Roughness Effect on Thermo-Elasto-Hydrodynamic Performance of a 170 o-Arc Partial Journal Bearing

In the current analysis, the effects of circumferential scratches along the inner surface of a 170o arc partial journal bearing has been numerically investigated. Their impact on the thermo-elastohydrodynamic performance characteristics, including maximum pressure, temperature, deformation, and stress, has been examined thoroughly. The ANSYS Fluent CFD commercial code was employed to tackle the iterative solution of flow and heat transfer patterns in the fluid film domain. They are then applied to the ANSYS Static Structure solver to compute the deformation and stress resulted in the solid bearing zone. A wide range of operating conditions has been considered, including the eccentricity ratio (0.8236 ≤ ε ≤ 0.9866) and scratch depth (0mm ≤ hs ≤ 0.224mm). In contrast, the bearing length-diameter ratio (L/D) and the rotation speed (N) have been fixed at 0.77 and 1500 rpm, respectively. The thermo-hydrodynamic pressure, temperature, stress, and deformation have all been computed. It was found that the scratch depth has a direct effect on the thermo-hydrodynamic performance of the partial bearings. Meanwhile, the deep central scratches are important, especially at scratch depth equal to 0.224mm.


INTRODUCTION
Partial journal bearing is one of the most common applications of tribology. It is widely used in industrial and daily life applications, including rotary kilns, cement mills, and many other rotating machineries. It consists of three main parts; the fixed part (bearing), running part (journal), and fluid layer (lubricant) between the two parts( bearing and journal). The lubricant is used to reduce wear, friction, and temperature generated due to friction, as shown in Fig. 1. Surface roughness can be defined as a component of surface texture. It is usually measured by the surface deviations formed perpendicularly compared to its ideal form. If such deviations are considerable, the surface is said to be rough; otherwise, it is considered smooth if it includes small deviations. The roughness of an engineered surface may be classified as: a random roughness resulting from surface finishing or a deterministic roughness planned intentionally to increase the lubrication characteristics of the hydro-dynamically lubricated thrust ring (Vyas, 2005). A very general classification for a solid surface is shown in Fig. 2. ( Sharma and Pandey, 2005) have analyzed the influence of longitudinal surface roughness on thermo-hydrodynamic lubrication. An infinitely wide plane slider bearing has been investigated numerically using a stochastic roughness model. As the height of surface roughness increases, it showed that the value of film-thickness ratio "at which maximum load-carrying capacity (isothermal) has been recorded" decreases. In contrast, a significant reduction in load-carrying capacity (thermal) has been recorded with the lubricant temperature rise due to the roughness parameter increase. (Dobrica et al., 2006) examined a specific numerical model viable on partial journal bearing operating in mixed lubrication region. Simulations have been done for various models of roughness and eccentric ratio (0.8-1.08). It was apparent that surface roughness affected all performance characteristics of bearing, including fluid film thickness, angle of attitude, and friction-torque. However, the roughness effect seems to have largely depending on the direction of roughness. Compared to smooth surfaces and by used hypothesis rigid pad (HD) model, it showed the largest effect of roughness resulting in an increase of (30%) in the minimum mean film-thickness and more of (54%) in friction torque. The roughness of isotropic properties had a smaller effect but still had a large impact on bearing performance. On the other hand, the longitudinal -roughness seemed had an effect only on friction-torque. When the deformation is allowed in pad response to the hydrodynamic-pressure model, it was observed that the overall effect of roughness is greatly diminished. The elasto-hydrodynamic lubricant analysis (EHL) for a 60º radial partial bearing is analyzed by (Bhat et al., 2007) using the CFD (Computing-Fluid-Dynamics) with CSD (Computing-Structural-Dynamics). This combined field analysis employs the calibers of the ANSYS / FLOTRAN commercially available finite element program with fluid-solid interaction (FSI) technology. The pressure is found by using computational fluid dynamics, considering that the flow is laminar. The distribution of deformations and stresses on the bush is obtained due to the pressure of pressure using the finite element method satisfying the boundary conditions. The circumferential scratches which appear in the inner bearing surface were studied analytically by  and explained their effect on the thermo-hydrodynamic performance-characteristics such as minimum film thickness (ℎ ), the maximum pressure ( ), mean oil film temperature ( ), and friction torque. The effects predicted were especially important for central-deep scratches. It seems that the most important parameter for measuring the intensity of scratching is the worn-out area. When the scratches spread over the inner bearing surface, they are likely to lead to the bearing's destruction, even if it is comparatively slim and represents a small section from the total bearing width. The other important parameter is the depth of the scratch, as deep scratches were found to reduce the local pressure about to surrounding pressure. It was also noticed that the density of scratch appears to be only important for scratches surface [ℎ < C/4], or when a few areas of bearing is destruction. Finally, smaller wear impacts are found when scratches are moved toward the bearings edges.  presented developed deterministic partial elasto-hydrodynamic journal bearing play in the mixed-lubrication system by taking the rough surface into account. Reynolds' equation was solved on a very thin grid, and the pad deformation resulting from isothermalpressure was taken into consideration. The results appeared the partial bearing's geometry and the shaft speed equal to 0.47 m / sec, at specific-pressure value ranging up to 50 MPs. The pad materials were taken into account for both iso-viscous and piezo-viscous oil lubricant. The simulation results were demonstrated in terms of specific pressure, relative eccentricity ratio, oil film thickness, contact extent, friction torques, etc. Surface roughness has been shown to have a large effect on the performance of bearing, mainly when the loads are high where the rough contact amount is available and large. The longitudinal-roughness trends appear weaker behavior, whereas transverse-roughness trends appear better overall performance. (Abass et al., 2010) have examined partial journal bearings' performance based on a steady-state thermo-hydrodynamic model (THD) for partial journal bearings. The generalized Reynold'sequation, the energy equation in oil-film, and the equation of heat transfer in pad and shaft are solved simultaneously. The shaft temperature has been found a large influence on the bearing performance, where both oil and bush temperature increase, with the rise in shaft temperature while the oil film thickness decreases. Isothermal hydrodynamic analysis was conducted numerically by (Dobrica and Fillon, 2012) to evaluate the scratched journal bearings' overall performance degradation. The scratches' severity was measured by using four parameters, namely the scratch depth, the scratched extent area, the scratches density, and the scratched location. To evaluate overall bearing performance degradation, several working parameters were calculated minimum oil film thickness (ℎ ), mean oil temperature ( ) and maximum hydrodynamic pressure ( ). Most of the examined parameters seem to have a direct impact on bearing performance, where it was found that the numerous/denser/deeper the scratches, the poorer the bearing performance. In general, the scratch depth seems to be the most dominant parameter, where if it is relatively small compared to film thickness, the bearing performance is slightly affected. Otherwise, the performance is severely affected when the scratches are getting deeper, which means that the deterioration in performance can be minimal in a low-load bearing and adverse in a high-load bearing, which similarly complicates the contrast from scratch effects. (Liang et al.,2016) investigated the hydrodynamic -performance of lubrication, a partial texturedsliding journal bearing utilizing the CFD ADINA program. The limit requirement of the phase change has been applied to the fluid field. It was found that texture found at the lubricant entrance Journal of Engineering Volume 27 January 2021 Number 1 20 area that the bearing performance can improve. Otherwise, bearing performance is reduced because of the texture found in the area of maximum pressure. While the texture found at the outlet region of lubricant has two various consequences: a portion of the texture found inside the divergent area of oil film improves the load-carrying capacity, but the portion outside the divergent area makes the load-carrying capacity decrease. In the current research, the effects of circumferential scratches along the inner surface of a 170ᵒarc partial journal bearing has been numerically studied. Based on an FSI analysis, the impact of scratches on the thermo-elasto-hydrodynamic performance characteristics, including maximum pressure, temperature, deformation, and stress, has been examined thoroughly and various design and operating conditions.

