CN110319922B - Blade torsional vibration displacement measurement method based on blade tip timing principle - Google Patents

Blade torsional vibration displacement measurement method based on blade tip timing principle Download PDF

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CN110319922B
CN110319922B CN201910607117.9A CN201910607117A CN110319922B CN 110319922 B CN110319922 B CN 110319922B CN 201910607117 A CN201910607117 A CN 201910607117A CN 110319922 B CN110319922 B CN 110319922B
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blade
blade tip
tip timing
torsional vibration
resonance
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CN110319922A (en
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段发阶
邓震宇
傅骁
牛广越
刘志博
程仲海
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Smartmens Tianjin Technology Co ltd
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Tianjin University
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    • G01MEASURING; TESTING
    • G01HMEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups

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Abstract

The invention relates to a blade torsional vibration displacement measurement method based on a blade tip timing principle, which is characterized in that two groups of blade tip timing sensors, namely an air inlet side blade tip timing sensor and an air outlet side blade tip timing sensor, are arranged at the same circumferential position on a rotary mechanical casing along the axial direction of a rotor and are used for measuring the time that the air inlet side and the air outlet side of the blade end of the same blade reach the blade tip timing sensor in the same circle; the two blade tip timing sensors are arranged at projection points of the maximum displacement position of the torsion resonance blade tip on the horizontal line of the static position of the blade tip, which is called a torsion resonance projection method, and the torsion resonance projection method is used for realizing the optimal positioning of the blade tip timing sensors by combining the torsion resonance parameters of the blade so as to ensure that the two blade tip timing sensors can accurately sample the blade tip arrival time signals under the condition that the blade generates torsion resonance and torsion non-resonance; and the measurement of the torsional vibration displacement of the blade is realized.

Description

Blade torsional vibration displacement measurement method based on blade tip timing principle
Technical Field
The invention belongs to the field of rotary machine state monitoring, in particular to a blade torsional vibration displacement measurement method based on a blade tip timing principle.
Technical Field
Important rotary machines such as aeroengines, steam turbines and the like are core components of key equipment such as military aircrafts, commercial aircrafts, generator sets, steam sets and the like in the fields of aerospace and industry. Especially, the moving blade is used as a core element for working of the rotary machine, and the working state of the moving blade directly influences the working efficiency and the conditions of safety, stability, long-period running and the like of the important key equipment. At present, a rotary blade vibration measurement technology based on a blade tip timing principle is a typical non-contact measurement method, and the basic principle is that a certain number of sensors are arranged on a rotary machine casing, the arrival time of a rotary blade passing through the sensors is measured, and the measurement of parameters of blade vibration such as vibration amplitude, vibration frequency, vibration phase and the like is realized through a relevant identification algorithm. Compared with the traditional offline blade state detection method, strain gauge method, frequency modulation method, acoustic method and other online detection methods, the blade tip timing technology has the advantages of non-contact measurement, real-time online monitoring, capability of measuring all blades and the like, and therefore has good engineering practicability.
On the one hand, the blade is one of the core components of a large rotary machine. Taking an aeroengine as an example, the working environment of the blade under the working condition is severe, and besides bearing centrifugal force, the blade is continuously influenced by the air flow exciting force, the atmospheric temperature difference, the high temperature and other environments. These external conditions create relatively complex periodic varying stresses on the rotating blades of the engine, and when the frequency of the external excitation force is at or near the natural frequency of a certain stage of the blade, the blade may experience faults such as blade cracks or blade breaks due to resonance. According to statistics, faults caused by mechanical vibration account for more than 60% of the total number of faults of the aero-engine, and blade vibration faults account for more than 70% of the total number of mechanical vibration faults, so that the blade vibration faults are important causes of the faults of the aero-engine, the vibration characteristics of the blades are researched, the running conditions of the blades are monitored on line in real time, and the method has important practical significance in research and development tests, state monitoring, fault diagnosis and other aspects of important rotating machinery such as the aero-engine, the steam turbine and the like.
