Method for calculating leakage rate of elastic sealing ring based on microscopic leakage channel under particle influence

Abstract

The invention relates to the technical field of elastic sealing ring performance detection, and particularly discloses an elastic sealing ring leakage rate calculation method based on a microscopic leakage channel under particle influence, which comprises the following steps: S1, determining an analysis method for the influence of a particle medium on the leakage rate; s2, determining statistical parameters of triangular peak sampling and particle size, distribution and quantity of particles; s3, establishing a correction model of the triangular peak microstructure of the rough surface under the influence of the granular medium; s4, determining the height of an actual leakage channel formed by the contact of the elastic rubber material and the metal surface; s5, establishing a leakage rate calculation model of a single leakage channel; and S6, in combination with the analysis method in the step S1 and the leakage rate calculation model of the single leakage channel in the step S5, establishing a total leakage rate calculation model. According to the scheme, a particle-to-morphology correction mechanism is incorporated into a leakage rate calculation method, so that the leakage rate of an actual working condition can be accurately reflected, and the applicability of a prediction model is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of performance detection of elastic sealing rings, and specifically provides a method for calculating the leakage rate of an elastic sealing ring based on microscopic leakage channels under the influence of particles. Background Art

[0002] Sealing rings, especially elastic sealing rings, are key sealing components widely used in engineering equipment. They fill the contact surface gap through elastic deformation to achieve the fluid sealing function, and are the core components to ensure the reliable operation of the equipment. Especially in offshore engineering, sealing rings are widely used as key components in underwater oil and gas production systems, deep-sea exploration equipment, and submarine pipeline connections. However, due to complex working conditions such as high pressure, formation debris, and extreme temperatures, if the sealing performance of the elastic sealing ring fails, it will directly threaten the operation and safety of the equipment. The leakage rate is an important indicator to evaluate the sealing performance. Therefore, it is crucial to calculate the influence of the leakage rate of the elastic sealing ring on its performance.

[0003] From the analysis of the microscopic mechanism, the sealing interface is not an ideal smooth surface. The existence of microscopic rough peaks leads to the formation of discrete micro-channels in the contact area, which become the main paths of leakage. At the same time, in the actual engineering environment, the sealing ring is often exposed to working conditions with particulate media. Particulate media such as dust and debris. The presence of particles will indirectly change the microscopic morphology of the rough peaks, thereby affecting the leakage rate of the sealing interface.

[0004] In the prior art, there is a patent application document with the publication number "CN119492482A" and the name "Calculation Method for Leakage Rate of Rubber Sealing Layer in Compressed Air Energy Storage Chamber", including: infrared temperature detectors are staggered at the crown and invert of the chamber respectively, and fiber optic temperature sensors are cross-set along the longitudinal direction and radial direction of the chamber respectively. The leakage position of the rubber sealing layer is determined by the temperature changes on the inner and outer surfaces of the rubber sealing layer, and high-pressure air is injected into the chamber.

[0005] This solution can calculate the leakage amount and leakage rate of the rubber sealing layer according to the heat conduction formula and the temperature detection data at the leakage position, and evaluate the operation efficiency of the air in the chamber during the compressed air energy storage process. However, the current calculation methods of leakage rate generally do not incorporate the particle-induced morphology correction mechanism, and it is difficult to accurately reflect the leakage rate under actual working conditions.

[0006] In summary, the leakage rate calculation methods in the prior art are limited in the applicability of the prediction model due to ignoring the influence of particulate media. Therefore, it is necessary to propose a morphology reconstruction method combined with particle correction to construct a leakage rate calculation model that is more in line with engineering reality, so as to improve the scientificity and reliability of the sealing ring design. Summary of the Invention

[0007] To solve the above problems, the present invention provides a method for calculating the leakage rate of an elastic sealing ring based on microscopic leakage channels under the influence of particles, which can effectively calculate the leakage rate of the sealing interface between the elastic sealing ring and the metal surface, facilitate the quantitative analysis of the sealing performance of the elastic sealing ring sealing system under particle medium conditions, and ensure the reliability of the sealing system.

