CN117346722B - Aeroengine blade profile contour measurement method based on three-coordinate measurement - Google Patents

Aeroengine blade profile contour measurement method based on three-coordinate measurement Download PDF

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CN117346722B
CN117346722B CN202311179695.XA CN202311179695A CN117346722B CN 117346722 B CN117346722 B CN 117346722B CN 202311179695 A CN202311179695 A CN 202311179695A CN 117346722 B CN117346722 B CN 117346722B
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blade
measurement
profile
leaf
measuring
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CN117346722A (en
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张桢
李聪
刘小涛
郭凯
舒力力
安瑾倬
刘冲
闫子航
李燚之
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Huazhong University of Science and Technology
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Huazhong University of Science and Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/20Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • General Physics & Mathematics (AREA)
  • Length Measuring Devices With Unspecified Measuring Means (AREA)

Abstract

The invention discloses a three-coordinate measurement-based aeroengine blade profile contour measurement method, which belongs to the field of blade profile contour measurement and blade processing quality detection, and adopts two groups of vertically arranged circular probes to measure each section of a blade, one group of the vertically arranged circular probes is used for measuring the section contour of the blade, the other group of the horizontally arranged circular probes is used for measuring the section contour of the blade, and the limitation of a single probe is avoided; dividing the blade into four parts of a blade basin, a blade back, a front edge and a rear edge for regional and sequential measurement, avoiding various interference problems and expanding the measurable range; the method can solve the difficulty in measuring the section profile of the blade, realize high-precision and rapid profile measurement, improve the efficiency of blade detection and realize high-precision measurement of a complex blade structure.

Description

Aeroengine blade profile contour measurement method based on three-coordinate measurement
Technical Field
The invention belongs to the field of blade measurement, and particularly relates to an aeroengine blade profile contour measurement method based on three-coordinate measurement.
Background
Aero-engine blades are known for their complex three-dimensional aerodynamic profiles, which are of great importance for their precise cross-sectional profile measurement and detection. The existing contact type measurement method such as a special numerical control machine tool and the like cannot realize the measurement of the whole three-dimensional curved surface. Non-contact measurement methods such as laser scanning have a problem that reflection affects the surface treatment with high requirements. The three-coordinate measuring machine can realize contact point measurement, but has the following problems: 1. when in measurement, the surface of the blade is easy to interfere with a measuring instrument; 2. the area with too large blade radian cannot be effectively measured.
Disclosure of Invention
Aiming at the defects or improvement demands of the prior art, the invention provides an aeroengine blade profile contour measuring method based on three-coordinate measurement, so as to realize high-precision and rapid measurement of the blade profile contour.
To achieve the above object, according to a first aspect of the present invention, there is provided an aeroengine blade profile measuring method based on three-coordinate measurement, comprising:
s1, dividing a profile curve of each section of a blade to be tested into four areas, namely a blade basin, a blade back, a front edge and a rear edge;
S2, under the measurement coordinate system of the blade to be measured, controlling the combined probe to conduct regional and sequential measurement on the profile curves of all the sections through a three-coordinate measuring instrument according to the clockwise or anticlockwise direction;
the combined probe comprises a horizontal probe and a vertical probe which are connected with each other;
The horizontal probe is used for measuring a leaf basin area and front and rear edge areas of the adjacent part of the leaf basin area to obtain leaf basin profile measurement data R1, and measuring a leaf back area and front and rear edge areas of the adjacent part of the leaf back area to obtain leaf back profile measurement data R2;
the vertical probe is used for measuring a trailing edge region, a part of the leaf basin and the leaf back region adjacent to the trailing edge region to obtain trailing edge profile measurement data R3, and is used for measuring a leading edge region, a part of the leaf basin and the leaf back region adjacent to the leading edge region to obtain leading edge profile measurement data R4;
And S3, fitting the measured data R1-R4 to obtain profile curves of all sections of the blade to be measured, and finally obtaining the profile of the blade to be measured.
