CN110750932A - Digital simulation method for rub-impact dynamic characteristics of blade disc-casing system - Google Patents

Abstract

The invention relates to a digital simulation method for rubbing dynamic characteristics of a blisk-cassette system. S1, a finite element model of an elastically supported roulette is established by using a shell element and a spring element, and a spring element and a Timoshenko beam are used to establish a finite element model. The element constructs the finite element model of the blade and the finite element model of the elastic casing; S2, establishes an interface coupling element between the finite element model of the wheel disc obtained in S1 and the finite element model of the blade, and obtains the preliminary dynamic model of the blisk; S3, adopts The Craig-Bampton method reduces the dimensionality of the preliminary blisk dynamics model and the casing dynamics model respectively; finally, the reduced blisk-casing system dynamics model is obtained by grouping; S4, using Lagrange multipliers The rubbing dynamics characteristics of the reduced blisk-cassette system dynamics model are solved by combining the method with the central difference method. The digital simulation method provided by the invention not only saves the financial cost and time cost of the test, but also greatly improves the calculation efficiency of acquiring the fault characteristics.

Description

Numerical simulation method of rubbing dynamic characteristics of blisk-cassette system

technical field

The invention belongs to the technical field of rubbing fault simulation between a rotor and a stator system, and in particular relates to a digital simulation method for rubbing dynamic characteristics of a blade disk-casing system.

Background technique

High-performance aero-engines are developing in the direction of light weight, high reliability and low cost. As a key component of aero-engines, the structure and performance of integral blisks play an important role in the design of high-performance aero-engines. In order to improve the aero-engine's aerodynamic efficiency and reduce its fuel consumption rate, reducing the clearance between the blade tip and the casing is the most direct and effective way, but it also increases the friction between the blade tip and the casing. possibility.

In addition, it is difficult to ensure the cyclic symmetry of the blisk structure during the manufacturing process. Potential faults such as eccentricity and detuning will further amplify the vibration of the blisk, thereby increasing the risk of rubbing between the blade tip and the casing. .

SUMMARY OF THE INVENTION

(1) Technical problems to be solved

Aiming at the existing technical problems, the present invention provides a digital simulation method for rubbing dynamic characteristics of a blade disk-casing system.

(2) Technical solutions

In order to achieve the above-mentioned purpose, the main technical scheme adopted in the present invention includes:

A digital simulation method for rubbing dynamic characteristics of a blisk-cassette system,

S1. The finite element model of the elastically supported roulette is established by using the shell element and the spring element, and the finite element model of the blade and the finite element model of the elastic casing are constructed by using the spring element and the Timoshenko beam element;

S2. Establish a coupling element between the finite element model of the wheel disc obtained in S1 and the finite element model of the blade to obtain a preliminary dynamic model of the blisk;

S3. Use the Craig-Bampton method to reduce the dimensionality of the preliminary blisk-casing system dynamics model respectively; finally, obtain the reduced blisk-casing system dynamics model by grouping;

S4. The rubbing dynamics characteristics of the reduced blisk-casing system dynamics model are solved by the combination of the Lagrange multiplier method and the central difference method.

Preferably, the method further includes: in S2, an interface coupling unit is used to establish a coupling relationship;

Wherein, the coupling relationship includes the coupling between the center point of the wheel disc and the central hole of the wheel disc and the coupling between the outer edge of the wheel disc and the blades.

Preferably, the method further includes: performing convergence processing on the reduced blisk-casing system dynamics model obtained in S3 to obtain a higher-precision blisk-casing system dynamics model.

Preferably, the method further includes: performing two dimension reductions on the finite element model of the twisted blade and the finite element model of the variable-section wheel disc respectively in S3, and performing one dimension reduction on the finite element model of the elastic casing.

Preferably, the element stiffness matrix of the coupling relationship of the i-th rigid coupling node pair between the center point O _d of the wheel disc and the center hole of the wheel disc is obtained by using the penalty function method as follows:

k _p =max(diag(K _d,e )) is the penalty stiffness, K _d,e is the structural stiffness matrix of the roulette, so the stiffness matrix of the entire rigid area is where _NI represents the number of nodes in the center hole of the roulette.

k表示第k个叶片；Preferably, the stiffness matrix of the k-th interface coupling element between the outer edge of the wheel disc and the blade is obtained by the penalty function method as

k represents the kth blade;

N_b表示叶片数目。The total coupling stiffness matrix between the outer edge of the disk and the blade is

N _b represents the number of leaves.

