Figure 9 - uploaded by Carl Howard
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A schematic of a 2-D bearing model showing an outer ring, an inner ring, a few rolling elements, and a rectangular defect (not to scale).
Source publication
This paper provides insights into the physical mechanism by which defect-related impulsive forces, and consequently, vibrations are generated in defective rolling element bearings. A dynamic nonlinear finite element model of a rolling element bearing with an outer raceway defect was numerically solved using the explicit dynamics finite element soft...
Contexts in source publication
Context 1
... gradual drop in the contact force between the three rolling elements, with the top surface of the defect -the defective surface of the outer raceway 586 (refer to Figure 9 to see the top surface of the defect). ...
Context 2
... contrast to the de-stressing event, it can be seen from the experi- comparison of the numerical and experimental envelope spectra in Figure 859 18 indicates that the numerical noise did not affect the bearing diagnosis, 860 which is generally conducted using the envelope analysis by demodulating 861 the vibration signals in high-frequency regions. ...
Context 3
... contrast to the de-stressing event, it can be seen from the experi- comparison of the numerical and experimental envelope spectra in Figure 859 18 indicates that the numerical noise did not affect the bearing diagnosis, 860 which is generally conducted using the envelope analysis by demodulating 861 the vibration signals in high-frequency ...
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Citations
... Researches have been reported on the mathematical modelling [1,2] and dynamic characteristic analysis [3,4] of rolling bearings with localized faults. The timevarying displacement excitations [5,6] and nonlinear Hertz contact deformations [7,8] were commonly considered in the defective rolling bearing dynamic model. ...
Inter-shaft bearings, critical components within aero-engine dual-rotor systems, are susceptible to localized faults due to their unique installation locations. This research delves into a distinctive dynamic phenomenon termed “paroxysmal impulse vibration”, which is subjected to localized faults in the outer ring of inter-shaft bearings. The vibration behavior of this phenomenon differ significantly from those of traditional continuous impulse vibrations. The mechanical mechanisms and analytic requirements governing the emergence of paroxysmal impulse vibrations are systematically studied. Three analytic prediction formulas are derived to anticipate these vibrations. A systematic prediction process is summarized, offering standardized guidance for forecasting paroxysmal impulse vibrations under various working conditions. Furthermore, the established prediction formulas and process forecast all specific frequency components of paroxysmal impulse vibrations. Experimental vibration tests on defective inter-shaft bearings align well with simulation outcomes, confirming the efficacy of the proposed prediction methods for paroxysmal impulse vibration. Additionally, a significant correlation between the frequency components in paroxysmal and continuous impulse vibration is revealed. This identified correlation provides a novel method for elucidating the presentation laws of all specific frequency components within traditional continuous impulse vibrations under different parameter conditions. The research of paroxysmal impulse vibration introduces novel perspectives on inter-shaft bearing vibration mechanisms, offering promising implications for the inter-shaft bearing failure diagnosis.
... This change in stiffness is due to the finite number of elements that carry the total load [9]. Singh et al. [10] stated that the generated vibration signals due to defects are caused by the restressing of the rolling elements. Consequently, when the ball hits the end of a defect, the impulse generates vibration signals and enlarges the defect's size. ...
This research introduces a groundbreaking method for bearing defect detection. It leverages ensemble machine learning (ML) models and conducts comprehensive feature importance analysis. The key innovation is the training and benchmarking of three tree ensemble models—Decision Tree (DT), Random Forest (RF), and Extreme Gradient Boosting (XGBoost)—on an extensive experimental dataset (QU-DMBF) collected from bearing tests with seeded defects of varying sizes on the inner and outer raceways under different operating conditions.
The dataset was meticulously prepared with categorical variable encoding and Min–Max data normalization to ensure consistent class distribution and model accuracy. Implementing the ML models involved a grid search method for hyperparameter tuning, focusing on reporting the models’ accuracy. The study also explores applying ensemble methods and using supervised and unsupervised learning algorithms for bearing fault detection. It underscores the value of feature importance analysis in understanding the contributions of specific inputs to the model’s performance. The research compares the ML models to traditional methods and discusses their potential for advanced fault diagnosis in bearing systems.
The XGBoost model, trained on data from actual bearing tests, outperformed the others, achieving 92% accuracy in detecting bearing health and fault location. However, a deeper analysis of feature importance reveals that the models weigh certain experimental conditions differently—such as sensor location and motor speed. This research’s primary novelties and contributions are comparative evaluation, experimental validation, accuracy benchmarking, and interpretable feature importance analysis. This comprehensive methodology advances the bearing health monitoring field and has significant practical implications for condition-based maintenance, potentially leading to substantial cost savings and improved operational efficiency.
... The nonlinear contact characteristic between the roller and race/failure area is the essential problem for the research on vibration responses [2,3] and fault features [4], and the introductions of the electrohydrodynamic lubrication theory greatly facilitate the development of rolling bearing dynamics [5,6]. With the advancement of computer technology, it is a new and helpful way to solve more complex contact problems considering the non-uniform surface [7], failure area [8], and lubricating medium [9], by using the finite element method. In addition, for the tangential friction at the rollerrace interface, especially the skidding phenomenon, Harris [10] and Gupta [11] et al. pioneered the corresponding investigations and carried out a great amount of work. ...
