Elastohydrodynamic lubrication calculation method and related device

Abstract

The invention discloses an elastohydrodynamic lubrication calculation method and a related device, a Reynolds equation corresponding to elastohydrodynamic lubrication is converted into an equivalent weak form, and subsequent solving is facilitated. The relation between the oil film thickness and the equivalent contact model is described through a film thickness equation, an elastohydrodynamic lubrication equivalent model is solved and determined according to the equivalent weak form and the film thickness equation, and the elastohydrodynamic lubrication equivalent model is used for describing the relation between the test parameters and the oil film pressure and the relation between the test parameters and the oil film thickness; the test parameters are parameters which are determined based on an equivalent weak form and a film thickness equation and are related to the oil film pressure and the oil film thickness. And correspondingly, in response to the obtained test value of the test parameter, determining the test oil film pressure and the test oil film thickness corresponding to the test value through the elastohydrodynamic lubrication equivalent model. On the basis, the corresponding oil film pressure and the corresponding oil film thickness can be obtained by directly inputting the test value, the oil film change conditions under different use conditions can be rapidly analyzed by changing the test value, and the universality is higher.

Description

Technical Field

[0001] The present application relates to the technical field of data processing, and particularly to a calculation method and related device for elastohydrodynamic lubrication. Background Art

[0002] Elastohydrodynamic Lubrication (EHL), abbreviated as elastohydrodynamic lubrication, is an important lubrication phenomenon widely existing in mechanical systems, and is mainly applied to key components such as rolling bearings, gears, and transmission devices.

[0003] The remarkable feature of elastohydrodynamic lubrication is that under the action of load, the contact area is usually very small, but the local area bears extremely high pressure. This high pressure will cause significant changes in the viscosity and density of the lubricant, and at the same time cause elastic deformation of the contact surface, forming a complex physical process of interaction between the lubricant film and the elastic body. Elastohydrodynamic lubrication has multiple key functions during mechanical operation. It can not only significantly reduce the frictional resistance and prevent surface wear, but also has an important impact on the dynamic performance such as vibration and noise of the friction pair system. The state of elastohydrodynamic lubrication (specifically referring to the oil film thickness and oil film pressure) is directly related to the performance and stability of the mechanical system.

[0004] Therefore, how to calculate elastohydrodynamic lubrication to determine its state is of great significance. However, the calculation methods adopted in the related technologies have the problem of poor generality. Summary of the Invention

[0005] In order to solve the above technical problems, the present application provides a calculation method and related device for elastohydrodynamic lubrication. In this way, by establishing an equivalent model of elastohydrodynamic lubrication, during the test stage or analysis stage, directly inputting the test values can obtain the corresponding oil film pressure and oil film thickness, and changing the test values can quickly analyze the changes in the oil film pressure and oil film thickness of the lubricating oil under different usage conditions, with higher generality and stronger universality.

[0006] The embodiments of the present application disclose the following technical solutions:

[0007] On the one hand, the embodiments of the present application provide a calculation method for elastohydrodynamic lubrication, and the method includes:

[0008] Obtain the Reynolds equation corresponding to elastohydrodynamic lubrication, where the Reynolds equation is used to describe the changes in the oil film pressure and oil film thickness of the lubricating oil, and the Reynolds equation is an equation in differential form;

[0009] Determine the equivalent weak form corresponding to the Reynolds equation, where the equivalent weak form is an equation in integral form, and the equivalent weak form is used to describe the changes in the oil film pressure and the oil film thickness;

[0010] Obtain the film thickness equation corresponding to the lubricating oil, where the film thickness equation is used to describe the relationship between the oil film thickness and the equivalent contact model, and the equivalent contact model is used to represent the contact between the rolling element and the raceway surface, and the lubricating oil forms an oil film on the contact surface between the rolling element and the raceway surface;

[0011] According to the equivalent weak form and the film thickness equation, solve and determine the elastohydrodynamic lubrication equivalent model, where the elastohydrodynamic lubrication equivalent model is used to describe the relationship between the test parameters and the oil film pressure and the oil film thickness, and the test parameters are parameters related to the oil film pressure and the oil film thickness determined based on the equivalent weak form and the film thickness equation;

[0012] In response to obtaining the test value of the test parameter, determine the test oil film pressure and the test oil film thickness corresponding to the test value through the elastohydrodynamic lubrication equivalent model.

[0013] On the other hand, an embodiment of the present application provides a calculation device for elastohydrodynamic lubrication, and the device includes an acquisition unit, a determination unit, and a solution unit:

[0014] The acquisition unit is used to obtain the Reynolds equation corresponding to elastohydrodynamic lubrication, where the Reynolds equation is used to describe the change of the oil film pressure and the oil film thickness of the lubricating oil, and the Reynolds equation is an equation in differential form;

[0015] The determination unit is used to determine the equivalent weak form corresponding to the Reynolds equation, where the equivalent weak form is an equation in integral form, and the equivalent weak form is used to describe the change of the oil film pressure and the oil film thickness;

[0016] The acquisition unit is further used to obtain the film thickness equation corresponding to the lubricating oil, where the film thickness equation is used to describe the relationship between the oil film thickness and the equivalent contact model, and the equivalent contact model is used to represent the contact between the rolling element and the raceway surface, and the lubricating oil forms an oil film on the contact surface between the rolling element and the raceway surface;

[0017] The solution unit is used to solve and determine the elastohydrodynamic lubrication equivalent model according to the equivalent weak form and the film thickness equation, where the elastohydrodynamic lubrication equivalent model is used to describe the relationship between the test parameters and the oil film pressure and the oil film thickness, and the test parameters are parameters related to the oil film pressure and the oil film thickness determined based on the equivalent weak form and the film thickness equation;

[0018] The determination unit is further used to, in response to obtaining the test value of the test parameter, determine the test oil film pressure and the test oil film thickness corresponding to the test value through the elastohydrodynamic lubrication equivalent model.

