Blade cold and hot deformation online measurement method based on blade tip timing technology

Abstract

The invention provides a blade cold and hot state deformation online measurement method based on a blade tip timing technology. The method comprises the following steps: step 1, establishing a blade tip contour deformation model; 2, based on the light spot triggering position and radius, a Gaussian radial basis function is adopted to represent a light spot; 3, setting an angle window function to restrain the Gaussian radial basis function; and 4, constructing an optimization objective function, and taking the maximum value of the blade top contour in the windowed Gaussian radial basis function. According to the invention, non-contact, high-precision and full-parameter static deformation measurement of the rotating blade in a high-temperature and high-pressure narrow space is realized.

Description

Technical Field

[0001] This invention relates to the field of turbomachinery technology, and in particular to an online measurement method for cold and hot deformation of blades based on blade tip timing technology. Background Technology

[0002] Blades are among the most critical working components of turbomachinery, widely used in high-performance equipment such as aero engines and heavy-duty gas turbines, which typically contain thousands of rotating blades. The geometric accuracy and mass balance of the blades directly affect not only aerodynamic efficiency but also structural stability. In actual operation, blades are subjected to complex centrifugal loads, aerodynamic forces, and thermal stresses over long periods, leading to static deformation of their cold-state geometry. These deformations typically manifest as axial movement, circumferential translation, and torsion. Failure to accurately identify these deformations will significantly impact overall engine performance and even threaten flight safety.

[0003] Existing blade deformation measurement methods based on optical tip timing technology treat the light spot as an ideal point source, ignoring the timing error caused by the finite size of the light spot. However, at the blade tip, especially in the leading and trailing edges, the blade thickness and the light spot size are on the same order of magnitude. This simplification introduces significant errors, leading to inaccurate measurement of the blade tip arrival time and consequently affecting the accuracy of deformation identification. In blade tip deformation identification, it is necessary to solve the tangency condition between the blade's thermal profile and multiple light spot circles. However, since the thermal profile is a complex curve and the light spot is circular, there is no analytical solution for their tangency relationship. Traditional methods struggle to stably and accurately determine the tangency point and corresponding deformation parameters, limiting the model's practicality and solvability. In traditional BTT systems, the beam emitted by the optical sensor diverges, causing instability in the size of the light spot's projection area at the blade tip when there are gaps or height changes. This variation affects the effective radius of the light spot, introducing measurement errors, particularly in measurements between different blades or different regions of the same blade, where stability is poor.

[0004] Therefore, those skilled in the art are dedicated to providing an online measurement method for the cold and hot deformation of blades based on blade tip timing technology, so as to realize non-contact, high-precision, and full-parameter static deformation measurement of rotating blades in a high-temperature, high-pressure, and confined space. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the technical problem to be solved by the present invention is how to provide an online measurement method for blade deformation under cold and hot conditions.

[0006] To achieve the above objectives, this invention provides an online measurement method for blade cold and hot deformation based on blade tip timing technology, comprising the following steps: Step 1: Establish a deformation model of the blade tip profile; Step 2: Based on the spot triggering position and radius, the spot is represented by a Gaussian radial basis function; Step 3: Set the corner window function to constrain the Gaussian radial basis function; Step 4: Construct an optimization objective function so that the blade tip profile reaches its maximum value in the windowed Gaussian radial basis function.

[0007] Furthermore, a convex lens is placed between the emitted beam and the blade, and the emitted beam is collimated after passing through the convex lens.

[0008] Further, step 1 includes: The cold profile of the blade tip is as follows:

[0009] In the formula, The coordinate vector of the blade tip profile point; The hot profile of the blade tip is the shape of the cold profile after translation and rotation:

[0010] In the formula, This is a two-dimensional rotation matrix used to rotate coordinates by an angle. ; It is a translation vector; The degrees of freedom of the simplified model are:

[0011] In the formula, For circumferential displacement, This represents axial displacement.

[0012] Furthermore, based on the tangency condition between the hot profile and the light spot, the position of the hot profile is obtained.

[0013] Furthermore, the objective function for solving the hot profile is:

[0014]

[0015] In the formula, Indicates a circular light spot. The objective function includes the triggering position of the light spot and the cold profile of the blade tip.

[0016] Furthermore, the model function for the light spot in step 2 is:

[0017] In the formula, The distance from the center of the light spot. For the first The beam radius of each probe and They are respectively Functions in the inner and outer regions of a circle The rate of change.

