THERMOHYDRODYNAMIC LUBRICATION ANALYSIS ON EQUILIBRIUM POSITION AND DYNAMIC COEFFICIENT OF JOURNAL BEARING

The finite element method （FEM） is introduced to calculate the oil film pressure and temperature distribution of a journal bearing. The perturbation is performed directly on the finite element equation. Consequently, the Jacobian matrices of the oil film forces are concisely obtained. The equilibrium position of the bearing with a given static load is found by the Newton-Raphson method. As byproducts, dynamic coefficients are obtained simultaneously without any extra computing time. From the numerical results, it is concluded that the effects of film temperature on stiffness coefficients are bigger than those on damping coefficients. With the increase of rotational speed, the load capacity and the stiffness coefficients of the journal bearing are increased when the eccentricity is small, while decreased when the eccentricity is big.

EFFECTS OF MANUFACTURING ERRORS ON GAS LUBRICATED JOURNAL BEARING WITH COMPLIANT SURFACE

A theoretical study has been performed to investigate the influence of manufacturing errors on the bearing housing of a gas lubricated journal bearing with compliant surface I in particular on the bearing load capacity. A gas film thickness distribution is presented, in which errors o f both circumferential and axial bearing housing are considered. The influence of the errors on bearing performance is compared between rigid and compliant surface bearings. It was shown that the compliant surface bearings are less sensitive to the manufacturing errors than the rigid surface bearings. Thelefore, the cost of compliant surface bearing could be reduced by setting a larger manufacturing error tolerance.

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.

DYNAMIC BEHAVIOR OF A CRACKED FLEXIBLE ROTOR SUPPORTED ON JOURNAL BEARINGS

The dynamic behavior of a cracked flexible rotor supported on three kinds ofjournal bearings is presented. Numerical experiments show that nonsynchronous responseswill happen due to the rotor crack, and the amplitudes of the nonsynchronous componentsbecome larger with the increase of crack. On the other hand, the fluid forces of journalbearings can suppress the nonsynchronous response. The (1/2) × or (3/2) × harmoniccomponent rarely appears for small crack near the rotating speed ratio Ω = 2Ωc or Ω =(2/3)Ωc. In the case of supercritical rotating speed, the additional 0× harmonic component is increased as the crack increases. The bearing parameters affect greatly the occur-rence of the nonsynchronous responses by means of exerting innuence on the critical spedand the stabi1ity of the 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.

Analysis of Thermoelastohydrodynamic Performance of Journal Misaligned Engine Main Bearings

To understand the engine main bearings＇ working condition is important in order to improve the performance of engine. However, thermal effects and thermal effect deformations of engine main bearings are rarely considered simultaneously in most studies. A typical finite element model is selected and the effect of thermoelastohydrodynamic（TEHD） reaction on engine main bearings is investigated. The calculated method of main bearing＇s thermal hydrodynamic reaction and journal misalignment effect is finite difference method, and its deformation reaction is calculated by using finite element method. The oil film pressure is solved numerically with Reynolds boundary conditions when various bearing characteristics are calculated. The whole model considers a temperature-pressure-viscosity relationship for the lubricant, surface roughness effect, and also an angular misalignment between the journal and the bearing. Numerical simulations of operation of a typical I6 diesel engine main bearing is conducted and importance of several contributing factors in mixed lubrication is discussed. The performance characteristics of journal misaligned main bearings under elastohydrodynamic（EHD） and TEHD loads of an I6 diesel engine are received, and then the journal center orbit movement, minimum oil film thickness and maximum oil film pressure of main bearings are estimated over a wide range of engine operation. The model is verified through the comparison with other present models. The TEHD performance of engine main bearings with various effects under the influences of journal misalignment is revealed, this is helpful to understand EHD and TEHD effect of misaligned engine main bearings.

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.

Nonlinear dynamics of flexible rotor system supported on fixed-tilting pad combination journal bearing

Based on the Reynolds equation with Reynolds boundary conditions, the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings. By doing so, a profile of nonlinear oil film force of single-pad journal bearings is established. According to the structure of combination journal bearings, nonlinear oil film force of combination journal bearing is obtained by retrieval, interpolation and assembly techniques. As for symmetrical flexible Jeffcott rotor systems supported by combination journal bearings, the nonlinear motions of the center of the rotor are calculated by the self-adaptive Runge-Kutta method and Poincar6 mapping with different rotational speeds. The numerical results show that the system performance is slightly better when the pivot ratio changes from 0.5 to 0.6, and reveals nonlinear phenomena of periodic, period-doubing, quasi-periodic motion, etc.