On the other hand, when the blade works, forced vibration is mainly generated under the action of external periodically-changing exciting force, and according to different vibration expression forms, the blade vibration can be divided into three vibration modes of bending vibration, torsional vibration and bending-torsion compound vibration. The same blade has a plurality of different resonance frequencies, which are divided into first-order resonance and second-order resonance … … from small to large according to the resonance frequency, when the frequency of external exciting force is consistent with the resonance frequency of a certain order of the blade, the blade is excited to generate resonance, and the resonance of different orders corresponds toThe vibration modes are not necessarily the same. In the invention, the vibration with the vibration frequency of the blade not greater than the first-order resonance frequency is called low-order vibration, and the vibration with the vibration frequency of the blade greater than the first-order resonance frequency is called high-order vibration. The mode of first order resonance of a blade is typically bending vibration, also known as first order bending vibration. The first-order bending vibration is a main cause of generating cracks and root breakage at the root of the blade, has larger hazard and is relatively easy to realize, so that the first-order bending vibration is studied intensively at home and abroad. The existing tip timing measurement method comprises a quick vector end trace method [1] Double parameter method [2] Autoregressive method [3] And arbitrary angular distribution method based on sensor [4] And the like, only one blade tip timing sensor is arranged at the same circumferential position of the rotary mechanical casing, so that the measurement of the bending vibration displacement of the blade can be realized, and the measurement of the torsional vibration displacement of the blade can not be realized.
On the other hand, the vibration modes of the high-order vibration of the blade comprise three vibration modes of bending vibration, torsional vibration and bending-torsional composite vibration, and blade cracks or corner-falling faults caused by the torsional vibration also occur frequently, but because the high-order vibration of the blade has the measurement problems of small amplitude, complex vibration mode, difficult sensor layout and the like, the measurement method of the high-order vibration parameter of the blade is not studied at home and abroad, and particularly, the measurement method of the parameter such as the torsional vibration displacement of the blade is not reported.
[1]I.Y.Zablotsky and Yu.A.Korostelev.Measurement of resonance vibrations of turbine blades with the ELURA device[J].Energomashinostroneniye,1970,Vol.2:36-39.
[2]S Heath.A New Technique for Identifying Synchronous Resonances Using Tip-Timing[J].Journal of Engineering for Gas Turbines and Power,2000,122(2):219-225.
[3]J.Gallego-Garrido,G.Dimitriadis,and J.R.Wright,A Class of Methods for the Analysis of Blade Tip Timing Data from Bladed Assemblies Undergoing Simultaneous Resonances—Part I:Theoretical Development[J].International Journal of Rotating Machinery,2007,Vol.2007:1-11.
[4] Ouyang Tao the technique for detecting vibration of rotary blade and identifying parameters based on tip timing [ D ]. Doctor academic paper, tianjin university, 2011.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a novel method for measuring the torsional vibration displacement of the blade based on the blade tip timing principle, the optimal positioning of a blade tip timing sensor is realized through a torsional resonance projection method, and the measurement of the torsional vibration displacement of the blade is realized by utilizing the blade tip deflection angle when torsional vibration occurs. The technical scheme of the invention is as follows:
the blade torsional vibration displacement measurement method based on the blade tip timing principle is characterized in that two groups of blade tip timing sensors, namely an air inlet side blade tip timing sensor and an air outlet side blade tip timing sensor, are arranged at the same circumferential position on a rotary mechanical casing along the axial direction of a rotor and are used for measuring the time that the air inlet side and the air outlet side of the same blade tip reach the blade tip timing sensor in the same circle; the two blade tip timing sensors are arranged at projection points of the maximum displacement position of the torsion resonance blade tip on the horizontal line of the static position of the blade tip, which is called a torsion resonance projection method, and the torsion resonance projection method is used for realizing the optimal positioning of the blade tip timing sensors by combining the torsion resonance parameters of the blade so as to ensure that the two blade tip timing sensors can accurately sample the blade tip arrival time signals under the condition that the blade generates torsion resonance and torsion non-resonance; the measurement of the torsional vibration displacement of the blade is realized by calculating the blade tip deflection angle generated when the blade generates torsional vibration and combining the trigonometric function relation between the distance between two blade tip timing sensors and the length of the blade tip.
