Sealing structure optimization method based on Latin hypercube design

Abstract

The invention relates to a sealing structure optimization method based on Latin hypercube design, and the method comprises the steps: determining a parameter variable of a sealing structure, and carrying out the sampling of the parameter variable based on a Latin hypercube design method; calculating the maximum direct stiffness value and the maximum fatigue life through the model; fusing the maximum direct stiffness value and the maximum fatigue life through a multi-target weighted summation method to construct a target function; fitting a quadratic polynomial regression model of the sampled data and the target function by applying a least square method, and introducing a particle swarm algorithm to optimize the regression model to obtain an optimal combination of the regression model; the Latin hypercube design method is adopted, so that the selection of the horizontal range of parameter variables of the sealing structure can be reduced, and computing resources are saved on the premise of not influencing the precision of an objective function; by applying a multi-target weighted summation method, the maximum direct rigidity and the maximum fatigue life are reasonably fused, and therefore it is ensured that the comprehensive performance of the sealing structure is optimized under the condition that the rigidity and the fatigue life are both considered.

Description

Technical Field

[0001] The invention relates to the technical field of turbine mechanical seal dynamics, and in particular to a seal structure optimization method based on Latin hypercube design. Background Art

[0002] Seals are key components for various turbine machinery to suppress fluid leakage and improve unit performance. Their performance directly affects the dynamic and static operating characteristics of the unit. High-performance sealing technology has become an important means to improve the core competitiveness in this field. Since seals usually work under rotor eccentricity in actual engineering applications, the pressure in the sealing chamber is unevenly distributed along the circumference, generating airflow excitation force acting on the rotor. The airflow force directly affects the system stiffness and critical speed. If the seal has negative stiffness, it will cause dynamic and static friction, leading to seal failure and causing large economic losses. Therefore, it is necessary to improve the seal structure to increase its stiffness to avoid negative values ​​and improve the safety of unit operation. At the same time, because seals usually work in rotating machinery, the fatigue life of the seal is also a key indicator affecting the safe operation of the unit. Improving the fatigue life of the seal while ensuring stiffness is one of the current research hotspots in the field.

[0003] For example, the "Optimization Design Method for Rotary Seals for Vehicle Wet Clutches" disclosed in patent announcement number CN103955581B establishes a general groove profile description equation for rotary seals; selects design variables as optimization objects, sets boundary constraints based on the allowable range of values ​​of the design variables; determines the objective function; performs optimization calculations; and optimizes the design of fluid dynamic lubrication for the rotary seal end face, so that the rotary seal end face generates a stronger fluid dynamic pressure to reduce friction and wear and improve the working performance and service life of the seal groove.

[0004] However, the use of algorithm optimization to solve the optimal structural parameters of the seal has the advantages of accuracy and reliability, but due to the large number of structural parameters and their corresponding level ranges, the calculation optimization process requires a lot of computing resources and time costs. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a sealing structure optimization method based on Latin hypercube design to solve the above problems.

[0006] The present invention provides the following technical solutions:

[0007] A sealing structure optimization method based on Latin hypercube design comprises the following steps:

[0008] Determine the parameter variables in the sealing structure optimization process, as well as the value range and constraint conditions of each parameter variable;

[0009] Based on the Latin hypercube design method, each parameter variable is uniformly sampled and K groups of sampling data are generated;

[0010] A computational fluid dynamics numerical model and a finite element model are parameterized and established based on the generated K groups of sampling data, and the maximum direct stiffness value and the maximum stress value corresponding to the K groups of sampling data are calculated, thereby calculating the maximum fatigue life of the sealing structure;

[0011] The objective function is constructed by integrating the maximum direct stiffness value and the maximum fatigue life through the multi-objective weighted summation method;

[0012] The least squares method is used to fit the quadratic polynomial regression model of K groups of sampling data and the objective function. The particle swarm algorithm is introduced to optimize the regression model and obtain the optimal combination of the regression model.

[0013] Preferably, the sealing structure has its geometric shape determined by j parameters, that is, x=(x1, x2, ..., x j ) is the geometric parameter of the seal, and the value range and constraint conditions of the parameter variables are determined, that is, m i ≤x i ≤M i , i=1,2,…,j;m i With M i Represents the parameter variable x i Upper and lower limit values.

[0014] Preferably, the ratio between the K groups of sampled data and the j parameters is a constant.

[0015] Preferably, the sealing structure determined by the K group of parameter variables is subjected to three-dimensional numerical modeling, meshing, boundary condition setting, numerical calculation and post-processing analysis, and the maximum direct stiffness value and maximum stress value in the post-processing results are extracted to calculate the maximum fatigue life value of the seal.

