Optimal Design of Lubricated Journal Bearing Under Surface Roughness Arrangement
Mohammad Tauviqirrahman Laboratory for Engineering Design
and Tribology, Department of Mechanical Engineering, Engineering
Faculty, Diponegoro University, Jl. Prof. Soedharto, Tembalang,
Semarang 50275, Indonesia
*e-mail:
P. Paryanto1,2
1Department of Mechanical Engineering, Diponegoro University,
Jl. Prof. Soedharto, Tembalang Semarang 50275, Indonesia
2Institute for Factory Automation and Production Systems (FAPS), Friedrich-
Alexander-Universität Erlangen- Nürnberg, Egerlandstr. 7-9, Erlangen,
91058, Germany
Harry Indrawan, Nur Cahyo, Arion Simaremare, Siti Aisyah PT PLN (Persero) Research Institute
Jl. Durentiga 102, Jakarta Selatan, 12760, Indonesia
Abstract— Journal bearings as machine elements have always been of particular interest due to widespread applications. However, high level of power loss limits the reliability of lubricated journal bearing. The current paper explores the possibility of employing the artificial roughness in bearing in order to enhance performance behavior based on computational fluid dynamics (CFD) analysis. The hydrodynamic performance is calculated by Navier-Stokes equation coupled with continuity equation with finite volume method. In order to obtain more accurate results, the multi- phase cavitation model is also considered in the computation.
The hydrodynamic pressure as well as the load support is presented for two kinds of loading (low vs high) varying the surface roughness levels. The results show that for heavy loaded bearing, the surface roughness has an important influence on the lubrication characteristics of the bearing, while for light loaded one, the surface roughness effect is not so significant. This study contributes to the improvement of the journal bearing performance.
Keywords—cavitation, Computational Fluid Dynamics (CFD), finite journal bearing, load support, surface roughness.
I. INTRODUCTION
Journal bearing are widely employed in various types of rotating devices such as automobile engines, gas turbines and steam turbines. These rotating devices often need to work under a higher operating speed and heavy loading with high efficiency. In order to achieve a longer life-time of these machines, the engineers have proposed various concepts of journal bearings with more realistic and efficient design of the journal bearing. Typically, the reliability and efficiency of the machinery strongly depends on the lubrication performance of the rotor-bearing system.
The lubrication of journal bearing has received great attention from the researcher community. As widely known, in general, no surfaces are smooth due to irregularities nature. In addition, the inaccurate surface finishing during manufacturing processes of journal bearing may yield an unexpected surface roughness level. Many works have been conducted for understanding the influence of surface roughness on hydrodynamically lubricated journal bearings, for example, in recent publications [1-3]. Some models for roughness, for example, Christensen stochastic model [1], Greenwood-Williamson (GW) contact model, and sinusoidal waviness model [3] have been used in many works and it was proven that the surface roughness has a strong effect on the lubrication performance.
Over the years, the concept of artificial roughness has been becoming increasingly popular in enhancing the performance of mechanical systems. This concept is practically applied by providing various shapes, orientation and sizes of roughness on plane surface. However, based on an extensive literature review, most of the studies dealing with the artificial roughness focused on the solar air heater, for example [4,5], while studies related to roughened journal bearing system are still limited.
In the recent times, due to the attractive features of artificial roughness, the bearing designers has focused their work attempt to explore the effect of artificial roughness on the journal bearing. Considering the growing interest in enhancing the bearing performance with less effort, this paper aims to is to explore the influence of artificial surface roughness on the tribological bearing performance based on the computational fluid dynamics (CFD) approach. In order to accommodate wide range of operating condition of bearing, two kinds of bearing loading are of particular interest, i.e. low vs high loading. Unlike most previous studies employing the Reynolds cavitation approach to model the cavitation phenomena [1-3] during bearing operation, this study uses more realistic cavitation model, that is mass-conserving multi-phase cavitation model to obtain more accurate results. As a note, the validity of this approach has been presented by previously published references [6-8]. In this work, the construction of the engineered bearing surface, on which certain region of bearing is roughened, while the other is set to very smooth, is conducted. In this way, the flow behavior in the liquid lubricated bearing can be altered so as the improved bearing characteristics can be achieved. Such hypothesis, then, will be examined based on the computational analysis. The ultimate objective of the present study is to suggest certain design that may adjust the enhancement of journal bearing performance by engineering the surface roughness.