The measurement of the torsional vibration displacement of the blade specifically comprises the following steps:
(1) When the rotor is at angular velocity omega n1 When the low-speed rotating blades do not vibrate, all blade tips rotate to be always positioned at the static positions of the blade tips when passing through the blade tip timing sensors of the air inlet side and the air outlet side, so that the time difference delta t between each circle of blades reaching the blade tip timing sensors of the air inlet side and the air outlet side is equal to the time difference delta t between each circle of blades reaching the blade tip timing sensors of the air inlet side and the air outlet side n1 =0, torsional vibration displacement of 0
(2) When the rotor is at angular velocity omega n2 High speed rotating blade generationTorsional vibration, when a certain blade rotates to pass through two blade tip timing sensors, the real-time position of the blade tip of the blade periodically changes between the maximum displacement positions of the blade tips of torsional resonance, and when the blade passes through the two blade tip timing sensors on the inlet side and the outlet side in turn in the nth turn, the circumferential arc length of the blade tip along with the rotation of the rotor is as follows:
L n2 =Ω n2 RΔt n2 =h 3 +h 4 n=1.2.3., where Ω n2 The high-speed rotation angular velocity of the rotor when the blade generates torsional vibration is represented by R, the rotation radius of the blade tip is represented by h 3 The sensor detects the displacement of the inlet edge of the blade end when in torsional vibration, h 4 For the sensor measurement leaf end edge of giving vent to anger displacement when torsional vibration, at this moment, the torsional vibration leaf end deflection angle of leaf end real-time position is:
wherein d is the distance between two blade tip timing sensors;
(3) Because the positioning of the two blade tip timing sensors is based on a torsional resonance projection method, the inlet blade tip timing sensor and the outlet blade tip timing sensor measure the arrival time of the edge of the blade tip, so that the obtained L n2 Not the true torsional vibration displacement generated by the blade tip edge;
the following trigonometric function relationship is used:wherein p is the tip length, the blade having an angular velocity Ω n2 The torsional vibration displacement generated by the two blade tip timing sensors rotating at high speed through the air inlet side and the air outlet side is as follows:
the maximum deflection angle alpha of the torsional resonance blade tip is obtained by a blade natural frequency test, and the rotor rotation angular velocity omega n1 And omega n2 Obtained through actual measurement of a rotor speed measuring system, and the tip of the blade rotatesThe radius R, the length p of the blade tip and the distance d between two blade tip timing sensors are obtained from a design drawing, and the time difference delta t between the blade tip and the two blade tip timing sensors is the same n1 And Deltat n2 Obtained by actual measurement of a blade tip timing sensor.
The method overcomes the defect that the traditional blade tip timing measurement method cannot measure the torsional vibration displacement of the blade, and provides a novel blade tip timing measurement method based on the blade tip timing principle.