MATHEMATICAL Model
The mathematical model in this study is divided into two parts. The first is the fluid film layer (lubricant), while the other is the solid structural (bearing or pad), as previously shown in Fig.1.
In this study, the bearing (bush) 's inner surface is scratched circumferentially along the pad length, as shown in Fig.3, where the bearing is assumed to be made of brass alloy. The governing equations used along with the appropriate boundary conditions required to close a mathematical model will be detailed for both the fluid film zone (lubricant) and solid zone (bearing), as follows:

Governing equations of fluid film zone (lubricant)
The partial differential equations governing the conservation of mass and momentum (Navier-Stokes equations) for the fluid film layer are as follows (Versteeg and Malalasekera, 2007): Journal of Engineering Volume 27 January 2021 Number 1 21 Where , p, u, v, w stand for the lubricant density, pressure, x, y, and z-velocity component, respectively. stands for the dynamic lubricant viscosity, and it is assumed to vary exponentially with lubricant temperature as: = − ( − ) (5) Where is the dynamic viscosity of the lubricant at the inlet temperature , while represents the temperature-viscosity coefficient of the lubricant. Besides the Navier-Stokes equations, the fluid-energy equation should be solved to find the temperature distribution of the film layer is as follows (Versteeg and Malalasekera, 2007): Where , , are respectively the lubricant specific heat, lubricant thermal conductivity, and lubricant temperature, while represents a source term.

