A method for predicting the leakage rate of a sealed surface based on a composite leakage channel model

Abstract

The application discloses a kind of based on composite leakage channel model's sealed surface leakage rate prediction method.Sealed surface is divided into area and is modeled to obtain the statistical parameter of each area of rough peak of sealed surface;The modeling of leakage channel is carried out to the area of sealed surface, according to the statistical parameter of rough peak of area, leakage channel is divided into two forms of triangular channel and trapezoidal channel, then according to the form of leakage channel processing, leakage rate is obtained;The total leakage rate of sealed surface is obtained by the comprehensive processing of the leakage rate of each area.The leakage channel between O-ring and sealed surface is divided into two forms of triangular channel and trapezoidal channel and fusion processing in the application, sufficiently reflect the influence of the topographic features of sealed surface on channel form and leakage rate, improve the accuracy of leakage rate prediction.

Description

Technical Field

[0001] This invention relates to a leakage prediction method in the field of O-ring static seals, specifically a method for predicting the leakage rate of a sealing surface based on a composite leakage channel model. Background Technology

[0002] O-ring seals, as one of the most common sealing methods, are designed to prevent leakage and loss of liquid or gaseous media. Because O-rings are simple and convenient to install, require little installation space, and, provided the structural design and material selection are appropriate, can provide a long-term sealing effect in the system under permissible operating conditions, O-ring seals are widely used in the sealing structures of various mechanical products and equipment.

[0003] O-ring seals utilize an O-ring elastic rubber ring for auxiliary sealing. Under compression, the O-ring can fill the gap between itself and the rough sealing surface to some extent, thus improving sealing reliability. Even so, at a microscopic level, the O-ring and the sealing surface cannot completely adhere. Areas where no contact occurs may form a gap penetrating the system. If the sealing medium flows out along this gap, leakage occurs, and this gap can be called a leakage path. To achieve performance prediction and high-precision design of O-ring seals, and ultimately improve the overall safety, reliability, and environmental protection of products and equipment, quantitative calculation of the static seal leakage rate between the O-ring and the sealing surface is essential.

[0004] Current methods for calculating O-ring seal leakage rates mostly focus on modeling and describing the leakage channels of the fluid at the sealing interface at a microscopic level, and then solving for the leakage rate of these channels. The classic Roth seal leakage model defines the profile of the leakage channel between the sealing surfaces in the form of a triangular wave. Based on this, models such as the spiral groove characteristic leakage channel model based on sine curves and the cosine wave leakage channel model based on fractal geometry have been developed. Combined with the theory of laminar flow of incompressible viscous fluids, these methods have been used to solve for the leakage rate between the O-ring and the sealing surface. In addition, some methods establish the relationship between contact topology and leakage rate at multiple scales based on percolation theory, which makes important contributions to the revelation of static sealing mechanisms; however, they lack certain applicability for engineering calculations of leakage rates.

[0005] In summary, existing methods for predicting the leakage rate of O-ring static seals mainly use a single geometric body to approximate the leakage path. While this simplifies the calculation process of the leakage rate, it is difficult to fully reflect the influence of the sealing surface characteristics on the leakage rate and thus cannot effectively guide engineering applications in practice. Summary of the Invention

[0006] To address the aforementioned issues, this invention provides a method for predicting the leakage rate of a sealing surface based on a composite leakage channel model. This method divides the leakage channel between the O-ring and the sealing surface into two forms: triangular channels and trapezoidal channels, and then integrates and processes them. This fully reflects the influence of the sealing surface morphology on the channel form and leakage rate, improving the accuracy of predicting the static seal leakage rate of the O-ring. It can be used for performance prediction and high-precision design of O-ring sealing structures, and has good engineering practical value.

[0007] The specific technical solution created by this invention is as follows:

[0008] S1. Divide the sealing surface into regions and perform modeling to obtain the roughness peak statistical parameters of each region of the sealing surface;

[0009] The sealing surface specifically refers to the sealing surface between the rough metal surface and the O-ring surface. O-rings are typically made of rubber.

