Oil film fluid domain geometric segmentation method considering oil cavity structure
By constructing an oil film fluid domain model of the oil cavity structure and performing multi-stage segmentation, the problem of the oil cavity's influence not being considered was solved, and accurate simulation of the oil film pressure distribution was achieved, thus improving the theoretical support for the oil cavity structure design and the operational reliability of the oil film bearing.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TAIYUAN HEAVY IND
- Filing Date
- 2026-01-28
- Publication Date
- 2026-06-09
AI Technical Summary
Existing technologies do not fully consider the effects of low eccentricity and large offset angle when simulating the oil cavity structure of oil film bearings. This results in a large deviation between the simulation results and the actual working conditions, and fails to accurately reflect the distribution of oil film pressure, thus affecting the rationality of the oil cavity structure design and the load-bearing capacity of the oil film bearing.
An oil film fluid domain geometric segmentation method considering the oil cavity structure is adopted. By constructing a fluid domain model with oil cavity geometric features and performing multi-stage progressive geometric segmentation, the core region with oil cavity features and the auxiliary region without oil cavity are divided to meet the requirements of structured grid discretization and obtain oil film pressure distribution data.
It achieves accurate replication of the geometric features of the oil cavity, improves the accuracy and efficiency of simulation calculation, provides theoretical support for the optimized design of the oil cavity structure, and enhances the operational reliability and load-bearing capacity of the oil film bearing under low eccentricity conditions.
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Figure CN122174431A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of oil film bearing technology, and particularly relates to a method for geometric segmentation of the oil film fluid domain taking into account the oil cavity structure. Background Technology
[0002] In the production of narrow strip steel, the final two rolling processes of the finishing mill place extremely high demands on the equipment's operational precision and stability. As a core component of the finishing mill, the oil film bearing's load-bearing capacity and operational reliability directly determine the quality of the rolled products and production efficiency. The working principle of an oil film bearing is to achieve lubrication and load bearing through an oil film formed between the journal and the bushing. The distribution of oil film pressure is a key factor affecting the bearing's load-bearing capacity, and this distribution is closely related to the bearing's eccentricity and offset angle.
[0003] The eccentricity of a bearing is determined by both its operating speed and load. When the finishing mill operates at high speed and low load, the bearing exhibits a low eccentricity, and the misalignment angle increases significantly. Under this specific condition, the geometry and location of the oil cavity within the bearing bushing have a significant impact on the formation and pressure distribution of the oil film, thus directly affecting the load-bearing capacity of the oil film bearing.
[0004] However, existing technologies for simulating and analyzing the oil film pressure distribution in oil film bearings do not fully consider the influence of the oil cavity structure under low eccentricity and large offset angle conditions. Traditional fluid domain modeling and segmentation methods often ignore the geometric features of the oil cavity or only process simple fluid domains without an oil cavity, resulting in significant deviations between simulation results and actual operating conditions, failing to accurately reflect the true distribution of oil film pressure. This technical deficiency directly leads to a series of problems: on the one hand, it is impossible to effectively verify the rationality of the geometric parameter design of the oil cavity, causing the oil cavity structure design to rely heavily on empirical judgment and lack precise theoretical support; on the other hand, it is difficult to optimize the oil cavity structure through simulation analysis, resulting in the oil film bearing's load-bearing capacity not being fully utilized under low eccentricity conditions, insufficient operational reliability, and even the possibility that an excessively large oil cavity area may affect the load-bearing performance of the oil film bearing at high speeds. Summary of the Invention
[0005] To address some or all of the technical problems existing in the prior art, this application provides a method for geometric segmentation of the oil film fluid domain that takes into account the oil cavity structure.
[0006] This application provides a method for geometric segmentation of the oil film fluid domain considering the structure of the oil cavity, including the following steps: Step S1: Construct an oil film fluid domain model containing the geometric features of the oil cavity. The model includes an eccentric oil film region formed by the bearing bushing and the journal, an eccentric oil cavity region, and an equivalent oil hole region, which together constitute a closed fluid domain. Step S2: Based on a preset benchmark, perform multi-stage progressive geometric segmentation on the fluid domain model, sequentially dividing the core region containing oil cavity features and the auxiliary region without oil cavity features; Step S3: By segmenting, each region meets the requirements of structured mesh discretization, and oil film pressure distribution data under low eccentricity conditions is obtained through simulation.
