Binocular structured light three-dimensional reconstruction and dynamic rotation matrix-based large-scale rotary equipment rotor multistage stacking concentricity accurate measurement method

Abstract

The invention discloses a binocular structured light three-dimensional reconstruction and dynamic rotation matrix-based large rotation equipment rotor multistage stacking concentricity accurate measurement method, and belongs to the technical field of non-contact optical measurement, three-dimensional reconstruction and assembly precision measurement. The method comprises the following steps: 1, binocular structured light three-dimensional reconstruction; step 2, dynamic rotation matrix correction: correcting the space attitude of the surface of the spigot, and converting all measured point clouds to a unified coordinate system for concentricity calculation; 3, multi-stage stacking eccentricity error evaluation under the polar coordinate system is carried out, the concentricity is rapidly calculated on the basis of a three-dimensional reconstruction result, and visual distribution of eccentricity errors is formed for subsequent online compensation; and 4, constructing a feed-forward + feedback compensation closed-loop system based on the measurement and error transfer model in the step 3, and correcting the eccentric error in real time in the assembly process. The defects that existing contact measurement is low in efficiency, contact damage exists, and multi-stage assembly accumulative errors cannot be evaluated and compensated in real time are overcome.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of non-contact optical measurement, three-dimensional reconstruction and precision assembly measurement, and particularly relates to a large-scale rotary equipment rotor multi-stage stacking concentricity precision measurement method based on binocular structured light three-dimensional reconstruction and dynamic rotation matrix. BACKGROUND

[0002] The rotor is the core component of an aero-engine, and its assembly quality directly affects the power performance and operation stability of the whole machine. During the multi-stage rotor stacking assembly process, the concentricity error and the cumulative eccentricity error are the main factors leading to rotor system dynamic imbalance, increased vibration and reduced service life. Therefore, high-precision measurement and control of the multi-stage rotor stacking concentricity have become an important technical requirement in the field of aero-engine assembly.

[0003] Currently, the rotor concentricity measurement mainly adopts contact measurement methods, such as inductive probes, contact micrometers and three-coordinate measuring machines. Representative methods include: 1) Inductive probe measurement method: the displacement is obtained by contact between the probe and the measured surface, and the circle runout and eccentricity are calculated. However, there are problems such as limited number of measurement points, difficulty in realizing global profile measurement, and probe contact force easily causing surface micro-deformation.

[0004] 2) Three-coordinate measuring machine measurement method: it can realize three-dimensional measurement of the whole profile, but it needs to disassemble the workpiece for offline measurement, which is complicated and inefficient, and difficult to meet the real-time measurement requirements of the engine assembly line.

[0005] In addition, in recent years, non-contact measurement methods based on structured light have emerged, which use cameras and projectors to obtain three-dimensional information of object surfaces. However, existing technologies mainly focus on point cloud reconstruction and topography measurement, and there is still a lack of systematic solutions combining non-contact measurement results with rotor assembly concentricity error modeling and dynamic compensation control.

[0006] For example, the existing technology proposes a method for measuring the concentricity of an aero-engine rotor using a contact displacement sensor, but it relies on contact measurement, which cannot avoid potential damage to the surface of the part, and does not have real-time dynamic compensation capability, which cannot meet the current intelligent assembly line's demand for efficient, high-precision, closed-loop control measurement technology.

[0007] Therefore, there is an urgent need for a new method that combines binocular structured light non-contact three-dimensional reconstruction, dynamic rotation matrix pose correction, polar coordinate system eccentricity error simulation and online compensation control, to realize high-precision measurement and closed-loop control of multi-stage rotor stacking concentricity, and to improve the automation level and assembly quality of engine assembly. SUMMARY

[0008] The application provides a large rotary equipment rotor multi-stage stacking concentricity precision measurement method based on binocular structured light three-dimensional reconstruction and dynamic rotation matrix, which is characterized in that non-contact optical measurement, dynamic posture correction and online compensation control are combined to overcome the defects of low efficiency, contact damage, inability to real-time evaluate and compensate multi-stage assembly cumulative error of the existing contact measurement.

