Optimization design method for cooling tower axial flow fan blade web plate structure

Abstract

The invention provides an optimal design method for a cooling tower axial flow fan blade web structure, and belongs to the technical field of optimal design of axial flow fans. The method comprises the following steps: firstly, performing simulation calculation on an initial structure of a blade to obtain stress distribution of the initial structure of the blade and obtain maximum equivalent stress; secondly, sampling to generate an initial sample set by taking the position and the angle of the web as design variables and the weight and the maximum equivalent stress of the initial structure of the blade as structural response, and performing finite element simulation on each sample point to obtain the blade weight and the maximum equivalent stress corresponding to the sample point; establishing a function relationship between the design variable and the structural response; and finally, solving an optimal web position and angle combination in the blade main body, and performing finite element simulation verification. According to the invention, both performance and light weight can be realized, and the running stability and reliability of the fan are improved; and meanwhile, the optimization precision is ensured, and the method has important engineering application value.

Description

Technical Field

[0001] The invention belongs to the technical field of axial flow fan optimization design, and relates to an optimization design method for a blade web structure of an axial flow fan of a cooling tower. Background Art

[0002] Axial flow fans in cooling towers are key equipment in the modern industrial field, and their performance directly affects cooling efficiency and operating costs. As the core component of the cooling tower, the fan blades are subject to the main loads including gravity, aerodynamic force, and centrifugal force. The web inside the blades is the main structure that bears shear force, which has an important influence on the stiffness and strength of the blades, thereby affecting the safe operation of the axial flow fan. In blade design, increasing the size of the web or adjusting the position and angle can improve the strength and stiffness, but often leads to an increase in blade weight. In addition, in traditional blade structure design, the position and angle of the internal web are often determined by engineering experience or experimental testing, which will significantly increase time and economic costs, and it is difficult to obtain the optimal position and angle of the web, which restricts the improvement of the comprehensive performance of the axial flow fan.

[0003] In view of the above problems, the present invention provides an optimization design method for the web structure of an axial flow fan blade based on a response surface model, which is applied to the optimal design of the position and angle of the blade web. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide an optimization design method for the web structure of an axial flow fan blade for a cooling tower in response to the defects involved in the background technology. The method optimizes the web position and angle based on a response surface model to obtain a fan blade with reduced weight and increased strength.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] An optimization design method for a web structure of a blade of an axial flow fan of a cooling tower, wherein the axial flow fan of the cooling tower is composed of a plurality of identical blade structures, each blade structure includes a blade body and a plurality of web structures located inside the blade body, and the number and position of the web structures are determined according to the optimization design method, and the optimization design method specifically includes the following steps:

[0007] Step 1: According to the requirements of the web structure design of the cooling tower axial fan blade, based on the aerodynamic shape of the blade body, the number of blades, the blade length, the operating speed and the installation method, the thickness distribution of the leading edge and the trailing edge of the blade body, the position and size of the blade shaft hole, and the thickness, position and angle of the web are preliminarily designed in the design space to obtain the initial structure of the blade.

[0008] Step 2: Calculate the weight of the initial structure of the blade obtained in step 1; perform numerical simulation calculations on the initial structure of the blade using a finite element simulation method to obtain the stress distribution of the initial structure of the blade, and further obtain the maximum equivalent stress of the initial structure of the blade, which is expressed by von Mises stress.

[0009] Step 3: Taking the web position and angle inside the blade body as the design variables, and the weight and maximum equivalent stress of the initial blade structure obtained in step 2 as the structural response, select the experimental design method to perform sampling in the design space to generate an initial sample set.

[0010] Step 4: Perform finite element simulation calculation on each sample point in the initial sample set obtained in step 3 to obtain the blade weight and maximum equivalent stress of the blade corresponding to each sample point.

[0011] Step 5: Based on the web position and angle inside the blade body, blade weight and maximum equivalent stress of the blade corresponding to each sample point, establish the functional relationship between the design variables and the structural response.

[0012] Step 6: Use the optimization algorithm to solve the optimal web position and angle combination inside the blade body.

[0013] Step 7: Perform finite element simulation verification on the blade with the optimal web position and angle to ensure that the optimization results meet the optimization objectives and constraints.

[0014] Furthermore, in step 1, the thickness distribution of the leading edge and trailing edge of the blade body is determined by the manufacturer's data and installation method; the position of the blade shaft hole is set at the thickest position of the blade body cross-section, and the size of the blade shaft hole is determined by the blade shaft diameter; the blade body contains multiple webs. In order to achieve lightweight design requirements, the thickness of the web should be as small as possible, which is determined by engineering experience combined with numerical simulation. The design of the initial position and angle of the web is to reduce the blade weight as much as possible while ensuring the blade strength, stiffness and buckling stability.

