibration performances of roller bearings are greatly affected by various localized defects. Thus, it is very important to analyze vibration characteristics of the roller bearings with the localized defects. In this paper, a nonlinear dynamic model is developed to formulate the effect of a localized defect on the vibration characteristics of a cylindrical roller bearing (CRB). A bump defect is formulated in this model. The defect profile is defined as a spherical one. The time-varying displacement excitation caused by the defect is modelled. Effects of the defect sizes on the vibration characteristics of the roller bearing are discussed. The simulation results show that the developed method can provide some guidance for understanding the vibration characteristics of the CRB with a bump defect.

High-power heavy-haul locomotive has already been the development trend of Chinese heavy load freight. As a vital equipment of the locomotive system, gear transmission system is usually employed to deliver the traction or the braking power between the traction motor and the wheel/rail contact interface. The increasing dynamic load of the gear transmission induced by the raising of locomotive traction or braking power is likely to cause failures to the gear transmission system, which will affect the reliability and safety of the railway vehicles. This paper established a spatial dynamics model of high-power heavy-haul locomotive considering dynamic effect of the gear transmission based on the multibody dynamics theory in which the gear transmission is established as a sub-model. The time-varying mesh stiffness of the gear pair with tooth root crack was obtained by ‘slice method’ which is an analytical mesh stiffness calculation approach based on the potential energy principle. The fault vibration characteristics of the gear transmission under the complicated excitations from the wheel/rail nonlinear contact, the rail geometric irregularity, and the periodic gear mesh process are studied.

Planetary gear transmission has a wide application in different areas due to its advantages such as compactness, large torque-to-weight ratio, reduced noise and vibrations. However, its dynamic responses are much more complex due to the complicated structures and relative motions, which make it difficult in the fault feature extractions at the view point of fault detection. Better understanding on the dynamic features of a planetary gear transmission and the corresponding internal excitation sources will benefit the fault feature extractions. In this paper, an analytical model for mesh stiffness calculation is developed based on the potential energy principle and uniformly curved Timoshenko beam theory, which enables exploring the effects of the tooth root crack fault and the flexible ring gear rim on the dynamic responses. Based on the developed model, the frequency spectrum structures of the planetary gear transmission can be revealed and analyzed theoretically in the presence of tooth crack and flexible ring gear. A case study is performed to demonstrate the effectiveness of the developed model, where the tooth root cracks are seeded in a tooth of the sun, planet, and ring gears. The simulated results indicate that the complicated modulation phenomenon can be observed where the causes of different frequency components can be revealed. This study is expected to be able to give some theoretical guidance on the identification of vibration sources for planetary gear transmissions.

Gear transmission is a key component in locomotive where it delivers the traction or braking forces between the motor and the wheelset. Its working performance has a direct effect on the operating reliability and safety. Therefore, investigation on the dynamic characteristics of the gear transmission in locomotives is very meaningful. In this study, a gear transmission-locomotive-track spatial coupled dynamic model is established based on the classical locomotive-track coupled dynamics and the gear dynamics theory. Based on this model, the dynamic responses of the gear transmission can be analysed under excitations from different track geometrical irregularity, and the dynamic performance of the gear transmission can be obtained. This paper also studies the effect law of the track irregularity on the vibration of the gear transmission by using statistical indicators RMS (Root Mean Square) and PtP (Peak-to-Peak). The results indicate that the track geometrical irregularity has an obvious impact to the dynamic performance of gear transmission. The dynamic response of the gear transmission will increase violently when the locomotive runs on the track in a worse condition. The results are expected to be capable of providing some references for fatigue life prediction and reliability analysis of the gear transmissions in locomotive.

