Rolling Element Research Articles

Methodology for calculating the support reactions of a statically indeterminate tractor drive axle final drive shaft

BACKGROUND: Currently, in the design of vehicle drive axles, bevel final drives are used, forming both statically determinate structures and statically indeterminate ones. In the first case, the bearings on which the bevel final drive shafts rest form two races of rolling elements, in the second case - three or more. Despite the prevalence of bevel final drive designs that form statically indeterminate structures, in the process of teaching the design and calculation of machine elements, statically determinate structures are considered. The relevance of the work lies in the formalization of the analytical calculation of the reactions of the supports of the bevel final drive, forming a statically indeterminate system, with the derivation of formulas for determining the reactions in the extra support. AIMS: The article aim is the formalization the methodology for calculating the support reactions of the drive axle bevel final drive, forming a statically indeterminate system, for calculating bearings. METHODS: The article uses mathematical dependencies of Analytical Mechanics to calculate reactions in the main supports, a corollary of Castigliano theorem and the Force method to calculate reactions in extra supports. "Mathcad" was used for mathematical calculations. RESULTS: A formalized method for the analytical calculation of support reactions in statically indeterminate systems has been developed and presented, using Castigliano theorem to solve static indetermination. The methodology application for calculating the support reactions of the statically indeterminate the Kirovets K-7 series tractors drive axle bevel final drive is considered. CONCLUSIONS: The dependencies obtained during the calculations make it possible to calculate the bevel final drive support reactions, the design of which forms a statically indeterminate system. The bevel final drive mathematical model obtained during the calculations can be used as a basis for developing software that automates this calculation.

An FBG-based method for load measurement of a cylindrical rolling element bearing

Abstract Contact forces between raceways and rolling elements of a bearing stand as crucial operational aspects defining the bearing’s performance. While monitoring bearing load through load cells or strain gauges on the shaft or housing is feasible, it may not precisely reflect the distributed load transmitted by the rollers directly to the raceways. This paper introduces a method to calculate these contact forces, relying on a linear assumption correlating the loads to the measured strains on the outer race of a bearing. In our research, we conducted both static and dynamic tests on cylindrical roller bearings through simulations and experiments. We designed an experimental test rig to conduct both static and dynamic experiments and utilized FBG optical fiber sensors for contact force measurement in bearings due to their multiple advantages, including high sensitivity, resistance to corrosion and magnetic interference, and ease of installation on the bearing outer race due to their shape and size. Our findings indicate a consistent linear relationship between contact forces and strains measured on the bearing’s outer race. Furthermore, we calculated the linear coefficient K values from three test groups: static tests under simulation study, static tests under experimental study, and dynamic tests under experimental study. The K values obtained from static tests (simulation and experimental studies) and dynamic tests (experimental study) align consistently. Following this, we calculated contact forces in both static and dynamic experiments by multiplying the measured strains with K. Our calculations resulted in an error percentage of less than 2% for static tests and below 5% for dynamic tests, highlighting the accuracy of our approach in determining these contact forces.

Impedance measurement of rolling bearings using an unbalanced AC wheatstone bridge

Industry 4.0 drives the demand for cost-efficient and reliable process data and condition monitoring. Therefore, visualizing the state of tribological contacts becomes important, as they are regularly found in the center of many applications. Utilizing rolling element bearings as sensors and monitoring their health by the electrical impedance method are promising approaches as it allows, e.g., load sensing and detection of bearing failures. The impedance cannot be measured directly, but there are various methods available. This paper discusses advantages and disadvantages and suggests the AC Wheatstone bridge as a reliable way of measuring impedances with low phase angles at sampling rates in the kHz range. The corresponding equations are introduced, a simulation built, an uncertainty mode and effects analysis carried out and sample measurement results of real rolling elements shown. It can be demonstrated that the AC Wheatstone bridge meets the proposed requirements for sensory utilization and condition monitoring when the bearing is operated in the hydrodynamic regime.