[0016] Preferably, the objective function F(x)=w1·f1(x)+w2·f2(x);

[0017] Among them, f1(x) is the maximum direct stiffness, f2(x) is the maximum fatigue life, w1 and w2 are the weighting coefficients of the maximum direct stiffness and the maximum fatigue life, respectively.

[0018] Preferably, the weighted coefficients of the maximum direct stiffness and the maximum fatigue life are:

[0019]

[0020] Among them, N, P, and T are the speed, pressure, and temperature of the working condition of the sealing structure respectively;

[0021] N ref , Pref 、T ref are the design reference values ​​of the sealing structure respectively;

[0022] a, b, c, m, and n are adjustment coefficients related to speed, pressure, and temperature, respectively;

[0023] Δσ is the maximum stress, σ is the fatigue limit, L ref is the reference life, L d is the design life;

[0024] Among them, a=0.4~0.6, m=0.3~0.4; b=0.3~0.5, n=0.4~0.5; c=0.1~0.2.

[0025] Preferably, maximum fatigue life

[0026] Among them, N f is the fatigue life, S0 is the fatigue strength coefficient, Δσ is the maximum stress value, and k is the fatigue strength attenuation exponent of the material.

[0027] Preferably, a multivariate quadratic polynomial regression model is selected to fit the K groups of sampled data and the objective function value to obtain a regression model of the nonlinear relationship between the objective function and the K groups of sampled data:

[0028] The regression model is expressed as:

[0029] Among them, f(x) is the predicted value of the objective function, that is, the predicted value of the weighted result of the maximum direct stiffness value and the maximum fatigue life; β0 is the intercept term; is a linear term; is a linear cross term; is a quadratic term; β i , β ij , β ii are the coefficients of linear terms, linear cross terms, and quadratic terms, respectively;

[0030] The least squares method was used to fit the above regression model.

[0031] Preferably, the regression model is optimized, the initial position, initial velocity, inertia weight, learning factor and number of iterations of the given particle swarm are set, constraints are set, the velocity and position of the particles are gradually updated using the particle swarm optimization algorithm, and a global search is performed by calculating the optimal solution in each iteration until the convergence conditions are met to complete the optimization of the sealing structure.

[0032] Preferably, 1) from the sealing structure model, determine the key geometric parameters and the initial position of the parameters x0 = (x1, x2, ..., x j ), given the initial velocity v0 = (v1, v2, ..., vj )T, inertia weight ω, individual learning factor c1, group learning factor c2, convergence accuracy ε, random numbers r1, r2 in the interval [0, 1];

[0033] 2) Optimize the regression model f(x), gradually update the position and speed of the particles through the particle swarm optimization algorithm, and in each iteration, update the individual historical optimal position and the historical optimal position of the group Search; at the same time, initialize the particle swarm, set the initial iteration number of the particle swarm to t = 0, and the current particle position is Calculate the fitness value of the optimal position searched by each particle;

[0034] 3) For each particle, based on its current speed, individual historical optimal position, and group historical optimal position, the particle’s speed is updated and its position is adjusted, thereby performing global and local searches and gradually approaching the optimal solution:

[0035] Speed ​​update formula:

[0036] Position update formula:

[0037] Individual optimal position update: If but

[0038] Group optimal position update: If but

[0039] 4) If If the difference between the fitness value of the optimal solution after the previous iteration and the fitness value of the optimal solution after this iteration is less than the convergence accuracy, the iteration is stopped and the output is That is the optimal solution for the required parameter variable; otherwise, let t+1=t and enter loop 3).

[0040] The present invention has the following beneficial technical effects:

[0041] The present invention adopts the Latin hypercube design method to reduce the horizontal range selection of the sealing structure parameter variables, saving computing resources without affecting the accuracy of the objective function;

[0042] By using the multi-objective weighted summation method, the maximum direct stiffness and the maximum fatigue life are reasonably integrated, thereby ensuring that the comprehensive performance of the sealing structure is optimized while taking both stiffness and fatigue life into consideration.

[0043] Fitting a quadratic polynomial regression model of the objective function and parameter variables by the least squares method can provide more accurate fitting and prediction of nonlinear relationships.

