A simulation prediction method for seal leakage based on interpolation function

Abstract

The present invention relates to a method for simulating and predicting seal leakage based on an interpolation function, and belongs to the technical field of mechanical seals, particularly metal-to-metal seals. A two-dimensional matrix conforming to a Gaussian distribution is established based on the seal to be tested, and the two-dimensional matrix is solved using a cubic interpolation method to obtain a binary interpolation function. The two-dimensional matrix is encrypted using the binary interpolation function to obtain a high-density two-dimensional matrix. The contact area ratio is determined based on the extrusion pressure between the sealing surfaces of the seal to be tested, and a critical height is obtained based on the contact area ratio. Based on the obtained critical height, it is determined whether a penetration domain exists on the high-density two-dimensional matrix to obtain a penetration result.

Description

Technical Field

[0001] The invention relates to a method for simulating and predicting seal leakage based on an interpolation function, and belongs to the technical field of mechanical seals, especially metal-to-metal seals. Background Art

[0002] In mechanical sealing technology, to prevent the leakage of high-pressure liquids or gases, a common approach is to increase the fit between the two sealing surfaces, improve the surface finish of both surfaces, and increase the extrusion pressure between the two surfaces. This is especially true in the field of high-pressure static metal-to-metal sealing. However, in mechanical structural design, there is currently neither a unified method nor a unified mathematical formula to determine whether a mechanical surface can form a seal under a certain pressure. Generally, the determination of sealing effectiveness in the field of high-pressure sealing relies on experimental verification, empirical prediction, and simulation methods.

[0003] Among them, experimental verification is costly and time-consuming, and empirical prediction relies on the engineering experience of engineers. In existing seal leakage simulation methods, percolation theory is often used for simulation. In each grid of the four-connected unit grid network, contact or non-contact points are formed in a certain probability. The contact area formed is as follows: Figure 1 As shown, a computer flow domain algorithm is used to determine whether a penetration domain has formed to determine leakage. By generating a large number of four-connected unit grid models and statistically analyzing the probability of the formation of flow penetration domains in the models, a general rule is derived to determine the influence of the probability of contact area occurrence on the probability of leakage in the four-connected unit grid model.

[0004] In addition to the four-connected unit grid model, there are also six-connected units and continuous percolation models. Figure 2 The probability model for forming a through-domain is basically the same as the four-connected unit grid model.

[0005] The existing continuous flow domain solution model can well simulate the influence of the contact area ratio (actual contact area / nominal contact area) on the probability of flow leakage. However, in the actual model, the contact or non-contact of each point is strongly correlated with the position of its adjacent points, because the height of each point is correlated with the height of the surrounding points, and the closer the distance, the stronger the correlation. Rough surfaces appear in the form of certain waves, and autocorrelation is an important feature of surface morphology. However, in the existing percolation theory model, whether or not contact is formed at each point appears in the form of a fixed probability. The fixed probability makes the contact or non-contact of each point have no correlation with whether or not the grid around the grid is in contact. This is inconsistent with the actual contact and is also the fundamental reason for the deviation of the prediction results.

[0006] Furthermore, in grid models, the scale of the grid corresponds to the wavelength of the simulated rough surface. A denser grid causes the simulated scale to change, and it is generally believed that the actual surface roughness corresponding to a denser grid is lower. This correspondence between grid scale and surface roughness limits the grid's simulation capabilities, significantly affecting the model's results using square or hexagonal grids. This also causes the model to ignore the effects of fluid flow in narrow slits on the seal. Summary of the Invention

[0007] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art and to propose a seal leakage simulation prediction method based on an interpolation function.