[0007] Preferably, in step S1, the construction of the fluid domain model includes: first, creating an eccentric circular oil film structure and stretching it along the length of the bushing to form a basic oil film fluid domain; then, stretching the closed area enclosed by the bushing inner hole and the eccentric oil cavity along the length of the oil cavity to form an eccentric oil cavity fluid domain; finally, stretching to form an equivalent oil hole feature, so that the equivalent oil hole and the eccentric oil cavity fluid domain constitute a closed body.
[0008] Preferably, the multi-stage progressive geometric segmentation in step S2 includes a first segmentation: dividing the fluid domain model into an eccentric cylindrical volume region with an oil cavity structure and an equivalent oil inlet volume region along the outer circular surface of the eccentric oil cavity.
[0009] Preferably, step S2 further includes a second division: constructing a reference plane γ1 based on the center line of the outer circle of the bushing and the center line of the equivalent oil hole, and creating a reference plane γ2 by having the center line of the outer circle of the bushing and the reference plane γ1 form a 90° angle. The reference plane γ2 divides the eccentric cylindrical volume region into two semi-cylindrical volume regions with oil cavities.
[0010] Preferably, step S2 further includes a third division: constructing reference planes α1 and α2 perpendicular to the central axis of the outer circle of the bushing on both end faces along the length direction of the eccentric oil cavity, respectively, dividing the two semi-cylindrical volume regions into two side regions without oil cavities and a middle region containing complete eccentric oil cavities.
[0011] Preferably, step S2 further includes a fourth division: establishing two reference planes β1 and β2 through the outer circular axis of the fluid domain and the boundary line between the oil cavity and the outer circle, dividing the middle region containing the oil cavity into an eccentric region without the oil cavity and a core region containing the oil cavity.
[0012] Preferably, step S2 further includes a fifth division: establishing a reference plane γ3 through the midpoint of the volume region length and parallel to the horizontal projection plane, and the orthogonal reference plane formed by the reference plane γ1 and the reference plane γ3 divides the core region of the oil-containing cavity into multiple sub-regions.
[0013] Preferably, step S2 further includes a sixth division, in which reference planes δ1 and δ2 are created by the midpoints c1 and c2 of the oil cavity arc and the outer circular axis of the fluid domain, respectively. The core sub-region containing the oil cavity formed by the orthogonal division of reference plane γ1 and reference plane γ3 is further divided into several small volume sub-regions that conform to the contour of the oil cavity arc surface.
[0014] The oil film fluid domain geometric segmentation method considering the oil cavity structure in this application has the following advantages and positive effects: (1) It realizes the precise geometric segmentation of the oil film fluid domain in the oil cavity structure, fully preserves the geometric features of the oil cavity, solves the problem of large simulation deviation caused by ignoring the influence of the oil cavity in the existing technology, and makes the simulation of oil film pressure distribution under low eccentricity conditions more realistic.
[0015] (2) By using a multi-stage progressive segmentation strategy, all segmented regions can be adapted to structured mesh discretization, thereby improving the efficiency and accuracy of simulation calculations and providing accurate data support for the rationality verification of oil cavity geometric parameters.
