Application of Computational Fluid Dynamics and Fluid Structure Interaction Techniques for Calculating the 3D Transient Flow of Journal Bearings Coupled with Rotor Systems

Journal bearings are important parts to keep the high dynamic performance of rotor machinery. Some methods have already been proposed to analysis the flow field of journal bearings, and in most of these methods simplified physical model and classic Reynolds equation are always applied. While the application of the general computational fluid dynamics （CFD）-fluid structure interaction （FSI） techniques is more beneficial for analysis of the fluid field in a journal bearing when more detailed solutions are needed. This paper deals with the quasi-coupling calculation of transient fluid dynamics of oil film in journal bearings and rotor dynamics with CFD-FSI techniques. The fluid dynamics of oil film is calculated by applying the so-called ＂dynamic mesh＂ technique. A new mesh movement approacb is presented while the dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. The proposed mesh movement approach is based on the structured mesh. When the joumal moves, the movement distance of every grid in the flow field of bearing can be calculated, and then the update of the volume mesh can be handled automatically by user defined function （UDF）. The journal displacement at each time step is obtained by solving the moving equations of the rotor-bearing system under the known oil film force condition. A case study is carried out to calculate the locus of the journal center and pressure distribution of the journal in order to prove the feasibility of this method. The calculating results indicate that the proposed method can predict the transient flow field of a journal bearing in a rotor-bearing system where more realistic models are involved. The presented calculation method provides a basis for studying the nonlinear dynamic behavior of a general rotor-bearing system.

Bifurcation and Chaos Analysis of Nonlinear Rotor System with Axial-grooved Gas-lubricated Journal Bearing Support

Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson-0-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincar6 map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.

Approximate Solution of Oil Film Load-carrying Capacity of Turbulent Journal Bearing with Couple Stress Flow

The instability of the rotor dynamic system supported by oil journal bearing is encountered frequently, such as the half speed whirl of the rotor, which is caused by oil film lubricant with nonlinearity. Currently, more attention is paid to the physical characteristics of oil film due to an oil-lubricated journal bearing being the important supporting component of the bearing-rotor systems and its nonlinear nature. In order to analyze the lubrication characteristics of journal bearings efficiently and save computational c[~brts, an approximate solution of nonlinear oil film forces of a finite length turbulent journal bearing with couple stress flow is proposed based on Sommerfeld and Ocvirk numbers. Reynolds equation in lubrication of a finite length turbulent .journal bearing is solved based on multi-parametric principle. Load-carrying capacity of nonlinear oil film is obtained, and the results obtained by different methods are compared. The validation of the proposed method is verified, meanwhile, the relationships of load-carrying capacity versus eccentricity ratio and width-to-diameter ratio under turbulent and couple stress working conditions are analyzed. The numerical results show that both couple stress flow and eccentricity ratio have obvious influence on oil film pressure distribution, and the proposed method approximates the load-carrying capacity of turbulent journal bearings efficiently with various width-to-diameter ratios. This research proposes an approximate solution of oil film load-carrying capacity of turbulent journal bearings with different width-to-diameter ratios, whicb are suitable for high eccentricity ratios and heavy loads.

Characteristics of the Main Journal Bearings of an Engine Based on Non-linear Dynamics

Many simple nonlinear main journal bearing models have been studied theoretically, but the connection to existing engineering system has not been equally investigated. The consideration of the characteristics of engine main journal bearings may provide a prediction of the bearing load and lubrication. Due to the strong non-linear features in bearing lubrication procedure, it is difficult to predict those characteristics. A non-linear dynamic model is described for analyzing the characteristics of engine main journal bearings. Components such as crankshaft, main journals and con rods are found by applying the finite element method. Non-linear spring/dampers are introduced to imitate the constraint and supporting functions provided by the main bearing and oil film. The engine gas pressure is imposed as excitation on the model via the engine piston, con rod, etc. The bearing reaction force is calculated over one engine cycle, and meanwhile, the oil film thickness and pressure distribution are obtained based on Reynolds differential equation. It can be found that the maximum bearing reaction force always occurs when the maximum cylinder pressure arises in the cylinder adjacent to that bearing. The simulated minimum oil film thickness, which is 3 μm, demonstrates the reliability of the main journal bearings. This non-linear dynamic analysis may save computing efforts of engine main bearing design and also is of good precision and close connection to actual engine main journal bearing conditions.