Uncertainty Quantification in the Prediction of Remaining Useful Life Considering Multiple Failure Modes

Abstract Despite the substantive literature on remaining useful life (RUL) prediction, less attention is paid to the influence of epistemic uncertainty and aleatory uncertainty in multiple failure behaviors in the accuracy of RUL. The research question in this study was: can uncertainties be quantified in predicting the RUL of systems with multiple failure modes? The first objective was to quantify the uncertainties in the prediction of RUL, considering known multiple failure modes. This objective used vibration data from accelerated degradation experiments of rolling element bearings. The second objective was to calculate the uncertainties in the prediction of RUL, considering the multiple failure modes as unknown. The experimental data used in this objective were from run-to-failure tests of Li-ion batteries. An analysis was performed on how the uncertainties affect the RUL prediction in systems with known multiple failure modes and systems where the multiple failure modes were unknown. A Bayesian neural network (BNN) was used to quantify epistemic and aleatory uncertainty while predicting RUL. The results of the qualitative uncertainties on RUL in systems with multiple failure modes were presented and discussed. Also, the study yielded an RUL uncertainty quantification model for multiple failure modes. The proposed framework's performance in the RUL prediction was demonstrated. Finally, the epistemic and aleatory uncertainties were quantified in the system's RUL. It was shown that systems that fail due to the same failure mode tend to have similar uncertainty values over time. The results in this paper may lead to the design of more reliable systems that exhibit multiple failure modes.

The Interior Contact-Aided Rolling Element

Abstract This work introduces an interior contact-aided rolling element (I-CORE) compliant mechanism that draws upon the concepts used for the contact-aided rolling element, cross-axis flexural pivot, and pre-curved flexible beam. The I-CORE incorporates a bilinear compressive stiffness response with an initial tailorable stiffness governed by the flexural geometry, followed by a stiffness curve governed by the material stiffness at the contact point. The I-CORE mechanism can achieve one or two degrees of rotational freedom as well as a single degree of translational freedom. The purpose of the present work was to introduce the I-CORE mechanism, as well as a pseudo-rigid-body replacement model (PRBM) of the I-CORE mechanism which was subsequently validated using both finite element analysis and benchtop mechanical testing. A pseudo-rigid body model was created for the I-CORE to simplify the rapid adaptation of this mechanism to different design applications. This model was validated using both finite element analysis and benchtop mechanical testing under both compression and rotation loading conditions. Additionally, multiple configurations of the device were created and evaluated in order to test its sensitivity to certain design features including the flexure width, flexure thickness, and the radius of the rounded contact surfaces. It was found that the model is sensitive to the thickness of the flexures and that despite some limitations, the pseudo-rigid body model is sufficiently accurate for initial design work. Some possible applications of the mechanism are proposed.

A study of measurement of raceway direct measurement of rolling bearings

Demands for improved fuel efficiency in automobiles and other vehicles have led to smaller, lighter power transmission device which result in high surface contact stress and a thin oil film, which in turn tends to cause the temperature of rolling bearings to rise. The most common temperature measurement method is to touch a thermocouple against the inner and outer rings, and this method has been used for many years. However, the method using thermocouples can only measure temperatures in a limited range near the measurement point. The authors applied the Seebeck effect, a phenomenon in which an electromotive force is generated when different metals are connected and a temperature difference is applied to bearings, to a method of measuring bearing raceway temperatures called the dynamic thermocouple method. In the dynamic thermocouple method, the average value of each contact points between the different metals generates the emf (electromotive force), so the temperature rise of all the each rolling elements in contact becomes the average value, and the exact point of temperature rise is not clear. Therefore, all but one rolling element was changed to electrically insulating zirconia balls. With this method, the contact points between many different metals became one, making it possible to identify the locations of temperature rises on the raceway surface. This method makes it possible to directly measure the temperature change of the raceway. The results of temperature measurements of the raceway surface using two types of bearings with different raceway accuracy showed a clear difference of temperature. The bearing with a poor raceway accuracy showed a temperature rise in the unloaded zone, and slippage was observed when the behavior of the rolling element was checked with a high-speed camera. Furthermore, in bearings with good raceway accuracy, the temperature of the raceway surface remained almost constant even in the non-load zone. By using the dynamic thermocouple method and observing the rolling elements with a high-speed camera, it was possible to correlate the bearing temperature rise with the behavior of the rolling elements.