II. METHOD A. Generation of Rough Surface
In the present work, the sand-grain model is adopted to characterize the roughness profile of the sleeve surface. For modelling the surface roughness, the modified law-of-the- wall for mean velocity is employed. This equation can be expressed as follows [9]:
* 1ln *
/
p p
w
u u u y
E B
where u*C k1/ 4 1/ 2 and B
1/
lnfr . For sand-grain roughness, B is affected by the physical roughness height Ks. According to Adams et al. [9], to correlate the Ks with the Ra (the average roughness often measured by profilometer), (2) below can be used: Ks0.5863Ra
This equation allows the effect of the geometrical average roughness Ra of the surface can be calculated. In this study, for simplicity the uniform sand-grain roughness is assumed.
B. Governing Equations for Lubrication and Fluid Model Based on the work principle of the journal bearing, two sliding surfaces are necessary for the formation of the bearing lubrication. In this work, the Navier-Stokes and continuity equations are used to solve the lubrication problem according to a finite-volume method. The commercial CFD software package ANSYS FLUENT® is employed.
The momentum equation can be described as:
i i 2 ij 23
. i
i j
Du p
G e u ij
Dt x x
The continuity equation is expressed as
( i) 0
i
x u
For more representative of the bearing characteristic, the flow is considered turbulent. The turbulent model of realizable k-ε is used with standard wall functions as near- wall treatment. Practically, in the journal bearing when the flow enters the divergent region, pressure might fall below the saturation vapor pressure, and the liquid would rupture and the cavitation occurs. Therefore, for more accurate results, in the present study the mass conserving multi-phase cavitation model of the Zwart-Gelber-Belamri is employed [10].
For the cavitation prediction, the vapor transport equation describing the liquid-vapor mass transfer (evaporation and condensation) is defined by the following [10]:
v
.
v v
Rg Rct
where αv refers to the volume fraction of vapor, while ρv
express the vapor density. Rg and Rc account for the mass transfer between the liquid and vapor phases in cavitation.
For Zwart-Gelber-Belamri model, the final form of the cavitation is as follows [10]:
if nuc
υ
υ υB
3α 1 ρ 2 P
, 3 ρP
g ev
v ap
p p R F
R
if υ υ υ
B
, 3αρ 2P P
v Rc cond 3 ρ
p p F
R
where RB refers to the bubble radius (= 10-6 m in this case), Fevap denotes the evaporation coefficient (= 50), Fcond
expresses the condensation coefficient (= 0.01), αnuc= denotes the nucleation site volume fraction (= 5x10-4), pv
represents the vapor pressure and ρl refers to the liquid density.
C. CFD Model and Boundary Condition
Fig. 1 reflects the CFD model and schematic illustration of a journal bearing with artificial roughness. A three- dimensional computational model of the bearing with roughness is required to determine the flow characteristics using the steady CFD. In this work, the commercial software ANSYS DesignModeler is used to generate a three-dimensional computational model.
(a)
(b)
Fig. 1. (a) 3D computational model with roughness zone (b) Schematic of partially roughened journal bearing in front view.
For modified journal bearing, the roughness is applied on the certain area of the bearing, i.e. from
= 60o to 150o. The inspiration for the current concept is based on the fact that the alteration of the fluid film characteristics of lubricated journal bearing through artificial surface roughness results in the enhancement of bearing performance, similar to the concept of surface texturing.The Ra (the average roughness) is adopted to represent the level of surface roughness. Two different values of roughness Ra, i.e. 0.1 µm (precise) and 12.5 µm (rough) are of particular interest. The main data of the journal bearing and the lubricant are presented in Table 1.
TABLE I. BEARING AND LUBRICANT DATA
Parameter Value Unit
Bearing radius R 50.145 mm
Shaft radius r 50 mm
Bearing length L 100 mm
Bearing clearance c 0.145 mm
Attitude angle 30 o
Eccentricity ratio ԑ 0.41; 0.81 -
Density of lubricant vapor ρsat 2 x 105 Pa-s Viscosity of lubricant vapor ηsat 1.2 kg/m3 Saturation pressure of vapor Psat 20.000 Pa
Lubricant density ρ 840 kg/m3
Lubricant viscosity η 0.0127 Pa-s
In order to improve the computation efficiency, in the present work, the lubricant film is meshed with the hexahedral element for creating the uniform mesh. In the analysis, the inlet pressure as well as the outlet pressure is set to atmospheric pressure (i.e. 101,325 Pa), while no-slip conditions on the rotor and bearing walls are assumed.