[0016] (3) The simulation can clarify the influence of the oil cavity structure on the oil film pressure distribution and bearing capacity, provide a theoretical basis for the optimized design of the oil cavity structure, and thus improve the operating reliability and service life of the oil film bearing under low eccentricity conditions, and ensure the continuous and stable operation of the finishing mill. Attached Figure Description
[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for further understanding of the embodiments of this application and constitute a part of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 This is a schematic diagram of the structure of the oil film fluid domain model of this application; Figure 2 This is a schematic diagram of the geometric characteristic parameters of the oil cavity in this application; Figure 3 This is a schematic diagram comparing the bearing bushing length and the oil cavity length of this application; Figure 4 This is a schematic diagram of the fluid domain structure after the first segmentation in this application; Figure 5 This is a schematic diagram of the fluid domain structure after the second segmentation in this application; Figure 6 This is a schematic diagram of the fluid domain structure after the third segmentation in this application; Figure 7 yes Figure 6Enlarged view of point A; Figure 8 This is a schematic diagram of the fluid domain structure after the fourth division in this application; Figure 9 This is a schematic diagram showing the positions of reference plane β1 and reference plane β2 in this application; Figure 10 This is a schematic diagram of each region of the fluid domain after the fourth segmentation in this application; Figure 11 This is a schematic diagram of the side where the equivalent oil hole is located after the fourth division in this application; Figure 12 This is a schematic diagram of the fluid domain structure after the fifth division in this application; Figure 13 This is a schematic diagram of the fluid domain structure after the sixth division in this application; Figure 14 This is a comparison diagram of the oil film pressure under a low eccentricity parameter of 0.7, with and without considering the oil cavity structure.
[0018] Explanation of reference numerals in the attached figures: 1-Bearing bushing; 11-Second segmented volume region one; 12-Second segmented volume region two; 111-Third segmented volume region one; 112-Third segmented volume region two; 113-Third segmented volume region three; 121-Third segmented volume region four; 122-Third segmented volume region five; 123-Third segmented volume region six; 1121-Fourth segmented volume region one; 1122-Fourth segmented volume region two; 1123-Fourth segmented volume region three; 1221-Fourth segmented volume region four; 1222-Fourth segmented volume region five; 1223-Fourth segmented volume region six; 11221-Fifth segmented volume region one; 11222-Fiveth segmented volume region two 11223 - Fifth Division Volume Region III; 11224 - Fifth Division Volume Region IV; 12221 - Fifth Division Volume Region V; 12222 - Fifth Division Volume Region VI; 12223 - Fifth Division Volume Region VII; 12224 - Fifth Division Volume Region VIII; 122211 - Sixth Division Volume Region I; 122212 - Sixth Division Volume Region II; 122221 - Sixth Division Volume Region III; 122222 - Sixth Division Volume Region IV; 122231 - Sixth Division Volume Region V; 122232 - Sixth Division Volume Region VI; 122241 - Sixth Division Volume Region VII; 122242 - Sixth Division Volume Region VIII; 2 - Equivalent Oil Hole. Detailed Implementation
[0019] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.
[0020] like Figures 1 to 13 As shown, this application provides a method for geometric segmentation of the oil film fluid domain that takes into account the structure of the oil cavity.
[0021] In the attached diagram, each mark represents: a: the outer circular surface of the eccentric oil cavity; b: the end face of the oil cavity.
[0022] like Figure 1 As shown, bearing bushing 1 is a cylindrical hollow component with an inner bore adapted for journal mounting. An eccentric oil cavity is located on the inner wall, extending along the length of the bushing but shorter than its total length. This provides a closed space for oil film formation. Through the relative movement between the inner bore and the journal, the oil cavity facilitates oil film storage and pressure regulation. The equivalent oil hole 2 is a cylindrical closed region, centered along the length of the fluid domain. One end connects to the eccentric oil cavity fluid domain, forming a complete closed body. This serves as the channel for simulating oil entering the oil cavity, providing reasonable oil inlet boundary conditions for fluid domain simulation, ensuring the integrity of the oil flow path, and avoiding pressure calculation deviations caused by boundary condition distortion during simulation.
[0023] The specific steps for this application are as follows: Step S1: Construct an oil film fluid domain model with oil cavity geometry features. The model includes an eccentric oil film region formed by the bearing bushing 1 and the journal, an eccentric oil cavity region, and an equivalent oil hole 2 region, which together constitute a closed fluid domain.