Experiment and Simulations on Lubrication Performance of EMP Journal Bearing

In recent years, much attention has been devoted to the design and operation of bearings made of elastic metal plastic (EMP). The surface of the bearing bush is covered by a layer of polymer PTFE(polytetrafluoroethylene). The physical performances of the polymer are quite different from that of metal. It can reduce friction because of its lower surface energy, and it is more difficult for the fluid to be adhered. Consequently, the slip will exist at the oil-bush interface. The journal bearings made of this material are researched in this article. Through test, the existence of slip is proven and the equation of the slip velocity for the EMP journal bearing is established when shear stress up to a certain value. Thus, the classical Reynolds equation is modified. The lubrication mechanism is analyzed by some simulation results.

Effects of Dimensional Tolerances on the Friction Power Loss of Hydrodynamic Journal Bearing System

According to the dimensional tolerances on hydrodynamic journal bearing system, a nonlinear oil film force model was established,and the Reynolds' equation was solved by adopting finite difference method. In order to fulfill different dimensional tolerances in the system,adopting 2kfactor design and using the eccentricity ratio corresponding to the stability critical curve,the effects of the friction power loss brought by the dimensional tolerances of the dynamic viscosity,bearing width,bearing diameter and journal diameter were analyzed. The effect on dynamic characteristics of the hydrodynamic journal bearing system was quantitatively analyzed,and the nonlinear dynamic analysis, modeling and calculation methods were studied while considering the manufacturing tolerances. The results show that in contrast to the impacts of the tolerances in journal diameter,dynamic viscosity and bearing width,the bearing diameter tolerance would lead to the rise in the power loss, and the dimensional tolerances have different degrees of impacts on the journal bearing system. The friction power loss decreased as the eccentricity ratio increased, and when the eccentricity ratio was 0. 695 the power loss came to the minimum.The investigation would find the best solution and reduce energy consumption,then control varieties of nonlinear dynamical behavior effectively,and provide a theoretical basis for hydrodynamic journal bearing system in parameter design.

FLUID FLOW SEPARATION CHARACTER ON NOVEL HYBRID JOURNAL BEARING

The influence of the structure and running parameters of a novel spiral oil wedge hybrid journal bearing on the fluid flow trace is investigated. The governing equation of the flow trace of lubricant is set up, and the simulation is carried out by using finite difference method. The results show that the lubricant flow status and end leakage quantity are greatly influenced by spiral angle,and that the rotating speed has little influence on the flow status. With advisable geometry design, the separation of lubricant between different oil wedges can be obtained, which can decrease the temperature rise effectively.

Unified Coordinate System Model for Performance Calculation of Fix-pad Journal Bearing with Different Pad Preload

Traditional model for calculating performance parameters of a fix-pad journal bearing leads to heavy workload, complicated and changeable formulae as it requires deriving various geometric formulae with different bearing types such as circular journal bearing, dislocated bearing and elliptic bearing. Considering different pad preload ratios for non-standard bearing, traditional model not only becomes more complicated but also reduces scalability and promotion of the calculation programs. For the complexly case of traditional model while dealing with various fix-pad journal bearings, unified coordinate system model for performance calculation of fix-pad journal bearing is presented in the paper. A unified coordinate system with the bearing center at the origin is established, and the eccentricity ratio and attitude angle of axis relative to each pad are calculated through the coordinates of journal center and each pad center. Geometric description of fix-pad journal bearing is unified in this model, which can be used for both various standard bearing and non-standard bearing with different pad preload ratios. Validity of this model is verified with an elliptical bearing. Performance of a non-standard four-leaf bearing with different pad preload ratios is calculated based on this model. The calculation result shows that increasing preload ratio of the pad 1 and keeping that of the left three pads constant improves bearing capacity, stiffness and damping coefficients. This research presents a unified coordinate system model unifies performance calculation of fix-pad journal bearings and studied a non-standard four-leaf bearing with different pad preload ratios, the research conclusions provides new methods for performance calculation of fix-pad journal bearings.

STUDY ON THE INFLUENCES OF BUBBLY OIL ON THE CAVITATION EROSION IN JOURNAL BEARINGS OF ENGINES

A simulating experimental device for journal bearings of engines is established by use of the mechanism of ultrasonic vibration This device can make the pressure inside the oil film changed at ultrasonic frequency,which enable the specimen surface to be damaged by cavitation erosion in a comparatively short time Connecting with the bubbly oil producing device,this rig can investigate the influence of bubbly oil on the cavitation erosion Through detailed experimental research it is found that the bubbly oil decreases the cavitation erosion in journal bearings of engines This result is analyzed reasonably from mechanism of cavitation erosion.