(3) Beneficial effects

The beneficial effects of the present invention are as follows: a digital simulation method for the rubbing dynamics characteristics of a blade disk-casing system provided by the present invention has the following beneficial effects:

First of all, the mathematical model is considered comprehensively, which can provide theoretical support for aero-engine designers or related practitioners. This simulation method can enable designers to optimize the design scheme, and can also provide theoretical guidance for technicians in the fault detection process of rotating and stator subsystems such as aero-engines. This method has fast operation speed and high precision.

Secondly, the use of digital simulation saves the financial cost and time cost of the test, and at the same time greatly improves the work efficiency.

Description of drawings

FIG. 1 is a schematic flowchart of a digital simulation method for rubbing dynamic characteristics of a blisk-cassette system provided by the present invention.

Detailed ways

In order to better explain the present invention and facilitate understanding, the present invention will be described in detail below with reference to the accompanying drawings and through specific embodiments.

As shown in Figure 1: the present embodiment discloses a digital simulation method for the rubbing dynamic characteristics of a blisk-cassette system, including the following steps:

S1. The finite element model of the elastically supported roulette is established by using the shell element and the spring element, and the finite element model of the blade and the finite element model of the elastic casing are constructed by using the spring element and the Timoshenko beam element;

S2. An interface coupling unit is established between the finite element model of the wheel disc obtained in S1 and the finite element model of the blade, and a preliminary dynamic model of the blisk-casing system is obtained;

S3. Use the Craig-Bampton method to reduce the dimensionality of the preliminary blisk-casing system dynamics model respectively; finally, obtain the reduced blisk-casing system dynamics model by grouping;

S4. The rubbing dynamics characteristics of the reduced blisk-casing system dynamics model are solved by the combination of the Lagrange multiplier method and the central difference method.

It should be noted that: the method described in this embodiment further includes: in S2, an interface coupling unit is used to establish a coupling relationship;

Wherein, the coupling relationship includes the coupling between the center point of the wheel disc and the central hole of the wheel disc and the coupling between the outer edge of the wheel disc and the blades.

The method described in this embodiment further includes: performing convergence processing on the reduced dynamic model of the blisk-casing system obtained in S3, and obtaining a blisk-machine with higher computational efficiency under the premise of ensuring the accuracy of the model Cassette system dynamics model.

The method described in this embodiment further includes: performing two dimension reductions on the finite element model of the twisted blade and the finite element model of the variable-section wheel disc respectively in S3, and performing one dimension reduction on the finite element model of the elastic casing.

In this embodiment, the penalty function method is used to obtain the coupling element stiffness matrix of the i-th rigid coupling node pair between the center point O _d of the wheel disc and the center hole of the wheel disc as:

k _p =max(diag(K _d,e )) is the penalty stiffness, K _d,e is the structural stiffness matrix of the roulette, so the stiffness matrix of the entire rigid area is where _NI represents the number of nodes in the center hole of the roulette.

k表示第k个叶片；In this embodiment, the stiffness matrix of the k-th interface coupling element between the outer edge of the wheel disc and the blade is obtained by the penalty function method as

k represents the kth blade;

N_b表示叶片数目。The total element stiffness matrix of the coupling relationship between the outer edge of the disk and the blade is

N _b represents the number of leaves.

The elastically supported blisk-cassette system in this embodiment is mainly divided into three parts: the disc, the blade and the casing.

The center O _d of the blisk consists of three wire springs (k _d,X , k _d,Y , k _d,Z ) and three torsion springs (k _d,rotX , k _d,rotY , k _d,rotZ ), and through The rigid area is connected with the central hole of the blisk. The casing is supported by a series of uniform radial (k _c,ri ) and tangential (k _c,ti ) wire springs.

It should be noted that the casing only considers in-plane (XOY plane) motion.

