CN111507043A - Rotor blade dynamic stress field measuring method and system based on blade end timing - Google Patents

Rotor blade dynamic stress field measuring method and system based on blade end timing Download PDF

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Publication number
CN111507043A
CN111507043A CN202010369992.0A CN202010369992A CN111507043A CN 111507043 A CN111507043 A CN 111507043A CN 202010369992 A CN202010369992 A CN 202010369992A CN 111507043 A CN111507043 A CN 111507043A
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blade
stress
unit
matrix
rotor blade
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乔百杰
陈雷
刘美茹
曹宏瑞
杨志勃
陈雪峰
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Xian Jiaotong University
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Xian Jiaotong University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Abstract

The invention discloses a method and a system for measuring a dynamic stress field of a rotor blade distributed along the circumferential direction of a casing based on a blade end timing sensor, wherein the method comprises the following steps: establishing a three-dimensional finite element model of the rotating blade to be detected, and extracting unit modal parameters of the three-dimensional finite element model of the blade; determining the number of timing sensors at the blade end, circumferential installation positions and angles; establishing a conversion factor matrix of the displacement of the single position unit at the blade end of the blade and the dynamic stress of the full-field unit, and establishing a conversion factor matrix of the displacement of the single position unit at the blade end of the blade and the equivalent stress of the full-field unit; acquiring the displacement of a blade end unit of a required rotor blade by using a blade end timing sensor; the unit dynamic stress measurement at any position and in any direction of the rotor blade is realized, and the unit equivalent stress measurement at any position of the rotor blade is realized. The method provided by the invention can realize the reconstruction calculation of the dynamic stress and the equivalent stress of the full-field unit of the rotor blade only by using the displacement of the measuring unit at the limited position of the blade end, has simple calculation process, can repeatedly measure and can realize online measurement.

Description

Rotor blade dynamic stress field measuring method and system based on blade end timing
Technical Field
The invention belongs to the technical field of non-contact vibration testing of rotor blades of rotating machinery, and particularly relates to a rotor blade dynamic stress field measuring method and system based on blade end timing.
Background
The blade is used as a core component of the aircraft engine, plays an important role in the normal operation of the engine, and the integrity of the blade directly influences the overall safe operation of the aircraft engine. Due to the influence of centrifugal force caused by high-speed rotation and the limitation of the material characteristics of the blade, the blade is easy to generate vibration fatigue cracks in the service process, and further faults such as fracture, unfilled corner and the like are caused. In the process of blade development and production, the vibration characteristics of the blade can be determined by measuring dynamic stress, and the method has a guiding effect on the modification and design of the blade; in the operation process of the aero-engine, the working state of the blade can be determined through measuring dynamic stress, whether the blade resonates at the working speed or not is judged, and the healthy operation condition of the blade is judged. The measurement of the dynamic stress of the rotor blade has great significance for the safe operation and maintenance of the aircraft engine. Modern aeroengines are widely developed by adopting structures such as small aspect ratio, integral vane discs and the like, and faults are easy to generate in a pneumatic excitation environment; the vibration modes of the blades are dense, the damping is reduced, and the blades are always in a multi-mode vibration working condition. Therefore, multi-modal coupled vibrations should not be ignored in high cycle fatigue life assessment of the blade. In addition, the equivalent stress adopts a stress contour line to represent the stress distribution condition in the model, so that the change of a stress result in the whole rotor blade can be clearly described, and an analyst can quickly determine the most dangerous area of the rotor blade. Therefore, the method has important research value for measuring the isoeffect force of the whole blade. For a long time, the aeroengine blade realizes dynamic strain measurement by sticking a strain gauge on the surface of a rotor blade, and then obtains dynamic stress by utilizing a strain-stress conversion relation, so that only the dynamic stress of limited blade limited positions can be measured, the reliability and the continuous working time are low, particularly for the turbine blade working in a high-temperature environment of more than 1000 ℃, the survival rate of the strain gauge is low and a measurement signal is easy to distort under high temperature, which greatly influences the accurate measurement of the dynamic stress. Due to the characteristic of high-speed rotation of the blades of the aero-engine, the non-contact measurement based on blade end timing becomes a development direction of research in the field of blade vibration testing. The measurement technique utilizes sensors mounted near the inside of the case to sense blade tip vibration information. This technique is known as the leaf-end timing technique. Because the measuring light spot of the blade end timing sensor has a certain area, a measuring point is actually a small-area unit, the measuring quantity of the strain gauge in the practical engineering application is the strain and stress value of the area, and compared with a node, the displacement, the dynamic stress and the dynamic strain of the measuring unit are considered to be more accordant with the practical engineering application and have more practical engineering value. Since the 20 th century 80 s when leaf-end timing technology was proposed, it has achieved widespread use and better development. The current tip timing technology is a hotspot concerned by aircraft engine manufacturing, testing booms and related scientific research institutions, and is applied to measurement and diagnosis work of blades, for example, a Non-invasive Stress measurement system (NSMS) is introduced by the american air force arnold engineering research and development center (aecc). Over decades of development, non-contact measurement based on leaf tip timing has become the most promising method to replace strain gauge contact stress measurement.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a rotor blade dynamic stress field measuring method and system based on blade end timing, solves the problem that the current blade dynamic stress reconstruction method is only suitable for dynamic stress estimation under single-mode vibration, and has the advantage of reconstructing dynamic stress and equivalent stress of all units on the surface and inside of the rotor blade at the same time.
The invention aims to realize the following technical scheme, and the method for measuring the dynamic stress field of the rotor blade based on the blade end timing comprises the following steps:
in the first step, a three-dimensional finite element model of a rotor blade to be measured is established, and unit modal parameters of the three-dimensional finite element model are extracted;
in the second step, determining the number of timing sensors at the blade end and circumferential installation positions and angles;
in the third step, a conversion factor matrix of the unit displacement of the single position of the blade and the dynamic stress of the full-field unit is established; establishing a conversion factor matrix of the unit displacement of the single position of the blade and the equivalent stress of the full-field unit;
in the fourth step, the displacement of the rotor blade end finite position unit is measured based on a blade end timing sensor;
in the fifth step, the unit dynamic stress of any position and any direction of the rotor blade is obtained based on the measured limited unit displacement and the conversion factor matrix of the unit displacement to the full-field unit dynamic stress;
and in the sixth step, obtaining the unit equivalent stress of any position of the rotor blade based on the measured finite unit displacement and a conversion factor matrix of the unit displacement to the full-field equivalent stress.
In the method, in the first step, the front n of the three-dimensional finite element model is extracted through modal analysismOrder modal parameters, including modal frequency fiAnd a size of 3ne× 1 displacement mode shape
Figure BDA0002473361200000021
Size of 6ne× 1 stress mode shape SiOf size ne× 1 equivalent stress mode shape
Figure BDA0002473361200000022
Constructing a rotor blade full-field displacement modal shape matrix
Figure BDA0002473361200000023
Size of 3ne×nmConstructing a rotor blade full-field stress modal shape matrix
Figure BDA0002473361200000024
Size of 6ne×nmConstructing a rotor blade full-field equivalent stress modal shape matrix
Figure BDA0002473361200000031
Size ne×nmWherein n ismRepresenting the number of modes, i representing the order of the modes, neThe number of rotor blade finite element model elements is indicated.
In the method, in a first step, the stresses of the elements in the finite element model of the rotor blade comprise 3 positive stresses σx、σy、σzAnd 3 shear stresses τxy、τya、τxzAnd 6 stress components are provided, and each unit has a stress mode shape in 6 directions.