[0019] In another aspect, an embodiment of the present application provides a computer device, which includes a processor and a memory:

[0020] The memory is used to store program codes and transmit the program codes to the processor;

[0021] The processor is used to execute the calculation method of elastohydrodynamic lubrication described in the above aspect according to the instructions in the program codes.

[0022] In another aspect, an embodiment of the present application provides a computer-readable storage medium, which is used to store a computer program, and the computer program is used to execute the calculation method of elastohydrodynamic lubrication described in the above aspect.

[0023] In another aspect, an embodiment of the present application provides a computer program product including instructions, which, when running on a computer, causes the computer to execute the calculation method of elastohydrodynamic lubrication described in the above aspect.

[0024] It can be seen from the above technical solutions that the Reynolds equation corresponding to elastohydrodynamic lubrication is converted into an equivalent weak form. Since the Reynolds equation is a differential-form equation and the equivalent weak form is an integral-form equation, it is more conducive to subsequent solution. And, a lubricating oil film is formed on the contact surface between the rolling element and the raceway surface. Therefore, it can be understood that the situation of the oil film is related to the situation of the rolling element and the raceway surface, specifically related to the contact situation between the two. Correspondingly, the relationship between the oil film thickness and the equivalent contact model is described by the film thickness equation, where the equivalent contact model can be used to represent the contact situation between the rolling element and the raceway surface. Therefore, the film thickness equation can directly reflect the relationship between the oil film thickness and the current contact situation, that is, related to the situation of the external load. Then, according to the equivalent weak form and the film thickness equation, an elastohydrodynamic lubrication equivalent model is solved and determined. The elastohydrodynamic lubrication equivalent model is used to describe the relationship between the test parameters and the oil film pressure and the oil film thickness. The test parameters are parameters related to the oil film pressure and the oil film thickness determined based on the equivalent weak form and the film thickness equation. Correspondingly, in response to obtaining the test value of the test parameter, the test oil film pressure and the test oil film thickness corresponding to the test value are determined through the elastohydrodynamic lubrication equivalent model. In this way, by establishing the elastohydrodynamic lubrication equivalent model, in the test stage or the analysis stage, directly inputting the test value can obtain the corresponding oil film pressure and oil film thickness, and changing the test value can quickly analyze the changes in the oil film pressure and oil film thickness of the lubricating oil under different usage conditions, with higher versatility and stronger universality. Description of the Drawings

[0025] To more clearly illustrate the technical solutions in the embodiments of the present application or the related art, the following will briefly introduce the drawings required for use in the description of the embodiments or the related art. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0026] Figure 1 It is a flowchart of a calculation method for elastohydrodynamic lubrication provided by an embodiment of the present application;

[0027] Figure 2 It is a schematic diagram of a ball-raceway contact model provided by an embodiment of the present application;

[0028] Figure 3 It is a schematic diagram of an equivalent elliptical contact model provided by an embodiment of the present application;

[0029] Figure 4 It is a schematic diagram of an application interface provided by an embodiment of the present application;

[0030] Figure 5 It is a schematic diagram of three-dimensional test results provided by an embodiment of the present application;

[0031] Figure 6 It is a schematic diagram of verification results based on pressure distribution provided by an embodiment of the present application;

[0032] Figure 7 It is a schematic diagram of test results of oil film pressure and oil film thickness under different entrainment velocities provided by an embodiment of the present application;

[0033] Figure 8 It is a schematic diagram of test results of oil film pressure and oil film thickness under non-contact external load provided by an embodiment of the present application;

[0034] Figure 9 It is a schematic diagram of a calculation framework for elastohydrodynamic lubrication provided by an embodiment of the present application;

[0035] Figure 10 It is a structural diagram of a calculation device for elastohydrodynamic lubrication provided by an embodiment of the present application. Detailed implementation manners

[0036] To enable those skilled in the art to better understand the solutions of the present application, the following will clearly and completely describe the technical solutions in the embodiments of the present application in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, rather than all embodiments. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present application.

[0037] The calculation method of elastohydrodynamic lubrication provided by the embodiments of the present application can be implemented by a computer device, which can be a terminal device or a server. Among them, the server can be an independent physical server, a server cluster or a distributed system composed of multiple physical servers, or a cloud server providing cloud computing services. The terminal device includes, but is not limited to, mobile phones, computers, intelligent voice interaction devices, smart home appliances, vehicle-mounted terminals, etc. The terminal device and the server can be directly or indirectly connected through wired or wireless communication methods, and the present application does not impose any restrictions on this.

[0038] Specifically, it is described through the following embodiments:

[0039] Figure 1 The following is a flowchart of a calculation method of elastohydrodynamic lubrication provided by the embodiments of the present application. Taking the terminal device as the aforementioned computer device as an example, the method includes:

[0040] S101: Obtain the Reynolds equation corresponding to elastohydrodynamic lubrication.

[0041] Among them, the Reynolds equation can be used to describe the change of the oil film pressure and the oil film thickness of the lubricating oil, and the Reynolds equation is an equation in differential form. Generally, the Reynolds equation of elastohydrodynamic lubrication (Reynolds equation) is as follows:

[0042]

[0043] In the above formula, P is the oil film pressure, h is the oil film thickness, η is the viscosity of the lubricating oil, u is the entrainment velocity, and ρ is the mass density of the lubricating oil.

[0044] S102: Determine the equivalent weak form corresponding to the Reynolds equation.