[0044] The introduction of particle swarm optimization can optimize the fitted regression model efficiently and accurately. It is not limited to a single sealing structure, but can be applied to sealing structures under a variety of different working conditions and complex parameter variable ranges. If the structural optimization of the sealing service life is further considered, the weight distribution of the objective function can be changed, and the optimal solution can still be identified through this method. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of the present invention;

[0046] Figure 2 It is a two-dimensional geometric schematic diagram of a sealing structure of the present invention;

[0047] Figure 3 It is a flow chart of the particle swarm optimization algorithm in the present invention.

[0048] Figure 4 It is the value range of the parameter variable of the present invention.

[0049] Figure 5 It is the random value of 6 groups of sampling data of the present invention. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0051] A sealed structure optimization method based on Latin hypercube design, such as Figure 1-3 As shown:

[0052] Step 1: Determine the parameter variables for optimizing the sealing structure, and determine the value range and constraint conditions of the parameter variables. Select the structure to be optimized for sealing, and determine its specific geometry through j parameters, i.e., x = (x1, x2, ..., x j ) is the geometric parameter of the seal; at the same time, in order to avoid internal interference of the structure and prevent errors such as failure to establish the sealing geometric structure, the value range and constraint conditions of the parameter variables are determined, that is, m i ≤x i ≤M i , i=1,2,…,j,m i With M i Represents the parameter variable x i Upper and lower limit values.

[0053] by Figure 2For example, the seal structure is determined by j = 4 parameters: w1 is the seal tooth width, w2 is the seal cavity width, h is the seal cavity depth, C r To seal the gap. In order to balance the design complexity and computing resources and meet the requirements of Latin hypercube design, it is also possible to better perform multi-objective optimization and set K = 1.5*j, thereby determining K = 6; based on the Latin hypercube design method, such as Figure 4 The figure shows the value range of the sampling data.

[0054] Step 2: Based on the K groups of sampling data generated by the Latin hypercube design method, parametric computational fluid dynamics simulation and finite element simulation are performed on these K groups of sampling data to obtain the maximum direct stiffness value and maximum stress value corresponding to the K groups of sampling data, thereby calculating the maximum fatigue life of the seal. The maximum direct stiffness value and the maximum fatigue life value are integrated as the objective function through the multi-objective weighted summation method, and different weights are assigned to the two characteristics.

[0055] For example: an aluminum alloy seal works on a rotating machine, the rotating machine speed N = 10000rpm; pressure P = 5MPa; temperature T = 120℃; N ref =15000rpm; P ref =8MPa; T ref =200℃; Sealing material fatigue strength ratio Seal life ratio The weight coefficient is set based on the working environment parameters. The high speed is greater than 5000RPM, the high pressure is greater than 6MPa, and the high temperature is greater than 200℃.

[0056] The larger a and m are under high speed conditions, the larger b and n are under high pressure conditions, and the larger c is under high temperature conditions.

[0057] In this example, the operating condition is high pressure and high speed, and a=0.6, m=0.4, b=n=0.5, and c=0.1 can be selected.

[0058] Therefore, the objective function is: F(x) = 1.77f1(x) + 2.94f2(x);

[0059] Since the particle swarm algorithm usually has a particle number K = 1.5*j, a total of 6 sets of sampling data are generated in this example, that is, each parameter variable has 6 samples. Figure 2 Taking a sealed structure as an example, six sets of random sampling data are generated using Latin hypercube design, such as Figure 5 shown.

[0060] The sealing structure determined by the six sets of sampling data is subjected to three-dimensional numerical modeling, meshing, boundary condition setting, numerical calculation and post-processing analysis. The maximum direct stiffness value and maximum stress value in the post-processing results are extracted to calculate the maximum fatigue life of the seal; F(x)=1.77f1(x)+2.94f2(x) is used as the objective function, denoted as y=(y1, y2, y3, y4, y5, y6) T .

[0061] Step 3: Use the least squares method to fit the quadratic polynomial regression model of the parameter variables and the objective function. The regression model is expressed as: Where f(x) is the predicted value of the objective function, that is, the predicted value of the weighted result of the maximum direct stiffness value and the maximum fatigue life, where β0 is the intercept term, is a linear term, is the linear cross term, is a quadratic term; β i , β ij , β ii are the coefficients of the linear term, linear cross term, and quadratic term, respectively.

