A method for obtaining the strength safety factor of a centrifugal impeller

Abstract

The present invention provides a method for obtaining the strength safety factor of a centrifugal impeller, which solves the problems of the existing calculation method that the solver iterates repeatedly during calculation, takes a long time, occupies a large amount of computing resources, cannot quickly know the safety of the impeller strength, and affects the design efficiency of the impeller. The present invention includes the following steps: step 1) establishing an elastic-plastic finite element calculation model of the impeller; step 2) statistically analyzing the plastic strain limit value; step 3) establishing the relationship between plastic strain and elastic stress; step 4) calculating the elastic stress limit value σ of the impeller lim ; step 5) calculating the elastic stress of the impeller; step 6) calculating the safety factor n; step 7) comparing the safety factor n with a preset value to finally know the safety of the impeller. The present invention combines the elastic and elastic-plastic finite element calculation methods of impeller strength into one calculation method, effectively solving the problems of long time consumption and large computing resource occupation of the elastic-plastic finite element method, thereby improving the design efficiency of the impeller.

Description

Technical Field

[0001] The present invention relates to a method for checking the strength and safety of a centrifugal impeller, and particularly to a method for obtaining the safety factor of the strength of a centrifugal impeller. Background Art

[0002] A centrifugal compressor is an important energy conversion device in engineering and is widely used in engineering fields such as energy, power, and chemical engineering. As the core component of a centrifugal compressor, the safe operation of the impeller is an important guarantee for the overall reliability of the centrifugal compressor. Therefore, it is necessary to calculate the strength of the impeller during the design stage to ensure its safety.

[0003] Currently, the finite element method is generally used for calculating the strength of the impeller. According to the relationship between the maximum stress of the impeller and the yield strength of the impeller material, the finite element calculation of the impeller strength is divided into two categories: elastic and elastoplastic. The elastic calculation method of the impeller is applicable to the case where the maximum stress is less than the yield strength of the material. At this time, the stress, strain, and external load are in a linear proportional relationship, the solution speed is fast, and the strength of the impeller is evaluated by the stress value. The elastoplastic calculation method of the impeller is applicable to the case where the maximum stress exceeds the yield strength of the material. At this time, local plastic deformation occurs in the impeller, and the stress, strain, and external load are in a non-linear relationship. The solver needs to repeatedly iterate to solve the stress and strain, and the strength of the impeller is evaluated by the plastic strain value.

[0004] The elastic calculation method is applicable to impellers with low linear velocity and low stress. With the change of engineering application requirements, the diameter of the impeller tends to be large, the linear velocity is generally high, the local stress exceeds the yield strength of the material, and plastic deformation occurs. In this case, the elastoplastic calculation method is usually used to obtain the plastic strain of the impeller, and then evaluate the strength of the impeller. However, the elastoplastic calculation method takes a long time and occupies a lot of computing resources, and the strength of the impeller cannot be quickly obtained during the design process, which affects the design efficiency of the impeller. Summary of the Invention

[0005] The present invention provides a method for obtaining the safety factor of the strength of a centrifugal impeller, which solves the problem that the existing finite element calculation methods for the strength of a centrifugal impeller are not unified and are divided into two types: elastic and elastoplastic. It also solves the problem that when the elastoplastic method is used for calculation, the solver repeatedly iterates, takes a long time, occupies a lot of computing resources, and cannot quickly obtain the safety of the strength of the impeller, which affects the design efficiency of the impeller.

[0006] The basic concept of the present invention is: calculating the maximum plastic strain of the impeller at different rotational speeds by the elastoplastic finite element method, statistically analyzing the calculation data of the impeller, determining the plastic strain limit value of the impeller, and then combining with the theoretical calculation formula to equivalently convert the limit plastic strain to the elastic stress value of the elastic finite element method, that is, converting the elastoplastic finite element calculation of the impeller into the elastic finite element calculation, unifying the two types of finite element calculation methods of elasticity and elastoplasticity into the elastic finite element calculation method, so as to achieve the purpose of calculating the strength of the impeller by using the elastic finite element method, quickly obtaining the safety of the impeller, and efficiently completing the design of the impeller.

