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The rotor system supported by the cylindrical roller bearings is widely used in various fields such as aviation, space and machinery due to its importance. In the study of the dynamic characteristics of the cylindrical roller bearings, it is important to accurately calculate the stiffness of the cylindrical roller bearings. The stiffness of the cylindrical roller bearings is very important in the analysis of the vibration characteristics of the rotor system. Therefore, in this paper, the method of creating a comprehensive stiffness model of the cylindrical roller bearing is mentioned. The purpose of this study is to improve the dynamic stability of the rotor system supported by the cylindrical roller bearing by accurately establishing the comprehensive stiffness calculation model of the cylindrical roller bearings.

In consideration of the radial clearance of the cylindrical roller bearing, the radial load acting on the cylindrical roller bearing was derived, and based on this, a model for calculating the Hertz contact stiffness of the cylindrical roller bearing was created. Based on the load considering the radial clearance, an oil film stiffness model of the cylindrical roller bearing was created under the elastohydrodynamic lubrication (EHL) theory. Then, the comprehensive stiffness was calculated by combining Hertz contact stiffness and the oil film stiffness of the cylindrical roller bearing, and the dynamic parameters are calculated by using the MATLAB program.

When the radial clearance of the cylindrical roller bearing is considered, the comprehensive stiffness is larger than when the radial clearance is not taken into account, and the radial clearance of the cylindrical roller bearing is an important factor that directly affects the comprehensive stiffness of the cylindrical roller bearing.

In this paper, based on Hertz contact theory and the EHL theory, the authors investigated the method of creating a comprehensive stiffness model of the cylindrical roller bearing considering the radial clearance. These results will contribute to the theoretical basis for studying the mechanics of cylindrical roller bearings and optimizing their structures, and they will provide an important theoretical basis for analyzing the dynamic characteristics of the rotor system supported by the cylindrical roller bearing.

This paper aims to understand the vibration characteristics of full ceramic ball bearings under grease lubrication, reduce the vibration of the bearings and improve their service life.

The Hertz contact stiffness formula for full ceramic ball bearings is constructed; the equivalent comprehensive stiffness calculation model and vibration model of full ceramic ball bearings are established. The dynamic characteristic test of full ceramic ball bearing under grease lubrication was carried out by using the bearing life testing machine, and its vibration was measured, and its vibration acceleration root-mean-square was obtained by software calculation and compared with the simulation results.

At the rotational speed of 12,000 r/min, the root-mean-square value of vibration acceleration is maximum 10.82 m/s², and the error is also maximum 7.49%. As the rotational speed increases, the oil film stiffness decreases. In the radial load of 600 N, the vibration acceleration root-mean-square is minimum 6.40 m/s², but its error is maximum 6.56%. As the radial load increases, the vibration of the bearing decreases and then increases, so under certain conditions increasing the radial load can reduce the bearing vibration. With different types of grease, the best preload is also different; low-speed heavy load should be used when the viscosity of the grease is large, and high-speed light load should be used when the choice of smaller viscosity grease is made.

It provides a theoretical basis for the application of full ceramic ball bearings under grease lubrication, which is of great significance for reducing the vibration of bearings as well as enhancing the service life of bearings.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2024-0094/

This paper aims to predict the dynamic behaviors of contact between the steel ball and raceway in the elastohydrodynamically lubricated ball linear guide, thus providing a guidance for lubrication design for ball linear guide.

Based on the point contact elastohydrodynamic lubrication (EHL) theory, the free vibration model of contact pair is presented to qualitatively analyze the effect of vibration on the film characteristics. The models of the film stiffness and damping coefficient under the EHL condition are built to investigate the effects of the working conditions on the dynamic parameters. The full numerical solutions are obtained using the multigrid technique.

It is found that there exists damping from the decay of oscillations of the pressure and film thickness in the lubricated ball linear guide. Furthermore, the working conditions of the high load or low velocity can lead to the increase in the film stiffness in the steel ball-raceway contact, but there is a reverse variation trend for the film damping coefficient.

The contact pair has been usually treated as dry in past studies on dynamics of the ball linear guide, and the damping is neglected. This research considers the actual lubrication and working conditions and predicts the dynamic behaviors of contact pair.

The purpose of this paper is to research on optimization of spindle bearing preload based on efficiency coefficient method and provide theoretical guidance for variable preload of intelligent spindle.

Based on an established thermo-mechanical coupling model of angular contact ball bearing with fix-position preload, temperature rise and axial stiffness of the bearing at different speeds and preload are analyzed, and life of the bearing is estimated by the improved L-P theory. The bearing temperature rise, axial stiffness and life data are standardized, and the preload is optimized by the efficiency coefficient method according to the requirements of operating conditions.