The edge artifact extraction method for Si3N4 ceramic bearing rolling element microcracks characterization

Aiming at the problem that the edge artifacts of Si3N4 ceramic bearing rolling element microcracks have low contrast, contain noise, and easily merge with the background, making it difficult to segment. A method based on 2D discrete wavelet transform and Otsu threshold segmentation is designed to achieve the extraction of microcrack edge artifact features. Wavelet decomposition is used to remove noise, while wavelet reconstruction features are used to restore lost details. Creation of 2D discrete wavelet transform functional equations combining wavelet reconstruction and wavelet decomposition to improve contrast and eliminate noise in images featuring edge artifacts. For the problem of feature edge artifacts that are difficult to remove, the threshold segmentation function equation is designed to maximize the interclass variance, and the optimal threshold value is selected to remove the edge artifacts. The experimental results show that the average PSNR of the Si3N4 ceramic bearing rolling body point, line, and surface microcrack edge artifact feature images enhanced by the method in this paper is close to 62.69 dB, and the average SSIM is about 0.77. The method in this paper improves the contrast of microcrack edge artifact features of Si3N4 ceramic bearing rolling bodies and makes the feature extraction effect of point, line, and surface microcrack edge artifacts more complete.

Edge segmentation method for Si3N4 bearing rolling elements microcracks with profile-distortion

For the profile-distortion of Si3N4 bearing rolling elements microcracks image. A coupling method of variable-scale truncated median filtering and detection-driven active contour model is proposed. Details are as follows. The sigmoid activation function is constructed to dynamically adjust the circular window. The local threshold truncation is designed to adapt to the characteristics of different regions in the image. The area threshold is defined to eliminate non-target features. The mean peak signal-to-noise ratio (PSNR) of filtered images is about 40.263. The edge overlap rate is as low as 0.1027. The mean accuracy of feature extraction is about 94.33 %. To sum up, the influence result from profile-distortion on the accuracy of feature extraction of Si3N4 bearing rolling elements microcracks is effectively solved.

Power Losses of Oil-Bath-Lubricated Ball Bearings—A Focus on Churning Losses

This study investigates the power losses of rolling element bearings (REBs) lubricated using an oil bath. Experimental tests conducted on two different deep-groove ball bearings (DGBBs) provide valuable insights into the behaviour of DGBBs under different oil levels, generating essential data for developing accurate models of power losses. Observations of the oil bath dynamics reveal the formation of an oil ring at high oil levels, as observed for planetary gear trains, leading to modifications in the oil flow behaviour. The experiments demonstrate that oil bath lubrication generates power losses comparable to injection lubrication when the oil level is low. However, as the oil level increases, so do the power losses due to increased drag within the bearing. This study presents a comprehensive model for calculating drag losses. The proposed drag power loss model accounts for variations in oil level and significantly improves loss predictions. A comparison of existing models with the experimental results shows good agreement for both bearings, demonstrating the effectiveness of the developed model in accounting for oil bath height in loss calculations.

Extraction method for characterizing microcracks on Si3N4 ceramic bearings rolling element with contour segmentation

AbstractAiming at the fuzzy diffusion characteristics of microcrack regions in Si3N4 ceramic bearing rolling elements, an adaptive region segmentation method is proposed to achieve precise extraction of microcrack features. The fuzzy diffusion effect of the microcrack region is analyzed, and a structural complexity matrix is defined to represent the degree of structural variation in the image. A threshold point is determined through histogram analysis, and the matrix dispersion rate is calculated using a box plot to update the correction factor, optimizing the overlap of noise in the microcrack image. The causes of distortion in the microcrack region are analyzed, and pixel points are assigned based on spatial metrics and LAB color features. The fuzzy boundaries and overlapping regions are segmented using the fuzzy C‐means clustering algorithm. A grid search algorithm is embedded to quantitatively evaluate the optimal combination of hyperparameters, enabling comprehensive extraction of microcrack features in Si3N4 ceramic bearing rolling elements. The optimized image achieves an average peak signal‐to‐noise ratio of 39.3, an information fidelity criterion of 7.9328, and an average extraction accuracy of approximately 0.92, effectively overcoming the impact of the fuzzy diffusion effect on the accuracy of microcrack feature extraction in Si3N4 ceramic bearing rolling elements.

