A method for obtaining gear overall error based on continuous segmented fitting Facet model

Abstract

The present invention discloses a gear overall error acquisition method based on a continuous piecewise fitting Facet model. The method performs global continuous piecewise fitting on the extracted gear edge sub-pixels, and suppresses the error accumulated by random noise of the edge during the measurement process by inversely calculating the sub-pixel coordinates through a fitting function. Combined with the gear overall error theory, a bidirectional cross-section gear overall error curve containing all tooth profile error information of the measured gear is automatically generated from the gear image edge information, so that it can not only instantly obtain single error information such as pitch deviation and tooth profile deviation in analytical measurement, but also obtain results such as tangential comprehensive deviation in functional measurement, which facilitates the analysis of the intrinsic relationship between various gear errors and the overall error, and can simultaneously obtain error terms of multiple target gears, greatly improving the gear error analysis capability and efficiency.

Description

Technical Field

[0001] The present invention belongs to the field of gear visual measurement, and specifically relates to a gear overall error acquisition method based on a continuous segmented fitting Facet model, which can be used to quickly acquire the overall error of a small-module involute spur gear. Background Art

[0002] Current common gear measurement technologies, whether using a gear measuring center or single or double meshing measurement, have limitations. Gear measuring centers cannot obtain functional measurement results such as tangential and radial composite deviations; and single or double meshing measurement cannot obtain analytical measurement results such as pitch and profile deviations. Gear overall error measurement can provide both functional and analytical results. However, the standard measuring element required by traditional gear overall error measuring instruments—the jump-tooth worm—is difficult to manufacture and lacks versatility, limiting their flexibility and adaptability between different products. This limits their scope of application.

[0003] At present, gear measurement technology based on machine vision is constantly developing, especially when the measurement object is a small module gear (module less than or equal to 1mm), its advantages are obvious. Small module gears have a large output, small tooth grooves, poor rigidity, and are difficult to clamp. The probe of traditional gear measuring instruments is difficult to enter the tooth groove for measurement. Even if it can be measured, it cannot achieve 100% full inspection due to insufficient measurement speed. Vision-based gear measurement methods have the advantages of high efficiency, no need for clamping, small module measurement, and simultaneous measurement of multiple target workpieces. However, the current gear vision measurement technology presents problems such as insufficient measurement accuracy and limited error information that can be obtained. First, the ordinary sub-pixel edge detection algorithm is easily affected by random noise when determining the direction and amplitude of the edge gradient, and the measurement accuracy is insufficient. Secondly, most gear vision measurement methods are limited to measuring one or two single errors, and there is no research on the method of obtaining the overall gear error, resulting in far insufficient gear error analysis capabilities. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the existing technology and propose a gear overall error acquisition method based on a continuous segmented fitting Facet model with higher accuracy and more complete error information. The method first performs global continuous segmented fitting on the extracted gear edge sub-pixels, and inversely calculates the sub-pixel coordinates through the fitting function to suppress the error accumulated by the random noise of the edge during the measurement process; secondly, combined with the gear overall error theory, a two-way cross-section gear overall error curve containing all the tooth profile error information of the measured gear is automatically generated from the gear image edge information, so that it can not only instantly obtain single error information such as pitch deviation and tooth profile deviation in analytical measurement, but also obtain results such as tangential comprehensive deviation in functional measurement, which facilitates the analysis of the intrinsic relationship between various gear errors and the overall error, and can simultaneously obtain the error terms of multiple target gears, greatly improving the gear error analysis capability and efficiency.

[0005] The technical solution adopted in the present invention is as follows:

[0006] The present invention is a method for obtaining the overall gear error based on a continuous segmented fitting Facet model, which is characterized by comprising the following steps:

[0007] First, the gear vision measurement system must be calibrated before measurement to determine the relationship between the gear image coordinate system and the world coordinate system. Next, projection images of multiple target spur gears are acquired and preprocessed using filtering, morphological operations, and segmentation.

[0008] The classic Canny operator is used to extract the pixel-level edges of the gear contour, and the edge transition pixel area is determined as the ROI (Region of Interest) area. The subsequent sub-pixel positioning algorithm will only be performed in this ROI area, which greatly saves calculation time.