[0008] The method for calculating the leakage rate of an elastic sealing ring based on microscopic leakage channels under the influence of particles provided by the present invention includes the following steps:

[0009] S1. Determine the analysis method for the influence of particle medium on the leakage rate;

[0010] S2. Determine the statistical parameters of triangular peak sampling and the particle size, distribution and quantity of particles;

[0011] S3. According to the analysis method in step S1, establish a correction model for the microscopic morphology of triangular peaks on the rough surface under the influence of particle medium;

[0012] S4. Determine the actual leakage channel height formed by the contact between the elastic rubber material and the metal surface;

[0013] S5. Taking the parameters obtained in steps S3 and S4 as known conditions, establish a leakage rate calculation model for a single leakage channel;

[0014] S6. Combining the analysis method in step S1 and the leakage rate calculation model for a single leakage channel in step S5, establish a total leakage rate calculation model.

[0015] Further, the analysis method in step S1 is specifically as follows:

[0016] Regard the elastic sealing ring as a smooth elastic surface, regard the metal as a rigid body with a rough surface, and regard the particles as rigid spheres; there are two cases for the particle size: the first case is that the particle size is less than 1 / 2 of the bottom side of the triangular peak and less than 1 / 2 of the peak height of the triangular peak. In this case, directly consider the blocking and reducing effect of the particle size on the leakage channel area; the second case is that the particle size is greater than 1 / 2 of the bottom side of the triangular peak or greater than 1 / 2 of the peak height of the triangular peak. In this case, analyze from the perspective of the change in the triangular peak morphology caused by the particles.

[0017] Further, the statistical parameters of triangular peak sampling in step S2 include the average peak height h, the average peak angle θ, and the average bottom side length z;

[0018] In step S2, the distribution and quantity of particles are determined by formula (1), and formula (1) is where A is the total amount of the triangular peak statistical sample, η is the particle concentration, A D is the number of particles located at the peak top, A G is the number of particles located at the peak valley.

[0019] Furthermore, the correction model in step S3 is specifically as follows:

[0020] For the case where the particle is at the peak of the peak, the geometric parameters of the equivalent triangular peak are represented by Formula 2, and Formula 2 is

[0021] For the case where the particle is at the trough of the peak, the geometric parameters of the equivalent triangular peak include Formula 3 when d ≤ z and Formula 4 when d > z;

[0022] When d ≤ z, Formula 3 is

[0023] When d > z, Formula 4 is

[0024] Among them, d represents the particle size; z represents the average bottom side length of the triangular peak; h represents the average peak height of the triangular peak; θ represents the average peak angle of the triangular peak; h D represents the corrected peak height when the particle is at the peak; z D represents the corrected bottom side length when the particle is at the peak; θ D represents the corrected peak angle when the particle is at the peak; h G represents the corrected peak height when the particle is at the trough; z G represents the corrected bottom side length when the particle is at the trough; θ G represents the corrected peak angle when the particle is at the peak.

[0025] Furthermore, after the correction model in step S3 determines the particle distribution and quantity in step S2, the number of triangular peaks N D and N G ;

[0026] N D is represented by Formula 5, and Formula 5 is

[0027] N G is represented by Formula 6, and Formula 6 is

[0028] Furthermore, the corrected statistical parameters of the triangular peak can be obtained. The corrected statistical parameters of the triangular peak include Formula 7, Formula 8, and Formula 9;

[0029] Formula 7 is

[0030] Formula 8 is

[0031] Formula 9 is

[0032] Among them, h KRepresents the corrected average peak height; Z K Represents the corrected average bottom side length; θ K Represents the corrected average peak angle.

[0033] Furthermore, the actual leakage channel height formed by the contact between the elastic rubber material and the metal surface in step S4 is represented by Equation Ten;

[0034] Equation Ten is

[0035] In the formula, H is the actual leakage channel height after extrusion, P is the contact pressure, H0 is the leakage channel height when just contacting without extrusion (P = 0) (H0 = h K ), K S is the sealing performance coefficient.

