Mobile large cylinder coaxiality measuring device and method and measuring point coordinate correction method

Through the combination of the mobile non-contact three-dimensional coordinate measurement device and the attitude tracking device, the problems of low efficiency and low accuracy of coaxiality measurement of large cylinders are solved, automatic rapid measurement and high-precision measurement are realized, and production efficiency and safety are improved.

CN119915203APending Publication Date: 2025-05-02SICHUAN AEROSPACE METROLOGY & TESTING INST
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Patent Information

Application Number
CN202411824471.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-12
Publication Date
2025-05-02

AI Technical Summary

Technical Problem

The existing coaxial measurement technology of large cylinders has problems such as low measurement efficiency, inability to achieve automatic and rapid measurement, low measurement accuracy, and safety hazards, and cannot meet future batch production efficiency and automation requirements.

Method used

The mobile non-contact three-dimensional coordinate measurement device and the attitude tracking device are adopted to collect multiple cross-sectional profile data of the product through the non-contact three-dimensional coordinate measurement device. The attitude tracking device tracks the attitude changes of the measurement unit in real time and performs coordinate corrections to realize automatic and rapid measurement of product coaxiality.

Benefits of technology

It realizes automatic and rapid measurement of the coaxiality of large cylinders, improves measurement accuracy and efficiency, reduces manual intervention, and improves production safety and efficiency.

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Abstract

The invention belongs to the technical field of cylinder coaxiality measurement, and particularly relates to a movable large cylinder coaxiality measuring device and method and a measuring point coordinate correction method. The measuring device comprises a non-contact three-dimensional coordinate measuring device, a posture tracking device and a control and data processing device. The non-contact three-dimensional coordinate measuring device comprises a measuring unit, and the measuring unit collects multiple pieces of section contour data of a product; the attitude tracking device tracks the attitude of the measurement unit in the measurement process, and attitude tracking data is used for correcting coordinate measurement errors introduced by attitude changes; and the control and data processing device sends a motion instruction to the non-contact three-dimensional coordinate measurement device according to the measurement point position file, receives measurement data of the non-contact three-dimensional coordinate measurement device and attitude tracking data of the attitude tracking device, and calculates the product coaxiality. The invention provides a movable large cylinder coaxiality measuring device and method and a measuring point coordinate correction method.
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Description

Technical Field

[0001] The invention belongs to the technical field of cylindrical coaxiality measurement, and in particular relates to a mobile large-scale cylindrical coaxiality measurement device, method and measuring point coordinate correction method. Background Art

[0002] Large coaxiality deviation of large cylinders may not only lead to a decline in the quality of part assembly and serious deformation of the shaft-hole fit, but also increase the vibration of parts under high-speed operation conditions, causing increased vibration and noise of the entire machine, which will have a significant impact on the service life and reliability of the parts and accelerate the wear of the mechanical structure.

[0003] The coaxiality measurement of large cylinders has inherent characteristics such as wide distribution of measuring points, high measuring point position accuracy, and high measurement accuracy. Currently, there is no fully automatic measuring device, and automatic and fast measurement cannot be achieved. The existing detection means mainly use laser trackers. In the state of suspension of production, multiple people manually detect point by point. The measurement process takes about 24 hours, the measurement efficiency is low, and the overall three-dimensional contour model of the product cannot be provided, which cannot meet the future batch production efficiency and automation requirements.

[0004] Secondly, for safety reasons, the number of operators must be strictly controlled at the production site. Therefore, when the inspectors enter the site, other personnel must leave. Obviously, the existing manual on-site measurement method affects production efficiency.

[0005] The current technology requires manual placement of measurement point targets, which has the following main disadvantages: 1) Manual placement has low measurement efficiency. 2) The product being measured is large in size, and manual placement requires high-altitude work, which poses a safety hazard. Summary of the invention

[0006] In order to solve the above problems existing in the prior art, the object of the present invention is to provide a mobile large-scale cylindrical coaxiality measuring device, method and measuring point coordinate correction method.