[0009] A projected image of a gear can be viewed as a matrix composed of numerous pixel units. Therefore, it can be divided into several smaller matrices, each with a specific grayscale distribution. Such an area is called a facet. The grayscale distribution function of each facet is a polynomial function of the pixels within its corresponding area. The 2D Facet model is a cubic bivariate surface model, which is a cubic bivariate polynomial fitted to the grayscale values ​​in the 2D neighborhood of the pixel center. The specific formula is as follows:

[0010] f(x,y)=a0+a1x+a2y+a3x 2 +a4xy+a5y 2 +a6xy 2 +a7x 2 y+a8x 3 +a9y 3 (1)

[0011] a0~a9 are the fitting coefficients of each polynomial. In order to reduce the amount of calculation, the tensor product of Chebyshev polynomials is used to generate an orthogonal polynomial group as the basis function g i (x, y) to reconstruct formula (1) and obtain formula (2). The parameters t and s are determined by the neighborhood:

[0012]

[0013] In the neighborhood of the gear pixel-level edge ROI, the coefficients a0 to a9 are fitted using the least squares method. The partial derivative of the polynomial is taken at the center of the neighborhood to obtain the second-order Hessian matrix:

[0014]

[0015] Where: r xx ,r yy ,r xy is the corresponding second-order partial derivative of the polynomial.

[0016] Assume that the unit eigenvector corresponding to the absolute value of the maximum eigenvalue of the Hessian matrix is ​​(n x ,n y ), then (n x ,n y ) is the unit normal vector of the gear edge contour. At a certain pixel point (x i ,y i ), the grayscale distribution function on the normal cross section is expanded by the second-order Taylor series, then the point on the cross section (x i +tn x ,y i +tn y ) can be expressed as:

[0017]

[0018] Where, let N = (tn x ,tn y ), r x ,r y is the first-order partial derivative of the polynomial.

[0019] The sub-pixel coordinate point of the gear profile is the point with the largest grayscale change rate, that is, the maximum value of the grayscale distribution function in the direction of the gradient vector. get:

[0020]

[0021] If tn x ,tn y Can satisfy both That is, the point where the first-order derivative is zero is located within the current pixel, and the sub-pixel coordinates of the gear profile are:

[0022]

[0023] Since random noise always exists in the gear profile in the image, the extracted sub-pixel coordinates will inevitably introduce positioning errors, and this error will accumulate and increase after the previous multiple steps of calculation. In order to suppress the positioning error introduced by random noise, the present invention performs a global continuous segmented fitting on the extracted gear profile sub-pixel coordinates, and divides the key gear profile into multiple segments such as tooth top, left / right tooth profile and tooth root for each gear tooth. The multi-segment fitting is performed using an error minimization model with equality constraints. The fitting function is continuous at the intersection of each segment, and the least squares regression coefficient of the model is derived by the Lagrange multiplier method. Because the edge characteristics at the tooth top, tooth profile and tooth root are different, the size of the random noise is also different. Such multi-segment fitting avoids the problem of large errors caused by using only one fitting curve to describe the gear profile.

[0024] Assume that the gear contour is divided into k segments, and each segment has m data (i.e., m sub-pixel coordinate points). The coordinates of the i-th sub-pixel point on the j-th gear contour segment are expressed as Represented by, where i = 1, 2, ... m, j = 1, 2, ... k, the sub-pixel point set of each interval is but:

[0025]

[0026] g(x (j) ) is the gear profile sub-pixel point dataset S j The previous set of linearly independent basis functions, X j It's S j The data in the matrix generated by the basis function group, the coefficient ε is to be determined j There are n+1, X is The diagonal block matrix of The block matrix of , then the continuous least squares regression model of the gear profile multi-segment interval can be expressed as:

[0027]

[0028] The equality constraint shows the continuity of the fitting function at each segment point of the gear profile. The Lagrangian function L(ε,λ) is established for the above equation:

[0029] L(ε,λ)=||Xε-y|| 2 +2λ T Zε (9)

[0030] λ is a column vector of length k-1. The regression coefficient ε can be obtained by taking the partial derivative of the Lagrangian function.

