Hydrodynamic analysis of journal bearing considering the effects of cavitation and minuscule particle

Journal bearing is the general element in the mechanical systems, which can provide the rotational motion of joints. The hydrodynamic analysis model of journal bearing is established and the effects of cavitation and minuscule particle are considered in the simulation model. The cavitation effects would be represented by the mixture model. Based on the CFD and DPM technology, the mixture lubrication medium of journal bearing is developed, which includes the minuscule element of solid in the lubrication film. And, the effects of structural parameters and operation conditions on the hydrodynamic characteristics of journal bearing is investigated. The simulation results could provide the suggestion for the design of structure and working condition.


Introduction
The hydrodynamic analysis of journal bearing is focused on the attention of researcher, which includes simplified analysis method, mesh divided technology and modeling technology.The matching design of structural parameters and operation conditions play an important role in the performance optimization of journal bearing [1][2][3].However, the phenomenon of cavitation often appears during the motion of journal bearing and the existence of minuscule particle (iron filings and stone) is unavoidable in the lubrication medium.Then, the influence of cavitation and minuscule particle on the lubrication characteristics of journal bearing would be discussed in the different working conditions.In addition, the modeling approach of journal bearing should be developed, which can describe the hydrodynamic behavior availability.
Based on the development of simulation technologies, the lubrication performance analysis of journal bearing has been studied [4][5].Wu and Zhao [6] developed the modeling method of bearing systems by CFD technology, and the oil-air multiphase flow was introduced in the simulation model.The results showed that the appearance of air phase had serious effects on the pressure distribution of lubrication film.Considering the friction effects, the mixed lubrication model of journal bearing was established by Sander and Allmaier [7].The simulation and experiment of journal bearing with non-Newtonian lubricant medium were conducted, the influence of various condition on the friction performance of journal bearing was revealed.Chen [8] conducted the hydrostatic evaluation and comparative analysis of journal bearing with the microstructural parameters.Then, the tribological characteristics of journal bearing was evaluated by the proposed method, and the effectiveness of this method was demonstrated by the experiment data.Based on the multiphase flow theory, Lin [9] built the hydrodynamic analysis model of water-lubrication journal bearing considering the cavitation effects.The numerical results revealed that the hydrodynamic behavior of journal bearing was close connected with the volume of cavitation, which caused the change of load carrying capacity.Rao [10] investigated the pressure distribution and load carrying capacity of journal bearing with the change of working conditions.And, the stability evaluation of journal bearing had been also conduced.
According to the above studies, the modeling of journal bearing is focused on the liquid-gas twophases.However, minuscule particle (iron filings and stone) is also the key element in the hydrodynamic response of journal bearing.In this work, the liquid-gas-solid three-phases model of journal bearing is established.And, the effects of minuscule particle on the hydrodynamic response of journal bearing are represented.The mapping relationship between design parameters and lubrication characteristics is also revealed.

Theory and modelling
The schematic of journal bearing is plotted in Fig. 1, which includes the inlet flow, bearing and groove.The clearance exists between journal and bearing, and the lubrication medium is filled with the zone.Based on the squeezed force of lubrication medium, the journal could move away from bearing [8,10].In the global coordinate systems, O b and O j are the centers of journal and bearing.The relative position between journal center and bearing center is eccentricity (e).And then, the rotational speed (ω), bearing diameter (D b ) and groove depth (h g ) are defined.According to the hydrodynamic lubrication theory, the motion of journal bearing should be satisfied with the mass conservation and momentum conservation [3,5].And then, the continuity equation and Navier-Stokers equations in the three directions (x, y, z) are employed in the calculation, which is written as: where  is the density of lubrication medium, u denotes the velocity vector, and S M is the momentum source.p and μ are the pressure and viscosity of lubrication film.
Meanwhile, the cavitation characteristics would be also shown in the simulation model, and the mixture density (  m ) and velocity vector of air (  

 
) are included.The expression can be obtained as: where where f is the mass fraction of air, γ denotes the effective exchange coefficient.
In addition, the minuscule particle (iron filings and stone) can be represented by the discrete element method, and the DPM model is employed to describe the solid phase.Then, the motion equation of minuscule particle is expressed as: where m v and p v are the velocities of liquid-air flow and solid.D C denotes drag force coefficient, ep R represents the relative Reynolds number, and o F is mass force.p d is the diameter of minuscule particle and  p is the density of minuscule particle.