[0045] Among them, the equivalent weak form is an equation in integral form, and the equivalent weak form is used to describe the change of the oil film pressure and the oil film thickness. Compared with the Reynolds equation, based on the equivalent weak form, the smoothness requirement of the equation can be reduced, which is convenient for using numerical techniques such as the finite element method for solution.

[0046] In practical applications, the equivalent weak form of the Reynolds equation can be derived through the Galerkin method. Generally, the equivalent weak form is as follows:

[0047]

[0048] In the above formula, δ P is a test function, Ω is the calculation domain, S is the integration range of a single integral, representing the integration range of x and the integration range of y respectively.

[0049] S103: Obtain the film thickness equation corresponding to the lubricating oil.

[0050] Among them, the film thickness equation is used to describe the relationship between the oil film thickness and the equivalent contact model. The equivalent contact model is used to represent the contact between the rolling element and the raceway surface, and the lubricating oil forms an oil film on the contact surface between the rolling element and the raceway surface. For better understanding, the following will be explained one by one:

[0051] 1. First, the following description is provided for the equivalent contact model:

[0052] The rolling element and the raceway surface can respectively indicate the two parties based on the contact of the lubricating oil in the mechanical system. The rolling element can produce mechanical behaviors (such as rolling, sliding, etc.) on the raceway surface, and the lubricating oil plays a lubricating role to reduce the frictional resistance, etc. during the generation of mechanical behaviors.

[0053] It can be understood that for different rolling elements and raceway surfaces, the contact situation between the two will be different, which will also affect the oil film pressure, oil film thickness, etc. of the lubricating oil.

[0054] For ease of understanding, the equivalent contact model can be obtained by equating the contact between the rolling element and the raceway surface to the contact between an equivalent elastic ellipsoid and a plane. The equivalent contact model is used to describe the elastic modulus relationship between the rolling element and the raceway surface, as well as the radius of curvature relationship between the rolling element and the raceway surface. Among them, the elastic modulus relationship and the radius of curvature relationship can be used to reflect the current contact situation between the rolling element and the raceway surface.

[0055] Specifically, it can be seen as Figure 2 the schematic diagram of a ball-raceway contact model described. On the left side of Figure 2 taking the deep groove ball bearing as an example, the ball contacts the inner raceway. In this regard, it can be equated to the contact between the elastic ellipsoid b and the rigid plane a, that is, equated to the contact between an equivalent elastic ellipsoid surface and a plane, and this plane can be considered an infinitely large flat plate.

[0056] Correspondingly, the aforementioned elastic modulus relationship can be expressed as:

[0057]

[0058] And, the aforementioned radius of curvature relationship can be expressed as:

[0059]

[0060] In the above formula, E' is the comprehensive elastic modulus, E1 is the elastic modulus of the rolling element, E2 is the elastic modulus of the inner raceway, ν1 is the Poisson's ratio of the rolling element, and ν2 is the Poisson's ratio of the inner raceway. And, R x is the comprehensive radius of curvature of the ellipsoid surface in the X direction, R 1x is the radius of curvature of the rolling element in the X direction, R 2xis the curvature radius of the inner raceway in the X direction, R y is the comprehensive curvature radius of the ellipsoidal surface in the Y direction, R 1y is the curvature radius of the rolling element in the Y direction, R 2x is the curvature radius of the inner raceway in the Y direction.

[0061] When equivalent to the contact between the equivalent elastic ellipsoidal surface and the plane, for the sake of simplified understanding, reference can also be made to Figure 3 a schematic diagram of an equivalent elliptical contact model shown in, where the area marked by the ellipse can be considered as the contact area between the ellipsoid and the plane, and a and b respectively represent the contact minor semi-axis and the contact major semi-axis.

[0062] 2. Secondly, the following explanations are provided for the film thickness equation:

[0063] Generally, the film thickness equation can be expressed as:

[0064]

[0065] In the above formula, h0 is the central film thickness, which is related to the contact external load. And it should be noted that s and t are used to distinguish from x and y, and they are still expressions about x and y after integral calculation.

[0066] S104: Solve and determine the elastohydrodynamic lubrication equivalent model according to the equivalent weak form and the film thickness equation.

[0067] Among them, the elastohydrodynamic lubrication equivalent model is used to describe the relationship between the test parameters and the oil film pressure and the oil film thickness. The test parameters are parameters determined based on the equivalent weak form and the film thickness equation and related to the oil film pressure and the oil film thickness.

[0068] S105: In response to obtaining the test values of the test parameters, determine the test oil film pressure and the test oil film thickness corresponding to the test values through the elastohydrodynamic lubrication equivalent model.

[0069] In this way, by establishing the elastohydrodynamic lubrication equivalent model, during the test stage or the analysis stage, directly inputting the test values can obtain the corresponding oil film pressure and oil film thickness, and changing the test values can quickly analyze the changes in the oil film pressure and oil film thickness of the lubricating oil under different usage conditions, with higher generality and stronger universality.

[0070] It should be noted that this application does not make any limitations on how to solve and determine the elastohydrodynamic lubrication equivalent model, as well as the test parameters, determining the test oil film pressure, and the test oil film thickness. For better understanding, this application will be described one by one through the following various embodiments.

[0071] First, an elastohydrodynamic plane geometric model can be established.

[0072] Specifically, in combination with the description of the equivalent contact model embodiments mentioned above, according to the size of the elliptical contact area of the roller raceway, the length in the X direction can be set as -2*a ≤ X ≤ 1.5*a, and the length in the Y direction can be set as -2*b ≤ Y ≤ 2*b, where a and b respectively represent the minor contact semi-axis and the major contact semi-axis. It can be understood that -2*a ≤ X ≤ 1.5*a is also the integration range of the single integral of x in the aforementioned equivalent weak form, and -2*b ≤ Y ≤ 2*b is also the integration range of the single integral of y in the aforementioned equivalent weak form.