[0024] like Figure 2 and Figure 3 As shown, the geometric features of the oil cavity are as follows, with specific parameters as follows: D: Inner diameter of bearing bushing; d: Journal (outer diameter of tapered sleeve); e1, e2: Eccentricity of oil cavity from center plane; R: Outer radius of oil cavity; L: Distance between equivalent oil hole 2 and center plane; L1: Length of oil cavity; L2: Length of bushing; D1: Diameter of equivalent oil hole 2.
[0025] First, an eccentric circular structure for the oil film is created. The outer diameter corresponds to the inner diameter of the bearing bushing 1, and the inner diameter corresponds to the diameter of the journal (outer circle of the tapered sleeve). The eccentricity is determined based on the inner radius of the bushing, the inner radius of the tapered sleeve, and the minimum oil film thickness. The eccentricity e1 of the oil film fluid domain is the difference between the inner radius of the bushing and the inner radius of the tapered sleeve and the minimum oil film thickness. The eccentric circular structure is stretched along the length of the bushing to form the basic oil film fluid domain. The stretching length of the eccentric circular fluid domain is the bushing length L2.
[0026] Next, a closed area is formed by using the boundary line between the inner hole of the bearing bushing 1 and the eccentric oil cavity as the boundary. This area is stretched along the length of the oil cavity to form the fluid domain of the eccentric oil cavity, ensuring that the geometric shape, position, size and other features of the oil cavity are completely replicated.
[0027] Finally, by stretching to construct the equivalent oil hole 2 feature, it is determined that the center of the equivalent oil hole 2 is located at the center of the fluid domain length direction. Its cross-sectional dimensions are designed so that the equivalent oil hole 2, after being stretched along the axis, forms a closed body with the eccentric oil cavity fluid domain, thus completing the construction of the entire fluid domain model. This ensures that the model includes the eccentric oil film region formed by the bearing bushing 1 and the journal, the eccentric oil cavity region, and the equivalent oil hole 2 region, which together constitute a complete closed fluid domain.
[0028] Step S2: As Figure 4 and Figure 13 As shown, based on a preset benchmark, the fluid domain model is subjected to multi-stage progressive geometric segmentation, which sequentially divides the core region containing oil cavity features and the auxiliary region without oil cavity features.
[0029] First segmentation: The fluid domain model is divided into two parts along the outer circular surface a of the eccentric oil cavity, namely the eccentric cylindrical volume region with oil cavity structure (including the core part of bearing bushing 1) and the equivalent oil hole 2 volume region, realizing the initial separation of the core working area and the oil inlet channel.
[0030] Second division: Based on the center line of the outer circle of the bushing and the center line of the equivalent oil hole 2, a reference plane γ1 is constructed. A reference plane γ2 is created at a 90° angle to γ1 through the center line of the outer circle of the bushing. The eccentric cylindrical volume region is divided into the second division volume region 11 and the second division volume region 12 along γ2. Both regions are semi-cylindrical volume regions with oil cavities.
[0031] Third division: Along the two end faces of the eccentric oil cavity, construct reference planes α1 and α2 perpendicular to the central axis of the outer circle of the bushing. Using these two planes as references, divide the second division volume region 11 into the third division volume region 111, the third division volume region 212, and the third division volume region 313. Similarly, divide the second division volume region 212 into the third division volume region 4121, the third division volume region 5122, and the third division volume region 6123. Among them, the third division volume region 212 and the third division volume region 5122 are the middle regions containing the complete eccentric oil cavity.
[0032] Fourth division: Establish reference planes β1 and β2 through the boundary line between the outer circular axis of the fluid domain and the oil cavity and the outer circle. Using these two planes as references, divide the third division volume region 2 112 into the fourth division volume region 1 1121, the fourth division volume region 2 1122, and the fourth division volume region 3 1123. Similarly, divide the third division volume region 5 122 into the fourth division volume region 4 1221, the fourth division volume region 5 1222, and the fourth division volume region 6 1223. Among them, the fourth division volume region 2 1122 and the fourth division volume region 5 1222 are the core regions containing the oil cavity.