[0007] The technical solution adopted by the present invention is:

[0008] A method for obtaining the safety factor of the strength of a centrifugal impeller, characterized in that it includes the following steps:

[0009] 1) Establish an elastoplastic finite element calculation model of the impeller

[0010] 1.1) Establish a three-dimensional model of the impeller in 3D CAD software. The model includes chamfers at the joints of the blades, the hub, and the shroud, and then import the model into the finite element analysis software;

[0011] 1.2) Set the elastoplastic parameters of the impeller material, including density, Poisson's ratio, elastic modulus, yield strength, stress-strain relationship. The stress-strain relationship adopts a bilinear kinematic hardening model, and the tangent modulus is E1;

[0012] 1.3) Considering the action of centrifugal force, apply the operating rotational speed ω around the rotation axis to the impeller;

[0013] 1.4) Set the radial direction of the impeller shaft hole to be free, and the circumferential and axial directions to be fixed;

[0014] 1.5) Set a reasonable mesh size to divide the impeller into tetrahedral elements;

[0015] 1.6) Set the elastoplastic nonlinear solution parameters, including solver type, time step, convergence criterion, and turn on the large deformation function;

[0016] 1.7) Set the result to output the plastic strain and then solve;

[0017] 2) Statistically analyze the plastic strain limit value

[0018] 2.1) Perform elastoplastic calculations on the impeller according to steps 1.1 to 1.7, perform elastoplastic calculations at multiple rotational speeds from 1.1ω to 2.0ω respectively, the rotational speed interval can be taken as 0.1ω, process the calculation results to obtain the maximum plastic strain of the impeller, and fit the data to draw the relationship curve between the maximum plastic strain and the rotational speed;

[0019] 2.2) Determine the plastic strain limit value ε of this type of centrifugal impeller according to the relationship curve between the maximum plastic strain of the impeller and the rotational speedp ;

[0020] 3) Establish the relationship between plastic strain and elastic stress

[0021] Using Neuber's formula (1), when the local plastic stress and strain are known, the local stress and strain are converted to elastic stress and strain, and the conversion relationship is as follows:

[0022]

[0023]

[0024]

[0025] Substitute formulas (2) and (3) into formula (1), and we get

[0026]

[0027]

[0028]

[0029] where K t is the elastic stress concentration factor, K σ is the stress concentration factor, K ε is the strain concentration factor, σ is the local stress, σ nom is the elastic nominal stress, ε is the local total strain, ε nom is the nominal strain, and E is the elastic modulus;

[0030] 4) Calculate the elastic stress limit value σ of the impeller lim

[0031] The local stress is calculated according to formula (7),

[0032] σ = σ s + E1·ε p (7)

[0033] According to formulas (6) and (7), the elastic stress limit value can be obtained:

[0034]

[0035] where:

[0036] σ s is the yield strength;

[0037] E is the elastic modulus;

[0038] E1 is the tangent modulus;

[0039] ε pis the plastic strain limit value determined in step 2.2);

[0040] K t is the elastic stress concentration factor;

[0041] ε e is the elastic strain;

[0042] 5) Impeller elastic stress calculation

[0043] 5.1) Establish a 3D model of the impeller in 3D CAD software. The model includes chamfers at the connections between the blades and the disk and the cover, and then import the model into the finite element analysis software;

[0044] 5.2) Set the elastic parameters of the impeller material, including density, Poisson's ratio, and elastic modulus;

[0045] 5.3) Only consider the action of centrifugal force, and add the maximum rotational speed ω of the impeller around the rotation axis in the impeller elastoplastic model max ;

[0046] 5.4) Require the radial freedom of the impeller shaft hole and the circumferential and axial fixed constraints;

[0047] 5.5) Set a reasonable mesh size to divide the impeller into tetrahedral elements;

[0048] 5.6) Set the solver type, output the von Mises stress as the result, and obtain the maximum von Mises stress σ mises and its position;

[0049] 6) Calculate the safety factor n:

[0050]

[0051] Where:

[0052] σ lim is the impeller elastic stress limit value obtained in step 4);

[0053] σ mises is the maximum von Mises stress of the impeller obtained in step 5);

[0054] 7) If the safety factor n is greater than the preset value, the impeller strength meets the design requirements; if the safety factor n is less than the preset value, the impeller strength does not meet the design requirements, and the impeller structure needs to be optimized and improved. After the improvement, go back to step 5).

[0055] Furthermore, in the said step 2.2), the plastic strain limit value ε p takes 0.01 - 0.015;

[0056] In the said step 4), the elastic stress concentration factor K tTake 0.95 to 1.05.

[0057] Further, in step 2.2), the plastic strain limit value ε p Take 0.01;

[0058] In step 4), the elastic stress concentration coefficient K t Take 1.

