Oil Film Stiffness Research Articles

An Improved Dynamic Modelling for Exploring Ball Bearing Vibrations from Time-varying Oil Film

Bearings are key components in rotating machinery, which is widely used in many fields, such as CNC machines, wind turbines and induction machines. The increasingly harsh operation environment can lead to wear and tear on raceways and reduce the precision and reliability of bearing or even machinery. Lubrication could relieve the wear to some degree, which is benefit to prolong the bearing’s life. Thus, investigation on the vibration responses under the influence of oil film is of great significance. However, for mechanism analysis, how to include the oil film into the bearing dynamic model affects the result and efficiency of solution. To address this problem, this study proposed a fast algorithm through load distribution and interpolation when calculating oil film stiffness and thickness during the solution of bearing vibration model. Analysis of oil film on vibration is carried out and a bearing test rig is designed to verify the proposed model. Numerical simulation result shows that rotational speed and load have vital effect on oil film and vibration, and oil film can play a role of shock absorption. The experimental result is consistent with the simulation, which shows that the proposed model has a better performance on modeling bearing vibration and the method of considering oil film is reasonable.

Dynamic behavior analysis of spiral bevel gears of helicopter’s intermediate reducer with vibration error and lubrication

In the dynamic simulation of spiral bevel gears (SBGs), the modeling and contact analysis of the SBGs are extremely complicated; therefore, dynamic analysis of the SBGs generally simplifies the SBG model. The vibration in the meshing process will cause the meshing trajectory to deviate, resulting in changes in the meshing stiffness, oil film thickness, and load distribution between teeth. These changes cannot be realized using simplified models. To accurately calculate the dynamic behavior of the SBG pair of the intermediate reducer of a helicopter under the influence of vibration displacement, a load-tooth contact analysis(LTCA) of the SBG with error was performed based on the finite element method(FEM) and gear meshing principle. A calculation method for the meshing stiffness, considering the errors and elastohydrodynamic lubrication (EHL) factors, is proposed. To establish the coupling nonlinear dynamic model of the tail drive thin-walled shaft Timoshenko beam element and SBG lumped mass methods, applied the Newmark conjugate gradient method. Changes in parameters such as vibration displacement, meshing trajectory, tooth side clearance, oil film thickness, and meshing stiffness were obtained. The results show that the contact stiffness after considering the oil film stiffness is reduced by 17.7% compared to that without considering the effect of the oil film, and the oil film stiffness fluctuates more because the coupled model takes into account the vibration effect of the time-varying system, and the amplitude increases by 18.5% compared to the commercial software. The coupled kinetic model calculates the dynamic meshing force, normal relative displacement, single tooth meshing period and oil film thickness, and finds that the amplitude of the relevant parameters increases. The obtained time-varying lubrication parameters provide a theoretical basis for studying the evolution of the transmission system under the loss of lubrication.

Dynamic analysis of the single rotor-bearing system considering the comprehensive stiffness and damping

Abstract 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 study of the analysis of the vibration characteristics of the rotor system, it is important to accurately calculate the stiffness and damping of the cylindrical roller bearings. Therefore, in this paper, the dynamic characteristics of the simple rotor-bearing system were analyzed based on the new dynamic model of the rotor system considering the comprehensive stiffness and damping model of the cylindrical roller bearing. In consideration of the radial clearance of the cylindrical roller bearing, the radial load acting on the cylindrical roller bearing is derived and based on this, the Hertz contact stiffness model of the cylindrical roller bearing is obtained. After obtaining the oil film stiffness model of the cylindrical roller bearing according to the EHL theory, the comprehensive stiffness of the cylindrical roller bearing was calculated by combining the Hertz contact stiffness and the oil film stiffness of the cylindrical roller bearing. After a comprehensive damping model of the cylindrical roller bearing considering the radial clearance was created, a dynamic model of the simple rotor-bearing system was created based on the comprehensive stiffness and damping model of the cylindrical roller bearing. The dynamic characteristics of the simple rotor-bearing system were analyzed using the MATLAB program. The amplitude of the simple rotor-bearing system considering the comprehensive stiffness and damping was reduced by 18.2% compared to the case where it was not considered. This shows that the structure of the cylindrical roller bearing has a restraining effect on the unbalanced response of the rotor system.