[0033] Fifth division: Establish a reference plane γ3 through the midpoint of the length of the volume region and parallel to the horizontal projection plane. Using the orthogonal reference plane formed by the longitudinal direction of reference plane γ1 and the transverse direction of γ3, divide the fourth-divided volume region 2 1122 into the fifth-divided volume region 1 11221, the fifth-divided volume region 2 11222, the fifth-divided volume region 3 11223, and the fifth-divided volume region 4 11224. Similarly, divide the fourth-divided volume region 5 1222 into the fifth-divided volume region 5 12221, the fifth-divided volume region 6 12222, the fifth-divided volume region 7 12223, and the fifth-divided volume region 8 12224.
[0034] Sixth division: Reference planes δ1 and δ2 are created by connecting the midpoints c1 and c2 of the oil cavity arc with the outer circular axis of the fluid domain, respectively. The core sub-regions containing the oil cavity formed in the fifth division—namely, the fifth division volume regions 5 (12221), 6 (12222), 7 (12223), and 8 (12224)—are further divided. The fifth division volume region 5 (12221) is further divided into the sixth division volume regions 1 (122211) and 2 (122212). The fifth volume region 6 (12222) is divided into the sixth volume region 3 (122221) and the sixth volume region 4 (122222). The fifth volume region 7 (12223) is divided into the sixth volume region 5 (122231) and the sixth volume region 6 (122232). The fifth volume region 8 (12224) is divided into the sixth volume region 7 (122241) and the sixth volume region 8 (122242), ultimately forming multiple tiny sub-regions that conform to the contour of the oil cavity's arc surface.
[0035] Step S3: By segmenting, each region meets the requirements of structured mesh discretization, and oil film pressure distribution data under low eccentricity conditions is obtained through simulation.
[0036] like Figure 14 As shown, all the small volume sub-regions obtained from the sixth division are imported into the simulation software. Since the geometric boundaries of each sub-region are regular planes or surfaces of revolution, high-quality structured meshes can be generated quickly. Based on the divided mesh, simulation parameters such as oil properties, boundary conditions, loads, and rotational speed parameters are set to simulate the oil film flow state under low eccentricity conditions. The oil film pressure distribution data is obtained through calculation, and then the influence of the oil cavity structure on the oil film pressure and bearing load-bearing capacity is analyzed.
[0037] This application achieves significant technical results through a scientific segmentation strategy and a precise implementation process: This application is the first to fully incorporate the oil cavity structure into the segmentation and simulation of the oil film fluid domain, solving the simulation bias problem caused by neglecting the influence of the oil cavity in existing technologies. The segmented fluid domain can accurately replicate the geometric features of the oil cavity, and the adaptability of the structured mesh improves the accuracy of the simulation calculation, making the oil film pressure distribution results under low eccentricity conditions closer to the actual operating state, and providing reliable theoretical data for the performance analysis of the oil cavity structure.
[0038] The segmentation method proposed in this application can clearly distinguish between the core region and auxiliary region of the oil cavity, allowing the simulation to focus specifically on the key parts where the oil cavity is located. This improves computational efficiency while ensuring the computational accuracy of the core region. Designers can verify the rationality of the oil cavity's geometric parameters (shape, position, length, etc.) through simulation results, thus overcoming the blindness of traditional experience-based design and providing precise theoretical support for the design of the oil cavity structure of oil film bearings.
[0039] This application, through simulation analysis, clearly understands the influence of the oil cavity structure on the oil film pressure distribution and bearing load-bearing capacity, and then optimizes the geometric parameters of the oil cavity accordingly. The optimized oil film bearing exhibits significantly improved load-bearing capacity under low eccentricity and large offset angle conditions, enhanced operational reliability, effectively reduced premature bearing wear or failure caused by uneven oil film pressure distribution, ensured continuous and stable operation of the finishing mill, and ultimately improved the rolling quality and production efficiency of narrow strip steel.
[0040] It should be noted that, unless otherwise expressly specified and limited, the term "connection" or its synonyms should be interpreted broadly in this document. For example, "connection" can be a fixed connection or a detachable connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be the internal communication of two elements or the interaction between two elements. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances. Furthermore, expressions such as "first" and "second" are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. At the same time, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. In addition, the terms "front," "rear," "left," "right," "upper," and "lower" in this document refer to the placement states shown in the accompanying drawings.