[0031] After the above steps, the global continuous piecewise fitting function of the gear profile can be calculated, and then the precise sub-pixel coordinates of the final gear profile can be inversely calculated based on the function.

[0032] After obtaining the sub-pixel coordinate set of the gear's key profile, in order to obtain the overall gear error information, it is necessary to fit the coordinates of the center point of the gear end section using the sub-pixel coordinate point set of the center hole profile of the gear end section. Then, based on the definition of relevant deviations in the gear accuracy standard ISO-1328.1:2013, the pitch deviation and tooth profile deviation of each gear tooth are obtained.

[0033] Assume that there are n sub-pixel edge coordinate points of the center hole contour of the gear end section, and the coordinates of each point are (x i ,y i ), i = 1 to n. Then the coordinates of the center of the gear hole (x0, y0) and the radius r can be obtained by least squares fitting, and the optimization objective function of the square error can be expressed as:

[0034]

[0035] Let parameters b1 = -2x0, b2 = -2y0, The values ​​of parameters b1, b2, and b3 should minimize S, so b1, b2, and b3 should satisfy:

[0036]

[0037] After expanding and solving the equation group, the values ​​of b1, b2, and b3 can be obtained. Substituting them into the circular coordinate equation can determine the center (x0, y0) and radius r of the gear center hole.

[0038] The calculation of the pitch deviation is carried out in the following steps: First calculate the measuring circle (diameter d m ) and the intersection of the tooth profile, the actual tooth pitch P of the gear i The arc length formed by the intersection of the adjacent tooth profiles on the same side and the measuring circle, assuming the number of teeth is z, the theoretical tooth pitch is P = πd m / z, then the single pitch deviation of any adjacent gear teeth is f pi =P i -P, the cumulative pitch deviation of k teeth is

[0039] Tooth profile deviation f at any point on the tooth profile evaluation segment f It can be given by the following formula:

[0040]

[0041] (x m ,y m ) is a point on the actual tooth profile, (x,y) is the distance between (x m ,y m ) The foot of the perpendicular line to the theoretical involute tooth profile, tooth profile deviation f f It is necessary to judge whether it is positive or negative. When the actual tooth profile point is outside the tooth area surrounded by the theoretical left and right tooth profiles, it is positive, and when it is inside, it is negative.

[0042] The overall gear profile error curve is formed by superimposing the tooth profile error according to the actual pitch error of each tooth. Assuming that the number of teeth of the gear is z, the pressure angle is α, the number of sampling points on the tooth profile is n, and F Pi is the cumulative deviation of the tooth pitch of the i-th tooth, f f(i,j) is the tooth profile error value of the jth point of the i-th tooth profile. The horizontal coordinate x of each point on the overall error curve is the gear roll angle coordinate corresponding to each point of the tooth profile The vertical coordinate y is incremented by the length of the graduated arc To express the deviation value of the gear being measured, u i,j is the jth point of the i-th tooth profile on the overall error curve The coordinate value of (in pixels). Considering the different measurement directions of pitch error and tooth profile error, the following synthesis formula should be obtained:

[0043] u i,j =F Pi +f f(i,j) / cosα 1≤i≤z; 1≤j≤n (13)

[0044] Since the values ​​obtained in the gear image are in pixels, they need to be converted into actual values ​​in microns. Here, they can be multiplied by the proportional coefficient (pixel equivalent) γ between the gear image coordinate system and the world coordinate system obtained by calibration of the gear vision measurement system:

[0045] u′ i,j =u i,j ·γ 1≤i≤z; 1≤j≤n (14)

[0046] Where u′ i,j is the overall gear error at the jth point on the i-th tooth profile (in microns).

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] 1) Compared to existing gear measurement centers and single / double-meshing measurement technologies, the vision-based gear overall error acquisition method proposed in this invention is a non-contact measurement method that requires no clamping and can simultaneously measure multiple target gears (the number of gears that can be measured simultaneously is related to the gear's outer diameter and the field of view of the gear vision measurement system). This significantly improves measurement efficiency, especially for small-module gears, which are produced in large quantities. The proposed method can achieve 100% full inspection. The technology of this invention can obtain both functional and analytical gear measurement results, effectively improving the ability to analyze gear errors.

