CN114623994A - Blade multi-modal coupling synchronous vibration parameter identification method based on blade tip timing - Google Patents

Blade multi-modal coupling synchronous vibration parameter identification method based on blade tip timing Download PDF

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CN114623994A
CN114623994A CN202210038627.0A CN202210038627A CN114623994A CN 114623994 A CN114623994 A CN 114623994A CN 202210038627 A CN202210038627 A CN 202210038627A CN 114623994 A CN114623994 A CN 114623994A
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blade
sensor
synchronous vibration
tip timing
vibration
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段发阶
支烽耀
牛广越
李芳怡
周琦
蒋佳佳
刘志博
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Tianjin University
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    • G01M7/00—Vibration-testing of structures; Shock-testing of structures
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    • G01—MEASURING; TESTING
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    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention relates to a blade multi-mode coupling synchronous vibration parameter identification method based on blade tip timing, which comprises the steps of measuring synchronous vibration parameters of a blade by utilizing a plurality of blade tip timing sensors arranged on a casing; obtaining synchronous vibration parameters of each order of modal of the blade from the blade tip timing data, and executing the following steps: installing a blade tip timing sensor on a rotating mechanical casing, and selecting one sensor as a No. 0 sensor; recording the vibration displacement value of the blade measured by each blade tip timing sensor; calculating the blade vibration displacement difference measured by other sensors relative to the sensor No. 0; acquiring a frequency multiplication range of the blade which is possible to synchronously vibrate around the rotating speed omega by means of a blade campbell diagram; solving the residual error and the root mean square value of the actually measured vibration displacement value difference of the solution vector; and calculating synchronous vibration parameters of the blades, including the amplitude, frequency and phase of each order of modal synchronous vibration of the blades.