[0009] The application is implemented by the following technical solutions: A large rotary equipment rotor multi-stage stacking concentricity precision measurement method based on binocular structured light three-dimensional reconstruction and dynamic rotation matrix, the method comprising the following steps: Step 1: binocular structured light three-dimensional reconstruction; Step 2: dynamic rotation matrix correction, the spatial posture of the joint surface is corrected, and all measured point clouds are converted to a unified coordinate system for concentricity calculation; Step 3: multi-stage stacking eccentric error evaluation in the polar coordinate system, the concentricity is quickly calculated on the three-dimensional reconstruction result, and the visual distribution of the eccentric error is formed for subsequent online compensation; Step 4: based on the measurement and error transmission model of step 3, a feedforward+feedback compensation closed-loop system is constructed to correct the eccentric error in real time during the assembly process.

[0010] Further, the step 1 comprises the following steps: Step 1.1: five-frequency six-step phase shift fringe projection and phase unwrapping; Step 1.2: absolute phase recovery; Step 1.3: five-order spline interpolation sub-pixel matching; Step 1.4: three-dimensional coordinate calculation.

[0011] Further, the step 1.1 specifically uses five-frequency six-step phase shift method to project the fringe and obtain the wrapped phase under each frequency:

[0012] In the formula, I(x,y) represents the gray value of the point (x,y) at the first step phase shift, k I(x,y) represents the gray value of the point (x,y) at the first step phase shift; x I(x,y) represents the gray value of the point (x,y) at the first step phase shift; y The step 1.2 specifically gradually unwraps the phase of each frequency by a multi-frequency phase unwrapping algorithm, and finally obtains the continuous absolute phase . x y ​​​​The step 1.3 is specifically a five-time spline interpolation, which is a high-order smooth curve fitting method, and the fitting curve has continuous first to fourth derivatives at each node by constructing a five-time polynomial function between data points, and the end second derivative can be selected as zero to obtain a pixel pair u L , v L )-( u R , v R ); The step 1.4 is specifically, according to the binocular camera calibration parameters, the spatial coordinates are calculated according to the triangulation principle:

[0013] Wherein, f is the focal length of the camera, B is the base length, d is the parallax.

[0014] Further, the step 2 includes the following steps: Step 2.1: extracting the rotor stop port normal vector; Step 2.2: tilt angle and rotation axis calculation; Step 2.3: constructing a directional error rotation matrix; Step 2.4: applying the rotation matrix for pose correction.

[0015] Further, the step 2.1 is specifically, according to the three-dimensional point cloud fitting, the unit normal vector of the rotor stop port surface is obtained: Wherein, Describes the inclination direction and size of the stop port surface relative to the Z axis of the world coordinate system; The step 2.2 is specifically, the tilt angle and rotation axis calculation

[0016] In the formula, , is the projection angle of the stop port surface in the X, Y direction; is the angle between the rotation axis and the XOY plane; is the tilt angle of the stop port surface normal vector and Z axis; The step 2.3 is specifically, and are substituted into, and the rotation matrix of the stop port surface to the ideal horizontal plane is constructed: ; The step 2.4 is specifically, the stop port point cloud is rotated and transformed:

[0017] This ensures that the stop surface is parallel to the XOY plane after correction, eliminating measurement deviations caused by orientation errors during rotor assembly, thereby guaranteeing that the measurement results of each stage of the rotor are calculated for eccentricity and concentricity under the same reference.

[0018] Furthermore, step 3 specifically involves establishing a multi-level rotor eccentricity error analytical evaluation method based on a polar coordinate system, which facilitates rapid calculation of concentricity on the three-dimensional reconstruction results and forms a visual distribution of eccentricity error for subsequent online compensation.

[0019] Furthermore, step 3.1 involves correcting the point cloud using the dynamic rotation matrix. x i , y i ), calculate its polar coordinate representation in the XOY plane; Step 3.2: Fitting the theoretical circle and calculating the single-stage eccentricity error; Step 3.3: Multi-level stacked eccentricity error propagation model.

[0020] Furthermore, step 3.1 specifically involves: the polar coordinate representation in the XOY plane is specifically as follows:

[0021] in, r i The radial distance from the point to the rotor axis is the core indicator for concentricity assessment. The position angle of the point is used to analyze the distribution characteristics of eccentricity error in the circumferential direction; Step 3.2 specifically involves: Using least squares circle fitting for the radius of the circle R f and the coordinates of the center of the circle ( x c , y c The coordinates of each point are converted to a fitted circular polar coordinate system.

