Blade shroud gap automatic scanning measurement method

Abstract

The application provides a kind of blade edge plate gap automatic scanning measurement method, belong to industrial processing technical field, the application establishes the correspondence of workpiece and machine coordinate system by constructing three-dimensional measurement coordinate system, adopts laser scanning probe to obtain high-density point cloud data by full circumferential automatic scanning, calculates geometric deviation by least square method fitting gap surface, constructs multidimensional error compensation vector field such as space position, optical system and material thermal expansion, establishes airflow model based on fluid mechanics and analyzes airflow characteristics by numerical solution and analytical solution method, converts measurement problem into traveling salesman problem and applies improved ant colony algorithm to optimize scanning path, carries out gap uniformity analysis, identifies abnormal law by fourier series expansion decomposition gap curve, finally generates comprehensive evaluation report, solves the core problem of multidimensional error affecting measurement accuracy.

Description

Technical Field

[0001] This invention belongs to the field of industrial processing technology, and specifically relates to an automatic scanning and measurement method for blade edge clearance. Background Technology

[0002] Blade rim clearance measurement is a critical technical step in the manufacturing and maintenance of turbomachinery, and its accuracy directly affects equipment operating efficiency and service life. Traditional blade rim clearance measurement mainly employs contact measuring tools and single-point laser ranging technology, obtaining discrete measurement data through manual sampling, and then analyzing and processing it using simple mathematical models. These methods are widely used in industrial production and equipment maintenance, but their limitations are becoming increasingly apparent in advanced turbine systems with high precision requirements.

[0003] However, traditional measurement techniques have significant drawbacks in practical applications: First, they cannot effectively identify and compensate for spatial position errors during the measurement process, leading to inaccurate positioning of measurement points; second, laser ranging systems themselves have optical system errors such as optical distortion and intensity deviation, affecting the reliability of measurement data; third, during long-term measurements, there are dimensional changes caused by material thermal expansion, and the error caused by this temperature effect is often ignored. These multidimensional error factors intertwine and affect the measurement results, causing significant deviations from the actual values.

[0004] With the increasing demands for precision control of blade sill clearance in high-end equipment such as aero-engines and industrial gas turbines, existing technologies struggle to address the challenge of high-precision measurement under the combined influence of multidimensional errors. Particularly under complex operating conditions such as high temperature and high pressure, the coupling effects of spatial position errors, optical system errors, and material thermal expansion errors become more pronounced, representing a key bottleneck restricting the improvement of measurement accuracy. Summary of the Invention

[0005] In view of this, the present invention provides an automatic scanning measurement method for blade edge gap, which can solve the problem that the measurement accuracy is affected by multi-dimensional errors such as spatial position error, optical system error and material thermal expansion in the prior art.

[0006] This invention is implemented as follows:

[0007] This invention provides an automatic scanning measurement method for blade rim clearance, comprising: constructing a three-dimensional measurement coordinate system, mounting the blade on a fixture platform, and establishing the correspondence between the workpiece coordinate system and the machine coordinate system; using a laser scanning probe to automatically scan the blade rim clearance in the full circumference and collect clearance point cloud data; fitting the blade rim clearance surface using the least squares method and calculating the geometric deviation between the measured surface and the theoretical model; constructing a comprehensive error compensation vector field and applying spatial position error compensation functions, optical system error compensation functions, and material thermal expansion error compensation functions for multi-dimensional error correction; establishing an airflow model for the rim clearance and performing numerical and analytical solutions; optimizing the scanning path; performing clearance uniformity analysis and deviation analysis, and generating a measurement evaluation report.

[0008] Based on the above technical solution, the automatic scanning measurement method for blade edge clearance of the present invention can be further improved as follows:

[0009] In the constructed three-dimensional measurement coordinate system, the workpiece coordinate system is a three-dimensional rectangular coordinate system established with the fixed point at the root of the blade as the origin, used to describe the relative positions and dimensional relationships of various parts of the blade in space; the machine coordinate system is a three-dimensional rectangular coordinate system established with the reference point of the measuring equipment as the origin, used to describe the absolute positions of various components of the measuring equipment and measuring points in space.

[0010] Furthermore, in the acquisition of gap point cloud data, the gap point cloud data is a set of spatial discrete points obtained by the laser scanning probe. Each point contains three-dimensional coordinate values ​​and reflection intensity information, which are used to describe the surface contour shape of the blade edge plate.

[0011] Furthermore, in the construction of the comprehensive error compensation vector field, the input of the spatial position error compensation function includes the spatial coordinate position obtained from the machine coordinate system, the measurement time obtained from the system clock, and the ambient temperature obtained from the temperature sensor, and the output is a three-dimensional spatial position correction vector applied to the gap point cloud data.

[0012] Furthermore, in the construction of the comprehensive error compensation vector field, the input of the optical system error compensation function includes the light signal intensity obtained from the laser scanning probe receiving unit, the target distance obtained from the position sensor, the incident angle obtained from the attitude sensor, and the material characteristic parameters of the reflective surface obtained from the material database. The output is the measurement correction amount applied to the gap point cloud data.

[0013] Furthermore, in the construction of the comprehensive error compensation vector field, the input of the material thermal expansion error compensation function includes the ambient temperature obtained from the temperature sensor, the material thermal expansion coefficient obtained from the material database, the measurement duration obtained from the system clock, and the material stress state obtained from the stress sensor, and the output is the thermal deformation correction factor applied to the measured surface.

[0014] Furthermore, in establishing the airflow model of the blade rim gap, the numerical solution method uses finite element analysis to discretize the flow field of the blade rim gap into grid elements, and solves the gas flow control equations through iterative calculation. The inputs include the gap boundary conditions obtained from the three-dimensional geometric model, the inlet velocity obtained from experimental data, the inlet pressure obtained from the pressure sensor, the operating temperature obtained from the temperature sensor, and the fluid viscosity obtained from the physical property database. The output is the flow field distribution state in the blade rim gap.

[0015] Furthermore, in establishing the airflow model of the blade rim gap, the analytical solution method is based on the simplified equations of fluid mechanics theory and uses the variable separation method to solve the airflow theory equations. The inputs include the fluid density obtained from the fluid property database, the airflow damping coefficient calculated based on the physical model, the fluid viscosity coefficient obtained from experimental data, the pressure gradient obtained from the boundary conditions, and the gap characteristic dimensions obtained from the geometric model. The output is a mathematical expression describing the variation law of the flow field in the blade rim gap.

[0016] Furthermore, in establishing the blade rim gap airflow model, the airflow numerical solution is a set of pressure distribution, velocity distribution, and temperature distribution data obtained by the numerical solution method on discrete grid points, used for predicting the gap change trend in the blade rim gap real-time diagnostic system; the airflow analytical solution is an analytical expression of the airflow characteristic function obtained by the analytical solution method, used for sensitivity analysis and optimization calculation of design parameters in the gap optimization design module.

[0017] Furthermore, the optimized scanning path transforms the gap measurement problem into a traveling salesman problem to find the optimal scanning path. An improved ant colony algorithm is applied to determine the order of measurement point visits, and a scanning path optimization matrix is ​​constructed to reduce measurement time and system motion errors.

[0018] This invention achieves precise correspondence between the workpiece coordinate system and the machine coordinate system by constructing a three-dimensional measurement coordinate system, and uses a laser scanning probe for full-circumferential automatic scanning to acquire high-density gap point cloud data. The core innovation lies in the construction of a comprehensive error compensation vector field, which systematically solves the problem of multi-dimensional error influence.

[0019] This invention overcomes the limitations of traditional technologies. The spatial position error compensation function effectively eliminates mechanical errors and positional offsets during the measurement system's movement; the optical system error compensation function accurately corrects optical distortion and intensity deviations during the laser scanning probe's imaging process; and the material thermal expansion error compensation function scientifically corrects dimensional deformation caused by temperature changes. These three compensation mechanisms work synergistically to fundamentally improve measurement accuracy.

[0020] In summary, this invention overcomes the challenges of handling the combined effects of spatial position errors, optical system errors, and material thermal expansion errors in existing technologies through a systematic multi-dimensional error compensation technique. Furthermore, airflow model analysis and optimized path planning based on high-density point cloud data further enhance measurement efficiency and analytical depth, providing reliable technical support for the precise measurement and optimized design of blade edge clearance. Attached Figure Description

[0021] Figure 1 A flowchart of an automatic scanning measurement method for blade rim clearance;

[0022] Figure 2 A front view of the automatic scanning and measuring device for blade rim clearance;

[0023] Figure 3 A schematic diagram of the laser scanning head of the automatic scanning measurement device for blade edge clearance;

[0024] Figure 4 This is a top view of the automatic scanning and measuring device for blade edge clearance;

[0025] The attached diagram lists the components represented by each number as follows:

[0026] 10. Blade; 20. Fixture platform; 30. Laser scanning head; 30. Servo motor; 31. Position sensor; 32. Attitude sensor; 40. X-axis; 50. Y-axis; 60. Z-axis. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0028] like Figure 1 The diagram shows a flowchart of an automatic scanning measurement method for blade rim clearance provided by the present invention, wherein the method includes the following steps:

[0029] S01. Construct a three-dimensional measurement coordinate system. Install the blade 10 on the fixture platform 20 with multi-degree-of-freedom adjustment function. Use a high-precision laser sensor to establish the correspondence between the workpiece coordinate system and the machine coordinate system and perform calibration.

[0030] S02. A laser scanning probe 30 is used to perform a full-circumferential automatic scan of the blade edge plate gap. The laser scanning probe moves along the blade edge plate contour at preset intervals to collect gap point cloud data and form a gap contour curve.

[0031] S03. Based on the gap point cloud data, fit the blade edge plate gap surface using the least squares method, calculate the geometric deviation between the measured surface and the theoretical model, and establish a gap distribution mapping map.

[0032] S04. Construct a comprehensive error compensation vector field and apply the spatial position error compensation function, the optical system error compensation function, and the material thermal expansion error compensation function to perform multi-dimensional error correction.

[0033] S05. Based on the fluid dynamics boundary layer theory, establish an airflow model for the gap between the flanges. Use numerical solution methods to perform finite element analysis on the airflow model to obtain the numerical solution of the airflow. Use analytical solution methods to derive the theoretical equations of the airflow to obtain the analytical solution of the airflow.

[0034] S06. The numerical solution of the airflow is applied to the real-time diagnostic system for blade rim clearance to predict the clearance change trend under different operating conditions; the analytical solution of the airflow is applied to the clearance optimization design module to guide the optimization of blade rim clearance design parameters.

[0035] S07. The gap measurement problem is transformed into a traveling salesman problem to find the optimal scanning path. An improved ant colony algorithm is applied to determine the order of measurement point visits and to construct a scanning path optimization matrix to reduce measurement time and system motion error.

[0036] S08. Perform gap uniformity analysis, calculate the standard deviation and variation trend of the blade edge gap in the circumferential position, and evaluate the degree of gap distribution uniformity.

[0037] S09. Establish a mathematical model of the gap between the sash plates, decompose the gap curve into fundamental frequency components and harmonic components using the Fourier series expansion method, and identify the abnormal change law of the gap.

[0038] S10. Perform deviation analysis, calculate the maximum deviation, average deviation and deviation distribution characteristics between the measured gap and the theoretical design gap, and generate a deviation heat map.

[0039] S11. Generate a measurement and evaluation report, including statistical results of gap values, uniformity analysis results, airflow performance analysis results, and deviation analysis results, to provide a basis for blade assembly quality control.

[0040] The workpiece coordinate system refers to a three-dimensional rectangular coordinate system established with the fixed point at the root of the blade as the origin, which is used to describe the relative positions and dimensional relationships of various parts of the blade in space.

[0041] The machine coordinate system refers to a three-dimensional rectangular coordinate system established with the reference point of the measuring equipment as the origin, which is used to describe the absolute position of each component of the measuring equipment and the measuring point in space.

[0042] The gap point cloud data refers to a large set of spatial discrete points obtained by the laser scanning probe. Each point contains three-dimensional coordinate values ​​and reflection intensity information, which are used to describe the surface contour shape of the blade edge plate.

[0043] The spatial position error compensation function is used to compensate for mechanical errors and position offsets generated during the movement of the measurement system. The inputs include the spatial coordinate position obtained from the machine coordinate system, the measurement time obtained from the system clock, and the ambient temperature obtained from the temperature sensor. The output is a three-dimensional spatial position correction vector applied to the gap point cloud data.

