Efficient numerical analysis method for multi-stage disk structure of aero-engine

Abstract

The present disclosure relates to the technical field of aero-engine simulation analysis, and particularly provides a numerical analysis efficient method for a multi-stage wheel disc structure of an aero-engine, which comprises the following steps: S1, a cyclic coordinate system is established to obtain a sector model stiffness matrix and an external force vector; S2, the internal degrees of freedom of the wheel disc are eliminated; S3, the degrees of freedom of the structure between the discs after the elimination of the internal degrees of freedom of the wheel disc are solved; S4, the internal degrees of freedom of all the wheel discs are solved by back substitution; and S5, a strain field and a stress field are obtained, and potential failure points are determined according to the strain field and the stress field. The precision and efficiency of numerical simulation of the multi-stage wheel disc structure can be improved.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of aero-engine simulation analysis, and particularly to a numerical analysis efficient method for a multi-stage disk structure of an aero-engine. BACKGROUND

[0002] The multi-stage disk structure represented by the aero-engine blade-disk system has a wide range of applications in engineering. The multi-stage disk structure is usually composed of multiple disks, and two adjacent disks are connected through an inter-disk structure. Each disk can be assumed to be a cyclically symmetric structure, that is, each disk can be considered to be derived from a sector by rotation repetition. The number of sectors at each stage of such a multi-stage disk structure is different, which results in that the multi-stage disk structure as a whole does not have cyclic symmetry although each disk is a cyclically symmetric structure, which makes it impossible to directly use the cyclic symmetry theory to solve the numerical simulation problem of the multi-stage disk structure.

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

[0004] How to improve the accuracy and efficiency of the numerical simulation of the multi-stage disk structure is one of the important problems to be solved in the field. SUMMARY

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

[0006] According to the numerical analysis efficient method for a multi-stage disk structure of an aero-engine provided by the present disclosure, the method comprises the following steps:

[0007] S1, a cyclic coordinate system is established to obtain a sector model stiffness matrix and an external force vector;

[0008] S2, the internal degrees of freedom of the disk are eliminated;

[0009] S3, the degrees of freedom of the inter-disk structure after the elimination of the internal degrees of freedom of the disk are solved;

[0010] S4, the displacements corresponding to the internal degrees of freedom of all the disks are solved by back substitution;

[0011] S5, the strain field and the stress field are obtained, and potential failure points are determined according to the strain field and the stress field.

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

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

[0014] S12, for each sector on the disk, a sector coordinate system is established, and the sector coordinate system takes the radial and tangential directions of the disk as the coordinate axes;

[0015] Wherein, the positions of the sectors on the same disk in the corresponding sector coordinate systems are the same.

[0016] According to one aspect of the present disclosure, the numerical analysis method for the multi-stage disk structure of an aero-engine is provided, wherein the step S2 condenses the internal degrees of freedom of all the disks onto the inter-stage structure through two-stage condensation technology.

[0017] According to one aspect of the present disclosure, the numerical analysis method for the multi-stage disk structure of an aero-engine is provided, wherein the step S2 comprises,

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

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

[0020] According to one aspect of the present disclosure, the numerical analysis method for the multi-stage disk structure of an aero-engine is provided, wherein in the process of the second condensation, the linear algebraic equation set corresponding to the internal degrees of freedom of the disk is constructed, and the coefficient matrix of the equation set is a block circulant matrix.

[0021] According to one aspect of the present disclosure, the numerical analysis method for the multi-stage disk structure of an aero-engine is provided, wherein in the process of solving the linear algebraic equation set, the block circulant matrix is converted into a block diagonal matrix to decouple the linear algebraic equation.

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

[0023] According to the numerical analysis efficient method for the multi-stage wheel disc structure of an aero-engine, after the displacements of the degrees of freedom corresponding to the condensed structure are obtained in step S4, the displacements of the degrees of freedom corresponding to all the wheel discs are obtained by twice back substitution based on the relationship between the main degrees of freedom and the auxiliary degrees of freedom in the two-stage condensation process.