Drawings
FIG. 1 shows a diagram of a leaf tip timing principle measurement architecture
FIG. 2 shows a structure diagram of blade torsional vibration displacement measurement
FIG. 3 shows a blade first order torsional vibration mode diagram
FIG. 4 shows a top view of a blade torsional vibration displacement measurement sensor positioning
FIG. 5 shows a blade torsional vibration displacement measurement top view
The reference numerals in the figures illustrate:
in fig. 1, 1 is a tip timing sensor; 2 is a rotary machine casing; 3 is a blade;
in fig. 2, 4 is an intake side tip timing sensor; 5 is an air outlet edge blade tip timing sensor; 6 is a leaf end air inlet edge, 7 is a leaf end air outlet edge, and 8 is a signal processing system;
in fig. 3, 9 is the tip; 10 is a vibration pitch line; 11 is a vibration node;
in fig. 4, 4 is an intake side tip timing sensor; 5 is an air outlet edge blade tip timing sensor; 11 is a vibration node; 12 is the maximum displacement position of the torsional resonance blade end; 13 is the maximum off angle of the torsional resonance leaf end; 14 is the displacement of the air inlet edge of the torsional resonance blade end; 15 is the displacement of the air outlet edge of the torsional resonance blade end; 16 is the tip rest position;
in fig. 5, 2 is a rotary machine casing; 4 is an air inlet edge blade tip timing sensor; 5 is an air outlet edge blade tip timing sensor; 12 is the maximum displacement position of the torsional resonance blade end; 16 is the tip rest position; 17 is the real-time position of the torsional vibration leaf end; 18 is the rotor axial horizontal line; 19 is the off angle of the torsional vibration leaf end; 20 is that the sensor measures the displacement of the air inlet edge of the blade end during torsional vibration; 21 is the displacement of the air outlet edge of the blade end measured by the sensor during torsional vibration; 22 is the displacement of the air inlet edge of the real leaf end during torsional vibration; and 23 is the displacement of the air edge of the real leaf end during torsional vibration.
Detailed Description
The steps of making and operating the present invention are intended to be described as exemplary embodiments of the present invention, and are not intended to be the only forms that may be making or using, but are intended to be included within the scope of the present invention for other embodiments that perform the same function.
In the invention, the top end of a blade is called a blade tip, the circumferential direction of a rotary mechanical casing is called a circumferential direction, the side of the blade facing the airflow direction is called an air inlet side, the side of the blade facing away from the airflow direction is called an air outlet side, and the circumferential distance difference generated by two blade tip timing sensors of the blade tip edge passing through the air inlet side and the air outlet side in the same circle during torsional vibration is called blade torsional vibration displacement, and the preferred embodiment of the invention is described in detail below with reference to the attached drawings of the specification.
Tip timing principle structural measurement is shown in fig. 1, and the existing tip timing measurement method [1-4] Only one blade tip timing sensor 1 is arranged at the same circumferential position of a rotary machine casing 2, when each blade 3 rotates to pass through the blade tip timing sensor 1, an arrival pulse signal is generated, and a signal processing system utilizes the pulse time when the blade 3 arrives at the blade tip timing sensor 1 to realize the measurement of the blade bending vibration displacement;
the blade torsional vibration displacement measurement structure is shown in fig. 2, two groups of blade tip timing sensors are arranged at the same circumferential position of a rotary mechanical casing along the axial direction of a rotor, when the low-rotation-speed blade does not vibrate and the high-rotation-speed blade does torsional vibrate, the time that the blade tip air inlet side 6 reaches the air inlet side blade tip timing sensor 4 and the blade tip air outlet side 7 reaches the air outlet side blade tip timing sensor 5 is measured, and the blade torsional vibration displacement measurement is realized through the signal processing system 8;
as shown in figure 3, when the blade vibrates, a connecting line formed by points with zero vibration displacement on the blade body is called a vibration node line, an intersection point of the vibration node line and the blade tip is called a vibration node, when the blade vibrates in a first-order torsional mode, the air inlet edge and the air outlet edge of the blade tip do relative torsional motion around the vibration node line 10 of the blade, parameters such as the vibration node line 10, the vibration node 11, resonance frequency, resonance amplitude and the like can be obtained through a blade natural frequency test, and the vibration node line is not necessarily positioned in the middle position of the blade body when the blade vibrates in a torsional mode, so that the vibration node 11 is not necessarily positioned in the middle point position of the blade tip 9;