[0044] The optical system error compensation function is used to correct the optical distortion and intensity deviation generated during the imaging process of the laser scanning probe. The inputs include the light signal intensity obtained from the laser scanning probe receiving unit, the target distance obtained from the position sensor 31, the incident angle obtained from the attitude sensor 32, and the material characteristic parameters of the reflective surface obtained from the material database. The output is the measurement correction amount applied to the gap point cloud data.

[0045] The material thermal expansion error compensation function is used to correct the size changes of the blade and measuring device caused by temperature changes. The inputs include the ambient temperature obtained from the temperature sensor, the material thermal expansion coefficient obtained from the material database, the measurement duration obtained from the system clock, and the material stress state obtained from the stress sensor. The output is the thermal deformation correction factor applied to the measured surface.

[0046] The numerical solution method refers to using finite element analysis technology to discretize the flow field in the blade edge gap into grid elements, and solving the gas flow control equations through iterative calculation. The inputs include the gap boundary conditions obtained from the three-dimensional geometric model, the inlet velocity obtained from experimental data, the inlet pressure obtained from the pressure sensor, the operating temperature obtained from the temperature sensor, and the fluid viscosity obtained from the physical property database. The output is the flow field distribution state in the blade edge gap.

[0047] The analytical solution method refers to solving the airflow theory equations by simplifying the equations based on fluid mechanics theory and using the variable separation method. The inputs include fluid density obtained from the fluid property database, airflow damping coefficient calculated based on the physical model, fluid viscosity coefficient obtained from experimental data, pressure gradient obtained from boundary conditions, and gap characteristic dimensions obtained from the geometric model. The output is a mathematical expression describing the variation law of the flow field in the blade edge gap.

[0048] The airflow numerical solution refers to the set of pressure distribution, velocity distribution and temperature distribution data on discrete grid points obtained by the numerical solution method, which is used to predict the gap change trend in the real-time diagnosis system of blade edge gap.

[0049] The airflow analytical solution refers to the analytical expression of the airflow characteristic function obtained by the analytical solution method, which is used for the design parameter sensitivity analysis and optimization calculation in the gap optimization design module.

[0050] The circumferential position refers to the angular position along the circumference of the blade edge plate, measured clockwise from the starting point of the blade leading edge, and is used for the gap uniformity analysis.

[0051] The Traveling Salesman Problem (TSP) refers to finding a closed loop that visits all measurement points once with the shortest path. The optimal scanning sequence is solved by constructing a distance matrix and a transformation cost matrix between measurement points derived from the machine coordinate system and applying the improved ant colony algorithm. The optimal scanning sequence is used to control the movement path of the laser scanning probe.

[0052] The Fourier series expansion method refers to a mathematical processing method that decomposes the periodic gap curve into a superposition of sine waves of different frequencies, which is used to analyze the frequency characteristics of the gap point cloud data. The frequency characteristics are used in the measurement evaluation report.

[0053] The deviation heatmap refers to a two-dimensional visual graphic that uses different shades of color to represent the magnitude of the deviation between the measured gap and the theoretical design gap, intuitively displaying the distribution and concentrated areas of the deviation. The deviation heatmap is included in the measurement evaluation report.

[0054] The improved ant colony algorithm refers to a path optimization algorithm that introduces a dynamic pheromone adjustment mechanism on the basis of the standard ant colony algorithm, used to solve the traveling salesman problem, wherein the pheromone concentration is dynamically updated based on the scanning path optimization matrix.

[0055] The scanning path optimization matrix refers to a two-dimensional matrix that describes the conversion cost between measurement points. The matrix element values ​​are determined by the distance in the machine coordinate system and the laser scanning probe attitude adjustment time.

[0056] The blade edge clearance real-time diagnostic system refers to a real-time monitoring and analysis system established based on the airflow numerical solution. It is used to monitor changes in blade edge clearance during equipment operation, promptly detect clearance anomalies, and issue early warnings.

[0057] The gap optimization design module refers to a design tool that uses the airflow analytical solution to guide the optimization of blade edge gap parameters. It is used to determine the optimal gap design value according to different operating conditions and improve equipment operating efficiency.

[0058] The specific implementation methods of the above steps are described in detail below.

[0059] like Figure 2-4 As shown, the specific implementation of step S01 involves constructing a high-precision three-dimensional measurement coordinate system. This system mounts the blade on a fixture platform with six degrees of freedom adjustment, including three translational degrees of freedom and three rotational degrees of freedom. The fixture platform is driven by a precision servo motor 30, achieving a positioning accuracy of ±5μm. First, three non-collinear feature points are selected at the blade root and marked as the origin O, the X-axis 40-degree direction point P, and the XY plane point P, respectively. A high-precision laser sensor (accuracy ±1μm) is used to scan and locate these three feature points, obtaining their position coordinates in the machine coordinate system. Then, based on the obtained coordinates of the three feature points, a workpiece coordinate system is established using a coordinate transformation algorithm. This algorithm employs the rigid body transformation principle, constructing a rotation matrix and translation vector to achieve the mapping relationship between the two coordinate systems. Next, a multi-point calibration method is used to verify the accuracy of the established coordinate system. Ten known position points on the blade surface are selected, and their coordinate values ​​are measured in both the workpiece coordinate system and the machine coordinate system. The calibration error is calculated using the least squares method. If the calibration error exceeds 8μm, the calibration process is repeated. The purpose of this step is to establish a unified measurement benchmark to ensure the accuracy and consistency of subsequent measurement data, and to provide a spatial positioning basis for gap scanning.

[0060] The specific implementation of step S02 involves using a high-precision laser scanning probe to perform a full-circumferential automatic scan of the blade edge clearance. First, the laser scanning probe employs the triangulation principle. A laser beam with a wavelength of 650nm is emitted from the laser source and focused onto the blade edge surface through a lens system. The reflected light is then converged onto a CCD sensor through a receiving lens. The target distance is calculated based on the positional changes of the laser spot on the CCD, with a measurement accuracy of 0.5μm and a measurement frequency of 5kHz. Then, based on the geometric characteristics of the blade edge, a scanning path is designed. The probe moves along the blade edge contour at preset intervals of 0.5mm to ensure the scanning density meets the requirements for clearance analysis. During the scanning process, the system acquires three-dimensional coordinate data and reflection intensity information in real time, forming a clearance point cloud dataset with a point cloud density of no less than 1mm. 2The area contains 50 sampling points. To ensure measurement stability, the system uses a real-time position error compensation algorithm, monitoring probe pose changes through a gyroscope and accelerometer, and performing real-time corrections, achieving pose compensation accuracy of ±2μm and ±0.01°. The high-density point cloud data acquired in this step provides the raw data foundation for subsequent gap analysis, enabling an accurate description of the full circumferential morphology of the blade edge gap.

[0061] The specific implementation of step S03 involves surface fitting and deviation analysis based on the acquired gap point cloud data. First, the point cloud data is preprocessed, and a statistical outlier filtering algorithm is used to remove noise points. This algorithm calculates the average distance from each point to its neighboring points based on the local statistical characteristics of the point cloud. If this distance exceeds three times the standard deviation, it is identified as an outlier and removed. Then, an improved RANSAC (Random Sample Consensus) algorithm is used to select sample points from the preprocessed point cloud to construct an initial surface model. This algorithm reduces the influence of outliers and improves fitting stability through iterative optimization. Next, B-spline surface fitting technology is applied to fit the gap point cloud into a continuous and smooth three-dimensional surface. During the fitting process, the least squares method is used to minimize the sum of squared distances from points to the surface, and the fitting accuracy is controlled within 5 μm. Subsequently, the fitted surface was compared with the theoretical design model. The normal distances from 5000 uniformly distributed sampling points on the measured surface to the theoretical surface were calculated, a deviation matrix was constructed, and a gap distribution mapping map was plotted. This mapping map uses a color coding method to visually display the gap distribution, with the deviation range divided into 10 levels, each represented by a different color. The purpose of this step is to quantify the actual morphology of the blade edge gap, providing a geometric basis for subsequent analysis and evaluation.

[0062] The specific implementation of step S04 is to construct a comprehensive error compensation vector field to realize multi-dimensional error correction. Firstly, a spatial position error compensation function is established. This function uses a polynomial fitting method to describe the motion error of the mechanical system, with input variables including spatial coordinate positions (x, y, z), measurement time t and ambient temperature T. The function takes the form of a polynomial series expansion, in which the coefficients are obtained through standard block calibration, and the output is a three-dimensional spatial position correction vector. Then, an optical system error compensation function is constructed. This function is based on the optical imaging principle, with inputs including optical signal intensity I, target distance d, incident angle θ and material characteristic parameter M. The function takes the form of a linear combination of various parameters and cross terms, the coefficients are determined through optical calibration experiments, and the output is a measured value correction amount. Next, a material thermal expansion error compensation function is established. This function is based on the principle of thermodynamics, with inputs including ambient temperature T, material thermal expansion coefficient α, measurement duration t and material stress state σ. The function expresses the functional relationship between temperature change and thermal expansion coefficient, the coefficients are determined through thermal deformation experiments, ΔT is the temperature change amount, and the output is a thermal deformation correction factor. Finally, the outputs of the three error compensation functions are synthesized into a comprehensive error compensation vector, and comprehensive correction of multi-dimensional errors is performed through vector synthesis. The purpose of this step is to improve measurement accuracy and eliminate the influences of mechanical error, optical error and thermal deformation error on the measurement result.

[0063] The specific implementation of step S05 is to establish and solve a blade platform clearance airflow model. Firstly, a mathematical model of the blade platform clearance airflow is established based on the hydrodynamic boundary layer theory. This model considers the fluid in the clearance as an incompressible viscous fluid, with an applicable Reynolds number range of 500<Re<3000. Then, a numerical solution method is used to solve the airflow model. This method uses finite element technology to discretize the flow field into hexahedral grid units, the number of grids is no less than 500,000, and the grid quality control parameters require an orthogonal quality greater than 0.8 and a skewness less than 0.2. The numerical solution adopts the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm to solve the Navier-Stokes equations. This algorithm is based on the pressure correction principle, adopts an iterative method to solve the velocity field and pressure field, and the iteration convergence criterion is set such that the residual is less than 10 -5 . The input boundary conditions include an inlet flow velocity of 100m / s, an inlet pressure of 1.01×10 5 Pa, a working temperature of 350°C, and a hydrodynamic viscosity of 1.8×10 -5The pressure, velocity, and temperature distributions in the gap region are calculated in Pa·s, forming a numerical solution for the airflow. Simultaneously, based on simplified fluid dynamics equations, an analytical solution for the airflow is derived using the separation of variables method. This method transforms complex partial differential equations into several ordinary differential equations and obtains closed-form solutions. The analytical solution expressions describe the analytical relationship between the velocity and pressure distributions, including parameters such as gap height, width, characteristic length, volumetric flow rate, fluid viscosity coefficient, and inlet pressure. The purpose of this step is to obtain the airflow characteristics of the gap, providing a fluid dynamic basis for gap diagnosis and optimized design.

[0064] The specific implementation of step S06 involves applying airflow numerical solutions to the diagnostic system and optimization design. First, a real-time diagnostic system for blade edge clearance is developed using airflow numerical solutions. This system, based on the principle of fluid-structure interaction, establishes a mapping relationship between clearance changes and airflow parameters. The system employs an artificial neural network algorithm to construct a prediction model. Inputs include parameters such as airflow velocity, pressure distribution, and temperature distribution, and the output is the predicted clearance change trend. The neural network uses a three-layer BP (backpropagation) structure with 20 hidden layer nodes, an activation function of sigmoid, and the Levenberg-Marquardt algorithm for training. The learning rate is set to 0.05, and the training error threshold is 10. -4 When the system detects a gap change exceeding a set threshold (±10% of the normal gap value), an early warning mechanism is triggered to alert maintenance personnel. Then, a gap optimization design module is developed using airflow analytical solutions. This module, based on sensitivity analysis principles, establishes a relationship model between gap parameters and equipment performance indicators. The module employs a multi-objective optimization algorithm to solve for the optimal gap parameters. The objective function includes three indicators: equipment efficiency, lifespan, and reliability, with weighting coefficients of 0.5, 0.3, and 0.2, respectively. The optimization algorithm uses an improved genetic algorithm with a population size of 100, a crossover probability of 0.8, a mutation probability of 0.05, 200 iterations, and a convergence criterion of the optimal solution changing by less than 10⁻⁶ for 20 consecutive generations. 6 The purpose of this step is to achieve real-time monitoring and early warning of the blade rim clearance status, and to provide a theoretical basis for the optimized design of clearance parameters.

