Rolling Ball Bearings Research Articles

Wear analysis of rolling bearing contact surfaces based on finite element method

Wear leads to the roughening of bearing surfaces, increased internal clearances, decreased rotational precision, and amplified vibration and noise, ultimately causing the bearing to fail to meet specified performance criteria. This study employs the quasi-static analysis method to examine bearing sliding behavior. Based on the Archard wear model and Hertz contact theory, a computational model for wear depth in lubricated conditions is established for rolling ball bearings, accounting for both the rolling and sliding of the rolling elements. The distribution law of load and wear coefficient along the raceway circumference are analyzed, along with the characteristics of stress and sliding velocity in the contact region. The study investigates the impact of rotational speed, load, surface roughness, and raceway curvature coefficient on the wear coefficient, wear depth, and minimum oil film thickness. Furthermore, sensitivity analysis is conducted on the parameters of the wear depth model. Finite element analysis, utilizing ANSYS Workbench, is employed to study the evolution of surface wear on the raceway of deep groove ball bearings and explore the dynamic relationship between contact stress and wear depth. These findings offer important theoretical guidance for the design, selection, and maintenance of rolling bearings.

Statistical Analysis of Vibration Signal Frequency During Inner Race Fault of Rolling Ball Bearings

Statistical Analysis of Vibration Signal Frequency During Inner Race Fault of Rolling Ball Bearings

МОДЕЛИРОВАНИЕ СОБСТВЕННЫХ ЧАСТОТ И АМПЛИТУДЫ ВЫНУЖДЕННЫХ КОЛЕБАНИЙ ВЕРТИКАЛЬНО-ФРЕЗЕРНОГО СТАНКА

The article demonstrate the technique for modeling the form of natural oscillations, as well as the amplitude and mode of forced oscillations of the HAAS VF-1 vertical milling machine. As initial data, a publicly available 3D model of load-bearing elements, information on the mass and dimensions of the spindle motor are used. In preparation for the simulation, the original solid model is idealized by removing small chamfers, fillets, and small diameter holes. Movable joints with linear rolling guides and ball bearings are replaced by rigid joints, since vibration damping in these units is not considered. During the first simulation, ten natural frequencies with the largest values of the oscillation amplitude are obtained. The second simulation shows, the influence of the spindle drive layout (coaxial installation of the electric motor with the spindle through a cam clutch or connection using a toothed belt transmission) and additional devices for dissipating vibration energy (mass and structural dampers in the form of structural elements articulated through plastic bushings) is revealed by the magnitude of forced steady-state oscillations that may occur during the processing of the part.

Ultra‐Robust and High‐Performance Rotational Triboelectric Nanogenerator by Bearing Charge Pumping

As an emerging technology to convert environmental high‐entropy energy into electrical energy, triboelectric nanogenerator (TENG) has great demands for further enhancing the service lifetime and output performance in practical applications. Here, an ultra‐robust and high‐performance rotational triboelectric nanogenerator (R‐TENG) by bearing charge pumping is proposed. The R‐TENG composes of a pumping TENG (P‐TENG), an output TENG (O‐TENG), a voltage‐multiplying circuit (VMC), and a buffer capacitor. The P‐TENG is designed with freestanding mode based on a rolling ball bearing, which can also act as the rotating mechanical energy harvester. The output low charge from the P‐TENG is accumulated and pumped to the non‐contact O‐TENG, which can simultaneously realize ultralow mechanical wear and high output performance. The matched instantaneous power of R‐TENG is increased by 32 times under 300 r/min. Furthermore, the transferring charge of R‐TENG can remain 95% during 15 days (6.4 × 106 cycles) continuous operation. This work presents a realizable method to further enhance the durability of TENG, which would facilitate the practical applications of high‐performance TENG in harvesting distributed ambient micro mechanical energy.