[0007] The technical solution adopted by the present invention is:

[0008] A mobile large cylindrical coaxiality measuring device, comprising a non-contact three-dimensional coordinate measuring device, a posture tracking device, and a control and data processing device;

[0009] The non-contact three-dimensional coordinate measuring device includes a measuring unit, which collects multiple cross-sectional profile data of the product;

[0010] The posture tracking device tracks the posture of the measuring unit of the non-contact three-dimensional coordinate measuring device during the measurement process, and the posture tracking data will be used to correct the coordinate measurement error introduced by the posture change;

[0011] The control and data processing device sends motion instructions to the non-contact three-dimensional coordinate measuring device according to the measurement point file, receives measurement data from the non-contact three-dimensional coordinate measuring device and posture tracking data from the posture tracking device, and calculates the coaxiality of the product.

[0012] Aiming at the inherent properties of coaxiality measurement of large-size precision products, such as wide distribution of measuring points, high precision of measuring point positions and high measurement accuracy, the present invention adopts a technical means combining posture tracking with mobile non-contact three-dimensional coordinate measurement to solve the shortcomings of low measurement efficiency of traditional laser trackers and limited circumferential measurement point coverage of new scanning laser trackers, thereby realizing automatic and rapid measurement of product coaxiality.

[0013] Coaxiality measurement uses coordinate points as measurement elements, and evaluates the coaxiality index of the product by fitting the points. During the measurement process, the posture data of the measuring unit is tracked in real time through the posture tracking device, and the coordinates of the measuring points are corrected using this data.

[0014] The product uses a non-contact three-dimensional coordinate measuring device to collect multiple cross-sectional profile data; at the same time, the posture tracking device is used to detect the posture changes of the measuring unit during the measurement process and perform coordinate correction. After all cross-sectional positions are corrected, the cross-sectional profile data are processed one by one to obtain the coordinates of the center of each cross-sectional circle, and all cross-sectional circle centers are fitted with a straight line to obtain a reference straight line. The distance d from each cross-sectional circle to the reference straight line is calculated. i , then the coaxiality of the product is 2×(d i ) Max .

[0015] The present invention automatically completes the measurement of product coaxiality and key section eccentricity according to the measuring point positions specified in the design, and automatically generates a test report after the measurement is completed, thereby realizing the automation of the measurement process and paperless management of the measurement data.

[0016] The present invention has a self-checking function. When the device is turned on, it can automatically self-check the relevant hardware. When the self-checking fails, there will be relevant prompts to ensure the safety of the device. It has a user authority management function, and different personnel have different authorities to ensure the safety of operation and data.

[0017] The present invention provides a concise and intuitive human-computer interaction interface, which is convenient for users to view data and perform operations. It supports the entry of basic information such as product numbers and test personnel; historical data query; and remote data transmission.

[0018] The measuring devices of the present invention are all supported by self-locking wheel hubs, which are easy to carry and convenient to disassemble and pack.

[0019] As a preferred embodiment of the present invention, the non-contact three-dimensional coordinate measurement includes a carrying unit, a carrying support plate is fixed on the carrying unit, an arc-shaped bracket is fixed on the carrying support plate, a circumferential motion component is connected to the arc-shaped bracket and can move circumferentially on the arc-shaped bracket with the product as the center, and the measuring unit is installed on the circumferential motion component.

[0020] As a preferred solution of the present invention, the measuring unit includes a contour scanning sensor and a posture target.

[0021] As a preferred solution of the present invention, the contour scanning sensor and the posture target are located in two orthogonal planes.

[0022] As a preferred solution of the present invention, the posture tracking device is an optical coordinate measuring device, which is used to track the coordinates of the posture target of the measuring unit.

[0023] As a preferred embodiment of the present invention, the circumferential motion assembly includes an arc-shaped rack guide fixed on an arc-shaped bracket, the arc-shaped rack guide includes an arc-shaped rack and an arc-shaped guide, a slider is sleeved on the arc-shaped guide, a motor is mounted on the slider, a gear is connected to the output end of the motor, and the gear is meshed with the arc-shaped rack; a measuring unit mounting plate is also fixed on the slider, and the measuring unit is mounted on the measuring unit mounting plate. When the measuring device is working normally, the driving carrier unit moves precisely to the designated detection axial position and stops moving. Driven by the motor, the gear meshes with the arc-shaped rack of the arc-shaped rack guide, so that the slider drives the measuring unit mounting plate and the measuring unit to move circumferentially around the product.