[0036] Furthermore, the linear flow velocity along the normal direction of the channel cross-section in a single channel under static seal obtained in step S5 is specifically represented by Equation Eleven;

[0037] Equation Eleven is

[0038] In the formula, v is the laminar flow velocity, ΔP is the medium pressure difference, μ is the hydrodynamic viscosity, L is the length of the leakage channel, and δ is the laminar height.

[0039] Furthermore, the leakage rate calculation model of a single leakage channel in step S5 is represented by Equation Twelve; Equation Twelve is

[0040] In the formula, q is the leakage rate of a single leakage channel; q is the leakage rate of a single leakage channel.

[0041] Furthermore, the total leakage rate calculation model in step S6 is represented by Equation Thirteen and Equation Fourteen;

[0042] Equation Thirteen is At this time, the particle size is greater than 1 / 2 of the bottom side of the triangular peak or greater than 1 / 2 of the peak height of the triangular peak;

[0043] Equation Fourteen is At this time, the particle size is less than 1 / 2 of the bottom side of the triangular peak and less than 1 / 2 of the peak height of the triangular peak;

[0044] In the formula, Q is the total leakage rate, and S is the length of the annular seal contact area of the sealing ring.

[0045] Compared with the prior art, the present invention can achieve the following beneficial effects: The elastic rubber ring sealing rate calculation method in this solution is based on a simplified model of the uniform distribution of rough triangular peaks on the metal surface, a leakage channel model, a model of the influence of particulate media on the rough peak morphology, and a correction model for triangular peak parameters. A leakage rate calculation method for elastic sealing rings based on microscopic leakage channels under the influence of particles is established. It can equate the influence of particles on the leakage of the sealing ring to the influence of particles on the surface rough peaks, effectively calculate the leakage rate of the sealing interface between the elastic sealing ring and the metal surface, and conveniently conduct a quantitative analysis of the sealing performance of the elastic sealing ring sealing system under particulate media conditions, ensuring the reliability of the sealing system. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 FIG. is a schematic diagram of the uniform arrangement of rough peaks on the metal surface in the leakage rate calculation method provided by an embodiment of the present invention; in the figure, M1 is the sealing ring, M2 is the real rough peak, M3 is the contact gap, J1 is the rough peak simplification, and J2 is the uniform distribution of rough peaks;

[0047] Figure 2 FIG. is a schematic diagram of triangular peaks and a single leakage channel in the leakage rate calculation method provided by an embodiment of the present invention; in the figure, (a) is the normalized triangular peak and (b) is the leakage channel;

[0048] Figure 3 FIG. is a schematic diagram when the particle is located at the top of the triangular peak in the leakage rate calculation method provided by an embodiment of the present invention, where d < z at this time;

[0049] Figure 4 FIG. is a schematic diagram when the particle is located at the valley of the triangular peak in the leakage rate calculation method provided by an embodiment of the present invention, where d < 2z at this time;

[0050] Figure 5 FIG. is a schematic diagram when the particle is located at the top of the triangular peak in the leakage rate calculation method provided by an embodiment of the present invention, where d > z at this time;

[0051] Figure 6 FIG. is a schematic diagram when the particle is located at the valley of the triangular peak in the leakage rate calculation method provided by an embodiment of the present invention, where d > 2z at this time;

[0052] Figure 7 FIG. is the overall flow of the leakage rate calculation method provided by an embodiment of the present invention DETAILED DESCRIPTION OF THE EMBODIMENTS

[0053] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the following further elaborates on the present invention in conjunction with the appended Figure 1-7 drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the present invention.

[0054] A method for calculating the leakage rate of an elastic sealing ring based on microscopic leakage channels under the influence of particles, comprising the following steps:

[0055] S1. Determine the analysis method for the influence of particle medium on the leakage rate, specifically as follows:

[0056] Regard the elastic sealing ring as a smooth elastic surface, regard the metal as a rigid body with a rough surface, and regard the particles as rigid spheres; there are two cases for the particle size: the first case is that the particle size is less than 1 / 2 of the bottom side of the triangular peak and less than 1 / 2 of the peak height of the triangular peak. At this time, directly consider the shielding and reduction effect of the particle size on the leakage channel area; the second case is that the particle size is greater than 1 / 2 of the bottom side of the triangular peak or greater than 1 / 2 of the peak height of the triangular peak. At this time, analyze from the perspective of the change in the triangular peak morphology caused by the particles.