[0059] Further, in the step of setting a reasonable mesh type, the impeller is divided into 10 - node tetrahedral elements;

[0060] Further, in step 1.5), the specific method of setting a reasonable mesh size to divide the impeller into 10 - node tetrahedral elements is as follows:

[0061] Set the overall mesh size of the impeller to the blade thickness value, the mesh size of all blade surfaces to half of the thickness value, and the transition fillets at the connections between the blades and the disk and the cover to be divided into at least 3 rows of elements.

[0062] The beneficial effects of the present invention compared with the prior art are as follows:

[0063] The method for obtaining the strength safety factor of a centrifugal impeller provided by the present invention, through elastoplastic finite - element calculation of the centrifugal impeller, statistically analyzes and determines the plastic strain limit value of the impeller, and then combines with the theoretical calculation formula to equivalently convert the limit plastic strain to the elastic stress value of the elastic finite - element method, that is, converts the elastoplastic calculation into an elastic calculation, combines the impeller strength calculation into one type of calculation, effectively solves the problems of long time consumption and large consumption of computing resources in the elastoplastic finite - element method, and thus improves the design efficiency of the impeller. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 is the relationship curve of the maximum plastic strain of the impeller and the rotational speed in an embodiment of the present invention;

[0065] Figure 2 is the relationship curve of the plastic strain - elastic stress conversion of the impeller in an embodiment of the present invention;

[0066] Figure 3 is the schematic diagram of the overall mesh size of the impeller in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0067] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0068] A method for obtaining the strength safety factor of a centrifugal impeller is as follows:

[0069] 1) Establish an elastoplastic finite - element calculation model of the impeller

[0070] 1.1) Establish a 3D model of the impeller in 3D CAD software. The model includes chamfers at the connections between the blades and the hub and the shroud, and then import the model into the finite element analysis software.

[0071] 1.2) Set the elastoplastic parameters of the impeller material, including density, Poisson's ratio, elastic modulus, yield strength, stress-strain relationship. The stress-strain relationship adopts a bilinear kinematic hardening model, and the tangent modulus is E1.

[0072] 1.3) Considering the action of centrifugal force, apply the operating speed ω around the rotation axis to the impeller.

[0073] 1.4) Set the radial direction of the impeller shaft hole to be free, and the circumferential and axial directions to be fixed.

[0074] 1.5) Set a reasonable mesh size to divide the impeller into 10-node tetrahedral elements. Specifically: as Figure 3 shown, set the overall mesh size of the impeller to be the blade thickness value, the mesh size of all blade surfaces to be half of the thickness value, and the transition fillets at the connections between the blades and the hub and the shroud to be divided into at least 3 rows of elements.

[0075] 1.6) Set the elastoplastic nonlinear solution parameters, including solver type, time step, convergence criterion, and enable the large deformation function.

[0076] 1.7) Set the result to output the plastic strain and then solve.

[0077] 2) Statistically analyze the plastic strain limit value

[0078] Perform elastoplastic calculations on the impeller according to steps 1.1 to 1.7. Conduct elastoplastic calculations at multiple speeds from 1.1ω to 2.0ω, and the speed interval can be taken as 0.1ω. Process the calculation results to obtain the maximum plastic strain of the impeller. Fit the data to plot the relationship curve between the maximum plastic strain and the speed. Through statistical analysis, when the maximum plastic strain of the impeller is 1% - 1.5%, the plastic strain increases rapidly. As Figure 1 shown, the plastic zone on the impeller surface gradually expands, cracks begin to initiate, and gradually expand to rupture and failure. Since the safety of the impeller is crucial to the compressor, conservatively consider that the plastic strain limit value of such centrifugal impellers is taken as ε p = 1%.

[0079] 3) Establish the relationship between plastic strain and elastic stress

[0080] When the local elastic nominal stress of elastic calculation exceeds the yield strength, the Neuber formula can be used to convert the elastic nominal stress and strain into local stress and strain. The maximum elastic stress of the centrifugal impeller usually appears in or near the connecting transition fillet area between the blade and the disk or the cover, which is an area affected by stress concentration. After simulation calculation, it meets the application conditions of the Neuber formula. Conversely, in the present invention, using the Neuber formula (1), when the local plastic stress and strain are known, the local stress and strain are converted into elastic stress and strain, and the elastic nominal stress can be calculated by formula (6). The conversion relationship is as Figure 2 shown, and the conversion between formulas is as follows:

[0081]

[0082]

[0083]

[0084] Substituting formulas (2) and (3) into formula (1), we get

[0085]

[0086]

[0087]

[0088] where K t is the elastic stress concentration coefficient, K σ is the stress concentration coefficient, K ε is the strain concentration coefficient, σ is the local stress, σ nom is the elastic nominal stress, ε is the local total strain, ε nom is the nominal strain, and E is the elastic modulus.