[0073] Based on this, compared with the numerical calculation model in the related art, there is no need to specify the elliptical Hertz contact area and its initial pressure distribution in this model, which is beneficial to improving the universality and generality.

[0074] Next, an elastohydrodynamic lubrication model can be established.

[0075] In practical applications, the oil film pressure and oil film thickness are also related to the viscosity, mass density, contact external load, etc. of the lubricating oil, and these are not fixed and are related to the oil film pressure. Therefore, in specific implementation, the density-pressure equation, load equation, and viscosity-pressure equation corresponding to the lubricating oil can also be obtained first. Accordingly, the elastohydrodynamic lubrication equivalent model can be solved and determined according to the equivalent weak form, film thickness equation, density-pressure equation, load equation, and viscosity-pressure equation.

[0076] Among them, the density-pressure equation is used to describe the relationship between the mass density of the lubricating oil and the oil film pressure, the load equation is used to describe the relationship between the external load borne by the oil film and the oil film pressure, and the viscosity-pressure equation is used to describe the relationship between the viscosity of the lubricating oil and the oil film pressure.

[0077] For example, the density-pressure equation can be expressed as:

[0078]

[0079] In the above formula, ρ0 is the mass density of the lubricating oil under normal pressure.

[0080] Since most of the equations involved in solving elastohydrodynamic lubrication are non-linear, this also leads to very poor stability in the numerical calculation process when solving based on the numerical calculation model in the related art, resulting in very low universality. In this regard, in order to further improve the universality, in another possible implementation manner, non-dimensionalization processing can also be performed, and then the non-dimensionalized equations are solved to enhance the universality.

[0081] In specific implementation, the film thickness equation, the pressure density equation, the load equation, and the viscosity-pressure equation can be dimensionless processed respectively to obtain the dimensionless film thickness equation, the dimensionless pressure density equation, the dimensionless load equation, and the dimensionless viscosity-pressure equation. Correspondingly, based on the equivalent weak form, the dimensionless film thickness equation, the dimensionless pressure density equation, the dimensionless load equation, and the dimensionless viscosity-pressure equation, the elastohydrodynamic lubrication equivalent model can be solved and determined.

[0082] For ease of understanding, the following explanations are also provided for the embodiments of the dimensionless processing:

[0083] First, the definition of dimensionless parameters can be determined as follows:

[0084]

[0085] In the above formula, P H is the maximum Hertz contact pressure. Generally, it can be determined by the following formula:

[0086]

[0087] where w is the external contact load.

[0088] Then, after the dimensionless processing, the obtained dimensionless equations can be as follows:

[0089] Reynolds equation:

[0090] Film thickness equation:

[0091] Load equation:

[0092] Pressure density equation: ρ * = 1 + (0.6×10 -9 p H P) / (1 + 1.7×10 -9 p H P)

[0093] Viscosity-pressure equation:

[0094] where: and, k e is the ellipticity ratio, and γ is the curvature radius ratio.

[0095] After that, by using the equivalent weak form and the above dimensionless governing equations for solution, the purpose of calculating and solving the elastohydrodynamic lubrication equivalent model based on the finite element method can be achieved.

[0096] In practical applications, for the convenience of subsequent use, for example, application programs such as COMSOL can be used to add a weak form partial differential equation (PDE) module. Among them, the weak form PDE interface allows users to directly input expressions in weak form, thereby realizing the modeling and solution of various physical problems. Therefore, in specific implementation, the equivalent weak form of the Reynolds equation obtained above can be input into the "weak form partial differential equation" module in a specified form, that is, an elastohydrodynamic lubrication model based on PDE is obtained.

[0097] In order to visually see the test results and ensure the accuracy of the test results, in another possible implementation, it is also possible to:

[0098] First, determine the mesh corresponding to the contact surface. This mesh is used to represent the contact surface, that is, it can be considered that the aforementioned computational domain and integration range are defined. Then, the constraint conditions and load conditions can be determined. Among them, the constraint conditions are used to represent that on the boundary of the mesh, the oil film pressure is equal to zero, and inside the mesh, the oil film pressure is greater than or equal to zero, and the load conditions are used to represent that the integration of the oil film pressure inside the mesh is equal to the contact external load. Based on this, subsequent solutions are all constrained by the constraint conditions and load conditions, avoiding the situation where the obtained results do not meet these conditions and become invalid solutions.

[0099] Correspondingly, in response to obtaining the test values of the test parameters, the test oil film pressure and test oil film thickness corresponding to the test values can be determined through the elastohydrodynamic lubrication equivalent model, and the test oil film pressure and test oil film thickness can be displayed inside the mesh. Based on this, the test results can be seen more intuitively.

[0100] In practical applications, the aforementioned constraint conditions can be expressed as:

[0101] On the boundary of the mesh, P = 0, and inside the mesh (that is, inside the contact plane), P ≥ 0.

[0102] And, the aforementioned load conditions can be expressed as:

[0103]

[0104] Among them, W is the contact external load.

[0105] It should also be noted that no limitations are imposed on the mesh in this application. Exemplarily, corresponding to the aforementioned contact equivalent model, the contact surface can be considered as a plane, so the mesh can be a quadrilateral.

[0106] In addition, this application does not make any restrictions on the test parameters. Exemplarily, the test parameters may include the viscosity of the lubricating oil under normal pressure, the mass density of the lubricating oil under normal pressure, the contact parameters of the equivalent contact model, the entrainment velocity, and the contact external load. Among them, the contact parameters of the equivalent contact model may include, for example, the aforementioned curvature radius in the X direction and the curvature radius in the Y direction. In addition, it may also include relevant parameters of the rolling elements and the raceway surface, such as metal material parameters, elastic modulus, Poisson's ratio, etc.