Study on Atomization Mechanism of Oil Injection Lubrication for Rolling Bearing Based on Stratified Method

The atomization mechanism of lubrication fluid in rolling bearings under high-speed airflow between the rings was investigated. A simulation model of gas–liquid two-phase flow in angular contact ball bearings was developed, and the jet lubrication process between the bearing rings was simulated using FLUENT computational fluid dynamics software (Ansys 19.2). The complex motion boundary conditions of the rolling elements were addressed through a layered approach. We can obtain more accurate boundary layer flow field changes and statistics of the diameter of oil particles in lubricating oil atomization, which lays the foundation for analyzing the law of influence on lubricating oil atomization. The results show that as the number of boundary layer layers increases, the influence of the boundary layer flow field on the lubricating oil is more obvious. The oil particle size is excessively flat, and the concentration of large particles of oil appears to decrease. As the speed increases, the amount of oil in the cavity decreases, but the oil droplets are also fragmented, which intensifies the atomization and reduces the particle diameter. This reduces the Sauter Mean Diameter (SMD), which is not conducive to the lubrication of the bearing. Under different injection pressures, when the injection pressure is large, it is beneficial to the lubrication of the bearing.

Motor Bearing Failure Identification Using Multiple Long Short-Term Memory Training Strategies

In the context of condition-based maintenance of rotating machines in manufacturing systems, the early diagnosis of possible faults related to rolling elements of the bearing is mainly based on techniques from artificial intelligence, namely, Machine Learning (ML) and Deep Learning (DL). Approaches based on using Deep Learning methods have been the most coveted in recent years. Among a variety of models, the type of architecture known as Long-Short-Term Memory (LSTM) of Recurrent Neural Network (RNN) has both the ability to capture long-term dependencies and to adapt to sequential data modeling. It is therefore able to work on data without any preprocessing. This paper studies using four types of LSTM networks to diagnose bearing faults in a classification approach. It aims to intervene on both the input parameters and the network architecture, to achieve high performance. The proposed method is carried out in two different ways. In the first case, the data inputs are raw frames of vibration signals. However, in the second case, the network inputs are pre-computed time-frequency features. The results clearly showed that LSTMs are more accurate with the latter.

The Role of the Working Fluid and Non-Ideal Thermodynamic Effects on Performance of Gas Lubricated Bearings

Abstract Small-scale turbomachinery operating at high rotational speed is a key technology for increasing the power density of energy and propulsion systems. A notable example is the turbine of an organic Rankine cycle turbogenerator for thermal recuperation from prime engines and industrial processes. Such systems typically operate with organic compounds characterized by complex molecular structures, to allow the design of efficient fluid machinery and flexibility in matching the heat source and sink temperature profiles. Gas bearings are considered advantageous compared to traditional oil-lubricated rolling element bearings for supporting the turbine rotor, enabling greater machine compactness and reduced complexity, and to avoid contamination of the working fluid. In certain operating conditions, however, the lubricant of the bearing is in thermodynamic states near the saturated vapor line or in the vicinity of the fluid critical point whereby non-ideal effects are relevant and may affect bearing performance. This work investigates the physics of thin film flows in gas bearings operating with fluids made by complex molecules. The influence of non-ideal thermodynamic effects on gas bearing performance is discussed by analysis of the fluid bulk modulus. Reduced values of the non-dimensional bulk modulus near the critical point or saturated vapor line decrease bearing performance. The main parameter characterizing the influence of molecular complexity on bearing performance is shown to be the acentric factor. For complex fluids with large acentric factors, the impact of non-ideal thermodynamic effects on non-dimensional bearing load capacity and rotor-dynamic characteristics is less pronounced.