[0065] The specific implementation of step S07 involves transforming the gap measurement problem into a traveling salesman problem and solving for the optimal scanning path. First, the set of measurement points is represented as a graph G = (V, E), where the vertex set V represents the measurement points, the edge set E represents the connections between measurement points, and the edge weight is the transition cost between measurement points. Then, a scanning path optimization matrix C is constructed, where the matrix element c represents the comprehensive cost of moving from measurement point i to measurement point j. The calculation formula is a weighted sum of two parts, including the Euclidean distance from point i to point j and the probe attitude adjustment time, with weight coefficients of 0.6 and 0.4, respectively. Next, an improved ant colony algorithm is applied to solve for the optimal scanning sequence. This algorithm introduces a dynamic pheromone adjustment mechanism based on the standard ant colony algorithm. The algorithm parameters are set as follows: number of ants m = 50, pheromone importance factor α = 1, heuristic factor β = 2, pheromone evaporation coefficient ρ = 0.1, initial pheromone concentration τ = 0.01, and maximum number of iterations NC = 200. In each iteration, the ant selects the next visit point based on the state transition probability, calculated using a weighted product of pheromone intensity and heuristic information. During iteration, the pheromone update rule includes both volatilization and deposition, with the deposition amount related to the quality of the ant's path construction. After the algorithm converges, the optimal scanning sequence is obtained, which controls the movement path of the laser scanning probe. This step optimizes measurement efficiency and reduces measurement time and motion errors.

[0066] The specific implementation of step S08 involves performing a gap uniformity analysis. First, circumferential sampling points are extracted from the gap point cloud data. A sampling point is selected every 1° along the circumferential direction of the blade edge, resulting in a total of 360 sampling points, forming a circumferential gap sampling set. Then, the statistical characteristics of the circumferential gap are calculated, including the maximum, minimum, average, and standard deviation. The average is the arithmetic mean of the gap values ​​at all sampling points, and the standard deviation is the root mean square of the sum of the squares of the differences between each point and the average. Next, a uniformity index U = 1 - σ / G is defined. The closer the index value is to 1, the more uniform the gap distribution. The circumferential gradient is then calculated, representing the rate of change of gap between adjacent sampling points, used to evaluate the smoothness of gap changes. Typically, good gap uniformity requires the ratio of the standard deviation to the average gap to be less than 0.1, and the absolute value of the maximum circumferential gradient to be less than 0.05 mm / °. Finally, a circumferential gap distribution curve is plotted, with the horizontal axis representing the circumferential angle (0°~360°) and the vertical axis representing the gap value, visually displaying the trend of gap changes along the circumferential direction. The purpose of this step is to assess the uniformity of the blade rim clearance distribution, providing a quantitative basis for clearance quality control.

[0067] The specific implementation of step S09 involves establishing a mathematical model of the rim gap and performing spectral analysis. First, the circumferential gap curve is represented as a function G(θ) of angle θ, where θ∈[0, 2π]. Then, the Fourier series expansion method is applied to decompose G(θ) into a superposition of fundamental and harmonic components, represented as a linear combination of a constant term and cosine and sine functions. In actual calculations, the Discrete Fourier Transform (DFT) algorithm is used to process the sampled data. This algorithm is implemented through the Fast Fourier Transform (FFT), with a computational complexity of O(NlogN), where N is the number of sampling points. Typically, the first 10 harmonic components are sufficient to reconstruct the original gap curve well, with the truncation error controlled within 5%. Next, the Fourier coefficient spectrum is analyzed, and the amplitude and phase spectra are plotted to identify the main harmonic components and their physical meanings. For example, the first harmonic usually represents the eccentricity of the gap, the second harmonic represents elliptical deformation, and higher harmonics may represent local defects or ripples. Finally, based on the harmonic analysis results, the abnormal variation patterns of the gap are identified, and an abnormal pattern library is established, including typical abnormal patterns such as eccentric, elliptical, wavy, locally bulging, and random fluctuation patterns. The purpose of this step is to reveal the frequency characteristics of the gap variation, providing a frequency domain analysis basis for gap anomaly diagnosis.

[0068] The specific implementation of step S10 involves performing deviation analysis. First, the measured gap surface is registered with the theoretical gap surface. The Iterative Closest Point (ICP) algorithm is used to achieve precise alignment of the two surfaces. The algorithm minimizes the sum of squared distances between the two surfaces iteratively, with convergence conditions defined as an average distance change of less than 1 μm between two consecutive iterations or more than 100 iterations. Then, 1000 points are uniformly sampled on the registered surface, and the normal deviation at each sampling point is calculated, representing the distance between the measured and theoretical points. Next, the deviation distribution characteristics are statistically analyzed, including the maximum positive deviation, maximum negative deviation, average deviation, and standard deviation. Typically, good gap control requires the absolute value of the maximum deviation to not exceed ±5% of the design gap, and the standard deviation to not exceed 2% of the design gap. Finally, a deviation heatmap is generated, using different colors to represent the magnitude of the deviation. The heatmap resolution is set to 100×100 pixels, and a two-color gradient scheme is used for color mapping, with positive deviations represented by red and negative deviations by blue. The color intensity is proportional to the absolute value of the deviation. The purpose of this step is to quantify the difference between the measured clearance and the design clearance, providing intuitive and visual results for clearance quality assessment.

[0069] The specific implementation of step S11 is to generate a measurement evaluation report. First, the statistical results of gap values are summarized, including the maximum gap value, the minimum gap value, the average gap value, the standard deviation, and the coefficient of variation (the ratio of the standard deviation to the average value). Then, the uniformity analysis results are integrated, including the uniformity index, the circumferential gradient distribution, and the smoothness evaluation result. The uniformity evaluation adopts a five-level evaluation standard: excellent (uniformity index U>0.95), good (0.9<U≤0.95), qualified (0.85<U≤0.9), poor (0.8<U≤0.85), and unqualified (U≤0.8). Next, the airflow performance analysis results are summarized, including flow field distribution characteristics, leakage estimation, and efficiency impact assessment. The flow field performance evaluation is based on three key parameters: flow resistance coefficient, leakage, and turbulence intensity, and the evaluation criteria are that the flow resistance coefficient is less than 1.5, the leakage is less than 1% of the design value, and the turbulence intensity is less than 5%. Then, the deviation analysis results are integrated, including the maximum deviation, the average deviation, the deviation distribution characteristics, and the pass rate (the percentage of points whose deviations are within the allowable range), and the qualification criterion is that the absolute value of the deviation is less than 5% of the design gap. Finally, a comprehensive evaluation conclusion is generated based on the above analysis results, using a weighted scoring method, with the weight distribution being 25% for gap value statistics, 25% for uniformity analysis, 30% for airflow performance analysis, and 20% for deviation analysis, with a total score of 100 points, and the evaluation grades are divided into: excellent (90 to 100 points), good (80 to 89 points), qualified (70 to 79 points), and unqualified (<70 points). The function of this step is to comprehensively evaluate the measurement results of the blade platform gap, and provide a decision-making basis for blade assembly quality control.

[0070] The mathematical models or calculation processes involved in the present invention are described in detail below.

[0071] The coordinate transformation algorithm involved in step S01 is expressed by the formula as follows:

[0072] The coordinate transformation relationship between the workpiece coordinate system and the machine coordinate system can be expressed as:

[0073] P m =R·P w +T;

[0074] In the formula, P m is the coordinate vector of the point in the machine coordinate system; P w is the coordinate vector of the point in the workpiece coordinate system; R is a rotation matrix; T is a translation vector.

[0075] The rotation matrix R is composed of three single-axis rotation matrices:

[0076] R=R z (γ)·R y (β)·R x (α);

[0077] In the formula, R x (α), R y (β), R z (γ) represents the matrix of rotation around the X-axis (40), Y-axis (50), and Z-axis (60), respectively; α, β, and γ are the rotation angles around the X-axis, Y-axis, and Z-axis, respectively, in radians.

[0078] The specific representations of each single-axis rotation matrix are as follows:

[0079]

[0080] The rotation angles α, β, and γ are calculated using the coordinates of the feature points. Specifically, this is achieved by selecting three non-collinear feature points at the leaf root (origin O, X-axis point P). x and point P in the XY plane y The coordinates in the machine coordinate system can be used to construct the three basis vectors of the workpiece coordinate system:

[0081]

[0082] The matrix formed by these three basis vectors is the rotation matrix R:

[0083]

[0084] The translation vector T is the coordinate of the origin O in the machine coordinate system.

[0085] The calibration error is calculated using the least squares method, and the formula is as follows:

[0086]

[0087] In the formula, E is the calibration error; n is the number of calibration points, where n = 10; Let be the measured coordinates of the i-th point in the machine coordinate system; Let be the theoretical coordinates of the i-th point in the workpiece coordinate system; |·| denotes the Euclidean norm of the vector.

[0088] The calibration error threshold is set to E threshold =8μm, if E>E threshold Then the calibration process needs to be repeated.

[0089] The calculation formula for the triangulation principle involved in step S02 is expressed as follows:

[0090] Distance calculation based on the principle of triangulation:

[0091]

[0092] In the formula, d is the distance from the target to the laser source; f is the focal length of the receiving lens; b is the distance from the laser source to the optical axis of the receiving lens; and p is the position offset of the laser spot on the CCD.

[0093] The formula for the real-time position error compensation algorithm is expressed as follows:

[0094] P corrected =P measured +ΔP position +ΔP posture ;

[0095] In the formula, P corrected Here are the compensated position coordinates; P measured The original measured coordinates; ΔP position This is the position error compensation amount; ΔP posture This is the attitude error compensation amount.

[0096] Calculation of position error compensation:

[0097]

[0098] In the formula, K p This is the position compensation coefficient, with a value ranging from 0.8 to 1.2; t represents the acceleration vector measured by the accelerometer; t is the measurement time interval.

[0099] Calculation of attitude error compensation:

[0100]

[0101] In the formula, K r This is the attitude compensation coefficient, with a value ranging from 0.9 to 1.1; This is the angular displacement vector measured by the gyroscope; The vector is the direction vector for measurement; × represents the cross product operation.

[0102] The point cloud preprocessing and surface fitting algorithms involved in step S03 are expressed in the following formulas:

[0103] Statistical outlier filtering algorithm:

[0104]

[0105] P i Let |d be an outlier, if |d| i -μ d |>3σ d ;

[0106] In the formula, μ d Let P be the point i The average distance to its k nearest neighbors; σ dd is the standard deviation of the distance; ij Let P be the point i The distance to its j-th nearest neighbor; k is the number of neighboring points, usually ranging from 8 to 20; 3 is the decision coefficient, representing a threshold of 3 times the standard deviation.

[0107] The improved RANSAC algorithm is implemented as follows:

[0108] First, a minimum sample set (at least 3 points) is randomly selected from the preprocessed point cloud to construct an initial surface model;

[0109] Then, calculate the distance from all points to the model, and assign points with distances less than a threshold τ. d Points that are true are considered interior points; otherwise, they are considered exterior points.

[0110] Next, if the number of interior points is greater than the threshold τ n If so, then refit the model using all interior points;

[0111] Repeat the above steps multiple times, and select the model with the most interior points as the final result.

[0112] Wherein, the distance threshold τ d Set to 5μm, interior point number threshold τ n Set it to 60% of the total number of point clouds.

[0113] The mathematical expression for B-spline surface fitting is as follows:

[0114]

[0115] In the formula, S(u, v) is the equation of the B-spline surface; P i，j N is the control point; i，p (u) and N j，q (v) represents the B-spline basis functions in the u and v directions, respectively; n and m represent the number of control points in the u and v directions minus 1, respectively; p and q represent the spline degrees in the u and v directions, respectively.

[0116] B-spline basis functions are defined recursively:

[0117]

[0118] The objective function for least squares fitting is:

[0119]

[0120] In the formula, E fit Q represents the fitting error; N is the number of point cloud data points; Q i Let S(u) be the i-th point cloud data point; i v i ) is the parameter (u iv i The corresponding surface point.