Once the hydrodynamic pressure is computed through (3), the load support of the lubricated journal bearing can be calculated as:
Load support
Aprd dy
For all following computation, the SIMPLE algorithm is employed in the velocity-pressure coupling. For the momentum equations, a first-order upwind discretization scheme is employed whilst for the volume fraction equation, the QUICK discretization scheme is used.
III. RESULTS
In engineering application, there is very high possibility that during manufacturing bearing, the surface of the bearing may have a roughness level which is different from the design requirement due to major manufacturing defects.
However, on the other side the potential of an artificially roughened surface to improve the lubrication performance has been noticed by many researchers. Therefore, in this research the effect of the roughness level of the partly roughened surface will be explored with respect to the lubrication performance of the journal bearing based on the computational fluid dynamic (CFD) method.
Fig. 2 reflects the prediction of the hydrodynamic pressure profile at different loadings (high load vs low load) varying surface characteristics. Based on Fig. 2 (a), it can be observed that in the case of low loaded journal bearing (ε = 0.41 in this case), the pressure profiles of journal bearing
with different surface characteristics have similar trends especially in the divergent region (180o-360o). The roughened journal bearing with low roughness level (Ra = 0.1 µm in this case) has a profile that coincides with smooth one. This is as expected because the surface with Ra = 0.1 is categorized to “precision” according to JIS B 0601-2001.
However, from Fig. 2 (a) it is found that the “rough” journal bearing with Ra = 12.5 µm generates the higher-pressure peak compared to conventional smooth (ideal) journal bearing and “precise” journal bearing. From the physical point of view, the higher the surface roughness level, the stronger the roughness effect on the lubrication behavior.
0 0.05 0.1 0.15 0.2 0.25
0 30 60 90 120 150 180 210 240 270 300 330 360
Hydrodynamicpressure (MPa)
Circumferential direction (degree) Smooth Ra 0.1 Ra 12.5
(a)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 30 60 90 120 150 180 210 240 270 300 330 360
Hydrodynamicpressure (MPa)
Circumferential direction (degree) Smooth Ra 0.1 Ra 12.5
(b)
Fig. 2. Hydrodynamic pressure distribution at different loadings, (a) low load (ε = 0.41), (b) high load (ε = 0.81)
To validate the above conclusion about the issue of the effect of surface roughness on the performance, the analysis of high loaded journal bearing is also explored in this study.
For this, the eccentricity ratio of the shaft is changed to be 0.81 and other input parameters for this analysis are the same as ones employed for the above computation at the low load.
Fig. 2 (b) depicts the pressure profile for high loaded journal bearing varying the surface roughness levels. There are two observations which can be made based on Fig. 2 (b). Firstly, the surface roughness is able to increase the hydrodynamic pressure profile as well as its peak pressure. As a consequence, the enhanced load support can be achieved. It seems that for two roughness levels considered here, the prediction of the pressure peaks is higher than that of the ideal bearing. It indicates that increasing the eccentricity
ratio alters the behavior of the hydrodynamic pressure very much.
Secondly, in the case of roughened journal bearing, increasing the surface roughness level (i.e. “precise” to
“rough” level in this case) does not have a significant influence on the pressure profile especially for heavy load bearing. However, in comparison with smooth bearing, the performance of the roughened journal bearing is superior irrespective of the roughness level.
Thirdly, two patterns of roughened journal bearing studied here generate the smaller cavitation area in the divergent area compared to ideal journal bearing. On the other words, the presence of the roughness applied on the certain area can minimize the occurrence of the cavitation phenomena. This is also the reason why the load support for roughened journal bearing is larger than that for the ideal bearing. Comparing the cases between the light load and heavy loaded bearings as shown in Fig. 2 (a) and 2 (b), it seems that in addition to the surface roughness, the eccentricity ratio has a significant effect on the performance.
These double effects (i.e. roughness and eccentricity) lead to the improved load support.
Fig. 3 shows the comparison of tribological performance between low loaded and high loaded journal bearing in terms of load support. Based on Fig. 3, it can be highlighted that for the low loaded journal bearing, the load support for
“rough” journal bearing is around 3,228 N or 2% higher compared to ideal smooth bearing. From the manufacturing point of view, it suggests that introducing the partial roughness on the bearing surface does not affect the load support very much.
0 1000 2000 3000 4000 5000 6000
Smooth Ra 0.1 Ra 12.5
Load Support (N)
Low load High load
Fig. 3. Comparison of load support performance between low loaded and high loaded journal bearings at different surface behaviors.