Nonlinear dynamic modeling and vibration analysis for early fault evolution of rolling bearings

In rotating machinery, the condition of rolling bearings is paramount, directly influencing operational integrity. However, the literature on the fault evolution of rolling bearings in their nascent stages is notably limited. Addressing this gap, our study establishes an innovative nonlinear dynamic model for early fault evolution of rolling bearings based on collision impact. Firstly, considering the fault evolution characteristics, the influence of the rolling element and fault structure, the dynamic model of early fault evolution between the rolling element and the local fault is established. Secondly, according to the Hertzian contact deformation theory, a nonlinear dynamic model of rolling bearings expressed as mass-spring is established. Thirdly, the energy contribution method is used to integrate the fault evolution model and the nonlinear dynamic model of the rolling bearing. A nonlinear dynamic model of early fault evolution of the rolling bearing is proposed by using the Lagrangian equation. Comparing the simulation results of the nonlinear dynamic with the experimental results, it can be seen that the numerical model can effectively predict the evolution process and vibration characteristics of the fault evolution of rolling bearings in the early stage.

Wind turbine condition monitoring dataset of Fraunhofer LBF

Fraunhofer wind turbine dataset contains monitoring data from a 750 W wind turbine, including accelerometers and tachometer, to capture structural response, bearing vibrations and rotational velocity. Additionally, temperatures, wind speed and wind direction have been measured, while weather conditions have been acquired from selected sources. Various damage scenarios, including mass imbalance, and aerodynamic imbalance as well as damages on bearings’ outer race, inner race and roller element have been implemented. The availability of time series data makes the dataset well suited for both machine learning and signal processing-based condition monitoring applications. The availability of heterogeneous sensors has created a dataset particularly suited for information fusion, data fusion, multi-sensor approaches, and holistic monitoring. Experiments were conducted in real-world conditions outside of a controlled laboratory environment, thereby introducing challenges such as variable rotor speed, noise, overloads, and other environmental factors. Consequently, the dataset is qualified for tasks involving uncertainty quantification and signal pre-processing. This document will detail the test equipment, experimental procedures, simulated damage cases and measurement parameters.

Rolling element bearing fault diagnosis under time-varying speed conditions based on improved wavelet packet transform and envelope order tracking

Abstract Rolling element bearings (REBs) are crucial components of rotating machinery and play an important role in industrial production. Failure of REBs can lead to significant economic losses and catastrophic accidents. In order to ensure their safe and stable operation, we propose a novel approach called EOT-IWPT which combines the envelope order tracking (EOT) with an improved wavelet packet transform algorithm (IWPT) for diagnosing failures in REBs under time-varying speed conditions. First, the time- domain vibration signal is resampled at constant angle intervels according to the phase of the rotating shaft to obtain the angle-domian signal. Next, the resampled signal is decomposed to sub-band signals using IWPT. Third, the squared envelope spectra (also called envelope order spectra) of the last layer wavelet packet coefficients are obtained by the Hilbert transform and the Fourier transform. Finally, the diagnostic results can be easily determined based on the squared envelope spectra. The procedure and performance of the proposed approach are illustrated and evaluated through simulation analysis, proving that the proposed method can effectively extract the fault features. Furthermore, experimental analysis results indicate that the proposed method outperforms both EOT-WPT and SK-EOT-BPF.