Performance of dynamically loaded journal bearings lubricated with couple stress fluids considering the elasticity of the liner

To take into account the couple stress effects, a modified Reynolds equation is derived for dynamically loaded journal beatings with the consideration of the elasticity of the liner. The numerical results show that the influence of couple stresses on the bearing characteristics is significant. Compared with Newtonian lubricants, lubricants with couple stresses increase the fluid film pressure, as a result enhance the load-carrying capacity and reduce the friction coefficient. However, since the elasticity of the liner weakens the couple stress effect, elastic liners yield a reduction in the load-carrying capacity and an increase in the friction coefficient. The elastic deformation of the bearing liner should be considered in an accurate performance evaluation of the journal bearing.

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.

Vibration characteristics of rotor system with tilting-pad journal bearing of elastic and damped pivots

In view of an entire dynamic model of tilting-pad journal bearing(TPJB) in which the pads swing and vibrate along geometric direction of preload, a TPJB of elastic and damped pivots was designed and manufactured. Vibration experiments were carried out under the conditions of different rotor bending stiffness and oil supply pressure to find out the relationship between the new bearing's vibration depression effect and other dynamic parameters of the rotor. The result shows that critical amplitudes can be efficaciously reduced while system's stability can be remarkably improved by this bearing. Besides, the bearing's effect of vibration depression weakens as the rotor bending stiffness increases, but heightens it as the oil supply pressure increases.

A Transient Thermohydrodynamics Study of Plain Journal Bearings Using Newton-Raphson Method Analysis

The present paper proposes three-dimensional model necessary to calculate the transient temperature field in a journal bearing submitted to a sudden change in speed and load and analyzes the bearing performance numerically. Thermal deformation of the bush and realistic thermal boundary conditions at oil and bush interface are considered. At each time step a Newton-Raphson method is used to solve the Reynolds equation, film thickness equation and the motion equation of the journal simultaneously to obtain the pressure distribution and the velocity of the journal center. Then the fluid film force is acquired through integral of fluid film force and the acceleration and position of the journal center are acquired through differences of the velocity. The energy equations of the oil film and the bush are solved simultaneously by using an efficient finite difference scheme. Then the transient three dimensional temperature field of the bearing is acquired by combining the energy equations and the Reynolds equation through the nodal temperature and pressure. It is found that the approaches introduced here converge quickly and save calculation time greatly.

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.

Complex nonlinear behaviors of a rotor dynamical system with non-analytical journal bearing supports

Nonlinear dynamic behaviors of a rotor dynamical system with finite hydrodynamic bearing supports were investigated. In order to increase the numerical accuracy and decrease computing costs, the isoparametric finite element method based on variational constraint approach is introduced because analytical bearing forces are not available. This method calculates the oil film forces and their Jacobians simultaneously while it can ensure that they have compatible accuracy. Nonlinear motion of the bearing-rotor system is caused by strong nonlinearity of oil film forces with respect to the displacements and velocities of the center of the rotor. A method consisting of a predictor-corrector mechanism and Newton-Raphson method is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of the bearing-rotor system. Meanwhile the dynamic coefficients of bearing are obtained. The nonlinear unbalance periodic responses of the system are obtained by using Poincaré-Newton-Floquet method and a combination of predic- tor-corrector mechanism and Poincaré-Newton-Floquet method. The local stability and bifuration behaviors of periodic motions are analyzed by the Floquet theory. Chaotic motion of long term dynamic behaviors of the system is analyzed with power spectrum. The numerical results reveal such complex nonlinear behaviors as periodic, quasi-periodic, chaotic, jumped and coexistent solutions.

A Study on the Stability Analysis and Optimum Design for Journal Bearings

Based on the establishment of a differential equation of motion and the solution of the oil film whirling locus of the Journal center, a method of judging the stability of bearing is presented. Meanwhile a method of bearing parameter optimization for the optimal stability is recommended. Finally, a short journal bearing is given as an example to illustrate the reasonableness and feasibility of the method.

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.

A COMPUTATIONAL APPROACH FOR PRESSURE DISTRIBUTION AND ROTORDYNAMIC COEFFICIENTS OF JOURNAL BEARINGS WITH COMBINED RADIAL AND MISALIGNMENT MOTIONS

A computational approach is presented to handle an enlarged linear rotordynamic model whichsimultaneously includes both radial and misalignment motions.The interactive force and momentbetween the rotating and non-rotating members are modeled using an adaptation of the classicalReynolds lubrication equation for incompressible laminar isoviscous films.First,the governingequation is derived and the method of solution is introduced based on a 2-dimension,9-point cen-tral difference.Second,force and moment components are computed by numerical integration ofthe film pressure distribution.Finally,the rotordynamic coefficients are yielded according to thegeneralized force gradients.