Auto Labeling Methods Developed Through Semi-Weakly Supervised Learning in Prognostics and Health Management Applications for Rolling Ball Bearing

In recent years, complex machine learning and deep learning algorithms have been used in prognostics and health management applications to monitor the state of industrial systems in real-time and predict failures in advance. However, the performance of these algorithms depends on the size of the collected labeled datasets. This study proposes a semi-weakly supervised learning method that creates label functions using a small amount of data and, consequently, combines weak supervision and semi-supervision methods to expand the labeled dataset for training. The proposed model training method creates labels automatically in the life prediction dataset of rolling element bearings, which were manually labeled by expert groups. The performance of the deep neural network is continuously improved through experiments, and a performance improvement similar to that of manually labeled training data is presented. Future research applications include meta-learner experiments (e.g., use of pre-trained word embedding or other model architectures) and more appropriate selection methods and definitions for the basic learner.

Predicting changes in radial and axial clearances in ball bearings lubricated with low-viscosity liquids

Parts of rolling bearings lubricated with low-viscosity fluids are subject to intense wear of the working surfaces. The bearing life cycle under these conditions depends on the wear rate of the friction surfaces. Therefore, it is important to establish the relationship between the wear rate, the change in the clearances and the duration of work. This paper presents the results of wear tests for rolling ball bearings. After the tests the radial and axial clearances were measured, their changes and the duration of operation were analyzed. Having determined the path of friction, the wear rates of the bearings were calculated based on the values of changes in the radial and axial clearances. The wear rate of the bearing on the axial and radial clearances was plotted against the reduced (equivalent) load. The obtained dependences were approximated with a confidence of at least 98%. The obtained analytical expressions allow us to perform express calculations for changes in the bearing clearances. This will make it possible to forecast the bearing service time, taking into account the wear of the working surfaces under specified conditions, while ensuring correct functioning of the support assembly.

MODERN TECHNOLOGIES FOR FINISHING BEARING ROLLWAYS

The most promising methods for improving the quality of the surfaces of the raceways of ball bearing rings with multipoint contact are pulse hardening ultra-sonic treatment and superfinish with an inclined abrasive bar. (Research purpose) The research purpose is studying modern technologies for improving the quality of the surfaces of the raceways of ball bearing rings with multipoint contact; to carry out mathematical modeling of the process of forming a rational geometric shape of a complex raceway surface during the application of ultrasonic treatment and superfin-ish with an inclined abrasive bar. (Materials and methods) It was noted that achieving a rational geometric shape of a complex raceway surface without the use of advanced processing devices is extremely difficult. It was determined that in the case of pulsed hardening ultrasonic treatment, the initial velocity V0 is reported to the steel ball in contact with the oscillating wall of the waveguide. Upon impact with the treated sur-face, the ball penetrates into it to a certain depth ∆сж, as a result, the surface of the treated part is exposed to a short-term compressive force Fсж. It was revealed that dur-ing the superfinish process, the workpiece rotates around its axis with an inclined abrasive bar, and an abrasive bar is pressed against the surface of the rolling track of the workpiece with force P. The oscillation axis of the bar is inclined at an angle to the axis of the workpiece. (Results and discussion) It was shown that the technologies of ultrasonic processing and superfinish with an inclined abrasive bar were tested on thrust-radial rolling bearings and ball bearings with multipoint contact. (Conclusions) In the first variant, during the smoothing process, the surface layer of the raceway of the ball bearing rings is deformed, the part and the tool are heated to higher tempera-tures, which in turn leads to rapid tool wear. In the second variant, the technology of processing the complex profile of the raceway of ball bearing rings requires special control. It is necessary to improve superfinish operations in the direction of increasing their technological capabilities.

Tribological properties of hexagonal boron nitride nanoparticles or graphene nanoplatelets blended with an ionic liquid as additives of an ester base oil

AbstractAntifriction synergies between an ionic liquid (IL) and nanopowders as additives of an ester base oil were analysed at rolling conditions. For this aim, two nanodispersions based on hybrid combinations of hexagonal boron nitride nanoparticles (h‐BN) or graphene nanoplatelets (GnP) with tri(butyl) ethylphosphonium diethylphosphate ionic liquid as additives in triisotridecyltrimellitate (TTM) base oil and the mixture of TTM and IL were analysed using two tribometer techniques. Film thickness characterisation and tribological tests were performed at rolling conditions [5% slide‐roll‐ratio (SRR)], under 50N and at operating temperatures of 30, 50 and 80°C. Stribeck curves showed that friction coefficients for the prepared lubricants are lower than those found for the TTM, being the best friction behaviour for the hybrid GnP nanolubricant. Furthermore, friction torque loss tests were performed in rolling ball bearings, observing that for the two hybrid nanolubricants lower friction torque values were obtained.