Dynamic stiffness and vibration analysis model of angular contact ball bearing considering vibration and friction state variation

Force and thermal effect are dominant in giving rise to variation of bearing dynamic stiffness and vibration. On the basis of test and theoretical analysis, the dynamic stiffness and vibration model of angle contact ball bearing considering vibration and friction state variation is established. Firstly, based on the quasi-statics of bearing and hydrodynamic lubrication theory, the motion and force relation between each parts are determined by considering the force and thermal effect. Secondly, the friction power consumption of bearing is calculated adopting integrated method, besides, the conduction heat resistance and convection heat resistance in the bearing system are achieved. A steady-state temperature calculation model of angle contact ball bearing-shaft-house system is built based on thermal network method. Finally, the dynamic stiffness and vibration model of angular contact ball bearing including the thermal-solid coupling effect is obtained, which is employed to realize the theoretical analysis of bearing dynamic stiffness and vibration, its accuracy is verified through typical test results. The calculation results shows that there is a good agreement between house test temperature and calculation temperature. The evolution rule of contact deformation and contact stiffness between ball and outer/inner ring over the whole life under excessive preload is the same. So does the oil film thickness and oil film stiffness. However, the curve shape and amplitude of contact angular between ball and outer/inner ring over the whole life is different. Bearing radial stiffness value has a more significant change than axial stiffness value, both of them represent an overall upward tendency. The radial clearance holds a negative correlation with house temperature, however, the radial displacement has a positive correlation with house temperature. The evolvement curve of contact angular affected by various preload and speed is opposite. The contact load between ball and outer/inner ring has the same trend influenced by preload and speed with EHL. The variation of preload has bigger effect on temperature rise than speed change. The oil film has little influence on contact angular, contact load and temperature under dry-lubricated or lightly lubricated condition.

An Improved Dynamic Transmission Error Model Applied on Coupling Analysis of Gear Dynamics and Elastohydrodynamic Lubrication

Abstract In order to study the coupling effect of cylindrical gear dynamics and elastohydrodynamic lubrication (EHL), based on dynamic theory, a dynamic model of a six degrees-of-freedom (6DOF) coupled system is established. Based on the numerical solution of EHL, an improved dynamic transmission error (DTE) model was established. The oil film stiffness, oil film damping, and center oil film thickness obtained by the numerical solution were used in the gear dynamics analysis. The dynamics and EHL characteristics of the gear system are analyzed and compared with the general model. The results show that by using the improved DTE model, the comprehensive stiffness and comprehensive damping of the gear increase and fluctuate slightly. The amplitude of the tooth surface meshing force and dynamic response decreases. Under the action of tooth surface meshing force, the oil film pressure and thickness show oscillation characteristics.

Contact Damping and Stiffness Calculation Model for Rough Surface Considering Lubrication in Involute Spur Gear

The contact properties of an interface are crucial to the performance of equipment, and it is necessary to study the contact damping and contact stiffness, especially in the case of mixed lubrication. A calculation model for contact damping and contact stiffness considering lubrication was proposed on the basis of the KE contact model and mixed elastohydrodynamic lubrication theory. Both the damping and the stiffness were composed of the oil film portion and the asperity contact portion. Since the damping and the stiffness of oil film mainly depended on the film thickness and the pressure, which can be obtained with the mixed lubrication model, another crucial point was to figure out the contribution of asperity contact. Ignoring the effect of the tangential deformation, the stiffness and the load determined with the normal deformation of the asperity were obtained. Then, the contact damping and the contact stiffness considering lubrication could be derived. Finally, the model was applied to the study of contact damping and stiffness of the involute spur gear.

Critical Speed Analysis of Sliding Bearing Rotor System Based On ANSYS

Sliding bearing rotor system plays an important role in rotating machinery, and its critical speed is a key index. In this paper, a sliding bearing rotor system is established, and the critical speed range is obtained by ANSYS Workbench software under different oil film stiffness, which provides guidance and basis for maintaining the stability of sliding bearing rotor system and avoiding resonance.