the positioning of the blade torsional vibration displacement measuring sensor is shown in fig. 4, when the blade torsional vibration occurs, the blade torsional vibration comprises two conditions of torsional non-resonance and torsional resonance, a certain tested blade is selected, when the torsional vibration occurs, the blade tip of the blade takes a blade tip static position 16 as a central position, periodic torsional movement is performed between the two torsional resonance blade tip maximum displacement positions 12, in order to ensure that the blade tip timing sensor can accurately measure the time signals of the blade tip inlet edge and the blade tip outlet edge reaching the blade tip timing sensor under the condition that the blade torsional non-resonance and the torsional resonance occur, the positioning of the two blade tip timing sensors needs to be determined by combining the blade torsional resonance parameters, the maximum displacement positions 12 and the maximum deflection angles 13 of the torsional resonance blade tip can be obtained through a blade natural frequency test, the blade tip length can be obtained through design, the setting alpha is the maximum deflection angle 13 of the torsional resonance blade tip, O is a vibration node 11, the line segment AB is the blade tip length, E is the mounting position of the blade tip timing sensor 4 at the inlet edge, F is the mounting position of the blade tip timing sensor 5 at the outlet edge, and h 1 For the displacement of the air inlet edge of the torsional resonance blade end 14, h 2 The air edge displacement 15 is given to the torsion resonance blade end;
when the blade is in a torsional resonance condition, the real-time position of the blade tip is periodically changed between two maximum displacement positions 12 of the blade tip of torsional resonance, at this time, the projection of the maximum displacement position 12 of the blade tip of torsional resonance on the horizontal line where the rest position 16 of the blade tip is positioned is a line segment EF, the EF length is the minimum value of the projection line segments of all the real-time positions of the blade tip on the horizontal line where the rest position 16 of the blade tip is positioned in the torsional vibration process of the blade, the maximum deflection angle 13 of the blade tip of torsional resonance is the maximum value of all the deflection angles of the blade in the torsional vibration process, the air inlet side displacement 14 of the blade tip of torsional resonance and the air outlet side displacement 15 of the blade tip of torsional resonance are the maximum values of all the torsional displacements of the blade in the torsional vibration process of the blade, at this time, the air inlet side blade tip timing sensor 4 is installed at the E point, the air outlet side blade tip timing sensor 5 is installed at the F point, and all the arrival time signals of the blade tips can be sampled under the condition that the blade is twisted;
when the blade is in a torsion non-resonance condition, the real-time position of the blade tip performs periodic torsion movement between two torsion resonance blade tip maximum displacement positions 12 (the torsion resonance blade tip maximum displacement positions 12 are not included), the projection of the real-time position of the blade tip on the horizontal line where the blade tip rest position 16 is located periodically changes between a line segment EF (without E and F points) and a line segment AB, and at the moment, two blade tip timing sensors at the E point and the F point can still sample all time signals of the blade tip reaching the two blade tip timing sensors;
because the condition that the blade passes through the blade tip timing sensor is in torsion non-resonance or torsion resonance cannot be confirmed, if the installation positions of the two blade tip timing sensors are moved from the E point and the F point to the O point, although all time signals of the torsion vibration blade end reaching the two blade tip timing sensors can still be sampled, when the blade is in torsion non-resonance condition and the vibration displacement of the blade is smaller, the time difference signals of the blade end passing through the two blade tip timing sensors are smaller, and at the moment, if the precision of a signal processing system is not high enough, the condition that the signals cannot be sampled possibly occurs; if the installation positions of two blade tip timing sensors are respectively moved from the point E and the point F to the point A and the point B, the condition that signal sampling is missed when torsional resonance or torsional non-resonance is generated on the blade but vibration displacement is large can be generated;
