Accurately predicting the performance of lubricated rolling elements is critical for certain key bearing applications. A widely employed simulation technique is quasi-static models, which although ...computationally efficient to implement, lack accuracy in predicting the kinematics of bearing components. This problem arises from their construction under kinematic assumptions, instead of solving the kinematic based on real frictional interactions. This paper presents a quasi-static model based on the minimum energy hypothesis for lubricated contacts, which determines the kinematic of the ball considering the effects of the frictional interactions governed by the elastohydrodynamic lubrication mechanism. The influence of kinematic variables on the sliding patterns and power loss distribution of the contact are analysed. The results are compared with other published quasi-static models, revealing substantial differences. The influence of the kinematic hypotheses on power losses are also studied at a bearing component scale. Finally, the effect of the governing lubrication mechanism of the contact is discussed, concluding that the limiting shear stress of the lubricant and the centrifugal forces have a significant effect on the kinematic of the ball.
•Development of a semi-analytical quasi-static model of ball-raceway contacts based on the minimum energy hypothesis.•Analysis of the influence of the pitch angle and pure rolling line locations on the contact kinematics and power losses.•Analysis of the impact of the working conditions on the pitch angle and comparison to literature models.•Study of the governing lubrication mechanism on kinematic and power loss behaviour.•Theoretical demonstration of the transition between inner and outer control raceway hypothesis.
•A new analytic method considering the axial preload and contact angle is developed.•The changes of the contact angle, internal load distribution and axial stiffness caused by the combined loads are ...studied.•The calculation time and computational resource of the proposed method are much less than those of the quasi-static method.•The proposed method can overcome the calculation error of the traditional static analytic method.
Performances and working life of angular contact ball bearings (ACBB) are determined by their internal load distribution and stiffness. To obtain accurate calculation results of the load distribution and stiffness of a preloaded ACBB with the combined loads, a new analytic method considering the axial preload and contact angle is developed for solving the internal load distribution and stiffness of the bearing. The changes of the contact angle, internal load distribution and axial stiffness caused by the combined loads are studied. The results from the proposed method are compared with those from the traditional static analytic method and the quasi-static method. The calculation results from the new analytic method considering the preload and contact angel are similar as those from the quasi-static method. However, the calculation time and computational resource of the proposed method are much less than those of the quasi-static method. The results show that the proposed method can overcome the calculation error of the traditional static analytic method. The computational accuracy and efficiency for calculating the load distribution and stiffness of the preloaded ACBBs may be greatly improved by the proposed method.
The rotor misalignment fault, which occurs only second to imbalance, easily occurs in the practical rotating machinery system. Rotor misalignment can be further divided into coupling misalignment and ...bearing misalignment. However, most of the existing references only analyze the effect of coupling misalignment on the dynamic characteristics of the rotor system and ignore the change of bearing excitation caused by misalignment. Based on the above limitations, a five degrees of freedom nonlinear restoring force mathematical model is proposed, considering misalignment of bearing rings and clearance of cage pockets. The finite element model of the rotor is established based on the Timoshenko beam element theory. The coupling misalignment excitation force and rotor imbalance force are introduced. Finally, the dynamic model of the ball bearing-coupling-rotor system is established. The radial and axial vibration responses of the system under misalignment fault are analyzed by simulation. The results show that the bearing misalignment significantly influences the dynamic characteristics of the system in the low-speed range, so bearing misalignment should not be ignored in modeling. With the increase of rotating speed, rotor imbalance and coupling misalignment have a greater impact. Misalignment causes periodic changes in bearing contact angle, radial clearance, and ball rotational speed. It also leads to reciprocating impact and collision between the ball and cage. In addition, misalignment increases the critical speed and the axial vibration of the system. The results can provide a basis for health monitoring and misalignment fault diagnosis of the rolling bearing-rotor system.
•An improved dynamic model of bearings with an outer raceway defect is proposed.•A localization index is built based on the mathematical principle of morphology.•Noise reduction and feature ...enhancement principle of the novel index is derived.•A new morphological filter and feature enhancement algorithm is proposed.
The location dimension of a bearing outer raceway defect plays an important guiding role in failure prediction and other aspects. Therefore, an improved dynamic model of bearings is proposed. The advantage of the model is that it can accurately simulate the impact characteristics of defective bearings and improve computational efficiency. Then, the relationship between the horizontal–vertical synchronized root mean square and the defect location dimension in different conditions is mapped using the model. Subsequently, a new index, named morphology horizontal–vertical synchronized root mean square (MHVS-RMS), is constructed based on the approximate analytical solution of the dynamic model of bearings and the mathematical principle of morphology. The function relationship between MHVS-RMS and the location dimension, as well as its principle of noise reduction and feature enhancement, are derived and proven. Finally, in view of the problem that noise interference in actual signals affects the accuracy of localization diagnosis, a new morphological filter and feature enhancement algorithm, named morphological scale-difference filter, is proposed via the above principles. The performance analysis results demonstrate that the proposed method can remarkably improve diagnosis accuracy.