In the method, in the second step, the number n of sensors are circumferentially arranged at the timing of the blade endbWith the number n of vibration modes measuredmThe relationship satisfies: n isb≥2nm+1, optimizing the position angle of the timing sensor at the blade end along the circumferential direction, and constructing a circumferential layout optimization matrix Tb：
Figure BDA0002473361200000032
Wherein, the layout optimization matrix TbSize nb×(2nm+1)，nbNumber of tip timing sensors, n, mounted for rotor blades circumferentially of the casingmRepresenting the number of modes, θjDenotes a tip timing sensor j (j ═ 1.. n)b) The arrangement angle of the casing relative to the speed sensor, the position of the casing where the speed sensor is located, is taken as a reference 0 DEG, EOiDenotes the excitation order (i ═ 1.., n) of a multi-modal vibration of the rotor bladem) (ii) a Eliminating the position where the sensor can not be installed in the circumferential direction of the casingAfter an angle, n is randomly selectedbThe circumferential angles form the initial matrix T optimized by the circumferential layoutb1And calculating the matrix condition number k1Repeating the random angle selection process R times, and respectively calculating the optimization matrix T formed by the angle selection processbi(i 1.., R), the angle combination in which the matrix condition number is the smallest is selected as the position angle at which the tip timing sensor is mounted in the circumferential direction of the casing.
In the method, in the third step, a conversion factor matrix of the unit displacement of the single position of the blade end of the rotor blade and the full-field unit dynamic stress of the rotor blade is constructed:
Figure BDA0002473361200000041
wherein S isi，jRepresenting the jth order stress mode shape of the ith unit of the finite element model of the blade, and since each unit has 6 directions of stress mode shapes, the matrix size is 6ne×nm；
Figure BDA0002473361200000042
Representing the jth order displacement mode vibration mode of a blade end timing measurement unit, wherein the conversion factor matrix is corresponding to the mode displacement from the full-field unit mode stress to a single unit mode;
constructing a conversion factor matrix of the unit displacement of the single position of the blade end of the rotor blade and the full-field equivalent stress of the blade:
Figure BDA0002473361200000043
matrix size ne×nm(ii) a Wherein the content of the first and second substances,
Figure BDA0002473361200000051
and representing the j-th order stress modal shape of the ith unit of the finite element model of the blade, wherein the conversion factor matrix is the correspondence from the full-field unit modal equivalent stress to the single unit modal displacement.
In the fourth step, the method utilizesnbThe blade end timing sensor obtains N in the Nth turn of the unit measured by the blade end of the rotor bladebObtaining the undersampled multi-mode vibration signal X of the leaf end unit by the vibration data of each time pointb(t); undersampled vibration signal Xb(t) obtaining n under multi-modal vibration of the rotor blade based on circumferential Fourier algorithm decouplingmOrder vibration parameters:
Figure BDA0002473361200000052
wherein the content of the first and second substances,
Figure BDA0002473361200000053
Aishowing the amplitude, f, of the ith order vibrationiRepresents the i-th order vibration mode frequency,
Figure BDA0002473361200000054
Representing the initial phase of the ith vibration; upper label
Figure BDA0002473361200000055
Represents a generalized inverse of the matrix; the superscript T represents the transposition of the matrix to obtain a decoupling rear leaf end unit nmStep vibration signal:
Figure BDA0002473361200000056
wherein, Xb，i(t) represents the decoupled ith order vibration signal (i ═ 1.., n)m)，ωiRepresenting the ith order circumferential frequency after decoupling, and t representing the moment of vibration of the rotor blades.
In the method, in the fifth step, the conversion factor matrix T of unit displacement and full-field dynamic stress and decoupled nmVibration signal Xb，i(t), the dynamic stress of all units of the full field of the rotor blade at any moment t is represented by the formula
Figure BDA0002473361200000057
Calculated, wherein:
Figure BDA0002473361200000058
the stress s (t) comprises a positive stress and a shear stress; wherein σi，xRepresenting the positive stress response, sigma, of the ith element of the finite element model of the blade in the x directioni，yRepresenting the positive stress response, sigma, of the ith element of the finite element model of the blade in the y directioni，zRepresenting the positive stress response, tau, of the ith element of the finite element model of the blade in the z directioni，xyRepresenting the shear stress response of the ith unit of the blade finite element model in the x-y direction, taui，yzRepresenting the shear stress response, tau, of the ith element of the finite element model of the blade in the y-z directioni，xzAnd showing the x-z direction shear stress response of the ith unit of the finite element model of the blade.
In the method, in the sixth step, the conversion factor matrix T from unit displacement to full-field equivalent stressseAnd n after decouplingmOrder vibration signal Xb，i(t) all unit equivalent stresses of the rotor blade at any time t blade full field are calculated by formula
Figure BDA0002473361200000061
And calculating to obtain the equivalent stress which is the synthetic equivalent value of the normal stress and the shearing stress, has no direction and is constant in a positive value.
According to another aspect of the invention, a measurement system for implementing the method comprises,
a plurality of tip timing sensors circumferentially arranged to the rotor blade case;
the blade end timing vibration measurement module is connected with the blade end timing sensor to measure multi-mode vibration signals of the blade end unit of the rotor blade;
the calculation unit is connected with the blade end timing vibration measurement module and comprises:
a modal analysis module configured to perform modal analysis based on the three-dimensional finite element model of the rotor blade to be tested to obtain the front n of the rotor blademOrder mode frequency fiMode of vibration of displacement
Figure BDA0002473361200000062
Harmonic stress mode shape SiAnd equivalent stress mode vibration mode
Figure BDA0002473361200000063
A measurement point optimization selection module configured to optimize the measurement number of the blade end timing sensors and the installation angle at the casing, wherein the blade end timing is circumferentially arranged with the sensor number nbWith the number n of vibration modes measuredmThe relationship satisfies: n isb≥2nm+1, determining the minimum number of sensors based on the modal number, and constructing a circumferential layout optimization matrix TbAfter the position angle at which the sensor cannot be installed in the circumferential direction of the casing is eliminated, n is randomly selectedbThe circumferential angles form an initial matrix T optimized in circumferential layoutb1And calculating the matrix condition number k1Repeating the random angle selection process R times, and respectively calculating the optimization matrix T formed by the angle selection processbi(i 1.., R), selecting an angle combination in which the matrix condition number is the smallest as a position angle at which the tip timing sensor is mounted in the circumferential direction of the casing,
a conversion factor matrix calculation module configured to construct a conversion factor matrix of blade tip unit displacement and full-field dynamic stress, construct a conversion factor matrix of blade tip unit displacement and full-field equivalent stress,
and the stress field reconstruction module is configured to calculate the normal stress, the shear stress and the equivalent stress of all units on the surface and inside of the blade at each rotation or any time of the rotor blade.
Advantageous effects
The method for measuring the dynamic stress field of the rotor blade based on the blade end timing can realize the measurement of the dynamic stress field and the equivalent stress field of the rotor blade under multi-mode vibration only by using the unit vibration displacement result of a single position of the blade. The dynamic stress and the equivalent effect force of the surface and the internal unit of the blade under multi-mode vibration can be measured. The method breaks through the limitation that the traditional dynamic stress reconstruction method based on the blade end timing can only approximately reconstruct the dynamic stress of a certain point of the blade under the single-mode vibration. The method provided by the invention can realize multi-mode vibration decoupling, has high measurement precision and simple calculation process, can realize on-line measurement, can save a large amount of strain gauge measurement consumption, and has simple reconstruction system process, easy realization and repeatable measurement.
