CN-122021192-A - Method for predicting vibration characteristics of engine composite material blade

CN122021192ACN 122021192 ACN122021192 ACN 122021192ACN-122021192-A

Abstract

The invention provides a method for predicting vibration characteristics of an engine composite material blade, which comprises the steps of establishing a blade geometric model, establishing a coordinate system according to the blade geometric model, obtaining coordinates of each point of the blade geometric model, calculating curvature radius and deflection of the blade, establishing a displacement field according to any point coordinate on the blade based on a first-order shear deformation theory, establishing a strain-displacement relation of the blade model, calculating strain energy, kinetic energy and centrifugal force potential energy of the blade according to the curvature radius, deflection and the strain-displacement relation, defining a vibration mode function by using a Chebyshev-Lorentz method, setting boundary conditions of the blade, obtaining undetermined coefficients, calculating characteristic values and characteristic vectors through driving coefficients and generalized characteristic value equations, and outputting vibration characteristics. The invention adopts the three-dimensional geometric model of the blade, and adopts the chebyshev-lorentz method to calculate the curvature and deflection in the rotation process of the blade through the first-order shear deformation theory, thereby predicting the vibration characteristic in the rotation process of the blade.

Inventors

NIU YAN
WANG HAO
WANG ZHAOQI
YAO MINGHUI
WU QILIANG
WANG CONG

Assignees

天津工业大学

Dates

Publication Date: 20260512
Application Date: 20260410

Claims (10)