Research on the stiffness characteristics and contact status of matched angular contact ball bearings considering the effect of varying spatial position of rolling ball

In engineering practice, bearings used as support components are usually installed in pairs in various rotating machines. The mechanical and contact characteristics of bearings play a crucial role in determining the operational accuracy, safety performance and stability of equipment. Numerous studies focused on single bearings have been reported form diffident aspects for enhancing service performance. However, the literature reports on the matched bearings are scarce due to the mutual coupling of rolling elements and the extremely complex stress conditions. Especially the stiffness fluctuation and internal contact status affected by the ball position are difficult to be observed and tested experimentally because of the complex and compact structure, which significantly impacts the safe and reliable operation of rotating machines. To overcome the above shortcomings, this paper investigates the effect of ball position on the stiffness characteristics and contact status of matched angular contact ball bearings based on the coordinate matrix transformation approach and Jones’ statics model. Then, the stiffness results of published literature are used as a benchmark to validate the accuracy of solution method of this paper. Finally, 7206B bearings with different installing forms are used as a numerical example to reveal the effect of ball position on the stiffness characteristics and contact status of matched angular contact ball bearings under different working conditions. The study provides a scientific guidance to investigate the mechanical characteristics and contact mechanism of multi-bearing system.

Spectrum-guided GAN with density-directionality sampling: Diverse high-fidelity signal generation for fault diagnosis of rotating machinery

In the field of fault diagnosis for rotating machinery, where available fault data are limited, numerous studies have employed a generative adversarial network (GAN) for data generation. However, the limited fault data for training GAN exacerbate GAN’s inherent training instability and mode collapse issues, which are induced by adversarial training. Moreover, the stochastic nature of random sampling for latent vectors sampling often results in low-fidelity and poor diversity generation, which negatively affects the fault diagnosis models. To address these issues, this paper presents two novel approaches: a spectrum-guided GAN (SGAN) and density-directionality sampling (DDS). SGAN mitigates training instability and mode collapse through combinatorial data utilization, adversarial spectral loss, and a tailored model structure. DDS ensures the high-fidelity and high-diversity of the generated data by selectively sampling the latent vectors through two steps: density-based filtering and directionality-based sampling in the feature space. Validation on both rotor and rolling element bearing datasets demonstrates that SGAN-DDS considerably improves classification results under the limited fault data. Furthermore, fidelity and diversity analyses are conducted to validate DDS, which increase the credibility of the proposed method; and offer advancement toward the application of deep-learning and GAN in industrial fields.

Extraction and classification of vibration features of rolling element bearing with increasing the rotational speed

Machinery components degrade over time due to continuous use. A reliable prognosis framework can improve machinery health by monitoring the behavior of its parts and providing warnings before critical failures occur. Bearings, which are essential components of rotating machinery, help maintenance personnel assess the machine’s condition during continuous wear. In this study, vibration data from roller bearings under various conditions and faults were collected. The Vibration analysis technique was employed to detect and classify different faults in bearings based on the characteristics of the vibration signals generated by the machinery. Faults can be detected, diagnosed, and classified by analyzing bearing vibration signatures using techniques such as frequency analysis, time-domain analysis, spectral analysis, and kurtogram classifiers. This enables appropriate maintenance actions to be taken in time, preventing further damage or failures.

An interpretable hybrid framework combining convolution latent vectors with transformer based attention mechanism for rolling element fault detection and classification

Failure of industrial assets can cause financial, operational and safety hazards across different industries. Monitoring their condition is crucial for successful and smooth operations. The colossal volume of sensory data generated and acquired throughout industrial operations supports real-time condition monitoring of these assets. Leveraging digital technologies to analyze acquired data creates an ideal environment for applying advanced data-driven machine learning techniques, such as convolutional neural networks (CNNs) and vision transformer (ViT) to detect faults and classify, enabling accurate prediction and timely maintenance of industrial assets. In this paper, we present a novel hybrid framework based on the local feature extraction ability of CNN with comprehensive understanding of transformer within a global context. The proposed method leverages the complex weight-sharing properties of CNNs and ability of transformers to understand the larger context of spatial relationships in large-scale patterns, making it applicable to datasets of varying sizes. Preprocessing methods such as data augmentation are used to train the model on the Case Western Reserve University (CWRU) dataset in order to increase generalization through computational efficiency. An average fault classification accuracy of 99.62% is accomplished over all three fault classes with an average time-to-fault detection of 38.4 ms. MFPT fault dataset is used to further validate the method with an accuracy of 99.17% for outer race and 99.26% for inner race. Moreover, the proposed framework can be modified to accommodate alternative convolutional models.