[0121] Fitting accuracy control conditions:

[0122] E fit <τ fit ;

[0123] Where, the fitting accuracy threshold τ fit =5μm.

[0124] Deviation calculation formula:

[0125]

[0126] In the formula, δ i S(u) represents the normal deviation of the i-th sampling point; i v i S represents a point on the measured surface; theory (u i v i () to design the corresponding points on the surface of the theoretical design; is the unit normal vector of the theoretical surface at that point; · represents the dot product of vectors.

[0127] The error compensation function formula involved in step S04 is expressed as follows:

[0128] Spatial position error compensation function:

[0129]

[0130] In the formula, f1(x, y, z, t, T) is the spatial position error compensation function; x, y, z are the spatial coordinate positions in mm; t is the measurement time in seconds; T is the ambient temperature in °C; a ijklm The coefficient is obtained through calibration using a standard block.

[0131] The specific steps for standard block calibration are as follows:

[0132] Step 1: Measure the size of the standard block using a laser sensor under different spatial locations, measurement times, and ambient temperatures;

[0133] Step 2: Calculate the difference between the measured value and the actual size of the standard block as the spatial position error;

[0134] Step 3: Establish the mapping relationship between spatial location, measurement time, ambient temperature, and error, and use the least squares method to fit the polynomial coefficients a. ijklm .

[0135] The three-dimensional spatial position correction vector output by the spatial position error compensation function:

[0136]

[0137] Where f 1x f 1y f 1z These are the components of function f1 in the x, y, and z directions, respectively.

[0138] Optical system error compensation function:

[0139] f2(I,d,θ,M)=b1I+b2d+b3θ+b4M+b5Id+b6Iθ+b7dθ+b8IdθM;

[0140] In the formula, f2(I, d, θ, M) is the optical system error compensation function; I is the light signal intensity in μW; d is the target distance in mm; θ is the incident angle in degrees; M is the material characteristic parameter, dimensionless; b1, b2, ..., b8 are coefficients determined through optical calibration experiments.

[0141] The specific steps of the optical calibration experiment are as follows:

[0142] Step 1: Under different light signal intensities, target distances, incident angles, and material conditions, use a laser scanning probe to measure the standard sample block;

[0143] Step 2: Record the difference between the measured value and the standard value as the optical system error;

[0144] Step 3: Establish the mapping relationship between light signal intensity, target distance, incident angle, material parameters and error, and use multivariate regression analysis to determine the coefficients b1, b2, ..., b8.

[0145] The measurement correction amount output by the optical system error compensation function:

[0146] Δd = f2(I, d, θ, M).

[0147] Material thermal expansion error compensation function:

[0148] f3(T,α,t,σ)=c1αΔT+c2αΔT 2 +c3αtΔT+c4σαΔT;

[0149] In the formula, f3(T, α, t, σ) is the material thermal expansion error compensation function; T is the ambient temperature in °C; α is the material thermal expansion coefficient in 10^-6 / ℃; t is the measurement duration in s; σ is the material stress state in MPa; ΔT=T-T0 is the temperature change, T0 is the reference temperature of 20℃; c1, c2, c3, c4 are coefficients determined through thermal deformation experiments.

[0150] The specific steps of the heat distortion test are as follows:

[0151] Step 1: In a temperature-controlled environment, record the dimensional changes of the standard sample at different temperatures;

[0152] Step 2: Measure the thermal deformation characteristics of the material under different stress states;

[0153] Step 3: Establish the relationship between temperature change, coefficient of thermal expansion, measurement time, stress state and thermal deformation, and use the least squares method to fit and determine the coefficients c1, c2, c3 and c4.

[0154] Heat distortion correction factor:

[0155] K T =f3(T, α, t, σ).

[0156] Calculation of the comprehensive error compensation vector:

[0157]

[0158] In the formula, This is the comprehensive error compensation vector; The vector for spatial position error compensation; Δd is the optical system error correction amount; K is the unit vector for the measurement direction; T This is the thermal distortion correction factor; This is the unit vector representing the direction of thermal expansion.

[0159] The airflow model equations involved in step S05 are expressed as follows:

[0160] The mathematical model of airflow in the rim gap based on boundary layer theory can be expressed as the Navier-Stokes equations:

[0161]

[0162] In the formula, ρ is the fluid density, with units of... t is the fluid velocity vector, in m / s; t is time, in s; p is pressure, in Pa; μ is the fluid dynamic viscosity, in Pa·s. This is the gravitational acceleration vector, with units of . For gradient operators; For the Laplace operator.

[0163] In finite element numerical solutions, the flow field is discretized into mesh elements, and an interpolation function is used within each element:

[0164]

[0165] In the formula, For any position in the flow field Physical quantities at a given location (such as velocity, pressure, etc.); For shape functions; φ i n is the physical quantity value at node i; e This represents the number of unit nodes.

[0166] The iterative process of the SIMPLE algorithm includes the following steps:

[0167] Step 1: Assume an initial pressure field p * ;

[0168] Step 2: Solve the momentum equation to obtain the velocity field.

[0169] Step 3: Solve the pressure correction equation to obtain the pressure correction amount p';

[0170] Step 4: Update the pressure field p = p * +α p p';

[0171] Step 5: Update the velocity field

[0172] Step 6: Check convergence. If convergence is not achieved, return to step 2.

[0173] Where, α p The stress relaxation factor has a value range of 0.1 to 0.3; the convergence criterion is that the residual is less than 10^-5.

[0174] In the analytical method, the simplified fluid dynamics equations are:

[0175]

[0176] In the formula, v x y is the flow velocity in the x-direction; y is the coordinate perpendicular to the wall; μ is the fluid viscosity. This represents the pressure gradient.

[0177] Apply the method of separation of variables, and consider the boundary condition v. x (0)=v x (h) = 0 (no slip condition on the wall), the analytical solution for the velocity distribution can be obtained:

[0178]

[0179] In the formula, h is the gap height.

[0180] Analytical solution for pressure distribution:

[0181]

[0182] In the formula, p0 is the inlet pressure; L is the characteristic length; Q is the volumetric flow rate; and b is the gap width.

[0183] The formula for the scan path optimization algorithm involved in step S07 is as follows:

[0184] Calculation of elements in the scan path optimization matrix C:

[0185] c ij =w1d ij +w2t ij ;

[0186] In the formula, c ij The total cost of moving from measurement point i to measurement point j; d ij t is the Euclidean distance from point i to point j, in mm; ij w1 is the probe attitude adjustment time, in seconds; w2 is the distance weighting coefficient, with a value of 0.6; w3 is the time weighting coefficient, with a value of 0.4.

[0187] Euclidean distance calculation:

[0188]

[0189] In the formula, (x i y i , z i ) and (x j y j , z j ) are the coordinates of measurement points i and j, respectively.

[0190] Attitude adjustment time calculation:

[0191] t ij =k1|θ j -θ i |+k2|φ j -φ i |;

[0192] In the formula, θ i and θ j φ represents the elevation angles at measurement points i and j, respectively, in degrees; i and φ j yaw angles at measurement points i and j are respectively, in degrees; k1 and k2 are time coefficients, with values ​​of 0.01s / degree and 0.012s / degree respectively.

[0193] In the improved ant colony algorithm, the state transition probability is calculated as follows:

[0194]

[0195] In the formula, Let τ be the probability that ant k moves from point i to point j; ij η represents the pheromone concentration along path (i, j); ij =1 / c ij This is heuristic information; α is the pheromone importance factor, with a value of 1; β is the heuristic factor, with a value of 2; allowed k Let k be the set of points that ant k is allowed to visit.

[0196] Pheromones update rules:

[0197]

[0198] In the formula, τ ij (t) and τ ij (t+1) represents the pheromone concentration after the t-th and t+1-th iterations on the path (i, j); ρ is the pheromone volatility coefficient, with a value of 0.1; m is the number of ants, with a value of 50. Let denot be the pheromone increment left by ant k on path (i, j).

[0199] Pheromonium increment calculation:

[0200]

[0201] In the formula, Q is a constant with a value of 100; L k The total length of the path constructed for ant k.

[0202] Dynamic pheromone adjustment mechanism:

[0203]

[0204] In the formula, γ is the dynamic adjustment coefficient, with a value of 0.5; L worst and L best These are the worst and best path lengths in the current iteration, respectively; δ ij δ represents the path advantage, where δ is the current optimal path when path (i, j) belongs to the path advantage. ij =1, otherwise δ ij =0.

[0205] The formula for gap uniformity analysis involved in step S08 is expressed as follows:

[0206] Calculation of statistical characteristics of circumferential clearance:

[0207] G max =max{G i |i = 1, 2, ..., n};

[0208] G min =min{G i |i = 1, 2, ..., n};

[0209]

[0210] In the formula, G i G represents the gap value at the i-th circumferential position; n is the number of sampling points, which takes the value 360; max G is the maximum gap value. min G is the minimum gap value. avg σ is the average gap value; σ is the standard deviation.

[0211] Calculation of uniformity index:

[0212]

[0213] In the formula, U is the uniformity index, which ranges from 0 to 1. The closer the value is to 1, the more uniform the gap distribution.

[0214] Circumferential gradient calculation:

[0215]

[0216] In the formula, θ represents the circumferential gradient at the i-th position, in mm / °. i Let be the angular position of the i-th sampling point.

[0217] The Fourier series expansion formula involved in step S09 is expressed as follows:

[0218] Expand the circumferential clearance curve G(θ) into a Fourier series:

[0219]

[0220] In the formula, G(θ) is the gap value at angle θ; a0 is a constant term; a n and b n θ is the coefficient of the nth harmonic; θ is the circumferential angle, ranging from [0, 2π].

[0221] Fourier coefficient calculation:

[0222]

[0223] For discrete sampling points, the discrete Fourier transform is used for calculation:

[0224]

[0225] In the formula, N is the number of sampling points; Let be the angle of the k-th sampling point.

[0226] Amplitude and phase of harmonic components:

[0227]

[0228] In the formula, A n φ is the amplitude of the nth harmonic; n Let be the phase angle of the nth harmonic.

[0229] The deviation analysis formula involved in step S10 is expressed as follows:

[0230] Objective function of the Iterative Closest Point (ICP) algorithm:

[0231]

[0232] In the formula, E ICP The registration error is represented by N; the number of points is represented by P. i For points in the source point cloud; Q i R represents a point in the target point cloud; R is the rotation matrix; and T is the translation vector.

[0233] ICP algorithm convergence condition:

[0234] or k>k max ;

[0235] In the formula, and τ represents the registration error of the k-th and (k-1)-th iterations, respectively; ICP The convergence threshold is set to 1 μm; k max This represents the maximum number of iterations, with a value of 100.

[0236] Normal deviation calculation:

[0237]

[0238] In the formula, δ i The normal deviation of the i-th sampling point; These are points on the measured curved surface; These are the points corresponding to the theoretical surface; is the unit normal vector of the theoretical surface at that point; · represents the dot product of vectors.

[0239] Calculation of deviation statistical characteristics:

[0240]

[0241] In the formula, The maximum positive deviation; The maximum negative deviation; σ is the average deviation; δ is the standard deviation; N is the number of sampling points, with a value of 1000.

[0242] Pass rate calculation:

[0243]

[0244] In the formula, R qualified For the pass rate; N qualified This refers to the number of points where the absolute value of the deviation does not exceed 5% of the design gap.

[0245] The comprehensive scoring formula for the measurement and evaluation report involved in step S11 is expressed as follows:

[0246] Overall score calculation:

[0247] S total = w1S1 + w2S2 + w3S3 + w4S4;

[0248] In the formula, S total S1 is the total score, with a maximum score of 100 points; S2 is the gap numerical statistical score, with a maximum score of 100 points; S3 is the uniformity analysis score, with a maximum score of 100 points; S4 is the airflow performance analysis score, with a maximum score of 100 points; w1, w2, w3, and w4 are the corresponding weighting coefficients, with values ​​of 0.25, 0.25, 0.3, and 0.2, respectively, and satisfying w1+w2+w3+w4=1.

[0249] Gap value statistical score calculation:

[0250]

[0251] In the formula, G max G is the maximum gap value. min G is the minimum gap value. avg This represents the average gap value. When the calculation result is less than 0, S1 = 0; when the calculation result is greater than 100, S1 = 100.