[0041] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.
Claims
1. A method for geometrically segmenting the oil film fluid domain considering the structure of an oil cavity, characterized in that, Includes the following steps: Step S1: Construct an oil film fluid domain model containing the geometric features of the oil cavity. The model includes an eccentric oil film region formed by the bearing bushing and the journal, an eccentric oil cavity region, and an equivalent oil hole region, which together constitute a closed fluid domain. Step S2: Based on a preset benchmark, perform multi-stage progressive geometric segmentation on the fluid domain model, sequentially dividing the core region containing oil cavity features and the auxiliary region without oil cavity features; Step S3: By segmenting, each region meets the requirements of structured mesh discretization, and oil film pressure distribution data under low eccentricity conditions is obtained through simulation.
2. The method for geometric segmentation of the oil film fluid domain considering the oil cavity structure according to claim 1, characterized in that, In step S1, the construction of the fluid domain model includes: first, creating an eccentric circular structure of oil film and stretching it along the length of the bushing to form a basic oil film fluid domain; then, stretching the closed area enclosed by the bushing inner hole and the eccentric oil cavity along the length of the oil cavity to form an eccentric oil cavity fluid domain; finally, stretching to form an equivalent oil hole feature, so that the equivalent oil hole and the eccentric oil cavity fluid domain constitute a closed body.
3. The method for geometric segmentation of the oil film fluid domain considering the oil cavity structure according to claim 1, characterized in that, The multi-stage progressive geometric segmentation in step S2 includes the first segmentation: dividing the fluid domain model into an eccentric cylindrical volume region with an oil cavity structure and an equivalent oil inlet volume region along the outer circular surface of the eccentric oil cavity.
4. The method for geometric segmentation of the oil film fluid domain considering the oil cavity structure according to claim 3, characterized in that, Step S2 also includes a second division: a reference plane γ1 is constructed based on the center line of the outer circle of the bushing and the center line of the equivalent oil hole. A reference plane γ2 is created by the center line of the outer circle of the bushing and the reference plane γ1 forming a 90° angle. The reference plane γ2 divides the eccentric cylindrical volume region into two semi-cylindrical volume regions with oil cavities.
5. The method for geometric segmentation of the oil film fluid domain considering the oil cavity structure according to claim 4, characterized in that, Step S2 also includes a third division: construct reference planes α1 and α2 perpendicular to the central axis of the outer circle of the bushing on both end faces along the length of the eccentric oil cavity, and divide the two semi-cylindrical volume regions into two side regions without oil cavities and a middle region containing complete eccentric oil cavities.
6. The method for geometric segmentation of the oil film fluid domain considering the oil cavity structure according to claim 5, characterized in that, Step S2 also includes a fourth division: establishing two reference planes β1 and β2 through the outer circular axis of the fluid domain and the boundary line between the oil cavity and the outer circle, dividing the middle region containing the oil cavity into an eccentric region without the oil cavity and a core region containing the oil cavity.
7. The method for geometric segmentation of the oil film fluid domain considering the oil cavity structure according to claim 6, characterized in that, Step S2 also includes a fifth division: a reference plane γ3 is established through the midpoint of the volume region length and parallel to the horizontal projection plane. The orthogonal reference plane formed by the reference plane γ1 and the reference plane γ3 divides the core region of the oil-containing cavity into multiple sub-regions.
8. The method for geometric segmentation of the oil film fluid domain considering the oil cavity structure according to claim 7, characterized in that, Step S2 also includes a sixth segmentation, in which reference planes δ1 and δ2 are created by the midpoints c1 and c2 of the oil cavity arc and the outer circular axis of the fluid domain, respectively. The core sub-region containing the oil cavity formed by the orthogonal segmentation of reference plane γ1 and reference plane γ3 is further segmented into several small volume sub-regions that conform to the contour of the oil cavity arc surface.