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Oct 14, 2024

A novel design of journal bearings for stability under shock loads | Scientific Reports

Scientific Reports volume 14, Article number: 22577 (2024) Cite this article 221 Accesses Metrics details Mechanical systems are expected to operate under various load conditions, and it is necessary

Scientific Reports volume 14, Article number: 22577 (2024) Cite this article

221 Accesses

Metrics details

Mechanical systems are expected to operate under various load conditions, and it is necessary to use a lubrication system to achieve reliability and stable performance. Journal bearings, which are used to achieve such stable lubrication, are representative of hydrodynamic lubrication bearings. In this study, groove-shaped structures and rubber were applied to the ends of the bearings to ensure stable lubrication performance under conditions where, for various reasons, shock loads are applied in addition to static loads under misaligned conditions. The groove structure and rubber contribute to stable lubrication performance by preventing contact between the shaft and bearing as well as absorbing shock loads through elastic deformation of the groove’s end due to oil film pressure. This novel design, which utilizes groove-type flexible structures and rubber, led to journal bearings that exhibited improved lubrication performance under various shock load conditions. When a shock load is applied to a mechanical system, the design proposed in this study contributes to improving the reliability of the mechanical system by enhancing its lubrication performance.

Among the numerous factors that cause breakdowns in mechanical systems, bearing malfunction stands out as the predominant issue, constituting 30 to 40% of all system failures1,2. This underscores the significance of implementing design or management strategies aimed at diminishing the occurrence of bearing failures, which is crucial for achieving efficient operation and maintenance (O&M) of mechanical systems. Rotating machinery commonly incorporates a vital component that is referred to as hydrodynamic journal bearings. These bearings comprise a fixed cylindrical unit that houses the rotating journal, which operates at a specific speed. Journal bearings mainly support the static load applied by the weight of the shaft among other sources, but they also receive shock loads caused by various other causes.

Shock refers to a brief force that is exerted over a short duration, which is typically less than the natural time period of the system it affects. In mechanical terms, it can be described as a sudden alteration in velocity, and it constitutes a significant consideration in the design of various systems and their constituent parts3. A shock load exerted on a structure triggers a dynamic amplification phenomenon that is influenced by the mass, damping, and stiffness of both the structure and the object applying the load4. In simpler terms, a shock load denotes a sudden and potentially damaging surge in weight that is akin to a “hammering effect.” Therefore, there is a need for an appropriate design method to provide stable lubrication against shock loads in journal bearings.

Even slight deviations in alignment between shafts and bearings—which can be caused by manufacturing discrepancies, off-center loads, or shaft deformations—can alter the distribution of the oil film. This misalignment results in fluctuations in oil-film pressure, load-carrying capacity, and frictional force within the bearing. Moreover, insufficient operational precision can prompt unwanted shaft vibrations5,6. Misalignment also adversely impacts the lubrication performance of journal bearings.

In terms of research methodology, existing investigations have encompassed several numerical studies7,8,9,10,11,12,13,14,15, experimental inquiries16, and a fusion of numerical analysis with experimental investigations17,18,19. Meanwhile, research efforts aiming to enhance this misalignment included approaches that involve refining the lubricant properties20, implementing profiles20,21, utilizing advanced materials22,23, and employing flexible structures12,13,24,25. In particular, the application of flexible structures to misaligned journal bearings has been shown to improve the lubrication characteristics under static loading conditions12 as well as under the influence of both static loads in the gravitational direction and shock loads13. However, under extreme operating conditions, contact occurs in existing journal bearings; this contact can be prevented with a flexible structure. However, the minimum oil film thickness is very small, resulting in unstable lubrication against shock loads. There is therefore a need for a novel design to address this problem.

Rubber exhibits unique characteristics in its response to mechanical deformation when compared to other materials. It can undergo substantial deformation under tension, compression, or torsion, and it can almost fully recover its original shape. Additionally, rubber possesses energy-absorbing properties26. Taking advantage of these properties of rubber, the current study attempted to apply rubber to the ends of journal bearings to improve their lubrication characteristics under impact load conditions.

