A method for calculating the thickness of an oil film in a solid-coated lubricated transmission system

Abstract

This invention relates to the field of lubrication transmission technology and discloses a method for calculating the oil film thickness of a solid-coated lubrication transmission system, comprising the following steps: introducing a frequency response function; introducing an equivalent elastic modulus; determining dimensionless parameters; modifying the Hamrock-Dowson formula; and calculating the oil film thickness formula. This invention applies extended Hertzian theory to calculate the oil film thickness of a coating-substrate contact system. It derives an equivalent elastic modulus applicable to solid-lubricated coating-substrate contact models, and considers the influence of roughness and the hardness of the coupled coating and substrate, introducing a roughness correction factor. f， Furthermore, this was applied to oil film thickness calculation, and a calculation model for oil film thickness in the coating substrate contact system was completed. By analyzing the influence of coating properties on the lubrication conditions and transmission performance of the transmission mechanism, theoretical support was provided for selecting lubrication coating materials with better lubrication performance.

Description

Technical Field

[0001] This invention relates to the field of lubrication and transmission technology, specifically to a method for calculating the oil film thickness of a solid coating lubrication and transmission system. Background Technology

[0002] High-precision aerospace gears and precision robotic arm joint gears require high transmission accuracy when using solid coating lubrication. Oil film thickness is a crucial indicator for evaluating the lubrication status of core components in transmission systems such as gears and bearings. Performance degradation is likely to occur under the extreme operating environments of space (such as wide temperature ranges, vacuum, low gravity, and strong radiation). Therefore, solid lubrication coatings are typically used to optimize gear transmission performance, improve wear resistance, friction reduction, and environmental adaptability, thereby meeting engineering application requirements.

[0003] Traditional elastohydrodynamic lubrication theory typically assumes that the contact pair materials are homogeneous and isotropic, which fails to accurately describe the elastic response of the coating-matrix composite structure. When the elastic moduli of the coating and the substrate differ significantly, the contact stress distribution and deformation characteristics are fundamentally different from those of homogeneous materials, leading to large deviations in film thickness prediction. Existing technologies oversimplify the treatment of coating effects, neglecting the coupling between the substrate and coating materials, resulting in limited applicability and poor numerical stability. Therefore, we propose a method for calculating the oil film thickness of a solid-coated lubrication transmission system. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the oil film thickness of a solid coating lubrication transmission system, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating the oil film thickness of a solid coating lubricated transmission system, comprising the following steps: S1. Introducing the frequency response function; the frequency response function of the normal displacement of a three-dimensional object surface with a lubricated coating due to pressure. ; S2, Introducing equivalent elastic modulus The shear modulus in the FRF expression Converted to equivalent elastic modulus of coating and substrate ; S3. Determination of dimensionless parameters, including the following formulas: ; ; ; ; ;in: W For load parameters; U For speed parameters; G These are viscosity-pressure parameters; S The slip ratio; P 1 represents the unit line load;R The equivalent radius of curvature, R 1. R 2 represents the radius of curvature of the two contacting bodies; η 0 represents the viscosity of the lubricating oil (Pa*s); u r This refers to the suction speed; α Viscosity coefficient (Pa) -1 ),and ; u s Where z is the sliding velocity and z is the viscosity-pressure index; S4, obtained through extensive numerical fitting based on the classic Hamrock-Dowson formula: ; S5. Calculate the formula for oil film thickness.

[0006] Optionally, the frequency response function ; in, ,in For contact force, h The coating thickness is dimensionless. These are the Poisson's ratios of the coating material and the substrate material, respectively. These are the shear moduli of the coating material and the substrate material, respectively.

[0007] Optional, equivalent elastic modulus Later I learned: ; By comparing the expression for FRF with the limiting cases of no coating and infinitely thick coating, an extended Hertzian theory definition of the equivalent elastic modulus is established. .

[0008] Optionally, S2 further includes setting a comprehensive equivalent elastic modulus e1; wherein, .