According to a second aspect of the present invention, there is provided an aero-engine blade profile measurement device based on three-coordinate measurement, comprising:
The first processing module is used for dividing the profile curve of each section of the blade to be tested into four areas of a blade basin, a blade back, a front edge and a rear edge;
the second processing module is used for controlling the combined probe to carry out regional and sequential measurement on the profile curves of the sections according to the clockwise or anticlockwise direction through the three-coordinate measuring instrument under the measurement coordinate system of the blade to be measured;
wherein the combined probe comprises a horizontal probe and a vertical probe;
The horizontal probe is used for measuring a leaf basin area and front and rear edge areas of the adjacent part of the leaf basin area to obtain leaf basin profile measurement data R1, and measuring a leaf back area and front and rear edge areas of the adjacent part of the leaf back area to obtain leaf back profile measurement data R2;
the vertical probe is used for measuring a trailing edge region, a part of the leaf basin and the leaf back region adjacent to the trailing edge region to obtain trailing edge profile measurement data R3, and is used for measuring a leading edge region, a part of the leaf basin and the leaf back region adjacent to the leading edge region to obtain leading edge profile measurement data R4;
And the third processing module is used for fitting the measurement data R1-R4 to obtain a section profile curve of each section of the blade to be tested.
According to a third aspect of the present invention, there is provided an aero-engine blade profile measurement system based on three-coordinate measurement, comprising: a computer readable storage medium and a processor;
the computer-readable storage medium is for storing executable instructions;
the processor is configured to read executable instructions stored in the computer readable storage medium and perform the method according to the first aspect.
According to a third aspect of the present invention there is provided a computer readable storage medium storing computer instructions for causing a processor to perform the method of the first aspect.
In general, the above technical solutions conceived by the present invention, compared with the prior art, enable the following beneficial effects to be obtained:
1. According to the method provided by the invention, two groups of vertically arranged circular probes are adopted to measure each section of the blade, one group of the circular probes is used for measuring the horizontal profile, and the other group of the circular probes is used for measuring the vertical profile, so that the limitation of a single probe is avoided; dividing the blade into four parts of a blade basin, a blade back, a front edge and a rear edge for regional and sequential measurement, avoiding various interference problems and expanding the measurable range; the method can solve the difficulty in measuring the section profile of the blade, realize high-precision and rapid profile measurement, improve the efficiency of blade detection and realize high-precision measurement of a complex blade structure.
2. According to the method provided by the invention, when the combined probe is adopted for measurement, as the horizontal probe and the vertical probe are adopted for measurement alternately, the probe must return to the original point at the left upper corner of the machine to return data when the probe is switched each time, then the measurement of the next section is started, and the probe is required to be manually controlled to contact with the measurement starting point, so that the starting point of the next section of contour is not accurately ensured to be the ending point of the measurement of the previous section of contour, and therefore, in order to ensure the accuracy of the data, a measurement track with partial overlapping is designed to improve the accuracy and the integrity of the data, and correspondingly, when the measurement data is processed, a corresponding processing mode of the de-overlapping data is designed, and the fitting accuracy is further ensured.
3. According to the method provided by the invention, the measurement coordinate system of the blade to be tested is established based on the six-point iteration method, so that the accuracy of a matching model can be improved; considering that because the blade profile is complex and has no locating points with definite characteristics, the actually selected points are difficult to ensure to be the points selected by software, if the locating points are not properly selected, the iterative process is easily interrupted due to interference, based on the points, four points are selected at the root of the blade, one point is selected at the leaf basin, and one point is selected at the top of the blade to be used as the locating points, so that the iterative process can be successfully executed, and the coordinate system to be detected is quickly established.