1. A method for predicting vibration characteristics of an engine composite blade is characterized by comprising the following steps of Establishing a blade geometric model; Establishing a polar coordinate system according to the blade geometric model, and acquiring coordinates of each point on the blade geometric model; Calculating the curvature radius and deflection of the blade; constructing a displacement field based on a first-order shear deformation theory according to any point coordinate on the blade; establishing a strain-displacement relation of the blade model according to the displacement field; calculating strain energy, kinetic energy and centrifugal force potential energy of the blade according to the curvature radius, deflection and strain-displacement relation; defining a vibration mode function by using the chebyshev-lorentz method, setting the boundary condition of the blade, and obtaining a coefficient to be determined; And calculating a characteristic value and a characteristic vector through the undetermined coefficient and a generalized characteristic value equation, and outputting the natural vibration frequency.
2. The method for predicting vibration characteristics of an engine composite blade according to claim 1, wherein the coordinates of any point on the blade are coordinates of any point on a median plane of the blade.
3. The method for predicting vibration characteristics of an engine composite blade according to claim 2, wherein said establishing polar coordinates from a blade geometry model comprises: And establishing a rotating shaft geometric model at a polar coordinate pole, and fixing the root of the blade geometric model on the circumferential wall of the rotating shaft geometric model.
4. The method for predicting vibration characteristics of an engine composite blade according to claim 3, wherein the radius of curvature and the deflection are calculated by calculating a pull Mei Jishu according to a position vector of any point on a blade geometric model and by calculating the pull-plum coefficient.
5. The method for predicting vibration characteristics of an engine composite blade according to claim 4, wherein the step of obtaining strain energy comprises the steps of: According to the first-order shear deformation theory, three displacement fields of the blade in the three directions in the coordinate system are calculated 、 And , , , , Wherein the method comprises the steps of 、 And Represents the displacement of any point along X, S and Z axes on the median plane of the pre-twisted composite material cylindrical plate, And Representing the transverse normal rotation along the S and X axes, Z representing the coordinate of any point on the median plane of the blade on the Z axis; the relationship between the strain produced during the movement of the blade and the displacement at any point is expressed as , Wherein the method comprises the steps of , , Wherein, the Indicating positive strain in the X-axis direction during blade movement, Indicating a positive strain in the direction of the S axis during blade movement, Representing the shear strain in the X-S plane during blade movement, Representing the shear strain in the X-Z plane during blade movement, Representing the shear strain in the S-Z plane during blade movement, 、、、 And The reference terms corresponding to the strains are respectively given, 、 And The primary terms corresponding to the strain term changing along with the Z axis are respectively adopted, For the radius of curvature of the blade in the X axial direction, The radius of curvature of the blade in the S-axis direction, The median plane radius in the blade model; The strain energy of the blade is , Wherein , And Representing tensile stiffness, bending-to-tensile coupling stiffness and bending stiffness, Representing the coefficient of elasticity of the blade material, Is the thickness of the cylindrical plate and is equal to the thickness of the cylindrical plate, Is the coordinate of any point on the median plane of the blade on the X-axis, For the circumferential angle of the blade model, For the length of the blade, In order to achieve a blade twist rate, Is the positive stress along the X-axis direction during the movement of the blade, Is the positive stress along the S-axis direction during the movement of the blade, Is the shear stress in the X-S plane during blade movement, Is the shear stress in the S-Z plane during blade movement, Is the shear stress in the X-Z plane during blade movement, Is the S-axis coordinate; the blade twist rate is related to the X-axis normal stress, the S-axis normal stress, the X-S plane tangential stress, the X-Z plane tangential stress, and the S-Z plane tangential stress as follows , Wherein, the In order to provide a matrix of coefficient of elasticity in the blade material, , , , For the shear correction coefficient during rotation of the blade, For the young's modulus of the blade material, Poisson's ratio for the blade material.
6. A method for predicting vibration characteristics of an engine composite blade according to claim 5, wherein obtaining kinetic energy comprises Acquiring the coordinates of any point on the middle plane of the blade in the undeformed state of the blade, and calculating the position vector of the point; calculating the displacement vector of any point of the middle position surface of the blade after deformation according to the deflection and the position vector; establishing a hub coordinate system according to the rotation center of the blade, and projecting the rotational speed of the blade into the hub coordinate system to obtain the rotational speed of the blade in the hub coordinate system; calculating according to the displacement vector of any point on the blade to obtain the deformation speed of the blade; Obtaining the synthetic speed of the blade in the moving process according to the deformation speed and the rotation speed; and calculating the kinetic energy of the system according to the synthesis speed.
7. The method for predicting vibration characteristics of an engine composite blade according to claim 6, wherein obtaining said centrifugal force potential energy comprises Calculating centrifugal force potential energy generated by rotation of blades as , Wherein the method comprises the steps of , And Representing displacements along X, S and the Z-axis, respectively, and setting the Z-direction displacement to zero, Is the centrifugal force in the X direction, Is the centrifugal force in the S direction, Is the centrifugal force in the Z-axis direction, , , Is a pull Mei Jishu.
8. The method for predicting vibration characteristics of an engine composite blade according to claim 7, wherein said vibration mode function comprises The root of the blade is connected to a rigid hub coordinate system, the other sides are not constrained by any, in modal analysis, the displacement of the rotating blade is periodic, expressed by the product between a modal amplitude function and a corresponding complex exponential term, , Wherein, the As a simple harmonic time dependent term, For rotating the natural frequency of the pretwisted plate in time The representation is made of a combination of a first and a second color, Is an imaginary number, and is used for the purpose of calculating, Is-1, and the vibration mode function of the vibration mode is As a function of the axial mode shape, As a function of the circumferential vibration mode, As a function of the radial mode shape, As a function of the angular vibration pattern about the X-axis, Is a vibration mode function of the blade along the S-axis direction.
9. The method for predicting vibration characteristics of an engine composite blade according to claim 8, wherein said blade boundary conditions include: the vibration mode function is expressed by chebyshev polynomial series, the geometrical boundary of the blade structure is restrained, , , , , , Wherein the method comprises the steps of A coefficient of uncertainty representing an axial displacement of the (m, n) th order, A coefficient of uncertainty representing the circumferential displacement of the (m, n) th order, A coefficient of uncertainty representing the radial displacement of the (m, n) th order, Representing the coefficient to be determined of the (m, n) th order around the X-axis corner modal auxiliary value, Representing the coefficient to be determined of the (m, n) th order around the S-axis corner modal auxiliary value; for axial displacement of the blades The boundary in the direction of the beam, For axial displacement of the blades The boundary in the direction of the beam, For circumferential displacement of the blades The boundary in the direction of the beam, For circumferential displacement of the blades The boundary in the direction of the beam, For radial displacement of the blades The boundary in the direction of the beam, For circumferential displacement of the blades The boundary in the direction of the beam, After the blades rotate around the X-axis The boundary in the direction of the beam, After the blades rotate around the X-axis The boundary in the direction of the beam, After the blade rotates around the S axis The boundary in the direction of the beam, After the blade rotates around the S axis The boundary in the direction of the beam, Chebyshev polynomials representing the axial direction of the blade, Chebyshev polynomials representing the circumference of the blade; dimensionless coordinates The following is shown , , Wherein the method comprises the steps of For the circumferential angle of the blade model, A boundary function expressed using chebyshev polynomials; First class chebyshev polynomials Is that , Is boundary condition Or (b) Direction.
10. A method for predicting vibration characteristics of an engine composite blade according to claim 9, wherein the tensile stiffness, the bending-tensile coupling stiffness and the bending stiffness are defined as a stiffness matrix Bringing the three directional displacement fields into centrifugal force potential energy U p and kinetic energy equation, and adopting Chebyshev-Letzz method to make variation of total energy equation U so as to obtain quality matrix ; According to the equation Calculating to obtain vibration characteristics; Wherein the method comprises the steps of D is a matrix of undetermined coefficients for the vibration characteristics to be solved.