Characteristics of wheel-rail dynamic interaction due to the rail corrugation in a high-speed railway are analyzed based on the theory of vehicle-track coupled dynamics in this paper. Influences of the corrugation wavelength and depth on the wheel-rail dynamic performance are investigated. The results show that, under the excitation of a measured rail corrugation, the wheel-rail dynamic interaction of high-speed railway is enhanced obviously, and the high-frequency dynamic force between wheel and rail is generated, which has an obvious impact on the vibrations of the wheelset and rail, and little effect on the vibration of the frame and carbody. If the corrugation wavelength is shorter than the sensitive wavelength, the wheel-rail vertical force will increase with the growth of the corrugation wavelength, otherwise, it will decrease. However, the wheel-rail vertical force keeps increasing with the growth of corrugation depth. Furthermore, if the corrugation wavelength is shorter than the sensitive wavelength, the wheel-rail vertical force will increase with the decrease of the running speed, otherwise, it will decrease. It is also found that the critical wavelength of corrugation increases with the growth of the corrugation depth and the running speed, and the critical depth of corrugation is nonlinearly related to the sensitive wavelength.

As one of the inherited displacement excitation sources which are related to the gear vibration and noise problems, gear transmission error always consists of two parts: gear tooth geometric error and tooth elastic deformation under transmitted load. The gear tooth geometric errors were directly employed as the displacement excitations in previous papers, which are not accurate. In this paper, a new method is developed to transform the gear tooth errors (TEs) to be the appropriate dynamic excitations through the mesh stiffness and the unloaded static transmission error (USTE), where the obtained displacement excitation curves, namely the USTE curves, are very different from the TE curves. Incorporation of the proposed model into the dynamic model of a planetary gear train enables the investigation of the TE effect on the dynamic excitations and vibrations. Two groups of TEs with different amplitudes are employed in the case studies. The results verify that the micro-scale TEs influence not only the dynamic displacement excitation, but also the total mesh stiffness and the planetary gear vibrations greatly.

Detecting chatter mark vibration in rolling mills operating under normal working conditions is difficult. A novel characteristic recognition method of chatter mark vibration, where the non-dimensional parameters are calculated with time varying signals and kurtosis under normal rolling mill operating conditions, is presented in this paper. The character of the chatter mark vibration signal is obtained by calculating the kurtosis value of each vibration signal segment obtained by subdividing the raw time varying vibration signal. The probability density function is utilized to reveal obvious differences between signals with respect to the normal and chatter conditions. The method overcomes the limitation of traditional spectrum analysis, which is sensitive to working conditions. Numerical simulation and experimental results show that the proposed method has better recognition capability than traditional spectrum analysis.

Gear transmission is a key element in locomotives where it delivers the traction or braking powers between the motor and the wheelset. Its dynamic performance and service reliability have a direct effect on the performance of the locomotive. Gear failures, such as tooth crack and the induced tooth breakage, are likely to deteriorate the dynamic performance of the locomotive or make the train out of control, or even cause disastrous derailment. Fortunately, these failures will also vary the vibration responses of the locomotive, which enables the possibility of vibration-based fault detection for locomotives. In this study, vibration features of a locomotive when a tooth root crack fault is in presence in one of its gear transmissions. Here, the results for a healthy locomotive and a gear tooth cracked locomotive are compared to reveal the fault vibration features. Also, effect of the rail geometric irregularity excitation is also considered. It is proven that the rail geometric irregularity could slur frequency structure which brings a challenge to the fault feature extraction. Application of the time synchronous averaging (TSA) technique is proven to be effective for solving this problem.

Ring gear is a key element for vibration transmission and noise radiation in the planetary gear system which has been widely employed in different areas, such as wind turbine transmissions. Its flexibility has a great influence on the mesh stiffness of internal gear pair and the dynamic response of the planetary gear system, especially for the thin ring cases. In this paper, the flexibility of the internal ring gear is considered based on the uniformly curved Timoshenko beam theory. The ring deformation is coupled into the mesh stiffness model, which enables the investigation on the effects of the ring flexibility on the mesh stiffness and the dynamic responses of the planetary gear. A method about how to synthesize the total mesh stiffness of the internal gear pairs in multi-tooth region together with the ring deformation and the tooth errors is proposed. Numerical results demonstrate that the ring thickness has a great impact on the shape and magnitude of the mesh stiffness of the internal gear pair. It is noted that the dynamic responses of the planetary gear set with equally spaced supports for the ring gear are modulated due to the cyclic variation of the mesh stiffness resulted from the presence of the supports, which adds more complexity in the frequency structure.