Drawings
FIG. 1 is a schematic diagram of a combined probe according to an embodiment of the present invention;
FIG. 2 is a schematic view of a blade positioning point according to an embodiment of the present invention;
FIG. 3 is a schematic view of each region of a blade according to an embodiment of the present invention;
FIG. 4 is a schematic view of each area of a measurement blade of a combined probe according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a track of each area of a measurement blade of a combined probe according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The embodiment of the invention provides an aeroengine blade profile contour measuring method based on three-coordinate measurement, which comprises the following steps:
s1, dividing a profile curve of each section of a blade to be tested into four areas, namely a blade basin, a blade back, a front edge and a rear edge;
S2, under the measurement coordinate system of the blade to be measured, controlling the combined probe to conduct regional and sequential measurement on the profile curves of all the sections through a three-coordinate measuring instrument according to the clockwise or anticlockwise direction;
the combined probe comprises a horizontal probe and a vertical probe which are connected with each other;
The horizontal probe is used for measuring a leaf basin area and front and rear edge areas of the adjacent part of the leaf basin area to obtain leaf basin profile measurement data R1, and measuring a leaf back area and front and rear edge areas of the adjacent part of the leaf back area to obtain leaf back profile measurement data R2;
the vertical probe is used for measuring a trailing edge region, a part of the leaf basin and the leaf back region adjacent to the trailing edge region to obtain trailing edge profile measurement data R3, and is used for measuring a leading edge region, a part of the leaf basin and the leaf back region adjacent to the leading edge region to obtain leading edge profile measurement data R4;
And S3, fitting the measured data R1-R4 to obtain profile curves of all sections of the blade to be measured, and finally obtaining the profile of the blade to be measured. For example, an interpolation method is adopted to process the profile curve of each section of the blade to be tested, and finally the profile of the blade to be tested is obtained.
Preferably, before the fitting of the measurement data R1 to R4, the method further comprises:
1) Sequencing the measurement data according to a measurement sequence;
2) Judging whether the distance between any two points is smaller than a preset threshold value, if so, only retaining the data points from R1 or R2 in the two points, returning to the step 1), and if not, ending.
Preferably, the two mutually perpendicular probes are circular probes with a diameter of 2 mm.
Considering the difficulty in establishing a measurement coordinate system, the accuracy of the matching model is not high, and based on this, preferably, the process of establishing the measurement coordinate system of the blade to be measured is as follows:
The three-dimensional model of the blade to be measured is led into a three-coordinate measuring instrument, a plurality of positioning points on the surface of the virtual blade are sequentially contacted by a combined probe through the three-coordinate measuring instrument, and a measurement coordinate system of the blade to be measured is established based on a six-point iteration method.
In actual operation, because the blade profile is complex and there is no locating point with clear characteristics, it is difficult to ensure that the actually selected point is the software selected point. If the setpoint selection is not appropriate, the iterative procedure is easily interrupted by interference, based on which preferably four points are selected at the root of the blade, one point is selected at the basin, and one point is selected at the tip of the blade as setpoint.
Specifically, the method provided by the invention comprises the following steps:
1. probe selection and calibration
According to the model of the aeroengine blade, different probes are required to be selected. In practice, a 5mm diameter probe is typically used, which does not require calibration of the position of the probe. However, if the blade length is longer, when the probe head measures the middle interface, the device for clamping the probe can interfere with the top end of the blade, the measurement can be automatically stopped, and the probe head with the diameter of 5mm is too large, so that certain influence can be caused on measurement data.
In view of measurement accuracy, a probe with a smaller diameter is preferred, so that an angle-adjustable probe with a diameter of 1mm can also be selected. In general, the shape of the blade is complex, so that the probe is inclined at a certain angle, and interference with the top end of the blade can be avoided when the section of the middle section is measured. Since the 1mm diameter adjustable angle probe is not the default probe, it is necessary to calibrate the probe, and determine the status of the probe by measuring different profile data of the standard sphere with the probe. However, if the bending angle of the blade is large, the probe needs to be inclined by a large angle, under the angle, the needle calibration procedure cannot be completed, and the state of the probe is generally determined by performing twelve profile detections on standard balls by the probe, but under the angle, only the profiles of 5-6 standard balls can be detected and stopped. If the measurement is forced, data errors are caused, the diameter of the probe is too small, the rigidity is insufficient, and errors can be caused by deformation in contact detection.
