Numerical analysis efficient algorithm for multi-stage wheel disc structure of aero-engine

Abstract

The invention relates to the technical field of aero-engine simulation analysis, and particularly provides an aero-engine multi-stage wheel disc structure-oriented numerical analysis efficient algorithm, which comprises the steps of S1, establishing a cyclic coordinate system, and obtaining a sector model stiffness matrix and an external force vector; s2, eliminating the internal degree of freedom of the wheel disc; s3, solving the degree of freedom of the inter-disc structure after the internal degree of freedom of the wheel disc is eliminated; s4, solving the internal degrees of freedom of all the wheel discs through back substitution; and S5, obtaining a strain field and a stress field, and judging a potential failure point according to the strain field and the stress field. The numerical simulation precision and efficiency of the multi-stage wheel disc structure can be improved.

Description

Technical Field

[0001] The present disclosure relates to the technical field of aircraft engine simulation analysis, and in particular to an efficient numerical analysis algorithm for a multi-stage wheel structure of an aircraft engine. Background Art

[0002] Multi-stage disc structures, represented by aircraft engine blade-disc systems, are widely used in engineering. Multi-stage disc structures are usually composed of multiple discs, and two adjacent discs are connected by an inter-disc structure. Each disc can be assumed to be a cyclically symmetrical structure, that is, each disc can be considered to be a sector repeated by rotation. This multi-stage disc structure generally has a different number of sectors per stage, which results in the multi-stage disc structure not having cyclic symmetry as a whole, although each disc is a cyclically symmetrical structure. This makes it impossible for us to directly use the cyclic symmetry theory to solve the numerical simulation problem of the multi-stage disc structure.

[0003] In order to improve computational efficiency, many studies have developed overall analysis methods for multi-level disk structures. In order to apply cyclic symmetry theory in the numerical analysis of multi-level disk structures, many multi-level cyclic symmetry methods assume that the responses of the sectors of the same disk have cyclic symmetry. In fact, the multi-level disk structure is not cyclically symmetric as a whole, so these multi-level cyclic symmetry analysis methods have a certain loss of accuracy.

[0004] How to improve the accuracy and efficiency of numerical simulation of multi-stage disk structures is one of the important issues to be solved urgently in this field. Summary of the invention

[0005] The present disclosure is proposed in view of the above problems. The present disclosure provides an efficient algorithm for numerical analysis of a multi-stage disk structure of an aircraft engine.

[0006] According to the present disclosure, an efficient numerical analysis algorithm for a multi-stage wheel structure of an aircraft engine includes:

[0007] S1, establish a cyclic coordinate system and obtain the sector model stiffness matrix and external force vector;

[0008] S2, eliminates the internal degrees of freedom of the wheel;

[0009] S3, solve the degrees of freedom of the inter-disk structure after eliminating the internal degrees of freedom of the roulette disk;

[0010] S4, back-substitution to solve the displacements corresponding to the internal degrees of freedom of all wheels;

[0011] S5, obtaining the strain field and the stress field, and determining the potential failure point according to the strain field and the stress field.

[0012] According to an aspect of the present disclosure, the efficient numerical analysis algorithm for aero-engine multi-stage disk structure is provided, wherein step S1 includes:

[0013] S11, establishing a roulette coordinate system with the center of the roulette wheel as the origin;

[0014] S12, establishing a sector coordinate system for each sector on the wheel disc, wherein the sector coordinate system takes the radial direction and tangential direction of the wheel disc as coordinate axes;

[0015] The sectors on the same wheel have the same position in their corresponding sector coordinate system.

[0016] According to an aspect of the present disclosure, an efficient algorithm for numerical analysis of a multi-stage disk structure for an aircraft engine is proposed, wherein step S2 condenses the internal degrees of freedom of all disks onto the inter-disk structure through a two-stage condensation technique.

[0017] According to an aspect of the present disclosure, the efficient numerical analysis algorithm for aero-engine multi-stage disk structure is proposed, wherein step S2 includes:

[0018] S21, perform the first condensation to condense the attached degrees of freedom of all sectors;

[0019] S22, performing a second condensation to condense all degrees of freedom in the roulette that are not shared with the inter-stage structure; wherein the properties of the block circulant matrix and group theory are used to reduce the amount of calculation and improve the calculation efficiency.