[0057] S2. Determine the statistical parameters of triangular peak sampling, the particle size, distribution and quantity of the particles. The statistical parameters of triangular peak sampling include the average peak height h, the average peak angle θ, and the average bottom side length z.

[0058] According to the regulations of the national standard GB / T1031-2009 for the sampling range, taking the metal surface with a surface roughness Ra = 3.2um as an example, the sampling length is 1mm, and the metal cross-section is statistically analyzed with the statistical parameter A = 150 to obtain the average peak height h of 5.2um, the average peak angle θ of 65.35°, the average bottom side length z of 6.67um, the particle concentration η is taken as 5%, and the particle sizes d are taken as 1um and 5um in two cases.

[0059] Determine the distribution and quantity of the particles through Formula 1. Formula 1 is where A is the total amount of triangular peak statistical samples, η is the particle concentration, A D is the number of particles located at the peak top, A G is the number of particles located at the peak valley.

[0060] For the case of d = 1um, the particle quantity is not calculated, and the total leakage rate is calculated separately;

[0061] For the case of d = 5um, the quantities of particles located at the peak top and peak valley are calculated as:

[0062] S3. According to the analysis method in step S1, establish a modified model of the microscopic morphology of triangular peaks on the rough surface under the influence of the particle medium. Specifically as follows:

[0063] For the case where the particles are at the peak top, the equivalent geometric parameters of the triangular peak are represented by Formula 2. Formula 2 is

[0064] Taking Formula 2 as an example, in this embodiment,

[0065] For the case where the particle is at the peak or valley, the geometric parameters of the equivalent triangular peak include Formula 3 when d ≤ z and Formula 4 when d > z;

[0066] When d ≤ z, Formula 3 is

[0067] Taking Formula 3 as an example, in this embodiment,

[0068] When d > z, Formula 4 is

[0069] Among them, d represents the particle size; z represents the average bottom side length of the triangular peak; h represents the average peak height of the triangular peak; θ represents the average peak angle of the triangular peak; the subscripts D and G respectively represent the correction values of z, h, and θ in the two cases where the particle size is at the peak and valley of the triangular peak. Specifically, h D represents the corrected peak height when the particle is at the peak; z D represents the corrected bottom side length when the particle is at the peak; θ D represents the corrected peak angle when the particle is at the peak; h G represents the corrected peak height when the particle is at the valley; z G represents the corrected bottom side length when the particle is at the valley; θ G represents the corrected peak angle when the particle is at the peak.

[0070] After the correction model determines the particle distribution and quantity in step S2, the number of triangular peaks N D and N G affected by the particle located at the peak and valley can be obtained;

[0071] N D is represented by Formula 5, and Formula 5 is

[0072] N G is represented by Formula 6, and Formula 6 is

[0073] In this embodiment,

[0074] Furthermore, the corrected statistical parameters of the triangular peak can be obtained. The corrected statistical parameters of the triangular peak include Formula 7, Formula 8, and Formula 9;

[0075] Formula 7 is

[0076] Formula 8 is

[0077] Formula 9 is

[0078] In this embodiment,

[0079] Among them, h K represents the corrected average peak height; Z K represents the corrected average bottom side length; θ K represents the corrected average peak angle.

[0080] S4. Determine the actual leakage channel height formed by the contact between the elastic rubber material and the metal surface. The actual leakage channel height formed by the contact between the elastic rubber material and the metal surface is represented by Equation Ten;

[0081] Equation Ten is

[0082] In the formula, H is the actual leakage channel height after extrusion, P is the contact pressure, H0 is the leakage channel height when just in contact without extrusion (P = 0) (H0 = h K ), K S is the sealing performance coefficient.