Based on this, as shown in fig. 1, the embodiment of the invention adopts two mutually perpendicular combined probes with the diameter of 2mm, so that the profile of the blade with any shape can be measured, and the measurement precision and the rigidity requirement can be met. The vertical probe and the horizontal probe are fixed at 90 degrees, one set of which maintains the vertical measuring blade cross-sectional profile and one set of which maintains the horizontal measuring blade cross-sectional profile. A multi-point calibration is performed using a standard sphere to correct for the status of the combined probe. As shown in fig. 2 and 3, the horizontal probe is used for measuring the profiles of the leaf basin and the leaf back, and the vertical probe is used for measuring the profiles of the front leaf edge and the rear leaf edge, so that the problem that a device for clamping the probe interferes with the blade is effectively avoided.
2. Establishment of blade measurement coordinate system
And selecting a default coordinate system by using Unigraphics software, and establishing a theoretical model of the aeroengine blade. Because the blade shape is complex, the origin of coordinates of its model is not on the blade, so that it is necessary to reestablish the coordinate system so that the measured coordinate system coincides with the coordinate system in the three-dimensional model. And importing QUINDOS a theoretical model into software to establish a measurement coordinate system in an actual environment. The three-dimensional model of the blade is opened by QUINDOS software, six positioning points on the surface of the blade are selected firstly, then the probe is controlled by the three-coordinate measuring instrument to sequentially contact the six positioning points, and the azimuth deviation is verified to meet the requirement of positioning tolerance through three-time matrix iterative computation, so that a measuring coordinate system is established on the three-coordinate measuring instrument, and the measuring coordinate system is overlapped with the coordinate system in the three-dimensional model.
In actual operation, because the blade profile is complex and there is no locating point with clear characteristics, it is difficult to ensure that the actually selected point is the software selected point. If the positioning point is not properly selected, the iterative process is easily interrupted due to interference, as shown in fig. 2, if four points A, B, E, D, one point C of the blade basin and one point F of the blade top are selected at the root of the blade, the iterative process can be successfully executed with higher precision.
3. Zoned data measurement
After the coordinate system is established, the position height of the probe is set, and the profile data of different sections of the blade are measured. If only a vertical probe is used, the same interference problem as in the first scheme exists, and if only a horizontal probe is used, the measurement cannot be performed due to the fact that the radian of the left and right edges of the blade is too large. Thus, as shown in FIG. 3, the blade is divided into four sections, the basin, the back, the leading edge, and the trailing edge. As shown in FIG. 4, the use of a horizontal probe to measure the leaf basin and the leaf back avoids interference problems, and the use of a vertical probe to measure the leading and trailing edges avoids problems that an excessively large arc horizontal probe cannot measure. And controlling the combined probe through the three-coordinate measuring instrument to carry out regional and sequential measurement on the profile curves of the sections according to the clockwise or anticlockwise direction.
As shown in FIG. 5, eight points A1, A2, B1, B2, C1, C2, D1 and D2 are selected on each height section of the blade to form four profile curves, wherein A1, B1, C1 and D1 are initial scanning points, and A2, B2, C2 and D2 are end scanning points. It should be noted that, considering that the combined probe performs regional and sequential measurement on the profile curves of each section of the blade according to the clockwise or anticlockwise direction, and the horizontal probe is used for measuring the leaf basin and the leaf back, and the vertical probe is used for measuring the front edge and the rear edge, the horizontal probe and the vertical probe are used alternately, however, when the probes are switched, the probes must return to the origin of the upper left corner of the machine first to return data, then the measurement of the next section is started, and the probe needs to be manually operated to contact with the measurement starting point, so that the starting point of the profile of the next section is not accurately ensured to be the ending point of the profile measurement of the last section, and therefore, in order to ensure the accuracy and the integrity of the data, the four profile curves have overlapping parts.