[0089] 4) Solve the elastic stress limit value of the impeller

[0090] The stress calculated by the finite element method takes into account the influence of stress concentration. Therefore, K t = 1. In step 2, the limit value ε p of the plastic strain has been obtained through a large number of simulation calculations. The corresponding local stress is calculated according to formula (7),

[0091] σ = σ s + E1·ε p (7)

[0092] According to formulas (6) and (7), the elastic stress limit value can be obtained:

[0093]

[0094] Among them, σ lim is the elastic stress limit value, ε e is the elastic strain, ε p is the limit value of plastic strain, σ s is the yield strength, E is the elastic modulus, and E1 is the tangent modulus.

[0095] 5) Impeller elastic stress calculation

[0096] 5.1) Establish a 3D model of the impeller in 3D CAD software. The model includes the chamfers at the connections between the blades and the hub and the shroud, and then import the model into the finite element analysis software.

[0097] 5.2) Set the elastic parameters of the impeller material, including density, Poisson's ratio, and elastic modulus;

[0098] 5.3) Only consider the action of centrifugal force, and apply the maximum rotational speed ω max .

[0099] 5.4) It is required that the radial direction of the impeller shaft hole is free, and the circumferential and axial directions are fixed and constrained.

[0100] 5.5) Set a reasonable mesh size to divide the impeller into 10-node tetrahedral elements. Similar to step 1.5), set the overall mesh size of the impeller to the blade thickness value, the mesh size of all blade surfaces to half of the thickness value, and the transition fillets at the connections between the blades and the hub and the shroud are divided into at least 3 rows of elements.

[0101] 5.6) Set the solver type, output the von Mises stress as the result, and obtain the maximum value σ mises of the von Mises stress and its position after solving and post-processing.

[0102] 6) Calculate the safety factor n according to the following formula:

[0103]

[0104] It can be seen from formula (8) that when the material is the same, since the yield strength, elastic modulus, and tangent modulus remain unchanged, the elastic limit stress of the impeller is a fixed value. For the safety factor calculation of the new structure impeller, only steps 5) and 6) need to be carried out.

[0105] 7) If the safety factor n is greater than the preset value (for example, the preset value is 1.25), the impeller can operate safely at the maximum rotational speed ω max ; if the safety factor n is less than the preset value, there is a safety risk when the impeller operates at the maximum rotational speed ω max . It is necessary to optimize and improve the impeller structure, and then go back to step 5) after the improvement.

[0106] Take the specific impeller design process as an example:

[0107] It is known that the material of a certain type of centrifugal impeller is FV520B, and the material density ρ = 7850 kg / m 3 , the yield strength σ s = 880 MPa, the Poisson's ratio ν = 0.3, the elastic modulus E = 2.0E5 MPa, and the tangent modulus E1 = 100 MPa.

[0108] 1) After performing elastoplastic finite element calculations according to steps 1 to 4 and conducting statistical analysis, it is obtained that the plastic strain limit value ε p = 0.012 for such centrifugal impellers made of FV520B material. Then, the elastic stress limit value of the impeller is calculated according to formula (8):

[0109]

[0110] For a newly designed impeller, the elastic finite element stress calculation of the impeller is carried out according to step 5). The rotational speed is set to the maximum rotational speed of the impeller, 1241.8 rad / s. After post-processing, the maximum von Mises stress σ mises = 1161.6 MPa.

[0111] The safety factor n is calculated according to formula (9):

[0112]

[0113] The safety factor n is greater than the preset value of 1.25, and the impeller can operate safely at the maximum rotational speed of 1241.8 rad / s.

[0114] The calculation method of the present invention can greatly shorten the impeller strength calculation time and save calculation resources. For an impeller divided into 10-node tetrahedral elements with 3,187,776 nodes and 2,180,016 elements, elastic and elastoplastic finite element calculations are carried out, and the calculation time and occupied resources are shown in Table 1.

[0115] Table 1 Comparison of elastic and elastoplastic finite element calculations

[0116] Elastic calculation Elastoplastic calculation Calculation time 9 minutes and 45 seconds 1 hour, 23 minutes and 53 seconds Total disk write data 4.5 GB 158.5 GB Total disk read data 1.7 GB 150.1 GB

[0117] For a large number of impellers, elastoplastic and elastic finite element calculations of the present invention are carried out. After comparison and analysis, the method of the present invention can obtain safety evaluation results consistent with those of elastoplastic finite elements.

