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The purpose of this paper is to propose an simple and efficient stiffness model for line contact under elastohydrodynamic lubrication (EHL) and to investigate the gear meshing stiffness by the proposed model.

The method combines the surface contact stiffness and film stiffness as EHL contact stiffness. The EHL contact stiffness can be calculated by the external load and displacement of the load action point. The displacement is the sum of deformation of the film and contact surface and is equal to the distance of the mutual approach of two contact bodies.

The conclusion is drawn that the contact stiffness calculated by the proposed model is smaller than that by the minimum film model and larger than that by the mean film model. It is also concluded that the gear meshing stiffness under EHL is slightly smaller than that under dry contact.

The EHL contact stiffness can be obtained by the increment of external load and mutual approach directly. The calculation of oil film stiffness and surface contact stiffness separately is avoided.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2019-0465

This study aims to study the gas film stiffness of the spiral groove dry gas seal.

The present study represents the first attempt to calculate gas film stiffness in consideration of the slipping effect by using the new test technology for dry gas seals. First, a theoretical model of modified generalized Reynolds equation is derived with slipping effect of a micro gap for spiral groove gas seal. Second, the test technology examines micro-scale gas film vibration and stationary ring vibration to determine gas film stiffness by establishing a dynamic test system.

An optimum value of the spiral angle and groove depth for improved gas film stiffness is clearly seen: the spiral angle is 1.34 rad (76.8º) and the groove depth is 1 × 10^–5 m. Moreover, it can be observed that optimal structural parameters can obtain higher gas film stiffness in the experiment. The average error between experiment and theory is less than 20%.

The present study represents the first attempt to calculate gas film stiffness in consideration of the slipping effect by using the new test technology for dry gas seals.

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/

The paper aims to determine whether the type selection and parameters determination of the compensation are most important for yielding the acceptable or optimized characteristics in design of hydrostatic bearings.

This paper utilizes the equations of flow equilibrium to determine the film thickness or displacement of worktable with respect to the recess pressure.

The stiffness due to compensation of constant‐flow pump increases monotonically as recess pressure increases. Also, the paper considers which is larger than that due to orifice compensation and capillary compensation at the same recess pressure ratio.

The findings show that the usage range of recess pressure and compensation parameters can be selected to correspond to the smallest gradient in variations of worktable displacement or film thickness.

In this study, the dynamic characteristics of the water-lubricated rubber bearing considering asperity contact are numerically studied, including water-film stiffness and damping coefficients and plastic-elastic contact stiffness coefficient.

The Kogut-Etsion elastic-plastic contact model is applied to calculate the contact stiffness coefficient at the bearing-bush interface and the perturbed method is used to calculate the stiffness and damping coefficients of water-film. In addition, the rubber deformation is determined by the finite element method (FEM) during the simulation. Parametric studies are conducted to assess the effects of the radial clearance, rubber thickness and elastic modulus on the dynamic characteristic of water-lubricated rubber bearing.

Numerical results indicate that stiffness and damping coefficients of water film and the contact stiffness of asperity are increased with the decreasing of the radial clearance and the dynamic coefficients are less sensitive to the rubber thickness compared with the elastic modulus of rubber. Furthermore, due to the existed groove, a sudden change of the water film direct stiffness and damping coefficients is observed when the eccentricity ratio ranges from 0.6 to 1.0.

It is expected this study can provide more information to establish a dynamic equation of water-lubricated rubber bearings exposed to mixed lubrication conditions.

The purpose of this study is to propose a new method to solve transient elasto-hydrodynamic lubrication (EHL) problem.

First, the steady-state EHL solution is modified so that the elastic deformation theory is combined with oil film stiffness distribution instead of steady-state Reynolds equation. Second, subsequent dynamic EHL procedure develops, recursively using transient distributed oil film stiffness and damping, where each time-marching solution is iteratively searched by ensuring both oil film force growth and elastic deformation update for each load increment.

This method increases calculation speed and provides both distributed EHL stiffness and damping for transient regimes.

This method is of interest for fast applications such as rolling bearings or gears.

The purpose of this paper is to investigate the effect of fluid–structure interaction in micro-scale on the performance of the hydrostatic spindle and improve the analysis precision of the dynamic performance of hydrostatic spindle.

Dynamic analysis of hydrostatic spindle before and after fluid–structure interaction is carried out according to stiffness and damping performance of the bearing, which demonstrates that the natural frequency and peak response of the spindle are increased in the micro-scale.

It is concluded from the simulation and experimental results that there is micro-scale effect in the actual operation of the spindle system and slippage exists in the oil film flow. The error between the modal detection result and the theoretical value is within 10 per cent, which also verifies the correctness of the above conclusions.

This paper analyzes the changes of the bearing performance parameters at macro- and micro-scale, which present the influence of the static and dynamic performance of the spindle in the micro-scale.

This study aims to find the dynamic performance parameters of the journal bearing with micro geometries patterning the arc (crescent) shape textures provided in three specific regions of the journal bearing: the full, the second half and the increasing pressure region. The dynamic behavior of textured journal bearings has been analyzed by computing dynamic parameters and linear and non-linear trajectories.

The lubricant flows between the bearing and journal surface are governed by Reynold’s equation, which has been solved by finite the element method. The dynamic performance parameters such as stiffness, damping, threshold speed, critical mass and whirl frequency ratio are examined under various operating conditions by considering various ranges of eccentricity ratios and texture depths. Linear and non-linear equations of motion have been solved with Ranga–Kutta method to get journal motion trajectories. Also, the impact of adding aluminum oxide and copper oxide nanoparticles to the base lubricant in combination with arc-shaped textures is analyzed to further see any enhancement in the performance parameters.

The findings demonstrated that direct stiffness and damping parameters increased to their maximum level with six textures in the pressure-increasing region when compared with the untextured surface. Also, nanoparticle additives showed improvements above the highest value attained with no inclusion of additives in the same region or quantity of textures.

Engineers may design bearings with improved stability and overall performance if they understand how texture form impacts dynamic properties.

This paper aims to study the influence degree of three factors affecting the vibration amplitude of aerostatic spindle and optimizes each factor.

The vibration amplitude of the spindle is characterized according to internal structure and operating characteristics of aerostatic spindle. The radial and axial vibration models of aerostatic spindle were established by the spring-damper system. The influence degree of main influencing factors on the spindle vibration amplitude was investigated through correlation analysis.

The results indicate that the crucial factor is aerostatic spindle speed and experiments validated that increasing spindle speed can enhance spindle stability. The influence of three factors on radial vibration is greater than that on axial vibration. Finally, the values of optimal working parameters were obtained by genetic algorithm.

The method in this article can effectively predict aerostatic spindle vibration amplitude and perfect the stability of aerostatic spindle.