Case study
The influence of cavitation and minuscule particle on the hydrodynamic behaviour of journal bearing is conducted in this section.The calculation parameters are listed in Tab. 1, and the various parameters include structural characteristics and operation conditions.Lubricant density (kg/m 3 ) 890

The effects of minuscule particle
In order to reveal the effects of minuscule particle on the hydrodynamic response of journal bearing, the minuscule particle is introduced into the oil-film.The eccentricity ratio is selected to 0.5 and the rotational speed is defined to 2000 rpm.And, the simulation results are displayed in Fig. 2.Although the value of hydrodynamic behaviour for journal bearing, the introduction of minuscule particle changes the distribution range and value of oil-film pressure.The maximum value of oil-pressure and bearing capacity can be improved by the existence of minuscule particle in the same condition.Moreover, the cavitation volume fraction of oil-film keeps a stable value, and the influence of minuscule particle would be consider.According to the simulation results, the suitable minuscule particle could improve the pressure value of oil-film.As well known that, the pressure of oil-film is close related with the value of bearing capacity.Then, the bearing capacity of oil-film is better than this value of journal bearing without minuscule particle.Meanwhile, the friction force and cavitation volume fraction of journal bearing keep the same value, which is the valuable phenomenon for the design of journal bearing.The structural parameters and operation condition are the key factors of hydrodynamic behavior for journal bearing, and it is also should be discussed.

The effects of structural parameters
The oil groove plays an important role in the lubrication characteristics of journal bearing.Then, the distribution characteristics of oil groove is discussed in this section.The number of oil groove is 2, 3, 5 and 6.The eccentricity ratio and rotational speed are defined to 0.5 and 2000 rpm.The simulation results are obtained in the steady state of journal bearing.Fig. 3 presents the pressure distribution of journal bearing, and it is obvious that the variation of groove position and groove number has the serious effects on the pressure value and distribution feature of oil-film.A larger number of groove could decrease the maximum pressure value of oil-film.When the groove is located in the high-pressure region, the pressure value of oil-film could be changed and the decline of oil-film pressure would appear.The oil-film pressure is close related to the bearing capacity of journal bearing, and this value decreases in the same condition.When the groove number is 2, the bearing capacity is 316 N and the friction force is 11 N.As the groove number increases to 6, the bearing capacity changes to 147 N and friction force is only 10.23 N.Meanwhile, the cavitation volume fraction is the key factor for evaluating the hydrodynamic behavior of journal bearing.With the different groove numbers, the cavitation volume fractions of oil-film are 5.51%, 8.28%, 3.2% and 1.89%, respectively.Although the friction force is only 9.42 N in the condition of groove number is 3, a larger cavitation volume fraction cannot be available in the design of journal bearing.Therefore, it is necessary to conduct the influence of operation condition on the lubrication performance of journal bearing in detail.

The effects of operation conditions
The relationship between operation conditions and lubrication characteristics of journal bearing is revealed in Figs. 4 and 5. And, the groove number is defined to 2. The growth of rotational speed and eccentricity ratio could improve the pressure of oil-film, and it is worth account that the higher rotation speed would cause the fluctuation of negative pressure in the bottom of journal bearing.growth of rotation speed and eccentricity ratio would improve the bearing capacity, the friction force and cavitation volume fraction could be also increased at the same time, which may cause adverse phenomenon of journal bearing.Then, the matching design between structural parameters and operation condition should be considered in the lubrication performance analysis.

Conclusions
A new modelling approach of journal bearing is established in this work, which considering the effects of cavitation and minuscule particle.The cavitation phenomenon is displayed by the multiphase flow model, and the minuscule particle is defined solid phase based on the DPM method.Moreover, the influence of minuscule particle (iron filings and stone) on the hydrodynamic response of journal bearing is investigated.And then, the groove number and oil film are defined to the variable of structural parameters in the case study.Furthermore, the simulation results also reveal the effects of operation conditions (rotational speed and eccentricity ratio) on the lubrication characteristics of journal bearing.The case studies could represent that the proposed method in this work could be suitable to evaluate the hydrodynamic behavior of journal bearing during the design process.

Figure 1 .
Figure 1.The structural characteristics of journal bearing.

Figure 2 .
Figure 2. The pressure distribution of oil-film: (a) Without minuscule particle, (b) With minusculeparticle.The influence of minuscule particle on the oil-film pressure of journal bearing is given in the Fig.2.According to the simulation results, the suitable minuscule particle could improve the pressure value of oil-film.As well known that, the pressure of oil-film is close related with the value of bearing capacity.Then, the bearing capacity of oil-film is better than this value of journal bearing without minuscule particle.Meanwhile, the friction force and cavitation volume fraction of journal bearing keep the same value, which is the valuable phenomenon for the design of journal bearing.The structural parameters and operation condition are the key factors of hydrodynamic behavior for journal bearing, and it is also should be discussed.

Figure 3 .
Figure 3.The pressure distribution of oil-film with different groove number: (a) Groove number is 2, (b) Groove number is 3, (c) Groove number is 5, (d) Groove number is 6.