[0020] According to an aspect of the present disclosure, an efficient algorithm for numerical analysis of multi-stage disc structures for aircraft engines is proposed, wherein, during the second condensation process, a group of linear algebraic equations corresponding to the internal degrees of freedom of the disc is constructed, and the coefficient matrix of the group of equations is a block circulant matrix.

[0021] According to an aspect of the present disclosure, an efficient algorithm for numerical analysis of multi-stage disk structures of aircraft engines is proposed, wherein, in the process of solving the linear algebraic equations, the block circulant matrix is ​​converted into a block diagonal matrix to decouple the linear algebraic equations.

[0022] According to an aspect of the present disclosure, an efficient algorithm for numerical analysis of a multi-stage disk structure for an aircraft engine is proposed, wherein in step S3, a direct method or a preconditioned conjugate gradient method is used to efficiently solve the corresponding set of linear algebraic equations.

[0023] According to an aspect of the present disclosure, an efficient algorithm for numerical analysis of a multi-stage disk structure for aircraft engines is proposed. In step S4, after obtaining the displacement of the corresponding degree of freedom of the structure after condensation, the relationship between the main degree of freedom and the subsidiary degree of freedom in the two-stage condensation process is used to perform back substitution and solve the problem twice, and finally the displacement corresponding to all the degrees of freedom of the entire multi-stage disk structure is obtained.

[0024] According to an aspect of the present disclosure, an efficient algorithm for numerical analysis of aero-engine multi-stage disk structures is proposed. In step S5, after the displacement response is obtained, variables such as the strain field and stress field of the structure are calculated based on geometric equations and Hooke's law.

[0025] According to an aspect of the present disclosure, an efficient numerical analysis algorithm for aero-engine multi-stage disc structures is proposed, wherein in step S5, stress analysis is used to identify areas with high stress or concentrated stress in the multi-stage disc structure and use them as potential failure points.

[0026] As described in detail below, according to an efficient numerical analysis algorithm for a multi-stage disc structure of an aero-engine according to an embodiment of the present disclosure, a cyclic coordinate system is established to obtain the stiffness matrix and external force vector of the sector model; the internal degrees of freedom of the disc are eliminated; the displacement corresponding to the degrees of freedom of the inter-disk structure after the internal degrees of freedom of the disc are eliminated is solved; the displacement corresponding to the internal degrees of freedom of all discs is solved by back substitution; the strain field and the stress field are obtained, and the potential failure point is determined according to the strain field and the stress field. The mechanical properties and structural response of the multi-stage disc system can be simulated and analyzed more quickly and accurately, the reliability and durability of the engine can be improved, and the stress distribution and deformation trend of the disc can be given more accurately, thereby helping to design a more reliable disc structure and extend the service life of the engine. Compared with not considering the coupling effect and performing numerical analysis on a single disc structure in isolation, the accuracy of the algorithm proposed in the present disclosure can be guaranteed, because compared with the numerical analysis of the entire multi-stage disc system, the efficient algorithm proposed in the present disclosure does not introduce any approximation, and compared with the numerical analysis of the entire multi-stage disc system, the efficient algorithm proposed in the present disclosure has significant computational efficiency. The disclosed method is easy to use and universal. The disclosed method reduces the demand for computer memory for analyzing large-scale multi-level roulette structures. Since the disclosed method is based on traditional finite element theory, it can be easily integrated into existing finite element software.

[0027] It is to be understood that both the foregoing general description and the following detailed description are exemplary, and are intended to provide further explanation of the technology as claimed. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The above and other purposes, features and advantages of the present disclosure will become more apparent by describing the embodiments of the present disclosure in more detail in conjunction with the accompanying drawings. The accompanying drawings are used to provide a further understanding of the embodiments of the present disclosure and constitute a part of the specification. Together with the embodiments of the present disclosure, they are used to explain the present disclosure and do not constitute a limitation of the present disclosure. In the accompanying drawings, the same reference numerals generally represent the same components or steps.