[0049] 2) Small-module gears have small tooth spaces, poor rigidity, and are difficult to clamp. Existing measurement technologies make it virtually impossible to measure them. However, the present invention allows for instantaneous acquisition of the overall error of small-module gears. Compared to conventional gear measurement technology, the present invention enables a leap from "unmeasurable" to "efficient measurement" for small-module gears. Furthermore, no clamping is required, thus avoiding the introduction of installation errors.

[0050] 3) Compared with the existing gear vision measurement method, the present invention improves the positioning accuracy of the sub-pixel algorithm based on the global continuous segmented fitting Facet model, thereby improving the positioning accuracy of the gear contour and obtaining more accurate gear error results. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The present invention will be further described below in conjunction with the accompanying drawings:

[0052] Figure 1 It is the structural diagram of the gear overall error visual measurement system.

[0053] Figure 2 (a) Key contour information extracted from spur gear image. Figure 2 (b) is an enlarged view of a tooth in the spur gear image.

[0054] Figure 3 This is the effect diagram of segmented tooth profile curve fitting with continuous constraints

[0055] Figure 4 These are the sub-pixel edge coordinate points of the gear extracted using the method of the present invention.

[0056] Figure 5 is the overall error curve of the gear section.

[0057] Figure 6 It is the overall error curve of the gear bidirectional section.

[0058] Figure 7 This is an example of applying the method of the present invention to complete tooth profile burr detection, which is represented by a Cartesian coordinate system.

[0059] Figure 8This is an example of applying the method of the present invention to complete tooth profile burr detection, which is represented by a circular coordinate system.

[0060] Figure 9 These are the detailed calculation steps of the gear overall error acquisition method based on the continuous segmented fitting Facet model proposed in the present invention.

[0061] The symbols in the accompanying drawings are:

[0062] 1—Camera bracket, 2—Slider, 3—Camera communication interface, 4—Industrial camera, 5—Telecentric lens, 6—Spur gear to be measured, 7—Glass plate, 8—LED backlight source, 9—Collected multi-target gear images, 10—Host. DETAILED DESCRIPTION

[0063] The present invention will be further described with reference to the accompanying drawings:

[0064] See Figure 1 The gear overall error acquisition method based on continuous segmented fitting Facet model proposed in this invention can be carried out Figure 1 The overall gear error visual measurement system shown in the figure is used to achieve this, which is responsible for gear image acquisition, gear image processing, gear error result measurement and characterization.

[0065] The camera bracket 1 is a precision fine-tuning dovetail manual slide bracket that can adjust the working distance of the industrial camera 4. The industrial camera 4 is connected to the camera bracket 1 through a slider 2, and the telecentric lens 5 is connected to the industrial camera 4 through a thread. During measurement, multiple spur gears 6 to be measured are placed on the glass plate 7, and the LED backlight source 8 illuminates from bottom to top. The gear cross-section image is imaged on the photosensitive components inside the industrial camera 4 through the telecentric lens 5. The collected multi-target gear images 9 are transmitted to the software of the host 10 through the camera communication interface 3 for processing, and finally the processed gear error data is calculated and characterized.

[0066] See Figure 2 、 Figure 3 and Figure 4 , demonstrating the effect of extracting sub-pixel coordinates of key contours of spur gears based on continuous segmented fitting Facet model. First, the multi-target gear image 9 collected is segmented into multiple local images containing only a single gear, and the gear image is pre-processed by filtering, morphological operations and other steps. Then, the method proposed in this invention is used to process a single gear image. Figure 2 a is the result of segmenting a single gear image from the multi-target gear image 9 and processing it using the method of the present invention. Figure 2 b shows an enlarged view of the key contour extracted from a gear tooth.

[0067] Firstly, the Canny operator is used to extract the pixel-level edge of the gear contour, and the transition pixel area near the pixel-level edge of the gear contour is used as the ROI area for subsequent processing, which greatly saves calculation time.