Thermoelastohydrodynamic Behavior of a Journal Bearing with Turbulent Flow

Turbulence is an irregular fluid motion in which the various flow properties such as velocity and pressure show random variations with time and position.A number of authors proposed different solutions e.g.for pressure distribution,temperature prediction and Thermo-Hydrodynamic(THD)analyses.In a fluid film bearing,the pressure in the oil film satisfies the Reynolds equation with a variation in the thickness of the lubricating film.In the presented cases of fluid-structure interaction analyses,all important phenomena accompanying bearing operation are considered,e.g.lubricant flow,structure movements and their deformations as well as heat transfer in case of thrust bearing.In this paper,the authors have developed an empirical relationship to determine the effect of lubrication when considering thermoelastohydrodynamic(TEHD)lubrication with turbulent flow.The critical point of this work is to import the matrix data(the pressure and temperature fields...)from the fluid domain to the internal surface of the bearing with a precision of the mesh especially in the contact surface.The results are presented in the median plane as a function of the bearing angle.A parametric study deals with the influence of rotation speed and the type of turbulence model on the pressure,temperature,deformation and stress intensity fields.

Increasing operational stability of journal bearing in hydraulic suspension micro-pump by herringbone grooved structure

The operational stability of radial journal bearings is the bottleneck that limits the reliability of hydraulic suspension micropump. Due to self-excited vibrations, the whirl amplitude of the plain journal bearing(PJB) is large at high rotational speeds,which will accelerate wear failure. It has been proven that employing herringbone grooved journal bearing(HGJB) is an effective method to reduce the whirl amplitude and improve operational stability. However, enhancing the stability of journal bearings in micro-pumps by herringbone grooved structures has rarely been studied, and its effect needs to be verified. We validated the mechanism of the stability improvement with the CFD method and compared the dynamic characteristics of HGJB and PJB by rotor dynamics evaluation and experiment. The experimental results show that under the same conditions the whirl amplitude of the HGJB decreases by 29.61% in the x direction and by 24.09% in the y direction compared with that of the PJB. This study reveals the effect of the herringbone grooved structure on the operational stability of bearings and may provide guidance for the reliability improvement of hydraulic suspension micro-pump.

Numerical Analysis on the Static Performance of Gas Journal Bearing by Using Finite Element Method

In this paper,finite element method is used to calculate the static performance of gas journal bearing,in which rotation speed term is introduced into the stiffness matrix of linear triangular element to realize the performance calculation of the bearing with rotation speed.The results indicate that the average gas film thicknesses corresponding to the maximum load capac-ity and stiffness,and the minimum attitude angle increase with the growth of orifice diameter.Load capacity and stiffness significantly improved with the increase of rotation speed,eccentricity ratio and supply pressure when the bearing has thin average gas film thickness.Attitude angle increases with the growth of rotation speed,while the growth rate slows down or even decreases at high speed.The most effective way of reducing attitude angle is to increase supply pressure.It can be found that rotation speed affects attitude angle through changing gas pressure difference between two orifices,while other parameters have the same effect by changing gas pressure at orifice outlet.

Numerical and experimental investigation on dynamic performance of bump foil journal bearing based on journal orbit

Widespread usage of bump-type foil journal bearing(BFJB) in oil-free microturbomachinery requires accurate predictions of dynamic performance characteristics, although it remains a challenging issue because BFJB reflects nonlinear both structurally and aerodynamically.This paper presented a simple experimental method to semi-directly obtain the minimum film thickness and dynamic stiffness of BFJB using the journal orbit. Numerical calculations and simulations are conducted to validate the experimental method. The micro-deformation and interaction of various foils are taken into consideration to improve the model precision. The results from the numerical model regarding the BFJB dynamic characteristics are compared with the experimental results coming from a dedicated test rig, which shows that the experimental results fluctuate obviously and agree not well with the numerical results at the start stage due to the presence of dry friction at that time, nevertheless, they show fantastic agreement as soon as a gas film is gradually generated to separate the shaft from the top foil. Therefore, the proposed experimental method is effective to predict film thickness and dynamic characteristics during the period from the lift-off time to the land-off time. The dynamic characteristics, along with the journal orbits also can be used to rapidly predict the dynamics behavior of rotor-bearing systems.

Rapid solution for analysis of nonlinear fluid film force and dynamic behavior of a tilting-pad journal bearing-rotor system with turbulent and thermal effects

To analyze the nonlinear dynamics of a tilting-pad journal bearing(TPJB)-rotor system with high accuracy and speed,the database method(DM)is modified to rapidly determine the nonlinear fluid film force(NFFF)of a TPJB while considering turbulent and thermal effects.A high-accuracy,large-capacity NFFF database for a single pad is constructed by numerically solving the turbulent adiabatic hydrodynamic model for five equivalent state variables of the journal,which are discretized in the pad coordinates.The remaining variables are not discretized in the DM.A combined linear and parabolic interpolation polynomial based on the database is established to accurately calculate the NFFF of the tilting pads;thus,the NFFF of a four-pad TPJB is obtained in the bearing coordinates.The DM is applied to analyze and compare the nonlinear dynamic behavior of a water-lubricated TPJB-Jeffcott rotor system with and without turbulent and thermal effects.The present DM solution without these effects and the previous DM solution are shown to be consistent.The results demonstrate the importance of the flow regime and the negligibility of temperature increases in the nonlinear dynamics of a water-lubricated TPJB.This work contributes to the accurate and efficient analysis of the nonlinear dynamics of high-speed TPJBs and low-viscosity-fluid-lubricated TPJBs.