[0024] As a preferred solution of the present invention, a roller is installed on the sliding block, and the roller overlaps the arc-shaped guide rail of the arc-shaped rack guide rail.

[0025] A mobile large cylindrical coaxiality measurement method comprises the following steps:

[0026] S1: The product uses a non-contact three-dimensional coordinate measuring device to collect multiple cross-sectional profile data;

[0027] S2: The posture tracking device detects the posture change of the measuring unit during the measurement process and performs coordinate correction;

[0028] S3: After all cross-section positions are corrected, the cross-section profile data are processed one by one to obtain the coordinates of the center of each cross-section, and the centers of all cross-sections are fitted with a straight line to obtain a reference straight line;

[0029] S4: Calculate the distance d from each section circle to the reference straight line i , then the coaxiality of the product is 2×(d i ) Max .

[0030] A method for correcting coordinates of measuring points for coaxiality measurement of a movable large cylindrical object comprises the following steps:

[0031] T1: The following measurement unit attribute parameters are known:

[0032] The coordinates of the light emission centers of the three attitude targets and the contour scanning sensor are:

[0033] A(x A ,y A , z A ); B(x B ,y B , z B ); C(x C ,y C , z C ); D(x D ,y D , z D );

[0034] The intersection point G(x G ,y G , z G );

[0035] Unit normal vector of the light-emitting surface of the profile scanning sensor

[0036] T2: Modified algorithm:

[0037] We can get the projection point E(x E ,y E , z E ), DE length is H;

[0038] Unit normal vector of face ABC:

[0039]

[0040] The equation of the line through the surface ABC is:

[0041]

[0042] Then we can solve for t:

[0043]

[0044] Substitute t into the equation of the line to obtain the coordinates of point E (x E ,y E , z E ):

[0045]

[0046] Similarly, we can get the coordinates of the projection point K of M on the surface ABC (x K ,y K , z K ); When taking measurements:

[0047] It is expressed as:

[0048]

[0049] Among them, a and b are parameters;

[0050] After moving for:

[0051]

[0052] Then the coordinates of point E' after moving are:

[0053]

[0054] Then the coordinates of point D' are:

[0055]

[0056] Similarly, we can get:

[0057]

[0058] Among them, e and f are parameters;

[0059] After moving for:

[0060]

[0061] Then the coordinates of point K' after moving are:

[0062]

[0063] Then the coordinates of point M' are:

[0064]

[0065] Where h is the modulus of vector MK;

[0066] It can be expressed as:

[0067]

[0068] Among them, c and d are parameters;

[0069] but:

[0070]

[0071] After correction calculation, the coordinates of the measuring point F are:

[0072]

[0073] Wherein, X and Z are the measured values ​​of the profile scanning sensor. The beneficial effects of the present invention are:

[0074] 1. The present invention automatically completes the measurement of product coaxiality and key section eccentricity according to the measuring point positions specified in the design, and automatically generates a test report after the measurement is completed, realizing the automation of the measurement process and paperless management of measurement data.

[0075] 2. The present invention has a self-checking function. When the device is turned on, it can automatically self-check the relevant hardware. When the self-checking fails, there will be relevant prompts to ensure the safety of the device. It has a user authority management function, and different personnel have different authorities to ensure operation and data security.

[0076] 3. The present invention provides a concise and intuitive human-computer interaction interface, which is convenient for users to view data and perform operations. It supports the entry of basic information such as product numbers and test personnel; historical data query; and remote data transmission.

[0077] 4. The measuring devices of the present invention are all supported by self-locking wheel hubs, which are easy to carry and convenient to disassemble and pack. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 It is a block diagram of the device composition of the present invention;

[0079] Figure 2 It is a structural schematic diagram of a non-contact three-dimensional coordinate measuring device;

[0080] Figure 3 It is a schematic diagram of the structure of the circumferential motion component;

[0081] Figure 4 This is the principle diagram of coaxiality solution;

[0082] Figure 5 It is the attitude correction principle diagram;

[0083] Figure 6 It is a schematic diagram of the measuring point coordinate correction model.