[0062] by Figure 2 For example, a sealing structure is set as x i =(x1, x2, x3, x4) to represent w1, w2, h, C respectively r Four parameter variables; the regression model is expressed as:

[0063] Set constraints: β i , x i , β ii , x i 2 i=1, 2, 3, 4; β ij , x i x j in i <j,j=1,2,3,4。

[0064] Assume b m =(b0, b1, ..., b m ) to represent β0, β i ,β ij ,β ii , where the number of linear terms and quadratic terms is k = 4, and the number of cross terms is k(k-1) / 2 = 6, so m = 14. Similarly, let a = (a0, a1, ..., a m ) to represent 1, x i , x i 2 , x i x j, m = 14. So the regression model of a single sample can be expressed as: From step 2, we can know that: in this example, the number of samples is 6, so the a corresponding to the 6 sets of sampled data can be expressed as a n =(a n0 , a n1 , …, a nm ), n=1, 2,...,K; K=6.

[0065] Therefore, the regression model can finally be expressed as: After applying the least squares method to fit the regression model, it is necessary to perform residual analysis on the regression model: minimize the predicted value f(a n ) and the square error of the actual target value (y in step 2), that is, Minimum.

[0066] The solution formula of the least squares method is: m =(X T X) -1 X T y. X is the design matrix, which contains the parameter variable combination of each sample. y is the target vector, which contains the actual value of each sample. In this embodiment, there are 6 samples and 14 regression coefficients, so the design matrix X is 6*15, which is specifically expressed as follows:

[0067]

[0068] y=(y1, y2, y3, y4, y5, y6) T ;

[0069] Given X and y, we can find b m ;

[0070] Thus we get the regression model:

[0071] Step 4, flowchart see Figure 3 , specifically including:

[0072] 1) By Figure 2 Sealing base structure model, determination of its key geometric parameters and initial position x 0 =(x1, x2, ..., x j ), given the initial velocity v 0 =(v1, v2, ..., v j ) T is 0.1 times the length of the parameter variable range, the inertia weight ω∈[0.4, 2], the individual learning factor c1 is equal to the group learning factor, c2 is 2, and the convergence accuracy = 1.0×10 -4 , random numbers r1, r2∈[0,1];

[0073] 2) The objective function to be optimized is the regression model f(x) in step 3. The particle position and velocity are gradually updated through the particle swarm optimization algorithm. In each iteration, the particle position and velocity are updated according to the individual historical optimal position. and the historical optimal position of the group At the same time, initialize the particle swarm, set the initial iteration number of the particle swarm to t = 0, and the current particle position is Calculate the fitness value of the optimal position searched by each particle;

[0074] 3) For each particle, based on its current speed, individual historical optimal position, and group historical optimal position, the particle’s speed is updated and its position is adjusted, thereby performing global and local searches and gradually approaching the optimal solution:

[0075] Speed ​​update formula:

[0076] Position update formula:

[0077] Individual optimal position update: If but

[0078] Group optimal position update: If but

[0079] 4) If If the difference between the fitness value of the optimal solution after the previous iteration and the fitness value of the optimal solution after this iteration is less than the convergence accuracy, the iteration is stopped and the output is That is the optimal solution for the required parameter variable; otherwise, let t+1=t and enter loop 3).

[0080] Embodiment 2: Contains all the contents of the embodiment:

[0081] Under low pressure, low speed and low temperature conditions, a=0.4, m=0.3, b=n=0.3, c=0.1.

[0082] Under low pressure, high speed and high temperature conditions, a=0.45, m=0.45, b=n=0.5, c=0.2.

[0083] Under high pressure, low speed and high temperature conditions, a=0.6, m=0.6, b=n=0.35, c=0.2.

[0084] Under high pressure, low speed and low temperature conditions, a=0.55, m=0.4, b=0.3, n=0.34, c=0.12.

[0085] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A sealing structure optimization method based on Latin hypercube design, characterized in that: The following steps are involved: Determine the parameter variables in the sealing structure optimization process, as well as the value range and constraint conditions of each parameter variable; Based on the Latin hypercube design method, each parameter variable is uniformly sampled and K groups of sampling data are generated; A computational fluid dynamics numerical model and a finite element model are parameterized and established based on the generated K groups of sampling data, and the maximum direct stiffness value and the maximum stress value corresponding to the K groups of sampling data are calculated, thereby calculating the maximum fatigue life of the sealing structure; The objective function is constructed by integrating the maximum direct stiffness value and the maximum fatigue life through the multi-objective weighted summation method; The least squares method is used to fit the quadratic polynomial regression model of K groups of sampling data and the objective function. The particle swarm algorithm is introduced to optimize the regression model and obtain the optimal combination of the regression model.