•A 3D clearance fit model between bearing rings and bearing pedestal is proposed.•A general analytical stiffness model of ball bearings in rotor systems is proposed.•A multi-supported rotor system is ...established and verified by the experiment.•The vibration and contact characteristics of bearings in the system are analyzed.
Clearance fit is a common assembly method for bearings in rotor systems, which leads to a certain clearance between the outer ring of the bearing and the bearing pedestal, that is, the fit clearance. The nonlinear factors caused by the fit clearance may affect the mechanical properties of the bearing and rotor system. Considering the fillet and six-degree-of-freedom (6-DOF) motion of the outer ring, a three-dimensional (3D) clearance fit model is proposed. In addition, considering the interference fit between the inner ring and spindle, an analytical stiffness model of ball bearings is developed. By coupling the clearance fit model and the analytical bearing stiffness model with a finite element (FE) model of a spindle, a dynamic model of a multi-supported rotor system is established and verified by the experiment, which fully considers the nonlinear factors of ball-raceway contact and outer ring-bearing pedestal contact. The effects of fit clearance, radial force, and axial force on the vibration behaviors and contact characteristics of the ball bearing in the system are analyzed. The results indicate that the larger fit clearance of the unilateral bearing may lead to misalignment of the bearing and reduce the bearing force. Under radial force, the bearing clearance and fit clearance are eliminated, which improves the stability of the system. At this time, further application of axial force causes the load-bearing area to become larger and weakens the variable compliance (VC) characteristics of the bearing. This investigation can provide technical support for the assembly and design of the bearing-rotor system.
This reprint focuses on the hot issue of bearing lubrication and thermal analysis, and brings together many cutting-edge studies, such as bearing multi-body dynamics, bearing tribology, new ...lubrication and heat dissipation structures, bearing self-lubricating materials, thermal analysis of bearing assembly process, bearing service state prediction, etc. The purpose of this reprint is to explore recent developments in bearing thermal mechanisms and lubrication technology, as well as the impact of bearing operating parameters on their lubrication performance and thermal behavior.
•A dynamic model of bearing-rotor systems with inner ring misalignment is proposed.•A nested iteration method for solving the dynamic model of the system is proposed.•Nonlinearities due to ...ball-raceway contact and 3D clearance are well considered.•Vibration characteristics of the system with inner ring misalignment are analyzed.
The inner ring dynamic misalignment of deep groove ball bearings (DGBBs), as a possible error type in practical engineering, has significant influences on the service performance of the rotor system. A novel dynamic model of the bearing-rotor system with inner ring dynamic misalignment and a model solving method based on the Newton-Raphson and Newmark-β nested iterations are proposed in this paper. This method perfectly integrates the quasi-static model of the ball bearing with the dynamic model of the rotor system. In addition, the proposed model can better consider the nonlinearity caused by the ball-raceway contact and the three-dimensional (3D) clearance inside the bearing. By comparing with the experiment, the accuracy of the proposed model is verified. On this basis, the effects of misalignment angle, radial clearance, and rotational speed on the dynamic characteristics of the system are analyzed. The results show that the inner ring dynamic misalignment introduces additional bearing force excitation and increases the vibration of the system. In addition, the inner ring dynamic misalignment cancels out the radial clearance, enhances the axial restraint of the system, and changes the axial vibration characteristics from soften-type to hardening-type nonlinearity.
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•A new spalling propagation assessment algorithm dependent on statistical features is presented.•Effective statistical features are determined and applied to estimate the damage level.•The spalling ...propagation assessment algorithm is verified by the test data.
Spalling is a main fatigue failure type of ball bearings. Vibration features of the bearing will be changed during the spalling propagation, which can be utilized to identify the spalling damage level. In this study, a new spalling propagation assessment algorithm dependent on the spectrum amplitude ratio and statistical features is established to identify the spalling damage location and level. The damage level is determined by the test fault samples in the listed test works. The spectrum amplitude ratio based on the bearing fault frequencies and spectrum amplitudes is applied to identify the damage location. 25 statistical features of the time-domain vibration signal are calculated. Pearson correlation coefficient (PCC) is used to determine the effective ones in the 25 statistical features presented by the previous works. The effective statistical features are applied to estimate the damage level. The test data given by the previous work in the list reference is utilized to verify the developed spalling propagation assessment algorithm. The results indicate that the established method can give a new approach to identify the spalling damage location and level of a ball bearing.
A comprehensive dynamic model of ball bearing focusing on structure flexible deformations is developed in this paper. The cage is split into several discrete segments linked by nonlinear springs to ...indicate the cage flexibility. The effect of cage flexibility on cage clearance is further considered. The race flexibility generated by assembly status variation of the shaft-bearing-housing system are then deduced, and the interplay mechanism between the race and other bearing components is analyzed. Finally, the effect of structure flexible deformations on bearing dynamic properties is investigated. The results indicate that rational design for structure flexibility can optimize bearing rotary performance.
•A dynamic model of ball bearing considering flexible deformations is proposed.•The effect of cage flexibility on pocket and guiding clearance is investigated.•Raceway flexible deformations due to the change of assembly state are analyzed.•The mechanism of flexible deformations on bearing dynamic performance is discussed.