[0068] In the gear contour ROI area, a 2D Facet model is used to fit a bivariate cubic polynomial of the grayscale distribution function in a 2D neighborhood centered on the pixel point. The tensor product of Chebyshev polynomials is used to generate an orthogonal polynomial group as a basis function to reconstruct the polynomial. The reconstructed polynomial is as follows:

[0069]

[0070] By taking partial derivatives of the polynomial at the center of the neighborhood, we can obtain the Hessian matrix:

[0071]

[0072] Assume that the unit eigenvector corresponding to the absolute value of the maximum eigenvalue of the Hessian matrix is ​​(n x ,n y ), then (n x ,n y ) is the unit normal vector of the gear profile. At a certain pixel point (x i ,y i ), the grayscale distribution function on the normal cross section is expanded by the second-order Taylor series, then the point on the cross section (x i +tn x ,y i +tn y ) can be expressed as:

[0073]

[0074] The sub-pixel coordinate point of the gear profile is the point with the largest grayscale change rate, that is, the maximum value of the grayscale distribution function in the direction of the gradient vector. get:

[0075] If tn x ,tn y Can satisfy both That is, the point where the first-order derivative is zero is located within the current pixel, and the sub-pixel coordinates of the gear profile are:

[0076] See Figure 3To reduce the errors accumulated by random noise at the edges of gear images during calculations, the present invention performs a global, continuous, piecewise fitting of the extracted sub-pixel coordinates of the gear profile. To improve fitting accuracy, a piecewise fitting method with global continuity constraints is proposed. Each tooth in the critical gear profile is divided into multiple segments: the addendum, left / right tooth profile, and tooth root. Multi-segment fitting is performed using an error minimization model with equality constraints. The fitting function at each segment intersection is continuous, and the least squares regression coefficients of the model are derived using the Lagrange multiplier method. Because the edge characteristics of the addendum, tooth profile, and tooth root differ, and the magnitude of random noise also varies, this multi-segment fitting method avoids the problem of large errors caused by using a single fitting curve to describe the critical gear profile.

[0077] Assume that the gear profile interval is divided into k segments, each segment has m data (i.e., m sub-pixel coordinate points), and the coordinates of the i-th sub-pixel point in the j-th segment are expressed as Indicates that i = 1, 2, ... m, j = 1, 2, ... k, and the sub-pixel point set of the gear profile in each interval is but:

[0078]

[0079] g(x (j) ) is the gear profile sub-pixel point dataset S j The previous set of linearly independent basis functions, X j It's S j The data in the matrix generated by the basis function group, the coefficient ε is to be determined j There are n+1, X is The diagonal block matrix of The block matrix of , then the continuous least squares regression model of the gear profile multi-segment interval can be expressed as:

[0080]

[0081] The equality constraint describes the continuity of the fitting function at each segment point of the gear profile. The Lagrangian function is established for the above equation: L(ε,λ)=||Xε-y|| 2 +2λ T Zε. λ is a column vector of length k-1. Taking the partial derivative of the Lagrangian function L(ε,λ), we can solve the least squares regression coefficient of the continuous piecewise fitting:

[0082]

[0083] Figure 4 The red lines in the middle represent the lines connecting the extracted sub-pixel coordinate points of the gear contour, and the blue arrows represent the gradient amplitude and direction of each sub-pixel point position of the gear contour.

[0084] After obtaining the sub-pixel coordinate set of the gear's key contour, in order to obtain the overall gear error information, it is necessary to fit the center point coordinates of the gear end section using the sub-pixel coordinate point set of the gear center hole contour. Then, based on the definition of relevant deviations in the gear precision standard ISO-1328.1:2013, the pitch deviation and tooth profile deviation information of each gear tooth is obtained.

[0085] Assume that there are n sub-pixel edge coordinate points of the gear center hole contour, and the coordinates of each point are (x i ,y i ), i = 1 to n. Then the coordinates of the center of the gear hole (x0, y0) and the radius r can be obtained by least squares fitting, and the optimization objective function S of the square error can be expressed as:

[0086]

[0087] By minimizing S, the coefficients of the objective function can be calculated and substituted into the circular coordinate equation to find the center (x0, y0) and radius r of the gear center hole.