Boundary conditions for fluid film zone (lubricant)
2.2.1. Hydrodynamic boundary conditions As solid walls surround the film flow, no-slip occurs on each journal and bearing surfaces. This implies that the lubricant particles in the rotating journal's vicinity always have zero velocity relative to the rotating shaft to maintain the non-slip condition. Moreover, the condition at the sidewalls bounding the film field is assumed to be at an atmospheric state, i.e. zero gauge pressure. Thus, the boundary conditions used are as shown in Fig.4 It is assumed that a γ fraction of the lubricant leaving the system is recirculated and mixed with a fresh amount of lubricant at colder condition, i.e., T0 =40°C, to maintain the working lubricant at acceptable operating conditions. Thus, the lubricant film temperature at the inlet section as: = Where Q stands for the lubricant volume flow rate across any of the non-solid boundaries enclosing the film layer.
Where K1 and K2 are coefficients used to predict the journal surface temperature defined as: 2.2.2.3. Side Surface of Film Layer Due to a negligibly thin layer of lubricant exposed to the ambient, the side surfaces of the lubricant can be assumed thermally insulated as: = 0

The Lubricant-Bearing Interface
The solution of temperature field in the solid bearing zone is linked to the temperature distribution in the fluid film through the surface of the interface between the two zones as follows: Where the temperature and heat transfer coefficient on the inner bearing surface & ℎ , are implicitly computed from the conjugate heat transfer rate between the fluid film field and the solid bearing zone.

Governing equations of the solid zone (bearing)
For the solid domain, the partial differential equations governing can be described using the second law of motion (

Hydrodynamic boundary conditions of the solid zone (bearing)
The solid bearing is exposed to an internal pressure load resulting from the lubricant flow field, while the external wall is considered to be fixed. Furthermore, the side boundaries are maintained free-loaded. Thus, the boundary conditions used are as shown in Fig. 5: D-At the journal bearing edges; = ± 2 → = 0 E-At the inner surface of bearing; = → = p( , ) (15) F-At the outer surface of bearing; = → = 0

Thermodynamic boundary conditions of the solid zone (bearing)
The thermal conditions that are required to bound the solid energy equation are divided into two types according to the region where they are applied to. The first type is the one that is applied over the inner surface of the bearing, which has already been stated before, i. e. Eq. 13. The other sort is applied over the outer and side surfaces of the bearing, which are subjected to free convection heat transfer as:

NUMERICAL ANALYSIS
The partitioned one-way coupling is employed in the fluid-solid interaction present. The fluid film pressure is first computed using the well-known ANSYS Fluent CFD commercial code. It is then transferred to the ANSYS Static Structure solid solver to compute the deformation and stress resulting in the solid bearing zone. Both fluid film and solid bearing zones have been discretized into a number of hexahedral elements, as shown in Fig. 6. The solution method used for CFD simulation is based on the second-order upwind differencing scheme. The discretized equations for the lubricant flow field have been solved iteratively according to the SIMPLE algorithm (Versteeg and Malalasekera, 2007). A user-defined UDF code has been written and compiled into ANSYS Fluent solver to compute the temperature-dependent lubricant viscosity, Eq. 5, and determine the lubricant temperature at the inlet boundary, Eq. 8, as well as the shaft surface, Eq.9. The grid dependency was checked for three sets of the film and solid mesh to examine the sensitivity of the results computed to the number of grid divisions along each of the physical coordinates, i.e., radial ni, circumferential nj, and axial n_k. In general, it has been observed that the number of divisions along the radial direction ni dominates the accuracy of the solution obtained, unlike the number of divisions along with the other two directions, i.e., nj or n_k, which have no noticeable impact, as shown in Table 1. A mesh grid size of (ni =2, nj =400, n_k =600) is considered for fluid flow zone. The maximum aspect ratio ranges from 9 to 57, minimum orthogonal quality ranges from 0.68 to 0.99, and maximum ortho-skew ranges from 0.0003 to 0.2.