as shown in FIG. 5, the blade torsional vibration displacement measurement is set to Ω n1 For the low-speed rotation angular velocity of the rotor when the blade is not vibrating, omega n2 For high rotor rotational angular velocity when the blade is torsionally vibrated, n is the number of rotor revolutions and typically the tip rest position 16 is not parallel to the rotor axial horizon 18;
1. when the rotor is at angular velocity omega n1 When the low-speed rotating blade does not vibrate, the blade tip rotates to be always positioned at the blade tip rest position 16 when passing through the air inlet side blade tip timing sensor 4 and the air outlet side blade tip timing sensor 5, so that the time difference delta t between each circle of blade reaching the air inlet side blade tip timing sensor 4 and the air outlet side blade tip timing sensor 5 n1 =0, torsional vibration displacement is 0;
2. when the rotor is at angular velocity omega n2 When the high-speed rotating blade generates torsional vibration, the blade tip rotates to pass through the real-time position of the air inlet side blade tip timing sensor 4 and the air outlet side blade tip timing sensor 5, the maximum displacement position 12 of the two torsional resonance blade tips of the blade periodically changes, the arbitrary real-time position 17 of the torsional vibration blade tip when the blade rotates to pass through the two blade tip timing sensors is selected without losing generality, and the time difference delta t of the blade tip reaching the air inlet side blade tip timing sensor 4 and the air outlet side blade tip timing sensor 5 is measured in the nth turn n2 The blade can be calculated as Ω n2 When torsional vibration occurs in high-speed rotation and passes through the two blade tip timing sensors, the circumferential arc length of the blade tip passing along with the rotation of the rotor is as follows:
L n2 =Ω n2 RΔt n2 ,n=1.2.3...(1)
wherein R is the tip radius of rotation due to Δt n2 Is usually small, so that the blade tip is at Δt n2 The circumferential arc length passing along with the rotation of the rotor in the time difference is approximately equal to the sum of the displacement 20 of the inlet edge of the blade end measured by the sensor during torsional vibration and the displacement 21 of the outlet edge of the blade end measured by the sensor during torsional vibration, namely:
L n2 =Ω n2 RΔt n2 =h 3 +h 4 ,n=1.2.3...(2)
in the formula, h 3 The sensor detects the displacement 20 h of the inlet edge of the blade end when in torsional vibration 4 For the sensor measuring the blade tip air inlet edge displacement 21 during torsional vibration, the value of the torsional vibration blade tip deflection angle 19 can be calculated by combining the torsional vibration blade tip deflection angle 19, the sensor measuring the blade tip air inlet edge displacement 20 during torsional vibration, the sensor measuring the blade tip air outlet edge displacement 21 during torsional vibration and the distance EF between two blade tip timing sensors:
wherein d is the distance between two tip timing sensors, namely the length of a line segment EF;
3. because the positioning of the two blade tip timing sensors is based on a torsional resonance projection method, the inlet blade tip timing sensor 4 and the outlet blade tip timing sensor 5 measure the arrival time which is not the edge of the blade tip, so the L is calculated by the formula (2) n2 Not the true torsional vibration displacement of the blade; the torsional vibration blade tip deviation angle 19, the blade tip air inlet edge displacement 20 measured by the torsional vibration sensor, the blade tip air outlet edge displacement 21 measured by the torsional vibration sensor, the real blade tip air inlet edge displacement 22 measured by the torsional vibration sensor, the real blade tip air outlet edge displacement 23 measured by the torsional vibration sensor, the distance between two blade tip timing sensors and the blade tip length have the following trigonometric function relation:
in the formula, h 5 The real leaf ends being in torsional vibrationIntake side displacement 22, h 6 For the displacement 23 of the trailing edge of a real blade during torsional vibration, p is the length of the trailing edge, i.e. the length of the line segment AB, combined with the trigonometric function in (4), the blade has an angular velocity Ω n2 The torsional vibration displacement generated by the high-speed rotation passing through the two blade tip timing sensors is as follows:
the maximum deflection angle alpha of the torsional resonance blade tip can be obtained by a blade natural frequency test, and the rotor rotation angular velocity omega n1 And omega n2 The blade tip rotation radius R, the blade tip length p and the distance d between two blade tip timing sensors can be obtained through actual measurement of a rotor speed measuring system, and the time difference delta t between the blade tip timing sensor and the two blade tip timing sensors can be obtained through a design drawing n1 And Deltat n2 Can be obtained by actual measurement of a blade tip timing sensor.

