CFD-based gear pump side plate end surface clearance lubrication characteristic simulation method

Abstract

The invention discloses a CFD (computational fluid dynamics)-based gear pump side plate end surface clearance lubrication characteristic simulation method. The method comprises the steps of 1, establishing a geometric oil film model; 2, performing grid division on the established geometric oil film model, and discretizing the model for subsequent calculation; 3, considering the lubrication condition in the gear pump, and establishing a lubrication model; 4, setting boundary conditions for the lubrication model, and determining external constraints of the model; 5, dispersing the model established in the step 3 on the grids in the step 2, and establishing an equation set; step 6, carrying out iterative calculation and solution on the established equation set to obtain a specific numerical result; step 7, performing force balance analysis according to a numerical result, and taking a force balance state as a convergence condition; and 8, visualizing a simulation result, and intuitively presenting an analysis result. The method has the advantages of being accurate in modeling and high in calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of simulation technology for lubrication performance of aviation fuel gear pumps, and specifically to a CFD-based simulation method for lubrication characteristics of the side plate end face clearance of a gear pump. Background Technology

[0002] As the most crucial component of an aero-engine fuel control system, the fuel pump's function is to supply fuel at a specific pressure and flow rate to the combustion chamber to meet thrust requirements under various operating conditions. External gear pumps, due to their simple structure, low specific mass, and strong anti-contamination capabilities, have been widely used as the main fuel pump in aero-engine fuel control systems. However, under long-term service conditions of heavy load, high speed, high temperature, and low viscosity, the lubrication effect of the gear pump's side plate friction pair significantly decreases, leading to direct metal-to-metal contact and excessive friction. Therefore, studying the lubrication characteristics of the gear pump's floating side plate will provide theoretical support and technical assurance for improving the gear pump's operational stability and long-term reliability.

[0003] Currently, scholars both domestically and internationally have developed a series of theoretical analysis and experimental verification methods for the lubrication characteristics of external gear pumps, especially for the lubrication characteristics of the oil film in the gap between the floating side plate of the gear pump and the gear end face.

[0004] Koc established a minimum film thickness calculation theory after theoretical and experimental analysis of the lubrication and sealing mechanism of the fixed-gap end plate of a high-pressure pump. This theory can predict the film thickness between the end plate and the gear end face. However, this theoretical method is based on the assumption that the lubrication gap of the side plate is fixed. In the actual operation of the gear pump, the gap between the floating side plate and the gear end face will be automatically adjusted according to factors such as pressure changes inside the pump to maintain good sealing performance and volumetric efficiency.

[0005] Internationally, Dwyer Joyce et al. proposed a time-of-fight (TOF) method to measure lubricating film thickness, utilizing the time difference between ultrasonic reflected waves. Domestically, Shanghai Jiao Tong University has developed oil film pressure measurement technology based on the Reynolds equation and piezoelectric thin-film sensors, using PVDF piezoelectric thin-film sensors to determine the pressure distribution at various points in the oil film. However, compared to this invention, these experimental methods and software simulation techniques are computationally expensive and time-consuming.

[0006] In summary, there is currently a very limited amount of available literature on the lubrication performance of the floating side plate end face gap in gear pumps, and a complete, detailed, efficient, and accurate modeling and simulation method is lacking. Summary of the Invention

[0007] To overcome the shortcomings of the existing technology, this invention proposes a simulation method for the lubrication characteristics of the side plate end face clearance of a gear pump based on CFD (Computational Fluid Dynamics). This method has the characteristics of accurate modeling and high computational efficiency.

[0008] The technical solution adopted in this invention is: A CFD-based simulation method for lubrication characteristics of gear pump side plate end face clearance includes the following steps; Step 1: Establish a geometric oil film model; Step 2: Mesh the established geometric oil film model to discretize it for subsequent calculations; Step 3: Consider the lubrication conditions inside the gear pump and establish a lubrication model; Step 4: Set boundary conditions for the lubrication model and define the external constraints of the model; Step 5: Discretize the model established in Step 3 on the grid from Step 2 and establish a system of equations; Step Six: Iterate and solve the established system of equations to obtain specific numerical results; Step 7: Perform force balance analysis based on the numerical results, using the force balance state as the convergence condition; Step 8: Visualize the simulation results to present the analysis results intuitively.