[0009] Optionally, in S4, based on the numerical simulation regression equation for elastohydrodynamic lubrication of rough surfaces, the film thickness at the center is... H c and minimum film thickness H min The calculation formula introduces a correction factor. f rough : ; ; in: Dimensionless roughness; V = ν / e 1 represents dimensionless hardness. ν is the root mean square roughness; ν is the Vickers hardness of the matrix.

[0010] Optionally, the formula for calculating the oil film thickness in S5 is: ; The actual film thickness is: ; in, This represents the actual oil film thickness.

[0011] Compared with the prior art, the present invention provides a method for calculating the oil film thickness of a solid coating lubrication transmission system, which has the following beneficial effects: 1. This method for calculating the oil film thickness of a solid-coated lubricated transmission system applies extended Hertzian theory to the calculation of oil film thickness in the coating-substrate contact system. It derives an equivalent elastic modulus applicable to the contact between solid-lubricated coated objects by deriving a coating-substrate contact model, and considers the influence of roughness and the hardness of the coupled coating and substrate. A roughness correction factor is introduced. f， This was then applied to oil film thickness calculation, resulting in a calculation model for oil film thickness in the coating substrate contact system.

[0012] 2. The method for calculating the oil film thickness of the solid coating lubrication transmission system, through the calculation model, can better reflect the film thickness and friction coefficient values, and achieve a quantitative description of the lubrication state, load distribution, and coating thickness effect. The analytical formula improves the calculation efficiency by 2 to 3 orders of magnitude compared with numerical solutions. In addition, the film thickness calculation model of this invention can be used to analyze the influence of coating properties on the lubrication conditions and transmission performance of the transmission mechanism, providing theoretical support for selecting lubrication coating materials with better lubrication performance. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the process structure of the present invention; Figure 2 This is a graph showing the ratio of the elastic modulus of the coating substrate to the minimum oil film thickness in this invention. Detailed Implementation

[0014] 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.

[0015] like Figures 1-2 As shown, the present invention provides a technical solution: a method for calculating the oil film thickness of a solid coating lubrication transmission system, comprising the following steps: S1, Introducing the frequency response function; the frequency response function of the normal displacement of a three-dimensional object surface with a lubricated coating due to pressure. : ; in ,in For contact force, h The coating thickness is dimensionless. These are the Poisson's ratios of the coating material and the substrate material, respectively. These are the shear moduli of the coating material and the substrate material, respectively.

[0016] S2, to combine the material responses of the coating and the substrate, introduces an equivalent elastic modulus. The definition of equivalent modulus is based on the following idea: the combined response of the coating and substrate can be regarded as the response of an equivalent half-plane, and the response of the equivalent half-plane can be expressed by the equivalent elastic modulus. To describe it. The shear modulus in the FRF expression. Converted to equivalent elastic modulus of coating and substrate , We can obtain the following formula: ; By comparing the expression for FRF with the limiting cases of no coating and infinitely thick coating, an extended Hertzian theory definition of the equivalent elastic modulus is established. E * : ; To reflect the overall elastic response parameters of the entire coating / substrate system under contact load and to lay the foundation for all subsequent dimensionless calculations, we define the overall equivalent elastic modulus e1: ; S3, the dimensionless parameter is determined, including the following formula:

[0017] in: W For load parameters; U For speed parameters; G These are viscosity-pressure parameters; S The slip ratio; P 1 represents the unit line load (N / M); R The equivalent radius of curvature (m) R 1. R 2 represents the radius of curvature of the two contacting bodies; η 0 represents the viscosity of the lubricating oil (Pa*s); u r The suction speed is (m / s). α Viscosity coefficient (Pa) -1 ),and ; u s Let be the sliding velocity (m / s), and z be the viscosity-pressure index; S4, obtained through extensive numerical fitting based on the classic Hamrock-Dowson formula: ; This function reflects: load W As the speed increases, the oil film thins slightly; U Increased oil film thickness; viscosity-pressure parameters G Increase, oil film thickens; For ellipticity correction, K When the value is 1 (point contact), the correction factor is approximately 0.39.