Skidding phenomenon is a critical cause of abnormal vibration, noise, and temperature rise of lubricated rolling bearings. It is affected by various factors such as the structure size, lubrication medium, thermal properties, and service conditions. Owing to the limited influence factors, the skidding mechanism of the lubricated rolling bearing under the fluid-solid-heat coupling effect is not well understood. Therefore, a fluid-solid-heat coupled dynamics model of the lubricated rolling bearing based on the dynamic and thermodynamic equations is developed in this study using the lumped parameter method and thermal network method. The time-varying geometrical parameter of the components, time-varying kinematic viscosity and density of the lubricant, and temperature raise and distribution of the bearing during the operation process are involved in this model, which can significantly affect the system parameters such as the equivalent nonlinear contact stiffness, friction coefficient, viscous drag, radial and circumferential clearances, and so on. To verify the accuracy of the proposed model, the cage slipping velocity and outer ring temperature rise are compared between simulation results and test data, respectively. The influence of the rotating speed of the inner ring and radial load on the temperature raise and skidding phenomenon is analyzed in detail. The results indicate that skidding behaviors and internal dynamic interactions are intensified under the thermal effect. Therefore, improving the heat dissipation efficiency of the bearing can alleviate skidding, especially under light load and high-speed conditions. It should be noted that the rotating speed of the ring and radial load are the primary factors affecting bearing temperature rise and skidding phenomenon.
... Besides, the author developed a more comprehensive bearing model and conducted further research [31,32]. In addition, Ref [33][34][35][36]used different modelling methods to analyze the dynamic characteristics of bearings, respectively. ...
... He did this by combining the signal spectrum envelope with the random excitation signal change. Singh [21] suggested a bearing display dynamics model based on the structure of the raceway and the contact characteristics of the rolling elements. He also studied the impact pulse phenomenon caused by the contact force when the rolling element passes through a local change in the structure of the raceway, and he showed how bearing vibrations are made. ...
... The motion connection of Eqs. (21), (20), and (19) creates the multi-body dynamic model of the bearing without cage protection: ...
Rolling bodies in cageless ball bearings without cage control will always hit each other. This causes the rolling bodies to wear out faster and decreases the bearing's performance. But most of the available references only look at how well the bearing works when the cage is in place. They do not look at how the inner ring's dynamic response changes when the cage is removed and the rolling elements' motion changes. On the basis of this, a nonlinear rolling-body dynamics model with six degrees of freedom and contact between rolling bodies is suggested. The dynamics model of an automatic discrete system is built on the motion coupling and functional slot discrete theories. The power hardware re-turn method is used to figure out how to solve the dynamics model. The results show that after the rotor falls into the inner ring, the rolling bodies will cause cumulative collision for a short time. Then, because of the function slot, the occasional collision between the rolling bodies would not cause cumulative collision again, and the inner ring motion will be more stable. When the speed of the rotor's fall goes up, the rolling bodies hit each other more often. This makes the inner ring move more steadily, but there is a limit. To make sure that the theoretical analysis and the results of the theoretical solution are right, a high-speed camera was used. To make sure that the theoretical analysis and the results of the theoretical solution are right, we built a bearing test platform to take pictures of the rolling body of the bearing as it moved. The image processing program is used to figure out the rolling body's angular speed, compare the test results to the theoretical study and make sure that the theoretical study is right. The theoretical study is compared to the test results to see if the theoretical study is right.
... The key parts are the outer and inner rings (races) and the rotating elements. Indeed, only the advent of advanced numerical calculation tools has allowed researchers to overcome the limitations of analytical solutions and therefore to take the accuracy of structural issues to a higher level (Demirhan and Kanber 2008;Singh et al. 2014;Xi et al. 2021). Amongst all the types of rolling bearings, ball bearings are certainly the most popular. ...
Rigorous protocols must be followed when mounting ball bearings to avoid structural damage and subsequent malfunctioning or unexpected failures. Unconventional mounting procedures may produce excessive contact pressures between the elements of the bearing, therefore the whole process must be well-understood and modelled to prevent unwanted effects. Specifically for angular ball bearings, fitting axial forces should always be applied over the raceway subjected to the shrink-fit to avoid contact forces arising on the ball. In the present study, such an axial force is applied unconventionally, such that the axial force is transferred to the shrink-fit raceway through the balls. In this scenario, the evaluation of the contact areas and the pressure distributions is accomplished by exploiting both analytical and FEM approaches, supported by bespoke experimental tests to determine the relevant frictional coefficients and mounting forces. The study demonstrated how analytical methods can successfully replace more demanding FEM-based tools for the evaluation of the bearing mounting force and contact pressure and extent. FEM modelling can, however, be more accurate when dealing with more generic boundary conditions and more intricate geometrical features involved.