[0009] Step one specifically involves: CFD simulation first requires creating a geometric model of the gear pump. SolidWorks software is used to accurately model the shape of the side plate end face, the gear contact surface, and the oil film area on the end face. The geometric model includes the geometric features of the gear, side plate, and oil film area, ensuring consistency with actual operating conditions.

[0010] Step two specifically involves: After the geometric model is established, the computational domain (i.e., the oil film region in step one) is imported into ANSYS's ICEM module for mesh generation; the quality of the mesh is crucial to the accuracy and efficiency of the calculation results.

[0011] In the area of ​​the side plate end face, the mesh needs to be finer to ensure that details such as oil film thickness and pressure changes can be accurately captured; unstructured mesh technology is used, selecting local meshes with higher density and appropriately refining them in the gear edge area.

[0012] Step three specifically involves: To facilitate the calculation of the oil film thickness at any point in the lubrication gap, a rectangular coordinate system is established with the center of the drive gear as the origin; The oil film thickness calculation formula is derived from three specific points in this coordinate system (in principle, any three points can be chosen, although the final equations will differ slightly, but the oil film thickness at each point can still be derived). Plus, take a little bit Based on the necessary and sufficient condition that the mixed product of the four points is zero, we obtain: Further refinement yields the formula for calculating the oil film thickness at any point in the region: in, This indicates the distance between the centers of the two gears. Given the gear tip circle radius, and assuming both gears have identical geometry, the oil film thickness is determined based on three specific points on the gear pair, plus a set of positional information. The oil film thickness at that point is calculated. For the simplified continuity equation with respect to By integrating and combining with the Navier-Stokes equations, the general form of the Reynolds governing equations for fluid flow in the side plate lubrication gap is derived: in and These represent the density and dynamic viscosity of the medium oil, respectively. For gradient operators, Indicates the pressure distribution of the oil film. The oil film thickness distribution will be derived later using geometric and mathematical principles; therefore, the gradient of the oil film thickness can also be explicitly solved. It is the extrusion speed of the side plate's axial movement. and These represent the velocities of the upper and lower surfaces of the lubricating oil film, respectively. In calculations, it is generally assumed that... , It is equal to the rotational speed of the gear. Therefore, the equation simplifies to, Furthermore, based on the quasi-static assumption—that the system changes sufficiently slowly, and can be approximated as being in static equilibrium at every instant—and temporarily ignoring the change in oil film thickness over time, the equation can be written as follows: Step four specifically involves: Solving any ordinary differential equation or partial differential equation depends on given boundary conditions. For diffusion problems, there are Dirichlet, Neumann, mixed, and symmetric boundary condition types. Using Dirichlet boundary conditions, the unknowns at the boundary are directly given. The value of the boundary element surface is treated the same as that of the internal element surface. When the surface vector does not overlap with the line connecting the centroid of the element and the boundary surface, the cross-diffusion term should be considered. in The surface vector of the mesh boundary is decomposed into two vectors: an orthogonal term and a cross-diffusion term. and The sum of, It is the pressure gradient on the boundary surface. These are the boundary surfaces and the main cells, respectively. The pressure value on top, This represents the distance vector from the cell center to the boundary surface. The cross-diffusion term is moved to the right side of the algebraic equation and treated as a source term. Step five specifically involves: Based on the mesh generation in step two and the lubrication model established in step three, the lubrication model is discretized on the mesh in this step to establish a discrete set of equations. For the diffusion term, apply Gauss-Green's formula to transform the volume integral into a surface integral: For unstructured meshes, surface vectors Vectors that may be connected to the centroids of coplanar units They are not collinear, if we use Indicates along the point and points The unit vector in the direction of the line, then therefore, The gradient in the direction is written as To achieve flux linearization in non-orthogonal grids, surface vectors It should be written as two vectors and The sum of, i.e. The contribution of the first term on the right-hand side of the above equation is similar to that in orthogonal meshes; the second term, called the cross-diffusion term, is due to the non-orthogonality of the mesh. According to... Depending on the direction of decomposition, there are multiple existing methods to... Decomposed into and The most stable over-relaxation method is employed, maintaining stability even when the mesh height is non-orthogonal; the gradient in the cross-diffusion term... The current gradient field is used for calculation and added as a source term to the right side of the algebraic equation to achieve the purpose of delaying the diffusion term; Green's formula is often used to calculate the gradient of a cell. in Let be the surface vector pointing outwards. Applying the mean value theorem, we obtain the relationship between the integral term on the left-hand side of the above equation and the average gradient over the volume. The integral term on the right-hand side approximates the integral on the unit surface by multiplying the value at the centroid of the unit surface by the area of ​​the unit surface. ,unit The pressure gradient on the surface is expressed as: The gradient value at the interface is obtained by taking the weighted average of the pressure gradients on both sides of the interface: in and Let be the geometric interpolation factor, and let be the sum of 1. Its value is related to the element surface. Distance from the center point of the unit and The distance is related; regarding the discretization of the source term, the source term is related to the pressure. Values ​​are independent; for a control volume, it can be written as: in For cells The average oil film thickness gradient on the surface For cells The speed at which it is measured. Step six specifically involves: Based on the discretization of the above model, the form of the discrete equation is obtained as follows: Taking a discrete cell as an example, it is called the master cell using a subscript. This indicates that its three neighboring cells are represented by subscripts. This means, therefore These represent the pressure values ​​in the main cell and the three adjacent cells, respectively. They also represent the oil density and viscosity. The oil film thickness value at the midpoint of each face in the main cell. Indicates the volume of the main cell; By organizing the pressure values ​​on the grid nodes, the discrete equation is obtained as follows:

[0013] There are many methods for solving this system of algebraic equations, such as Cramer's rule, Gaussian elimination, matrix decomposition, and iterative methods (Jacobi iteration, Gauss-Seidel iteration), etc. The specific method chosen for the problem can yield the oil film thickness distribution and pressure distribution in the gap between the side plate end faces.

[0014] Step seven specifically involves: Based on the pressure distribution, a force analysis is performed on the gear pump side plate to determine whether the force balance criterion is met. If the force is unbalanced, the oil film thickness change rate is updated using the Powell hybrid root-finding algorithm until the force balance criterion is met. The Powell hybrid quadrature algorithm operates as follows: Initialization: Select a starting point (i.e., a set of initial values) and set n direction vectors (usually unit vectors), such as two unit vectors (0, 1) and (1, 0) in a two-dimensional problem. Perform a one-dimensional search along each direction vector to find the descent step size that reduces the objective function by the most along that direction, and update the position. Check if the new position reduces the function value; if it does, retain the new direction; otherwise, replace the direction with the direction of the old position. After completing one round of searching in n directions, connect the initial point and the endpoint of this round of searching to form a new direction. Replace the first direction in the original direction group with this new direction to form the direction group for the next round of iteration. Repeat the search for multiple rounds of iteration. When the preset maximum number of iterations is reached, or the change in the objective function value is less than a certain minimum threshold, or the change in position is less than a specified threshold, the iteration stops, and the point obtained is considered to be the approximate optimal solution.

[0015] Next, the equation for the rate of change of oil film thickness is quadrated to find the instantaneous value of the gap height at three points. Substituting this value into the oil film thickness model yields the oil film thickness distribution across the entire plane and outputs the corresponding oil film pressure distribution.

[0016] Step eight specifically involves: By discretizing and solving the lubrication model, the oil film thickness distribution and oil film pressure distribution of the gear pump side plate end face gap are obtained. The data are then imported into Tecplot and relevant parameters are set for visualization.

[0017] The beneficial effects of this invention are: This invention provides a complete CFD-based simulation method for the lubrication characteristics of gear pump side plates. Based on fluid mechanics theory, this method establishes a simulation model that can simulate oil film characteristics to model the lubrication and contact behavior of a real oil pump under different load spectrum conditions, revealing the dynamic lubrication change mechanism of the sliding bearing in an aero-engine fuel pump under dynamic and multi-field coupling effects. Through CFD simulation, the lubrication performance of the side plate end face under various operating conditions can be comprehensively analyzed, and the performance changes of the pump under different working conditions can be predicted, providing a reference for engineering personnel in operation management and parameter adjustment. Furthermore, technicians can formulate more reasonable maintenance strategies based on the side plate end face lubrication performance data obtained from CFD simulation.

[0018] Compared to traditional simulation methods, CFD simulations, based on the fundamental equations of fluid mechanics, can more accurately describe the real physical behavior of fluids. Some traditional simulation methods may employ simplified models or empirical formulas, resulting in relatively lower accuracy when dealing with complex fluid problems. Furthermore, modern CFD technology can be easily coupled with other disciplines such as elasticity, heat conduction, and electromagnetics, enabling more realistic simulations of multiphysics coupling problems in practical engineering.