This research introduces a design strategy aiming to enhance the lubrication properties within misaligned journal bearings when subjected to shock loads from different directions alongside static loads. A numerical investigation was conducted to enhance lubrication performance, which incorporated a flexible structure capable of elastic deformation under oil film pressure at the bearing’s end, along with rubber.

To achieve the aims of the present work, it is necessary to conduct an elasto-hydrodynamic lubrication (EHL) analysis because the bearing surface undergoes elastic deformation due to oil film pressure in the groove-shaped flexible structure of the journal bearing. Journal bearings become misaligned due to shock, etc., which causes meatal-to-metal contact between the shaft and the end of the bearing, as shown in Fig. 1a. This contact causes wear and eventually leads to breaks or seizures. However, as has been done in previous studies, a groove-shaped flexible structure is applied to prevent contact caused by elastic deformation of the groove, as shown in Fig. 1b. The analysis was conducted under the condition that static load and impact load only act in the direction of gravity. In this study, we aim to prevent contact and improve lubrication performance by applying rubber along with a flexible structure, as shown in Fig. 1c. Figure 1c depicts a design in which rubber is inserted into both ends of the journal bearing. In Fig. 1c, the rubber (rubber-1) is located in the middle of the bearing area between the groove and the lubricant; its thickness is tr and its length is inserted as the length of the groove area (lf). Moreover, as can be seen in Fig. 1c, a represents the thickness of the bearing area between the groove and the lubricant, while a1 represents the height of the groove area.

(a) Metal-to-metal contact in misaligned journal bearing. (b) Non-contact by applying in flexible structure in misaligned journal bearing. (c) Non-contact by applying a flexible structure and rubber in misaligned journal bearing.

For this analysis, the dimensionless Reynolds equation in a cylindrical coordinate system was applied as shown in Eq. (1).

where the dimensionless variables are follows, with pa representing the atmospheric pressure:

O1 and O2 represent the shaft centers that are located at both ends of the bearing. In Fig. 2b and c, two circles depict cross-sections of the shaft projected onto the x-y plane, with O1 and O2 as their respective centers. The eccentricity ‘e’ represents the distance on the x-y plane between O and the bearing center (Ob). The angle ‘ψ’ on the x-y plane indicates the altitude angle between the load direction and the straight line passing through O and Ob. The tilting direction of the shaft aligns with θw and the tilting amount ‘e’’ equals half the distance between O1 and O2 on the x-y plane13.

The dimensionless equation for oil film thickness is shown in Eq. (3).

where the dimensionless variables are:

In Eq. (4) above, parameters ε and ε′ signify the eccentricity and tilting ratios of the shaft, respectively.

Moreover, c represents the clearance when the shaft and the bearing are in concentric state, and he represents the variation in oil film thickness due to elastic deformation. In other words, the film thickness varies due to the eccentricity of the shaft and the applied load, resulting in the generation of oil film pressure based on this changed film thickness. This pressure induces deformation of the lubricated surface of bearing. The calculation couples the film pressure with the deformation of the lubricated surface. Here, he represents the oil film thickness due to elastic deformation.

The oil film force, which is labeled as fo, originates from the oil-film pressure illustrated in Fig. 2a.

The dimensionless components of the oil film force in x and y directions, which are respectively named FOX and FOY, were determined using Eqs. (5) and (6), respectively. The oil-film force was computed using Eq. (7).

where the dimensionless variables are as follows:

where fox, foy are components of the oil film force in the x and y directions, respectively, fo is the oil film force, r is the radius of bearing, η is absolute viscosity of the lubricant and ω is the angular velocity of bearing.

(a) Schematic of misaligned journal bearing (x-y plane). (b) Shaft in bearing with eccentric and tilted motion (x-y plane). (c) Shaft in bearing with eccentric and tilted motion (y-z plane).

A hexahedral mesh was applied to the finite element model for a journal bearing. The preference for a hexahedral mesh in numerical calculations stems from its superior resolution and faster processing when compared to a tetrahedral mesh27. Moreover, an appropriate mesh level based on the journal bearing analysis conducted in a previous study13 was applied. The analysis employed 208 elements in the circumferential direction and 54 elements in the axial direction, aside from the groove region and rubber region, where 12 and 8 elements were used in the axial direction, respectively. This resulted in a total element count of 558,240. The convergence criteria were set at a value of 10− 3 for continuity, velocity, and deformation. The convergence criterion used is not very stringent. Based on previous numerical analyses12,13, comparing results with a convergence criterion of 10− 5, the difference in minimum film thickness was within 5%. Therefore, in terms of the numerical analysis to verify the improvement in lubrication characteristics, a convergence criterion of 10− 3 was applied.