[0010] S2. Model the leakage channels in the sealing surface area. Based on the roughness peak statistical parameters of the area, divide the leakage channels into two forms: triangular channels and trapezoidal channels. This makes the entire sealing surface form a composite leakage channel model of triangular channels and trapezoidal channels. Then, process the leakage channels according to their forms to obtain the leakage rate.

[0011] S3. The total leakage rate of the sealing surface is obtained by comprehensively processing the leakage rates of each area.

[0012] Step S1 specifically involves:

[0013] S11. Divide the sealing surface into multiple regions. Based on the root mean square roughness σ and autocorrelation length β of each region of the sealing surface obtained by pre-measurement, establish a contour numerical model of each region described by the Gaussian distribution function and the exponential autocorrelation function using a digital filtering method based on autoregressive time series.

[0014] S12. Uniformly sample the amplitude of the sealing surface on the contour numerical model of each region to obtain the roughness peak statistical parameters of the sealing surface, which are used to characterize the roughness peak of the sealing surface.

[0015] The rough peak statistical parameters include average peak height h, average peak angle θ, and average peak spacing Δχ. The average peak height h is defined as the average peak height of all rough peaks within the sampling length. The average peak angle θ is defined as the mean of the angles formed between each rough peak and its adjacent sampling points within the sampling length. The average peak spacing Δχ is defined as the ratio of the sampling length to the number of rough peaks within the sampling length.

[0016] In step S2, the sealing contact of the sealing surface is regarded as the contact between a smooth elastic surface and a rough rigid surface. The leakage channel formed by the sealing surface after being squeezed by the contact is regarded as a channel that is evenly distributed along the sealing surface. The leakage channel is divided into two forms: triangular channel and trapezoidal channel. The cross section of the triangular channel is an isosceles triangle, and the cross section of the trapezoidal channel is an isosceles trapezoid.

[0017] In practice, the O-ring surface can be considered a smooth, elastic surface, and the rough metal surface can be considered a rough, rigid surface. The gap between the O-ring surface and the rough metal surface is considered a channel evenly distributed around the circumference of the O-ring, and the sealing medium leaks radially along the O-ring within the leakage channel. The rough metal surface can be considered as being formed by multiple isosceles triangular strips arranged in a specific configuration.

[0018] If multiple isosceles triangular strips are arranged closely without gaps, a triangular channel is formed between adjacent isosceles triangular strips;

[0019] If multiple isosceles triangular strips are arranged at intervals, a trapezoidal channel is formed between adjacent isosceles triangular strips.

[0020] In step S2, the leakage rate is obtained by processing according to the leakage channel type, specifically as follows:

[0021] S21. Determine whether the leakage channel is a triangular channel or a trapezoidal channel based on the statistical parameters of the rough peak;

[0022] S22. Determine the original height of the leakage channel based on its type;

[0023] S23. Then determine the height of the leakage channel after contact extrusion based on the original height of the leakage channel;

[0024] S24. Calculate the leakage rate on the leakage channel of each area of ​​the sealing surface.

[0025] The specific steps of S21 are as follows:

[0026] When the average peak height h, average peak angle θ, and average peak spacing Δχ in the rough peak statistical parameters satisfy When this occurs, the leakage path is a triangular channel;

[0027] When the average peak height h, average peak angle θ, and average peak spacing Δχ in the rough peak statistical parameters satisfy When this occurs, the leakage channel is a trapezoidal channel.

[0028] The specific steps of S22 are as follows:

[0029] When the leakage channel is a triangular channel, the original height δ1 of the leakage channel is:

[0030] When the leakage channel is a trapezoidal channel, the original height δ2 of the leakage channel is: δ2 = h.

[0031] Specifically, step S23 involves obtaining the height of the leakage channel after contact extrusion according to the following formula:

[0032]

[0033] Among them, h R H represents the channel height after contact. R H is the channel height before contact. For a triangular channel, H is... R =δ1, for a trapezoidal channel, H R =δ²; e represents the natural constant, σ m K represents the contact pressure at the contact surfaces. S The leakage channel filling factor reflects the ability of the sealing elastic material to fill the leakage channel under a certain pressure. It is an inherent property of the sealing material and can be obtained through experimental measurement.