Wherein the measuring track should follow the contour curve of each section in a clockwise or counter-clockwise direction, for example: according to the clockwise direction of the contour curve of each section, the leaf basin area is taken as a first measuring area, and then the trailing edge, the leaf back and the leading edge area are sequentially measured. The measurement trajectory of the combined probe is accordingly: firstly, measuring a leaf basin area and partial front and rear edge areas A1 to A2 adjacent to the leaf basin area by a horizontal probe A to obtain leaf basin profile measurement data R1, and then measuring a rear edge area and partial leaf basin and leaf back areas D1 to D2 adjacent to the rear edge area by a vertical probe B to obtain rear edge profile measurement data R3; measuring a blade back region and front and rear edge regions C1 to C2 adjacent to the blade back region by using the method A to obtain blade back profile measurement data R2; and finally, measuring the front edge area and the adjacent partial leaf pots and the adjacent leaf back areas B1 to B2 by using the B to obtain front edge profile measurement data R4.
4. Data processing
Because the adopted three-coordinate measuring machine is in contact measurement and the probe is in a spherical structure, spherical probe radius compensation is needed to be carried out on the obtained point data, and coordinate errors caused by contact measurement are eliminated. The built-in radius compensation program of the three-coordinate measuring machine with partial model can directly carry out radius compensation on the measured data. If the adopted three-coordinate measuring machine does not have a radius compensation program, any existing radius compensation method can be adopted to carry out radius compensation on the measured data.
Sorting data obtained by measuring four areas and subjected to radius compensation according to a measurement sequence, removing flying spots, traversing the sorted data, comparing coordinates of two adjacent points, judging that the two points are repeated if the coordinates of the two points are very close (for example, smaller than a certain preset threshold), preferentially reserving the points from measuring the profile data of the leaf basin or the profile data of the leaf back, and deleting the points from measuring the profile data of the leaf edge, wherein the overall shape of the aircraft blade is determined by considering the leaf basin and the leaf back; repeating the previous step until all the data are traversed, obtaining a data set which does not contain repeated points, and fitting the data set (for example, fitting by adopting a least square method), so as to obtain the profile curve of each section of the blade to be tested.
The embodiment of the invention provides an aeroengine blade profile contour measuring device based on three-coordinate measurement, which comprises the following components:
The first processing module is used for dividing the profile curve of each section of the blade to be tested into four areas of a blade basin, a blade back, a front edge and a rear edge;
the second processing module is used for controlling the combined probe to carry out regional and sequential measurement on the profile curves of the sections according to the clockwise or anticlockwise direction through the three-coordinate measuring instrument under the measurement coordinate system of the blade to be measured;
wherein the combined probe comprises a horizontal probe and a vertical probe;
The horizontal probe is used for measuring a leaf basin area and front and rear edge areas of the adjacent part of the leaf basin area to obtain leaf basin profile measurement data R1, and measuring a leaf back area and front and rear edge areas of the adjacent part of the leaf back area to obtain leaf back profile measurement data R2;
the vertical probe is used for measuring a trailing edge region, a part of the leaf basin and the leaf back region adjacent to the trailing edge region to obtain trailing edge profile measurement data R3, and is used for measuring a leading edge region, a part of the leaf basin and the leaf back region adjacent to the leading edge region to obtain leading edge profile measurement data R4;
and the third processing module is used for fitting the measurement data R1-R4 to obtain contour curves of all sections of the blade to be tested.
The embodiment of the invention provides an aeroengine blade profile contour measuring system based on three-coordinate measurement, which comprises the following steps: a computer readable storage medium and a processor;
the computer-readable storage medium is for storing executable instructions;
the processor is configured to read executable instructions stored in the computer readable storage medium and perform a method as in any of the embodiments described above.