Drawings
Various advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. It is obvious that the drawings described below are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. Also, like parts are designated by like reference numerals throughout the drawings.
In the drawings:
FIG. 1 is a schematic flow chart of a preferred example of a method for measuring a dynamic stress field of a rotor blade based on tip timing according to the present invention;
2(a) to 2(b) are schematic structural diagrams of a rotor blade dynamic stress field measurement system based on tip timing provided by the invention, wherein t fig. 2(a) is a rotor blade dynamic stress field reconstruction system composition; FIG. 2(b) is a schematic circumferential installation diagram of a blade tip timing vibration measurement module and a blade tip timing sensor;
FIG. 3 is a schematic representation of simulated rotor blade dynamic load excitation locations and tip timing sensor (BTT) test point locations in one embodiment;
4(a) -4 (i) are displacement mode shapes and stress mode shapes of a rotor blade according to an embodiment, wherein FIG. 4(a) is a first order displacement mode shape; FIG. 4(b) first order stress mode; FIG. 4(c) first order equivalent stress mode; FIG. 4(d) second order displacement mode; FIG. 4(e) second order stress mode; FIG. 4(f) second order equivalent stress mode; FIG. 4(g) third order displacement mode; FIG. 4(h) third order stress mode; FIG. 4(i) third order equivalent stress mode;
FIG. 5 is a schematic representation of a tip displacement vibration signal measured by 7 tip timing sensors for an exemplary embodiment of a rotor blade;
FIG. 6 is a multi-modal decoupling of rotor blade vibration displacement signals in one embodiment;
7(a) -7 (c) are the results of comparing the dynamic stress of unit 213 of the blade body with the real dynamic stress in the stress field of the reconstructed rotor blade in one embodiment, wherein FIG. 7(a) compares the three positive stress components with the real dynamic stress; FIG. 7(b) results of comparing three shear stress components with true dynamic stress; FIG. 7(c) reconstructed equivalent stress versus true equivalent stress results;
8(a) -8 (c) are the comparison of the dynamic stress of the unit number 7052 of the root in the reconstructed stress field of the rotor blade with the real dynamic stress in one embodiment, wherein FIG. 8(a) compares the three positive stress components with the real dynamic stress; FIG. 8(b) results of comparing three shear stress components with true dynamic stress; fig. 8(c) reconstructed equivalent stress and real equivalent stress comparison results.
The invention is further explained below with reference to the figures and examples.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to fig. 1 to 8 (c). While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present invention is defined by the appended claims.
For the purpose of facilitating understanding of the embodiments of the present invention, the following description will be made by taking specific embodiments as examples with reference to the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present invention.
For better understanding, fig. 1 is a flow chart of a method for measuring a dynamic stress field of a rotor blade based on tip timing, and as shown in fig. 1, the method for measuring a dynamic stress field of a rotor blade based on tip timing comprises the following steps:
in a first step S1, establishing a three-dimensional finite element model of a rotor blade to be measured, and extracting unit modal parameters of the three-dimensional finite element model;
in a second step S2, determining the number and positions of the tip timing sensors installed along the circumferential direction of the casing;
in a third step S3, establishing a conversion factor matrix of the blade end single unit displacement and the full-field unit dynamic stress, and establishing a conversion factor matrix of the equivalent stress from the unit displacement to the full-field unit;
in a fourth step S4, the tip end unit displacement of the rotor blade is acquired based on the tip end timing sensor,
in a fifth step S5, obtaining a unit dynamic stress of the rotor blade at any position and in any direction based on the unit displacement and a conversion factor matrix to a full-field dynamic stress;
in a sixth step S6, a unit equivalent stress at any position of the rotor blade is obtained based on the unit displacement and a matrix of scaling factors to full field equivalent stress.
In one embodiment of the method, in a first step S1, the first n of the three-dimensional finite element model is extracted by modal analysismOrder unit modal parameters including modal frequency fiAnd a size of 3ne× 1 displacement mode shape
Figure BDA0002473361200000081
Size of 6ne× 1 stress mode shape SiOf size ne× 1 equivalent stress mode shape
Figure BDA0002473361200000082
Constructing a rotor blade full-field displacement modal shape matrix
Figure BDA0002473361200000091
Size of 3ne×nmConstructing a rotor blade full-field stress modal shape matrix
Figure BDA0002473361200000092
Size of 6ne×nmConstructing a rotor blade full-field equivalent stress modal shape matrix
Figure BDA0002473361200000093
Size ne×nmWherein n ismRepresenting the number of modes, i representing the order of the modes, neThe number of rotor blade finite element model elements is indicated.
In the method, in a first step, the stresses of each rotor blade finite element model element comprise 3 positive stresses σx、σy、σzAnd 3 shear stresses τxy、τyz、τxzThere are 6 stress components in total.
In one embodiment of the method, in a second step S2, the number n of rotor blade tip timing sensors mounted in the circumferential direction of the casing isbAnd number n of vibration modesmThe relationship of (1) is: n isb≥2nm+1。
In one embodiment of the method, in a second step S2, the positions and angles of the tip timing sensors mounted in the circumferential direction are optimized to construct a circumferential layout optimization matrix Tb：
Figure BDA0002473361200000094
Wherein, the layout optimization matrix TbSize nb×(2nm+1)，θjDenotes a tip timing sensor j (j ═ 1.. n)b) Arrangement angle of the housing relative to the rotational speed sensor, the housing in which the rotational speed sensor is locatedAs a reference datum 0 deg., nbIndicating the total number of tip timing sensors arranged circumferentially of the casing, EOiDenotes the excitation order (i ═ 1.. n.) of a multi-modal vibration of the rotor bladem) (ii) a After the position angle of the casing which cannot be provided with the sensor in the circumferential direction is eliminated, n is randomly selectedbThe circumferential angles form the initial matrix T optimized by the circumferential layoutb1And calculating the matrix condition number k1Repeating the random angle selection process R times, and respectively calculating the optimization matrix T formed by the angle selection processbi(i 1.., R), the angle combination in which the matrix condition number is the smallest is selected as the position angle at which the tip timing sensor is mounted in the circumferential direction of the casing.
In one embodiment of the method, in a third step S3, a matrix of scale factors of rotor blade tip single position unit displacements and blade full field unit dynamic stresses is constructed:
Figure BDA0002473361200000101
wherein S isi，jRepresenting the jth order stress mode shape of the ith unit of the finite element model of the blade, and since each unit has 6 directions of stress mode shapes, the matrix size is 6ne×nm；
Figure BDA0002473361200000102
Representing the jth order displacement mode vibration mode of the blade end timing measurement unit, namely the conversion factor matrix is corresponding to the mode displacement from the full-field unit mode stress to a single unit mode;
constructing a conversion factor matrix of the unit displacement of the single position of the blade end of the rotor blade and the full-field equivalent stress of the blade:
Figure BDA0002473361200000103
matrix size ne×nm(ii) a Wherein the content of the first and second substances,
Figure BDA0002473361200000111
and showing the j-th order stress mode shape of the ith unit of the finite element model of the blade.
In one embodiment of the method, in the fourth step S4, n is usedbThe blade end timing sensor obtains N in the Nth turn of the unit measured by the blade end of the rotor bladebObtaining the undersampled multi-mode vibration signal X of the leaf end unit by the vibration data of each time pointb(t); undersampled vibration signal Xb(t) obtaining n under multi-modal vibration of the rotor blade based on circumferential Fourier algorithm decouplingmOrder vibration parameters:
Figure BDA0002473361200000112
wherein the content of the first and second substances,
Figure BDA0002473361200000113
Aishowing the amplitude, f, of the ith order vibrationiRepresents the i-th order vibration mode frequency,
Figure BDA0002473361200000114
Representing the initial phase of the ith vibration; upper label
Figure BDA0002473361200000115
Represents a generalized inverse of the matrix; the superscript T represents the transposition of the matrix to obtain a decoupling rear leaf end unit nmStep vibration signal:
Figure BDA0002473361200000116
wherein, Xb，i(t) represents the decoupled ith order vibration signal (i ═ 1.., n)m)，ωiRepresenting the ith order circumferential frequency after decoupling, and t representing the moment of vibration of the rotor blades.