[0034] The specific steps of S24 are as follows:

[0035] S241. The number N of leakage channels in the area is determined by the following formula:

[0036]

[0037] Where πD is the length of the entire sealing surface, D is the inner diameter of the O-ring in the specific implementation, and α is the area division angle expressed in radians;

[0038] S242. Calculate the leakage rate of the sealing surface:

[0039] For a triangular channel, the leakage rate q1 of the triangular channel is calculated using the following formula based on the leakage channel height after contact compression:

[0040]

[0041] For a trapezoidal channel, the leakage rate q2 of the trapezoidal channel is calculated using the following formula based on the height of the leakage channel after contact compression:

[0042]

[0043] Where Δp represents the pressure difference across the leakage channel, μ is the fluid dynamic viscosity, and L is the length of the leakage channel, the value of which is equal to the width of the sealing contact area of ​​the O-ring along the radial direction.

[0044] Specifically, step S3 involves summing the leakage rates of all regions to obtain the total leakage rate of the sealing surface.

[0045] This invention calculates the leakage rate between an O-ring and a sealing surface based on a composite leakage channel model. First, based on the statistical parameters of the sealing surface roughness peak, the leakage channel between the O-ring and the sealing surface is defined as a composite leakage channel model containing both triangular and trapezoidal channels. Then, the leakage channel form is determined and the original height of the leakage channel is determined using the statistical parameters of the sealing surface roughness peak. The height of the leakage channel after contact compression is determined using the Roth sealing leakage model. Finally, the leakage rate on the leakage channel of the entire sealing surface is predicted according to different leakage channel forms.

[0046] The beneficial effects of this invention are as follows:

[0047] (1) The present invention defines the leakage channel between the O-ring and the sealing surface as a simple geometric body represented by elementary functions, which simplifies the topological form of the sealing contact, reduces the computational complexity, and improves the processing efficiency.

[0048] (2) The present invention defines the leakage channel between the O-ring and the sealing surface as a composite leakage channel model that includes two forms: triangular channel and trapezoidal channel. The two channel forms can be converted to each other under different rough surface statistical parameters. Compared with the existing single geometric channel model, it is more flexible and more realistically reflects the influence of the sealing surface morphology on the leakage channel form and leakage rate, thereby improving the accuracy of leakage rate prediction.

[0049] (3) The O-ring seal leakage rate prediction method provided by the present invention establishes an explicit mapping relationship between the sealing surface morphology parameters and the channel leakage rate through leakage channel parameters. The physical meaning of the channel model parameters is clear, which can directly guide the performance prediction and high-precision design of O-ring seal structures and has good engineering practical value. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the O-ring sealing structure in this invention. (a) shows the sealing structure in its initial state, and (b) shows the sealing structure in its contact compression state.

[0051] Figure 2 This is a flowchart of the leakage rate prediction method of the present invention.

[0052] Figure 3 This is a schematic diagram of the numerical model of the local contour of the sealing surface in this invention.

[0053] Figure 4 This is a schematic diagram of the triangular channel in this invention.

[0054] Figure 5 This is a schematic diagram of the trapezoidal channel in this invention. Detailed Implementation

[0055] The invention will be further illustrated below using an O-ring sealing structure as an example.

[0056] Figure 1 This is a schematic diagram of an O-ring seal structure, including a sealing surface, an O-ring, and a sealing groove. The O-ring is placed in the sealing groove, and the contact area between the O-ring and the sealing surface is the main sealing area of ​​this structure. Under the action of clamping force and the pressure of the sealing medium, the O-ring undergoes elastic deformation and presses tightly against the sealing surface to prevent leakage of the sealing medium, thereby achieving a seal. The basic parameters of the sealing system include: O-ring inner diameter 88.49 mm, O-ring cross-sectional diameter 3.53 mm, O-ring material is nitrile rubber, sealing contact area width 3.1 mm, sealing contact equivalent pressure 8 MPa, sealing medium equivalent pressure 7 MPa, sealing medium dynamic viscosity 0.0087 Pa·s, ambient temperature 300 K, and ambient pressure 0.1 MPa.