Description

Blade multi-mode coupling synchronous vibration parameter identification method based on blade tip timing
Technical Field
The invention relates to a blade multi-mode coupling synchronous vibration parameter identification method based on blade tip timing.
Background
The high-rotating-speed blade is used as a core acting element of important equipment such as an aircraft engine, a steam turbine, a gas turbine, a flue gas turbine, a blower and the like, and the health state of the high-rotating-speed blade is very important for the operation safety of a rotating machine. The blade tip timing is used as a technology for effectively measuring the vibration of the rotary blade, and the real-time monitoring of the blade vibration and the fault diagnosis of the blade can be realized. Compared with the traditional strain gauge measurement, the blade tip timing has the advantages of non-contact, low penetration and capability of realizing full-blade measurement. The tip timing is used as an undersampling measurement method, and a challenge is provided for vibration parameter identification based on the tip timing. In order to extract blade vibration parameters from the undersampled signals, parameter identification methods such as circumferential Fourier fitting, single parameter, double parameter and space algorithm are developed. However, during operation of the high-speed blades, multi-mode coupling synchronous vibration occurs. The research of identifying the synchronous vibration parameters of the multi-modal coupling of the blade by using the blade tip technology is rarely reported, and how to identify the multi-modal coupling synchronous vibration parameters of the blade by using the blade tip timing is a problem to be solved in the prior art.
Disclosure of Invention
The invention aims to provide a blade multi-mode coupling synchronous vibration parameter identification method based on blade tip timing, aiming at the problems in the prior art. According to the method, firstly, the difference value of the vibration displacement values of the blade measured by the multi-blade tip timing sensor is calculated, then the frequency traversal range is obtained according to the Campbell diagram, and finally the vibration amplitude, frequency, phase and frequency parameters of the blade when multi-modal coupling synchronous vibration occurs are obtained, so that multi-modal coupling synchronous vibration parameter identification of the blade is effectively realized. The technical scheme is as follows:
a blade multi-mode coupling synchronous vibration parameter identification method based on blade tip timing is characterized in that a plurality of blade tip timing sensors mounted on a casing are utilized to measure blade synchronous vibration parameters; acquiring synchronous vibration parameters of each order of modal of the blade from the blade tip timing data, and executing the following steps:
1) the tip timing sensor is installed on a rotating mechanical casing, one sensor is selected as a sensor No. 0, the rotating direction of the blade is the positive direction, and the numbers of other tip timing sensors are as follows: 1,2, …, n, and the included angles of the sensors relative to the number 0 are respectively delta alpha1,Δα2,…,Δαn；
2) A certain blade generates multi-mode coupling synchronous vibration at the rotating speed omega, and the vibration displacement value of the blade measured by each blade tip timing sensor is recorded:
Y＝(y0 y1 y2 … yn)T (1)
3) calculating the blade vibration displacement difference measured by other sensors relative to the sensor No. 0:
ΔY＝(Δy1 Δy2 … Δyn)T (2)
4) obtaining the frequency multiplication range of the blade which is possible to synchronously vibrate around the rotating speed omega by using a blade Campbell diagram, and setting the frequency multiplication range of the ith order mode which is possible to synchronously vibrate as EOimin～EOimaxWhen i is 1,2, …, m is the maximum modal order, the traversal interval of the frequency factor under each order mode is represented as:
EOi∈{EOi|0,EOimin≤EOi≤EOimax} (3)
5) traversing the frequency multiplication intervals under the modes of each order, and solving a corresponding solution vector X by using the formulas (4) and (5):
Figure RE-GDA0003616289720000021
X＝(x1 x2 … x2m)T＝(BTB)-1BTΔY (5)
6) solving a residual error E of the solution vector X and the actually measured vibration displacement value difference value delta Y and a root mean square value S thereof by using an equation (6) and an equation (7):
E＝BX-ΔY (6)
Figure RE-GDA0003616289720000022
7) comparing all residual square root values S, and recording the frequency multiplication number EO corresponding to each order mode when S is minimumi *Sum vector X*When the corresponding EO is presenti *Synchronizing the frequency multiplication number of the vibration for each order of mode;
8) and (3) calculating blade synchronous vibration parameters by using the expressions (29) to (10), wherein the blade synchronous vibration parameters comprise the amplitude, the frequency and the phase of each order mode synchronous vibration of the blade, and the phase is the initial phase when the blade reaches the sensor 0.
The ith order modal synchronous vibration amplitude:
Figure RE-GDA0003616289720000023
ith order mode synchronous vibration frequency:
fi＝EOi *·Ω (9)
the ith order mode synchronous vibration phase:
Figure RE-GDA0003616289720000024
due to the adoption of the technical scheme, the invention has the following advantages:
(1) in the method provided by the invention, the Blade Tip Timing (BTT) sensor can be installed at any angle and is not limited by installation conditions.
(2) The invention does not need an OPR (optical phase response) sensor for blade tip timing, and solves the problem that the OPR sensor is difficult to install in the traditional blade tip timing method.
(3) The invention provides a method for identifying multi-mode coupled synchronous vibration parameters of a blade.
Drawings
FIG. 1 is a schematic view of tip timing sensor angles.
FIG. 2 is a flow chart of a blade multi-modal coupling synchronous vibration parameter identification method based on blade tip timing.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
The invention provides a blade multi-mode coupling synchronous vibration parameter identification method based on blade tip timing. The blade tip timing is to measure synchronous vibration parameters of the blades by utilizing a plurality of Blade Tip Timing (BTT) sensors arranged on a casing; in the multi-mode coupling, the blades synchronously vibrate at a certain one-order or multi-order at a certain rotating speed; the synchronous vibration is carried out, and the vibration frequency is integral multiple of the rotation speed frequency; the parameter identification method is used for acquiring parameters of amplitude, frequency, phase and frequency multiplication of each order modal vibration of the blade from the blade tip timing data.