In one embodiment of the method, in the fifth step S5, all the unit dynamic stresses on the surface and inside of the rotor blade at any time are measured according to the formula
Figure BDA0002473361200000117
It is calculated that the stress s (t) includes a normal stress and a shear stress.
In one embodiment of the method, in the sixth step S6, the equivalent stresses of all the elements on the surface and inside of the rotor blade at any time are measured according to the formula
Figure BDA0002473361200000118
And calculating to obtain that the stress is the equivalent value of the normal stress and the shear stress, has no direction and is constant at a positive value.
For a further understanding of the present invention, the present invention will be further described with reference to fig. 1 to 8(c) and the embodiments, it should be emphasized that the following description is only exemplary, and the application of the present invention is not limited to the following examples.
FIG. 1 is a schematic flow chart of a method for measuring a dynamic stress field of a rotor blade based on blade end timing, which is completed by the invention, and comprises the steps of measuring a vibration displacement signal of a single blade end position unit by using a blade end timing sensor installed in the circumferential direction of a casing, realizing multi-mode vibration decoupling by using a circumferential Fourier algorithm, constructing a conversion factor matrix of blade end unit displacement of the rotor blade and dynamic stress of all units in a full field, and realizing reconstruction of the dynamic stress field of the blade; and constructing a conversion factor matrix of the central displacement of the blade end unit of the rotor blade and the equivalent stress of all units in the full field, and realizing the full-field equivalent stress reconstruction of the blade. Fig. 2(a) to 2(b) are schematic structural diagrams of a rotor blade dynamic stress field measurement system based on tip timing, which includes a rotation speed synchronization sensor and a non-contact sensor (a tip timing sensor), and constitutes a signal acquisition module, and the method includes the following specific steps:
1) extracting modal parameters of the three-dimensional finite element model: referring to FIG. 3, a three-dimensional finite element model of a simulated turbine blade made of titanium alloy and having a density of 4539.5Kg/m was created using ANSYS finite element analysis software3Poisson's ratio of 0.3, modulus of elasticity 142200MPa, blade length 100mm, root maximum thickness 15mm, tip maximum thickness 9.6mm, and tip rotation angle 31.2 ° with respect to blade root, the finite element types are solid element SO L ID186 and shell element SHE LL 281, the element size is 2mm, the shell element is divided at the tip face, SO L ID186 elements are divided for the whole blade body, the total number of elements is 7228, wherein 7099 solid elements are provided129 shell units are used for simulating blade end units for measuring the timing displacement of the blade end, the bottom surface of the blade is fixedly restrained, the rotating speed of 15000RPM is applied to the blade, and the rotating working state of the turbine blade is simulated;
2) obtaining the first three-order modal parameter, namely n, by using ANSYS finite element analysis software m3; modal frequency of fiOf size 3ne× 1 displacement mode shape
Figure BDA0002473361200000121
Size of 6ne× 1 stress mode shape SiOf size ne× 1 equivalent stress mode shape
Figure BDA0002473361200000122
Wherein the first three-order modal frequency is f1＝1696.8Hz、f2＝2829.3Hz、f35018.9 Hz; full-field stress vibration mode of structural rotor blade
Figure BDA0002473361200000123
Size of 6ne×nmFull-field equivalent stress vibration mode of rotor blade
Figure BDA0002473361200000124
Size ne×nmThe stress mode vibration patterns are shown in fig. 4(a) to 4 (f); i denotes the order of the mode, ne7228 is the number of units of the model; the stress includes 3 positive stresses σx、σy、σzAnd 3 shear stresses τxy、τyz、τxzThere are 6 stress components in total, i.e. 6 stress mode shapes per cell.
3) Determining the number of timing sensors at the blade end and the circumferential installation position: circumferential installation number n of timing sensors at blade end of rotor blade casingbAnd number n of vibration modesmThe relationship of (1) is: n isb≥2nm+ 1; in this case, the vibration mode of the first three stages of the turbine blade is focused, and n is takenm3; the minimum number of timing sensors at the circumferential blade end of the casing is nbIn this case, 7 leaf tips are selected as 7 timing sensorsA machine;
constructing a circumferential layout optimization matrix Tb：
Figure BDA0002473361200000125
Wherein, measure the optimization matrix TbSize nb×(2nm+1)＝7×7，EOiRepresenting the excitation order under multi-modal vibration, taking the position of the rotation speed sensor as a reference 0 DEG position thetajDenotes the j (j ═ 1.., n)b) The installation angle of the blade end timing sensor relative to the rotating speed sensor in the casing; the three excitation orders concerned in the case are EO7, EO18 and EO32 respectively, and the first three-order vibration modes of the turbine blade are excited simultaneously at the same rotating speed; randomly selecting n in the circumferential direction of the casingbTaking the angle of 7 degrees as the installation position of the timing sensor at the blade end; computing blade end timing circumferential layout optimization matrix TbA condition number κ; and repeating the process R of randomly selecting angles for 500 times, respectively calculating matrix condition numbers, and selecting a measuring point layout scheme with the minimum condition number kappa. In the example, the circumferential installation angles of the selected 7 blade end timing sensors are 3.6 degrees, 118.8 degrees, 183.6 degrees, 190.8 degrees, 302.4 degrees, 316.8 degrees and 352.8 degrees, and the corresponding measuring point optimization matrix TbThe condition number of (2) is 3.9952.
4) Establishing a conversion factor matrix of the central displacement of the single-point unit of the blade and the full-field dynamic stress: constructing a conversion factor matrix of the unit displacement of the single position of the blade end of the rotor blade and the dynamic stress of the full-field unit of the blade:
Figure BDA0002473361200000131
the matrix size is 46368 × 3, a conversion factor matrix of the unit displacement of the single position of the blade end of the rotor blade and the full-field equivalent stress of the blade is constructed:
Figure BDA0002473361200000141
the matrix size is 7728 × 3.
5) Transient analysis is carried out on the simulated rotor blade in ANSYS finite element software, the mass damping coefficient is set to α -26.6579, and the stiffness damping coefficient is set to β -1.4066 × 10-7The rotating speed is set to 12000RPM, multi-mode vibration of a rotor blade caused by aerodynamic load is simulated, and multi-frequency simple harmonic excitation force f (t) ═ cos (2 pi f) is applied to the X direction of a No. 7024 node of a blade end1t)+10cos(2πf2t)+20cos(2πf3t), taking the stress field after transient analysis stabilization as a reference of a reconstruction result for comparison and verification; using nbObtaining blade end multi-mode vibration signals X in the Nth turn of the rotor blade by 7 blade end timing sensorsb(t), see fig. 5; the blade end timing sensor samples X-direction vibration signals of a No. 7215 shell unit at the blade end every time a rotor blade rotates for one circle, 7 sensors acquire 7 data points in total, 20 circles of 140 data are acquired in total, and the sampling signals are under-sampled; also, fig. 5 shows the sampling frequency fsThe data length of the X-direction vibration signal of the leaf end 7215 under 20000Hz is N-2000, and the sampling time is t-N/fsLocal signal within 0.09s-0.1s of 0.1 s.