[0057] Figure 2 The flowchart of the leakage rate prediction method of the present invention is shown below. Figure 2 As shown, the implementation process of this embodiment of the invention includes the following steps:

[0058] S1. Obtain the roughness peak statistical parameters for each region of the sealing surface;

[0059] S11. Divide the sealing surface into multiple regions. Based on the root mean square roughness σ and autocorrelation length β of the sealing surface obtained by pre-measurement, calculate the root mean square roughness σ and autocorrelation length β of each region of the sealing surface. Use a digital filtering method based on autoregressive time series to establish a contour numerical model of each region described by Gaussian distribution function and exponential autocorrelation function.

[0060] In this embodiment, the sealing surface is divided into four regions along the circumference of the O-ring. The rough metal surface forming the sealing surface is obtained by machining. The sealing surface in each region has the same root mean square roughness and autocorrelation length. The pre-measured root mean square roughness σ = 0.8 μm and autocorrelation length β = 1 μm. Figure 3 The figure shows the established numerical model of the local contour of the sealing surface.

[0061] S12. Uniformly sample the amplitude of the sealing surface on the contour numerical model of each region to obtain the roughness peak statistical parameters of the sealing surface, which are used to characterize the roughness peak of the sealing surface.

[0062] The statistical parameters of rough peaks include average peak height h, average peak angle θ, and average peak spacing Δχ. The average peak height h is defined as the average peak height of all rough peaks within the sampling length. The average peak angle θ is defined as the mean of the angles formed between each rough peak and its adjacent sampling points within the sampling length. The average peak spacing Δχ is defined as the ratio of the sampling length to the number of rough peaks within the sampling length.

[0063] In this embodiment, sampling parameters of 500 μm total sampling length, 100 μm evaluation length, and 1 μm sampling interval were used to uniformly sample the amplitude height on the generated numerical model of the sealed surface profile. The statistical parameters of the rough peak are shown in Table 1.

[0064] Table 1 Statistical Parameters of Sealing Surface Roughness Peak

[0065] Rough peak statistical parameters Average peak height h Average peak angle θ Average peak spacing Δχ Statistical value 1.018μm 159° 3.61μm

[0066] S2. Obtain the leakage rate of each area of ​​the sealing surface by processing according to the leakage channel type;

[0067] S21. Model the leakage channel of the sealing surface between the O-ring and the rough metal surface. Consider the sealing contact of the sealing surface as the contact between a smooth elastic surface and a rough rigid surface. Consider the leakage channel formed by the sealing surface after contact compression as a channel that is uniformly distributed along the sealing surface. The leakage channel is divided into two forms: triangular channel and trapezoidal channel. The channel cross section of the triangular channel is an isosceles triangle, and the channel cross section of the trapezoidal channel is an isosceles trapezoid.

[0068] In practice, the O-ring surface can be considered a smooth, elastic surface, and the rough metal surface can be considered a rough, rigid surface. The gap between the O-ring surface and the rough metal surface is considered a channel evenly distributed around the circumference of the O-ring, and the sealing medium leaks radially along the O-ring within the leakage channel. The rough metal surface can be considered as being formed by multiple isosceles triangular strips arranged in a specific configuration.

[0069] If multiple isosceles triangular strips are arranged closely together without gaps, such as Figure 4 As shown, a triangular channel is formed between adjacent isosceles triangular strips;

[0070] If multiple isosceles triangular strips are arranged at intervals, such as Figure 5 As shown, a trapezoidal channel is formed between adjacent isosceles triangular strips.