[0252] Uniformity analysis score calculation:

[0253]

[0254] In the formula, U is the uniformity index; σ is the standard deviation of the gap; G avg This represents the average gap value.

[0255] Calculation of airflow performance analysis score:

[0256] S3 = w 31 S 31 +w 32 S 32 +w 33 S 33 ;

[0257] In the formula, S 31The score is based on the flow resistance coefficient, with a maximum score of 100 points; S 32 Score for leakage amount, with a maximum score of 100; S 33 Scoring is given for turbulence intensity, with a maximum score of 100 points; w 31 w 32 w 33 These are the corresponding weighting coefficients, with values ​​of 0.3, 0.4, and 0.3, respectively, and satisfying w 31 +w 32 +w 33 =1.

[0258] Flow resistance coefficient score calculation:

[0259]

[0260] In the formula, ξ is the actual flow resistance coefficient; max The maximum allowable flow resistance coefficient is set to 1.5. When the calculated result is less than 0, S is taken as... 31 =0.

[0261] Leakage score calculation:

[0262]

[0263] In the formula, Q represents the actual leakage amount; Q design For design flow; Q design ×1% represents the maximum permissible leakage. When the calculated result is less than 0, take S. 32 =0.

[0264] Turbulence intensity score calculation:

[0265]

[0266] In the formula, I represents the actual turbulence intensity; max The maximum allowable turbulence intensity is set to 5%. When the calculated result is less than 0, S is taken as... 33 =0.

[0267] Deviation analysis score calculation:

[0268] S4 = w 41 S 41 +w 42 S 42 ;

[0269] In the formula, S 41 The score for the maximum deviation is 100 points; S 42 The pass rate is scored, with a maximum score of 100 points; w 41 and w 42 These are the corresponding weighting coefficients, with values ​​of 0.4 and 0.6, and satisfying w 41+w 42 =1.

[0270] Maximum deviation score calculation:

[0271]

[0272] In the formula, The maximum positive deviation; For the maximum negative deviation; G design G represents the design clearance value. design ×5% is the maximum allowable deviation. When the calculation result is less than 0, take S. 41 =0.

[0273] Pass rate score calculation:

[0274] S 42 =R qualiified ;

[0275] In the formula, R qualified The pass rate is expressed as a percentage.

[0276] The construction principles and functions of each equation will now be explained in detail:

[0277] The coordinate transformation algorithm in step S01 is based on the principle of rigid body transformation. The transformation between the workpiece coordinate system and the machine coordinate system is achieved by combining rotation matrices and translation vectors, which is the most basic transformation relationship between two coordinate systems in three-dimensional space. The rotation matrix R is decomposed into basic rotations about the three coordinate axes. This decomposition gives the coordinate transformation a clear geometric meaning, making it easy to understand and implement. The calibration error is calculated using the least squares method. This method can comprehensively consider the deviations of multiple calibration points, providing a quantitative assessment of the overall transformation accuracy and ensuring the reliability of the coordinate system establishment.

[0278] The triangulation principle formula in step S02 is derived based on the principle of similar triangles, converting the position offset on the CCD into actual distance through simple geometric relationships. The real-time position error compensation algorithm considers two factors: acceleration and angular velocity, corresponding to position and attitude errors respectively, with a compensation coefficient K. p and K r The algorithm can be determined through experimental calibration, resulting in more accurate compensation. Its advantage lies in its ability to handle dynamic errors during measurement in real time, thus improving the accuracy of the scanning data.

[0279] The statistical outlier filtering algorithm in step S03 is based on the local statistical characteristics of point cloud data. It identifies outliers using the mean distance and standard deviation, with three times the standard deviation used as the judgment threshold, a commonly used confidence interval selection in statistics. The improved RANSAC algorithm, through random sampling and consistency testing, can robustly fit the model even in the presence of noise and outliers, making it particularly suitable for point cloud data processing. B-spline surface fitting technology uses a linear combination of basis functions to represent complex surfaces, exhibiting local support and good continuity. Compared to polynomial fitting, B-spline fitting is more adaptable to local deformations and can more accurately describe the complex shape of the blade edge. Least squares fitting balances the contribution of all data points by minimizing the sum of squared distances from points to the surface, obtaining the globally optimal fitting result.

[0280] The three error compensation functions in step S04 target errors from different sources. The spatial position error compensation function uses a five-element high-order polynomial to describe complex spatial error distributions, encompassing the influence of spatial coordinates, time, and temperature. The high-order terms capture nonlinear effects, and the cross-terms express the coupling effects between factors. The optical system error compensation function considers four main influencing factors: light signal intensity, target distance, incident angle, and material properties. Its function form includes linear and interaction terms, reflecting both the independent influence of each factor and the interaction between them. The material thermal expansion error compensation function is based on thermodynamic principles, considering the combined effects of temperature changes, material properties, time, and stress state on thermal deformation. The first-order term represents linear thermal expansion, the second-order term captures nonlinear effects, the time term reflects thermal hysteresis, and the stress term considers the modulation effect of stress on thermal expansion. The comprehensive error compensation vector integrates the three types of errors through vector synthesis, achieving coordinated correction of multi-dimensional errors and significantly improving measurement accuracy.

[0281] The airflow model in step S05 is based on the Navier-Stokes equations, which are fundamental equations describing the motion of viscous fluids. These equations include inertial terms, pressure gradient terms, viscous terms, and external force terms, comprehensively reflecting the physical nature of fluid motion. Finite element numerical solutions discretize the flow field into mesh elements, and through shape function interpolation within the elements, transform the continuous partial differential equations into a system of discrete algebraic equations. The SIMPLE algorithm uses an iterative approach to solve the velocity and pressure fields, ensuring mass conservation through pressure correction; it is a classic method for solving incompressible flow problems. For analytical solutions, by assuming laminar, steady-state, and fully developed flow, the Navier-Stokes equations are simplified. The separation of variables method transforms the complex partial differential equations into ordinary differential equations, yielding closed-form analytical expressions for the velocity and pressure distributions in the gaps, providing a theoretical basis for subsequent optimization design.

[0282] Step S07, the scan path optimization, transforms the measurement problem into the Traveling Salesman Problem, a classic combinatorial optimization problem. The construction of the scan path optimization matrix considers both spatial distance and attitude adjustment time, balancing their importance through weighting coefficients. The improved ant colony algorithm, based on ant collective foraging behavior, utilizes a pheromone mechanism to achieve positive feedback, guiding the search towards a high-quality solution. The design of the state transition probability balances existing experience (pheromone) and greedy strategies (heuristic information), and the dynamic pheromone adjustment mechanism strengthens the reinforcement of high-quality paths, enabling the algorithm to more effectively escape local optima and find globally optimal or near-optimal scan paths.

[0283] The uniformity index in step S08 is defined as the complement of the ratio of the standard deviation to the mean. This dimensionless index allows for comparison of gaps at different scales, and its value range is limited to 0-1, intuitively reflecting the degree of uniformity. The circumferential gradient calculation uses the difference quotient form to quantify the rate of change of the gaps in space, which is of great significance for identifying local abrupt change regions.

[0284] The Fourier series expansion method in step S09 is a powerful tool for analyzing the spectral characteristics of periodic signals, decomposing the complex gap curve into a superposition of fundamental frequency and harmonic components. The constant term a0 represents the average value of the gap. The first harmonic typically reflects overall eccentricity, the second harmonic exhibits elliptical deformation, and higher harmonics correspond to more complex local variations. This decomposition method not only helps in understanding the gap variation pattern but also identifies abnormal patterns and provides a basis for frequency domain diagnosis.

[0285] The Iterative Closest Point (ICP) algorithm in step S10 is a classic method for point cloud registration, finding the optimal transformation relationship between two point clouds through iterative optimization. The normal deviation calculation considers directional factors and reflects the actual gap deviation more accurately than simple Euclidean distance. The calculation of statistical characteristics comprehensively describes the deviation distribution, including extreme values, average values, and dispersion, providing a quantitative basis for quality assessment.

[0286] The comprehensive scoring system in step S11 employs a multi-level weighted approach, integrating evaluation results from four aspects: clearance value, uniformity, airflow performance, and deviation analysis. The score calculation for each sub-item considers the physical meaning and quality requirements of the corresponding indicator, and the weight allocation reflects the relative importance of each evaluation dimension. This scoring system provides a comprehensive and quantitative evaluation of the blade rim clearance quality, offering an objective basis for assembly quality control.

[0287] In summary, these equations systematically describe the entire process of automatic scanning measurement of blade sill clearance, covering key aspects such as coordinate transformation, error compensation, surface fitting, airflow analysis, path optimization, and quality assessment. The construction of each equation fully considers physical principles and engineering practice; the function forms and parameter selection are based on theoretical grounds while also taking into account application requirements, forming a complete, rigorous, and practical measurement methodology. The innovation of these equations lies in their comprehensive consideration of multi-source errors, multi-dimensional analysis, and multi-index evaluation, providing reliable technical support for high-precision measurement and optimized design of blade sill clearance.

[0288] Specifically, the principle of this invention is based on the scientific foundations of modern precision measurement, multidimensional error compensation, and computational fluid dynamics. First, by establishing the correspondence between the workpiece coordinate system and the machine coordinate system, a spatial reference system for measuring the blade edge clearance is established, laying the foundation for high-precision measurement. The laser scanning probe automatically collects high-density point cloud data at preset intervals, and uses the least squares method to fit and form the clearance surface, providing the original data basis for the measurement.

[0289] The core technological advantage of this invention lies in its multi-dimensional error compensation mechanism. The spatial position error compensation function calculates a three-dimensional spatial position correction vector using parameters such as the machine coordinate system position, system clock measurement time, and ambient temperature, effectively eliminating motion errors in the mechanical system. The optical system error compensation function accurately corrects optical measurement deviations based on parameters such as light signal intensity, target distance, incident angle, and reflective surface material characteristics. The material thermal expansion error compensation function calculates a thermal deformation correction factor based on ambient temperature, material thermal expansion coefficient, measurement duration, and material stress state, effectively offsetting temperature effects. These three error compensation functions work synergistically to form a comprehensive error compensation vector field, achieving systematic compensation for multi-dimensional errors.

[0290] In terms of airflow analysis, this invention establishes an airflow model for the flange gap based on the boundary layer theory of fluid mechanics, and innovatively employs both numerical and analytical methods for analysis. The numerical method obtains the flow field distribution through finite element analysis, while the analytical method derives the airflow theoretical equations through the separation of variables method. This dual solution mechanism provides both the numerical characteristics of the flow field under specific operating conditions and reveals the theoretical laws governing airflow changes, providing a scientific basis for gap optimization design.

[0291] Measurement path optimization is another innovation of this invention. The gap measurement problem is transformed into a traveling salesman problem, and an improved ant colony algorithm is applied to determine the optimal order of visiting measurement points, effectively reducing measurement time. This algorithm continuously optimizes the scanning path by dynamically adjusting pheromone concentration, reducing additional errors caused by system movement and further improving measurement accuracy.

[0292] Furthermore, this invention utilizes mathematical methods such as gap uniformity analysis, Fourier series expansion, and deviation analysis to deeply mine measurement data, identify abnormal gap variation patterns, and provide theoretical support for the optimized design of blade edge gaps. In summary, this invention effectively solves the core problem of multidimensional errors affecting measurement accuracy in existing technologies through a systematic multidimensional error compensation mechanism and scientific data analysis methods.