[0029] Figure 1 It is a schematic diagram and flow chart of the implementation of the algorithm proposed in the present disclosure;

[0030] Figure 2 It is a schematic diagram of the finite element model of the multi-stage wheel structure;

[0031] Figure 3 It is a schematic diagram of the finite element mesh of the sector model of the multi-stage wheel structure;

[0032] Figure 4 It is a schematic diagram of the analysis coordinate system of the algorithm proposed in the present disclosure;

[0033] Figure 5 is a schematic diagram of the wheel disk stiffness matrix in the analytical coordinate system proposed in the present disclosure;

[0034] Figure 6 It is a schematic diagram of the block diagonalization of the roulette stiffness matrix in the algorithm proposed in the present disclosure. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solution and advantages of the present disclosure more obvious, the exemplary embodiments according to the present disclosure will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present disclosure, rather than all the embodiments of the present disclosure, and it should be understood that the present disclosure is not limited to the exemplary embodiments described here.

[0036] Please refer to Figures 1 to 6 The present disclosure proposes an efficient algorithm for numerical analysis of a multi-stage wheel structure of an aero-engine, which includes the following steps:

[0037] S1, establish a cyclic coordinate system, please refer to Figure 4 , obtain the sector model stiffness matrix and external force vector; in specific implementation, use the cyclic symmetry of each disk in the multi-level wheel structure to establish a cyclic coordinate system. In such a coordinate system, the positions of the sectors belonging to the same level of disks in the established coordinate system are the same, so the stiffness matrices of the sectors belonging to the same level of disks in the established coordinate system are also the same. The number of the cyclic coordinate systems is multiple, specifically, the following steps are included:

[0038] S11, establish a roulette coordinate system with the center of the roulette as the origin. In a specific implementation, the roulette coordinate system is a coordinate system established with the center of the roulette as the origin and two mutually perpendicular radial directions as the horizontal coordinate and the vertical coordinate, such as Figure 4 The xy coordinate system in .

[0039] S12, for each sector on the wheel, a sector coordinate system is established, and the sector coordinate system uses the radial and tangential directions of the wheel as coordinate axes; in the process of establishing the sector coordinate system, a local Cartesian coordinate system is first established for the degree of freedom of one of the sectors, which is called the basic coordinate system, and the coordinate systems where the degrees of freedom of other sectors are located are formed by rotating the basic coordinate system by appropriate angles. For details, please refer to Figure 4 The x1y1 coordinate system, x2y2 coordinate system, x3y3 coordinate system, x4y4 coordinate system, x5y5 coordinate system, x6y6 coordinate system, x7y7 coordinate system, x8y8 coordinate system, x9y9 coordinate system, x 10 y 10 Coordinate system, x 11 y 11 Coordinate system and x 12 y 12 Coordinate system. In such a coordinate system, the positions of the sectors of the same level of the wheel are the same in the coordinate system, so the stiffness matrices of the sectors of the same level of the wheel are also the same in the coordinate system. Taking advantage of the structural and assembly characteristics of the multi-level wheel, when meshing the multi-level wheel structure, it is necessary to ensure that: (1) the mesh of each disk can be formed by rotating and repeating the mesh of the basic sector, and (2) the nodes of the interface between the disks and the disk structure are matched. Then use general finite element software or write a program to generate the stiffness matrix and external force vector of the sector model.

[0040] S2, eliminate the internal degrees of freedom of the roulette. The degrees of freedom of each roulette can be divided into the degrees of freedom shared with the inter-disk structure and the internal degrees of freedom unique to the roulette. The internal degrees of freedom of all roulettes can be condensed to the inter-disk structure using the condensation technology. This process can be divided into two condensations. The degrees of freedom of the sector are divided into the main degrees of freedom and the subsidiary degrees of freedom. The main degrees of freedom refer to the degrees of freedom shared by a sector and the sectors on both sides, as well as the degrees of freedom shared by the sector and the inter-disk structure. The remaining degrees of freedom of the sector are called subsidiary degrees of freedom.