Stability analysis of long hydrodynamic journal bearings based on the journal center trajectory

In this study,we observe that there are two threshold speeds(stability threshold speed and second threshold speed)for the long journal bearing,which is different for the short bearing.When the rotating speed is below the stability threshold speed,the stability boundary nearly coincides with the clearance circle,and the journal center gradually returns to the equilibrium point after being released at an initial point.If the rotating speed is between the stability threshold speed and the second threshold speed,after being released at an initial point,the journal center converges to a contour containing the equilibrium point.In this situation,for a higher rotating speed,the corresponding contour is also larger.When the rotating speed exceeds the second threshold speed,the journal gradually moves towards the bearing surface after being released at an initial point.

Nonlinear dynamic analysis of low viscosity fluid-lubricated tilting-pad journal bearing for different design parameters

To reveal nonlinear dynamic rules of low viscosity fluid-lubricated tilting-pad journal bearings(TPJBs),the effects of design parameters on journal center orbits and dynamic minimum film thicknesses of water-lubricated TPJBs with and without static loads are investigated.The hydrodynamic bearing force used in the nonlinear dynamic analysis is an approximate analytical solution including the turbulence effect.The results reveal the methods for vibration suppression and load capacity improvement and give an optimal pivot offset and clearance ratio that can maximize the minimum film thickness.The results also show that four-pad TPJBs with loads between pads are preferred due to good dynamic performance and load capacity.This study would provide some guidance for nonlinear design of low viscosity fluid-lubricated TPJBs under dynamic loads.

Transformation between polar and rectangular coordinates of stiffness and dampness parameters in hydrodynamic journal bearings

The stiffness and dampness parameters of journal bearings are required in rectangular coordinates for analyzing the stability boundary and threshold speed of oil film bearings.On solving the Reynolds equation,the oil film force is always obtained in polar coordinates;thus,the stiffness and dampness parameters can be easily obtained in polar coordinates.Therefore,the transformation between the polar and rectangular coordinates of journal bearing stiffness and dampness parameters is discussed in this study.

OPERATOR-SPLITTING METHOD FOR ANALYSIS OF CAVITATION IN LIQUID-LUBRICATED HERRINGBONE GROOVED JOURNAL BEARING

This paper presents an Operator -Splitting Method (OSM) for the solution of the universal Reynolds equation. Jakoobsson-Floberg-Olsson (JFO) pressure conditions were incorporated for the study of cavitation in a liquid-lubricated journal bearings. Shear flow component of the oil film was first solved by a modified upwind finite difference method. The solution of the pressure gradient flow component was completed by the Galerkin finite element method. Present OSM solutions for a slider bearing are in agreement with Elord's results. OSM was then applied to herringbone grooved journal bearing in this work. The film pressure, cavitation areas, load capacity and attitude angle were obtained with JFO pressure conditions. The calculated load capacities are in agreement with Hirs's experimental data. A comparison of the present results and those predicted by the Reynolds pressure conditions shows some differences. The numerical results indicate that the load capacity and the critical mass of journal (linear stability indicator) are higher, and the attitude angle is lower than those predicted by Reynolds pressure conditions in cases of high eccentricities.

Spherical contact mechanical analysis of roller cone drill bits journal bearing

Fang contact model is introduced to analyze stress of the spherical fixed ring journal bearing.Developed calculation programs in the MATLAB software which are utilized to calculate the contact characteristics of roller cone drill bits spherical fixed ring journal bearing.In addition,effects of external load,radius clearance values,and material parameter on the mechanics performance were investigated.The results show that the value of external load has a direct pronounced effect on the contact characteristics of journal bearing.There is a significant positive correlation between contact pressure and external load,radius clearance value,and the Young's modulus of material.However,there is an evident negative correlation between contact radius of journal bearing and radius clearance value,and the Young's modulus of material.The smaller radius clearance value of journal bearing is,the more centralized contact region will be,so the corresponding contact pressure will be higher.From the perspective of reducing friction and wear,we need select the materials which have high strength and good toughness.Not only might this can improve the wear resistance,it also effectively decreases the contact pressure.In this case,we can prolong the service life of roller cone drill bits journal bearing.