[0071] S22. Determine whether the leakage channel is triangular or trapezoidal based on the statistical parameters of the rough peak, and determine the original height of the leakage channel based on the leakage channel form;

[0072] When the average peak height h, average peak angle θ, and average peak spacing Δχ in the rough peak statistical parameters satisfy When the leakage path is triangular, the original height δ1 of the leakage path is:

[0073] When the average peak height h, average peak angle θ, and average peak spacing Δχ in the rough peak statistical parameters satisfy When the leakage channel is trapezoidal, the original height δ2 of the leakage channel is: δ2 = h.

[0074] In this embodiment, The leakage channel is a triangular channel, with an original channel height of [missing information].

[0075] S23. Then determine the height of the leakage channel after contact extrusion based on the original height of the leakage channel;

[0076] The height of the leakage channel after contact extrusion can be obtained using the following formula:

[0077]

[0078] Among them, h R H represents the channel height after contact. R H is the channel height before contact. For a triangular channel, H is... R =δ1, for a trapezoidal channel, H R =δ²; e represents the natural constant, σ m K represents the contact pressure at the contact surfaces. S The leakage channel filling factor reflects the ability of the sealing elastic material to fill the leakage channel under a certain pressure. It is an inherent property of the sealing material and can be obtained through experimental measurement.

[0079] In this embodiment, H R =δ1,σ m =8MPa; K S =4.93MPa.

[0080] h was calculated R =0.065μm.

[0081] S24. Calculate the leakage rate on the leakage channel of each area of ​​the sealing surface.

[0082] S241. The number N of leakage channels in the area is determined by the following formula:

[0083]

[0084] Where πD is the length of the entire sealing surface, D is the inner diameter of the O-ring in the specific implementation, and α is the area division angle expressed in radians.

[0085] In this embodiment, D = 88.49 mm.

[0086] S242. Calculate the leakage rate of the sealing surface:

[0087] For a triangular channel, the leakage rate q1 of the triangular channel is calculated using the following formula based on the leakage channel height after contact compression:

[0088]

[0089] For a trapezoidal channel, the leakage rate q2 of the trapezoidal channel is calculated using the following formula based on the height of the leakage channel after contact compression:

[0090]

[0091] Where Δp represents the pressure difference across the leakage channel, μ is the fluid dynamic viscosity, and L is the length of the leakage channel, the value of which is equal to the width of the sealing contact area of ​​the O-ring along the radial direction.

[0092] In this embodiment, Δp = 6.9 MPa, μ = 0.0087 Pa·s, L = 3.1 mm, and the leakage rate q1 of each region of the sealing surface is calculated to be 0.395 × 10⁻⁶. -4 mm 3 / s.

[0093] S3. The total leakage rate of the sealing surface is Q = 1.58 × 10⁻⁶, obtained by summing the leakage rates of all four regions in this embodiment. -4 mm 3 / s.

[0094] The basic principles and main features of the present invention have been described in detail above with reference to the accompanying drawings. The present invention defines the leakage channel between the O-ring and the sealing surface as a composite leakage channel model that includes both triangular and trapezoidal channels. This model fully reflects the influence of the sealing surface morphology on the channel form and leakage rate, improving the accuracy of leakage rate prediction. At the same time, the leakage channel is represented by a simple geometric shape described by elementary functions, which simplifies the topological form of the sealing contact and reduces the computational complexity. It can directly guide the performance prediction and high-precision design of O-ring sealing structures and has good engineering practical value.

[0095] This invention is not limited to the embodiments described above. Those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications are also considered within the scope of protection of this invention. Contents not described in detail in this specification are prior art known to those skilled in the art.