[0022] In the formula, Indicates the first i The radial distance of each point relative to the center of the fitted circle; This represents the angular position of each point relative to the center of the fitted circle; Calculate eccentricity error e i :

[0023] Step 3.3 specifically involves: In the multi-stage rotor stack assembly, the small eccentricity of each stage rotor will have a geometric amplification effect in the subsequent assembly, which is specifically shown as follows:

[0024] In the formula, represents the rotation matrix of the first stage; n represents the total eccentricity vector of the n-1 stage; represents the self eccentricity vector of the n stage. n

[0025] Further, the step 4 is specifically as follows: Step 4.1: feedforward compensation; Step 4.2: feedback compensation; Step 4.3: system composition: fine adjustment of the push rod unit: μm level translation adjustment can be carried out in the X and Y directions; Clamp rotating mechanism: small angle swing is provided to correct the directional error; Controller: according to the simulation and measurement results, the compensation instruction is calculated, and the actuator is driven.

[0026] Further, the step 4.1 is specifically as follows: according to the simulation predicted multi-stage cumulative eccentricity trend, the fine adjustment displacement and rotation angle required by the next assembly stage are calculated to offset the cumulative error; The formula is as follows:

[0027] In the formula, is the eccentricity error predicted by simulation.

[0028] The step 4.2 is specifically as follows: after the feedforward adjustment, the residual eccentricity is measured again, and if the residual eccentricity is greater than the set threshold, the feedback fine adjustment compensation is entered.

[0029] The beneficial effects of the present application are as follows: The present application overcomes the defects of the existing contact measurement, such as contact damage, limited measurement points, low efficiency, and the existing structure light measurement which can only reconstruct the shape and cannot perform dynamic modeling and control of the assembly error by combining binocular structure light non-contact three-dimensional reconstruction, directional error rotation matrix posture correction, multi-stage eccentricity error evaluation and online compensation control in the polar coordinate system.

[0030] ​​Compared with the prior art, the present application realizes high-precision, real-time and non-contact measurement of the concentricity of the multi-stage rotor stack, the measurement uncertainty is controlled within ±5pm, the single-piece measurement time is shortened to 2-3 seconds, and the cumulative amplification effect of the eccentricity error in the assembly process can be accurately predicted by combining the rotation matrix correction and the polar coordinate error transmission model. Through the feedforward+feedback compensation closed-loop control, the dynamic correction of the rotor assembly concentricity error is realized within the range of ≤5pm, which greatly improves the automation level and assembly quality of the multi-stage rotor assembly of the aero-engine, and has significant engineering application value and popularization prospect. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 is a five times spline interpolation sub-pixel matching method flowchart of the present application.

[0032] Figure 2 is a method flowchart of the present application. DETAILED DESCRIPTION

[0033] In the following description, specific details are set forth such as particular system configurations, techniques, etc., in order to provide a thorough understanding of the embodiments of the present application. However, persons skilled in the art will understand that the present application can be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present application with unnecessary detail.

[0034] It should be understood that the term "comprising" as used in the specification and the appended claims indicates the presence of the recited features, integers, steps, operations, elements, and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0035] It should also be understood that the terms used in the present application specification are only for the purpose of describing specific embodiments and are not intended to limit the present application. As used in the present application specification and the appended claims, the singular forms "a", "an" and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0036] The technical solutions in the embodiments of the present application are described clearly and completely in the following description of the drawings of the present application specification. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0037] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0038] A method for accurately measuring the concentricity of multi-stage stacked rotors in large rotary equipment based on binocular structured light 3D reconstruction and dynamic rotation matrix, the method comprising the following steps: Step 1: Binocular structured light 3D reconstruction; Step 2: Dynamic rotation matrix correction, correct the spatial attitude of the stop surface, and convert all measured point clouds to a unified coordinate system for concentricity calculation; Step 3: Evaluation of multi-level stacking eccentricity error in polar coordinate system. The concentricity is quickly calculated on the 3D reconstruction results, and a visual distribution of eccentricity error is formed for subsequent online compensation. Step 4: Based on the measurement and error propagation model in Step 3, construct a feedforward + feedback compensation closed-loop system to correct eccentricity error in real time during the assembly process.

[0039] Furthermore, step 1 includes the following steps: Step 1.1: Five-frequency, six-step phase-shifting fringe projection and phase unwrapping; Step 1.2: Absolute phase recovery; Step 1.3: Fifth-order spline interpolation subpixel matching; Step 1.4: Calculate the three-dimensional coordinates.