[0107] For better understanding, the embodiments of this application also provide a schematic diagram of an application interface as shown in Figure 4 Using functions such as an application developer, the solved and determined model is encapsulated to form an independently executable application program. The test parameters are displayed on the left side of the application page for the user to input the corresponding test values, and a grid is displayed on the right side for showing the test results.

[0108] In specific implementation, on the one hand, in order to ensure the convergence accuracy, etc., during encapsulation, the convergence accuracy defaultly provided by functions such as an application developer can be adopted, or a fully coupled algorithm with better convergence can be selected. Based on this, it is beneficial to ensure the convergence and accuracy of the test results.

[0109] On the other hand, after encapsulation, calculation verification can also be performed. Specifically, known conditions, that is, test values, can be input on the application interface, and the graph of the oil film pressure and the oil film thickness can be drawn and then verified. For example:

[0110] First, the test values shown in the following table can be input:

[0111]

[0112]

[0113] It should be noted that the above table is only an example of the test values and does not make any restrictions.

[0114] Then, click Calculate to obtain the test results. For example, the test results can be as shown in Figure 5 shown.

[0115] In practical applications, one of the verification methods of the elastohydrodynamic lubrication model is to reduce the viscosity of the lubricating oil to an extremely small value so that the effect of the lubricating oil can be ignored, thus approaching the pure elastic contact under the condition of no lubrication. At this time, the calculated pressure distribution should be consistent with the classical Hertz contact pressure distribution. This method uses the Hertz theory as a benchmark to evaluate the accuracy of the elastohydrodynamic lubrication model.

[0116] Therefore, for this application, this method can also be used for verification. Specifically, by reducing the test value of the test parameter of viscosity to the lowest, a schematic diagram of the verification result based on the pressure distribution as shown in Figure 6 is obtained. It can be seen that the pressure distribution is almost the same as the Hertz pressure distribution, so it shows that the model is reliable in calculating the elastohydrodynamic lubrication problem.

[0117] As can be seen from the above technical solution, converting the Reynolds equation corresponding to elastohydrodynamic lubrication into an equivalent weak form is more conducive to subsequent solution because the Reynolds equation is a differential-form equation while the equivalent weak form is an integral-form equation. And, an oil film is formed on the contact surface between the rolling element and the raceway surface. Therefore, it can be understood that the situation of the oil film is related to the situations of the rolling element and the raceway surface, specifically related to the contact situation between the two. Correspondingly, the relationship between the oil film thickness and the equivalent contact model is described by the film thickness equation. Among them, the equivalent contact model can be used to represent the contact situation between the rolling element and the raceway surface, so that the film thickness equation can directly reflect the relationship between the oil film thickness and the current contact situation, that is, related to the situation of the external load. Then, according to the equivalent weak form and the film thickness equation, the elastohydrodynamic lubrication equivalent model is solved and determined. The elastohydrodynamic lubrication equivalent model is used to describe the relationship between the test parameter and the oil film pressure and the oil film thickness. The test parameter is a parameter related to the oil film pressure and the oil film thickness determined based on the equivalent weak form and the film thickness equation. Correspondingly, in response to obtaining the test value of the test parameter, the test oil film pressure and the test oil film thickness corresponding to the test value are determined through the elastohydrodynamic lubrication equivalent model. In this way, by establishing the elastohydrodynamic lubrication equivalent model, in the test stage or the analysis stage, directly inputting the test value can obtain the corresponding oil film pressure and oil film thickness, and changing the test value can quickly analyze the changes in the oil film pressure and oil film thickness of the lubricating oil under different usage conditions, with higher versatility and stronger universality.

[0118] It can be seen that directly inputting the test value can obtain the corresponding oil film pressure and oil film thickness, which is very convenient. Correspondingly, when the test value is changed, the changes in the oil film pressure and oil film thickness under different usage conditions can be quickly analyzed. For this, the following examples are provided for illustration:

[0119] 1. Analyze the influence of different entrainment velocities on the distribution of the oil film pressure and the distribution of the oil film thickness of elastohydrodynamic lubrication

[0120] Specifically, reference can be made to Figure 7 the schematic diagram of the test results of the oil film pressure and the oil film thickness under different entrainment velocities as shown. It can be seen that:

[0121] As the entrainment speed increases, the position where the second pressure peak appears continuously moves away from the outlet region; at the same time, the peak value of the second pressure peak continuously increases with the increase of the entrainment speed. The influence of the entrainment speed on the lubricating oil film thickness distribution is manifested in that as the entrainment speed increases, the lubricating oil film thickness also gradually increases, the position where the minimum oil film thickness appears continuously moves away from the outlet region, and the minimum oil film thickness in the region also gradually increases.

[0122] 2. Analyze the influence of different contact external loads on the distribution of oil film pressure and oil film thickness in elastohydrodynamic lubrication

[0123] Specifically, reference can be made to Figure 8 the schematic diagram of the test results of oil film pressure and oil film thickness under a non-contact external load shown in the figure, and it can be seen that:

[0124] The influence of the contact external load on the lubricating oil pressure distribution is manifested in that as the contact external load increases, the position where the second pressure peak appears continuously approaches the outlet region; at the same time, the peak value of the second pressure peak continuously decreases with the increase of the contact external load. And, the influence of the contact external load on the lubricating oil film thickness distribution is manifested in that as the load increases, the lubricating oil film thickness also gradually decreases, the position where the minimum oil film thickness appears continuously approaches the outlet region, and the minimum oil film thickness in the region also gradually decreases.

[0125] Of course, it is also possible to analyze the influence of other test parameters on the oil film pressure and oil film thickness under different values according to actual needs.