... Most of these models have been developed for specific problems [39][40][41][42][43][44][45]. Other studies using dynamic simulation models use simplified friction calculations and focus on structural deformation or vibration analysis [45][46][47][48][49][50][51][52][53][54][55][56][57]. Therefore, their use in general problems could lead to unreliable results. ...
In the presented work, a parametric multibody simulation model is presented that is capable of predicting the friction torque and kinematics of tapered roller bearings. For a highly accurate prediction of bearing friction, consideration of solid and lubricant friction is mandatory. For tapered roller bearings in particular, the friction in the contact between the rolling element and raceway is of importance. Friction forces in the contact between the rolling element end face and inner ring rib as well as roller cage pocket contacts are also considered in the model. A large number of tests were carried out to validate the model in terms of the simulated frictional torque. Influencing variables such as speed, axial load, radial load, and temperature were investigated. The simulation results show good agreement with the measured friction torque, which confirms that the model is well suited to predict frictional torques and therefore the kinematics of tapered roller bearings.
... The rotor and casing were modeled by the FEM to highlight the impulse vibration transmissibility characteristic. Singh developed a planar dynamic FEM of a cylinder roller bearing [18] to explore the impact force generation mechanism with the roller passing through the defect on the outer race. Multiple impulsive forces were observed when the roller strikes the end edge of the fault, which led to the ringing of a bearing. ...
... During the roller passing through the defect on the raceway, three potential contact points exist. Contacts are between the roller and the entry, base, and the trailing of the fault [18,23]. The contact deformation between the roller and the defective outer/inner raceway is determined by the penetration between the contacting bodies. ...
An accurate dynamic model is significant for the understanding of defect induced dynamic characteristics of rolling element bearings, which further contributes to effective diagnosis and prognosis of bearings. In the development of dynamic models of bearings, how to model the contacts between the defective component and normal component is of vital importance. Existing contact models use displacement excitation instead of actual roller-defective raceway contact and thus leave space for improvement. To fill in this gap, this paper proposes a new dynamic model of rolling element bearings with a defect on the inner or outer raceway in a rotating reference frame with the gyroscopic effect and gravity force considered. In the proposed model, the contact between the roller and the defective raceway is modeled based on the instant positions of the rollers, cage, inner ring and outer ring. The effectiveness of the proposed model is validated through simulation and experiment studies. The results have shown that compared with the existing models, the proposed model exhibits a more gradual load change in the stressing stage and the restressing stage when the roller passes through the defect, yielding a more accurate modeling of the real contact of bearing components.
... The dynamics model of bearing [38] is equated to n vibration models with mass, stiffness and damping. The bearing is mainly subjected to the support reaction force of the shaft and the support force of the gearbox. ...
... Petersen et al. [27][28][29] established the system dynamics equations based on the displacement excitation function and analyzed the characteristics of the system stiffness and contact force change under different fault dimensions, i.e., the stiffness decreases in the loading direction and increases in the unloading direction, and also proposed a method for accounting for the finite rolling element size, which means that the time-frequency characteristics of the low-frequency event that occurs when a rolling element enters the defect entry and the multiple high-frequency events that occur when it exits the defect can be predicted more accurately. Sarabjeet et al. [30] used the explicit dynamics finite element software package LS-DYNA to build a rolling bearing fault model, and after an in-depth analysis of the numerically estimated dynamic contact forces between the rolling elements and the raceways of a bearing, it was found that the re-stressing of the rolling elements that occurs near the end of a raceway defect generates a burst of multiple short-duration force impulses, and the contact forces and accelerations generated on the exit of the rolling elements out of the defect compared to when they strike the defective surface are much higher. ...
By analyzing the support of load-carrying rolling elements when the rolling elements fall into the fault position, the dynamics model of a rolling bearing variable stiffness system with local faults is proposed, considering the retention factor of the contact deformation. Then, this paper researches the change of effective contact stiffness, contact deformation, contact force, and the total effective stiffness of the rolling elements. The results show that the contact stiffness of the rolling elements abruptly decreases when the rolling elements fall into the fault position. The contact deformation and contact force of the load-carrying rolling elements in the load zone increase, rebalancing the external radial load while causing a sudden reduction in the total effective stiffness, resulting in the vibration of the system. When different rolling elements fall into the outer ring fault position, the change in total effective stiffness and the system response are equal in magnitude. Additionally, there is a significant outer race fault characteristic frequency accompanied by frequency multiplication in the fault characteristic spectrums. When different rolling elements fall into the inner race fault position, the total effective stiffness is modulated by the inner race rotation and varies dramatically, resulting in the amplitude of the system time domain vibration response also being modulated by the inner race rotation and varying dramatically. Additionally, there is a significant inner race rotational frequency accompanied by frequency multiplication, an inner race fault characteristic frequency accompanied by frequency multiplication, and a side frequency in the fault characteristic spectrums. The research can provide some reference for the effective diagnosis of the rolling bearing fault.