Planetary gear has a broad application in industry due to its advantages. However, most of the mesh stiffness calculation for the planetary gears is based on the assumption that the effect of the ring flexibility is ignored. In this paper, the ring deformation based on the uniformly distributed Timoshenko beam theory is coupled into the gear mesh stiffness model of the internal gear pair. Based on this model, the effect of the ring deformation on the internal gear mesh stiffness can be carried on. In this paper, the effect of the support type (fixed support and pin support), ring thickness and number of supports on the mesh stiffness are investigated. It is demonstrated that the ring thickness and the number of supports have a great impact on the mesh stiffness of the internal gear pair while the influence of the support type is little. In addition, the mesh stiffness appears to be periodic with the number of the periodicities exactly equal to the number of the supports.

Gear tooth root crack, as one of the popular gear tooth failures, is always caused by the dynamic load or excessive load applied to the tooth. It will devastate the working performance of the gear system, by problems such as vibration and noise, or even lead to a broken tooth, which will stop the normal working process of the gear system. It has attracted wide attention from researchers. However, the previous studies focused their concentration only on the mesh stiffness reduction due to tooth root crack, while the tooth plastic inclination due to tooth bending damages like gear tooth root crack is seldom considered. In this paper, a tooth plastic inclination model for spur gear with tooth root crack is developed by regarding the cracked tooth as a cantilever beam. It influences not only the displacement excitation but also the mesh stiffness and load-sharing factor among tooth pairs in mesh. The simulation results obtained by incorporating the tooth plastic inclination deformation model together with the tooth root crack model into a 21-Degree-of-Freedom planetary gear dynamic model indicate that the tooth plastic inclination has a significant effect on the performance of the gear system rather than the mesh stiffness reduction due to tooth root crack.

Planetary gear is widely used in different areas due to its advantages such as compactness, large torque-to-weight ratio, large transmission ratios, reduced noise and vibrations. However, the tooth faults like cracks are seldom concentrated. In this paper, a mesh stiffness model of internal gear pair with a tooth root crack in the ring gear is derived based on the potential energy principle. The mesh stiffness model is incorporated into the dynamic model of a one-stage planetary gear set with 21-degree-of-freedom (DOF) to investigate the effect of the internal gear tooth root crack. The crack cases with different dimensions are designed in this paper to demonstrate their influences on the mesh stiffness and the dynamic performance of the planetary gear set. The simulated results show that bigger reduction in mesh stiffness is caused by the growth in the crack size. And the impulsive vibrations and sidebands can be observed in the dynamic response of the planetary gear set in time and frequency domains, respectively. Both their amplitudes increase as the crack propagation which supply the possibility for them to be the indicators in the condition monitoring and fault diagnosis of planetary gear system.

Gear tooth deviations are the main excitation sources for gear dynamic responses. However, it is seldom considered in the analytical mesh stiffness model except for some computational analysis like finite element method. To make up this gap, a general analytical mesh stiffness model is proposed in this paper to include the effect of the gear tooth errors. This proposed model establishes the relationship between the gear tooth errors and the total mesh stiffness, load sharing among different tooth pairs in mesh and loaded static transmission errors (LSTE). It is suitable for not only the gear pairs with low contact ratio (LCR), but also the gear pairs with high contact ratio (HCR). Two spur gear pair models, namely one with LCR between 1 and 2 and the other one with HCR between 2 and 3, are used to demonstrate the effectiveness of the proposed mesh stiffness model. Influences of the TPM, applied torque and gear tooth root crack on the mesh stiffness, load sharing and loaded static transmission errors are also investigated.