[0024] According to the numerical analysis efficient method for the multi-stage wheel disc structure of an aero-engine, after the displacements of the degrees of freedom corresponding to the condensed structure are obtained in step S4, the displacements of the degrees of freedom corresponding to all the wheel discs are obtained by twice back substitution based on the relationship between the main degrees of freedom and the auxiliary degrees of freedom in the two-stage condensation process.

[0025] According to the numerical analysis efficient method for the multi-stage wheel disc structure of an aero-engine, the regions with relatively large stress or stress concentration in the multi-stage wheel disc structure are identified through stress analysis in step S5, and are taken as potential failure points.

[0026] As will be described in detail below, according to the numerical analysis efficient method for the multi-stage wheel disc structure of an aero-engine, the stiffness matrix of the sector model and the external force vector are obtained by establishing a rotating coordinate system; the internal degrees of freedom of the wheel disc are eliminated; the displacements of the degrees of freedom corresponding to the structure between the wheel discs after the elimination of the internal degrees of freedom of the wheel disc are solved; the displacements of the internal degrees of freedom of all the wheel discs are solved by back substitution; the strain field and the stress field are obtained, and the potential failure points are determined based on the strain field and the stress field. The mechanical properties and the structural response of the multi-stage wheel disc system can be simulated and analyzed more quickly and accurately, the reliability and the durability of the engine are improved, the stress distribution and the deformation trend of the wheel disc can be more accurately given, and thus a more reliable wheel disc structure can be designed, and the service life of the engine is prolonged. Compared with the numerical analysis of a single wheel disc structure without considering the coupling effect, the accuracy of the algorithm can be guaranteed, because compared with the numerical analysis of the entire multi-stage wheel disc system, the improved algorithm does not introduce any approximation, and compared with the numerical analysis of the entire multi-stage wheel disc system, the improved algorithm has a significant computational efficiency. The method has ease of use and universality, and the analysis of large-scale multi-stage wheel disc structures requires less computer memory. Since the method is based on the 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 intended to provide further explanation of the subject technology. BRIEF DESCRIPTION OF DRAWINGS

[0028] The above and other objects, features and advantages of the present disclosure will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings. The drawings provided in the disclosure serve to provide a further understanding of the embodiments of the present disclosure, constitute a part of the specification and are used for explaining the present disclosure together with the specification, but do not limit the present disclosure. In the drawings, the same reference numerals generally refer to the same components or steps throughout the drawings.

[0029] Figure 1 is a schematic diagram of an implementation of the algorithm proposed in the present disclosure and a flowchart;

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

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

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

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

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

[0035] In order to make the objects, technical solutions and advantages of the present disclosure more obvious, the following will describe the example embodiments according to the present disclosure in detail with reference to the drawings. Obviously, the described embodiments are only part of the embodiments of the present disclosure, not all the embodiments of the present disclosure, and it should be understood that the present disclosure is not limited by the example embodiments described herein.

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

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

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

[0039] S12, for each sector on the wheel disk, establish a sector coordinate system, and the sector coordinate system takes the radial and tangential directions of the wheel disk as the coordinate axes; in the process of establishing the sector coordinate system, first, a local Cartesian coordinate system is established for the degrees of freedom of one of the sectors, which is called the basic coordinate system, and the coordinate systems of the degrees of freedom of other sectors are formed by rotating the basic coordinate system by an appropriate angle, please refer to the x1y1 coordinate system, the x2y2 coordinate system, the x3y3 coordinate system, the x4y4 coordinate system, the x5y5 coordinate system, the x6y6 coordinate system, the x7y7 coordinate system, the x8y8 coordinate system, the x9y9 coordinate system, the x 10 y 10 coordinate system, the x 11 y 11 coordinate system, and the x 12 y 12 coordinate system in Figure 4 . In such a coordinate system, the positions of the sectors belonging to the same level wheel disk in the established coordinate system are the same, so the stiffness matrices of the sectors belonging to the same level wheel disk in the established coordinate system are also the same. By using the structure and assembly characteristics of the multi-level wheel disk, when the multi-level wheel disk structure is meshed, the following conditions must be met: (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 interfaces between the disks and the inter-disk structure must be matched. Then, the stiffness matrix and the external force vector of the sector model are generated by using a general finite element software or by programming.