The optimized preload meets comprehensive requirements of the bearing temperature rise, axial stiffness and life under different operating conditions.

In the past studies, it is rarely reported that temperature rise, stiffness and life of the bearing under thermo-mechanical coupling effect are used as objective functions to optimize preload at different speeds.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2020-0205/

The purpose of this study is to investigate the strain rate effect on the problem of low-velocity impact (LVI) on a beam, including silicon nitride and stainless steel materials.

Based on the nonlinear Hertz impact mechanism, the energies related to the impactor and the beam are written, and motion equations are derived using the Lagrangian mechanics and Ritz method. The strain rate term is represented as a damping matrix in the equations of motion. In the issue of LVI on the silicon nitride and stainless steel beam, the effect of internal viscous damping coefficient in simply–simply and clamped–free boundary conditions are studied. Also, the influence of the volume fraction index in the range between zero and one and greater than one on the impact response is investigated.

The results make it clear that the strain rate parameter had little effect on the response in LVI. Also, an increase in the volume fraction index has led to a decrease in the contact force and an increase in the rebound velocity of the impactor.

The effect of strain rate on LVI is theoretically studied in this paper, while in most of the papers, this effect is investigated experimentally and numerically.

As a core rotating component of power machinery and working machinery, the rotor system is widely used in the fields of machinery, electric power and aviation. When the system operates at high speed, the system stability is of great importance. To enhance the system stability, squeeze film damper (SFD) is being installed in the rotor system to alleviate vibration. The purpose of this paper is to first classify the rotor system into two types, the dual rotor system and the single rotor system, and to comprehensively and specifically mention the method of generating the dynamic model. Next, based on the establishment of a dynamic model with and without SFD in the rotor system, the optimization design of the rotor system with SFD was carried out using a genetic algorithm. Through sensitivity analysis, SFD clearance, shaft stiffness and oil viscosity were determined as design variables of the rotor system, and the objective function was the minimization of the maximum amplitude of the rotor system with SFD within the operation speed range.

In this paper, first, the rotor system was classified into two types, namely, the dual rotor system and the single rotor system, and the method of creating a dynamic model was comprehensively and specifically mentioned. Here, the dynamic model of the rotor system was derived in detail for the single rotor system and the dual rotor system with and without SFD. Next, based on the establishment of a dynamic model with and without SFD in the rotor system, the optimization design of the rotor system with SFD was carried out using a genetic algorithm. The sensitivity analysis of the unbalanced response was carried out to determine the design variables of the optimization design. Through sensitivity analysis, SFD clearance, shaft stiffness and oil viscosity were determined as design variables of the rotor system, and the objective function was the minimization of the maximum amplitude of the rotor system with SFD within the operation speed range.

SFD clearance, shaft stiffness and oil viscosity were determined as design variables of the rotor system through sensitivity analysis of the unbalanced response. These three variables are basic factors affecting the amplitude of the rotor system with SFD.

In the existing studies, only a dynamic model of a single rotor system with SFD was created, and the characteristic values of pure SFD were selected as optimization variables and optimization design was carried out. But in this study, the rotor system was classified into two types, namely, the dual rotor system and the single rotor system, and the method of creating a dynamic model was comprehensively and specifically mentioned. In addition, optimization design variables were selected and optimized design was performed through sensitivity analysis on the unbalanced response of factors affecting the vibration characteristics of the rotor system.

The purpose of this study is to investigate the dynamic behavior of the ball bearing with cage broken.

By analyzing the complicated relationship and interactions among the ball bearing elements, the dynamic modelling of the ball bearing with broken cage was established, and the dynamic simulations were conducted by solving the ball bearing dynamic equations using varying-step Runge–Kutta integration.

The computational results show that there is considerable distinguishment in the dynamic characteristics between the normal cage and the broken cage of the bears. The broken cage makes the trajectory of the cage erratic, and the vibration amplitude is much bigger than that of the normal cage, which makes the motion of the cage unstable. When one of the cage lintels breaks up, the two adjacent balls will collide with each other; what is worse, this may make the balls crush because of the high amplitude of the collision force. The broken cage makes the cage-race interaction force much larger than that of the normal cage, which could promote the guiding ring and quicken the cage wear-failure.