[0019] On the other hand, compared with experimental methods, the CFD-based method for studying the lubrication characteristics of floating side plate end face gaps eliminates the need for physical models and actual testing, significantly reducing R&D costs. Furthermore, CFD numerical calculations allow for rapid parameter adjustments and simulations, yielding results under numerous different operating conditions in a short time, thus accelerating the research and design process. Moreover, compared to real-world experiments, CFD simulation methods offer high safety and excellent repeatability. Attached Figure Description

[0020] Figure 1 This is an exploded view of a 3D model of a gear pump.

[0021] Figure 2 This is a diagram illustrating the mesh division and topology information of the gap between the side plate end faces.

[0022] Figure 3 This is a model diagram of the oil film thickness in the gap between the side plate end faces.

[0023] Figure 4 This is a diagram showing the distribution of oil film thickness in the gap between the side plate end faces.

[0024] Figure 5 This is a diagram showing the oil film pressure distribution across the gap between the side plate end faces.

[0025] Figure 6 This is a flowchart of the CFD simulation of the lubrication characteristics of the side plate end face of a gear pump. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Taking a certain aviation fuel gear pump as an example, Figure 1 This is a specific 3D model of the structure of an external gear pump, mainly composed of driving and driven gears, a drive shaft, a pump body, and bearings. The gear pump's drive shaft rotates, causing the main gear to rotate. During rotation, the volume between the teeth of the driving and driven gears decreases and then increases again. This pressurizing effect converts the mechanical energy extracted by the drive shaft into pressure energy, thus increasing the pressure. During operation, the fixed bearing remains stationary, while the floating bearing achieves pressure compensation through axial fretting. A lubrication interface (end-face oil film) is formed between the sliding bearing and the gear end face. This friction pair is called the gear end face-side plate pair, or simply the side plate pair. After the geometric model is established, the computational domain is meshed. The model of the computational region is imported into ICEM for mesh generation. In the side plate end face region, the mesh needs to be finer to ensure accurate capture of details such as oil film thickness and pressure changes. This invention employs unstructured meshing technology, selecting local meshes with higher density and appropriately refining them in the gear edge region. The refined unstructured mesh of the computational region (end face oil film) is shown below. Figure 2 As shown.

[0028] From the appendix Figure 2 As can be seen, the information storage method of unstructured meshes is illustrated using a gear as an example. For nodes storing nodes... Its corresponding element index Its topological information is defined; for a surface element Cell indexes on both sides and endpoint index Its topological information is defined; for cells its adjacent cell index Node index and face element index Its topological information is defined. Furthermore, the normal vector between two cells is defined as pointing from the smaller cell to the larger cell.

[0029] To facilitate the calculation of the oil film thickness at any point in the lubrication gap, an origin is established as follows: Figure 3 The rectangular coordinate system shown.

[0030] From three specific points in this coordinate system Plus, take a little bit Based on the necessary and sufficient condition that the mixed product of the four points is zero, we can obtain: Further refinement yields the formula for calculating the oil film thickness at any point in the region: in, This indicates the distance between the centers of the two gears. Let be the addendum circle radius of the gear teeth, and the two gears have the same geometric information. From the above formula, it can be seen that the oil film thickness is determined based on three specific locations of the gear pair, plus a set of positional information. Then the oil film thickness at that point can be calculated. For the simplified continuity equation regarding... By integrating and combining with the Navier-Stokes equations, the general form of the Reynolds control equations for fluid flow in the side plate lubrication gap can be derived: in and These represent the density and dynamic viscosity of the medium oil, respectively. For gradient operators, Indicates the pressure distribution of the oil film. The oil film thickness distribution will be derived later using geometric and mathematical principles; therefore, the gradient of the oil film thickness can also be explicitly solved. It is the extrusion speed of the side plate's axial movement. and These represent the velocities of the upper and lower surfaces of the lubricating oil film, respectively. In calculations, it is generally assumed that... , It is equal to the rotational speed of the gear. Therefore, the equation simplifies to, Furthermore, based on the quasi-static assumption—that the system changes sufficiently slowly, and can be approximated as being in static equilibrium at every instant—and temporarily ignoring the change in oil film thickness over time, the equation can be written as follows: Solving any ordinary differential equation or partial differential equation depends on given boundary conditions. For diffusion problems, there are Dirichlet, Neumann, mixed, and symmetric boundary condition types. This invention employs the Dirichlet boundary condition, directly specifying the unknowns at the boundary. The value of . Boundary element surfaces are treated the same as internal element surfaces. When the surface vector does not overlap with the line connecting the centroid of the element and the boundary surface, the cross-diffusion term should be considered. The cross-diffusion term is also moved to the right side of the algebraic equation and treated as a source term.