[0015] Furthermore, in step 2, the equivalent pressure load of a blade with a known aerodynamic shape under design conditions is calculated by a computational fluid dynamics (CFD) method, and based on the material properties, equivalent pressure load, gravity load and centrifugal load data of the blade, the initial structure of the blade is simulated and calculated using finite element simulation analysis software to obtain the weight and maximum equivalent stress of the initial structure of the blade.

[0016] Furthermore, in step 3, the web position parameter p inside the blade body is i The range of variation is: The web angle parameter θ inside the blade bodyi The range of variation is: The and are the lower and upper limits of the web position variables inside the blade body, and are the lower and upper limits of the angle variable. The Latin hypercube sampling experimental design method is used to generate the initial sample set in the design space.

[0017] Furthermore, in step 5, based on the design variables and the structural response, the response surface model is used to interpolate or fit the functional relationship between the web position and angle inside the blade body, the blade weight and the maximum equivalent stress of the blade to obtain the functional relationship between the design variables and the structural response; the determination coefficient R is used to 2 , Adjust the determination coefficient The fitting effect of the response surface model is evaluated by using statistical indicators such as mean square error (MSE). The response surface model includes but is not limited to a polynomial model, a Kriging model, a radial basis function model, and an artificial neural network model.

[0018] Furthermore, in step 6, the optimization algorithm used is a multi-objective genetic algorithm, and its specific expression is:

[0019] Design variables: web position p inside the blade body i and angle θ i , x=[p i ,θ i ],(i=1,2,…,n)

[0020] Optimization goal: Minimum blade weight, f1(x) = min{M(x)}; Maximum equivalent stress of the blade is lower than the maximum equivalent stress before optimization, f2(x) = σ max (x) / σ max,0 <1.

[0021] Constraints: strength constraint, σ max (x)≤σ s ; Stiffness constraint, δ max (x)≤δ allow .

[0022] Where n is the number of webs inside the blade body; M(x) is the weight of the blade. Changing the position and angle of the webs inside the blade body will change the height of the webs, thereby changing the weight of the blade. Therefore, the weight of the blade depends on the position and angle of the webs inside the blade body; σ max (x) is the maximum equivalent stress of the blade, σ max,0 is the maximum equivalent stress of the initial structure of the blade; σ s is the yield strength of the material used for the blade; δallow is the maximum allowable deformation of the blade.

[0023] The optimization goal is to minimize f1(x) and make f2(x) less than 1.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] (1) The present invention optimizes the web position and angle inside the blade body through a multi-objective genetic algorithm, seeks the optimal web position and angle combination, reduces the weight of the blade, reduces the maximum equivalent stress of the blade, and correspondingly improves the strength of the blade, achieving a balance between performance and lightweight, and improving the stability and reliability of the fan operation.

[0026] (2) The present invention uses a response surface model instead of a simulation model, which greatly reduces the calculation cost compared to the traditional finite element analysis method that requires a large amount of simulation calculations during the optimization process, while ensuring the optimization accuracy, and has important engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The present invention is a flow chart of an optimization design method for a blade web structure of an axial flow fan in a cooling tower.

[0028] Figure 2 It is the web structure of the cooling tower axial fan blade before optimization.

[0029] Figure 3 It is an optimized cooling tower axial fan blade web structure. DETAILED DESCRIPTION

[0030] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings.

[0031] The present invention may be implemented in many different forms and should not be considered limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

[0032] The present invention provides a cooling tower axial fan blade web structure optimization design method, the process is as follows Figure 1 As shown. Specifically including the following steps:

[0033] Step 1: According to the requirements of the web structure design of the cooling tower axial fan blade, based on the aerodynamic shape of the blade body, the number of blades, the blade length, the operating speed and the installation method, the thickness distribution of the leading edge and the trailing edge of the blade body, the position and size of the blade shaft hole, and the thickness, position and angle of the web are preliminarily designed in the design space to obtain the initial structure of the blade.

[0034] The aerodynamic shape of the blade body is obtained by the computational fluid dynamics (CFD) method, and the number of blades, blade length, operating speed and installation method are provided by the cooling tower axial flow fan manufacturer.

[0035] In this embodiment, the number of blades of the cooling tower axial flow fan is 6, and the 6 blades are evenly distributed along the circumference. The structure of each blade is exactly the same, the blade length is 2m, the operating speed is 240rpm, and each blade is connected to the hub through the blade shaft.