[0018] Furthermore, the corner window function introduced in step 3 is:

[0019] In the formula, and This represents the range of angles within which the corner window function reaches its maximum value of 1. The transition band parameter for controlling the window function as it decreases from 1 to 0; in,

[0020] In the formula, The central angle of the window function. The angle is half the width.

[0021] Furthermore, the windowed Gaussian radial basis function is:

[0022] In the formula, For an effective spot model, For corner window functions, These are Gaussian radial basis functions; in,

[0023] .

[0024] Furthermore, in step 4, for each light spot circle... In the hot blade profile Find its nearest point :

[0025]

[0026] Furthermore, the optimization objective function in step 4 = for: .

[0027] The present invention has at least the following beneficial technical effects: This invention explicitly considers the geometric dimensions of the light spot in the model, describing the contact process between the light spot and the blade tip surface as tangent between the blade and the light spot circle. It establishes a precise mapping relationship between the trigger time and the actual position of the blade tip for self-checking. By utilizing the tangency condition between the light spot circles formed by multiple sensors and the blade's thermal profile, the thermal deformation parameters are jointly solved, thus avoiding the systematic bias under the point light spot assumption and significantly improving the deformation measurement accuracy of thin blades. This model enhances the system's sensitivity to small-sized structural changes, improving the reliability and practical engineering applicability of deformation identification.

[0028] This invention combines radial basis functions with angular window functions, introducing a numerical solution mechanism to accurately fit the hot blade profile and efficiently search for the tangent point of the light spot circle, thereby stably solving the tangency condition. The radial basis function smoothly models the light spot, ensuring the profile can be optimized towards the tangent point in the plane. The angular window function then limits the possible tangent angle range, narrowing the search space. Combining these two methods constructs the objective function, and numerical optimization is used to search for points satisfying the tangency and gradient parallelism conditions, thus achieving accurate deformation parameter extraction. This results in a stable solution between the complex blade tip profile and the geometric constraints of the light spot, improving solution robustness and accuracy while significantly reducing computational overhead.

[0029] This invention introduces a convex lens assembly at the head of the optical BTT sensor to collimate the emitted light beam, thereby maintaining a constant spot size under different blade clearance conditions and effectively improving the system's anti-interference capability and measurement consistency. By adding a convex lens at the front end of the sensor, the diverging light is transformed into a collimated beam, ensuring that the size of the spot at the blade tip remains essentially unchanged regardless of the blade tip clearance. This eliminates the interference of spot geometric changes on measurement accuracy at the source, significantly improving the measurement stability and anti-interference capability of the BTT system under different operating conditions, making it particularly suitable for scenarios with fluctuating blade tip clearance in practical engineering.

[0030] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0031] Figure 1 This is a flowchart of the online measurement method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the measuring device according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the degree of freedom transformation in an embodiment of the present invention; Figure 4 This is a schematic diagram of the triggering process in an embodiment of the present invention. Detailed Implementation

[0032] The preferred embodiments of the present invention are described below to make the technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0033] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0034] This invention provides an online measurement method for cold and hot deformation of blades based on blade tip timing technology. It introduces a modeling method with finite spot size into the triggering model of the blade tip timing sensor and the blade. By constructing a geometric model that includes the actual spot area, the ability to accurately restore the triggering position of the blade tip is effectively improved.

[0035] like Figure 2 The diagram shows a schematic of the online measurement device for blade cold and hot deformation based on tip timing technology according to the present invention. The optical sensor used for online measurement is fixed on the housing, and the blade rotates around the axis inside the housing. The optical sensor consists of a central emitting fiber core and several receiving fibers surrounding it. The emitted light beam is collimated by a convex lens at the front end of the sensor. When the blade passes through the detection area of ​​the collimated beam, i.e., when the blade tip just passes the light spot, the receiving fibers collect the reflected light and transmit it to the photoelectric converter, thereby generating a pulse signal. Due to the use of a convex lens, the emitted light spot is considered to be of a finite size, rather than an idealized point light source.

[0036] In one specific embodiment, there are three optical sensors, which are respectively arranged at the leading edge (LE), middle (MID) and trailing edge (TE) of the blade.

[0037] like Figure 1 As shown in the figure, the main process of the online measurement method for blade cold and hot deformation based on blade tip timing technology in this embodiment is as follows.

[0038] Step 1: Establish a deformation model of the blade tip profile.

[0039] The cold profile of the blade tip is represented as follows:

[0040] In the formula, is the coordinate vector of the blade tip profile point.