[0126] In practical applications, by analyzing the changes in oil film pressure and oil film thickness under different usage conditions, the lubrication state can be more directly described, assisting engineers in designing a more reasonable (such as with less frictional resistance) lubrication system, avoiding direct metal contact between the rolling elements and the raceway surface, thereby avoiding friction and wear, etc. Of course, a reasonable lubrication system is also beneficial to reducing the friction coefficient of the mechanical system, improving the transmission efficiency, extending the service life of the machine, and reducing energy consumption, etc.

[0127] After adopting the present application, it is possible to provide the distribution of the oil film thickness and oil film pressure of the lubricating oil, thereby providing theoretical support for the design of the lubrication system to design a more reasonable lubrication system and ensure the maximization of the lubrication effect.

[0128] For the convenience of understanding, the embodiment of the present application also provides a Figure 9 schematic diagram of a calculation framework for elastohydrodynamic lubrication shown in the figure, specifically:

[0129] First, the elastohydrodynamic lubrication model equations can be determined, such as the Reynolds equation, film thickness equation, pressure - density equation, etc. as described above. Then, dimensionless processing can be carried out to determine the dimensionless equations. Moreover, it is rewritten into an equivalent weak form, and the equivalent weak form is input into the weak - form partial differential equation module to establish the elastohydrodynamic lubrication model. Specifically, it can include: setting of the equivalent weak - form module, mesh generation, setting of boundary conditions, setting of film thickness equation, viscosity - pressure equation, pressure - density equation, etc.

[0130] After that, initialization and finite - element solution can be carried out to obtain the test results. Also, post - processing of the test results can be performed, such as obtaining the schematic diagrams shown in the foregoing Figure 7 、 Figure 8 embodiments.

[0131] Generally speaking, this application proposes an efficient and reliable elastohydrodynamic lubrication calculation method, aiming to solve the problem of fluid dynamics and solid elasticity coupling under complex lubrication conditions. It is mainly based on the elastohydrodynamic lubrication theory, adopts the finite - element method, and uses the classical Reynolds equation as the basis of the mathematical model. Through a series of optimized calculation processes, high - precision lubrication characteristic analysis is achieved.

[0132] During the construction of the method, on the one hand, the partial differential equation (PDE) is dimensionless processed, so that it has higher generality and applicability after being dimensionless. This processing can effectively simplify the problem scale while maintaining sensitivity to changes in the scales of different physical quantities. On the other hand, the dimensionless equation is transformed into the weak form (Weak Formulation), laying the foundation for finite - element discrete solution. In the numerical solution process, the weighted residual method (such as Galerkin) can also be introduced to further discretize the weak form into a finite - element equation set that can be solved by numerical methods.

[0133] Through this calculation process, an elastohydrodynamic lubrication analysis model with strong universality and high calculation stability is constructed. This method not only ensures the convergence and accuracy of the calculation results in theoretical derivation but also can meet the requirements of complex lubrication conditions in practical applications, such as lubrication scenarios in high - load, high - speed rotating bearings or gear systems. This model provides an efficient tool for solving elastohydrodynamic lubrication problems in industrial design and also lays a foundation for in - depth research in fields such as lubricating material design and lubricant optimization.

[0134] It can be understood that it basically corresponds to the method embodiment, so the relevant parts can refer to the partial description of the method embodiment.

[0135] Figure 10 The figure shows the structure diagram of a calculation device for elastohydrodynamic lubrication provided by an embodiment of this application. The device includes an acquisition unit 1001, a determination unit 1002, and a solution unit 1003:

[0136] The obtaining unit 1001 is configured to obtain a Reynolds equation corresponding to elastohydrodynamic lubrication. The Reynolds equation is used to describe the variation of the oil film pressure and the oil film thickness of the lubricating oil, and the Reynolds equation is an equation in differential form;

[0137] The determining unit 1002 is configured to determine an equivalent weak form corresponding to the Reynolds equation. The equivalent weak form is an equation in integral form, and the equivalent weak form is used to describe the variation of the oil film pressure and the oil film thickness;

[0138] The obtaining unit 1001 is further configured to obtain a film thickness equation corresponding to the lubricating oil. The film thickness equation is used to describe the relationship between the oil film thickness and an equivalent contact model. The equivalent contact model is used to represent the contact between the rolling element and the raceway surface. The lubricating oil forms an oil film on the contact surface between the rolling element and the raceway surface;

[0139] The solving unit 1003 is configured to solve and determine an elastohydrodynamic lubrication equivalent model according to the equivalent weak form and the film thickness equation. The elastohydrodynamic lubrication equivalent model is used to describe the relationship between test parameters and the oil film pressure and the oil film thickness. The test parameters are parameters determined based on the equivalent weak form and the film thickness equation and related to the oil film pressure and the oil film thickness;

[0140] The determining unit 1002 is further configured to, in response to obtaining a test value of the test parameter, determine a test oil film pressure and a test oil film thickness corresponding to the test value through the elastohydrodynamic lubrication equivalent model.

[0141] In a possible implementation manner, the equivalent contact model is obtained by equivalent the contact between the rolling element and the raceway surface to the contact between an equivalent elastic ellipsoidal surface and a plane. The equivalent contact model is used to describe the relationship of the elastic modulus between the rolling element and the raceway surface and the relationship of the radius of curvature between the rolling element and the raceway surface.

[0142] In a possible implementation manner, the obtaining unit is further configured to:

[0143] Obtain a density-pressure equation, a load equation, and a viscosity-pressure equation corresponding to the lubricating oil. The density-pressure equation is used to describe the relationship between the mass density of the lubricating oil and the oil film pressure. The load equation is used to describe the relationship between the external load borne by the oil film and the oil film pressure. The viscosity-pressure equation is used to describe the relationship between the viscosity of the lubricating oil and the oil film pressure;

[0144] The solving unit is further configured to solve and determine the elastohydrodynamic lubrication equivalent model according to the equivalent weak form, the film thickness equation, the density-pressure equation, the load equation, and the viscosity-pressure equation.