2. The sealing structure optimization method based on Latin hypercube design according to claim 1, characterized in that: The sealing structure has its geometric shape determined by j parameters, namely x = (x1, x2, ..., x j ) is the geometric parameter of the seal, and the value range and constraint conditions of the parameter variables are determined, that is, m i ≤x i ≤M i , i=1,2,…,j; m i With M i Represents the parameter variable x i Upper and lower limit values.

3. The sealing structure optimization method based on Latin hypercube design according to claim 2 is characterized in that: The ratio between K sets of sampled data and j parameters is a constant.

4. The sealing structure optimization method based on Latin hypercube design according to claim 2 is characterized in that: The sealing structure determined by the K group of parameter variables is subjected to three-dimensional numerical modeling, meshing, boundary condition setting, numerical calculation and post-processing analysis. The maximum direct stiffness value and maximum stress value in the post-processing results are extracted to calculate the maximum fatigue life value of the seal.

5. The sealing structure optimization method based on Latin hypercube design according to claim 1, characterized in that: The objective function F(x)=w1·f1(x)+w2·f2(x); Among them, f1(x) is the maximum direct stiffness, f2(x) is the maximum fatigue life, w1 and w2 are the weighting coefficients of the maximum direct stiffness and the maximum fatigue life, respectively.

6. The sealing structure optimization method based on Latin hypercube design according to claim 5, characterized in that: The weighting coefficients of maximum direct stiffness and maximum fatigue life are: Among them, N, P, and T are the speed, pressure, and temperature of the working condition of the sealing structure respectively; N ref , P ref , T ref are the design reference values ​​of the sealing structure respectively; a, b, c, m, and n are adjustment coefficients related to speed, pressure, and temperature, respectively; Δσ is the maximum stress, σ is the fatigue limit, L ref is the reference life, L d is the design life; Among them, a=0.4~0.6, m=0.3~0.4; b=0.3~0.5, n=0.4~0.5; c=0.1~0.

2.

7. The sealing structure optimization method based on Latin hypercube design according to claim 1 is characterized in that: Maximum fatigue life Among them, N f is the fatigue life, S0 is the fatigue strength coefficient, Δσ is the maximum stress value, and k is the fatigue strength attenuation exponent of the material.

8. The sealing structure optimization method based on Latin hypercube design according to claim 1, characterized in that: The multivariate quadratic polynomial regression model is used to fit the K groups of sampling data and the objective function value, and the regression model of the nonlinear relationship between the objective function and the K groups of sampling data is obtained: The regression model is expressed as: Among them, f(x) is the predicted value of the objective function, that is, the predicted value of the weighted result of the maximum direct stiffness value and the maximum fatigue life; β0 is the intercept term; is a linear term; is a linear cross term; is a quadratic term; β i , β ij , β ii are the coefficients of linear terms, linear cross terms, and quadratic terms, respectively; The least squares method was used to fit the above regression model.

9. The sealing structure optimization method based on Latin hypercube design according to claim 8, characterized in that: The regression model is optimized. The initial position, initial velocity, inertia weight, learning factor and number of iterations of the particle swarm are given. Constraints are set and the particle swarm optimization algorithm is used to gradually update the velocity and position of the particles. A global search is performed by calculating the optimal solution in each iteration until the convergence conditions are met to complete the optimization of the sealing structure.

10. The sealing structure optimization method based on Latin hypercube design according to claim 9, characterized in that: 1) From the sealing structure model, determine its key geometric parameters and the initial position of the parameters x0 = (x1, x2, ..., x j ), given the initial velocity v0 = (v1, v2, ..., v j )T, inertia weight ω, individual learning factor c1, group learning factor c2, convergence accuracy ε, random numbers r1, r2 in the interval [0, 1]; 2) The objective function to be optimized is the regression model f(x) in step 3. The particle position and velocity are gradually updated through the particle swarm optimization algorithm. In each iteration, the particle position and velocity are updated according to the individual historical optimal position. and the historical optimal position of the group Search; at the same time, initialize the particle swarm, set the initial iteration number of the particle swarm to t = 0, and the current particle position is Calculate the fitness value of the optimal position searched by each particle; 3) For each particle, based on its current speed, individual historical optimal position, and group historical optimal position, the particle’s speed is updated and its position is adjusted, thereby performing global and local searches and gradually approaching the optimal solution: Speed ​​update formula: Position update formula: Individual optimal position update: If but Group optimal position update: If but 4) If If the difference between the fitness value of the optimal solution after the previous iteration and the fitness value of the optimal solution after this iteration is less than the convergence accuracy, the iteration is stopped and the output is That is the optimal solution for the required parameter variable; otherwise, let t+1=t and enter loop 3).

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