Description

Method for predicting vibration characteristics of engine composite material blade Technical Field The invention belongs to the field of blade dynamics, and particularly relates to a method for predicting vibration characteristics of an engine composite material blade. Background In an aeroengine, engine blades serve as a rotating structure, play an important role in the aeroengine, and provide necessary power for an aircraft. The dynamics research of the blade is important to the reliability and stability of the blade, and is even a necessary condition for avoiding fatigue failure of the blade. In an aeroengine, a blade is one of the failure-prone parts. In order to improve the strength, impact resistance, heat resistance and damage resistance of the blade, various engine blades conforming to the materials are developed. In practical engineering application, the engine blade is always in a complex thermal environment, vibration response caused by rapid dynamic change in the structure is unavoidable, the geometrical model of the blade is complex, the faced rotating speed range is wider, the resonance rotating speed is quite large in the process of changing the rotating speed of the aeroengine, the vibration characteristic of the blade under dangerous rotating speed is researched in a starting stage, the traditional resonance research usually avoids low-order resonance of the blade in the rotating speed range of the engine, but the resonance hazard cannot be effectively reduced. It is therefore necessary to predict the vibration characteristics of the blade at the design stage. Disclosure of Invention In view of the above, the present invention aims to provide a method for predicting vibration characteristics of an engine composite blade, so as to predict the vibration characteristics of the blade. In order to achieve the above purpose, the technical scheme of the invention is realized as follows: a method for predicting vibration characteristics of an engine composite blade comprises the following steps of Establishing a blade geometric model; Establishing a polar coordinate system according to the blade geometric model, and acquiring coordinates of each point on the blade geometric model; Calculating the curvature radius and deflection of the blade; constructing a displacement field based on a first-order shear deformation theory according to any point coordinate on the blade; establishing a strain-displacement relation of the blade model according to the displacement field; calculating strain energy, kinetic energy and centrifugal force potential energy of the blade according to the curvature radius, deflection and strain-displacement relation; defining a vibration mode function by using a chebyshev-lorentz method, setting boundary conditions of the blade, and obtaining undetermined coefficients; And calculating a characteristic value and a characteristic vector through the undetermined coefficient and a generalized characteristic value equation, and outputting vibration frequency and mode. Further, the coordinates of any point on the blade are coordinates of any point on the median plane of the blade. Further, the establishing polar coordinates according to the blade geometric model comprises And establishing a rotating shaft geometric model at a polar coordinate pole, and fixing the root of the blade geometric model on the circumferential wall of the rotating shaft geometric model. Further, a pull Mei Jishu is calculated according to a position vector of any point on the blade geometric model, and the curvature radius and the deflection are calculated according to a pull plum coefficient. Further, obtaining strain energy includes: According to the first-order shear deformation theory, three displacement fields of the blade in the three directions in the coordinate system are calculated 、And, , , , Wherein the method comprises the steps of、AndRepresents the displacement of any point along X, S and Z axes on the median plane of the pre-twisted composite material cylindrical plate,AndRepresenting the transverse normal rotation along the S and X axes, Z representing the coordinate of any point on the median plane of the blade on the Z axis; the relationship between the strain produced during the movement of the blade and the displacement at any point is expressed as , Wherein the method comprises the steps of, , Wherein, the Indicating positive strain in the X-axis direction during blade movement,Indicating a positive strain in the direction of the S axis during blade movement,Representing the shear strain in the X-S plane during blade movement,Representing the shear strain in the X-Z plane during blade movement,Representing the shear strain in the S-Z plane during blade movement,、、、AndThe reference terms corresponding to the strains are respectively given,、AndThe primary terms corresponding to the strain term changing along with the Z axis are respectively adopted,For the radius of curvature of the blade i