Spalling in contact surface of rail is a typical form of rolling contact fatigue, which is a difficult problem to solve in railway. Once the spalling occurs in the rail, the wheel-rail dynamic interaction will become more severe. The wheel-rail dynamic interaction is investigated based on the theory of vehicle-track coupled dynamics in this paper, where the excitation modes of the rail spalling failure are taken into consideration for high-speed wheel-rail system. A modified excitation model of rail spalling failure is proposed. It can enable the investigations on two kinds of excitation modes in wheel-rail system due to the rail spalling, including the pulse and the harmonic excitation modes. The excitation mode can be determined by the ratio of the spalling length to its critical length. Thus, the characteristics of wheel-rail dynamic vibration excited by two kinds of excitation are simulated in detail. Consequently, the limited value of the spalling length is suggested for high-speed railway.

Gear tooth crack will cause changes in vibration characteristics of gear system, based on which, operating condition of the gear system is always monitored to prevent a presence of serious damage. However, it is also a unsolved puzzle to establish the relationship between tooth crack propagation and vibration features during gear operating process. In this study, an analytical model is proposed to investigate the effect of gear tooth crack on the gear mesh stiffness. Both the tooth crack propagations along tooth width and crack depth are incorporated in this model to simulate gear tooth root crack, especially when it is at very early stage. With this analytical formulation, the mesh stiffness of a spur gear pair with different crack length and depth can be obtained. Afterwards, the effects of gear tooth root crack size on the gear dynamics are simulated and the corresponding changes in statistical indicators – RMS and kurtosis are investigated. The results show that both RMS and kurtosis increase with the growth of tooth crack size for propagation whatever along tooth width and crack length. Frequency spectrum analysis is also carried out to examine the effects of tooth crack. The results show that sidebands caused by the tooth crack are more sensitive than the mesh frequency and its harmonics. The developed analytical model can predict the change of gear mesh stiffness with presence of a gear tooth crack and the corresponding dynamic responses could supply some guidance to the gear condition monitoring and fault diagnosis, especially for the gear tooth crack at early stage.

Planetary gears are widely used in the industry due to their advantages of compactness, high power-to-weight ratios, high efficiency, and so on. However, planetary gears such as that in wind turbine transmissions always operate under dynamic conditions with internal and external load fluctuations, which accelerate the occurrence of gear failures, such as tooth crack, pitting, spalling, wear, scoring, scuffing, etc. As one of these failure modes, gear tooth crack at the tooth root due to tooth bending fatigue or excessive load is investigated; how it influences the dynamic features of planetary gear system is studied. The applied tooth root crack model can simulate the propagation process of the crack along tooth width and crack depth. With this approach, the mesh stiffness of gear pairs in mesh is obtained and incorporated into a planetary gear dynamic model to investigate the effects of the tooth root crack on the planetary gear dynamic responses. Tooth root cracks on the sun gear and on the planet gear are considered, respectively, with different crack sizes and inclination angles. Finally, analysis regarding the influence of tooth root crack on the dynamic responses of the planetary gear system is performed in time and frequency domains, respectively. Moreover, the differences in the dynamic features of the planetary gear between the cases that tooth root crack on the sun gear and on the planet gear are found.