[0008] The technical solution of the present invention is:

[0009] A method for predicting seal leakage by simulation based on an interpolation function, the method comprising the following steps:

[0010] The first step is to establish a two-dimensional matrix that conforms to the Gaussian distribution according to the seal to be tested, where the sealing surface of the seal to be tested includes an upper metal surface and a lower metal surface;

[0011] In the second step, a two-dimensional matrix established in the first step is used as a known quantity using a cubic interpolation method to calculate a binary interpolation function, and the obtained binary interpolation function is used as a fitting function for the sealing surface of the seal to be tested;

[0012] The third step is to use the binary interpolation function obtained in the second step to encrypt the two-dimensional matrix established in the first step with an encryption multiple of n to obtain a high-density two-dimensional matrix;

[0013] The fourth step is to determine the contact area ratio according to the extrusion pressure between the sealing surfaces of the seal to be tested;

[0014] In the fifth step, a critical height is obtained based on the contact area ratio determined in the fourth step, and a penetration result is obtained by judging whether a penetration domain exists on the high-density two-dimensional matrix determined in the third step based on the obtained critical height.

[0015] Step 6: Repeat steps 1 to 5 for no less than 1000 times, and calculate the probability of penetration or non-penetration in the obtained penetration results.

[0016] In the first step, the two-dimensional matrix that conforms to the Gaussian distribution is a random two-dimensional matrix of W0×L0;

[0017] Where W0 is the matrix width, W0=2*W / S;

[0018] L0 is the matrix length, L0=2*L / S;

[0019] W is the width of the sealing ring of the seal to be tested, that is, the length of the mechanical protrusion structure along the direction of liquid leakage;

[0020] S is the main period length of the sealing surface of the seal to be tested. The method for obtaining S is: the feed rate of the tool during processing is used as the main period length. The method for obtaining S can also be: the main frequency f is obtained by performing spectrum analysis on the contours after subtracting the contours of the upper and lower sealing surfaces to be tested, and the main period length is obtained by the formula S = 1 / f;

[0021] L is the length of the sealing ring of the seal to be tested, that is, the average value of the outer contour and inner contour of the ring;

[0022] The mean value of the Gaussian distribution of the matrix is set to 0, and the standard deviation is the square root of the sum of the variance of the upper surface profile height and the variance of the lower surface profile height.

[0023] In the second step, the method for obtaining the binary interpolation function is: using interp2() in MATLAB to generate the binary interpolation function, or using the interpolate.interp2d() statement of the scipy library in Python to generate the binary interpolation function;

[0024] In the third step, the encryption multiple n depends on the requirements for modeling precision and the performance of the actual computer. Generally, the encryption multiple n is 10.

[0025] In the fourth step, the contact area ratio γ is:

[0026]

[0027] Wherein, μ1 is the Poisson's ratio of the upper metal surface material, μ2 is the Poisson's ratio of the lower metal surface material, E1 is the bulk modulus of the upper metal surface material, E2 is the bulk modulus of the lower metal surface material, P is the extrusion pressure between the upper and lower metal surfaces of the seal to be tested, S1 is the main period length of the upper metal surface profile, S2 is the main period length of the lower metal surface profile, R1 is the surface roughness of the upper metal surface, and R2 is the surface roughness of the lower metal surface;

[0028] In the fifth step, the critical height α is obtained by:

[0029] γ = a1 / (a1+a2), where a1 is the number of values in the high-density two-dimensional matrix that are greater than the critical height α, and a2 is the number of values in the high-density two-dimensional matrix that are less than the critical height α;

[0030] In a high-density two-dimensional matrix, points with heights greater than the critical height are defined as contact points, and points with heights less than the critical height are defined as non-contact points. When the non-contact points form a penetration domain in the width direction of the sealing ring band of the seal to be tested, the penetration result is penetration. When the non-contact points do not form a penetration domain in the width direction of the sealing ring band of the seal to be tested, the penetration result is non-penetration.

[0031] In the sixth step, the probability of penetration under fixed working conditions is counted to determine the probability of leakage on the surface. Generally, this probability will rapidly approach 1 at a value as the surface contact area ratio increases. This value is the critical contact area ratio. Generally, it is only necessary to determine the critical contact area ratio.

[0032] Beneficial effects

[0033] (1) The method of the present invention uses an interpolation function fitting method based on the square grid model to construct a high-density two-dimensional matrix. The rough surface represented by this matrix can better reflect the actual rough surface morphology. Therefore, the calculated probability of leakage is more reliable.