[0041] In the specific implementation, step S2 condenses the internal degrees of freedom of all the wheels onto the inter-wheel structure through a two-level condensation technique. In the implementation process, this step includes the following specific steps:

[0042] S21, the first condensation is performed to condense the attached degrees of freedom of all sectors; since the stiffness matrix of each sector is the same in the cyclic coordinate system, only one sector needs to be condensed to eliminate the internal degrees of freedom of all sectors of a wheel, which can greatly improve the analysis efficiency. The control equation of the specific implementation process is:

[0043]

[0044] Among them, s represents the auxiliary degree of freedom, m represents the main degree of freedom, and R i represents the equivalent stiffness matrix of the sector after condensation, n i represents the equivalent right-hand side term of the sector after condensation.

[0045] After the first cohesion, the degrees of freedom of the roulette also include the degrees of freedom of the interfaces of each sector and the degrees of freedom of each sector connected to the inter-disk structure. At this time, the degrees of freedom of the roulette can still be divided into two parts, the degrees of freedom that belong to the disk (subsidiary degrees of freedom) and the degrees of freedom that are common to the disk and the inter-disk structure (main degrees of freedom).

[0046] S22, perform a second condensation to condense all the degrees of freedom in the roulette that are not shared with the inter-stage structure; wherein the properties of the block circulant matrix and group theory are used to reduce the amount of calculation and improve the efficiency of calculation. In the process of the second condensation, a linear algebraic equation group corresponding to some degrees of freedom of the roulette is constructed, and the coefficient matrix A of the equation group is i is a block circulant matrix, b i is the right-hand side term, the B matrix and q i The definition is as shown in formula (5) and (6):

[0047]

[0048] b i =[(q i ) T (q i ) T …(q i ) T (q i ) T ] T

[0049]

[0050] The matrix diagram is as follows Figure 5 shown.

[0051] In the second condensation, all the attached degrees of freedom are condensed. After these two condensations, all the internal degrees of freedom of the disks can be condensed to the disk structure. Because the stiffness matrix of each sector is the same and the disks have cyclic symmetry, only one sector needs to be condensed in the first condensation. In the second condensation, the properties of the block circulant matrix and group theory can be used to reduce the amount of calculation and improve the efficiency of calculation.

[0052] In the condensation process, it is necessary to solve the linear algebraic equations corresponding to some degrees of freedom of the disk. In the process of solving the linear algebraic equations, the block circulant matrix is ​​converted into a block diagonal matrix, such as Figure 6 , so that the linear algebraic equations can be decoupled. Due to the cyclic symmetry of each roulette wheel, the stiffness matrix of each roulette wheel is a block circulant matrix. Similarly, the stiffness matrix corresponding to the internal degrees of freedom of the roulette wheel is also a block circulant matrix. For a system of linear algebraic equations whose coefficient matrix is ​​a block circulant matrix, group theory is an efficient solution tool. Based on the irreducible representation of group theory, the block circulant matrix can be converted into a block diagonal matrix. When the coefficient matrix of the system of linear algebraic equations is a block diagonal matrix, the system of linear algebraic equations is decoupled, and the system of linear algebraic equations corresponding to each sub-block can be solved independently, which greatly improves the efficiency of solving the system of linear algebraic equations. At the same time, since it is no longer necessary to decompose the stiffness matrix of the entire structure, the algorithm proposed in the present disclosure can greatly improve the computational efficiency while reducing the demand for computer memory, further improving the applicability of the numerical algorithm proposed in the present disclosure.

[0053] S3, solve the degrees of freedom of the inter-disk structure after eliminating the internal degrees of freedom of the roulette disk; after steps S1 and S2, the internal degrees of freedom of the roulette disk are eliminated. When the internal degrees of freedom of all disks are condensed, the remaining degrees of freedom of the entire multi-stage roulette system are the degrees of freedom of the inter-disk structure. The inter-disk structure is generally small in scale and has few corresponding degrees of freedom. Therefore, the linear algebraic equations corresponding to the condensed structure can be efficiently solved using the direct method or the preconditioned conjugate gradient method. During implementation, the direct method or the preconditioned conjugate gradient method is used to efficiently solve the corresponding linear algebraic equations.

[0054] S4, back-substitution to solve the displacements corresponding to the internal degrees of freedom of all the wheels; after obtaining the displacement of the condensed structure, the relationship between the main degrees of freedom and the subsidiary degrees of freedom in the two-stage condensation process can be used to back-substitute the solution twice, and finally the displacements corresponding to all the degrees of freedom of the entire multi-stage wheel structure can be obtained.