[0040] Furthermore, step 1.1 specifically involves using a five-frequency, six-step phase-shifting method to project fringes and obtain the wrap-around phase at each frequency:

[0041] In the formula, Indicates the first k During phase shift ( x , y The grayscale value of the point. This indicates that during the first phase shift ( x , y The grayscale value of the point. This indicates that during the second phase shift ( x , y The grayscale value of the point. This indicates that during the third phase shift ( x , y The grayscale value of the point. This indicates that during the 4th phase shift ( x , y The grayscale value of the point. representing the gray value of the point at the phase shift in step 5 x , y ; The step 1.2 is specifically, by a multi-frequency phase unwrapping algorithm, the phase of each frequency is gradually unfolded, and finally the continuous absolute phase is obtained. The step 1.3 is specifically, the five times spline interpolation is a high-order smooth curve fitting method, by constructing a five times polynomial function between the data points, the fitting curve has continuous first to fourth derivatives at each node, and the second derivative at the end can be selected as zero (natural boundary condition), compared with the cubic spline interpolation, the curvature change is smoother, the fitting residual is smaller, and it is suitable for sub-pixel level accurate fitting of phase or pixel displacement data, which improves the stereo matching accuracy and stability, and obtains the pixel pair u L , v L )-( u R , v R ; The step 1.4 is specifically, according to the binocular camera calibration parameters, the spatial coordinates are calculated according to the triangulation principle:

[0042] Wherein, f is the focal length of the camera, B is the base length, d is the parallax.

[0043] Further, due to the existence of a small directional error (tilt) when the rotor socket is assembled, the posture difference exists between the upper and lower rotors, and further affects the overall concentricity evaluation and cumulative eccentric error calculation. The space posture of the socket surface needs to be corrected, and all the measured point clouds are converted to a unified coordinate system for concentricity calculation.

[0044] The step 2 includes the following steps: Step 2.1: Extracting the normal vector of the rotor socket; Step 2.2: Tilt angle and rotation axis calculation; Step 2.3: Constructing the directional error rotation matrix; Step 2.4: Applying the rotation matrix for posture correction.

[0045] Further, the step 2.1 is specifically, the unit normal vector of the rotor socket surface is fitted according to the three-dimensional point cloud: Wherein, Describes the tilt direction and size of the socket surface relative to the Z axis of the world coordinate system. ​​​​The step 2.2 is specifically, the inclination angle and the rotation axis calculation

[0046] In the formula, , is the projection angle of the stop surface in the X, Y direction; is the angle between the rotation axis and the XOY plane (i.e. the rotation axis direction); is the inclination angle of the stop surface normal vector and Z the rotation axis (i.e. the rotation angle size); The step 2.3 is specifically, the inclination angle and the rotation axis are substituted, and a rotation matrix of the stop surface to the ideal horizontal plane is constructed: ; The step 2.4 is specifically, the stop surface point cloud is rotated and transformed:

[0047] The stop surface is parallel to the XOY plane after correction, and the measurement deviation caused by the directional error during the rotor assembly is eliminated, so as to ensure that the measurement results of each stage rotor are calculated under the same reference of eccentricity and concentricity.

[0048] Further, the step 3 is specifically, a multi-stage rotor eccentric error analytical evaluation method based on a polar coordinate system is established, which is convenient for quickly calculating the concentricity on the three-dimensional reconstruction result, and forming a visual distribution of the eccentric error, which is used for subsequent online compensation.

[0049] Further, step 3.1 calculates the polar coordinate representation of the point cloud (r, θ) in the XOY plane after the dynamic rotation matrix correction; x i , y i The purpose is to facilitate the distribution analysis of the eccentricity at each angle position when fitting the circle model, and to easily couple the angle-amplitude relationship calculation with the result after the rotation matrix correction; Step 3.2: fitting a theoretical circle and single-stage eccentric error calculation; Step 3.3: multi-stage stacked eccentric error transmission model.

[0050] Further, the step 3.1 is specifically: the polar coordinate representation in the XOY plane is specifically,

[0051] Among them, r i is the radial distance from the point to the rotor axis, which is the core index of concentricity evaluation; The position angle of the point is used to analyze the distribution characteristics of eccentricity error in the circumferential direction; Step 3.2 specifically involves: Using least squares circle fitting for the radius of the circle R f and the coordinates of the center of the circle ( x c , y c The coordinates of each point are converted to a fitted circular polar coordinate system.