[0034] (2) The method of the present invention uses Hertz theory to determine the contact area ratio based on the extrusion pressure. Based on the contact area ratio, it determines whether a point is in contact in a high-density two-dimensional matrix. Compared with the method of randomly generating contact points in a square grid model, this construction method takes into account the influence of surface texture on sealing, and the resulting leakage probability is more reliable.

[0035] (3) The method of the present invention can intuitively judge whether leakage occurs between two surfaces under a certain extrusion pressure because the two-dimensional matrix in the first step can be replaced by data obtained from experimental sampling, while the other steps remain unchanged. It can interact well with experimental data, facilitating simulation and judgment in engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a two-dimensional matrix cloud diagram of Gaussian distribution;

[0037] Figure 2 A high-density two-dimensional matrix cloud image generated based on a two-dimensional matrix cloud image of a Gaussian distribution;

[0038] Figure 3 The cloud diagram of the sealed and unsealed flow matrix. DETAILED DESCRIPTION

[0039] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0040] A method for predicting seal leakage by simulation based on an interpolation function, the method comprising the following steps:

[0041] The first step is to establish a two-dimensional matrix that conforms to the Gaussian distribution according to the seal to be tested, where the sealing surface of the seal to be tested includes an upper metal surface and a lower metal surface;

[0042] In the second step, a two-dimensional matrix established in the first step is used as a known quantity using a cubic interpolation method to calculate a binary interpolation function, and the obtained binary interpolation function is used as a fitting function for the sealing surface of the seal to be tested;

[0043] The third step is to use the binary interpolation function obtained in the second step to encrypt the two-dimensional matrix established in the first step with an encryption multiple of n to obtain a high-density two-dimensional matrix;

[0044] The fourth step is to determine the contact area ratio according to the extrusion pressure between the sealing surfaces of the seal to be tested;

[0045] In the fifth step, a critical height is obtained based on the contact area ratio determined in the fourth step, and a penetration result is obtained by judging whether a penetration domain exists on the high-density two-dimensional matrix determined in the third step based on the obtained critical height.

[0046] Step 6: Repeat steps 1 to 5 for no less than 1000 times, and calculate the probability of penetration or non-penetration in the obtained penetration results.

[0047] In the first step, the two-dimensional matrix that conforms to the Gaussian distribution is a random two-dimensional matrix of W0×L0;

[0048] Where W0 is the matrix width, W0=2*W / S;

[0049] L0 is the matrix length, L0=2*L / S;

[0050] W is the width of the sealing ring of the seal to be tested, that is, the length of the mechanical protrusion structure along the direction of liquid leakage;

[0051] S is the main period length of the sealing surface of the seal to be tested. The method for obtaining S is: the feed rate of the tool during processing is used as the main period length. The method for obtaining S can also be: the main frequency f is obtained by performing spectrum analysis on the contours after subtracting the contours of the upper and lower sealing surfaces to be tested, and the main period length is obtained by the formula S = 1 / f;

[0052] L is the length of the sealing ring of the seal to be tested, that is, the average value of the outer contour and inner contour of the ring;

[0053] The mean value of the Gaussian distribution of the matrix is set to 0, and the standard deviation is the square root of the sum of the variance of the upper surface profile height and the variance of the lower surface profile height.

[0054] In the second step, the method for obtaining the binary interpolation function is: using interp2() in MATLAB to generate the binary interpolation function, or using the interpolate.interp2d() statement of the scipy library in Python to generate the binary interpolation function;

[0055] In the third step, the encryption multiple n depends on the requirements for modeling precision and the performance of the actual computer. Generally, the encryption multiple n is 10.