Claims (1)

1. The blade torsional vibration displacement measurement method based on the blade tip timing principle is characterized in that two groups of blade tip timing sensors, namely an air inlet side blade tip timing sensor and an air outlet side blade tip timing sensor, are arranged at the same circumferential position on a rotary mechanical casing along the axial direction of a rotor and are used for measuring the time that the air inlet side and the air outlet side of the same blade tip reach the blade tip timing sensor in the same circle; the two blade tip timing sensors are arranged at projection points of the maximum displacement position of the torsion resonance blade tip on the horizontal line of the static position of the blade tip, which is called a torsion resonance projection method, and the torsion resonance projection method is used for realizing the optimal positioning of the blade tip timing sensors by combining the torsion resonance parameters of the blade so as to ensure that the two blade tip timing sensors can accurately sample the blade tip arrival time signals under the condition that the blade generates torsion resonance and torsion non-resonance; the method for measuring the torsional vibration displacement of the blade is realized by calculating the blade tip deflection angle generated when the blade generates torsional vibration and combining the trigonometric function relation between the distance between two blade tip timing sensors and the length of the blade tip, and comprises the following steps:
(1) When the rotor is at angular velocity omega n1 When the low-speed rotating blades do not vibrate, all blade tips rotate to be always positioned at the static positions of the blade tips when passing through the blade tip timing sensors of the air inlet side and the air outlet side, so that the time difference delta t between each circle of blade tips reaching the blade tip timing sensors of the air inlet side and the air outlet side is equal to the time difference delta t between each circle of blade tips n1 =0, torsional vibration displacement is 0;
(2) When the rotor is at angular velocity omega n2 When a certain blade rotates to pass through two blade tip timing sensors, the real-time position of the blade tip of the blade periodically changes between the maximum displacement positions of the blade tips of torsional resonance, and when the blade passes through the two blade tip timing sensors on the air inlet side and the air outlet side in turn in the nth turn, the circumferential arc length of the blade tip passing along with the rotation of the rotor is as follows:
L n2 =Ω n2 RΔt n2 =h 3 +h 4 n=1.2.3., where Ω n2 The high-speed rotation angular velocity of the rotor when the blade generates torsional vibration is represented by R, the rotation radius of the blade tip is represented by h 3 The sensor detects the displacement of the inlet edge of the blade end when in torsional vibration, h 4 For the sensor measurement leaf end edge of giving vent to anger displacement when torsional vibration, at this moment, the torsional vibration leaf end deflection angle of leaf end real-time position is:
wherein d is the distance between two blade tip timing sensors;
(3) Because the positioning of the two blade tip timing sensors is based on a torsional resonance projection method, the inlet blade tip timing sensor and the outlet blade tip timing sensor measure the arrival time of the edge of the blade tip, and the arrival time is obtained n2 Not the true torsional vibration displacement generated by the blade tip edge; the following trigonometric function relationship is used:wherein p is the tip length, the blade having an angular velocity Ω n2 The torsional vibration displacement generated by the two blade tip timing sensors rotating at high speed through the air inlet side and the air outlet side is as follows:
the maximum deflection angle alpha of the torsional resonance blade tip is obtained by a blade natural frequency test, and the rotor rotation angular velocity omega n1 And omega n2 The rotor speed measuring system is used for actually measuring and obtaining the rotation radius R of the blade tip, the length p of the blade tip and the distance d between two blade tip timing sensors, the time difference delta t between the blade tip and the two blade tip timing sensors is obtained from a design drawing n1 And Deltat n2 Obtained by actual measurement of a blade tip timing sensor, h 5 The displacement of the air inlet edge of the real blade end during torsional vibration is h 6 The displacement of the air edge of the real leaf end during torsional vibration.
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