[0083] To calculate the actual channel height, it is necessary to determine the pressure difference between the media on both sides of the leakage channel. Here, the pressure difference ΔP is taken as 5 MPa, and the sealing performance coefficient KS of the elastic rubber material is taken as 10 MPa. Then:

[0084]

[0085] S5. Taking the parameters obtained in Step S3 and Step S4 as known conditions, establish a leakage rate calculation model for a single leakage channel. According to the N - S equation, the linear velocity along the normal direction of the channel cross - section in a single channel under static seal is obtained, which is specifically represented by Equation Eleven;

[0086] Equation Eleven is

[0087] In the formula, v is the laminar flow velocity, ΔP is the pressure difference of the medium, μ is the dynamic viscosity of the fluid, L is the length of the leakage channel, and δ is the laminar height.

[0088] The leakage rate calculation model for a single leakage channel in Step S5 is represented by Equation Twelve;

[0089] Equation Twelve is

[0090] In the formula, q is the leakage rate of a single leakage channel; q is the leakage rate of a single leakage channel.

[0091] First, it is necessary to determine the length L of the leakage channel and the hydrodynamic viscosity μ. According to most actual engineering projects, take L = 2 mm and μ = 0.03 Pa·s. Then, based on the triangular peak correction parameter obtained in step S2, the normal line velocity along the channel cross-section in a single channel under static seal obtained from the N - S equation, and by integrating the channel cross-sectional area, the volume flow rate in the channel can be obtained, that is, the leakage rate of a single leakage channel:

[0092]

[0093] S6. Combine the analysis method in step S1 and the leakage rate calculation model of a single leakage channel in step S5 to establish a total leakage rate calculation model. The total leakage rate calculation model is represented by Formula Thirteen and Formula Fourteen;

[0094] Formula Thirteen is At this time, the particle size is greater than 1 / 2 of the bottom edge of the triangular peak or greater than 1 / 2 of the peak height of the triangular peak;

[0095] Formula Fourteen is At this time, the particle size is less than 1 / 2 of the bottom edge of the triangular peak and less than 1 / 2 of the peak height of the triangular peak;

[0096] In the formula, Q is the total leakage rate, and S is the length of the annular seal contact area of the sealing ring.

[0097] Before calculating the total leakage rate, it is also necessary to determine the length S of the annular seal contact area of the sealing ring to obtain the total number of leakage channels in the sealing area. According to the leakage channel length L taken in step S3, take the length S of the annular seal contact area of the sealing ring as 30 mm.

[0098] For the case of particle size d = 1 μm, only consider the blocking effect of particles on the leakage channel. Therefore, the total leakage rate (at this time H0 = h):

[0099]

[0100] For the case of particle size d = 5 μm, according to the leakage rate calculation results of a single leakage channel calculated in step (3), sum the leakage rates of each leakage channel to obtain the total leakage rate:

[0101]

[0102] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for calculating the leakage rate of an elastic sealing ring based on microscopic leakage channels under the influence of particles, characterized in that, It includes the following steps: S1. Determine the analysis method for the influence of particulate medium on the leakage rate; S2. Determine the statistical parameters of triangular peak sampling, the particle size, distribution and quantity of particles; S3. According to the analysis method in step S1, establish a correction model for the microscopic morphology of triangular peaks on the rough surface under the influence of particulate medium; S4. Determine the actual leakage channel height formed by the contact between the elastic rubber material and the metal surface; S5. Taking the parameters obtained in steps S3 and S4 as known conditions, establish a leakage rate calculation model for a single leakage channel; S6. Combining the analysis method in step S1 and the leakage rate calculation model for a single leakage channel in step S5, establish a total leakage rate calculation model.

2. The method for calculating the leakage rate of an elastic sealing ring based on microscopic leakage channels under the influence of particles according to claim 1, wherein The analysis method in step S1 is specifically as follows: Regard the elastic sealing ring as a smooth elastic surface, regard the metal as a rigid body with a rough surface, and regard the particles as rigid spheres; there are two cases for the particle size: the first case is that the particle size is less than 1 / 2 of the base of the triangular peak and less than 1 / 2 of the peak height of the triangular peak. In this case, directly consider the shielding and reduction effect of the particle size on the leakage channel area; the second case is that the particle size is greater than 1 / 2 of the base of the triangular peak or greater than 1 / 2 of the peak height of the triangular peak. In this case, analyze from the perspective of the change in the triangular peak morphology caused by the particles.