And then decoupling by utilizing a circumferential Fourier algorithm to obtain the rotor blade nmOrder vibration parameters:
Figure BDA0002473361200000142
wherein the content of the first and second substances,
Figure BDA0002473361200000143
Aishowing the amplitude, f, of the ith order vibrationiRepresents the i-th order vibration mode frequency,
Figure BDA0002473361200000144
Representing the initial phase of the ith vibration; upper label
Figure BDA0002473361200000145
Represents a generalized inverse of the matrix; superscript T represents the transpose of the matrix; further, vibration signals of each order of the decoupling rear blade end unit are obtained：
Figure BDA0002473361200000146
Wherein, Xb，i(t) represents the decoupled ith order vibration signal (i ═ 1.., n)m)，ωiRepresenting the ith order circumferential frequency after decoupling, and t representing the moment of vibration of the rotor blades.
FIG. 6 shows the first three-order vibration mode decoupling results of the turbine blade displacement signals in the embodiment.
4) All unit dynamic stresses on the surface and inside of the rotor blade at any moment are calculated by formula
Figure BDA0002473361200000151
Calculating to obtain; equivalent stress of all units on the surface and inside of the rotor blade at any moment through a formula
Figure BDA0002473361200000152
And calculating to obtain the stress which is the synthetic equivalent value of the stress, has no direction and is constant in a positive value.
Taking the unit No. 213 of the blade body of the rotor blade and the unit No. 7052 of the blade root as the typical representative of the high-precision reconstruction of the dynamic stress field (see FIG. 3), the conclusion is also applicable to other units, wherein, FIGS. 7(a) to 7(c) are the results of comparing the dynamic stress of the unit No. 213 of the blade body with the real dynamic stress and the equivalent stress in the stress field of the rotor blade reconstructed in one embodiment, FIGS. 8(a) to 8(c) are the results of comparing the dynamic stress of the unit No. 7052 of the blade root with the real dynamic stress and the equivalent stress in the stress field of the rotor blade reconstructed in one embodiment, FIGS. 7(a) to 8(c) show that the reconstructed dynamic stress signal is highly consistent with the real dynamic stress and the equivalent stress, and in order to quantitatively evaluate the performance of the method for measuring the dynamic stress field of the rotor blade of the present invention, at t ∈ []s interval, the relative error between the reconstructed signal and the true stress is calculated, and the unit sigma of the blade body 213 in FIG. 7(a)x、σy、σzThe relative errors of the three positive stresses are 5.98%, 11.01% and 6.11%, respectively, and the unit tau of the blade body 213 in FIG. 7(b)xy、τyz、τxzThree scissorsThe relative errors of the stress are respectively 8.27%, 8.44% and 10.42%, and the relative error of the equivalent stress of the blade body No. 213 unit in FIG. 7(c) is 5.53%; unit σ of leaf root 7052 in FIG. 8(a)x、σy、σzThe relative errors of the three positive stresses are respectively 10.07%, 12.04% and 7.91%, and the leaf root No. 7052 unit tau in FIG. 8(b)xy、τyz、τxzThe relative errors of the three shear stresses are 6.49%, 7.33% and 8.59%, respectively, and the relative error of the equivalent stress of the blade body No. 7052 element in FIG. 8(c) is 4.14%. Therefore, the method for measuring the dynamic stress field of the rotor blade based on the blade end timing can reconstruct the dynamic stress field and the equivalent stress result of the blade with high precision.
The method provided by the invention realizes the reconstruction of the whole dynamic stress field of the rotor blade only by utilizing the displacement of a single unit at the blade end, can realize the measurement of the normal stress, the shear stress, and other effect forces of all units on the surface and inside of the rotor blade under multi-mode vibration, has simple calculation process, and is easy for on-line measurement. The above description is only a preferred embodiment of the present invention, and can be applied to the vibration test of the fan/compressor/turbine blade of the rotating machinery such as an aircraft engine, a gas turbine, a steam turbine, etc., without limiting the present invention.
In one embodiment, the method comprises the steps of:
1) extracting unit modal parameters of the three-dimensional finite element model of the blade;
2) determining the number of timing sensors at the blade end and the circumferential installation position of the casing;
3) establishing a conversion factor matrix of the blade end unit displacement and the full-field unit dynamic stress of the blade, and determining the conversion factor matrix of the blade end unit displacement and the full-field unit equivalent stress;
4) acquiring the displacement of a blade end unit of the rotor blade by using a blade end timing sensor;
5) the unit dynamic stress measurement of any position and direction of the rotor blade is realized;
6) and realizing unit equivalent stress measurement of any position of the rotor blade.
Further, step 1) establishing a three-dimensional finite element model of the rotor blade,extracting the three-dimensional finite element model front n through modal analysismOrder unit modal parameters including modal frequency fiAnd a size of 3ne× 1 displacement mode shape
Figure BDA0002473361200000161
Size of 6ne× 1 stress mode shape SiOf size ne× 1 equivalent stress mode shape
Figure BDA0002473361200000162
Constructing a rotor blade full-field displacement modal shape matrix
Figure BDA0002473361200000163
Size of 3ne×nmConstructing a rotor blade full-field stress modal shape matrix
Figure BDA0002473361200000164
Size of 6ne×nmFull-field equivalent stress modal vibration mode of rotor blade
Figure BDA0002473361200000165
Size ne×nmWherein n ismRepresenting the number of modes, i representing the order of the modes, neThe number of rotor blade finite element model elements is indicated.
In the method, in a first step, the stresses of each rotor blade finite element model element comprise 3 positive stresses σx、σy、σzAnd3shear stress tauxy、τyz、τxzTotal of 6 stress components
Further, step 2) the number n of blade end timing sensors arranged on the rotor blade along the circumferential direction of the casingbWith the number n of multimode vibration measurementsmThe relationship of (1) is: n isb≥2nm+1。
Optimizing the position and angle of the timing sensor at the blade end along the circumferential direction, and constructing a circumferential layout optimization matrix Tb：
Figure BDA0002473361200000166
Wherein, the layout optimization matrix TbSize nb×(2nm+1)，θjDenotes a tip timing sensor j (j ═ 1.. n)b) Arrangement angle of the casing with respect to the rotation speed sensor (0 DEG < theta)iLess than 360 degrees, the position of the casing where the rotating speed sensor is positioned is used as a reference datum 0 degree, nbIndicating the total number of tip timing sensors arranged circumferentially of the casing, EOiDenotes the excitation order (i ═ 1.. n.) of a multi-modal vibration of the rotor bladem) (ii) a After the position angle of the casing which cannot be provided with the sensor in the circumferential direction is eliminated, n is randomly selectedbThe circumferential angles form the initial matrix T optimized by the circumferential layoutb1And calculating the matrix condition number k1Repeating the random angle selection process R times, and respectively calculating the optimization matrix T formed by the angle selection processbi(i 1.., R), the angle combination in which the matrix condition number is the smallest is selected as the position angle at which the tip timing sensor is mounted in the circumferential direction of the casing.
Further, step 3), constructing a conversion factor matrix of the unit displacement of the single position of the blade end of the rotor blade and the dynamic stress of the full-field unit of the blade:
Figure BDA0002473361200000171
wherein S isi，jRepresenting the jth order stress mode shape of the ith unit of the finite element model of the blade, and since each unit has 6 directions of stress mode shapes, the matrix size is 6ne×nm；
Figure BDA0002473361200000172
Representing the jth order displacement mode vibration mode of the blade end timing measurement unit, namely the conversion factor matrix is corresponding to the mode displacement from the full-field unit mode stress to a single unit mode;
constructing a conversion factor matrix of the unit displacement of the single position of the blade end of the rotor blade and the full-field equivalent stress of the blade:
Figure BDA0002473361200000181
matrix size ne×nm(ii) a Wherein the content of the first and second substances,
Figure BDA0002473361200000182
and showing the j-th order stress mode shape of the ith unit of the finite element model of the blade.