Claims

1. A method for obtaining the strength safety factor of a centrifugal impeller, characterized by comprising the following steps: 1) Establish an elastic-plastic finite element calculation model of the impeller 1.1) Establish a three-dimensional model of the impeller in 3D CAD software. The model includes chamfers at the connections between the blades and the hub and the shroud. Then import the three-dimensional impeller model into the finite element analysis software; 1.2) Set the elastoplastic parameters of the impeller material, including density, Poisson's ratio, elastic modulus, yield strength, and stress-strain relationship. The stress-strain relationship adopts a bilinear kinematic hardening model, and set the tangent modulus as E1; 1.3) Considering the action of centrifugal force, apply the operating speed ω around the rotation axis to the impeller; 1.4) Set the radial direction of the impeller shaft hole to be free, and the circumferential and axial directions to be fixed; 1.5) Set a reasonable grid size to divide the impeller into 10-node tetrahedral elements; among them, The overall mesh size of the impeller is the blade thickness value, the mesh size of all blade surfaces is half of the thickness value, and the transition fillets at the connections between the blades and the hub and the shroud are divided into at least 3 rows of elements; 1.6) Set the elastoplastic nonlinear solution parameters, including solver type, time step, convergence criterion, and enable the large deformation function; 1.7) Set the result to output the plastic strain and then solve to obtain the plastic strain value; 2) Statistically analyze the plastic strain limit value 2.1) Perform elastoplastic calculations on the impeller according to steps 1.1 to 1.

7. Conduct elastoplastic calculations at multiple speeds from 1.1ω to 2.0ω, with a speed interval of 0.1ω. Process the calculation results to obtain the maximum plastic strain value of the impeller, and fit the data to plot the relationship curve between the maximum plastic strain value and the speed; ω is the speed of the impeller; 2.2) Determine the plastic strain limit value ε of such centrifugal impellers according to the relationship curve between the maximum plastic strain of the impeller and the rotational speed. p ; The plastic strain limit value ε p is taken as 0.01 to 0.015; 3) Establish the relationship between plastic strain and elastic stress Using Neuber's formula (1), when the local plastic stress and strain are known, convert the local stress and strain to elastic stress and strain. The conversion relationship is as follows: Substitute formulas (2) and (3) into formula (1) to get Where K t is the elastic stress concentration factor, K σ is the stress concentration factor, K ε is the strain concentration factor, σ is the local stress, σ nom is the elastic nominal stress, ε is the local total strain, ε nom is the nominal strain, E is the modulus of elasticity; 4) Calculate the elastic stress limit value σ of the impeller lim The local stress is calculated according to formula (7), σ = σ s + E1·ε p (7) According to formulas (6) and (7), the elastic stress limit value can be obtained: Where: σ s is the yield strength; E is the elastic modulus; E1 is the tangent modulus; ε p is the plastic strain limit value determined in step 2.2); K t is the elastic stress concentration coefficient; the elastic stress concentration coefficient K t ranges from 0.95 to 1.05; ε e is the elastic strain; 5) Impeller elastic stress calculation 5.1) Establish a three-dimensional model of the impeller in 3D CAD software. The model includes chamfers at the connections between the blades and the hub and the shroud. Then import the model into the finite element analysis software; 5.2) Set the elastic parameters of the impeller material, including density, Poisson's ratio, and elastic modulus; 5.3) Considering only the action of centrifugal force, add the maximum rotational speed ω of the impeller around the rotation axis to the elastoplastic model of the impeller max ; 5.4) Require the radial direction of the impeller shaft hole to be free, and the circumferential and axial directions to be fixed constraints; 5.5) Set a reasonable mesh size to divide the impeller into tetrahedral elements; The said setting of a reasonable mesh type is to divide the impeller into 10-node tetrahedral elements; 5.6) Set the solver type, and the result outputs the von Mises stress. After the solution calculation, the maximum von Mises stress σ mises and its position are obtained; 6) Calculate the safety factor n Where: σ lim is the impeller elastic stress limit value obtained in step 4); σ mises is the maximum von Mises stress of the impeller obtained in step 5); 7) If the safety factor n is greater than the preset value, the impeller strength meets the design requirements; if the safety factor n is less than the preset value, the impeller strength does not meet the design requirements. The impeller structure needs to be optimized and improved. After improvement, return to step 5) until the safety factor n is greater than the preset value.

2. According to the method for obtaining the strength safety factor of a centrifugal impeller described in claim 1, wherein: In the said step 2.2), the plastic strain limit value ε p is taken as 0.01; In the said step 4), the elastic stress concentration coefficient K t is taken as 1.

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