[0056] In the fourth step, the contact area ratio γ is:

[0057]

[0058] Wherein, μ1 is the Poisson's ratio of the upper metal surface material, μ2 is the Poisson's ratio of the lower metal surface material, E1 is the bulk modulus of the upper metal surface material, E2 is the bulk modulus of the lower metal surface material, P is the extrusion pressure between the upper and lower metal surfaces of the seal to be tested, S1 is the main period length of the upper metal surface profile, S2 is the main period length of the lower metal surface profile, R1 is the surface roughness of the upper metal surface, and R2 is the surface roughness of the lower metal surface;

[0059] In the fifth step, the critical height α is obtained by:

[0060] γ = a1 / (a1+a2), where a1 is the number of values in the high-density two-dimensional matrix that are greater than the critical height α, and a2 is the number of values in the high-density two-dimensional matrix that are less than the critical height α;

[0061] In a high-density two-dimensional matrix, points with heights greater than the critical height are defined as contact points, and points with heights less than the critical height are defined as non-contact points. When the non-contact points form a penetration domain in the width direction of the sealing ring band of the seal to be tested, the penetration result is penetration. When the non-contact points do not form a penetration domain in the width direction of the sealing ring band of the seal to be tested, the penetration result is non-penetration.

[0062] In the sixth step, the probability of penetration under fixed working conditions is counted to determine the probability of leakage on the surface. Generally, this probability will rapidly approach 1 at a value as the surface contact area ratio increases. This value is the critical contact area ratio. Generally, it is only necessary to determine the critical contact area ratio.

[0063] Example

[0064] In a high-pressure oil pump mechanical seal, the compression pressure between the two sealing surfaces is P, the Young's modulus of the upper surface is E1, and the surface roughness is Ra1, while the Young's modulus of the lower surface is E2, and the surface roughness is Ra2. The Poisson's ratio of the upper surface is μ1, and the Poisson's ratio of the lower surface is μ2. When machining the upper and lower surfaces, the tool feed is S, and the sealing ring is annular with an inner diameter of d1 and an outer diameter of d2.

[0065] The width W of the sealing ring is d2-d1, and the length L of the sealing ring is 2*π*(d2-d1).

[0066] The matrix width W0 is calculated, W0 = [2*W / S]; the matrix length L0 is calculated, L0 = [2*L / S]; [] is rounded.

[0067] Calculate the Gaussian distribution random matrix z: z = z1*sqrt(Ra1^2+Ra2^2)*0.001 (because the unit of Ra is μm, it needs to be multiplied by 0.001). The upper surface roughness is Ra1, the lower surface roughness is Ra2, and z1 is a random matrix generated with a standard Gaussian distribution, with a standard deviation of 1. The generated matrix cloud is as follows Figure 1 shown.

[0068] Set the encryption multiple n=10

[0069] Construct a cubic interpolation function f. Use f = scipy.interpolate.interp2d(x,y,z,kind='cubic') in Python. x is a one-dimensional matrix [0,1*W / W0,2*W / W0,3*W / W0…W], and y is a one-dimensional matrix [0,1*L / L0,2*L / L0,3*L / L0…L].

[0070] Calculate the high-density two-dimensional matrix a and generate it in Python using the statement a=f(xnew,ynew), where xnew is a one-dimensional matrix [0,1*W / (W0*n),2*W / (W0*n),3*W / (W0*n)……W] and ynew is a one-dimensional matrix [0,1*L / (L0*n),2*L / (L0*n),3*L / (W0*n)……L]. The generated high-density two-dimensional matrix is as follows: Figure 2 shown.

[0071] Using the known quantities, the contact area ratio γ is obtained as:

[0072]

[0073] Calculate the critical height α. Expand the high-density two-dimensional matrix a into a one-dimensional matrix a1, and then use the sort function to sort the matrix from largest to smallest. If the number of elements in the one-dimensional matrix is m, the critical height α is the [m*γ]th value in the sorted one-dimensional matrix, i.e., m*γ rounded to the nearest integer.

[0074] In a high-density two-dimensional matrix, let the values less than or equal to α be replaced by 0, and the values greater than α be replaced by 1. The resulting matrix is the flow matrix d. At this time, through the calculation method of the flow domain, it is determined whether there is a region connected by points with a value greater than 1 that runs through the front and back of the d matrix, that is, forming a penetration domain, such as Figure 3 As shown, the left picture shows that no through-domain is formed, i.e., it is sealed, while the right picture shows that a through-domain is formed, i.e., leakage occurs.

[0075] The above process was repeated 1000 times, and statistics showed that leakage occurred 2 times under this working condition, that is, the sealing probability was 0.998. According to the process document requirement, the sealing defective rate is less than 3‰. The simulation results show that the sealing performance of this working condition is good and can be mass-produced.