[0145] In a possible implementation manner, the solving unit is further configured to:

[0146] Perform dimensionless processing on the film thickness equation, the density-pressure equation, the load equation, and the viscosity-pressure equation respectively to obtain a dimensionless film thickness equation, a dimensionless density-pressure equation, a dimensionless load equation, and a dimensionless viscosity-pressure equation;

[0147] Solve and determine the elastohydrodynamic lubrication equivalent model according to the equivalent weak form, the dimensionless film thickness equation, the dimensionless density-pressure equation, the dimensionless load equation, and the dimensionless viscosity-pressure equation.

[0148] In a possible implementation manner, the determining unit is further configured to:

[0149] Determine the grid corresponding to the contact surface, where the grid is used to represent the contact surface;

[0150] Determine the constraint conditions and the load conditions. The constraint conditions are used to represent that at the boundary of the grid, the oil film pressure is equal to zero, and inside the grid, the oil film pressure is greater than or equal to zero. The load conditions are used to represent that the integral of the oil film pressure inside the grid is equal to the external contact load;

[0151] In response to obtaining the test value of the test parameter, determine the test oil film pressure and the test oil film thickness corresponding to the test value through the elastohydrodynamic lubrication equivalent model, and display the test oil film pressure and the test oil film thickness inside the grid.

[0152] In a possible implementation manner, the test parameter includes the viscosity of the lubricating oil under atmospheric pressure, the mass density of the lubricating oil under atmospheric pressure, the contact parameter of the equivalent contact model, the entrainment velocity, and the external contact load.

[0153] As can be seen from the above technical solutions, converting the Reynolds equation corresponding to elastohydrodynamic lubrication into an equivalent weak form is more conducive to subsequent solution because the Reynolds equation is a differential-form equation while the equivalent weak form is an integral-form equation. Moreover, an oil film is formed on the contact surface between the rolling elements and the raceway surface. Therefore, it can be understood that the condition of the oil film is related to the conditions of the rolling elements and the raceway surface, specifically related to the contact condition between the two. Correspondingly, the relationship between the oil film thickness and the equivalent contact model is described by the film thickness equation. Among them, the equivalent contact model can be used to represent the contact condition between the rolling elements and the raceway surface, so that the film thickness equation can directly reflect the relationship between the oil film thickness and the current contact condition, that is, related to the condition of the external load. Then, according to the equivalent weak form and the film thickness equation, the elastohydrodynamic lubrication equivalent model is solved and determined. The elastohydrodynamic lubrication equivalent model is used to describe the relationship between the test parameters and the oil film pressure and the oil film thickness. The test parameters are parameters related to the oil film pressure and the oil film thickness determined based on the equivalent weak form and the film thickness equation. Correspondingly, in response to obtaining the test value of the test parameter, the test oil film pressure and the test oil film thickness corresponding to the test value are determined through the elastohydrodynamic lubrication equivalent model. In this way, by establishing the elastohydrodynamic lubrication equivalent model, in the test stage or the analysis stage, directly inputting the test value can obtain the corresponding oil film pressure and oil film thickness, and changing the test value can quickly analyze the changes in the oil film pressure and oil film thickness of the lubricating oil under different usage conditions, with higher generality and stronger universality.

[0154] On the other hand, an embodiment of the present application provides a computer device, which includes a processor and a memory:

[0155] The memory is used to store program codes and transmit the program codes to the processor;

[0156] The processor is used to execute the calculation method of elastohydrodynamic lubrication provided in the above embodiment according to the instructions in the program codes.

[0157] This computer device may include a terminal device or a server, and the aforementioned calculation device for elastohydrodynamic lubrication may be configured in this computer device.

[0158] On the other hand, an embodiment of the present application further provides a storage medium, which is used to store a computer program, and the computer program is used to execute the calculation method of elastohydrodynamic lubrication provided in the above embodiment.

[0159] In addition, an embodiment of the present application further provides a computer program product including instructions, which when running on a computer, causes the computer to execute the calculation method of elastohydrodynamic lubrication provided in the above embodiment.

[0160] Those of ordinary skill in the art can understand that all or part of the steps to implement the above method embodiments can be completed by hardware related to program instructions. The foregoing program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps including those of the above method embodiments; and the foregoing storage medium can be at least one of the following media: read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disc, etc., which can store program codes.

[0161] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the partial descriptions of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative efforts.

[0162] It should be noted that in this article, relational terms such as "first" and "second" (if any) are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including a..." does not exclude the existence of additional identical elements in the process, method, article or device including the said element.

[0163] The above has introduced in detail a calculation method and related device for elastohydrodynamic lubrication provided by the embodiments of the present application. Specific examples are used in this article to elaborate on the principle and implementation manner of the present application. The description of the above embodiments is only used to help understand the method of the present application. At the same time, for those of ordinary skill in the art, according to the method of the present application, there will be changes in the specific implementation manner and application scope.

[0164] In summary, the content of this specification should not be construed as a limitation on this application. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be covered by the protection scope of this application. Moreover, based on the implementation manners provided in the above aspects of this application, further combinations can be made to provide more implementation manners.