[0052] In the formula, Indicates the first i The radial distance of each point relative to the center of the fitted circle; This represents the angular position of each point relative to the center of the fitted circle; Calculate eccentricity error e i :

[0053] Step 3.3 specifically involves: In multi-stage rotor stacking assembly, the small eccentricity of each stage rotor will produce a geometric amplification effect in subsequent assembly, specifically manifested as follows:

[0054] In the formula, Indicates the first n -1 level rotation matrix; This represents the total eccentricity vector at level n-1; Indicates the first n Level self-eccentric vector.

[0055] Furthermore, step 4 specifically includes the following steps: Step 4.1: Feedforward compensation; Step 4.2: Feedback and Compensation; Step 4.3: Execution system components: Fine-tuning push rod unit: capable of μm-level translational adjustment along the X and Y directions; Clamp rotation mechanism: provides small-angle oscillation to correct orientation errors; Controller: Calculates compensation commands based on simulation and measurement results, and drives the actuators.

[0056] Furthermore, step 4.1 specifically involves: calculating the fine-tuning displacement and rotation angle required for the next assembly stage based on the multi-level cumulative eccentricity trend predicted by simulation, in order to offset the cumulative error; Formula expression:

[0057] wherein, is the eccentricity error of the simulation prediction.

[0058] The step 4.2 is specifically: after the feedforward adjustment, re-measurement is performed, and if the residual eccentricity is greater than a set threshold, feedback fine adjustment compensation is entered.

[0059] Specifically, the application can be applied to the measurement and control process of multi-stage rotor assembly of an aero-engine. In actual application, a non-contact measurement platform composed of a binocular structured light measurement system can be built on an assembly line, five-frequency six-step phase shift stripes are projected by a projector, images are collected by left and right cameras, sub-pixel level unwrapping and stereo matching of phase are realized by using five times spline interpolation, and high-precision three-dimensional point cloud of the contour of the stop port of each stage rotor is quickly obtained.

[0060] For each stage rotor, the normal vector of the stop port surface is fitted, and a directional error rotation matrix is used for dynamic attitude correction, and all stage point clouds are converted to a unified reference coordinate system; then the corrected point cloud is converted to a polar coordinate system, a theoretical circle is fitted, the radial eccentricity error of each point is calculated, a multi-stage stack eccentricity error transfer model is established by combining multi-stage rotation matrix coordinate transformation, and the cumulative distribution of the overall eccentricity error after assembly is predicted.

[0061] Combined with the simulation prediction result of the eccentricity error, a feedforward compensation instruction can be generated to drive the fine adjustment push rod and rotating mechanism of the assembly fixture to perform μm-level translation or micro-angle adjustment on the rotor. After adjustment, re-measurement is performed for verification, and if the residual error exceeds the threshold, feedback compensation is continued, and finally the rotor assembly concentricity error can be controlled within 5 μm. This embodiment effectively overcomes the problems of contact damage, low efficiency and inability to dynamically compensate existing in the traditional contact measurement, realizes high-precision, real-time, non-contact closed-loop control of the concentricity of the multi-stage rotor assembly of the aero-engine, and has good engineering application value.

Claims

1. A large rotary equipment rotor multi-stage stack concentricity precision measurement method based on binocular structured light three-dimensional reconstruction and dynamic rotation matrix, characterized by, The method comprises the following steps: Step 1: binocular structured light three-dimensional reconstruction; Step 2: dynamic rotation matrix correction, correcting the spatial posture of the rotor stop surface, converting all measured point clouds to a unified coordinate system for concentricity calculation; Step 3: multi-level stacked eccentric error evaluation in polar coordinate system, calculating the concentricity on the three-dimensional reconstruction result, and forming the visual distribution of the eccentric error for subsequent online compensation; Step 4: based on the measurement and error transmission model of step 3, a feedforward + feedback compensation closed-loop system is constructed to correct the eccentric error in real time during assembly.

2. The method of claim 1, wherein, The step 1 comprises the following steps: Step 1.1: five-frequency six-step phase shift fringe projection and phase unwrapping; Step 1.2: absolute phase recovery; Step 1.3: five times spline interpolation sub-pixel matching; Step 1.4: three-dimensional coordinate calculation.