[0293] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0294] The specific implementation of step S01 involves constructing a high-precision three-dimensional measurement coordinate system. The blade is mounted on a fixture platform with six degrees of freedom adjustment, including three translational degrees of freedom and three rotational degrees of freedom. The fixture platform is driven by a precision servo motor, achieving a positioning accuracy of ±5μm. First, three non-collinear feature points are selected at the root of the blade and marked as the origin O, the X-axis point P, etc. x and point P in the XY plane y A high-precision laser sensor is used to scan and locate these three feature points, obtaining their position coordinates in the machine coordinate system. Then, based on the obtained coordinates of the three feature points, a coordinate transformation algorithm is used to establish the coordinate transformation relationship between the workpiece coordinate system and the machine coordinate system, which can be expressed as: P m =R·P w +T, where P m P is the coordinate vector of a point in the machine coordinate system; w Let R be the coordinate vector of the point in the workpiece coordinate system; R is the rotation matrix; and T is the translation vector. The rotation matrix R is composed of three single-axis rotation matrices: R = R z (γ)·R y (β)·R x (α), where R x (α), R y (β), R z (γ) represents the rotation matrix around the X, Y, and Z axes, respectively; α, β, and γ are the rotation angles around the X, Y, and Z axes, respectively, in radians. The specific representations of each single-axis rotation matrix are as follows: Based on the three selected feature points, three basis vectors of the workpiece coordinate system can be constructed: The matrix formed by these three basis vectors is the rotation matrix R, and the translation vector T is the coordinate of the origin O in the machine coordinate system. Next, the accuracy of the established coordinate system is verified using a multi-point calibration method. Ten known position points on the blade surface are selected, and their coordinate values ​​are measured in both the workpiece coordinate system and the machine coordinate system. The calibration error is calculated using the least squares method. In the formula, E is the calibration error; n is the number of calibration points, where n = 10; Let be the measured coordinates of the i-th point in the machine coordinate system; Let be the theoretical coordinates of the i-th point in the workpiece coordinate system; if the calibration error exceeds the threshold E threshold If the value is 8μm, the calibration process is repeated. The purpose of this step is to establish a unified measurement benchmark, ensure the accuracy and consistency of subsequent measurement data, and provide a spatial positioning basis for gap scanning.

[0295] The specific implementation of step S02 involves using a high-precision laser scanning probe to perform a full-circumferential automatic scan of the blade edge clearance. First, the laser scanning probe employs the triangulation principle. A laser beam with a wavelength of 650nm is emitted from the laser source and focused onto the blade edge surface through a lens system. The reflected light is then converged onto a CCD sensor through a receiving lens. The target distance is calculated based on the positional change of the laser spot on the CCD, with a measurement accuracy of 0.5μm and a measurement frequency of 5kHz. The distance calculation formula is: In the formula, d is the distance from the target to the laser source; f is the focal length of the receiving lens; b is the distance from the laser source to the optical axis of the receiving lens; and p is the position offset of the laser spot on the CCD. Then, based on the geometric characteristics of the blade edge plate, a scanning path is designed, and the probe moves along the blade edge plate contour at preset intervals of 0.5 mm to ensure that the scanning density meets the requirements of gap analysis. During the scanning process, the system acquires three-dimensional coordinate data and reflection intensity information in real time, forming a gap point cloud dataset with a point cloud density of no less than 1 mm. 2 The area contains 50 sampling points. To ensure measurement stability, the system uses a real-time position error compensation algorithm, which monitors the probe's pose changes using a gyroscope and accelerometer, and performs real-time corrections. The compensation formula is: P corrected =P measured +ΔP position +ΔP posture In the formula, P corrected Here are the compensated position coordinates; P measured The original measured coordinates; ΔP position The position error compensation amount is calculated as follows: Where K p This is the position compensation coefficient, with a value ranging from 0.8 to 1.2; ΔP is the acceleration vector measured by the accelerometer; t is the measurement time interval; ΔP posture The attitude error compensation amount is calculated as follows: Where K r This is the attitude compensation coefficient, with a value ranging from 0.9 to 1.1; This is the angular displacement vector measured by the gyroscope; The measurement direction vector achieves pose compensation accuracy of ±2μm and ±0.01°. The high-density point cloud data acquired in this step provides the raw data foundation for subsequent gap analysis, enabling an accurate description of the full circumferential morphology of the blade sill gap.

[0296] The specific implementation of step S03 is based on surface fitting and deviation analysis of the acquired gap point cloud data. First, the point cloud data is preprocessed, and a statistical outlier filtering algorithm is used to remove noise points. The algorithm calculates the average distance from each point to its neighboring points based on the local statistical characteristics of the point cloud. If this distance exceeds three times the standard deviation, it is identified as an outlier and removed. The specific calculation formula is as follows: The judgment condition is: if |d i -μ d |>3σ d Then P i Let μ be an outlier, where μ is an outlier. d Let P be the point i The average distance to its k nearest neighbors; σ d d is the standard deviation of the distance; ij Let P be the point i The distance to its j-th nearest neighbor; k is the number of neighboring points, typically ranging from 8 to 20. Then, an improved random sampling consensus algorithm is used to select sample points from the preprocessed point cloud to construct an initial surface model. This algorithm reduces the influence of outliers and improves fitting stability through iterative optimization. Next, B-spline surface fitting technology is applied to fit the gap point cloud into a continuous and smooth three-dimensional surface, the mathematical expression of which is: In the formula, S(u, v) is the equation of the B-spline surface; P i，j N is the control point; i，p (u) and N j，q (v) represents the B-spline basis functions in the u and v directions, respectively; n and m represent the number of control points in the u and v directions minus 1, respectively; p and q represent the spline degrees in the u and v directions, respectively. During the fitting process, the least squares method is used to minimize the sum of squared distances from points to the surface. The objective function is: In the formula, E fit Q represents the fitting error; N is the number of point cloud data points; Q i Let S(u) be the i-th point cloud data point; i v i ) is the parameter (u i v i The corresponding surface points; the fitting accuracy is controlled within 5μm, i.e., E fit <5μm. Subsequently, the fitted surface was compared with the theoretical design model, and the normal distance from 5000 uniformly distributed sampling points on the measured surface to the theoretical surface was calculated. The deviation calculation formula is as follows: In the formula, δi S(u) represents the normal deviation of the i-th sampling point; i v i S represents a point on the measured surface; theory (u i v i () to design the corresponding points on the surface of the theoretical design; This represents the unit normal vector of the theoretical surface at that point. Then, a deviation matrix is ​​constructed, and a gap distribution map is plotted. This map uses color coding to visually display the gap distribution, with the deviation range divided into 10 levels, each represented by a different color. The purpose of this step is to quantify the actual morphology of the blade edge gap, providing a geometric basis for subsequent analysis and evaluation.

[0297] The specific implementation of step S04 involves constructing a comprehensive error compensation vector field to achieve multi-dimensional error correction. First, a spatial position error compensation function is established. This function uses a polynomial fitting method to describe the motion error of the mechanical system, and its expression is: In the formula, f1(x, y, z, t, T) is the spatial position error compensation function; x, y, z are the spatial coordinate positions in mm; t is the measurement time in seconds; T is the ambient temperature in °C; a ijklm The coefficients are obtained through standard block calibration, and the output is a three-dimensional spatial position correction vector. Then, an optical system error compensation function is constructed. This function is based on the principle of optical imaging and is expressed as: f2(I, d, θ, M)=b1I+b2d+b3θ+b4M+b5Id+b6Iθ+b7dθ+b8IdθM, where f2(I, d, θ, M) is the optical system error compensation function; I is the light signal intensity in μW; d is the target distance in mm; θ is the incident angle in degrees; M is the material characteristic parameter, dimensionless; b1, b2, ..., b8 are coefficients determined through optical calibration experiments, and the output is the measurement correction Δd=f2(I, d, θ, M). Next, a material thermal expansion error compensation function is established. This function is based on the principle of thermodynamics and is expressed as: f3(T, α, t, σ)=c1αΔT+c2αΔT 2 The formula is: f3(T, α, t, σ) = c3αtΔT + c4σαΔT, where f3(T, α, t, σ) is the material thermal expansion error compensation function; T is the ambient temperature in °C; α is the material thermal expansion coefficient in 10^-6 / ℃; t is the measurement duration in seconds; σ is the material stress state in MPa; ΔT = T - T0 is the temperature change, T0 is the reference temperature of 20℃; c1, c2, c3, c4 are coefficients determined through thermal deformation experiments, and the output is the thermal deformation correction factor K. T=f3(T, α, t, σ). Finally, the outputs of the three error compensation functions are synthesized into a comprehensive error compensation vector: where, is the comprehensive error compensation vector; is the unit vector in the measurement direction; is the unit vector in the thermal expansion direction. The purpose of this step is to improve measurement accuracy and eliminate the influences of mechanical errors, optical errors and thermal deformation errors on the measurement results.

[0298] The specific implementation of step S05 is to establish and solve a blade platform clearance airflow model. First, a mathematical model of the airflow in the blade platform clearance is established based on the hydrodynamic boundary layer theory, which is expressed as the Navier-Stokes equation: where ρ is the fluid density, in kg / m 3 ; is the fluid velocity vector, in m / s; t is the time, in s; p is the pressure, in Pa; μ is the dynamic viscosity of the fluid, in Pa·s; is the gravitational acceleration vector, in m / s 2 ; this model considers the fluid in the clearance as an incompressible viscous fluid, with an applicable Reynolds number range of 500<Re<3000. Then, a numerical solution method is used to solve the airflow model. This method uses finite element technology to discretize the flow field into hexahedral mesh units, the number of meshes is no less than 500,000, and the mesh quality control parameters require the orthogonal quality to be greater than 0.8 and the skewness to be less than 0.2. Interpolation functions are used in each unit to represent physical quantities: where, is the physical quantity at any position in the flow field ; is the shape function; φ i is the physical quantity value at node i; n e is the number of unit nodes. The numerical solution adopts the semi-implicit pressure coupled equation algorithm to solve the Navier-Stokes equation. Based on the pressure correction principle, this algorithm solves the velocity field and the pressure field in an iterative manner, and the iteration convergence criterion is set such that the residual is less than 10-5. The input boundary conditions include an inlet flow velocity of 100 m / s, an inlet pressure of 1.01×10^5 Pa, a working temperature of 350°C and a dynamic fluid viscosity of 1.8×10^-5 Pa·s. The data set of pressure distribution, velocity distribution and temperature distribution in the clearance area is calculated to form a numerical airflow solution. At the same time, based on the simplified hydrodynamic equation, the variable separation method is applied to derive the analytical airflow solution, and the simplified equation is: where v x is the flow velocity in the x direction; y is the coordinate perpendicular to the wall surface; considering the boundary condition v x (0)=v x(h) = 0 (no slip condition on the wall), thus obtaining the analytical solution for the velocity distribution: In the formula, h is the gap height. The analytical solution for pressure distribution is: In the formula, p0 is the inlet pressure; L is the characteristic length; Q is the volumetric flow rate; and b is the gap width. This step aims to obtain the gap airflow characteristics, providing a fluid dynamic basis for gap diagnosis and optimized design.

[0299] The specific implementation of step S06 involves applying airflow numerical solutions to the diagnostic system and optimization design. First, a real-time diagnostic system for blade edge clearance is developed using airflow numerical solutions. This system, based on the principle of fluid-structure interaction, establishes a mapping relationship between clearance changes and airflow parameters. The system employs an artificial neural network algorithm to construct a prediction model. Inputs include parameters such as airflow velocity, pressure distribution, and temperature distribution, and the output is the predicted clearance change trend. The neural network uses a three-layer backpropagation structure with 20 hidden layer nodes, an activation function of sigmoid, and the Levenberg-Marquardt algorithm for training. The learning rate is set to 0.05, and the training error threshold is 10. -4 When the system detects a gap change exceeding a set threshold (±10% of the normal gap value), an early warning mechanism is triggered to alert maintenance personnel. Then, a gap optimization design module is developed using airflow analytical solutions. This module, based on sensitivity analysis principles, establishes a relationship model between gap parameters and equipment performance indicators. The module employs a multi-objective optimization algorithm to solve for the optimal gap parameters. The objective function includes three indicators: equipment efficiency, lifespan, and reliability, with weighting coefficients of 0.5, 0.3, and 0.2, respectively. The optimization algorithm uses an improved genetic algorithm with a population size of 100, a crossover probability of 0.8, a mutation probability of 0.05, 200 iterations, and a convergence criterion of the optimal solution changing by less than 10 for 20 consecutive generations. -6 The purpose of this step is to achieve real-time monitoring and early warning of the blade rim clearance status, and to provide a theoretical basis for the optimized design of clearance parameters.