Claims

1. A method for predicting the leakage rate of a sealing surface based on a composite leakage channel model, characterized in that, The specific steps are as follows: S1. Divide the sealing surface into regions and perform modeling to obtain the roughness peak statistical parameters of each region of the sealing surface; S2. Model the leakage channels in the area of ​​the sealing surface. Based on the roughness peak statistical parameters of the area, divide the leakage channels into two forms: triangular channels and trapezoidal channels. Then, process the leakage channels according to their forms to obtain the leakage rate. S3. The total leakage rate of the sealing surface is obtained by comprehensively processing the leakage rates of each region; Step S1 specifically involves: S11. Divide the sealing surface into multiple regions, and determine the root mean square roughness of each region of the sealing surface based on the pre-measured root mean square roughness. and autocorrelation length A numerical model of the contour of each region, described by a Gaussian distribution function and an exponential autocorrelation function, is established using a digital filtering method based on autoregressive time series. S12. Uniformly sample the amplitude of the sealing surface on the contour numerical model of each region to obtain the roughness peak statistical parameters of the sealing surface, which are used to characterize the roughness peak of the sealing surface. The rough peak statistical parameters include the average peak height. Average peak angle and average peak spacing Among them, the average peak height Defined as the average peak height and average peak angle of all coarse peaks within the sampling length. The average peak spacing is defined as the mean of the angles formed between each coarse peak and its adjacent sampling point within the sampling length. Defined as the ratio of the sampling length to the number of rough peaks within the sampling length; In step S2, the sealing contact of the sealing surface is regarded as the contact between a smooth elastic surface and a rough rigid surface. The leakage channel formed by the sealing surface after being squeezed by the contact is regarded as a channel that is evenly distributed along the sealing surface. The leakage channel is divided into two forms: triangular channel and trapezoidal channel. The cross section of the triangular channel is an isosceles triangle, and the cross section of the trapezoidal channel is an isosceles trapezoid.

2. The method for predicting the leakage rate of a sealing surface based on a composite leakage channel model according to claim 1, characterized in that: In step S2, the leakage rate is obtained by processing according to the leakage channel type, specifically as follows: S21. Determine whether the leakage channel is a triangular channel or a trapezoidal channel based on the statistical parameters of the rough peak; S22. Determine the original height of the leakage channel based on its type; S23. Then determine the height of the leakage channel after contact extrusion based on the original height of the leakage channel; S24. Calculate the leakage rate on the leakage channel of each area of ​​the sealing surface.

3. The method for predicting the leakage rate of a sealing surface based on a composite leakage channel model according to claim 2, characterized in that: The specific steps of S21 are as follows: When the average peak height in the rough peak statistical parameters Average peak angle and average peak spacing satisfy When this occurs, the leakage path is a triangular channel; When the average peak height in the rough peak statistical parameters Average peak angle and average peak spacing satisfy When this occurs, the leakage channel is a trapezoidal channel.

4. The method for predicting the leakage rate of a sealing surface based on a composite leakage channel model according to claim 2, characterized in that: The specific steps of S22 are as follows: When the leakage channel is a triangular channel, the original height of the leakage channel for: = ; When the leakage channel is a trapezoidal channel, the original height of the leakage channel for: = .

5. The method for predicting the leakage rate of a sealing surface based on a composite leakage channel model according to claim 2, characterized in that: Specifically, step S23 involves obtaining the height of the leakage channel after contact extrusion according to the following formula: ； in, The height of the channel after contact; The height of the channel before contact, for a triangular channel, = For trapezoidal channels, = e represents the natural constant. The contact pressure at the contact surface; The filling factor for the leakage channel.

6. The method for predicting the leakage rate of a sealing surface based on a composite leakage channel model according to claim 2, characterized in that: The specific steps of S24 are as follows: S241. The number N of leakage channels is determined by the following formula: ； , The length of the entire sealing surface. An angle is used to divide a region into areas, expressed in radians. S242. For a triangular channel, the leakage rate of the triangular channel is calculated using the following formula based on the leakage channel height after contact compression. : ； For trapezoidal channels, the leakage rate is calculated using the following formula based on the height of the leakage channel after contact compression. : ； in, This indicates the pressure difference across the leak channel. Where is the fluid dynamic viscosity, and L is the length of the leakage channel.

7. The method for predicting the leakage rate of a sealing surface based on a composite leakage channel model according to claim 1, characterized in that: Specifically, step S3 involves summing the leakage rates of all regions to obtain the total leakage rate of the sealing surface.

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