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For the bearing zone, a grid size of (ni =10, nj =400, n_k =600) is considered, the aspect ratio equals 1.20 with minimum orthogonal of 0.999 and maximum ortho-skew of 4.44*10-3. Accordingly, for all the simulations to be carried out, the selected grid dimensions result in a reasonable mesh quality in the current investigation.  Due to the lack of research presented in the field of scratched partial journal bearings, the methodology adopted in the present work has been validated against the numerical data computed by (Dobrica and Fillon, 2012) regarding the thermo-hydrodynamic performance of a scratched partial journal bearing. The focus is to inspect the hydrodynamic and thermal patterns while operation for five journal bearings of different scratch depth ( =0, C/8, C/4, C/2, and C), as in Fig. 8, where the design parameters regarding the cases tested are detailed in Table 2. The lengthdiameter ratio (L/D) equals (0.77) and the clearance -radiusratio (C/R) equals (0.0016). The journal operates at 1500 rpm, and the ISO VG 32 oil is supplied at 40ᵒC. A global thermal model is used to account for oil heating due to viscous effects. It is supposed that 30% of the oil is supplied at 40ᵒC, and 70% of the flow is recirculating. The oil used density is set to 860 kg/m 3 and its dynamic viscosity to 0.03 Pa.s. The pressure profile variation along the journal pad is generally in agreement with that presented by (Dobrica and Fillon, 2012). However, there is a significant mismatch in the values of maximum pressure computed, especially in the cases where deep scratches have been applied, i.e. ≥ C/2. This is attributed to the fact that the model solved by (Dobrica and Fillon, 2012) is not complete and includes many approximations that may have led to serious overestimations in the pressure produced. Due to the 2-dimensionality of the model adopted, no considerations have been given to the thermal conditions at the bush and journal surfaces, where 15% of the heat generated due to friction was assumed to be dissipated by the bush and journal surfaces, while the rest to be carried away by the lubricant. On the other hand, the current simulation considers more advanced procedures. A three-dimensional solution has been conducted based on more realistic boundary conditions applied, whether on the bush and journal surfaces or at the inlet and outlet sections of the bearing.

RESULTS AND DISCUSSION
The effect of the circumferential scratches spread on the entire bearing surface, even if they are relatively thin and only represent a small amount of the total bearing width, which may lead to the destruction of the bearing. The dimensions of scratched partial journal bearing considered in the current analysis are detailed in Table 2.  In light of these results, scratch depth is actually shown as the main parameter governing scratch effects: in the case of a smooth surface (ℎ = 0 ) In other words, no scratches on the entire bearing surface, where the maximum pressure developed in fluid film thickness, is shown in Fig.9(a). Surface scratches (ℎ =0.125 ) and (ℎ =0.25 )have almost no large effect on bearing performance, as in Fig .9(b, c). As the scratch depth equals half value from radial clearance (ℎ =0.5 ) have destructive effects, as shown in Fig.9(d). At last, the deeper scratch equal to radial clearance (ℎ = ) the pressure distribution on the bearing surface has been severely affected, where extremely high-pressure levels are generated, as shown in Fig.9(e). This is due to the increased flow of oil in the scratch areas, which has a cooling effect. In fact, at the same deflection (and hence the same minimum film thickness), the scratched bearing will generate a much higher oil flow rate than the non-worn bearing, thus operating at a lower temperature (but also providing a lower bearing capacity).  Fig .10 shows the relation between scratch depth and thermo-hydrodynamic oil film pressure for both smooth and the scratch surface where the maximum static pressure found at the scratch depth equal to radial clearance (ℎ = ). Fig .11 shows the static oil film temperature for smooth and scratch surface where the maximum static temperature found at the scratch depth equal to radial clearance (ℎ = ). Fig. 12. shows the temperature distribution on oil film for arc bearing.  As temperature levels rise due to heat generated by friction in the film layer, the solid bearing zone undergoes a thermal expansion varying locally according to the temperature gradients found at each spot of the bush. The bearing's inner surface is exposed to deformation due to the oil film   Due to that thermal deformation, the bearing is further stressed due to the temperature gradients generated. The wear deformation is always throughout the model. The occurrence of failure and was not taken into account, but the purpose is to calculate the stress only, as shown in

CONCLUSIONS
The remarks concluded are as follows: 1-For a scratched journal bearing with a small scratch depth, i.e. ℎ = 8 ⁄ , the pressure is slightly affected. On the other hand, the performance is severely affected at deep scratches, i.e. ℎ = , where the bearing is likely subjected to complete damage due to severe mechanical and thermal loads concentrated on certain spots. 2-In scratched journal bearings, the maximum pressure developed in the oil is significantly affected by the extent of scratches depth. At a small depth of scratches, i.e. ℎ = 8 ⁄ , the pressure has been marginally affected compared to the deeper scratches, i.e. ℎ = 2 ⁄ , where the pressure is significantly increased. Similarly, the deepest scratches, i.e. ℎ = , result in severe effects on the pressure distribution on journal bearing surface where the pressure can be of destructive levels at certain spots. 3-The maximum deformation is generated at maximum pressure when the scratch depth equals the clearance value(ℎ = ). 4-The stresses are generated at maximum pressure when the scratch depth equals to the clearance value(ℎ =C).