[0084] In the figure: 1-carrying unit; 2-carrying unit support plate; 3-arc bracket; 4-measuring unit mounting plate; 5-motor; 6-measuring unit; 7-arc rack guide; 8-slider. DETAILED DESCRIPTION

[0085] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0086] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0087] like Figure 1 As shown, the mobile large cylindrical coaxiality measuring device of this embodiment includes a non-contact three-dimensional coordinate measuring device, a posture tracking device, and a control and data processing device;

[0088] The non-contact three-dimensional coordinate measuring device includes a measuring unit 6, which collects multiple cross-sectional profile data of the product;

[0089] The posture tracking device tracks the posture of the measuring unit 6 of the non-contact three-dimensional coordinate measuring device during the measurement process, and the posture tracking data will be used to correct the coordinate measurement error introduced by the posture change;

[0090] The control and data processing device sends motion instructions to the non-contact three-dimensional coordinate measuring device according to the measurement point file, receives measurement data from the non-contact three-dimensional coordinate measuring device and posture tracking data from the posture tracking device, and calculates the coaxiality of the product.

[0091] Aiming at the inherent properties of coaxiality measurement of large-size precision products, such as wide distribution of measuring points, high precision of measuring point positions and high measurement accuracy, the present invention adopts a technical means combining posture tracking with mobile non-contact three-dimensional coordinate measurement to solve the shortcomings of low measurement efficiency of traditional laser trackers and limited circumferential measurement point coverage of new scanning laser trackers, thereby realizing automatic and rapid measurement of product coaxiality.

[0092] The product uses a non-contact three-dimensional coordinate measuring device to collect multiple cross-sectional profile data; at the same time, the posture tracking device detects the posture change of the measuring unit 6 during the measurement process and performs coordinate correction. After all cross-sectional positions are corrected, the cross-sectional profile data are processed one by one to obtain the coordinates of the center of each cross section, and all cross-sectional center points are fitted with a straight line to obtain a reference straight line. The distance d from each cross-sectional circle to the reference straight line is calculated. i, then the coaxiality of the product is 2×(d i ) Max .

[0093] The present invention automatically completes the measurement of product coaxiality and key section eccentricity according to the measuring point positions specified in the design, and automatically generates a test report after the measurement is completed, thereby realizing the automation of the measurement process and paperless management of the measurement data.

[0094] The present invention has a self-checking function. When the device is turned on, it can automatically self-check the relevant hardware. When the self-checking fails, there will be relevant prompts to ensure the safety of the device. It has a user authority management function, and different personnel have different authorities to ensure the safety of operation and data.

[0095] The present invention provides a concise and intuitive human-computer interaction interface, which is convenient for users to view data and perform operations. It supports the entry of basic information such as product numbers and test personnel; historical data query; and remote data transmission.

[0096] The measuring devices of the present invention are all supported by self-locking wheel hubs, which are easy to carry and convenient to disassemble and pack.

[0097] Specifically, Figure 2 and Figure 3 As shown, the non-contact three-dimensional coordinate measurement includes a carrying unit 1, a carrying support plate is fixed on the carrying unit 1, an arc-shaped bracket 3 is fixed on the carrying support plate, a circumferential motion component is connected to the arc-shaped bracket 3 and can move circumferentially on the arc-shaped bracket 3 with the product as the center, and a measuring unit 6 is installed on the circumferential motion component.

[0098] The measuring unit 6 includes a contour scanning sensor and a posture target. The contour scanning sensor and the posture target are located in two orthogonal planes. The posture tracking device is an optical coordinate measuring device, which is used to track the coordinates of the posture target of the measuring unit 6.

[0099] Specifically, Figure 3 As shown, the circumferential motion assembly includes an arc-shaped rack guide rail 7 fixed on the arc-shaped bracket 3, and the arc-shaped rack guide rail 7 includes an arc-shaped rack and an arc-shaped guide rail. A slider 8 is sleeved on the arc-shaped guide rail, and a motor 5 is installed on the slider 8. The output end of the motor 5 is connected to a gear, and the gear is meshed with the arc-shaped rack; the slider 8 is also fixed with a measuring unit mounting plate 4, and the measuring unit 6 is mounted on the measuring unit mounting plate 4. When the measuring device works normally, the carrier unit 1 moves accurately to the designated detection axial position and stops moving. Driven by the motor 5, the gear meshes with the arc-shaped rack of the arc-shaped rack guide rail 7, so that the slider 8 drives the measuring unit mounting plate 4 and the measuring unit 6 to move circumferentially with the product as the center.