[0300] The specific implementation of step S07 involves transforming the gap measurement problem into a traveling salesman problem and solving for the optimal scan path. First, the set of measurement points is represented as a graph G = (V, E), where the vertex set V represents the measurement points, the edge set E represents the connections between measurement points, and the edge weight is the transformation cost between measurement points. Then, a scan path optimization matrix C is constructed, with the matrix element calculation formula as follows: c ij =w1d ij +w2t ij In the formula, c ij The total cost of moving from measurement point i to measurement point j; d ij Let the Euclidean distance from point i to point j be: t ij The probe attitude adjustment time is calculated as: tij =k1|θ j -θ i |+k2|φ j -φ i |, where θ i and θ j The pitch angles at measurement points i and j are φ, respectively. i and φ j Let be the yaw angles at measurement points i and j, respectively; k1 and k2 are time coefficients, with values ​​of 0.01 s / degree and 0.012 s / degree, respectively; w1 is the distance weighting coefficient, with a value of 0.6; and w2 is the time weighting coefficient, with a value of 0.4. Next, an improved ant colony algorithm is applied to solve for the optimal scanning sequence. This algorithm introduces a dynamic pheromone adjustment mechanism based on the standard ant colony algorithm. The state transition probability is calculated using the following formula: In the formula, Let τ be the probability that ant k moves from point i to point j; ij η represents the pheromone concentration along path (i, j); ij =1 / c ij This is heuristic information; α is the pheromone importance factor, with a value of 1; β is the heuristic factor, with a value of 2; allowed k Let be the set of points that ant k is allowed to visit. The pheromone update rule is: In the formula, ρ is the pheromone evaporation coefficient, with a value of 0.1; m is the number of ants, with a value of 50; Let be the pheromone increment left by ant k on path (i, j). If ant k passes through path (i, j), then... Otherwise, it is 0, where Q is a constant with a value of 100, and L k The total length of the path constructed for ant k. The dynamic pheromone adjustment mechanism is as follows: In the formula, γ is the dynamic adjustment coefficient, with a value of 0.5; L worst and L best These are the worst and best path lengths in the current iteration, respectively; δ ij δ represents the path advantage, where δ is the current optimal path when path (i, j) belongs to the path advantage. ij =1, otherwise δ ij =0. After the algorithm converges, the optimal scanning sequence is obtained, which is used to control the movement path of the laser scanning probe. The purpose of this step is to optimize measurement efficiency and reduce measurement time and motion error.

[0301] The specific implementation of step S08 involves performing gap uniformity analysis. First, circumferential sampling points are extracted from the gap point cloud data. One sampling point is selected every 1° along the circumferential direction of the blade edge, resulting in a total of 360 sampling points, forming a circumferential gap sampling set. Then, the statistical characteristics of the circumferential gap are calculated, including the maximum value G. max =max{G i |i=1,2,…,n}、Minimum value G min =min{G i |i=1,2,…,n}, average value and standard deviation In the formula, G i Let be the gap value at the i-th circumferential position; n is the number of sampling points, which takes the value 360. Next, define the uniformity index. The closer the value of this index is to 1, the more uniform the gap distribution. The circumferential gradient is then calculated. In the formula, θ represents the circumferential gradient at the i-th position, in mm / °. i Let represent the angular position of the i-th sampling point. Generally, good clearance uniformity requires the ratio of the standard deviation to the average clearance to be less than 0.1, and the absolute value of the maximum circumferential gradient to be less than 0.05 mm / °. Finally, a circumferential clearance distribution curve is plotted, with the horizontal axis representing the circumferential angle (0°–360°) and the vertical axis representing the clearance value, visually displaying the trend of clearance variation in the circumferential direction. The purpose of this step is to evaluate the uniformity of the blade rim clearance distribution, providing a quantitative basis for clearance quality control.

[0302] The specific implementation of step S09 involves establishing a mathematical model of the shroud gap and performing spectral analysis. First, the circumferential gap curve is expressed as a function G(θ) of angle θ, where θ∈[0, 2π]. Then, the Fourier series expansion method is applied to decompose G(θ) into a superposition of fundamental frequency and harmonic components, with the expansion being: In the formula, a0 is a constant term; a n and b n These are the coefficients of the nth harmonic. Fourier coefficient calculation:

[0303] For discrete sampling points, the discrete Fourier transform is used for calculation: In the formula, N is the number of sampling points; Let be the angle at the k-th sampling point. In actual calculations, the Discrete Fourier Transform algorithm is used to process the sampled data. This algorithm is implemented through the Fast Fourier Transform, with a computational complexity of O(NlogN), where N is the number of sampling points. Typically, taking the first 10 harmonic components is sufficient to reconstruct the original gap curve well, with the truncation error controlled within 5%. Next, the Fourier coefficient spectrum is analyzed to calculate the amplitude and phase of the harmonic components: In the formula, A n φ is the amplitude of the nth harmonic; n Let be the phase angle of the nth harmonic. By plotting the amplitude and phase spectra, the main harmonic components and their physical meanings are identified. For example, the first harmonic typically represents the eccentricity of the gap, the second harmonic represents elliptical deformation, and higher harmonics may represent local defects or ripples. Finally, based on the harmonic analysis results, the abnormal variation patterns of the gap are identified, and an anomaly pattern library is established, including typical anomaly patterns such as eccentric, elliptical, wavy, locally bulging, and random fluctuation patterns. The purpose of this step is to reveal the frequency characteristics of the gap variation, providing a frequency domain analysis basis for gap anomaly diagnosis.

[0304] The specific implementation of step S10 involves performing deviation analysis. First, the measured gap surface is registered with the theoretically designed gap surface. An iterative nearest-point algorithm is used to achieve precise alignment of the two surfaces. The objective function of the algorithm is: In the formula, E ICP The registration error is represented by N; the number of points is represented by P. i For points in the source point cloud; Q i Let R be a point in the target point cloud; R be the rotation matrix; and T be the translation vector. The algorithm convergence condition is: or k>k max In the formula, and τ represents the registration error of the k-th and (k-1)-th iterations, respectively; ICP The convergence threshold is set to 1 μm; k max The maximum number of iterations is set to 100. Then, 1000 points are uniformly sampled on the registered surface, and the normal deviation at each sampling point is calculated: In the formula, δ i The normal deviation of the i-th sampling point; These are points on the measured curved surface; These are the points corresponding to the theoretical surface; Let be the unit normal vector of the theoretical surface at that point. Next, the statistical deviation distribution characteristics, including the maximum positive deviation, are analyzed. Maximum negative deviation average deviation Sum of deviations and standard deviations Calculate the pass rate: wherein, R qualified is the pass rate; N qualified is the number of points where the absolute value of the deviation does not exceed 5% of the design clearance. Generally, good clearance control requires that the absolute value of the maximum deviation does not exceed ±5% of the design clearance, and the standard deviation does not exceed 2% of the design clearance. Finally, a deviation heat map is generated, where different colors are used to represent the deviation magnitude, the resolution of the heat map is set to 100×100 pixels, a two-color gradient scheme is adopted for color mapping, positive deviations are represented by a red color system, negative deviations are represented by a blue color system, and the color depth is proportional to the absolute value of the deviation. The purpose of this step is to quantify the difference between the measured clearance and the design clearance, and provide an intuitive visualization result for clearance quality assessment.

[0305] The specific implementation of step S11 is to generate a measurement and evaluation report. First, the statistical results of clearance values are summarized, including the maximum clearance value, the minimum clearance value, the average clearance value, the standard deviation, and the coefficient of variation (the ratio of the standard deviation to the average value). Then, the uniformity analysis results are integrated, including the uniformity index, the circumferential gradient distribution and the smoothness evaluation result. The uniformity evaluation adopts a five-level evaluation standard: excellent (uniformity index U>0.95), good (0.9<U≤0.95), qualified (0.85<U≤0.9), poor (0.8<U≤0.85) and unqualified (U≤0.8). Next, the airflow performance analysis results are summarized, including flow field distribution characteristics, leakage estimation and efficiency impact assessment. The flow field performance assessment is based on three key parameters: flow resistance coefficient, leakage and turbulence intensity, and the evaluation criteria are that the flow resistance coefficient is less than 1.5, the leakage is less than 1% of the design value, and the turbulence intensity is less than 5%. Then, the deviation analysis results are integrated, including the maximum deviation, average deviation, deviation distribution characteristics and pass rate, and the qualification standard is that the absolute value of the deviation is less than 5% of the design clearance. Finally, a comprehensive evaluation conclusion is generated based on the above analysis results, and a weighted scoring method is used to calculate the total score: S total =w1S1+w2S2+w3S3+w4S4, wherein, S total is the total score, with a full score of 100 points; S1 is the clearance value statistical score, which is calculated as: S2 is the uniformity analysis score, which is calculated as: S3 is the airflow performance analysis score, which is calculated as: S3=w 31 S 31 +w 32 S 32 +w 33 S 33 , wherein S 31 is the flow resistance coefficient score, S 32 is the leakage score, S 33 is the turbulence intensity score; S4 is the deviation analysis score, which is calculated as: S4=w 41 S 41+w 42 S 42 S 41 S is the score for the maximum deviation. 42 The pass rate score is calculated using w1, w2, w3, and w4, which are the corresponding weighting coefficients with values ​​of 0.25, 0.25, 0.3, and 0.2, respectively. Evaluation levels are categorized as: Excellent (90–100 points), Good (80–89 points), Pass (70–79 points), and Unqualified (<70 points). This step aims to comprehensively evaluate the blade rim clearance measurement results, providing a basis for decision-making regarding blade assembly quality control.

[0306] Through the specific implementation of steps S01 to S11 above, this method achieves high-precision automatic scanning measurement of blade rim clearance. First, a unified coordinate system is established to ensure the spatial reference for measurement. Then, a high-precision laser scanning probe is used to acquire clearance point cloud data. Next, various algorithms are employed to process and analyze the point cloud data, including surface fitting, error compensation, airflow model solving, path optimization, uniformity analysis, spectral analysis, and deviation analysis. Finally, a comprehensive evaluation report is generated. Compared with traditional measurement methods, this method has the following advantages: First, high measurement accuracy, improving measurement accuracy to the micrometer level through multi-dimensional error compensation; second, high measurement efficiency, reducing measurement time and motion errors through path optimization algorithms; third, comprehensive analysis, combining geometric features, fluid characteristics, and spectral characteristics for multi-dimensional evaluation of the clearance; and fourth, strong practicality, providing a complete solution from measurement to evaluation. The application of this method can significantly improve the measurement accuracy and control level of blade rim clearance, ensuring equipment operating efficiency and reliability.

[0307] The innovations of this method are mainly reflected in the following aspects: First, a comprehensive error compensation mechanism is proposed, unifying spatial position error, optical system error, and material thermal expansion error into a single compensation framework; second, a gap airflow model based on fluid dynamics is established, organically combining geometric measurement with performance evaluation; third, an improved ant colony algorithm is introduced to optimize the scanning path, improving measurement efficiency; fourth, the Fourier series expansion method is used to analyze the circumferential distribution characteristics of the gap, providing a new method for anomaly diagnosis; and fifth, a comprehensive scoring system based on multi-index weighting is constructed, realizing the quantitative evaluation of gap quality. These innovations together constitute an efficient, accurate, and practical automatic scanning measurement method for blade edge gaps.

[0308] To better understand and implement this invention, a specific application scenario is provided below as Example 2: At a gas turbine research center, the blade clearance of a medium-sized gas turbine's high-pressure impeller was measured. The impeller has a diameter of 450 mm, contains 72 blades, is designed to operate at 350°C, and has a theoretical blade tip clearance of 0.8 mm. To ensure the gas turbine maintains good sealing and operating efficiency during high-speed operation, researchers used the automatic blade blade clearance scanning measurement method of this invention for detailed measurement and analysis.

[0309] First, the researchers established a measurement coordinate system, mounted the blade on a fixture platform with six degrees of freedom adjustment, and calibrated it using a laser sensor with an accuracy of ±0.8 μm. By selecting three non-collinear feature points at the blade root, a workpiece coordinate system was established, and the coordinate transformation accuracy was verified through 10 calibration points. The calibration result error was 5.2 μm, below the threshold requirement of 8 μm, meeting the measurement accuracy requirements.

[0310] Then, the researchers used a 650nm laser scanning probe to scan the blade edge clearance. The measurement frequency was set to 4kHz, and a measurement point was taken every 0.4mm along the blade edge profile, collecting approximately 15,000 point cloud data points. During the measurement process, the system automatically applied a position error compensation algorithm, with a position compensation coefficient K. p The attitude compensation coefficient K is 1.05. r The value is 0.98, which significantly improves the stability of the measurement.