[0088] The calculation of the pitch deviation is carried out in the following steps: First calculate the measuring circle (diameter d m ) and the intersection of the tooth profile, the actual tooth pitch P of the gear i The arc length formed by the intersection of the adjacent tooth profiles on the same side and the measuring circle, assuming the number of teeth is z, then the theoretical tooth pitch is P = πd m / z, then the single pitch deviation of any adjacent gear teeth is f pi =P i -P, the cumulative pitch deviation of k teeth is

[0089] Tooth profile deviation f at any point on the tooth profile evaluation segment f It can be given by the following formula:

[0090]

[0091] (x m ,y m ) is a point on the actual tooth profile obtained by measurement, (x, y) is the distance between (x m ,y m ) The foot of the perpendicular line drawn to the theoretical involute tooth profile, tooth profile deviation f f It is necessary to judge whether it is positive or negative. When the actual tooth profile point is outside the tooth area surrounded by the theoretical left and right tooth profiles, it is positive, and when it is inside, it is negative.

[0092] The overall gear profile error curve is formed by superimposing the tooth profile error according to the actual pitch error of each tooth. Assuming that the number of teeth of the gear is z, the pressure angle is α, the number of sampling points on the tooth profile is n, and FPi Cumulative deviation of tooth pitch of tooth i, f f(i,j) is the tooth profile error value of the jth point of the i-th tooth profile. The horizontal coordinate x of each point on the overall error curve is the gear roll angle corresponding to each point of the tooth profile The vertical coordinate y is the deviation value of the gear being measured u i,j is the deviation value of the jth point of the i-th tooth profile on the overall error curve (in pixels). Considering the different measurement directions of the pitch error and the tooth profile error, the overall gear error can be obtained by the following formula:

[0093] u i,j =F Pi +f f(i,j) / cosα1≤i≤z;1≤j≤n

[0094] Since the values ​​obtained in the gear image are in pixels, they need to be converted into actual values ​​in microns. Here, we multiply it by the proportional coefficient (pixel equivalent γ) between the gear image coordinate system and the world coordinate system obtained by calibration of the gear vision measurement system: u′ i,j =u i,j ·γ. Among them, u′ i,j is the overall gear error at the jth point on the i-th tooth profile (in microns).

[0095] See Figure 5 From the gear section overall error curve, the gear tangential comprehensive deviation F can be analyzed. i ′ and the combined tangential deviation of one tooth f i ′, the cumulative total deviation of the tooth pitch F p , cumulative pitch deviation F pk and the single pitch deviation f pt , total tooth profile deviation F α (including tooth profile shape deviation f fα and tooth profile inclination deviation F Hα ), coxa pitch deviation f pb . F i ′ and f i ′ should be taken on the cross-section overall error curve. The outer contour of the curve is the cross-section tangential comprehensive total deviation curve. The maximum change of the cross-section tangential comprehensive total deviation curve along the x-coordinate range of 0 to 360° is F i ′, the maximum change of the y coordinate within the 360° / z range of the x coordinate is f i ′.

[0096] See Figure 6 From the gear bidirectional section overall error curve, the gear radial runout F can be analyzed. r , representing a pair of deviation value points C of the fixed chord position of the gear tooth (or tooth groove) L、C R (or C L ′、C R ′) should be located at the same x-coordinate, and the development angles to the tooth top (or tooth root) points of their respective tooth profile deviation curves should be equal. L 、C R (or C L ′、C R ′) is L C (or L C ′), the maximum change is the radial runout F r .

[0097] Figure 7 and Figure 8 An application example of the method of the present invention is shown, which is used to detect burrs on tooth surfaces. Figure 7 and Figure 8 There are two forms of expression of the overall error curve of the gear. Figure 7 The overall gear error curve is expressed using the Cartesian coordinate system. Figure 8 The gear's overall error curve is represented using a circular coordinate system. Circular coordinate values ​​are calculated using distances along the inscribed or circumscribed circle of the error curve. Both methods can be used to decompose the individual gear errors. Representation using Cartesian coordinates better aligns with human error curve observation habits, while circular coordinates provide a more intuitive representation of the overall gear error at various angles along the gear's circumference. Therefore, the two representations can be switched as needed.

