Dynamic strain field measuring method and system for rotor blade based on blade tip timing

A dynamic strain field measuring method for a rotor blade based on blade tip timing to obtain sensing blade tip vibration information by virtue of blade tip timing sensors mounted close to an inner side of a casing, comprising the following steps:

• in the first step (S1), determining a to-be-measured rotor blade for the dynamic strain field measuring;
• establishing a three-dimensional finite element model of the to-be-measured rotor blade, and extracting modal parameters of the three-dimensional finite element model, wherein the three-dimensional finite element model is made of a metal with a density, a Poisson ratio and an elasticity modulus;
• the rotor blade has a length, a thickness and a width;
• the three-dimensional finite element model has a plurality of nodes in total;
• and two side surfaces of a root of the rotor blade are fixedly restricted to simulate a working state of the rotor blade;
• and wherein strains comprises six strain components, including the three positive strains εx, εy, εz and three shearing strains γxy, γyz, γxz;
• and wherein in the first step (S1), first nm order modal parameters:
• a modal frequency fi, a displacement modal shape ϕi with the size being ndof×1 and a strain modal shape ψi with the size being 2ndof×1, of the three-dimensional finite element model are extracted by modal analysis, and a full-field strain modal shape matrix, ψ=[ψ1,ψ2, . . . ,ψnm] with the size being 2ndof×nm, of the rotor blade is constructed, wherein nm represents for a modal number, i represents for a modal order, ndof represents for the number of degrees of freedom of the finite element model of the rotor blade, ndof=3 nn, and nn represents for the number of nodes of the finite element model of the rotor blade;
• in the second step (S2), determining the number and circumferential mounting positions of the blade tip timing sensors, wherein the blade tip timing sensors are mounted in a circumferential direction of the casing;
• in the second step (S2), a relationship between the number nbtt of the blade tip timing sensors mounted in a circumferential direction of a rotor blade of the casing and the multimodal number nm of vibration is that:
• nbtt≥2nm+1;
• and
• a measuring point selection matrix Sbtt arranged in a circumferential direction of each of the blade tip timing sensors in the casing under multimodal excitation is constructed:
• S
• btt
• =
• 
• [
• ⁠
• 1
• sin
• ⁡
• (
• EO
• 1
• ⁢
• θ
• 1
• )
• cos
• ⁡
• (
• EO
• 1
• ⁢
• θ
• 1
• )
• …
• sin
• ⁡
• (
• EO
• n
• m
• ⁢
• θ
• 1
• )
• cos
• ⁡
• (
• EO
• n
• m
• ⁢
• θ
• 1
• )
• 1
• sin
• ⁢
• (
• EO
• 1
• ⁢
• θ
• 2
• )
• cos
• ⁡
• (
• EO
• 1
• ⁢
• θ
• 2
• )
• …
• sin
• ⁢
• (
• EO
• n
• m
• ⁢
• θ
• 2
• )
• cos
• ⁡
• (
• EO
• n
• m
• ⁢
• θ
• 2
• )
• ⋮
• ⋮
• ⋮
• ⋮
• ⋮
• ⋮
• 1
• sin
• ⁢
• (
• EO
• 1
• ⁢
• θ
• n
• btt
• )
• cos
• ⁡
• (
• EO
• 1
• ⁢
• θ
• n
• btt
• )
• …
• sin
• ⁡
• (
• EO
• n
• m
• ⁢
• θ
• n
• btt
• )
• cos
• ⁡
• (
• EO
• n
• m
• ⁢
• θ
• n
• btt
• )
• ⁠
• ]
• wherein the size of the measuring point selection matrix Sbtt is nbtt×(2n+1), θj represents for layout angles of the blade tip timing sensors (j=1, . . . nbtt) in the casing, nbtt represents for the total number of the (j=1, . . . nbtt) to blade tip timing sensors arranged in the circumferential direction, and EOi represents for a concerned excitation order (i=1, . . . nm);
• a position where a rotating speed sensor is located serves as a reference 0°, a limited mounting angle range of the casing is removed, and nbtt angles are randomly selected in the circumferential direction of the casing to serve as mounting positions of the blade tip timing sensors;
• and the condition number κ of the blade tip timing measuring point selection matrix Sbtt is calculated, a random process is repeated for R times, and a measuring point layout when the condition number κ of the matrix is minimum is selected therefrom;
• in the third step (S3), establishing a mapping relationship between single-point displacement and full-field dynamic strains of the blade;
• in the fourth step (S4), acquiring blade tip single-point displacement of the rotor blade based on the blade tip timing sensors, wherein the blade tip single-point displacement of the rotor blade is acquired based on the blade tip timing sensors;
• and
• in the fifth step (S5), realizing, by the single-point displacement, dynamic strain measurement in any position and direction of the rotor blade based on the mapping relationship;
• thereby realizing a reconstruction of full-field dynamic strains of the rotor blade by only utilizing finite measuring points of a tip of the rotator blade, and
• reconstructing the full-field dynamic strains of the blade, wherein the blade tip timing sensors are mounted according to the number and circumferential mounting positions determined in the second step (S2).