Oil Film Stiffness of Double Involute Gears Based on Thermal EHL Theory

Lubrication failure is one of the main failure forms of gear failure. Time varying meshing stiffness is an important factor affecting the dynamic behavior of gears. However, the influence of oil film stiffness is usually ignored in the research process. In this paper, according to the meshing characteristics of double involute gears, based on the non-Newtonian thermal EHL theory, a new calculation method of normal and tangential oil film stiffness for double involute gears is established by the idea of subsection method. The oil film stiffness difference between double involute gears and common involute gears is analyzed, and the influence of tooth waist order parameters, working conditions, and thermal effect on the oil film stiffness are studied. The results reveal that there are some differences between normal and tangential oil film stiffness between double involute gears and common involute gears, but there is little difference. Compared with the torque, rotation speed and initial viscosity of the lubricating oil, the tooth waist order parameters have less influence on the oil film stiffness. Thermal effect has a certain influence on normal and tangential oil film stiffness, which indicates that the influence of thermal effect on the oil film can not be ignored. This research proposes a calculation method of normal and tangential oil film stiffness suitable for double involute gears, which provides a theoretical basis for improving the stability of the transmission.

Study on critical speed of three-watt tilting pad bearing-rotor system

By establishing the model of three-watt tilting tile bearing and rotor system and studying the critical speed of three-watt tilting tile bearing and rotor system, the factors affecting its critical speed are obtained. The oil film stiffness coefficient and damping coefficient of sliding bearing and the mass of the counterweight plate added in the mixed bearing supporting rotor system all have a certain influence on the overall critical speed of the system. In this paper, a rotor model was established using DyRobes rotor dynamics analysis software. The critical rotational speed of the three-watt tilting tile bearing/rotor system was investigated by means of the oil film stiffness of the three-watt tilting tile bearing at different rotational speeds and changing the weight of the counterweight plate.

Safety Threshold of the Oil Film Stiffness of a CVT Pulley–Sheet Friction Pair Based on Mixed Lubrication Theory

The instability of oil film stiffness in mixed elastohydrodynamic lubrication (EHL) is a prominent cause of the fretting wear of continuously variable transmission pulley–metal sheet friction pairs. In severe cases, it can induce dynamic system failure. In this study, an oil film normal stiffness model equivalent to a massless spring element is established using linear contact mixed EHL theory. The effects of microscopic parameters (roughness amplitude) and macroscopic operating parameters (torque ratio) on the oil film stiffness in the pulley–sheet contact area are studied. The film stiffness increases initially and then decreases with an increase in roughness amplitude. In addition, it increases continuously and then stabilizes with an increase in torque ratio. The effects of macro- and microparameters are considered and a safety threshold model of oil film stiffness is established. Results show that oil film stiffness exhibits the highest safety stability when the roughness amplitude is 0.10 μm and the torque ratio is 0.8. The influence of roughness amplitude on the safety threshold of oil film stiffness is greater than that of torque ratio.

Inclination angle effect of tribological performance for hydrostatic bearing having tilting oil pad under variable viscosity conditions

In order to improve tribological performance of hydrostatic bearing, an innovative hydrostatic bearing structure having tilting oil pad is designed. During the operation, the semicircular boss at the bottom of the oil pad can realize the circumferential micro-motion. It generates additional dynamic pressure, and forms the static and dynamic pressure mixing support, make up for the static pressure loss, and solves the problems such as low precision and unstable operation of the numerical control equipment under the high speed and heavy load conditions. According to the tribological principle and lubrication theory, bearing capacity, flow rate, oil film thickness equation and oil film stiffness for hydrostatic and dynamic hybrid bearing are derived under variable viscosity conditions. The simulation model of hydrostatic bearing having tilting oil pad is established. ANSYS software is used to analyze the distribution of oil film temperature field and oil film pressure field under different inclination angles. The effects of tilting oil pad inclination angle on oil film tribological performance and oil film stiffness are obtained. The results show that the hydrostatic bearing having tilting oil pad can generate additional dynamic pressure in high speed operation, make up the loss of static pressure. When the inclination angle is 0.0044°, oil film temperature rise is 34.8 ℃, the average pressure is 622.2 KPa, oil film stiffness is 54104 N/µm, the comprehensive lubrication performance is optimal, the oil film stiffness is the largest, and the operation accuracy and stability of hydrostatic bearing are improved.