[0031] After the model is established, it needs to be discretized and solved. For the diffusion term, the volume integral is transformed into a surface integral using Gauss-Green's formula: For unstructured meshes, surface vectors Vectors that may be connected to the centroids of coplanar units They are not collinear, if we use Indicates along the point and points The unit vector in the direction of the line, then therefore, The gradient in the direction is written as To achieve flux linearization in non-orthogonal grids, surface vectors It should be written as two vectors and The sum of, i.e. (31) The contribution of the first term on the right-hand side of the above equation is similar to that in orthogonal meshes. The second term, called the cross-diffusion term (non-orthogonal term), is caused by the non-orthogonality of the mesh. According to... Depending on the direction of decomposition, there are multiple existing methods that can... Decomposed into and Examples of methods include minimum correction, orthogonal correction, and super-relaxation. This invention employs the most stable super-relaxation method, which remains stable even when the mesh height is non-orthogonal.

[0032] The gradient in the cross-diffusion term The current gradient field is used for calculation and added as a source term to the right-hand side of the algebraic equation to achieve a delay correction for the diffusion term. Gradient calculations are primarily performed at grid points; gradient values ​​at boundaries can be obtained through interpolation. Green's theorem is frequently used to calculate the gradient of a cell. in Let be the surface vector pointing outwards. Applying the mean value theorem, we obtain the relationship between the integral term on the left-hand side of the above equation and the average gradient over the volume. The integral term on the right-hand side approximates the integral on the unit surface by multiplying the value at the centroid of the unit surface by the area of ​​the unit surface. ,unit The pressure gradient on the surface is expressed as: The gradient value at the interface is obtained by taking the weighted average of the pressure gradients on both sides of the interface: in and Let be the geometric interpolation factor, and let be the sum of 1. Its value is related to the element surface. Distance from the center point of the unit and The distance is related; regarding the discretization of the source term, the source term is related to the pressure. Values ​​are independent; for a control volume, it can be written as: in For cells The average oil film thickness gradient on the surface For cells The speed at which it is measured. Step six specifically involves: Based on the discretization of the above model, the form of the discrete equation is obtained as follows: Taking a discrete cell as an example, it is called the master cell using a subscript. This indicates that its three neighboring cells are represented by subscripts. This means, therefore These represent the pressure values ​​in the main cell and the three adjacent cells, respectively. They also represent the oil density and viscosity. The oil film thickness value at the midpoint of each face in the main cell. Indicates the volume of the main cell; By organizing the pressure values ​​on the grid nodes, the discrete equation is obtained as follows:

[0033] There are many methods for solving this system of algebraic equations, such as Cramer's rule, Gaussian elimination, matrix decomposition, and iterative methods (Jacobi iteration, Gauss-Seidel iteration), etc. The specific method can be selected according to the specific problem to obtain the oil film thickness distribution and pressure distribution in the gap between the side plate end faces.

[0034] Based on the obtained pressure distribution, a force analysis is performed on the gear pump side plate to determine if the force balance criterion is met. An optimization algorithm (e.g., the Powell hybrid method) is then used to update the oil film thickness change rate until the force balance criterion is satisfied. Next, an iterative method (e.g., the Euler explicit method) is used to find the instantaneous value of the three-point gap height. Substituting this value into the oil film thickness model yields the oil film thickness distribution across the entire plane and outputs the corresponding oil film pressure distribution.

[0035] By discretizing and solving the lubrication model, the oil film thickness and pressure distribution in the clearance between the side plates of the gear pump can be obtained. The data can then be imported into Tecplot and relevant parameters set for visualization. A simulation result diagram of an aviation fuel gear pump can be referenced. Figure 4 and Figure 5 .

[0036] from Figure 4 and Figure 5 It can be seen that the thickness of the oil film and the pressure distribution in the gap between the gear pump side plates exhibit a certain regularity from the inlet to the outlet.