An embodiment of the present invention provides a computer readable storage medium, where the computer readable storage medium stores computer instructions for causing a processor to perform a method according to any of the embodiments above.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (7)

1. The method for measuring the profile of the blade profile of the aeroengine based on three-coordinate measurement is characterized by comprising the following steps of:
s1, dividing a profile curve of each section of a blade to be tested into four areas, namely a blade basin, a blade back, a front edge and a rear edge;
S2, under the measurement coordinate system of the blade to be measured, controlling the combined probe to conduct regional and sequential measurement on the profile curves of all the sections through a three-coordinate measuring instrument according to the clockwise or anticlockwise direction;
the combined probe comprises a horizontal probe and a vertical probe which are connected with each other;
The horizontal probe is used for measuring a leaf basin area and front and rear edge areas of the adjacent part of the leaf basin area to obtain leaf basin profile measurement data R1, and measuring a leaf back area and front and rear edge areas of the adjacent part of the leaf back area to obtain leaf back profile measurement data R2;
the vertical probe is used for measuring a trailing edge region, a part of the leaf basin and the leaf back region adjacent to the trailing edge region to obtain trailing edge profile measurement data R3, and is used for measuring a leading edge region, a part of the leaf basin and the leaf back region adjacent to the leading edge region to obtain leading edge profile measurement data R4;
s3, fitting the measured data R1-R4 to obtain profile curves of all sections of the blade to be measured, and finally obtaining the profile of the blade to be measured;
In step S3, before the fitting of the measurement data R1 to R4, the method further includes:
1) Sequencing the measurement data according to a measurement sequence;
2) Judging whether the distance between any two points is smaller than a preset threshold value, if so, only retaining the data points from R1 or R2 in the two points, returning to the step 1), and if not, ending.
2. The method of claim 1, wherein the two mutually perpendicular probes are each circular probes having a diameter of 2 mm.
3. Method according to any of claims 1-2, wherein the establishment of the measurement coordinate system of the blade to be measured is:
the three-dimensional model of the blade to be measured is led into a three-coordinate measuring instrument, a combined probe is controlled by the three-coordinate measuring instrument to sequentially contact with a plurality of positioning points on the surface of the virtual blade, and a measurement coordinate system of the blade to be measured is established based on a six-point iteration method.
4. A method according to claim 3, characterized in that four points are selected at the root of the blade, one point is selected at the basin and one point is selected at the tip of the blade as anchor point.
5. Aeroengine blade profile contour measurement device based on three-dimensional measurement, characterized by comprising:
The first processing module is used for dividing the profile curve of each section of the blade to be tested into four areas of a blade basin, a blade back, a front edge and a rear edge;
the second processing module is used for controlling the combined probe to carry out regional and sequential measurement on the profile curves of the sections according to the clockwise or anticlockwise direction through the three-coordinate measuring instrument under the measurement coordinate system of the blade to be measured;
wherein the combined probe comprises a horizontal probe and a vertical probe;
The horizontal probe is used for measuring a leaf basin area and front and rear edge areas of the adjacent part of the leaf basin area to obtain leaf basin profile measurement data R1, and measuring a leaf back area and front and rear edge areas of the adjacent part of the leaf back area to obtain leaf back profile measurement data R2;
the vertical probe is used for measuring a trailing edge region, a part of the leaf basin and the leaf back region adjacent to the trailing edge region to obtain trailing edge profile measurement data R3, and is used for measuring a leading edge region, a part of the leaf basin and the leaf back region adjacent to the leading edge region to obtain leading edge profile measurement data R4;
the third processing module is used for fitting the measurement data R1-R4 to obtain a section profile curve of each section of the blade to be tested;
before the fitting of the measurement data R1 to R4, the method further comprises:
1) Sequencing the measurement data according to a measurement sequence;
2) Judging whether the distance between any two points is smaller than a preset threshold value, if so, only retaining the data points from R1 or R2 in the two points, returning to the step 1), and if not, ending.
6. An aeroengine blade profile measurement system based on three-dimensional measurements, comprising: a computer readable storage medium and a processor;
the computer-readable storage medium is for storing executable instructions;
The processor is configured to read executable instructions stored in the computer readable storage medium and perform the method of any one of claims 1-4.
7. A computer readable storage medium storing computer instructions for causing a processor to perform the method of any one of claims 1-4.
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