[0055] S5, obtaining the strain field and the stress field, and determining the potential failure point according to the strain field and the stress field.

[0056] After obtaining the displacements corresponding to all degrees of freedom through S4, the variables such as the strain field and stress field of the structure can be further calculated according to the geometric equation and Hooke's law. Stress field analysis can help identify areas with high stress or stress concentration in the multi-stage wheel structure. These areas are usually potential failure points and may cause fatigue damage, crack initiation and other problems due to high stress. By identifying these high-stress areas, measures such as optimizing the design, improving materials or adding supports can be taken to reduce stress or stress concentration and improve the reliability of components.

[0057] In the above, with reference to the accompanying drawings, an efficient numerical analysis algorithm for aero-engine multi-stage disc structures according to the disclosed embodiment is described. By establishing a cyclic coordinate system, the stiffness matrix and external force vector of the sector model are obtained; the internal degrees of freedom of the disc are eliminated; the degrees of freedom of the inter-disk structure after the internal degrees of freedom of the disc are eliminated are solved; the internal degrees of freedom of all discs are solved by back substitution; the strain field and stress field are obtained, and the potential failure point is determined based on the strain field and stress field. The mechanical properties and structural response of the multi-stage disc system can be simulated and analyzed more quickly and accurately, the reliability and durability of the engine can be improved, and the stress distribution and deformation trend of the disc can be given more accurately, thereby helping to design a more reliable disc structure and extend the service life of the engine. Compared with the case of ignoring the coupling effect and performing numerical analysis on a single roulette structure in isolation, the accuracy of the algorithm proposed in the present disclosure can be guaranteed, because compared with the numerical analysis of the entire multi-stage roulette system, the improved algorithm proposed in the present disclosure does not introduce any approximation, and compared with the numerical analysis of the entire multi-stage roulette system, the improved algorithm proposed in the present disclosure has significant computational efficiency. For a multi-stage cyclic periodic structure (9,250,698 degrees of freedom) containing 5 roulettes and 4 inter-disk structures, the results and time of analyzing the overall model using commercial software are used as references. The displacement and stress errors obtained by this method are 0.188% and 0.59% respectively, and the computational efficiency is 6.8 times that of the traditional method. The method disclosed in the present disclosure is easy to use and universal. The present disclosure reduces the demand for computer memory for analyzing large-scale multi-stage roulette structures. Since the present disclosure is based on traditional finite element theory, it can be easily integrated into existing finite element software.

[0058] The basic principles of the present disclosure are described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, effects, etc. mentioned in the present disclosure are only examples and not limitations, and it cannot be considered that these advantages, strengths, effects, etc. are required by each embodiment of the present disclosure. In addition, the specific details disclosed above are only for the purpose of illustration and ease of understanding, and are not limitations. The above details do not limit the present disclosure to the necessity of adopting the above specific details to be implemented.

[0059] The block diagrams of the devices, apparatuses, equipment, and systems involved in this disclosure are only illustrative examples and are not intended to require or imply that they must be connected, arranged, and configured in the manner shown in the block diagrams. As will be appreciated by those skilled in the art, these devices, apparatuses, equipment, and systems can be connected, arranged, and configured in any manner. Words such as "including," "comprising," "having," and the like are open words, referring to "including but not limited to," and can be used interchangeably therewith. The words "or" and "and" used herein refer to the words "and / or," and can be used interchangeably therewith, unless the context clearly indicates otherwise. The word "such as" used herein refers to the phrase "such as but not limited to," and can be used interchangeably therewith.

[0060] Additionally, as used herein, "or" used in a list of items beginning with "at least one" indicates a separate list, so that, for example, a list of "at least one of A, B, or C" means A or B or C, or AB or AC or BC, or ABC (i.e., A and B and C). Furthermore, the word "exemplary" does not mean that the example described is preferred or better than other examples.

[0061] It should also be noted that in the system and method of the present disclosure, each component or each step can be decomposed and / or recombined. Such decomposition and / or recombination should be regarded as equivalent solutions of the present disclosure.