3. The method of claim 2, wherein, The step 1.1 is specifically using five-frequency six-step phase shift method to project stripes, and obtaining wrapped phases under each frequency: wherein the gray value of the point at the first step phase shift k the gray value of the point at the second step phase shift x , y ) the gray value of the point at the third step phase shift the gray value of the point at the fourth step phase shift x , y ) the gray value of the point at the fifth step phase shift The step 1.2 is specifically to unfold the phase of each frequency step by step by a multi-frequency phase unwrapping algorithm, and finally obtain a continuous absolute phase ; The step 1.3 is specifically, five times spline interpolation is through the construction of five polynomial function between data points, make the fitting curve has continuous first to fourth order derivative at each node, and the end of the second derivative can be selected as zero to get the pixel pair u L , v L )-( u R , v R ); The step 1.4 is specifically calculating the spatial coordinates according to the binocular camera calibration parameters and the triangulation principle: wherein, f is the camera focal length, B is the baseline length, d is the parallax.

4. The method of claim 1, wherein, The step 2 comprises the following steps: Step 2.1: extracting the normal vector of the rotor stop; Step 2.2: calculating the tilt angle and rotation axis; Step 2.3: constructing a directional error rotation matrix; Step 2.4: applying the rotation matrix for posture correction.

5. The method of claim 4, wherein, The step 2.1 is specifically, the unit normal vector of the rotor neck surface is obtained according to three-dimensional point cloud fitting: Wherein, The deflection direction and size of the neck surface relative to the Z axis of the world coordinate system are described. The step 2.2 is specifically calculating the tilt angle and rotation axis In the formula, , is the projection angle of the stop surface in the X, Y direction; is the angle between the rotation axis and the XOY plane; is the inclination angle of the stop surface normal vector and the axis of the lens; Z is the inclination angle of the stop surface normal vector and the axis of the lens; The step 2.3 is specifically to construct the rotation matrix of the stop face to the ideal horizontal plane: and Substitute, construct the rotation matrix of the stop face to the ideal horizontal plane: ； The step 2.4 is specifically rotating the stop surface point cloud: Make the stop surface parallel to the XOY plane after correction, eliminate the measurement deviation caused by directional error during rotor assembly, and ensure that the measurement results of each level of rotor are calculated under the same reference for eccentricity and concentricity.

6. The method of claim 1, wherein, The step 3 is specifically establishing a multi-level rotor eccentric error analytical evaluation method based on polar coordinate system, which is convenient for quickly calculating the concentricity on the three-dimensional reconstruction result, and forming the visual distribution of the eccentric error for subsequent online compensation.

7. The method of claim 6, wherein, Step 3.1 Compute the polar representation of the point cloud (XOY) in the XOY plane after correction by the dynamic rotation matrix x i , y i ) Step 3.2: fitting a theoretical circle and single-level eccentric error calculation; Step 3.3: multi-level stacked eccentric error transmission model.

8. The method of claim 7, wherein, The step 3.1 is specifically the polar coordinate representation in the XOY plane, which is specifically wherein, r i is the radial distance from the point to the rotor axis, which is the core index of concentricity evaluation; is the position angle of the point, which is used to analyze the distribution characteristics of eccentric error in the circumferential direction. The step 3.2 is specifically Fitting a circle radius using least squares R f with the center of the circle coordinates x c , y c converts each point coordinate to the fitted circle polar coordinate system: wherein represents the radial distance of the i th point relative to the center of the fitted circle; represents the angular position of each point relative to the center of the fitted circle; Computing eccentricity errors e i : The step 3.3 is specifically In the multi-level stacked assembly of the rotor, the small eccentricity of each level of rotor will be geometrically amplified in subsequent assembly, which is specifically wherein represents the rotation matrix of the n -1st stage; represents the total eccentricity vector of the n-1st stage; represents the rotation matrix of the n stage itself eccentricity vector.

9. The method of claim 1 wherein, The step 4 comprises the following steps: Step 4.1: feedforward compensation; Step 4.2: feedback compensation; Step 4.3: execution system composition: fine adjustment push rod unit: can be adjusted by μm level translation along X, Y direction; Clamp rotating mechanism: provides small angle swing to correct the directional error; Controller: calculates the compensation instruction according to the simulation and measurement result, and drives the execution mechanism.

10. The method of claim 9, wherein, The step 4.1 is specifically: according to the simulation predicted multi-level cumulative eccentricity trend, calculating the fine adjustment displacement and rotation angle required by the next assembly level to offset the cumulative error; Formula representation: wherein, is the eccentricity error for the simulation prediction. The step 4.2 is specifically: after feedforward adjustment, re-measurement is performed, and if the residual eccentricity is greater than the set threshold, feedback fine adjustment compensation is entered.

Images