Further, step 4) utilizes nbThe blade end timing sensor obtains N in the Nth turn of the unit measured by the blade end of the rotor bladebObtaining the undersampled multi-mode vibration signal X of the leaf end unit by the vibration data of each time pointb(t); undersampled vibration signal Xb(t) obtaining n under multi-modal vibration of the rotor blade based on circumferential Fourier algorithm decouplingmOrder vibration parameters:
Figure BDA0002473361200000183
wherein the content of the first and second substances,
Figure BDA0002473361200000184
Aishowing the amplitude, f, of the ith order vibrationiRepresents the i-th order vibration mode frequency,
Figure BDA0002473361200000185
Representing the initial phase of the ith vibration; upper label
Figure BDA0002473361200000186
Represents a generalized inverse of the matrix; the superscript T represents the transposition of the matrix to obtain a decoupling rear leaf end unit nmStep vibration signal:
Figure BDA0002473361200000187
wherein, Xb，i(t) represents the decoupled ith order vibration signal (i ═ 1.., n)m)，ωiRepresenting the ith order circumferential frequency after decoupling, and t representing the moment of vibration of the rotor blades.
Further, step 5) the rotor blade at any momentAll unit dynamic stresses on the surface and inside, via the formula
Figure BDA0002473361200000188
It is calculated that the stress s (t) includes a normal stress and a shear stress.
Further, in step 6), equivalent stress of all units on the surface and inside of the rotor blade at any moment is calculated according to the formula
Figure BDA0002473361200000191
And calculating to obtain the stress which is the synthetic equivalent value of the stress, has no direction and is constant in a positive value.
In one embodiment, in a third step S3, a scaling relationship between the blade single position unit displacement and the full field unit dynamic stress is established; and establishing a conversion relation between the displacement of the single position unit of the blade and the Mises equivalent stress of the full-field unit.
In one embodiment, in the sixth step (S6), cell Mises equivalent stresses at any position of the rotor blade are obtained based on a scaling relationship between the measured finite cell displacements and the cell displacements to full-field Mises equivalent stresses.
In another aspect, a measurement system for implementing a method includes,
a plurality of tip timing sensors disposed on the rotor blade case;
the blade end timing vibration measurement module is connected with the blade end timing sensor to measure multi-mode vibration signals of the blade end unit of the rotor blade;
the calculation unit is connected with the blade end timing vibration measurement module and comprises:
a mode analysis module configured to perform a mode analysis to obtain the front n of the rotor blade based on the three-dimensional finite element model of the rotor blade to be testedmOrder mode frequency fiMode of vibration of displacement
Figure BDA0002473361200000192
Harmonic stress mode shape SiAnd equivalent stress mode vibration mode
Figure BDA0002473361200000193
A measurement point optimization selection module configured to optimize the measurement number of the blade end timing sensors and the installation angle at the casing, wherein the blade end timing is circumferentially arranged with the sensor number nbWith the number n of vibration modes measuredmThe relationship satisfies: n isb≥2nm+1, determining a minimum number of sensors based on the number of modes; optimizing the position and angle of the timing sensor at the blade end along the circumferential direction, and constructing a circumferential layout optimization matrix TbTaking the position of the rotating speed sensor in the casing as a reference datum 0 degree, and randomly selecting n after eliminating the position angle at which the sensor cannot be installed in the circumferential direction of the casingbThe circumferential angles form the initial matrix T optimized by the circumferential layoutb1And calculating the matrix condition number k1Repeating the random angle selection process R times, and respectively calculating the optimization matrix T formed by the angle selection processbi(i 1.., R), selecting an angle combination in which the matrix condition number is the smallest as a position angle at which the tip timing sensor is mounted in the circumferential direction of the casing,
a conversion factor matrix calculation module configured to construct a conversion factor matrix of blade tip unit displacement and full-field dynamic stress, construct a conversion factor matrix of blade tip unit displacement and full-field equivalent stress,
and the stress field reconstruction module is configured to calculate the normal stress, the shear stress and the equivalent stress of all units on the surface and inside of the blade at each rotation or any time of the rotor blade.
In one embodiment, the blade tip timing vibration measurement module comprises a rotating speed sensor, a signal conditioning module and a time-displacement conversion module.
In one embodiment, the measurement system further comprises a display unit and an open-wire communication device, the open-wire communication device comprising a 4G/GPRS or internet communication module.
In one embodiment, the modal analysis module, the measurement point optimization module, the conversion matrix calculation module or the dynamic stress field reconstruction module is a general processor, a digital signal processor, an Application Specific Integrated Circuit (ASIC) or a Field Programmable Gate Array (FPGA),
in one embodiment the modal analysis module, the measurement point optimization module, the transformation matrix calculation module or the dynamic stress field reconstruction module comprises a memory comprising one or more of a read only memory ROM, a random access memory RAM, a flash memory or an electronically erasable programmable read only memory EEPROM.
In another aspect of the present invention, there is provided a system for a method for measuring a dynamic stress field of a rotor blade based on tip timing as described above, including:
a modal analysis module: carrying out modal analysis on the three-dimensional finite element model of the blade by using finite element analysis software, and extracting the front n of the three-dimensional finite element model through the modal analysismOrder unit modal parameters including modal frequency fiAnd a size of 3ne× 1 displacement mode shape
Figure BDA0002473361200000201
Size of 6ne× 1 stress mode shape SiOf size ne× 1 equivalent stress mode shape
Figure BDA0002473361200000202
Constructing a rotor blade full-field displacement modal shape matrix
Figure BDA0002473361200000203
Size of 3ne×nmConstructing a rotor blade full-field stress modal shape matrix
Figure BDA0002473361200000204
Size of 6ne×nmConstructing a rotor blade full-field equivalent stress modal shape matrix
Figure BDA0002473361200000205
Size ne×nmWherein n ismRepresenting the number of modes, i representing the order of the modes, neThe number of rotor blade finite element model elements is indicated.
A measuring point optimization module: rotor blade casing circumferenceNumber n of timing sensors for installing blade endsbttAnd number n of vibration modesmThe relationship of (1) is: n isb≥2nm+ 1; optimizing the position and angle of the timing sensor at the blade end along the circumferential direction, and constructing a circumferential layout optimization matrix Tb：
Figure BDA0002473361200000206
Wherein, the layout optimization matrix TbSize nb×(2nm+1)，θjDenotes a tip timing sensor j (j ═ 1.. n)b) Arrangement angle theta of the casing relative to the rotation speed sensorj(j＝1，...nb) Taking the position of the rotating speed sensor on the casing as a reference datum for 0 degree; after the position angle of the casing which cannot be provided with the sensor in the circumferential direction is eliminated, n is randomly selectedbThe circumferential angles form the initial matrix T optimized by the circumferential layoutb1And calculating the matrix condition number k1Repeating the random angle selection process R times, and respectively calculating the optimization matrix T formed by the angle selection processbi(i 1.., R), the angle combination in which the matrix condition number is the smallest is selected as the position angle at which the tip timing sensor is mounted in the circumferential direction of the casing.