3. The method for calculating the leakage rate of the elastic sealing ring based on the microscopic leakage channel under the influence of particles according to claim 1, characterized in that, The statistical parameters of triangular peak sampling in step S2 include the average peak height h, the average peak angle θ, and the average base length z; In step S2, the distribution and quantity of particles are determined by formula (1), and formula (1) is where A is the total amount of the triangular peak statistical samples, η is the particle concentration, A D is the number of particles located at the peak top, and A G is the number of particles located at the peak valley.

4. The method for calculating the leakage rate of the elastic sealing ring based on the microscopic leakage channel under the influence of particles according to claim 1, characterized in that The correction model in step S3 is specifically as follows: For the case where the particle is at the peak, the geometric parameters of the equivalent triangular peak are represented by Equation 2, and Equation 2 is For the case where the particles are in the peak valley, the equivalent geometric parameters of the triangular peak include formula three when d ≤ z and formula four when d > z; When d ≤ z, Equation 3 is When d > z, Equation Four is Among them, d represents the particle size; z represents the average bottom side length of the triangular peak; h represents the average peak height of the triangular peak; θ represents the average peak angle of the triangular peak; h D represents the corrected peak height when the particle is at the peak; z D represents the corrected bottom side length when the particle is at the peak; θ D represents the corrected peak angle when the particle is at the peak; h G represents the corrected peak height when the particle is at the trough; z G represents the corrected bottom side length when the particle is at the trough; θ G represents the corrected peak angle when the particle is at the peak.

5. The method for calculating the leakage rate of an elastic sealing ring based on microscopic leakage channels under the influence of particles according to claim 4, wherein After the correction model in step S3 determines the particle distribution and quantity in step S2, the number N of triangular peaks affected by the particles located at the peak and valley can be obtained D and N G ; N D represented by Formula 5, which is N G represented by Formula VI, which is Furthermore, the corrected statistical parameters of the triangular peak can be obtained. The corrected statistical parameters of the triangular peak include formula seven, formula eight and formula nine; Equation Seven is Formula VIII is Formula Nine is Among them, h K represents the corrected average peak height; Z K represents the corrected average base length; θ K represents the corrected average peak angle.

6. The method for calculating the leakage rate of the elastic sealing ring based on the microscopic leakage channel under the influence of particles according to claim 5, wherein The actual leakage channel height formed by the contact between the elastic rubber material and the metal surface in step S4 is represented by formula ten; Formula ten is Wherein, H is the actual height of the leakage channel after extrusion, P is the contact pressure, and H0 is the height of the leakage channel when just contacting without extrusion (P = 0) (H0 = h K ), K S is the sealing performance coefficient.

7. The method for calculating the leakage rate of the elastic sealing ring based on the microscopic leakage channel under the influence of particles according to claim 6, wherein In step S5, the linear velocity along the normal direction of the channel cross-section in a single channel under static seal is obtained according to the N-S equation, which is specifically represented by formula eleven; Formula XI is In the formula, v is the laminar flow velocity, ΔP is the medium pressure difference, μ is the hydrodynamic viscosity, L is the length of the leakage channel, and δ is the laminar height.

8. The method for calculating the leakage rate of an elastic sealing ring based on microscopic leakage channels under the influence of particles according to claim 7, wherein The leakage rate calculation model for a single leakage channel in step S5 is represented by formula twelve; Equation XII is In the formula, q is the leakage rate of a single leakage channel; q is the leakage rate of a single leakage channel.

9. The method for calculating the leakage rate of an elastic sealing ring based on microscopic leakage channels under the influence of particles according to claim 8, wherein The total leakage rate calculation model in step S6 is represented by formula thirteen and formula fourteen; Formula XIII is At this time, the particle size is greater than 1 / 2 of the base of the triangular peak or greater than 1 / 2 of the peak height of the triangular peak; Formula XIV is At this time, the particle size is less than 1 / 2 of the bottom edge of the triangular peak and less than 1 / 2 of the peak height of the triangular peak; In the formula, Q is the total leakage rate, and S is the length of the annular seal contact area of the sealing ring.

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