The multi-mode coupled vibration of the blade refers to synchronous vibration of two or more orders of the blade at a certain rotating speed. The blade vibration displacement can now be written as:
Figure RE-GDA0003616289720000031
wherein A isi,EOi,
Figure RE-GDA0003616289720000036
(i is 1,2, …, m is the maximum modal order) is the modal vibration amplitude, frequency multiplication factor and initial phase of each order, and Ω is the rotation speed frequency. Setting n leaf apex timing sensors to be arranged according to the rotation direction, wherein the sensor angle is as follows: alpha is alpha0,α1,α2,…,αn. Any one of the sensors is a 0-th sensor, and the rotation direction isIn the positive direction, the angular difference between sensor j and sensor 0 is: delta alpha1,Δα2,…,ΔαnAs shown in fig. 1. The displacement values measured by different blade tip timing sensors are as follows:
Figure RE-GDA0003616289720000032
the moment when the blade reaches the sensor 0 is the time zero point t0When 0, the blade reaches sensor j at the time:
Figure RE-GDA0003616289720000033
wherein k is the number of revolutions. The blade vibration displacement difference measured by the sensor j relative to the sensor 0 is as follows:
Figure RE-GDA0003616289720000034
after deployment can be written as:
Figure RE-GDA0003616289720000035
when the blade synchronously vibrates at constant speed, different sensors measure to obtain constant displacement values y0,y1,y2,…,yn. The difference between the displacement values of sensor j and sensor 0 is Δ y1,Δy2,…,ΔynExpressed as:
ΔY＝(Δy1 Δy2 … Δyn)T (16)
the difference in the measured vibration displacement values of the sensors can be expressed as:
ΔY＝BX (17)
Figure RE-GDA0003616289720000041
Figure RE-GDA0003616289720000042
regarding the vector X as an unknown vector, regarding the matrix B as a coefficient matrix, and regarding the equation as Ai,
Figure RE-GDA0003616289720000046
(i ═ 1,2, …, m) for a total of 2m unknown parameters. Therefore, if the coupling of m-order modes is solved, the number of required sensors is at least 2m, and the more the number of sensors is, the more accurate the identification result is. When the number of the sensors is more than 2m, the above equation is an overdetermined linear equation set. If the frequency is doubled EOiOther vibration parameters can be solved by the least square method, as known. In practical application, the modal frequency multiplication number EO of each orderiCan be estimated or obtained by a priori knowledge such as a campbell diagram. Thus, certain EO may be selectediRange, it is traversed. Let EO be the frequency range of possible synchronous vibration of ith order (i ═ 1,2, …, m) modeimin～EOimaxThen, the frequency multiplication traversal interval under each order of mode is:
EOi∈{EOi|0,EOimin≤EOi≤EOimax} (20)
to EO as possibleiRespectively substituting into the equation system, and solving a corresponding solution vector X by a least square method:
X＝(BTB)-1BTΔY (21)
the residue of the least squares solution X substituted into equation (18) and the actual measured vibration displacement value difference Δ Y is defined as:
E＝BX-ΔY (22)
wherein E ═ E (E)1 e2 … en)T。
The square mean root of the residual E represents the magnitude of the deviation of the traversal estimate from the actual measurement:
Figure RE-GDA0003616289720000043
setting the frequency multiplication number of actual vibration of each step of the blade as
Figure RE-GDA0003616289720000044
Time, theoretical coefficient matrix B*And solution vector X*The formula (17) is completely satisfied, i.e. the corresponding displacement residual error magnitude S*0. Considering various errors existing in actual measurement, when the traversal frequency multiplication is correct, S takes the minimum value. Thereby obtaining a solution vector X*And calculating the synchronous vibration parameters of the blades by the following formula:
angular frequency of vibration of each order:
ωi＝2πEOi *·Ω (24)
vibration amplitude of each order:
Figure RE-GDA0003616289720000045
vibration phase of each order (initial phase when the blade reaches sensor 0):
Figure RE-GDA0003616289720000051
the flow chart of the blade multi-modal coupling synchronous vibration parameter identification method based on blade tip timing in the embodiment of the invention is shown in FIG. 2, and the specific implementation process is as follows:
(1) 7 blade tip timing sensors are installed on a rotating mechanical casing, one of the sensors serves as a sensor No. 0, and included angles of other sensors relative to the sensor No. 0 are respectively as follows: delta alpha1＝18.4°,α2＝36°,α3＝53.6°,α4＝72.3°,α5＝119.5°,α6＝238.9°。
(2) The blade 1 generates multi-mode coupling synchronous vibration at 3000rpm, and the blade tip timing sensor records the blade vibration displacement value Y (2mm,1.8544mm,0.0292mm,0.2577mm, -2.5661mm, -1.1159mm, -1.1067mm)T。
(3) Calculate othersThe blade vibration displacement difference delta Y measured by the sensor relative to the sensor No. 0 is (-0.1456mm, -1.9708mm, -1.7423mm, -4.5661mm, -3.1159mm, -3.1067mm)T。
(4) With the aid of the vane campbell diagram, coupled vibration of a first-order mode and a second-order mode of the vane can occur around the rotating speed of 3000rpm, and the frequency multiplication traversal interval is shown as a formula (27) and a formula (28). In addition, because synchronous vibration exceeding 6 orders of modes hardly occurs in the blade operation process, only the frequency multiplication interval of the synchronous vibration possibly occurring in 1-6 orders of modes is needed.
EO1∈{EO1|0≤EOi≤4} (27)
EO2∈{EO2|0,7≤EO2≤11} (28)
(5) Traversing the frequency multiplication interval, and solving the corresponding solution vector X by using the formula (18) and the formula (21).
(6) And solving a residual error E and a root mean square value S of the solution vector X and the actually measured vibration displacement value difference delta Y by using the formula (22) and the formula (23), and comparing all the residual error root mean square values S.
(7) S when the root mean square value of the residual error is minimum*0.0014, the corresponding frequency multiplier is: EO (ethylene oxide)1 *＝2、EO2 *9. The corresponding solution vector X is (2.0023, -0.0028, -0.0020, -1.0012)T。
(8) The amplitude, the frequency and the phase of the first-order modal vibration of the blade are respectively as follows:
Figure RE-GDA0003616289720000052
f1＝EO1 *·Ω＝2×50＝100Hz (30)
Figure RE-GDA0003616289720000053
the amplitude, the frequency and the phase of the second-order modal vibration of the blade are respectively as follows:
Figure RE-GDA0003616289720000054
f2＝EO2 *·Ω＝9×50＝450Hz (33)
Figure RE-GDA0003616289720000055

