# US 11,898,453 B1 · Method for extracting natural frequency difference between blades by single blade tip timing sensor or uniformly distributed blade tip timing sensors > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 11,898,453 B1 - Document ID: US11898453B1 - Status: Granted - Kind: B1 - Application number: 17/970,361 - Filed: 2022-10-20 - Granted: 2024-02-13 - Earliest claimed: 2022-10-20 - Assignees: Xi'an Jiaotong University - Applicants: Xi'an Jiaotong University - Inventors: Zhibo Yang; Jiahui Cao; Xuefeng Chen; Zengkun Wang; Laihao Yang; Shaohua Tian; Haoqi Li; Wenbo Li - Web page: https://patentgrep.com/patent/US11898453B1 ## CPC - F01D 21/003: {Arrangements for testing or measuring (for measuring vibrations G01H)} - G01M 5/0016: {of aircraft wings or blades} - G01M 5/0066: {by exciting or detecting vibration or acceleration (vibration testing of structures G01M7/00)} - G01M 15/14: Testing gas-turbine engines or jet-propulsion engines - F05D 2260/83: Testing, e.g. methods, components or tools therefor - F05D 2270/304: Spool rotational speed - F05D 2270/821: Displacement measuring means, e.g. inductive - F01D: NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES (machines or engines for liquids F03; non-positive displacement pumps F04D) - G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR - F05D: INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS ## Abstract The present disclosure discloses a method for extracting a natural frequency difference between blades by a single blade tip timing sensor or uniformly distributed blade tip timing sensors. The method includes the following steps: acquiring actual arrival time of a rotating blade by using a single blade tip timing sensor or uniformly distributed blade tip timing sensors, and converting a difference between theoretical arrival time and the actual arrival time into displacement data of a blade tip according to a rotational speed and a blade length of the rotating blade; selecting displacement data of blade tips of two rotating blades with the same blade length at the same rotational speed; intercepting the displacement data, performing discrete Fourier transform respectively, and making a sampling frequency approximate to an average rotational speed to obtain spectrum data. ## Claims ### Claim 1 A method for extracting a natural frequency difference between blades by a single blade tip timing sensor or uniformly distributed blade tip timing sensors, comprising the following steps: a first step (S1): acquiring actual arrival time of a rotating blade by using a single blade tip timing sensor or uniformly distributed blade tip timing sensors, and converting a difference between theoretical arrival time and the actual arrival time into displacement data of a blade tip according to a rotational speed and a blade length of the rotating blade; a second step (S2): selecting displacement data of blade tips of two rotating blades with the same blade length at the same rotational speed; a third step (S3): intercepting the displacement data, performing discrete Fourier transform respectively, with a sampling frequency approximate to an average rotational speed, to obtain spectrum data; and a fourth step (S4): respectively extracting, from the spectrum data, frequency remainders corresponding to the aliased natural frequencies of the two blades, and performing subtraction on the two frequency remainders to obtain the natural frequency difference between the two blades. ### Claim 2 (depends on 1) The method according to claim 1, wherein in the first step (S1), the single blade tip timing sensor collects the arrival time t of each blade, and a difference between theoretical arrival time and the actual arrival time is converted into a blade tip displacement according to the rotational speed fr and the blade length R of the blade, and an expression is as follows: x(ti,j)=2πR·fr·(ti,j−ti,j), where ti,j represents the actual arrival time of an i-th blade at a j-th turn; ti,j represents the theoretical arrival time, t _ i , j = 60 · ( θ i + a k ) 2 ⁢ π ⁢ n , where θi represents an angle of the i-th blade based on amounting position of a rotational speed sensor, αk represents an angle of a k-th sensor based on the mounting position of the rotational speed sensor, n is the rotational speed, and x(ti,j) represents the displacement of the ith blade at the j-th turn and at time ti,j. ### Claim 3 (depends on 2) The method according to claim 2, wherein the rotating process of the blade is an acceleration or deceleration process of a predetermined acceleration or a constant speed process; and in the rotating process, gas nozzles distributed uniformly in a circumferential direction are used to simulate gas excitation. ### Claim 4 (depends on 3) The method according to claim 3, wherein for the acceleration or deceleration process, displacement data for a displacement sequence number interval near a formant of one displacement of two blade displacements is selected, displacement data for the same displacement sequence number interval of the other blade displacement is selected, and the sampling frequency fs is approximately equal to the average rotational speed, f s ≈ n p N 2 - N 1 + 1 ⁢ ∑ i = N 1 N 2 f ri , where np represents the number of the sensors, N1 and N2 respectively represent intercepted data indexes, and fri represents the rotational speed of i-th data at sampling time. ### Claim 5 (depends on 1) The method according to claim 1, wherein in the third step (S3), the intercepted two segments of discrete displacement data are subjected to discrete Fourier transform to obtain the spectrum data, X ⁡ ( k ) = ∑ n = 0 N - 1 x ⁡ ( n ) ⁢ cos ⁡ ( 2 ⁢ π ⁢ k ⁢ n N ) - i ⁢ ∑ n = 0 N - 1 x ⁡ ( n ) ⁢ sin ⁡ ( 2 ⁢ π ⁢ k ⁢ n N ) , where x(n) is a signal obtained by sampling, i is an imaginary number symbol, i=√{square root over (−1)}, N is a length of an acquired signal, x is the number of elements, n is an iteration number, traversing is performed from 0 to N−1, that is, all elements in x are taken, k is an integer from 0 to N−1, and X(k) represents kth data after discrete Fourier transform. ### Claim 6 (depends on 5) The method according to claim 5, wherein in the fourth step (S4), since the sampling frequency is equal to rotational speed frequency, according to analysis on the aliasing situation of rotational frequency and multiplied frequency thereof, an under sampled spectrum is obtained by performing discrete Fourier transform on the original signal sequence, the frequency appears near the zero frequency in the under sampled spectrum, the frequency in the under sampled spectrum after blade vibration frequencies are aliased is extracted after a rotational speed frequency component is excluded, a frequency component with the maximum amplitude is extracted from the under sampled spectrum and is referred to as a frequency remainder fsub, the natural frequency difference Δf=f2sub−f1sub, and f2sub, f1sub respectively refer to the frequency remainders of a blade 2 and a blade 1.