[0040] S2, eliminate the internal degrees of freedom of the wheel disk. The degrees of freedom of each wheel disk can be divided into the degrees of freedom common to the inter-disk structure and the internal degrees of freedom unique to the wheel disk. By using the condensation technique, the internal degrees of freedom of all the wheel disks can be condensed onto the inter-disk structure, and this process can be divided into two condensation processes. The degrees of freedom of the sector are divided into the main degrees of freedom and the auxiliary degrees of freedom. The main degrees of freedom refer to the degrees of freedom common to a sector and the sectors on both sides, as well as the degrees of freedom common to the sector and the inter-disk structure, and the remaining degrees of freedom of the sector are called the auxiliary degrees of freedom.

[0041] In the implementation, step S2 condenses the internal degrees of freedom of all the wheel disks onto the inter-disk structure by using a two-stage 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] (1)

[0044] (2)

[0045] (3)

[0046] Among them, s represents the auxiliary degree of freedom, m represents the main degree of freedom, represents the equivalent stiffness matrix of the sector after condensation, represents the equivalent right-hand side term of the sector after condensation.

[0047] After the first cohesion, the roulette's degrees of freedom also include the degrees of freedom of the interfaces between the sectors and the inter-disk structure. At this point, the roulette's degrees of freedom can still be divided into two parts: the degrees of freedom that belong exclusively to the disk (supplementary degrees of freedom) and the degrees of freedom that are shared between the disk and the inter-disk structure (primary degrees of freedom).

[0048] S22, perform a second condensation to condense all the degrees of freedom in the wheel 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. In the process of the second condensation, a linear algebraic equation system corresponding to some degrees of freedom of the wheel is constructed, and the coefficient matrix of the equation system is is a block circulant matrix, is the right-hand term, Matrix and The definition is as shown in formula (5) and (6):

[0049] (4)

[0050] (5)

[0051] (6)

[0052] The matrix diagram is as follows Figure 5 shown.

[0053] In the second condensation, all the subsidiary degrees of freedom are condensed. After the two condensations, all the internal degrees of freedom of the disks are condensed to the inter-disk structure. Because the stiffness matrix of each sector is the same and each disk has cyclic symmetry, only one sector needs to be condensed in the first condensation, and the property of the block cyclic matrix and group theory can be used to reduce the calculation amount and improve the calculation efficiency in the second condensation.

[0054] In the condensation process, a linear algebraic equation set corresponding to the partial degrees of freedom of the disk needs to be solved. In the process of solving the linear algebraic equation set, the block cyclic matrix is converted into a block diagonal matrix, as shown in Figure 6 , so that the linear algebraic equation is decoupled. Due to the cyclic symmetry of each disk, the stiffness matrix of each disk is a block cyclic matrix. Similarly, the stiffness matrix corresponding to the internal degrees of freedom of the disk is also a block cyclic matrix. For a linear algebraic equation set with a block cyclic matrix, group theory is an efficient solving tool. Based on the irreducible representation of group theory, the block cyclic matrix can be converted into a block diagonal matrix. When the coefficient matrix of the linear algebraic equation set is a block diagonal matrix, the linear algebraic equation set is decoupled, and each sub-block corresponding linear algebraic equation set can be solved independently, which greatly improves the solving efficiency of the linear algebraic equation set. At the same time, since the decomposition of the stiffness matrix of the entire structure is no longer needed, the algorithm disclosed in the present application greatly improves the calculation efficiency while reducing the demand for computer memory, further improving the applicability of the numerical algorithm disclosed in the present application.