[0036] In the design space, the thickness distribution of the leading and trailing edges of the blade body, the position and size of the blade shaft hole, and the thickness, position and angle of the web are preliminarily designed to obtain the initial structure of the blade, such as Figure 2 As shown. The leading and trailing edge thickness distribution of the blade body is determined by the manufacturer's data and installation method; the blade shaft hole is located at the thickest position of the blade body cross section, and the size of the blade shaft hole is determined by the blade shaft diameter; the blade body contains multiple webs. To meet the requirements of lightweight design, the web thickness should be as small as possible, which is determined by engineering experience combined with numerical simulation. The initial position and angle of the web are designed to reduce the blade weight as much as possible while ensuring the blade strength, stiffness and buckling stability.

[0037] In this embodiment, the thickness of the blade body is 2mm, the diameter of the shaft hole inside the blade body is 50mm, and the thickness of the four webs inside the blade body is 2mm. Taking the blade chord as the reference line and the center of the blade shaft hole as the reference point, the angle parameter θ1 between web 1 and the blade chord is 93°, and the position parameter p1 between web 1 and the blade axis is 130mm; the angle parameter θ2 between web 2 and the blade chord is 95°, and the position parameter p2 between web 2 and the blade axis is 40mm; the angle parameter θ3 between web 3 and the blade chord is 85°, and the position parameter p3 between web 3 and the blade axis is 35mm; the angle parameter θ4 between web 4 and the blade chord is 85°, and the position parameter p4 between web 4 and the blade axis is 80mm.

[0038] Step 2: Calculate the weight of the initial structure of the blade obtained in step 1; perform numerical simulation calculations on the initial structure of the blade using a finite element simulation method to obtain the stress distribution of the initial structure of the blade, and further obtain the maximum equivalent stress of the initial structure of the blade, which is expressed by von Mises stress.

[0039] The equivalent pressure load of a blade with a known aerodynamic shape under design conditions is calculated by the Computational Fluid Dynamics (CFD) method. Based on the material properties, equivalent pressure load, gravity load and centrifugal load data of the blade, the initial structure of the blade is simulated and calculated using finite element simulation analysis software to obtain the weight and maximum equivalent stress of the initial structure of the blade.

[0040] In this embodiment, the weight of the initial structure of the blade is calculated by the finite element simulation analysis software ANSYS to be 14.79 kg, and the maximum equivalent stress of the initial structure of the blade is 61.57 MPa.

[0041] Step 3: Taking the web position and angle inside the blade body as the design variables, and the weight and maximum equivalent stress of the initial blade structure obtained in step 2 as the structural response, select the experimental design method to perform sampling in the design space to generate an initial sample set.

[0042] In this embodiment, the web position variable inside the blade body is defined as the vertical distance between each web and the center of the blade shaft hole, and the position variables of the four webs are p1, p2, p3 and p4; the web angle variable inside the blade body is defined as the angle between each web and the blade chord, and the angle variables of the four webs are θ1, θ2, θ3 and θ4, such as Figure 2 shown.

[0043] The web position variable p inside the blade body i The range of variation (design space) is: The web angle variable θ inside the blade body i The range of variation (design space) is: and are the lower and upper limits of the location variable, and are the lower and upper limits of the angle variable. Specifically:

[0044] In this embodiment, 0.8p i0 ≤p i ≤1.2p i0 , 75°≤θ i ≤105°, p i0 is the web position of the initial blade structure.

[0045] The Latin hypercube sampling experimental design method is used to generate the initial sample set in the design space. Specifically:

[0046] This embodiment has 8 design variables. To ensure uniform coverage of the sampling space and sufficient model accuracy, 80 sample points are generated by comprehensively considering computing resources and optimizing accuracy.

[0047] Step 4: Perform finite element simulation calculation on each sample point in the initial sample set obtained in step 3 to obtain the blade weight and maximum equivalent stress of the blade corresponding to each sample point.

[0048] Step 5: Based on the web position and angle inside the blade body, blade weight and maximum equivalent stress of each sample point, establish the functional relationship between the design variables and the structural response. Specifically:

[0049] Taking the Kriging model as an example (not limited to the Kriging model), the n sample points obtained by sampling are: In this embodiment, n=80, m=8.

[0050] The n structural responses calculated using the finite element simulation method for these n sample points are: Among them, Y1 is the weight response value of the blade, and Y2 is the maximum equivalent stress response value of the blade.

[0051] The Kriging model between the design variables and the structural response is established using a model building tool. In this embodiment, the Kriging model is established using the Response Surface component in the ANSYS software.