In addition, calculations for the pressure of the oil film and the elastic deformation of the lubrication surface are performed based on the initial states of each interface at time zero. The calculation method involves the time implicit approach and utilizes the Newton-Raphson method for computation. Once converged values are computed at time zero, consecutive analyses are conducted for the interpretation of load magnitude variations over time. During this process, convergence happens when the difference in oil film thickness compared to the previous step is less than 10− 3, after which the force exerted by oil film pressure is calculated. If it differs from the given load, the attitude angle and axis eccentricity are updated, and the process iterates to recalculate the oil film thickness. When the force due to oil film pressure equals the applied load, calculations for the next step are performed.

It is necessary to use appropriate boundary conditions to solve the Reynolds equation (Eq. (1)). The dimensionless boundary conditions applied to the analysis are as follows.

The dimensionless pressure condition at the bearing ends and oil feeding hole is as shown in Eq. (9).

where Pb is defined as in Eq. (10)

The boundary conditions of the pressure in the cavitation region and the pressure in the oil film rupture region are shown in Eqs. (11) and (12), respectively.

where the direction of n is perpendicular to the oil film fracture boundary line.

Moreover, the displacement at the inner end of the flexible structure is as shown in Eq. (13).

where U(u/r) is dimensionless displacement and Lf is dimensionless length of the flexible structure.

Further, the geometries of the journal bearing, the flexible structure, rubber are represented by dimensionless parameters as specified in Eq. (14).

where l is the length of the bearing.

Bearing steel was used as the material for the bearing, while the rubber used in the analysis had elastic moduli of 1 MPa, 10 MPa, and 100 MPa along with a Poisson’s ratio of 0.5. Since the elastic modulus of rubber ranges from approximately 1 MPa to 100 MPa, three types of elastic moduli were applied. The dimensionless elastic modulus of the bearing (E*) and rubber (Er*) used in the analysis are given in Eq. (15).

where E and Er are the elastic moduli of bearing and rubber, respectively.

There was no slippage between the rubber and bearing materials; instead, perfect contact conditions were applied. In other words, in the area where rubber was inserted into the bearing, elastic deformation analysis was conducted using the elastic modulus and Poisson’s ratio properties of the rubber.

The software (COMSOL) employs a finite element method to transform the nonlinear governing equations into algebraic equations that can be iteratively solved. In the numerical analysis, the hydrodynamic bearing module is used to analyze hydrodynamic lubrication, the solid mechanics module is used to study the elastic deformation of the bearing, and the solid-bearing coupling module facilitates interaction between these two modules.

In this analysis, a study was conducted on the conditions in which both static load and shock load were applied to the journal bearing, as shown in Fig. 3a. The static load and shock load were applied in the direction of gravity. As illustrated in Fig. 3b, the static load was applied as a constant value, while the shock load was applied in a sine function attenuating form. Moreover, the maximum value of the shock load was twice the static load.

(a) Direction of static and shock loads. (b) Magnitude and type of static and shock loads.