Claims

1. A simulation prediction method for seal leakage based on interpolation function, characterized in that The steps of the method include: The first step is to establish a two-dimensional matrix that conforms to the Gaussian distribution according to the seal to be tested, where the sealing surface of the seal to be tested includes an upper metal surface and a lower metal surface; In the second step, a two-dimensional matrix established in the first step is used as a known quantity using a cubic interpolation method to calculate a binary interpolation function, and the obtained binary interpolation function is used as a fitting function for the sealing surface of the seal to be tested; The third step is to use the binary interpolation function obtained in the second step to encrypt the two-dimensional matrix established in the first step with an encryption multiple of n to obtain a high-density two-dimensional matrix; The fourth step is to determine the contact area ratio according to the extrusion pressure between the sealing surfaces of the seal to be tested; In the fifth step, a critical height is obtained based on the contact area ratio determined in the fourth step, and a penetration result is obtained by judging whether a penetration domain exists on the high-density two-dimensional matrix determined in the third step based on the obtained critical height. Step 6: Repeat steps 1 to 5 for no less than 1000 times, and calculate the probability of penetration or non-penetration in the obtained penetration results; In the fourth step, the contact area ratio γ is: Wherein, μ1 is the Poisson's ratio of the upper metal surface material, μ2 is the Poisson's ratio of the lower metal surface material, E1 is the bulk modulus of the upper metal surface material, E2 is the bulk modulus of the lower metal surface material, P is the extrusion pressure between the upper and lower metal surfaces of the seal to be tested, S1 is the main period length of the upper metal surface profile, S2 is the main period length of the lower metal surface profile, R1 is the surface roughness of the upper metal surface, and R2 is the surface roughness of the lower metal surface; In the fifth step, the critical height α is obtained by: γ=a1 / (a1+a2), where a1 is the number of values greater than the critical height α in the high-density two-dimensional matrix, and a2 is the number of values less than the critical height α in the high-density two-dimensional matrix.

2. The method for simulation prediction of seal leakage based on interpolation function according to claim 1, characterized in that: In the first step, the two-dimensional matrix that conforms to the Gaussian distribution is a random two-dimensional matrix of W0×L0; Where W0 is the matrix width, W0=2*W / S; L0 is the matrix length, L0=2*L / S; W is the width of the sealing ring of the seal to be tested; L is the length of the sealing ring of the seal to be tested; S is the main period length of the sealing surface of the seal to be tested.

3. The method for simulation prediction of seal leakage based on interpolation function according to claim 2, characterized in that: The method for obtaining S is: the feed rate of the tool during processing is used as the main cycle length.

4. The method for simulation prediction of seal leakage based on interpolation function according to claim 2, characterized in that: The method for obtaining S is: perform spectrum analysis on the surface profile of the seal to be tested to obtain the main frequency f, and obtain the main period length through the formula S=1 / f.

5. A method for simulating and predicting seal leakage based on an interpolation function according to any one of claims 1 to 4, characterized in that: In the second step, the method for obtaining the binary interpolation function is: using interp2() in matlab to generate the binary interpolation function.

6. A method for simulating and predicting seal leakage based on an interpolation function according to any one of claims 1 to 4, characterized in that: In the second step, the method for obtaining the binary interpolation function is: using the interpolate.interp2d() statement of the scipy library in Python to generate the binary interpolation function.

7. The method for simulation prediction of seal leakage based on interpolation function according to claim 1, characterized in that: In the third step, the encryption multiple n is 10.

8. A method for simulating and predicting seal leakage based on an interpolation function according to any one of claims 1 to 4, characterized in that: In the fifth step, the method for determining whether penetration occurs is as follows: In a high-density two-dimensional matrix, points with heights greater than the critical height are defined as contact points, and points with heights less than the critical height are defined as non-contact points. When the non-contact points form a penetration domain in the width direction of the sealing ring band of the seal to be tested, the penetration result is penetration. When the non-contact points do not form a penetration domain in the width direction of the sealing ring band of the seal to be tested, the penetration result is non-penetration.

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