[0041] The hot profile (after deformation) of the blade tip represents the shape of the cold profile after translation and rotation:

[0042] In the formula, This is a two-dimensional rotation matrix used to rotate the coordinates by an angle. ; This is the corresponding translation vector.

[0043]

[0044] like Figure 3 As shown, using the above relationships, the degrees of freedom of the simplified model are compressed into three scalars: rotation angle. Circumferential displacement and axial displacement . This is commonly referred to as the reverse twist angle. and It covers bending and chordal movement, so the deformation of the entire blade can be effectively calculated using these three scalars.

[0045] Step 2: Based on the spot triggering position and radius, the spot is represented by a Gaussian radial basis function.

[0046] In such Figure 2 In the static reference frame shown (casing reference frame), there are three BTT sensors. Fixedly mounted on the casing, its corresponding light spot remains stationary relative to the reference frame. Considering the effective area of ​​each light spot, represented by a circle in the figure, the sensor... The coordinates of the center of the emitted light spot in this reference frame are: .like Figure 4 As shown, the interaction process between the leaf tip and the sensor light spot includes the following stages: a) The pressure surface is initially tangent to the light spot. At this moment, the receiving fiber begins to receive the reflected light, and the pulse waveform voltage begins to rise. This moment is defined as... The corresponding blade position is in Figure 4 The figure in (a) is represented by a dashed line.

[0047] b) As the leaf continues to move forward, the overlap area between the leaf tip and the light spot gradually increases, causing the pulse voltage to rise accordingly.

[0048] c) When the leaf tip completely covers the light spot, the received signal reaches a stable maximum value, and a plateau segment appears in the waveform.

[0049] d) As the blade continues to advance, the overlap area between the blade and the light spot gradually decreases, and the pulse voltage begins to drop.

[0050] e) Finally, the suction surface of the leaf tip is tangent to the light spot, and the leaf is about to leave the light spot. At this moment, the reflected light disappears, and the pulse voltage drops to zero. This moment is defined as... The corresponding blade position is in Figure 4 In figure (a), the solid line represents the line.

[0051] According to such Figure 4 The rotating reference frame shown in Figure (b) is in which the blade tip remains stationary while the optical sensor... Negative direction movement. Utilizing the sensors at the moment of contact with the pressure surface. The trigger time can be calculated by determining the position of each spot center in the rotating reference frame using the following method. :

[0052]

[0053] In the formula, This indicates the leading edge point of blade #b in the rotating reference frame. coordinate, Indicates sensor In a stationary reference frame coordinate, For the number of laps, For sensors In a stationary reference frame coordinate.

[0054] Similarly, when the light spot is about to leave the leaf tip (i.e., tangent to the suction surface), the center position of the light spot can be calculated:

[0055]

[0056] Angular displacement function This is acquired through a key phase sensor, which detects key markers mounted on the rotor shaft or disk. Typically, the time of the first key phase trigger is defined as time zero. When only one key phase marker is mounted on the rotor, the... Circle trigger time The corresponding angular displacement is Integer multiples of.

[0057] Using BTT technology, after acquiring the trigger position of the light spot, and combining it with the cold-state profile of the blade tip, the position of the hot-state profile can be accurately determined based on tangency conditions. In a plane, the definition of a light spot circle is:

[0058] In the formula, Represents a set of sensors. This indicates the type of lateral surface of the blade tip—pressure surface (ccv) and suction surface (cvx). For the sensor The radius of the light spot. The center coordinates of each light spot circle are represented in the rotating reference frame as follows: .

[0059] Blade tip thermal profile Set together with the light spot circle The following tangency conditions must be met: 1) Should be with each Tangent; 2) At each tangent point place, and The gradient directions should remain parallel.

[0060] These tangency conditions can be expressed as:

[0061] in, The hot profile of the blade tip The implicit form of expression, Represents the boundary circle of each light spot The equation.

[0062] Using the above conditions, the deformation parameters of the hot blade can be solved, and the optimal objective function is:

[0063]

[0064] This includes the triggering locations of all light spots, as well as the cold profile of the leaf tip.

[0065] The cold-state blade tip profile, obtained through coordinate measurement or optical scanning, is typically represented by hundreds of discrete points, making the tangency condition difficult to solve analytically. Furthermore, due to measurement errors, the actual light spot may deviate from the ideal circle. Therefore, the light spot is modeled as a continuous function on a plane and represented using the Gaussian radial basis function (GRBF), as follows:

[0066] In the formula, is the independent variable, representing the distance from the center of the light spot; Indicates the first The spot radius of each sensor probe; parameters and They represent in Functions in the inner and outer regions of a circle The rate of change.