[0062] Various changes, substitutions, and modifications of the techniques described herein may be made without departing from the teachings defined by the appended claims. Furthermore, the scope of the claims of the present disclosure is not limited to the specific aspects of the processes, machines, manufactures, compositions of events, means, methods, and actions described above. Currently existing or later to be developed processes, machines, manufactures, compositions of events, means, methods, or actions that perform substantially the same functions or achieve substantially the same results as the corresponding aspects described herein may be utilized. Thus, the appended claims include such processes, machines, manufactures, compositions of events, means, methods, or actions within their scope.

[0063] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the present disclosure. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of the present disclosure. Therefore, the present disclosure is not intended to be limited to the aspects shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

[0064] The above description has been given for the purpose of illustration and description. In addition, this description is not intended to limit the embodiments of the present disclosure to the forms disclosed herein. Although multiple example aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, changes, additions and sub-combinations thereof.

Claims

1. An efficient algorithm for numerical analysis of multi-stage disk structures of aircraft engines, characterized in that: include: S1, establish a cyclic coordinate system and obtain the sector model stiffness matrix and external force vector; S2, eliminates the internal degrees of freedom of the wheel; S3, solve the degrees of freedom of the inter-disk structure after eliminating the internal degrees of freedom of the roulette disk; S4, back-substitution to solve the internal degrees of freedom of all wheels; S5, obtaining the strain field and the stress field, and determining the potential failure point according to the strain field and the stress field.

2. The efficient numerical analysis algorithm for aero-engine multi-stage disk structure according to claim 1 is characterized in that: Step S1 includes: S11, establishing a roulette coordinate system with the center of the roulette wheel as the origin; S12, establishing a sector coordinate system for each sector on the wheel disc, wherein the sector coordinate system takes the radial direction and tangential direction of the wheel disc as coordinate axes; The sectors on the same wheel have the same position in their corresponding sector coordinate system.

3. The efficient numerical analysis algorithm for aero-engine multi-stage disk structure according to claim 1 is characterized in that: Step S2 condenses the internal degrees of freedom of all the wheels onto the inter-disk structure through a two-level condensation technique.

4. The efficient numerical analysis algorithm for aero-engine multi-stage disk structure according to claim 3 is characterized in that: Step S2 comprises, S21, perform the first condensation to condense the attached degrees of freedom of all sectors; S22, performing a second condensation to condense all degrees of freedom in the roulette that are not shared with the inter-stage structure; wherein the properties of the block circulant matrix and group theory are used to reduce the amount of calculation and improve the calculation efficiency.

5. The efficient numerical analysis algorithm for aero-engine multi-stage disk structure according to claim 4 is characterized in that: In the second condensation process, a linear algebraic equation group corresponding to some degrees of freedom of the roulette wheel is constructed, and the coefficient matrix of the equation group is a block circulant matrix.

6. The efficient numerical analysis algorithm for aero-engine multi-stage disk structure according to claim 5, characterized in that: In the process of solving the linear algebraic equations, the block circulant matrix is ​​converted into a block diagonal matrix to decouple the linear algebraic equations.

7. The efficient numerical analysis algorithm for aero-engine multi-stage disk structure according to any one of claims 1 to 6, characterized in that: In step S3, the corresponding linear algebraic equations are efficiently solved using a direct method or a preconditioned conjugate gradient method.

8. The efficient numerical analysis algorithm for aero-engine multi-stage disk structure according to any one of claims 1 to 6, characterized in that: In step S4, after obtaining the degrees of freedom corresponding to the condensed structure, the relationship between the main degrees of freedom and the subsidiary degrees of freedom in the two-stage condensation process is used to solve the problem twice, and finally all the degrees of freedom of the entire multi-stage roulette structure are obtained.

9. The efficient numerical analysis algorithm for aero-engine multi-stage disk structure according to any one of claims 1 to 6, characterized in that: In step S5, after the displacement response is obtained, the strain field and stress field of the structure are calculated according to the geometric equation and Hooke's law.

10. The efficient numerical analysis algorithm for aero-engine multi-stage disk structure according to any one of claims 1 to 6, characterized in that: In step S5, stress analysis is used to identify areas with high stress or concentrated stress in the multi-stage wheel structure and use them as potential failure points.

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