In this embodiment, the roulette is discretized using self-made eight-node Mindlin-Reissner shell elements, while the blades and casing are discretized using self-made two-node Timoshenko beam elements. In particular, it should be pointed out that when establishing the finite element model of the blisk, there are two key interface coupling relationships, namely the coupling between the center point of the disk and the center hole of the disk and the coupling between the outer edge of the disk and the blades. coupling. The wheel center point O _d and the wheel center hole are rigid surface constraints. Taking the i-th node pair O _di as an example, the corresponding displacement constraint equations in XOY, YOZ and ZOX are unified as:

in,

k_p＝max(diag(K_d,e))为罚刚度，K_d,e为轮盘的结构刚度矩阵。Based on formula (1), the coupling element stiffness matrix of the i-th rigid coupling node pair is obtained by the penalty function method

k _p =max(diag(K _d,e )) is the penalty stiffness, and K _d,e is the structural stiffness matrix of the roulette.

So the coupled stiffness matrix of the entire rigid region can be written as where _NI represents the number of nodes in the center hole of the roulette.

The element matrix of the roulette is constructed based on the fixed coordinate system OXYZ, and the element matrix of the blade is constructed based on the local coordinate system ok x _k y _k z _k , where the subscript _k represents the kth blade.

Therefore, during the matrix grouping of blades and discs, the main node at the outer edge of the disc and the main node at the root of the blade must satisfy the compatibility condition of the interface displacement.

Taking the coupling between the roulette and the _kth blade as an example, the transformation matrix from the ok x _k y _k z _k coordinate system to the OXYZ coordinate system is:

According to the displacement compatibility, the displacement constraint equation of the k-th interface coupling element in OXYZ can be expressed as:

[I _6×6 T _k ]·q _k =0 (3)

In the formula, Then, the stiffness matrix of the k-th interface coupling element is obtained by the penalty function method

The total stiffness matrix of the interface coupling elements of the disc and all blades can be written uniformly as N _b represents the number of leaves.

The differential equation of motion of the blisk-casing system with rubbing fault in this embodiment can be written as:

和u分别为加速度，速度和位移向量；λ_N和F_ext分别为拉格朗日乘子和外力向量。而

where M, C, D and K are the mass matrix, Coriolis force (gyro) matrix, Rayleigh damping matrix and stiffness matrix, respectively; B _c is the contact constraint matrix;

and u are acceleration, velocity and displacement vectors, respectively; λ _N and F _ext are Lagrange multipliers and external force vectors, respectively. and

In the formula, N _cp represents the number of blades in contact with the casing.

Considering the large number of degrees of freedom of the blisk-casing system, in order to improve the computational efficiency, the necessary model dimension reduction must be carried out. In this embodiment, the Craig-Bampton method (CBM) is used to establish the dimensionality reduction model of the system. According to the basic principle of dimensionality reduction of the CBM method, the degrees of freedom of the disc, blade and casing are firstly divided into two parts: the slave degrees of freedom and the master degrees of freedom. The corresponding motion equations are as follows:

和

分别代表位移，速度和加速度向量。In the formula, the superscript X represents the disc, blade or casing; M, C and K represent the mass matrix, Coriolis force (gyro) matrix and stiffness matrix respectively; F is the external force vector; degrees and principal degrees of freedom; u,

and

represent the displacement, velocity and acceleration vectors, respectively.

The physical displacement u ^X and the generalized displacement q ^X can be written as:

为保留的前l阶固定界面正则模态。In the formula,

is the retained first-order fixed interface regular mode.

Substituting formula (6) into formula (5), the motion equation of the dimensionally reduced disc, blade or casing can be obtained:

In the formula,

In order to establish the final dimensionality reduction model of the bladed disc-cassette system, in this embodiment, a two-step dimensionality reduction method is used for the bladed disc, and a one-step dimensionality reduction method is used for the casing.