Nonparametric Bayesian reliability analysis of masked data with dependent competing risks

The characteristic of dependence widely exists among different failure modes of systems, which brings extra difficulty for the reliability analysis. In this paper, a nonparametric Bayesian analysis method is proposed for dependent masked data under accelerated lifetime test with censoring. Using the copula function, the dependence structure is constructed among the competing failure modes which can be viewed as the components in a series system. By establishing the transformational relationship between the subsurvival functions and the survival functions, the estimators of components’ reliability can be derived from the nonparametric Bayesian estimators of the subsurvival functions when a Dirichlet multivariate process prior is considered. A simulation study is given to illustrate the effectiveness of the proposed methods and the influence of the degree of dependence on the performance of the estimation procedure. It is shown that the dependence between failure modes should not be ignored because ignoring the dependence may lead to serious errors. A numerical example based on a life test of rolling ball bearings is presented as an application of the proposed methodology.

Multi-Dimensional Mathematical Wear Models of Vibration Generated by Rolling Ball Bearings Made of AISI 52100 Bearing Steel

The paper features the development of multi-dimensional mathematical models used for evaluating the impact of selected factors on the vibration generated by 6304ZZ type rolling ball bearings from three manufacturers in the aspect of the wear process. The bearings were manufactured of AISI 52100 bearing steel. The analyzed factors included the inner and outer raceways’ roundness and waviness deviations, radial clearance and the total curvature ratio. The models were developed for vibration recorded in three frequency ranges: 50–300 Hz, 300–1800 Hz and 1800–10,000 Hz. The paper includes a specification of the principles of operation of innovative measuring systems intended for testing bearing vibration, raceway geometries and radial clearance. Furthermore, it features a specification of particular stages of the multi-dimensional mathematical models’ development and verification. Testing with the purpose of statistical evaluation of the analyzed factors is also presented. The test results and mathematical models indicate that the inner raceway’s waviness deviation had a dominant impact on the vibration examined in all frequencies. The roundness and waviness deviation of bearing raceways made of AISI 52100 steel propagates the bearing wear process.

Research accuracy of final formation profile of rolling ball bearings by various methods.

An important role in the further operation of rolling bearings is played by the shape of the grooves of the ball bearing rings. That is why it is necessary to pay special attention to the formation of their profile. To study the shape of the trough, we studied a batch of ball bearing rings using the method of measuring the size of the stamps. Since the bearing also works with small radial loads, it is necessary to press in not only at right angles. Additionally, we propose to strengthen the effect of indentation. From the experiments it can be seen that there is a different distribution of stresses along the contact area for bearings of the same size. Based on this, it can be argued that the accuracy of the machining process is insufficient. Therefore, there is a need to improve the accuracy of shaping the profile of ball bearing rings by advanced technologies. To do this, we propose to use imitation completion. After this procedure, after conducting experiments, one can again see how the characteristics of the raceway profile of ball bearings have qualitatively changed, and, accordingly, their durability.

Dynamic modeling and abnormal contact analysis of rolling ball bearings with double half-inner rings

The rolling ball bearing with double half-inner rings is widely used in rotating machinery due to its remarkable space-saving structure, convenience of installation and load-carrying capacity. This paper focuses on dynamic modeling and abnormal contact analysis of rolling ball bearing with double half-inner rings. Firstly, an analytic dynamic model of the bearing is proposed with consideration of lubricant resistance and cage effect under working conditions. Then, the dynamic model is applied for the contact analysis between rolling balls and bearing rings, and the boundary between normal contact (i.e., two-point contact) and abnormal contact (i.e., three-point contact) is given. All the numerical simulations are verified with the experiments. The results can provide helpful guidance for the design and troubleshoot of rolling ball bearings with double half-inner rings.