The lubrication characteristics were evaluated after the design was improved by applying a groove-type flexible structure to the end of the journal bearing and inserting rubber under operating conditions where a shock load was applied in addition to the static load. When the given shock load reaches its maximum and the static load and shock load act together, the total load becomes three times the static load. These conditions lead to contact between the shaft and bearing. However, when only the flexible structure is applied, contact does not occur, but a sufficient oil film is not formed, which results in an unstable lubrication state. Figure 4 shows the analysis results obtained when the newly proposed design was applied to conditions with poor lubrication characteristics despite the application of a flexible structure in the previous study11. Figure 4a illustrates the dimensionless minimum film thickness across the entire analysis domain concerning the variation in Lg (the dimensionless thickness of the inserted rubber) and elastic modulus of rubber. With the same elastic modulus of rubber, an increase in Lg leads to an increase in the dimensionless minimum film thickness (Hm). This indicates that as the thickness of the inserted rubber increases, the bearing end deforms more readily due to oil film pressure, thus maintaining a stable lubrication state. Moreover, with Lg held constant, as the dimensionless elastic modulus of the rubber increases, the dimensionless minimum film thickness decreases. This can be attributed to the reduced likelihood of deformation occurring at the bearing end as the elastic modulus of rubber increases. Figure 4a also presents the rate of increase (∆) of the dimensionless minimum film thickness when both the flexible structure and rubber are applied together, using the dimensionless minimum film thickness when only the flexible structure is applied as the reference value. Under the design conditions highlighted in red (Lg = 0.5, Er* = 0.0763) in Fig. 4a, it can be seen that the minimum film thickness increases by approximately 15 times compared to when only the flexible structure is applied. This significant increase indicates a notable improvement in the lubrication situation. Among the analysis results, the design condition marked in blue (Lg = 0.2, Er* = 7.63 exhibits the smallest minimum film thickness. However, even in this scenario, the minimum film thickness is approximately five times larger than when only the flexible structure is applied. This underscores that employing a groove-type flexible structure and rubber at the end of the journal bearing enables stable lubrication even under static and shock load conditions.

Figure 4c and depict the dimensionless minimum film thickness and dimensionless maximum deformation with variations in dimensionless time for two cases: one where only the flexible structure was utilized, and the other where both the flexible structure and rubber were inserted. The result obtained when only the flexible structure is applied is represented by the black line. In this instance, compared to cases where both the flexible structure and rubber were incorporated, the maximum deformation was minimal, and the minimum film thickness was substantially smaller. This suggests that the groove-type flexible structure alone cannot ensure a sufficient oil film due to the limited deformation caused by the oil film pressure under conditions of applied shock load.

Meanwhile, examining the blue and black lines in Fig. 4c and d reveals that the maximum deformation is greater compared to when only the flexible structure is employed, thus leading to an increase in the minimum film thickness. This observation is supported by Fig. 4b, which shows significant deformation occurring at the end of the bearing. The graphs depicting the change in minimum film thickness and maximum deformation over time demonstrate that when the flexible structure and rubber are combined, elastic deformation due to oil film pressure occurs effectively, ultimately resulting in a larger oil film.

For practical applications, it is necessary to design a manufacturing process for inserting rubber into the bearing part and an effective method for bonding rubber and bearing steel.

(a) Dimensionless minimum film thickness across the entire analysis domain. (b) Dimensionless displacement at both ends of the bearing. (c) Dimensionless minimum film thickness with dimensionless time. (d) Dimensionless maximum displacement with dimensionless time.

The current work presented an effective design to provide stable lubrication under conditions of static and shock loads on misaligned journal bearings. By applying a groove-type flexible structure and rubber at the end of the journal bearing, elastic deformation easily occurs due to oil film pressure, thus preventing contact between the shaft and bearing, and ultimately forming a sufficient oil film. Moreover, rubber has various elastic moduli; for effective elastic deformation of journal bearings, it is beneficial to apply rubber with a small elastic modulus. Further, the thicker the applied rubber is, the more effective it is in forming a stable oil film. If applied to journal bearings with the newly proposed design in mechanical systems where impact loads frequently occur, it will contribute to improving the durability of bearings and mechanical systems.

Data is provided within the manuscript or supplementary information.

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This work was supported by the Korea Hydro & Nuclear Power Co. (2023) and Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) (No.20214000000010).

Department of Mechanical System Engineering, Dongguk University – WISE Campus, Gyeongju, 38066, Republic of Korea

Sung-Ho Hong

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H.S. wrote and reviewed the main manuscript.

Correspondence to Sung-Ho Hong.

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Hong, SH. A novel design of journal bearings for stability under shock loads. Sci Rep 14, 22577 (2024). https://doi.org/10.1038/s41598-024-73178-1

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Received: 10 May 2024

Accepted: 16 September 2024

Published: 29 September 2024

DOI: https://doi.org/10.1038/s41598-024-73178-1

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