[0100] The slider 8 is provided with a roller, which overlaps with the arc-shaped guide rail of the arc-shaped rack guide rail 7 .

[0101] like Figure 4 As shown, the mobile large cylindrical coaxiality measurement method of this embodiment includes the following steps:

[0102] S1: The product uses a non-contact three-dimensional coordinate measuring device to collect multiple cross-sectional profile data;

[0103] S2: The posture tracking device detects the posture change of the measuring unit 6 during the measurement process and performs coordinate correction;

[0104] S3: After all cross-section positions are corrected, the cross-section profile data are processed one by one to obtain the coordinates of the center of each cross-section, and the centers of all cross-sections are fitted with a straight line to obtain a reference straight line;

[0105] S4: Calculate the distance d from each section circle to the reference straight line i , then the coaxiality of the product is 2×(d i ) Max .

[0106] Coaxiality measurement uses coordinate points as measurement elements, and evaluates the coaxiality index of the product by fitting the points. During the measurement process, the posture data of the measuring unit 6 is tracked in real time by the posture tracking device, and the coordinates of the measuring points are corrected using the data.

[0107] Establish Figure 6 In the modified model shown, the profile scanning sensor and attitude target are located in two orthogonal planes.

[0108] Correction principle Figure 5 As shown, the coordinate correction method of the measuring point of the mobile large cylindrical coaxiality measurement includes the following steps:

[0109] T1: The following measurement unit attribute parameters are known:

[0110] The coordinates of the light emission centers of the three attitude targets and the contour scanning sensor are:

[0111] A(x A ,y A , z A ); B(x B ,y B , z B ); C(x C ,y C , z C ); D(x D ,y D , z D );

[0112] The intersection point G(x G ,y G , zG );

[0113] Unit normal vector of the light-emitting surface of the profile scanning sensor

[0114] T2: Modified algorithm:

[0115] We can get the projection point E(x E ,y E , z E ), DE length is H;

[0116] Unit normal vector of face ABC:

[0117]

[0118] The equation of the line through the surface ABC is:

[0119]

[0120] Then we can solve for t:

[0121]

[0122] Substitute t into the equation of the line to obtain the coordinates of point E (x E ,y E , z E ):

[0123]

[0124] Similarly, we can get the coordinates of the projection point K of M on the surface ABC (x K ,y K , z K );

[0125] When taking measurements, Figure 6 All points are marked with a "'" symbol to distinguish them from the initial model. For example, the center point of the light outlet of the contour scanning sensor is D at the initial stage and D' during measurement.

[0126] in, It is expressed as:

[0127]

[0128] Determine parameters a and b;

[0129] After moving for:

[0130]

[0131] Then the coordinates of point E' after moving are:

[0132]

[0133] Then the coordinates of point D' are:

[0134]

[0135] Similarly, we can get:

[0136]

[0137] Determine parameters e and f;

[0138] After moving for:

[0139]

[0140] Then the coordinates of point K' after moving are:

[0141]

[0142] Then the coordinates of point M' are:

[0143]

[0144] Where h is the modulus of vector MK; It can be expressed as:

[0145]

[0146] Determine parameters c and d;

[0147] but:

[0148]

[0149] After the above correction calculation, the coordinates of the measuring point F are:

[0150]

[0151] Where X and Z are the measured values ​​of the profile scanning sensor.

[0152] The present invention is not limited to the above-mentioned optional implementation modes. Anyone can derive other various forms of products under the inspiration of the present invention. However, no matter what changes are made in the shape or structure, all technical solutions that fall within the scope defined by the claims of the present invention fall within the protection scope of the present invention.

Claims

1. A mobile large cylindrical coaxiality measuring device, characterized in that: It includes non-contact three-dimensional coordinate measuring device, posture tracking device, control and data processing device; The non-contact three-dimensional coordinate measuring device comprises a measuring unit (6), wherein the measuring unit (6) collects a plurality of cross-sectional profile data of a product; The posture tracking device tracks the posture of the measuring unit (6) of the non-contact three-dimensional coordinate measuring device during the measurement process, and the posture tracking data is used to correct the coordinate measurement error introduced by the posture change; The control and data processing device sends motion instructions to the non-contact three-dimensional coordinate measuring device according to the measurement point file, receives measurement data from the non-contact three-dimensional coordinate measuring device and posture tracking data from the posture tracking device, and calculates the coaxiality of the product.