[0067] Step 3: Set the angle window function to constrain the Gaussian radial basis function.

[0068] like Figure 4 As shown, at the instant the blade enters or leaves the sensing area, only a portion of the light spot may overlap with the blade profile. Therefore, a corner window function needs to be introduced to constrain the above equation. The corner window function is:

[0069] In the formula, and This indicates the range of angles within which the corner window function takes the maximum value of 1. This is the transition band parameter that controls the window function as it decreases from 1 to 0.

[0070] To facilitate parameter configuration, a central angle is introduced. and angle half width Instead of direct representations of the minimum and maximum angles:

[0071] in, This represents the central angle of the window function. It represents its angular half-width.

[0072] An effective spot model can be represented by a windowed GRBF, denoted as It is a corner window function. With GRBF function The product of:

[0073] This function depends on the distance from the center of the light spot. point The polar coordinate distance and angle are expressed as follows:

[0074]

[0075] Step 4: Construct an optimization objective function so that the blade tip profile reaches its maximum value in the windowed Gaussian radial basis function.

[0076] After constructing the windowed Gaussian radial basis function, the three deformation parameters The objective function can be determined through the following steps.

[0077] For each light spot circle In the hot blade profile Find its nearest point :

[0078]

[0079] Construct the objective function = :

[0080] The objective function aims to find the maximum value of the blade tip profile in the plane, and the theoretical location of the maximum value is tangent to all light spots.

[0081] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for online measurement of blade deformation under cold and hot conditions based on tip-time technology, characterized in that, Includes the following steps: Step 1: Establish a deformation model of the blade tip profile; Step 2: Based on the spot triggering position and radius, the spot is represented by a Gaussian radial basis function; Step 3: Set the corner window function to constrain the Gaussian radial basis function; Step 4: Construct an optimization objective function so that the blade tip profile reaches its maximum value in the windowed Gaussian radial basis function.

2. The online measurement method for blade cold and hot deformation based on tip timing technology as described in claim 1, characterized in that, A convex lens is placed between the emitted beam and the blade, and the emitted beam is collimated after passing through the convex lens.

3. The online measurement method for blade cold and hot deformation based on tip timing technology as described in claim 2, characterized in that, Step 1 includes: The cold profile of the blade tip is as follows: In the formula, The coordinate vector of the blade tip profile point; The hot profile of the blade tip is the shape of the cold profile after translation and rotation: In the formula, This is a two-dimensional rotation matrix used to rotate coordinates by an angle. ; It is a translation vector; The degrees of freedom of the simplified model are: In the formula, For circumferential displacement, This represents axial displacement.

4. The online measurement method for blade cold and hot deformation based on tip timing technology as described in claim 3, characterized in that, The position of the hot profile can be obtained by solving the tangency condition between the hot profile and the light spot.

5. The online measurement method for blade cold and hot deformation based on tip timing technology as described in claim 4, characterized in that, The objective function for solving the hot profile is: In the formula, Indicates a circular light spot. The objective function includes the triggering position of the light spot and the cold profile of the blade tip.

6. The online measurement method for blade cold and hot deformation based on tip timing technology as described in claim 5, characterized in that, The model function for the light spot in step 2 is: In the formula, The distance from the center of the light spot. For the first The beam radius of each probe and They are respectively Functions in the inner and outer regions of a circle The rate of change.

7. The online measurement method for blade cold and hot deformation based on tip timing technology as described in claim 6, characterized in that, The corner window function introduced in step 3 is: In the formula, and This represents the range of angles within which the corner window function reaches its maximum value of 1. The transition band parameter for controlling the window function as it decreases from 1 to 0; in, In the formula, The central angle of the window function. The angle is half the width.

8. The online measurement method for blade cold and hot deformation based on tip timing technology as described in claim 7, characterized in that, The windowed Gaussian radial basis function is: In the formula, For an effective spot model, For corner window functions, These are Gaussian radial basis functions; in, 。 9. The online measurement method for blade cold and hot deformation based on tip timing technology as described in claim 8, characterized in that, In step 4, for each light spot circle In the hot blade profile Find its nearest point : 。 10. The online measurement method for blade cold and hot deformation based on tip timing technology as described in claim 9, characterized in that, The optimization objective function in step 4 = for: 。

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