This embodiment verifies the model dimensionality reduction technique proposed in the previous embodiment with a numerical example. The parameter settings of the roulette, blade and casing are shown in Table 1. It should be noted that the calculation of component-level frequency error is relative to the unreduced model. When the blade modal truncation number η _b ≥ 3, the maximum frequency error of the first 7 natural frequencies of the reduced blade is 3.456%, and when the modal truncation number η _d ≥ 1 of the roulette, the maximum frequency error of the reduced roulette wheel is 1.728%. The first reduced blade and roulette models are grouped, and the blisk is further reduced into a blisk model with lower degrees of freedom through the second dimension reduction. When the reduced roulette modal truncation order η _bd ≥ 86 and the rotational speed n∈[0,15000] rpm, the maximum frequency error of the first 100 natural frequencies of the quadratic reduced blisk model is 2.061%. Furthermore, it is assumed in this patent that the elastically supported blisk system is subjected to an unbalanced load at the center O _d with an excitation frequency of 1×n/60. In order to improve the computational efficiency as much as possible and reduce the number of degrees of freedom of the system, η _bd = 2, 4 and 86 are selected in this patent to verify the dynamic frequency characteristics of the system. Taking the results obtained with η _bd =86 as the benchmark, when n∈[0,15000] rpm, η _bd =4 is sufficient to ensure the accuracy of the reduced model results.

In this embodiment, η _b =η _d =η _bd =4 is preset during model dimension reduction. In addition, for the casing, after reducing the dimension of the model, it is all transferred to the modal coordinates, and there is no so-called main node of the casing. In addition, in this embodiment, the modal truncation number η _c of the casing is assumed in the calculation process. = 11. It should be pointed out that the degrees of freedom of the blisk-cassette system with elastic support before and after dimension reduction are 15021×15021 and 125×125, respectively, which indicates that the system degrees of freedom are finally reduced by 99.17%.

Table 1 Material and geometric parameter settings

The technical principles of the present invention have been described above with reference to specific embodiments. These descriptions are only for explaining the principles of the present invention, and cannot be interpreted as limiting the protection scope of the present invention in any way. Based on the explanations herein, those skilled in the art can think of other specific embodiments of the present invention without creative efforts, and these methods will all fall within the protection scope of the present invention.

Claims (6)

1. a digital simulation method for the rubbing dynamics of a blade disc-casing system, is characterized in that, S1. The finite element model of the elastically supported roulette is established by using the shell element and the spring element, and the finite element model of the blade and the finite element model of the elastic casing are constructed by using the spring element and the Timoshenko beam element; S2. An interface coupling unit is established between the finite element model of the wheel disc obtained in S1 and the finite element model of the blade, and a preliminary dynamic model of the blisk is obtained; S3. Use the Craig-Bampton method to reduce the dimensionality of the preliminary blisk-casing system dynamics model respectively; finally, obtain the reduced blisk-casing system dynamics model by grouping; S4. The rubbing dynamics characteristics of the reduced blisk-casing system dynamics model are solved by the combination of the Lagrange multiplier method and the central difference method. 2. The simulation method according to claim 1, wherein the method further comprises: adopting an interface coupling unit to establish a coupling relationship in S2; Wherein, the coupling relationship includes the coupling between the center point of the wheel disc and the central hole of the wheel disc and the coupling between the outer edge of the wheel disc and the blades. 3. The simulation method according to claim 2, wherein the method further comprises: performing convergence processing on the reduced blisk-casing system dynamics model obtained in S3, on the premise of ensuring the accuracy of the model A more computationally efficient dynamic model of the blisk-cassette system is obtained. 4 . The simulation method according to claim 3 , wherein the method further comprises: in S3 , the finite element model of the twisted blade and the finite element model of the variable-section wheel disc are respectively reduced in dimension twice, and the elastic casing is dimensionally reduced. 5 . The finite element model is subjected to a dimensionality reduction. 5. The simulation method according to claim 4, characterized in that, The coupling element stiffness matrix of the i-th rigid coupling node pair between the center point O _d of the wheel disc and the central hole of the wheel disc is obtained by using the penalty function method as

k _p =max(diag(K _d,e )) is the penalty stiffness, K _d,e is the structural stiffness matrix of the roulette, so the stiffness matrix of the entire rigid area is

where _NI represents the number of nodes in the center hole of the roulette. 6. The simulation method according to claim 5, characterized in that, The stiffness matrix of the k-th interface coupling element between the outer edge of the disc and the blade is obtained by the penalty function method as

k represents the kth blade; The total coupling stiffness matrix between the outer edge of the disk and the blade is N _b represents the number of leaves.

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