A conversion factor matrix calculation module: constructing a conversion factor matrix of the unit displacement of the single position of the blade end of the rotor blade and the dynamic stress of the full-field unit of the blade:
Figure BDA0002473361200000211
matrix size of 6ne×nm(ii) a Constructing a conversion factor matrix of the unit displacement of the single position of the blade end of the rotor blade and the full-field equivalent stress of the blade:
Figure BDA0002473361200000221
matrix size ne×nm。
The blade end timing vibration measurement module: comprises a plurality ofThe system comprises a leaf end timing sensor, at least one rotating speed sensor, a signal conditioning module and a time-displacement conversion module; using nbThe blade end timing sensor obtains N in the Nth turn of the unit measured by the blade end of the rotor bladebObtaining the undersampled multi-mode vibration signal of the leaf end unit by the vibration data of each time point, wherein the undersampled vibration signal X isb(t) decoupling by means of a circumferential Fourier algorithm to obtain n under multi-modal vibration of the rotor blademOrder vibration parameters:
Figure BDA0002473361200000222
wherein the content of the first and second substances,
Figure BDA0002473361200000223
Aishowing the amplitude, f, of the ith order vibrationiRepresents the i-th order vibration mode frequency,
Figure BDA0002473361200000224
Representing the initial phase of the ith vibration; upper label
Figure BDA0002473361200000225
Represents a generalized inverse of the matrix; the superscript T represents the transpose of the matrix.
Further, a decoupling trailing-blade-end unit n is obtainedmStep vibration signal:
Figure BDA0002473361200000226
wherein, Xb，i(t) represents the decoupled ith order vibration signal (i ═ 1.., n)m)，ωiRepresenting the ith order circumferential frequency after decoupling, and t representing the moment of vibration of the rotor blades.
A stress field reconstruction module: all unit dynamic stresses on the surface and inside of each rotor blade of the rotor blade are calculated by the formula
Figure BDA0002473361200000227
Calculating to obtain stress S (t) comprising normal stress and shear stress; equivalent stress of all units on the surface and inside of each rotating blade of the rotor blade is calculated by formula
Figure BDA0002473361200000231
And calculating to obtain the stress which is the synthetic equivalent value of the stress, has no direction and is constant in a positive value.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and application fields, and the above-described embodiments are illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto without departing from the scope of the invention as defined by the appended claims.

Claims (9)

1. A method for measuring a dynamic stress field of a rotor blade based on tip timing, the method comprising the steps of:
in the first step (S1), a three-dimensional finite element model of a rotor blade to be measured is established, and unit modal parameters of the three-dimensional finite element model are extracted;
in a second step (S2), determining the number of tip timing sensors and the circumferential mounting position and angle;
in the third step (S3), a conversion factor matrix of the blade single position unit displacement and the full-field unit dynamic stress is established; establishing a conversion factor matrix of the unit displacement of the single position of the blade and the equivalent stress of the full-field unit;
in a fourth step (S4), measuring the rotor blade tip finite position element displacement based on the tip timing sensor;
in the fifth step (S5), the unit dynamic stress of any position and any direction of the rotor blade is obtained based on the measured finite unit displacement and the conversion factor matrix of the unit displacement to the full-field unit dynamic stress;
in a sixth step (S6), a unit equivalent stress at any position of the rotor blade is obtained based on the measured finite unit displacement and a matrix of scaling factors of the unit displacement to full field equivalent stress.
2. The method of claim 1, whichPreferably, in the first step (S1), the three-dimensional finite element model front n is extracted by modal analysismOrder modal parameters, including modal frequency fiAnd a size of 3ne× 1 displacement mode shape
Figure FDA0002473361190000011
Size of 6ne× 1 stress mode shape SiOf size ne× 1 equivalent stress mode shape
Figure FDA0002473361190000012
Constructing a rotor blade full-field displacement modal shape matrix
Figure FDA0002473361190000013
Size of 3ne×nmConstructing a rotor blade full-field stress modal shape matrix
Figure FDA0002473361190000014
Size of 6ne×nmConstructing a rotor blade full-field equivalent stress modal shape matrix
Figure FDA0002473361190000015
Size ne×nmWherein n ismRepresenting the number of modes, i representing the order of the modes, neThe number of rotor blade finite element model elements is indicated.
3. The method according to claim 2, wherein in the first step (S1), the stresses of the elements in the finite element model of the rotor blade comprise 3 positive stresses σx、σy、σzAnd 3 shear stresses τxy、τyz、τxzAnd 6 stress components are provided, and each unit has a stress mode shape in 6 directions.
4. The method of claim 1, wherein in the second step (S2), the tip is timed to arrange circumferentially the number of sensors nbWith the number n of vibration modes measuredmThe relationship satisfies: n isb≥2nm+1, optimizing the position angle of the timing sensor at the blade end along the circumferential direction, and constructing a circumferential layout optimization matrix Tb：
Figure FDA0002473361190000021
，
Wherein, the layout optimization matrix TbSize nb×(2nm+1)，nbNumber of tip timing sensors, n, mounted for rotor blades circumferentially of the casingmRepresenting the number of modes, θjDenotes a tip timing sensor j (j ═ 1.. n)b) The position of the casing relative to the speed sensor is used as a reference O DEG, EOiDenotes the excitation order (i ═ 1.., n) of a multi-modal vibration of the rotor bladem) (ii) a After the position angle of the casing which cannot be provided with the sensor in the circumferential direction is eliminated, n is randomly selectedbThe circumferential angles form the initial matrix T optimized by the circumferential layoutb1And calculating the matrix condition number k1Repeating the random angle selection process R times, and respectively calculating the optimization matrix T formed by the angle selection processbi(i 1.., R), the angle combination in which the matrix condition number is the smallest is selected as the position angle at which the tip timing sensor is mounted in the circumferential direction of the casing.
5. The method according to claim 2, wherein in a third step (S3), a matrix of scale factors of rotor blade tip single position unit displacements and full field unit dynamic stresses of the rotor blade is constructed:
Figure FDA0002473361190000031
wherein S isi，jRepresenting the jth order stress mode shape of the ith unit of the finite element model of the blade, and since each unit has 6 directions of stress mode shapes, the matrix size is 6ne×nm；
Figure FDA0002473361190000032
Representing the jth order displacement mode vibration mode of a blade end timing measurement unit, wherein the conversion factor matrix is corresponding to the mode displacement from the full-field unit mode stress to a single unit mode;
constructing a conversion factor matrix of the unit displacement of the single position of the blade end of the rotor blade and the full-field equivalent stress of the blade:
Figure FDA0002473361190000041
matrix size ne×nm(ii) a Wherein the content of the first and second substances,
Figure FDA0002473361190000042
and representing the j-th order stress modal shape of the ith unit of the finite element model of the blade, wherein the conversion factor matrix is the correspondence from the full-field unit modal equivalent stress to the single unit modal displacement.
6. The method of claim 5, wherein in the fourth step (S4), n is utilizedbThe blade end timing sensor obtains N in the Nth turn of the unit measured by the blade end of the rotor bladebObtaining the undersampled multi-mode vibration signal X of the leaf end unit by the vibration data of each time pointb(t); undersampled vibration signal Xb(t) obtaining n under multi-modal vibration of the rotor blade based on circumferential Fourier algorithm decouplingmOrder vibration parameters:
Figure FDA0002473361190000043
wherein the content of the first and second substances,
Figure FDA0002473361190000044
Aishowing the amplitude, f, of the ith order vibrationiRepresents the i-th order vibration mode frequency,
Figure FDA0002473361190000045
Representing the i-th order vibration initiationA phase; upper label
Figure FDA0002473361190000046
Represents a generalized inverse of the matrix; the superscript T represents the transposition of the matrix to obtain a decoupling rear leaf end unit nmStep vibration signal:
Figure FDA0002473361190000047
wherein, Xb，i(t) represents the decoupled ith order vibration signal (i ═ 1.., n)m)，ωiRepresenting the ith order circumferential frequency after decoupling, and t representing the moment of vibration of the rotor blades.