Claims

1. A calculation method for elastohydrodynamic lubrication, characterized in that, The method includes: Obtaining the Reynolds equation corresponding to elastohydrodynamic lubrication, where the Reynolds equation is used to describe the variation of the oil film pressure and the oil film thickness of the lubricating oil, and the Reynolds equation is an equation in differential form; Determining the equivalent weak form corresponding to the Reynolds equation, where the equivalent weak form is an equation in integral form, and the equivalent weak form is used to describe the variation of the oil film pressure and the oil film thickness; Obtaining the film thickness equation corresponding to the lubricating oil, where the film thickness equation is used to describe the relationship between the oil film thickness and the equivalent contact model, and the equivalent contact model is used to represent the contact between the rolling element and the raceway surface, and the lubricating oil forms an oil film on the contact surface between the rolling element and the raceway surface; According to the equivalent weak form and the film thickness equation, solving to determine an elastohydrodynamic lubrication equivalent model, where the elastohydrodynamic lubrication equivalent model is used to describe the relationship between the test parameters and the oil film pressure and the oil film thickness, and the test parameters are parameters determined based on the equivalent weak form and the film thickness equation and related to the oil film pressure and the oil film thickness; In response to obtaining the test value of the test parameter, determining the test oil film pressure and the test oil film thickness corresponding to the test value through the elastohydrodynamic lubrication equivalent model.

2. The method according to claim 1, characterized in that, The equivalent contact model is obtained by equivalent the contact between the rolling element and the raceway surface to the contact between an equivalent elastic ellipsoid surface and a plane, and the equivalent contact model is used to describe the relationship of the elastic modulus between the rolling element and the raceway surface and the relationship of the radius of curvature between the rolling element and the raceway surface.

3. The method according to claim 1, characterized in that The method further includes: Obtaining the density-pressure equation, the load equation, and the viscosity-pressure equation corresponding to the lubricating oil, where the density-pressure equation is used to describe the relationship between the mass density of the lubricating oil and the oil film pressure, the load equation is used to describe the relationship between the external load borne by the oil film and the oil film pressure, and the viscosity-pressure equation is used to describe the relationship between the viscosity of the lubricating oil and the oil film pressure; The solving to determine the elastohydrodynamic lubrication equivalent model according to the equivalent weak form and the film thickness equation includes: Solving to determine the elastohydrodynamic lubrication equivalent model according to the equivalent weak form, the film thickness equation, the density-pressure equation, the load equation, and the viscosity-pressure equation.

4. The method according to claim 3, wherein The solving to determine the elastohydrodynamic lubrication equivalent model according to the equivalent weak form, the film thickness equation, the density-pressure equation, the load equation, and the viscosity-pressure equation includes: Performing non-dimensionalization processing on the film thickness equation, the density-pressure equation, the load equation, and the viscosity-pressure equation respectively to obtain a non-dimensionalized film thickness equation, a non-dimensionalized density-pressure equation, a non-dimensionalized load equation, and a non-dimensionalized viscosity-pressure equation; Solving to determine the elastohydrodynamic lubrication equivalent model according to the equivalent weak form, the non-dimensionalized film thickness equation, the non-dimensionalized density-pressure equation, the non-dimensionalized load equation, and the non-dimensionalized viscosity-pressure equation.

5. The method according to claim 1, wherein The method further includes: Determining the grid corresponding to the contact surface, where the grid is used to represent the contact surface; Determine the constraint conditions and load conditions. The constraint conditions are used to represent that on the boundary of the grid, the oil film pressure is equal to zero, and inside the grid, the oil film pressure is greater than or equal to zero. The load conditions are used to represent that the integration of the oil film pressure inside the grid is equal to the contact external load; In response to obtaining the test value of the test parameter, determining the test oil film pressure and test oil film thickness corresponding to the test value through the elastohydrodynamic lubrication equivalent model includes: In response to obtaining the test value of the test parameter, determining the test oil film pressure and test oil film thickness corresponding to the test value through the elastohydrodynamic lubrication equivalent model, and displaying the test oil film pressure and the test oil film thickness in the grid.

6. The method according to any one of claims 1-5, characterized in that, The test parameters include the viscosity of the lubricating oil under atmospheric pressure, the mass density of the lubricating oil under atmospheric pressure, the contact parameters of the equivalent contact model, the entrainment velocity, and the contact external load.

7. A calculation device for elastohydrodynamic lubrication, characterized in that, The device includes an acquisition unit, a determination unit, and a solution unit: The acquisition unit is used to acquire the Reynolds equation corresponding to elastohydrodynamic lubrication. The Reynolds equation is used to describe the variation of the oil film pressure and oil film thickness of the lubricating oil, and the Reynolds equation is an equation in differential form; The determination unit is used to determine the equivalent weak form corresponding to the Reynolds equation. The equivalent weak form is an equation in integral form, and the equivalent weak form is used to describe the variation of the oil film pressure and the oil film thickness; The acquisition unit is further used to acquire the film thickness equation corresponding to the lubricating oil. The film thickness equation is used to describe the relationship between the oil film thickness and the equivalent contact model. The equivalent contact model is used to represent the contact between the rolling element and the raceway surface, and the lubricating oil forms an oil film on the contact surface between the rolling element and the raceway surface; The solution unit is used to solve and determine the elastohydrodynamic lubrication equivalent model according to the equivalent weak form and the film thickness equation. The elastohydrodynamic lubrication equivalent model is used to describe the relationship between the test parameters and the oil film pressure and the oil film thickness. The test parameters are parameters related to the oil film pressure and the oil film thickness determined based on the equivalent weak form and the film thickness equation; The determination unit is further used to, in response to obtaining the test value of the test parameter, determine the test oil film pressure and test oil film thickness corresponding to the test value through the elastohydrodynamic lubrication equivalent model.

8. A computer device, characterized in that, The computer device includes a processor and a memory: The memory is used to store program code and transmit the program code to the processor; The processor is used to execute the method according to any one of claims 1-6 according to the instructions in the program code.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program, and the computer program is used to execute the method according to any one of claims 1-6.

10. A computer program product including instructions, which when running on a computer, causes the computer to execute the method according to any one of claims 1-6.

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