Claims (1)

1. a blade multi-mode coupling synchronous vibration parameter identification method based on blade tip timing is characterized in that a plurality of blade tip timing sensors mounted on a casing are utilized to measure blade synchronous vibration parameters; acquiring synchronous vibration parameters of each order of modal of the blade from the blade tip timing data, and executing the following steps:
1) the tip timing sensor is installed on a rotating mechanical casing, one sensor is selected as a sensor No. 0, the rotating direction of the blade is the positive direction, and the numbers of other tip timing sensors are as follows: 1,2, …, n, and the included angles of the sensors relative to the number 0 are respectively delta alpha1,Δα2,…,Δαn；
2) A certain blade generates multi-mode coupling synchronous vibration under the rotating speed omega, and the vibration displacement value of the blade measured by each blade tip timing sensor is recorded:
Y＝(y0 y1 y2 … yn)T (1)
3) calculating the blade vibration displacement difference measured by other sensors relative to the sensor No. 0:
ΔY＝(Δy1 Δy2 … Δyn)T (2)
4) obtaining the frequency multiplication range of the blade which is possible to synchronously vibrate around the rotating speed omega by using a blade Campbell diagram, and setting the frequency multiplication range of the ith order mode which is possible to synchronously vibrate as EOimin～EOimaxWhen i is 1,2, …, m is the maximum modal order, the traversal interval of the frequency factor under each order mode is represented as:
EOi∈{EOi|0,EOimin≤EOi≤EOimax} (3)
5) traversing the frequency multiplication intervals under the modes of each order, and solving a corresponding solution vector X by using the formulas (4) and (5):
Figure FDA0003469328390000011
X＝(x1 x2 … x2m)T＝(BTB)-1BTΔY (5)
6) solving a residual error E of the solution vector X and the actually measured vibration displacement value difference value delta Y and a root mean square value S thereof by using an equation (6) and an equation (7):
E＝BX-ΔY (6)
Figure FDA0003469328390000012
7) comparing all residual square root values S, and recording the frequency multiplication number EO corresponding to each order mode when S is minimumi *Sum vector X*When the corresponding EO is presenti *Synchronizing the frequency multiplication number of the vibration for each order of mode;
8) and (3) calculating synchronous vibration parameters of the blade by using the equations (8) to (10), wherein the synchronous vibration parameters comprise the amplitude, the frequency and the phase of each order mode synchronous vibration of the blade, and the phase is the initial phase when the blade reaches the sensor 0.
The ith order mode synchronous vibration amplitude is as follows:
Figure FDA0003469328390000021
ith order mode synchronous vibration frequency:
fi＝EOi *·Ω (9)
the ith order mode synchronous vibration phase:
Figure FDA0003469328390000022
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Publication number Priority date Publication date Assignee Title
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CN104697623A (en) * 2014-10-24 2015-06-10 南京航空航天大学 Method of recognizing asynchronous vibration parameters of blades under variable speed excitation
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CN110851963A (en) * 2019-10-25 2020-02-28 西安交通大学 Casing circumferential arrangement method of blade end timing sensor
WO2020192621A1 (en) * 2019-03-22 2020-10-01 西安交通大学 Measurement method for rotor blade dynamic strain field based on blade tip timing and system thereof
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101629846A (en) * 2009-07-31 2010-01-20 天津大学 Method for detecting synchronous vibration parameters of high-speed rotary blade under constant speed
US20130247671A1 (en) * 2011-09-13 2013-09-26 Kabushiki Kaisha Toshiba Blade vibration measuring apparatus
CN104697623A (en) * 2014-10-24 2015-06-10 南京航空航天大学 Method of recognizing asynchronous vibration parameters of blades under variable speed excitation
CN105424160A (en) * 2015-11-20 2016-03-23 天津大学 Method for realizing blade synchronous vibration parameter identification
WO2020192621A1 (en) * 2019-03-22 2020-10-01 西安交通大学 Measurement method for rotor blade dynamic strain field based on blade tip timing and system thereof
CN110851963A (en) * 2019-10-25 2020-02-28 西安交通大学 Casing circumferential arrangement method of blade end timing sensor
CN112179480A (en) * 2020-08-26 2021-01-05 西安交通大学 Method and system for identifying timing vibration parameters of harmonic superposition fitting blade tip and electronic equipment

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Application publication date: 20220614