7. The method of claim 6, wherein in a fifth step (S5), the matrix of scale factors T and decoupled n from the cell displacement and full-field dynamic stressmVibration signal Xb，i(t), the dynamic stress of all units of the full field of the rotor blade at any moment t is represented by the formula
Figure FDA0002473361190000051
Calculated, wherein:
Figure FDA0002473361190000052
the stress s (t) comprises a positive stress and a shear stress; wherein σi，xRepresenting the positive stress response, sigma, of the ith element of the finite element model of the blade in the x directioni，yRepresenting the positive stress response, sigma, of the ith element of the finite element model of the blade in the y directioni，zRepresenting the positive stress response, tau, of the ith element of the finite element model of the blade in the z directioni，xyRepresenting the shear stress response of the ith unit of the blade finite element model in the x-y direction, taui，yzRepresenting the shear stress response, tau, of the ith element of the finite element model of the blade in the y-z directioni，xzAnd showing the x-z direction shear stress response of the ith unit of the finite element model of the blade.
8. The method of claim 7, wherein the sixth stepIn step (S6), the matrix T of scale factors for the shift from cell to full-field equivalent stressseAnd n after decouplingmOrder vibration signal Xb，i(t) all unit equivalent stresses of the rotor blade at any time t blade full field are calculated by formula
Figure FDA0002473361190000053
And calculating to obtain the equivalent stress which is the synthetic equivalent value of the normal stress and the shearing stress, has no direction and is constant in a positive value.
9. A measurement system for carrying out the method of any one of claims 1 to 8, the measurement system comprising,
a plurality of tip timing sensors circumferentially arranged to the rotor blade case;
the blade end timing vibration measurement module is connected with the blade end timing sensor to measure multi-mode vibration signals of the blade end unit of the rotor blade;
the calculation unit is connected with the blade end timing vibration measurement module and comprises:
a modal analysis module configured to perform modal analysis based on the three-dimensional finite element model of the rotor blade to be tested to obtain the front n of the rotor blademOrder mode frequency fiMode of vibration of displacement
Figure FDA0002473361190000061
Harmonic stress mode shape SiAnd equivalent stress mode vibration mode
Figure FDA0002473361190000062
A measurement point optimization selection module configured to optimize the measurement number of the blade end timing sensors and the installation angle at the casing, wherein the number n of the blade end timing circumferentially arranged sensorsbWith the number n of vibration modes measuredmThe relationship satisfies: n isb≥2nm+1, determining the minimum number of sensors based on the modal number, and constructing a circumferential layout optimization matrix TbEliminating the position angle of the casing which can not be mounted with the sensor in the circumferential directionThen, n is randomly selectedbThe circumferential angles form an initial matrix T optimized in circumferential layoutb1And calculating the matrix condition number k1Repeating the random angle selection process R times, and respectively calculating the optimization matrix T formed by the angle selection processbi(i 1.., R), selecting an angle combination in which the matrix condition number is the smallest as a position angle at which the tip timing sensor is mounted in the circumferential direction of the casing,
a conversion factor matrix calculation module configured to construct a conversion factor matrix of blade tip unit displacement and full-field dynamic stress, construct a conversion factor matrix of blade tip unit displacement and full-field equivalent stress,
and the stress field reconstruction module is configured to calculate the normal stress, the shear stress and the equivalent stress of all units on the surface and inside of the blade at each rotation or any time of the rotor blade.
CN202010369992.0A 2020-04-29 2020-04-29 Rotor blade dynamic stress field measuring method and system based on blade end timing Pending CN111507043A (en)

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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112362275A (en) * 2020-10-27 2021-02-12 湖南工业大学 Method and device for reducing timing measurement deviation of blade vibration blade end under variable rotating speed
CN112763103A (en) * 2020-12-24 2021-05-07 中国飞行试验研究院 Non-contact dynamic stress calibration method for rotor blade
CN113029481A (en) * 2021-02-25 2021-06-25 中国人民解放军国防科技大学 Method for measuring torsional vibration of blade
CN113624381A (en) * 2021-07-26 2021-11-09 中国船舶重工集团公司第七0三研究所 Non-contact measurement and calculation method for dynamic stress of moving blade of ship gas turbine

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104268335A (en) * 2014-09-23 2015-01-07 工业和信息化部电子第五研究所 Vibration fatigue life predication method and system for micro-packaging assembly
CN106528932A (en) * 2016-10-09 2017-03-22 西安交通大学 Vibration stress numerical analysis method for turbomachinery blades
CN109060326A (en) * 2018-07-19 2018-12-21 北京航空航天大学 A kind of turbine blade root position simulation test piece and design method
CN109883380A (en) * 2019-03-22 2019-06-14 西安交通大学 A kind of rotor blade displacement field measurement method and its system based on blade tip-timing
CN110375690A (en) * 2019-03-22 2019-10-25 西安交通大学 A kind of rotating vane contactless displacement field measurement method and its system
CN110608710A (en) * 2019-03-22 2019-12-24 西安交通大学 Rotor blade dynamic strain field measuring method and system based on blade end timing

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104268335A (en) * 2014-09-23 2015-01-07 工业和信息化部电子第五研究所 Vibration fatigue life predication method and system for micro-packaging assembly
CN106528932A (en) * 2016-10-09 2017-03-22 西安交通大学 Vibration stress numerical analysis method for turbomachinery blades
CN109060326A (en) * 2018-07-19 2018-12-21 北京航空航天大学 A kind of turbine blade root position simulation test piece and design method
CN109883380A (en) * 2019-03-22 2019-06-14 西安交通大学 A kind of rotor blade displacement field measurement method and its system based on blade tip-timing
CN110375690A (en) * 2019-03-22 2019-10-25 西安交通大学 A kind of rotating vane contactless displacement field measurement method and its system
CN110608710A (en) * 2019-03-22 2019-12-24 西安交通大学 Rotor blade dynamic strain field measuring method and system based on blade end timing

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
HAO LIN等: "Effects of thermal and mechanical combined load on blade stress and fatigue life characteristic", 《2017 IEEE INTERNATIONAL CONFERENCE ON MECHATRONICS AND AUTOMATION (ICMA)》 *
马辉等: "变厚度壳单元的旋转叶片振动响应分析", 《机械设计与制造》 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112362275A (en) * 2020-10-27 2021-02-12 湖南工业大学 Method and device for reducing timing measurement deviation of blade vibration blade end under variable rotating speed
CN112362275B (en) * 2020-10-27 2021-08-13 湖南工业大学 Method and device for reducing timing measurement deviation of blade vibration blade end under variable rotating speed
CN112763103A (en) * 2020-12-24 2021-05-07 中国飞行试验研究院 Non-contact dynamic stress calibration method for rotor blade
CN113029481A (en) * 2021-02-25 2021-06-25 中国人民解放军国防科技大学 Method for measuring torsional vibration of blade
CN113624381A (en) * 2021-07-26 2021-11-09 中国船舶重工集团公司第七0三研究所 Non-contact measurement and calculation method for dynamic stress of moving blade of ship gas turbine
CN113624381B (en) * 2021-07-26 2023-10-03 中国船舶重工集团公司第七0三研究所 Non-contact measurement and calculation method for ship gas turbine moving blade stress

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