A different result is highlighted when the eccentricity ratio is changed to be higher value to compensate the heavy load. From Fig. 3, it can be revealed that the deviation of the load support between ideal smooth bearing and roughened bearing is relatively high, i.e. 23% and 20%, respectively, for the Ra = 0.1 µm and 12.5 µm. Based on these results, a reference guide can be made from the perspective of the manufacture. If the journal bearing is designed to operate in heavy loading, the application of partially roughened bearing surface is recommended irrespective of the surface roughness level. For light loaded bearing, the surface roughness level which may exist on the surface due to finishing process does not have a significant effect.
IV. DISCUSSION
As widely known, with the increasing complexity of the rotating machinery behavior, CFD (computational fluid dynamics) is considered as an effective tool able to capture the 3D flow effects for many applications (design, safety studies) in more detail. This is because the CFD consists of the use of numeric methods and powerful computers to solve the governing mathematical equations. Moreover, the more representative results predicted by CFD are key to guaranteeing and enhancing the adequate performance of rotating machinery. Therefore, in the present work, three- dimensional computational fluid dynamics (3D CFD) model was created to simulate the fluid film of a partially roughened journal bearing.
Over the last few decades, growing concerns over environmental and energy sustainability have attracted numerous researchers including tribologists around the world to create the performance of the rotating machinery (for example turbines, pumps and generators) in more efficient way. The industrial journal bearing which often found in turbines system is an important component in present-day heavy rotating machinery. Due to the presence of the sliding surfaces, in practice the journal bearing always corresponds to the friction and the power loss. Indeed, in rotating machines the industrial bearings present the most important power losses [11]. Additionally, high level of friction limits the reliability of journal bearing. Globally, according to the study of Holmberg and Erdemir [12], the friction roughly consumes one-fifth of all energy used worldwide. By improving the lubrication performance of journal bearing (by enhancing the load support and thus reducing the power loss as indicated in this study), the time saving as well as the energy in operational condition of turbines can be achieved.
The technology in tribology (lubrication, friction, and wear) as conducted in the present work becomes an important aspect to accelerate a better mechanical design. In this context, the main findings presented here can be directly connected with energy efficiency and reliability. In more detail, from the tribology research point of view some key problems which has been solved in this work are:
1. The modified journal bearings have successfully designed in this work to enhance their lubrication performance. The surface modification of the journal bearing has been applied by providing the surface roughness partly on the zone certain with different roughness levels.
2. The load support as a main indicator of lubrication calculated for the case of modified journal bearing with low surface roughness level has been proven to be larger up to 2% and 20%, respectively, for low loading and high loading in comparison to smooth journal bearing. This finding is feasible to expect promising utilization of artificial roughness in journal bearings of gas/steam turbine to enhance their performance, and thus their reliability. As a note, the journal bearing often found in power plant always works under extreme operating conditions (heavy load and high rotating velocity). The increased load support of the modified journal by 20% bearing as highlighted in this research, of course, can transmit more external loads with the same power. It means that the with the same operation
cost, the bearing can support 20% higher load compared to the traditional journal bearing (without artificial roughness). On the other words, the design of modified journal bearing presented here offers the significant energy saving of the operation of steam/gas turbines during power generation cycle.
From the view point of practical application, the surface configuration of the bearing by applying the surface roughness is relatively simple and is thus easy to be manufactured. The prospect of the performance enhancement of the journal bearing is extremely encouraging, since the required design of bearing surface is quite simple.
For future works, the study will be extended to investigate the performance of modified thrust bearing of water turbine. The wide range of the surface roughness level will be of particular interest in terms of the load support as well as the friction force.
V. CONCLUSION
In the present work, the effect of surface roughness on finite length journal bearing was studied using computational fluid dynamic (CFD) method. In order to obtain more realistic result, the multi-phase cavitation model was taken into account. In this work, the rotating displacement of journal shaft (i.e. the eccentricity ratio) is the main quantity of interest as an unknown variable to represent the value of loading of the bearing.
The investigations reveal that the surface roughness has a significant effect on the pressure distribution and the load support for heavy loading of the bearing. It indicates that for light loaded bearing, the roughness effect is not so significant to enhance the bearing performance. Therefore, it is not necessary to engineer the bearing surface.
Based on the conducted research, it is also be concluded that partially roughened bearing with high roughness level can improve the bearing performance up to 20% in comparison with smooth (non-roughened) bearing.
Consequently, the longer life-time of bearing can be achieved. Overall, the verified high load support enhancement of the optimal design of journal bearing demonstrates the potential applications of artificial roughness in many rotating machinery including turbines, generator etc.
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