A triboelectric rolling ball bearing with self-powering and self-sensing capabilities

With the popularization of the Internet of Things (IoT) and big-data technology, the requirement for intelligent rolling bearings has grown exponentially. In this paper, a novel intelligent rolling bearing, called triboelectric rolling ball bearing (TRBB), with self-powering and self-sensing capabilities is proposed. The structure of a mechanical rolling bearing is directly adopted for the TRBB, and a triboelectric nanogenerator with rolling free-standing mode is devised by pasting flexible interdigital electrodes on the outer ring of the TRBB. On the premise of maintaining the structural integrity of the rolling bearings, direct contact between the electrodes and rolling balls is avoided, and the service life of the TRBB can thus be guaranteed. Because of the contact electrification between the rolling ball and outer ring, electricity is generated when the TRBB supports the rotor and rotates. The electrical output characteristics of the TRBB are measured at different rotating speeds, and the peak power with optimal load resistance is found. The root mean square value and frequency of output current are employed as the two rotational speed indicators. Design parameters, such as those of cage, structural dimensions, ball material and outer ring material, are analyzed to investigate their effects on the sensitivity of the TRBB. Rotating speed curves obtained using the two indicators are compared with those of a commercial sensor. Two abnormal states, rolling ball missing and electrode breakage, are considered to assess other self-sensing capabilities of the TRBB. Tests for continuous running and different rotor weights are carried out to illustrate the durability and stability of the TRBB, respectively. Tests on load capacitance charging and driving of low-power devices are also conducted to analyze the self-powering capability of the TRBB. This work presents a multi-functional self-powering and self-sensing system, wherein the fabricated TRBB has widespread application prospects in the development of IoT.

Comparison of analytical and numerical solution of bearing contact analysis

In this paper, an effort has been put to analyze the rolling ball bearing using finite element analysis the contact pressure level, stress or displacement behavior of rolling ball bearing. The obtained results were then compared with the analytical results obtained through the methodology of Hertz theory, which means composition and solution of analytical formulas and equations based on specific ball bearing parameters in order achieve optimal results to demonstrate an almost identical similarity of results of numerical and analytical solution and correct setting up of the given simulation in computational software ANSYS Workbench.

Vibration analysis and comparison of the damaged and undamaged rolling ball bearing

Abstract This article deals with vibration analysis and the processing of the vibration signal obtained during the experimental measurement on a rotary shaft at start-up, constant speeds and run-out, with a ball bearing roller. The next step of the research is the introduction and application of mathematical and numerical methods for the processing of input and measured data using diagnostic and mathematical software. The principle of measurement and processing was to compare the results of oscillation of an undamaged bearing with several types of damaged bearings with corresponding deformations in the orbits. The purpose of the research and comparison was to achieve optimal results (in terms of amplitude values, the occurrence of eigenvalue vibrations and the resonance phenomenon) of individual bearings with corresponding impulses in the orbits and to obtain calibration diagrams as a tool for possible prediction of bearings in operation.

Badanie zależności tarcia tocznego od promienia kulki łożyskowej

There are two alternative historical laws of rolling resistance formulated by French scientist Coulomb and Dupuit. It has been decided to verify experimentally again, which of these laws describes freely rolling ball bearings on a hard surface better. An inducement to carrying out the measurements was the idea of the constant thickness of roadbed, which is consistent with Dupuit's theory. Measurements have been done using the damped oscillations in the pendulum bearings. Results have shown better consistency with the Coulomb's theory with small, but measurable deviations. These deviations were successfully explained by the so called "Cobblestones model". Parameters designated by this model have been successfully verified by the surface roughness's profile measurement. An additional theoretical aspect of this work is distinguishing two types of rolling friction force: dynamical and kinematical in an analogy to two types of specific heat capacity in the thermodynamics of gases.