[0055] S3, solving the degrees of freedom of the inter-disk structure after eliminating the internal degrees of freedom of the disk; after steps S1 and S2, the internal degrees of freedom of the disk are eliminated. After the internal degrees of freedom of all the disks are condensed, the remaining degrees of freedom of the entire multi-stage disk system are the degrees of freedom of the inter-disk structure. The inter-disk structure generally has a small scale, and the corresponding degrees of freedom are also small, so the linear algebraic equation set corresponding to the condensed structure can be efficiently solved by using the direct method or the preconditioned conjugate gradient method. In implementation, the corresponding linear algebraic equation set is efficiently solved by using the direct method or the preconditioned conjugate gradient method.

[0056] S4, back substitution to solve the displacement corresponding to the internal degrees of freedom of all the disks; after obtaining the displacement of the condensed structure, the relationship between the primary degrees of freedom and the subsidiary degrees of freedom in the two-stage condensation process can be used to solve twice back substitution, and finally the displacement corresponding to all the degrees of freedom of the entire multi-stage disk structure is obtained.

[0057] S5, obtaining the strain field and the stress field, and judging the potential failure point according to the strain field and the stress field.

[0058] After obtaining the displacements corresponding to all degrees of freedom through S4, 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 of high stress or stress concentration in the multi-stage disk structure, which are usually potential failure points that may cause fatigue failure, crack initiation and other problems due to high stress. By identifying these high stress areas, measures such as optimizing design, improving materials or adding support can be taken to reduce stress or stress concentration and improve the reliability of the component.

[0059] The above describes a numerical analysis efficient method for a multi-stage disk structure of an aero-engine according to an embodiment of the present disclosure, by establishing a cyclic coordinate system, obtaining the sector model stiffness matrix and external force vector; eliminating the internal degrees of freedom of the disk; solving the degrees of freedom of the inter-disk structure after eliminating the internal degrees of freedom of the disk; back substitution to solve the internal degrees of freedom of all disks; obtaining the strain field and stress field, and judging the potential failure points according to the strain field and stress field. The mechanical properties and structural response of the multi-stage disk system can be simulated and analyzed more quickly and accurately, improving the reliability and durability of the engine, and the stress distribution and deformation trend of the disk can be more accurately given, thereby helping to design a more reliable disk structure and prolong the service life of the engine. Compared with numerical analysis of a single disk structure without considering coupling effects, the accuracy of the algorithm of the present disclosure can be guaranteed, because compared with numerical analysis of the entire multi-stage disk system, the improved efficient algorithm of the present disclosure does not introduce any approximation, and compared with numerical analysis of the entire multi-stage disk system, the improved efficient algorithm of the present disclosure has significant computational efficiency. For an example of a multi-stage cyclic periodic structure containing 5 disks and 4 inter-disk structures (9,250,698 degrees of freedom), the results and time of the analysis of the overall model using commercial software are used as a reference, the displacement and stress errors obtained by the present method are 0.188% and 0.59% respectively, and the computational efficiency is 6.8 times that of the traditional method. The method of the present disclosure has ease of use and universality, and the present disclosure reduces the computer memory requirements for analyzing large-scale multi-stage disk structures. Since the present disclosure is based on the traditional finite element theory, it can be easily integrated into existing finite element software.

[0060] The above describes the basic principles of the present disclosure in combination with specific embodiments, but it should be noted that the advantages, advantages, effects and the like mentioned in the present disclosure are only examples and not limitations, and these advantages, advantages, effects and the like cannot be considered as the must-have of each embodiment of the present disclosure. In addition, the above specific details are only for the purpose of example and for the purpose of understanding, and are not limited to the present disclosure which must use the above specific details to implement.