[0018] Considering the effects of roughness and hardness, a correction value is added. Based on the numerical simulation regression equation for elastohydrodynamic lubrication of rough surfaces, the central film thickness is adjusted. H c and minimum film thickness H min The calculation formula introduces a correction factor. f rough :

[0019] in: Dimensionless roughness; V = ν / e 1 represents dimensionless hardness; ν is the root mean square roughness; ν is the Vickers hardness of the matrix.

[0020] S5, Finally, we obtain the formula for calculating oil film thickness: ;

[0021] The actual film thickness is: ; in, This represents the actual oil film thickness.

[0022] In this embodiment, the calculation model can better reflect the film thickness and friction coefficient values, and achieve a quantitative description of lubrication state, load distribution, and coating thickness effect. The analytical formula improves the calculation efficiency by 2 to 3 orders of magnitude compared to numerical solutions. In addition, the film thickness calculation model of this invention can be used to analyze the influence of coating properties on the lubrication conditions and transmission performance of the transmission mechanism, providing theoretical support for selecting lubrication coating materials with better lubrication performance. The present invention has been described in detail above. However, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, any modifications or improvements that do not depart from the spirit of the present invention are within the scope of protection of the present invention.

Claims

1. A method for calculating the thickness of a film of oil in a solid-coated lubricated transmission system, characterized in that, Includes the following steps: S1, introducing a frequency response function; determining a frequency response function of the normal displacement of the surface of the three-dimensional object with lubricating coating due to pressure ; S2, Introducing the equivalent elastic modulus Converting the shear modulus in the FRF expression to the equivalent elastic modulus of the coating and substrate ; S3. Determination of dimensionless parameters, including the following formulas: ; ; ; ; ;in: W These are the load parameters; U For speed parameters; G These are viscosity-pressure parameters; S The slip ratio; P 1 represents the unit line load; R The equivalent radius of curvature, R 1. R 2 represents the radius of curvature of the two contacting bodies; η 0 represents the viscosity of the lubricating oil; u r This refers to the suction speed; α Where is the viscosity-pressure coefficient, and ; u s Where z is the sliding velocity and z is the viscosity-pressure index; S4, according to the classical Hamrock-Dowson formula, by a large number of numerical fitting: ; S5. Calculate the formula for oil film thickness.

2. The method for calculating the oil film thickness of a solid coating lubricated transmission system as described in claim 1, characterized in that, The frequency response function ; in, ,in For contact force, h The coating thickness is dimensionless. These are the Poisson's ratios of the coating material and the substrate material, respectively. These are the shear moduli of the coating material and the substrate material, respectively.

3. The method for calculating the oil film thickness of a solid coating lubricated transmission system as described in claim 1, characterized in that, The S2 includes: equivalent elastic modulus Later I learned: ; By comparing the expression for FRF with the limiting cases of no coating and infinitely thick coating, an extended Hertzian theory definition of the equivalent elastic modulus is established. .

4. The method for calculating the oil film thickness of a solid coating lubricated transmission system as described in claim 3, characterized in that, The S2 further includes setting a comprehensive equivalent elastic modulus e1; wherein... .

5. The method for calculating the oil film thickness of a solid coating lubricated transmission system as described in claim 1, characterized in that, In S4, based on the numerical simulation regression equation for elastohydrodynamic lubrication of rough surfaces, the film thickness at the center is... H c and minimum film thickness H min The calculation formula introduces a correction factor. f rough : in: Dimensionless roughness; V = ν / e 1 represents dimensionless hardness. ν is the root mean square roughness; ν is the Vickers hardness of the matrix.

6. The method for calculating the oil film thickness of a solid coating lubricated transmission system as described in claim 1, characterized in that, The formula for calculating the oil film thickness in S5 is as follows: The actual film thickness is: ;in, This represents the actual oil film thickness.

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