[0037] Figure 6 The paper demonstrates a detailed calculation process for CFD simulation of the oil film characteristics on the side plate end face of a gear pump. The process first gives the gear geometric parameters, establishes a physical model of the gear pump, and divides the oil film mesh. Then, it gives the initial oil film thickness, establishes the oil film thickness equation, and calculates the oil film thickness. At the same time, it uses the Reynolds equation to calculate or correct the oil film gradient. Then, it solves the two together to obtain the oil film pressure. Then, it judges the force balance condition. If it is not satisfied, it is recalculated or corrected. If it is satisfied, the final film thickness and pressure can be obtained.

Claims

1. A CFD-based simulation method for lubrication characteristics of the side plate end face clearance of a gear pump, characterized in that, Includes the following steps; Step 1: Establish a geometric oil film model; Step 2: Mesh the established geometric oil film model to discretize it for subsequent calculations; Step 3: Consider the lubrication conditions inside the gear pump and establish a lubrication model; Step 4: Set boundary conditions for the lubrication model and define the external constraints of the model; Step 5: Discretize the model established in Step 3 on the grid from Step 2 and establish a system of equations; Step Six: Iterate and solve the established system of equations to obtain specific numerical results; Step 7: Perform force balance analysis based on the numerical results, using the force balance state as the convergence condition; Step 8: Visualize the simulation results to present the analysis results intuitively.

2. The CFD-based simulation method for lubrication characteristics of gear pump side plate end face clearance according to claim 1, characterized in that, Step one specifically involves: The SolidWorks software was used to accurately geometrically model the shape of the side plate end face, the contact surface of the gear, and the area of ​​the oil film on the end face. The geometric model included the geometric features of the gear, side plate, and oil film area to ensure that it was consistent with the actual working conditions.

3. The CFD-based simulation method for lubrication characteristics of gear pump side plate end face clearance according to claim 1, characterized in that, Step two specifically involves: Import the oil film region from step one into the ICEM module of ANSYS for mesh generation; In the area of ​​the side plate end face, the mesh needs to be finer to ensure that the details of oil film thickness and pressure changes can be accurately captured; unstructured mesh technology is used, selecting local meshes with higher density and appropriately refining them in the gear edge area.

4. The CFD-based simulation method for lubrication characteristics of gear pump side plate end face clearance according to claim 1, characterized in that, Step three specifically involves: Establish a rectangular coordinate system with the center of the driving gear as the origin; From three specific points in this coordinate system Plus, take a little bit Based on the necessary and sufficient condition that the mixed product of the four points is zero, we obtain: Further refinement yields the formula for calculating the oil film thickness at any point in the region: in, This indicates the distance between the centers of the two gears. Given the gear tooth tip circle radius, and assuming both gears have identical geometry, the above formula shows that the oil film thickness is determined based on three specific points on the gear pair, plus a set of position information. The oil film thickness at that point is calculated; the simplified continuity equation is applied to... By integrating and combining with the Navier-Stokes equations, the general form of the Reynolds governing equations for fluid flow in the side plate lubrication gap is derived: in and These represent the density and dynamic viscosity of the medium oil, respectively. For gradient operators, Indicates the pressure distribution of the oil film. The oil film thickness distribution will be derived later using geometric and mathematical principles. It is the extrusion speed of the side plate's axial movement. and These represent the velocities of the upper and lower surfaces of the lubricating oil film, respectively. In calculations, it is generally assumed that... , The value is equal to the rotational speed of the gear; therefore, the equation simplifies to: Based on the quasi-static assumption—that the system changes sufficiently slowly and can be approximated as being in static equilibrium at every instant—and temporarily ignoring the change in oil film thickness over time, the equation can be written as follows:

5. The CFD-based simulation method for lubrication characteristics of gear pump side plate end face clearance according to claim 1, characterized in that, Step four specifically involves: Using Dirichlet boundary conditions, the unknowns at the boundary are directly given. The value of the boundary element surface is treated the same as that of the internal element surface. When the surface vector does not overlap with the line connecting the centroid of the element and the boundary surface, the cross-diffusion term should be considered. in The surface vector of the mesh boundary is decomposed into two vectors: an orthogonal term and a cross-diffusion term. and The sum of, It is the pressure gradient on the boundary surface. These are the boundary surfaces and the main cells, respectively. The pressure value on top, This represents the distance vector from the center of the cell to the boundary surface. The cross-diffusion term is moved to the right side of the algebraic equation and treated as a source term.