Investigation of cavitation evolution and hydrodynamic performances of oil film seal with spiral groove

This paper presents cavitation action of the oil film seal with downstream-pumping spiral groove and effect of cavitation on the hydrodynamic performances. A hydrodynamic lubricant model with JFO cavitation boundary is established and the visual experiments of cavitation under different working conditions are conducted, the cavitation evolution acquired and the theoretical and experimental leakage compared. Results show that higher speed effectively promotes cavitation but higher oil pressure inhibits it. Both increasing groove number and decreasing groove angle with limits reduce the cavitation zone but effects of them on the cavitation boundaries are different. By comparison, the cavitation occurrence plays an active role in the reduction of film thickness, improvement of oil film stiffness and the reduction of leakage.

Research on Vibration Excitation Estimation of Warship Propulsion Shafting Based on Waveguide Theory

The propeller excitation can be estimated by measuring the vibration response of the shafting, but there are many difficulties, such as difficult to implement, difficult to determine the boundary conditions and so on. For this reason, the waveguide model of different shaft segments on the shafting and the waveguide transfer relationship between the connected shaft segments are established based on the waveguide theory, and the waveguide coefficient is estimated combined with the vibration response observation data. The estimation of longitudinal oil film stiffness of thrust bearing and admittance of thrust bearing housing and hull connection structure is avoided, and the method of propeller longitudinal excitation based on waveguide transfer relation is verified by a specific example. The results show that the method is feasible and effective, and provides a new method for accurately grasping the actual propeller excitation.

Study on Vibration and Bifurcation of an Aeroengine Rotor System with Elastic Ring Squeeze Film Damper

To analyze the problem of vibration and bifurcation in the rotor system of the aeroengine with the elastic ring squeeze film damper (ERSFD) and elastic supports, the theoretical equation of the dynamic rotor system is developed in this paper, based on the rotor system, elastic ring squeeze film damper (ERSFD), and three elastic supports. The estimated analytical solution of the oil film force is solved using the short bearing approximation theory and the semi‐oil film inference theory in the suspension and the inner and outer boss contact. Considering the oil film stiffness and damping of rolling bearings, the rolling bearing force model is established based on the elastohydrodynamic lubrication (EHL) theory. By the average method, the vibration and bifurcation modes are obtained concerning the bearing coefficient and parameters. The range optimization of parameters can be appropriately improved to enhance the dynamic characteristics of the device given different parameters of the hole of oil seepage, the stiffness, the position of elastic supports, and other structural parameters.

Analysis of lubrication performance for internal meshing gear pair considering vibration

The thermal elasto-hydrodynamic lubrication characteristics of the internal meshing gears in a planetary gear train under vibrations were examined considering the influence of the modification coefficient and time-varying meshing stiffness. Based on dynamic theory of the gear system, a dynamic model of the planetary gear train was established. The lubrication performances of modified gear systems under vibrations and static loads were analyzed. Compared with other transmission types, the best lubrication effect could be produced by the positive transmission. A thicker lubricating oil film could be formed, and the friction coefficient and oil film flash temperature are the smallest. Increasing modification coefficient improves the lubrication performance continuously but intensifies the engage-in and tooth-change impact. For the planetary and inner gears, the increase in the modification coefficient also leads a decrease in the oil film stiffness.

Oil film characteristics and flow field analysis of asymmetrical hydrostatic support structure with full hydraulic fixed-length shear servo cylinder

The heavy-duty servo cylinder is the main actuator of the full-hydraulic fixed-length shear. The cylinder requires horizontal articulated mounting for accurate curve forces. The output of the curvilinear force causes the piston rod to be subjected to a dynamic bias load, and the presence of the bias load adversely affects the servo cylinder seal structure. In this paper, an asymmetric hydrostatic support structure is designed in the guide sleeve for the bias load problem of the servo cylinder, and the anti-offset capacity of the structure is theoretically studied. The oil film characteristics and oil film stiffness of the structure are deduced and analyzed. Fluent software is used to simulate, and then analyze the influence of inlet pressure, piston rod speed, eccentricity and partial load on the performance of asymmetric static pressure bearing oil film. Asymmetrical hydrostatic support structure servo hydraulic cylinder test bench is built for anti-bias load performance and friction performance experiments. The research results show that the new asymmetric hydrostatic support structure has a good effect on balancing the dynamic partial load, effectively reducing the friction of the servo cylinder and making the automatic alignment of the piston rod and the guide sleeve, which proves that the technology can be effective, increase the service life of the servo hydraulic cylinder and then improve the overall efficiency of the full hydraulic dividing shear, while broaden the application field of the heavy duty servo cylinder.