It was found that the vibration features resulted from tooth crack and sliding on the contact interfaces due to speed variation are very similar with each other, which is difficult to distinguish. So, it is meaningful to study whether they are the same or not. Firstly, a finite element model of a spur gear pair in mesh with tooth crack at pitch circle is established to calculate the effect of tooth crack on gear mesh stiffness. Then, combined with the tooth crack through mesh stiffness, a spur gear dynamic model with six degrees of freedom (dof) is developed to extract the dynamic features affected by the tooth crack. The tooth surface friction due to different relative velocity is also involved to study its effects on the dynamic characteristics of the gear system. Finally, comparisons are made between the dynamic features of the gear system with tooth crack and the tooth surface sliding to expose their effects to supply some theoretical guidance on fault detection.Copyright © 2012 by ASME

Waviness of rolling element bearings, as one of the most concerned factors, would greatly influence the dynamic and acoustic performances of machines. In this paper, a new algorithm of vibro-acoustic coupling, which is based on the displacement mapping method by applying the displacement history obtained from a 6-DOF bearing dynamic model to be as the boundary condition of the finite element model of the bearing housing, is developed to predict the effect of waviness on the vibration and acoustic features of the bearing. The displacement excitation of the circumferential surface of bearing housing can be obtained by vector synthesis of bearing rigid displacement from the 6-DOF bearing dynamic model. This new method enables not only the reduction in computational cost, but also simulation of the bearing waviness under different sizes. A 6308 deep groove ball bearing model with outer race waviness is taken as an example case to examine the effectiveness of the new algorithm. The simulation results show that the new algorithm is able to predict the vibration and acoustic features of the bearing with waviness.Copyright © 2012 by ASME

Geared transmission systems are widely applied to transmit power, torque and high rotational speed, and as well as change the direction of rotational motion. Their performances and efficiencies depend greatly on the integrity of the gear structure. Hence, health monitoring and fault detection in geared systems have gained much attention. Often, as a result of inappropriate operating conditions, application of heavy load beyond the designed capacity or end of fatigue life, gear faults frequently occur in practice. When fault happens, gear meshing characteristics, including mesh stiffness that is one of the important dynamic parameters, can be affected. This sudden change in mesh stiffness can induce shock vibration as the faulty gear tooth passes through the engagement zone. In this study, a finite element model representing the crack at the tooth root of a spur gear is developed. The theory is applied to investigate the effect of different crack sizes and the corresponding change in mesh stiffness. In addition, a lumped parameter model is formulated to examine the effect of tooth fault on gear dynamic response.Copyright © 2011 by ASME

The rear axle gear is one of the key parts of transmission system for automobiles. Its healthy state directly influences the security and reliability of the automotives. However, non-stationary and nonlinear characteristics of gear vibration due to load and speed fluctuations, makes it difficult to detect and diagnosis the faults from the transmission gear. To solve this problem a fault prognosis and diagnosis method based on a combination of radial basis function(RBF) and back-propagation (BP) neural networks is proposed in this paper. Firstly, a moving average pretreatment is used to suppress the time series fluctuation of vibration characteristic parameter tie series and reduce the interference of random noise. Then, the RBF network is applied to the pretreated parameter sequences for fault prognosis. Furthermore, based on self-learning ability of neural networks, characteristic parameters for different common faults are learned by a BP network. Then the trained BP neural network is utilized for fault diagnosis of the rear axle gear. The results show that the proposed method has a good performance in prognosing and diagnosing different faults from the rear axle gear.

Chatter vibration generated during the steel rolling process not only seriously limit the mill performance, but also degrade the surface quality of the steel plate. By analysing the vibration signals from a steel plate mill, Sendzimir 20-high mill, a frequency modulation phenomenon can be observed in the mill chatter vibration signal. In order to monitor and control the chatter vibration during the steel rolling process, an algorithm based on the second order cyclic autocorrelation demodulation is proposed to extract the mill chatter vibration signal. The algorithm is the coupling of frequency analysing, band-pass filtering, second order cyclic autocorrelation calculation and envelope analysing method, and the results of chatter mark vibration can be shown as the waveform in sliced into time domain (SITD) and sliced into frequency domain (SIFD). The experimental results have shown that the modulation frequency is close to the rotational frequency of the intermediate rolls, and it is also shown that mill chatter mark vibration could be evaluated by monitoring the amplitude of the demodulated component whose frequency is close to the rotational frequency of the second intermediate rolls.