Static structural analysis of rolling ball bearing

In this paper, an effort has been put to analyze the rolling ball bearing using finite element analysis the contact pressure level, stress or displacement behavior of rolling ball bearing. The obtained results were then compared with the analytical results obtained through the methodology of Hertz theory in order to demonstrate an almost identical similarity of results and correct setting up of the given simulation in computational software ANSYS Workbench.

Dynamic Analysis of a Rotor System Supported on Squeeze Film Damper with Air Entrainment

Squeeze film dampers (SFDs) are widely used in compressors and turbines to suppress the vibration while traversing critical speeds. In practical applications, air ingestion from the outside environment and cavitation may lead to a foamy lubricant that weakens oil film damping and dynamic performance of rotor system. In this paper, a rigid rotor model is established considering both lateral and pitching vibration under different imbalance excitations to evaluate the effect of air entrainment on rotor system. Tests with three different imbalances are carried out on a rotor-SFD apparatus. Volume controlled air in mixture ranging from pure oil to all air are supplied to the SFD. The transient response of rotor is measured in the experiments. The results show that two-phase flow produces significant influence on the system stability and dynamical response. The damping properties are weakened by entrained air, such as the damping on high frequency components of rolling ball bearing. Super-harmonic resonance and bifurcation are observed, as well as the low frequency components due to air entrainment.

A New Dynamic Model of Ball-Bearing Rotor Systems Based on Rigid Body Element

Ball-bearing rotor systems are key components of rotating machinery. In this work, a new dynamic modeling method for ball-bearing rotor systems is proposed based on rigid body element (RBE). First, the concept of RBE is given, and then the rotor is divided into several discrete RBEs. Every two adjacent RBEs are connected by imaginary springs, whose stiffness is calculated according to properties of the RBEs. Second, all the parts of rolling ball bearings (i.e., outer ring, inner ring, ball, and cage) are considered as RBEs, and Gupta's model is employed to model bearings which include radial clearance, waviness, pedestal effect, etc. Finally, the rotor and all the rolling ball bearings are coupled to develop a dynamic model of the ball-bearing rotor system. The vibration responses of the ball-bearing rotor system can be calculated by solving dynamic equations of each RBE. The proposed method is verified with both simulation and experiment. The RBE model of the rotor is compared with its finite element (FE) model first, and numerical simulation shows the validity of the RBE model. Then, experiments are conducted on a rotor test rig which is supported with two rolling ball bearings as well. Good agreements between measurement and simulation show the ability of the model to predict the dynamic behavior of ball-bearing rotor systems.

A systematic study of ball passing frequencies based on dynamic modeling of rolling ball bearings with localized surface defects

Ball passing frequencies (BPFs) are very important features for condition monitoring and fault diagnosis of rolling ball bearings. The ball passing frequency on outer raceway (BPFO) and the ball passing frequency on inner raceway (BPFI) are usually calculated by two well-known kinematics equations. In this paper, a systematic study of BPFs of rolling ball bearings is carried out. A novel method for accurately calculating BPFs based on a complete dynamic model of rolling ball bearings with localized surface defects is proposed. In the used dynamic model, three-dimensional motions, relative slippage, cage effects and localized surface defects are all considered. Moreover, localized surface defects are modeled accurately with consideration of the finite size of the ball, the additional clearance due to material absence, and changes of contact force directions. The reasonability of the proposed method for the prediction of dynamic behaviors of actual ball bearings with localized surface defects and for the calculation of BPFs is discussed by investigating the motion characteristics of a ball when it rolls through a defect. Parametric investigation shows that the shaft speed, external loads, the friction coefficient, raceway groove curvature factors, the initial contact angle, and defect sizes have great effects on BPFs. For a loaded ball bearing, the combination of rolling and sliding in contact region occurs, and the BPFs calculated by simple kinematical relationships are inaccurate, especially for high speed, low external load, and large initial contact angle conditions where severe skidding occurs. The hypothesis that the percentage variation of the spacing between impulses in a defective ball bearing was about 1–2% reported in previous investigations can be satisfied only for the conditions where the skidding effect in a bearing is slight. Finally, the proposed method is verified with two experiments.