[0052] Verify the constructed Kriging model to ensure its accuracy and reliability. Use the finite element simulation calculation results (true values) of each sample point in the sample set obtained in step 4 to compare with the prediction results of the Kriging model, calculate the error between the predicted value and the true value, and use the root mean square error (RMSE) indicator to evaluate the accuracy of the constructed Kriging model. If the root mean square error RMSE is less than 1%, it indicates that the accuracy of the constructed Kriging model is sufficient.

[0053] In this embodiment, the root mean square error RSME of the Kriging model constructed using the Response Surface component in the ANSYS software is 2.78×10 -10 , indicating that the accuracy of the constructed Kriging model is sufficient.

[0054] Step 6: Use the multi-objective genetic algorithm NSGA-II to solve the optimal web position and angle combination inside the blade body. The specific mathematical model expression is:

[0055] Design variables: web position p inside the blade body i and angle θ i , x=[pi ,θ i ],(i=1,2,…,n)

[0056] Optimization goal: Minimum blade weight, f1(x) = min{M(x)}; Maximum equivalent stress of the blade is lower than the maximum equivalent stress before optimization, f2(x) = σ max (x) / σ max,0 <1.

[0057] Constraints: strength constraint, σ max (x)≤σ s ; Stiffness constraint, δ max (x)≤δ allow .

[0058] Where n is the number of webs inside the blade body; M(x) is the weight of the blade. Changing the position and angle of the webs inside the blade body will change the height of the webs, thereby changing the weight of the blade. Therefore, the weight of the blade depends on the position and angle of the webs inside the blade body; σ max (x) is the maximum equivalent stress of the blade, σ max,0 is the maximum equivalent stress of the initial structure of the blade; σ s is the yield strength of the material used for the blade; δ allow is the maximum allowable deformation of the blade.

[0059] The optimization goal is to minimize f1(x) and make f2(x) less than 1.

[0060] In this embodiment, the weight of the initial structure of the blade is 14.79 kg, and the maximum equivalent stress σ of the initial structure of the blade is max,0 is 61.57MPa, and the yield strength of the blade material (aluminum alloy 6063-T6) is s is 170MPa, and the maximum allowable deformation of the blade is allow The weight of the blade optimized by the multi-objective genetic algorithm NSGA-II is 14.56 kg, and the maximum equivalent stress of the blade is 55.41 MPa. The web position and angle inside the optimized blade body: the angle parameter θ1 between web 1 and the blade chord is 88.22°, and the position parameter p1 between web 1 and the blade axis is 146.87 mm; the angle parameter θ2 between web 2 and the blade chord is 92.29°, and the position parameter p2 between web 2 and the blade axis is 46.84 mm; the angle parameter θ3 between web 3 and the blade chord is 81.62°, and the position parameter p3 between web 3 and the blade axis is 39.14 mm; the angle parameter θ4 between web 4 and the blade chord is 87.91°, and the position parameter p4 between web 4 and the blade axis is 94.36 mm.

[0061] Step 7: Perform finite element simulation verification on the blade with the optimal web position and angle to ensure that the optimization results meet the optimization objectives and constraints.

[0062] In this embodiment, the weight of the optimized blade is reduced by 0.23kg, or 2%, compared with the initial blade; the maximum equivalent stress of the blade is reduced by 6.16MPa, or 10%, compared with the initial blade. The optimization goal in step 6 is achieved. In addition, the maximum equivalent stress of the optimized blade is 55.41MPa, which is less than the yield strength of the blade material of 170MPa, and the maximum deformation of the blade is 4.2mm, which is less than the maximum allowable deformation of 13mm, satisfying the constraint conditions in step 6.

[0063] The final blade web structure optimization results are as follows: Figure 3 shown.

[0064] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications 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. An optimization design method for a web structure of a blade of an axial flow fan for a cooling tower, wherein the axial flow fan for a cooling tower is composed of a plurality of identical blade structures, each blade structure comprising a blade body and a plurality of web structures located inside the blade body, wherein the number and position of the web structures are determined according to the optimization design method, and wherein: The optimization design method specifically comprises the following steps: Step 1: According to the requirements of the cooling tower axial fan blade web structure design, based on the aerodynamic shape of the blade body, the number of blades, the blade length, the operating speed and the installation method, the thickness distribution of the leading edge and the trailing edge of the blade body, the position and size of the blade shaft hole, and the thickness, position and angle of the web are preliminarily designed in the design space to obtain the initial structure of the blade; Step 2: Calculate the weight of the initial structure of the blade obtained in step 1; perform numerical simulation calculation on the initial structure of the blade using a finite element simulation method to obtain the stress distribution of the initial structure of the blade and the maximum equivalent stress of the initial structure of the blade; Step 3: Taking the web position and angle inside the blade body as the design variables, and the weight and maximum equivalent stress of the initial structure of the blade obtained in step 2 as the structural response, select the experimental design method to sample in the design space to generate an initial sample set; Step 4: Perform finite element simulation calculation on each sample point in the initial sample set obtained in step 3 to obtain the blade weight and maximum equivalent stress of the blade corresponding to each sample point; Step 5: Based on the web position and angle inside the blade body, blade weight and maximum equivalent stress of each sample point, establish the functional relationship between the design variables and the structural response; Step 6: Use the optimization algorithm to solve the optimal web position and angle combination inside the blade body; Step 7: Perform finite element simulation verification on the blade with the optimal web position and angle to ensure that the optimization results meet the optimization objectives and constraints.