[0311] For the acquired point cloud data, the researchers first applied a statistical outlier filtering algorithm for preprocessing, setting the number of neighborhood points k to 12, which removed approximately 2.3% of outliers. Then, a gap surface model was constructed using B-spline surface fitting technology, with 35 and 42 control points in the u and v directions, respectively, and spline degree 3 in both directions, achieving a fitting accuracy of 3.7 μm.

[0312] To improve measurement accuracy, researchers applied a comprehensive error compensation mechanism. The coefficients of the spatial position error compensation function were obtained through standard block calibration, and some key coefficients are shown in Table 1.

[0313] Table 1 Key Coefficients of Spatial Location Error Compensation Function

[0314] coefficient X direction value Y-direction value Z-direction value <![CDATA[a 1000 ]]> 0.0025 0.0019 0.0031 <![CDATA[a 0100 ]]> 0.0018 0.0027 0.0022 <![CDATA[a 0010 ]]> 0.0029 0.0023 0.0035 <![CDATA[a 0001 ]]> 0.0015 0.0012 0.0018 <![CDATA[a 1100 ]]> 0.0008 0.0009 0.0011 <![CDATA[a 0110 ]]> 0.0007 0.0010 0.0009

[0315] The coefficients of the optical system error compensation function were determined through optical calibration experiments, and the results are shown in Table 2.

[0316] Table 2 Coefficients of Optical System Error Compensation Function

[0317]

[0318]

[0319] The coefficients of the material's thermal expansion error compensation function were determined through a thermal deformation experiment, where c1 = 0.92, c2 = 0.15, c3 = 0.06, and c4 = 0.04. The ambient temperature during the measurement was 24.5℃, and the material's thermal expansion coefficient was 11.2 × 10⁻⁶. -6 / ℃, measurement duration is 35 minutes.

[0320] Researchers established and solved an airflow model for the gap between the flanges. The flow field was discretized into 625,000 hexahedral mesh elements using the finite element method, with an average mesh quality of 0.87. The Navier-Stokes equations were solved using a semi-implicit pressure coupling equation algorithm, and the residuals converged to 8.5 × 10⁻⁶. -6 The input boundary conditions include an inlet velocity of 92 m / s, an inlet pressure of 1.02 × 10⁵ Pa, and an operating temperature of 345 °C. The calculated airflow characteristic parameters of the gap region are shown in Table 3.

[0321] Table 3. Airflow characteristic parameters in the gap region

[0322] parameter Minimum value Maximum value average value Pressure (Pa) 0.82×10^5 1.05×10^5 0.94×10^5 Speed ​​(m / s) 75.3 138.7 105.2 Temperature (°C) 332.5 358.3 344.6 Turbulence intensity 0.018 0.047 0.032

[0323] To improve measurement efficiency, researchers optimized the scanning path using an improved ant colony algorithm. The algorithm parameters were set as follows: number of ants m = 45, pheromone importance factor α = 1, heuristic factor β = 2.2, pheromone evaporation coefficient ρ = 0.12, and dynamic adjustment coefficient γ = 0.45. After 185 iterations, the algorithm converged, and the optimal scanning path obtained was 37.5% shorter than the original path, significantly improving measurement efficiency.

[0324] The researchers performed a gap uniformity analysis on the measurement results, and the results are shown in Table 4:

[0325] Table 4 Results of Gap Uniformity Analysis

[0326] parameter numerical values Maximum gap value (mm) 0.875 Minimum gap value (mm) 0.722 Average gap value (mm) 0.802 Standard deviation (mm) 0.065 Uniformity index 0.919 Maximum circumferential gradient (mm / °) 0.0435

[0327] The circumferential distribution characteristics of the gap were analyzed using the Fourier series expansion method. The amplitudes and phases of the first five harmonic components are shown in Table 5.

[0328] Table 5 Fourier coefficients of the circumferential distribution of the gap

[0329] order Amplitude (mm) Phase (rad) 0 0.802 - 1 0.048 0.84 2 0.032 1.57 3 0.018 0.36 4 0.009 2.15 5 0.005 1.22

[0330] Researchers used the iterative nearest-point algorithm to register the measured surface with the theoretically designed surface. The algorithm converged after 76 iterations with a registration error of 0.7 μm. 1000 points were uniformly sampled on the registered surface, and the normal deviation was calculated. The results are shown in Table 6.

[0331] Table 6. Results of Deviation Analysis

[0332] parameter numerical values Maximum positive deviation (mm) 0.075 Maximum negative deviation (mm) -0.078 Average deviation (mm) 0.002 Standard deviation (mm) 0.031 Pass rate (%) 96.3

[0333] Finally, the researchers generated a comprehensive evaluation report, calculated the total score and scores for each sub-item, and the results are shown in Table 7:

[0334] Table 7 Overall Evaluation Score

[0335] Evaluation Project Weight Score Weighted score Gap value statistics 0.25 82.5 20.63 homogeneity analysis 0.25 91.9 22.98 Airflow performance analysis 0.30 88.7 26.61 Deviation analysis 0.20 90.2 18.04 Overall score 1.00 - 88.26

[0336] According to the evaluation criteria, the blade rim clearance quality is rated as "good".

[0337] Traditional blade edge clearance measurements typically employ contact methods, such as micrometers or measuring arms, or simple non-contact methods like single-point laser ranging. These traditional methods suffer from low measurement accuracy (generally only around 0.05 mm), a limited number of measurement points (usually only 5-10 points per blade), the inability to achieve real-time dynamic measurement, and difficulty in compensating for systematic errors. Furthermore, traditional methods struggle to correlate measurement data with airflow performance, making a comprehensive and quantitative evaluation of the clearance impossible.

[0338] In comparison, the method of this invention brings significant progress: First, the measurement accuracy is improved by an order of magnitude, reaching the micrometer level; second, it achieves full-circumferential high-density scanning, providing complete gap distribution information; third, it significantly reduces measurement errors through a comprehensive error compensation mechanism; fourth, it combines geometric measurement with airflow analysis, providing more practical evaluation results; and fifth, it improves measurement efficiency and diagnostic capabilities through innovative technologies such as path optimization and Fourier analysis.

[0339] It should be noted that the variables involved in this invention are explained in detail in Table 8-10 below.

[0340] Table 8. Variable Explanation Table a

[0341]

[0342] Table 9. Variable Explanation Table b

[0343]

[0344]

[0345] Table 10 Variable Explanation Table c

[0346]

[0347]

[0348] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. An automatic scanning measurement method for blade rim clearance, characterized in that, include: S01. Construct a three-dimensional measurement coordinate system, install the blade on a fixture platform with multi-degree-of-freedom adjustment function, and use a high-precision laser sensor to establish the correspondence between the workpiece coordinate system and the machine coordinate system and perform calibration. S02. A laser scanning probe is used to perform a full-circumferential automatic scan of the blade edge plate gap. The laser scanning probe moves along the blade edge plate contour at preset intervals to collect gap point cloud data and form a gap contour curve. S03. Based on the gap point cloud data, fit the blade edge plate gap surface using the least squares method, calculate the geometric deviation between the measured surface and the theoretical model, and establish a gap distribution mapping map. S04. Construct a comprehensive error compensation vector field and apply the spatial position error compensation function, the optical system error compensation function, and the material thermal expansion error compensation function to perform multi-dimensional error correction. S05. Based on the fluid dynamics boundary layer theory, establish an airflow model for the gap between the flanges. Use numerical solution methods to perform finite element analysis on the airflow model to obtain the numerical solution of the airflow. Use analytical solution methods to derive the theoretical equations of the airflow to obtain the analytical solution of the airflow. S06. The numerical solution of the airflow is applied to the real-time diagnostic system for blade rim clearance to predict the clearance change trend under different operating conditions; the analytical solution of the airflow is applied to the clearance optimization design module to guide the optimization of blade rim clearance design parameters. S07. The gap measurement problem is transformed into a traveling salesman problem to find the optimal scanning path. An improved ant colony algorithm is applied to determine the order of measurement point visits and to construct a scanning path optimization matrix to reduce measurement time and system motion error. S08. Perform gap uniformity analysis, calculate the standard deviation and variation trend of the blade edge gap in the circumferential position, and evaluate the degree of gap distribution uniformity. S09. Establish a mathematical model of the gap between the sash plates, decompose the gap curve into fundamental frequency components and harmonic components using the Fourier series expansion method, and identify the abnormal change law of the gap. S10. Perform deviation analysis, calculate the maximum deviation, average deviation and deviation distribution characteristics between the measured gap and the theoretical design gap, and generate a deviation heat map. S11. Generate a measurement and evaluation report, including statistical results of gap values, uniformity analysis results, airflow performance analysis results, and deviation analysis results, to provide a basis for blade assembly quality control.

2. The automatic scanning measurement method for blade rim clearance according to claim 1, characterized in that, In the constructed three-dimensional measurement coordinate system, the workpiece coordinate system is a three-dimensional rectangular coordinate system established with the fixed point at the root of the blade as the origin, used to describe the relative positions and dimensional relationships of various parts of the blade in space; the machine coordinate system is a three-dimensional rectangular coordinate system established with the reference point of the measuring equipment as the origin, used to describe the absolute positions of various components of the measuring equipment and measuring points in space.

3. The automatic scanning measurement method for blade rim clearance according to claim 2, characterized in that, The gap point cloud data is a set of spatial discrete points obtained by the laser scanning probe. Each point contains three-dimensional coordinates and reflection intensity information, which are used to describe the surface contour shape of the blade edge plate.

4. The automatic scanning measurement method for blade rim clearance according to claim 3, characterized in that, In the construction of the comprehensive error compensation vector field, the input of the spatial position error compensation function includes the spatial coordinate position obtained from the machine coordinate system, the measurement time obtained from the system clock, and the ambient temperature obtained from the temperature sensor, and the output is a three-dimensional spatial position correction vector applied to the gap point cloud data.

5. The automatic scanning measurement method for blade rim clearance according to claim 4, characterized in that, In the construction of the comprehensive error compensation vector field, the input of the optical system error compensation function includes the light signal intensity obtained from the laser scanning probe receiving unit, the target distance obtained from the position sensor, the incident angle obtained from the attitude sensor, and the material characteristic parameters of the reflective surface obtained from the material database. The output is the measurement correction amount applied to the gap point cloud data.

6. The automatic scanning measurement method for blade rim clearance according to claim 5, characterized in that, In the construction of the comprehensive error compensation vector field, the input of the material thermal expansion error compensation function includes the ambient temperature obtained from the temperature sensor, the material thermal expansion coefficient obtained from the material database, the measurement duration obtained from the system clock, and the material stress state obtained from the stress sensor. The output is a thermal deformation correction factor applied to the measured surface.

7. The automatic scanning measurement method for blade rim clearance according to claim 6, characterized in that, In establishing the airflow model of the blade rim gap, the numerical solution method uses finite element analysis to discretize the flow field of the blade rim gap into grid elements, and solves the gas flow control equations through iterative calculation. The inputs include the gap boundary conditions obtained from the three-dimensional geometric model, the inlet velocity obtained from experimental data, the inlet pressure obtained from the pressure sensor, the operating temperature obtained from the temperature sensor, and the fluid viscosity obtained from the physical property database. The output is the flow field distribution state in the blade rim gap.

8. The automatic scanning measurement method for blade rim clearance according to claim 7, characterized in that, In establishing the airflow model of the blade rim gap, the analytical solution method is based on the simplified equations of fluid mechanics theory and uses the variable separation method to solve the airflow theory equations. The inputs include fluid density obtained from the fluid property database, airflow damping coefficient calculated based on the physical model, fluid viscosity coefficient obtained from experimental data, pressure gradient obtained from boundary conditions, and gap characteristic dimensions obtained from the geometric model. The output is a mathematical expression describing the variation law of the flow field in the blade rim gap.

9. The automatic scanning measurement method for blade rim clearance according to claim 8, characterized in that, In the establishment of the blade rim clearance airflow model, the numerical solution of the airflow is a set of pressure distribution, velocity distribution and temperature distribution data on discrete grid points obtained by the numerical solution method, which is used to predict the clearance change trend in the real-time blade rim clearance diagnosis system; the analytical solution of the airflow is an analytical expression of the airflow characteristic function obtained by the analytical solution method, which is used for design parameter sensitivity analysis and optimization calculation in the clearance optimization design module.

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