6. The CFD-based simulation method for lubrication characteristics of gear pump side plate end face clearance according to claim 1, characterized in that, Step five specifically involves: Based on the mesh generation in step two and the lubrication model established in step three, the lubrication model is discretized on the mesh in this step to establish a discrete set of equations. For the diffusion term, apply Gauss-Green's formula to transform the volume integral into a surface integral: For unstructured meshes, surface vectors Vectors that may be connected to the centroids of coplanar units They are not collinear, if we use Indicates along the point and points The unit vector in the direction of the line, then therefore, The gradient in the direction is written as To achieve flux linearization in non-orthogonal grids, surface vectors It should be written as two vectors and The sum of, i.e. The contribution of the first term on the right-hand side of the above equation is similar to that in orthogonal meshes; the second term, called the cross-diffusion term, is due to the non-orthogonality of the mesh. According to... Depending on the direction of decomposition, there are multiple existing methods to... Decomposed into and The most stable over-relaxation method is employed, which maintains stability even when the mesh height is non-orthogonal. The gradient in the cross-diffusion term The current gradient field is used for calculation and added as a source term to the right side of the algebraic equation to achieve the purpose of delaying the correction of the diffusion term; Green's Gauss formula is often used to calculate the gradient of a cell: in Let be the surface vector pointing outwards. Applying the mean value theorem, we obtain the relationship between the integral term on the left-hand side of the above equation and the average gradient over the volume. The integral term on the right-hand side approximates the integral on the unit surface by multiplying the value at the centroid of the unit surface by the area of ​​the unit surface. ,unit The pressure gradient on the surface is expressed as: By taking the weighted average of the pressure gradients on both sides of the interface, the gradient value on that interface is obtained: in and Let be the geometric interpolation factor, and let be the sum of 1. Its value is related to the element surface. Distance from the center point of the unit and The distance is related; regarding the discretization of the source term, the source term is related to the pressure. Values ​​are independent; for a control volume, it can be written as: in For cells The average oil film thickness gradient on the surface For cells The speed on.

7. The CFD-based simulation method for lubrication characteristics of gear pump side plate end face clearance according to claim 1, characterized in that, Step six specifically involves: Based on the discretization of the above model, the form of the discrete equation is obtained as follows: Taking a discrete cell as an example, it is called the master cell using a subscript. This indicates that its three neighboring cells are represented by subscripts. This means, therefore These represent the pressure values ​​in the main cell and the three adjacent cells, respectively. They also represent the oil density and viscosity. The oil film thickness value at the midpoint of each face in the main cell. Indicates the volume of the main cell; By organizing the pressure values ​​on the grid nodes, the discrete equation is obtained as follows:

8. The CFD-based simulation method for lubrication characteristics of gear pump side plate end face clearance according to claim 1, characterized in that, Step seven specifically involves: Based on the pressure distribution, a force analysis is performed on the gear pump side plate to determine whether the force balance criterion is met. If the force is unbalanced, the oil film thickness change rate is updated using the Powell hybrid root-finding algorithm until the force balance criterion is met. The Powell hybrid quadrature algorithm operates as follows: Initialization: Select a starting point and set n direction vectors. Perform a one-dimensional search along each direction vector to find the descent step size that reduces the objective function by the most along that direction, and update the position. Check whether the new position reduces the function value. If it does, retain the new direction; otherwise, replace the direction with the direction of the old position. After completing one round of searching in n directions, connect the initial point and the end point of this round of searching to form a new direction. Replace the first direction in the original direction group with this new direction to form the direction group for the next round of iteration. Repeat the search for multiple rounds of iteration. When the preset maximum number of iterations is reached, or the change in the objective function value is less than a certain minimum threshold, or the change in position is less than a specified threshold, the iteration stops, and the point obtained is considered to be the approximate optimal solution. Next, the equation for the rate of change of oil film thickness is quadrated to find the instantaneous value of the gap height at three points. The value is then substituted into the oil film thickness model to obtain the oil film thickness distribution on the entire plane and output the corresponding oil film pressure distribution.

9. The CFD-based simulation method for lubrication characteristics of gear pump side plate end face clearance according to claim 1, characterized in that, Step eight specifically involves: By discretizing and solving the lubrication model, the oil film thickness distribution and oil film pressure distribution of the gear pump side plate end face gap are obtained. The data are then imported into Tecplot and relevant parameters are set for visualization.

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