This study can provide important ideas for the fault identification of the ball bearing with cage broken.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-01-2020-0042/

Under fix-position preload, the high rotation speed of the angular contact ball bearing exacerbates the frictional heat generation, which causes the increase of the bearing temperature and the thermal expansion. The high rotation speed also leads to the centrifugal expansion of the bearing. Under the thermal and centrifugal effect, the structural parameters of the bearing change, affecting the mechanical properties of the bearing. The mechanical properties of the bearing determine its heat generation mechanism and thermal boundary conditions. The purpose of this paper is to study the effect of centrifugal and thermal effects on the thermo-mechanical characteristics of an angular contact ball bearing with fix-position preload.

Because of operating conditions, elastic deformation occurs between the ball and the raceway. Assuming that the surfaces of the ball and channel are absolutely smooth and the material is isotropic, quasi-static theory and thermal network method are used to establish the thermo-mechanical coupling model of the bearing, which is solved by Newton–Raphson iterative method.

The higher the rotation speed, the greater the influence of centrifugal and thermal effects on the bearing dynamic parameters, temperature rise and actual axial force. The calculation results show that the effects of thermal field on bearing dynamic parameters are more significant than the centrifugal effect. The temperature rise and actual axial force of the bearing are measured. Comparing the calculation and the experimental results, it is found that the temperature rise and the actual axial force of the bearing are closer to reality considering thermal and centrifugal effects.

In the past studies, the thermo-mechanical coupling characteristics research and experimental verification of angular contact ball bearing with fix-position preload are not concerned. Research findings of this paper provide theoretical guidance for spindle design.

The purpose of this paper is to investigate the effect of the cage-pocket wear on the dynamic behavior of the ball bearing.

Through analyzing the complicated relationship and interactions among the ball bearing elements, the dynamic modeling of the ball bearing was established considering the gravity, drag force from the oil, hydrodynamic effect on the cage and the dynamic simulations with different amounts of the cage-pocket wear loss of the ball bearing (BPWL) were obtained by solving the ball bearing dynamic equations using Runge–Kutta method.

The results show that the trajectory of the cage’s centroid presents two vibration modes with different amplitudes. In addition, those two different forms of trajectory of different amplitudes emerge alternatively with BPWL increase moreover the diameter of the trajectory decrease significantly with the BPWL increasing, which is consistent with the experimental result and last BPWL has lightly effect on the average skidding ratio of the cage, however, the BPWL would produce significant effects on the fluctuation of the skidding ratio, which can directly reflect the stability of motion to a certain extent.

Practice shows that the bearing failure resulting from the cage accounts for 25 per cent of the total failure of the rolling bearings. However, few discussions about how the wear of the cage-pocket would influence the dynamic characteristics of the cage. This study can provide important ideas for the design of bearing cage-pocket size and the fault identification of the ball bearing to decrease the failure rate caused by the cage.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-12-2019-0535/

The purpose of this paper is to investigate the non-linear characteristics and stability of the rolling bearing–axle coupling system under the excitation of the axle/wheel speed of railway freight cars, so as to put forward a rationale for judging the vibration law and running stability of railway freight wagon.

Considering the effects of eccentric force of the railway wagon axle, the non-linear resistance of the wagon and non-linear support forces of axle box rolling bearings, a centralized mass model of rolling bearing-axle coupling system of railway freight wagon is presented on the basis of the theory of rotor dynamics and non-linear dynamics. Then the Runge-Kutta method is adopted to solve the non-linear response of the proposed system, and numerical simulation including bifurcation diagrams, axis trajectory curves, phase plane plots, Poincaré sections and amplitude spectras are analysed when the axle rotating speed is changed. Meantime, the relation curve between Floquet multiplier and axle rotating speed, which affects the stability of coupling system, is plotted by numerical method based on the Floquet theory and method.

The simulation results of the dynamic model reveal the abundant dynamic behaviour of the coupling system when the axle rotating speed changes, including single period, quasi period, multi-period and chaotic motion, as well as the evolution law from multi-period motion to chaotic motion. And especially, the bearing–axle coupling system is in stable state with a single period motion when the axle rotating speed changes from 410 rpm to 510 rpm, in which the running speed of railway freight wagon is changed from 62 km/h to 80 km/h, the vibration displacement of the coupling system in X direction is between 1.2 mm and 1.8 mm, and the vibration displacement of the coupling system in Y direction is between 1.0 mm and 1.45 mm. Meanwhile, the influence law of axle rotating speed on the stability is obtained by comparing the bifurcation diagram and Floquet multiplier graph of the coupling system.

The numerical simulation data obtained in this study can provide a theoretical evidence for designing the running speed of railway freight wagon, utilizing or controlling the non-linear dynamic behaviours of the proposed coupling system, and ensuring the stability of railway freight wagons.