[0061] The block diagrams of devices, apparatuses, equipment, systems referred to in the present disclosure are merely illustrative examples and are not intended to require or imply that the connection, arrangement, configuration must be as shown in the block diagrams. These devices, apparatuses, equipment, systems can be connected, arranged, configured in any manner as will be appreciated by those skilled in the art. Words such as "include," "contain," "have," etc. are open-ended words that are to be interpreted to mean "including but not limited to," and are to be interpreted not to exclude other items. The words "or" and "and" as used herein are to be interpreted as the word "and / or," and are to be interpreted not to exclude other items. The word "such as" as used herein is to be interpreted as the phrase "such as but not limited to," and is to be interpreted not to exclude other items.

[0062] Also, as used herein, the term "or" as used in the context of "at least one of A, B, or C" means A or B or C or any combination thereof. Further, the term "example" is used to mean "serving as an example, instance, or illustration," and is not to be construed as preferred or advantageous over other examples. The term "include" is used to mean "comprise or consist of, whether or not associated with the term "including."

[0063] It is also important to note that the systems and methods of the present disclosure can be embodied in a variety of forms including, but not limited to, a data processor, a computer program product, a computer, one or more tangible computer readable storage devices, one or more computer-implemented methods, information, or a bit of information. Additionally, the systems and methods of the present disclosure can be embodied as one or more computers or computer-implements methods that can be used in a networked environment.

[0064] Various changes, modifications and improvements in the herein described technologies can be made within the teachings of the technology, particularly in light of the above teachings. It is therefore intended that the here disclosed technology not be limited to the particular composition, means, methods and / or acts described as the only approach to implementing the here disclosed technology. Accordingly, the here disclosed technology is to be considered as broadly applicable in the art implicated by this disclosure. The scope of the here disclosed technology is indicated by the appended claims, and all changes and modifications that come within the meaning and range of equivalents are intended to be embraced therein.

[0065] The above description of the disclosed aspects is meant to be illustrative of the application and not limiting, as the same is intended to be encompassed by the following claims. Various modifications of the aspects, in addition to those described, will be apparent to one of ordinary skill in the art from the disclosure and have been contemplated. It is intended that the application be construed as including all such modifications as fall within the scope thereof.

[0066] The foregoing description has been presented for the purposes of illustration and description. Furthermore, the description is not intended to limit the embodiments of the disclosure to the forms disclosed herein. Although the various example aspects and embodiments have been described herein with regard to particular aspects and embodiments, those skilled in the art will recognize that certain modifications, changes, substitutions, additions and sub-combinations can be made without departing from the spirit of the disclosure.

Claims

1. An efficient numerical analysis method for aero-engine multi-stage disk structures, characterized by: 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 wheel disk; S4, back-substitution to solve the internal degrees of freedom of all wheels; S5, obtaining the strain field and stress field, and determining the potential failure point based on the strain field and stress field; 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 uses the radial and tangential directions of the wheel disc as coordinate axes; The sectors on the same wheel have the same position in their corresponding sector coordinate system; Step S2 condenses the internal degrees of freedom of all the wheels onto the inter-disk structure through a two-stage condensation technique; Step S2 includes, 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 wheel 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 computation and improve computational efficiency; In the second condensation process, a linear algebraic equation system corresponding to some degrees of freedom of the roulette wheel is constructed, and the coefficient matrix of the equation system is a block circulant matrix; 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 wheel structure are obtained; In step S5, stress analysis is performed to identify areas with high stress or concentrated stress in the multi-stage wheel structure and use them as potential failure points.

2. The efficient numerical analysis method for aero-engine multi-stage disk structure according to claim 1, 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.

3. The efficient numerical analysis method for aero-engine multi-stage disk structure according to any one of claims 1 to 2, characterized in that: In step S3, the corresponding linear algebraic equations are efficiently solved using a direct method or a preconditioned conjugate gradient method.

4. The efficient numerical analysis method for aero-engine multi-stage disk structure according to any one of claims 1 to 2, 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.

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