2. The optimization design method for the web structure of the cooling tower axial fan blade according to claim 1, characterized in that: In step 1, the thickness distribution of the leading edge and trailing edge of the blade body is determined by the manufacturer's data and installation method; the position of the blade shaft hole is set at the thickest position of the blade body cross-section, and the size of the blade shaft hole is determined by the blade shaft diameter; the blade body contains multiple webs, and the thickness of the webs is determined by engineering experience combined with numerical simulation. The initial position and angle of the webs are designed to reduce the weight of the blade on the premise of ensuring the strength, stiffness and buckling stability of the blade.

3. The optimization design method for the web structure of the cooling tower axial fan blade according to claim 1, characterized in that: In step 2, the equivalent pressure load of a blade with a known aerodynamic shape under design conditions is calculated by a computational fluid dynamics (CFD) method. Based on the material properties, equivalent pressure load, gravity load and centrifugal load data of the blade, the initial structure of the blade is simulated and calculated using finite element simulation analysis software to obtain the weight and maximum equivalent stress of the initial structure of the blade.

4. The optimization design method for the web structure of the cooling tower axial fan blade according to claim 1, characterized in that: The maximum equivalent stress in step 2 is expressed in terms of von Mises stress.

5. The optimization design method for the web structure of the cooling tower axial fan blade according to claim 1, characterized in that: In step 3, the web position parameter p inside the blade body i The range of variation is: The web angle parameter θ inside the blade body i The range of variation is: The and are the lower and upper limits of the web position variables inside the blade body, and are the lower and upper limits of the angle variable.

6. The optimization design method for the web structure of the cooling tower axial fan blade according to claim 1, characterized in that: In step 3, a Latin hypercube sampling experimental design method is used to perform sampling in the design space to generate an initial sample set.

7. The optimization design method for the web structure of the cooling tower axial fan blade according to claim 1, characterized in that: In step 5, based on the design variables and the structural response, the response surface model is used to interpolate or fit the functional relationship between the web position and angle inside the blade body, the blade weight and the maximum equivalent stress of the blade to obtain the functional relationship between the design variables and the structural response.

8. The optimization design method for the web structure of the cooling tower axial fan blade according to claim 1, characterized in that: In step 5, the response surface model includes but is not limited to a polynomial model, a Kriging model, a radial basis function model, and an artificial neural network model; the determination coefficient R is used. 2 , Adjust the determination coefficient The fitting effect of the response surface model was evaluated by the mean square error (MSE) statistical indicators.

9. The optimization design method for the web structure of the cooling tower axial fan blade according to claim 1, characterized in that: In step 6, the optimization algorithm used is a multi-objective genetic algorithm.

10. The optimization design method for the web structure of the cooling tower axial fan blade according to claim 9, characterized in that: The specific expression of the multi-objective genetic algorithm is: Design variables: web position p inside the blade body i and angle θ i , x=[p i ,θ i ], where i = 1, 2, ..., n; Optimization goal: Minimum blade weight, f1(x) = min{M(x)}; Maximum equivalent stress of the blade is lower than the maximum equivalent stress before optimization, f2(x) = σ max (x) / σ max,0 <1; Constraints: strength constraint, σ max (x)≤σ s ; Stiffness constraint, δ max (x)≤δ allow ; Where n is the number of webs inside the blade body; M(x) is the weight of the blade. Changing the position and angle of the webs inside the blade body will change the height of the webs, thereby changing the weight of the blade. Therefore, the weight of the blade depends on the position and angle of the webs inside the blade body; σ max (x) is the maximum equivalent stress of the blade, σ max,0 is the maximum equivalent stress of the initial structure of the blade; σ s is the yield strength of the material used for the blade; δ allow is the maximum allowable deformation of the blade; The optimization goal is to minimize f1(x) and make f2(x) less than 1.

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