Research on dynamic characteristics and identification method of local defect on the roll surface

Local defects are generally produced on the surfaces of roll during long-term work, which not only causes abnormal vibration of the roll mill but also affects the quality of the produced steel strips. In particular, identifying the defects on a well-lubricated roll surface is a challenge. Therefore, a time-varying oil film stiffness model is proposed based on the elastohydrodynamic lubrication theory. A Sendzimir twenty-high roll mill model was developed and combined with the time-varying oil film stiffness model to analyse the vibration characteristics of the roll mill. Simultaneously, a new method for real-time identification of the defect sizes during the rolling process was proposed. Agreement between the simulated and experimental results was used to validate the effectiveness of the proposed model. The changes to the oil film stiffness and roll mill vibration characteristics for different defect sizes on the roll surface are thus analyzed to provide theoretical support for the identification of the local defects.

Research on the Lubrication Characteristics of Harmonic Gear Transmission Meshing Areas

To analyse the lubrication characteristics of harmonic gears and lay the foundation for the study of its gear tooth failure performance and dynamic characteristics, based on the tooth contact geometry of harmonic gear, the integrated curvature radius, tooth load, and entrainment velocity at the meshing point of the gear teeth in the harmonic gear transmission are analysed. A finite-length line contact elastohydrodynamic lubrication (EHL) model for harmonic gears is established. The numerical calculation method is used to solve the oil film thickness and pressure distribution in the lubricating area, and the effects of rotational speed and temperature on the contacting load ratio and film thickness ratio of the meshing area are studied, as well as the change of oil film stiffness under different working conditions. The results show that along the meshing direction, the pressure is small at the end and reaches a peak at the centre, and the film thickness is the largest in the entrance area and is evenly distributed in the centre contact area. As the speed increases, the gear tooth contact load ratio decreases, the oil film thickness ratio increases, the stiffness of the oil film decreases significantly, and the lubrication effect is improved; but the temperature has the opposite effect. Proper increase of rotation speed and decrease of oil temperature can effectively improve the lubrication characteristics of the system.

Oil pressure and viscosity influence on stiffness of the hydrostatic spindle bearing of a medium-sized circular grinding machine

In surface finishing of a grinding machine, the dimension accuracy of the workpiece is most affected by the stiffness of the spindle. For the hydrostatic spindle of a medium-sized circular grinding machine, the primary factors affecting the oil film stiffness are bearing structure parameters, lubrication characteristics, and working conditions. In this study, the effects of lubricant pressure and oil viscosity on the stiffness of the hydrostatic spindle based on the working conditions were investigated. The oil viscosity affects the spindle by increasing the stiffness that corresponds to the increase in viscosity in the range of 0.001–0.002 Pa[Formula: see text]S, while the stiffness proportionally increases with pump pressure changing in the range of 3–5 MPa. Experimental results also indicate that based on the stiffness of the bearing, a viscosity of 0.002 Pa[Formula: see text]S, pump pressure of 5 MPa, and load range of 500–1000 N are the most feasible working conditions for hydrostatic spindle associated with the fine-machining process on a medium-sized external grinding machine.

Research on Friction and Impact Load Response of Ship Shafting

Liang, X. and Ji, H., 2020. Research on friction and impact load response of ship shafting. In: Gong, D.; Zhang, M., and Liu, R. (eds.), Advances in Coastal Research: Engineering, Industry, Economy, and Sustainable Development. Journal of Coastal Research, Special Issue No. 106, pp. 514–517. Coconut Creek (Florida), ISSN 0749-0208.With the increase of rotating speed, the vibration speed of impact load increases. The slower, the slower and the faster, the vibration maintenance time is also different. This shows that when the rotation speed of the shaft changes, the oil-film lubrication characteristics of the bearing change, and the oil-film stiffness and oil-film damping of the bearing change, thus showing the support of the sliding bearing. Different from the fixed elastic damping bearing, which is not affected by rotating speed, the oil film dynamically changes its support stiffness and variable damping characteristics. Therefore, when the rotating speed is in the self-excited vibration region of the sliding bearing, the impact time is long, and the amplitude attenuation is slow. When the rotating speed is not in the self-excited vibration region of the bearing, it is in good agreement with the theoretical calculation results.