2. A mobile large cylindrical coaxiality measuring device according to claim 1, characterized in that: The non-contact three-dimensional coordinate measurement comprises a transport unit (1), a transport support plate is fixed on the transport unit (1), an arc-shaped bracket (3) is fixed on the transport support plate, a circumferential motion component is connected to the arc-shaped bracket (3) and can move circumferentially on the arc-shaped bracket (3) with the product as the center, and a measuring unit (6) is installed on the circumferential motion component.

3. A mobile large cylindrical coaxiality measuring device according to claim 2, characterized in that: The measuring unit (6) comprises a profile scanning sensor and a posture target.

4. The mobile large cylindrical coaxiality measuring device according to claim 3 is characterized in that: The profile scanning sensor and the attitude target are located in two orthogonal planes.

5. The mobile large cylindrical coaxiality measuring device according to claim 3 is characterized in that: The posture tracking device is an optical coordinate measuring device, which is used to track the coordinates of the posture target of the measuring unit (6).

6. The mobile large cylindrical coaxiality measuring device according to claim 2 is characterized in that: The circumferential motion component comprises an arc-shaped rack guide rail (7) fixed on the arc-shaped bracket (3), the arc-shaped rack guide rail (7) comprises an arc-shaped rack and an arc-shaped guide rail, a slider (8) is sleeved on the arc-shaped guide rail, a motor (5) is mounted on the slider (8), an output end of the motor (5) is connected to a gear, and the gear meshes with the arc-shaped rack; a measuring unit mounting plate (4) is also fixed on the slider (8), and the measuring unit (6) is mounted on the measuring unit mounting plate (4).

7. The mobile large cylindrical coaxiality measuring device according to claim 2 is characterized in that: The slider (8) is provided with a roller, which overlaps with the arc-shaped guide rail of the arc-shaped rack guide rail (7).

8. A mobile large cylindrical coaxiality measuring method, using the mobile large cylindrical coaxiality measuring device according to claim 4, characterized in that: The following steps are involved: S1: The product uses a non-contact three-dimensional coordinate measuring device to collect multiple cross-sectional profile data; S2: The posture tracking device detects the posture change of the measuring unit (6) during the measurement process and performs coordinate correction; S3: After all cross-section positions are corrected, the cross-section profile data are processed one by one to obtain the coordinates of the center of each cross-section, and the centers of all cross-sections are fitted with a straight line to obtain a reference straight line; S4: Calculate the distance d from each section circle to the reference straight line i , then the coaxiality of the product is 2×(d i ) Max .

9. A method for correcting coordinates of measuring points for coaxiality measurement of a mobile large cylindrical object, used in the method for coaxiality measurement of a mobile large cylindrical object as claimed in claim 8, characterized in that: The following steps are involved: T1: The following measurement unit attribute parameters are known: The coordinates of the light emission centers of the three attitude targets and the contour scanning sensor are: A(x A ,y A ,z A );B(x B ,y B ,z B );C(x C ,y C ,z C );D(x D ,y D ,z D ); The X axis of the profile scanning sensor intersects the ABC surface at G(x G ,y G , z G ); Unit normal vector of the light-emitting surface of the profile scanning sensor T2: Modified algorithm: We can get the projection point E(x E ,y E , z E ), DE length is H; Unit normal vector of face ABC: The equation of the line through the surface ABC is: Then we can solve for t: Substitute t into the equation of the line to obtain the coordinates of point E (x E ,y E , z E ): Similarly, we can get the coordinates of the projection point K of M on the surface ABC (x K ,y K , z K ); When taking a measurement: It is expressed as: Among them, a and b are parameters; After moving for: Then the coordinates of point E' after moving are: Then the coordinates of point D' are: Similarly, we can get: Among them, e and f are parameters; After moving for: Then the coordinates of point K' after moving are: Then the coordinates of point M' are: Where h is the modulus of vector MK; It can be expressed as: Among them, c and d are parameters; but: After correction calculation, the coordinates of the measuring point F are: Where X and Z are the measured values ​​of the profile scanning sensor.