[0098] The gear cross-sectional overall error curve clearly shows a noticeable burr defect on the left tooth profile of tooth number 6. Furthermore, the initial segment of the overall error curve for the left tooth surface begins at a roll angle of 360° / z / 2, rather than at a roll angle of 0°. This is because the left tooth profile of the corresponding number is rotated counterclockwise by an angle of 360° / z / 2 more than the right tooth profile, and adjacent teeth are spaced 360° / z apart.

[0099] Figure 9 The detailed steps of the gear overall error acquisition method based on continuous piecewise fitting Facet model are described.

[0100] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A gear overall error acquisition method based on continuous segmented fitting Facet model, characterized in that: The following steps are included: First, the gear vision measurement system must be calibrated before measurement to determine the relationship between the gear image coordinate system and the world coordinate system. Next, projection images of multiple target spur gears are acquired and preprocessed. The Canny operator is used to extract pixel-level edges of the gear contour, and the edge transition pixel region is identified as the ROI. Subsequent sub-pixel positioning algorithms will only be performed within this ROI. The projected image of a gear is a matrix composed of numerous pixel units, which can be divided into several smaller matrices. Each small matrix region satisfies a certain grayscale distribution, and each small matrix region is called a facet. The grayscale distribution function of each facet is a polynomial function of the pixels in its corresponding area. The 2D facet model is a cubic bivariate surface model, which is fitted with a cubic bivariate polynomial based on the grayscale values ​​in the 2D neighborhood of the pixel center. A global continuous segmented fitting is performed on the extracted sub-pixel coordinates of the gear profile. The key gear profile is divided into the addendum, left / right tooth profile, and tooth root for each tooth. An error minimization model with equality constraints is used for multi-segment fitting. The fitting function is continuous at the intersection of each segment, and the least squares regression coefficients of the model are derived using the Lagrange multiplier method. After the above steps, the global continuous piecewise fitting function of the gear profile is calculated, and then the precise sub-pixel coordinates of the final gear profile can be inversely calculated based on the function; After obtaining the sub-pixel coordinate set of the key contour of the gear, the coordinates of the center point of the gear end section are fitted using the sub-pixel coordinate point set of the center hole contour of the gear end section. The pitch deviation and tooth profile deviation of each gear tooth are obtained according to the gear accuracy standard. The overall gear section error curve is formed by overlapping the tooth profile error according to the actual indexing of each tooth; let the number of teeth of the gear be z, the pressure angle be α, the number of sampling points on the tooth profile be n, and F Pi is the cumulative deviation of the tooth pitch of the i-th tooth, f f(i,j) is the tooth profile error value of the jth point on the i-th tooth profile; the horizontal coordinate x of each point on the overall error curve is the gear rolling angle coordinate corresponding to each point on the tooth profile The vertical coordinate y is incremented by the length of the graduated arc To express the deviation value of the gear being measured, u i,j is the jth point of the i-th tooth profile on the overall error curve Coordinate values; considering the different measurement directions of pitch error and tooth profile error, the following synthetic formula should be obtained: u i,j =F Pi +f f(i,j) / cosα 1≤i≤z;1≤j≤n (13) Since the value obtained in the gear image is in pixels, it can be multiplied by the proportional coefficient γ between the gear image coordinate system and the world coordinate system obtained by calibration of a gear vision measurement system: in' i,j =in i,j ·γ 1≤i≤z;1≤j≤n (14) Where u′ i,j is the overall gear error at the jth point on the i-th tooth profile.

2. The method for obtaining the overall gear error based on the continuous segmented fitting Facet model according to claim 1 is characterized in that: The specific formula for fitting a bivariate cubic polynomial using the grayscale values ​​in the 2D neighborhood of the pixel center is as follows: <h2 style=";text-align:left;direction:ltr">f(x,y)=a0+a1x+a2y+a3x<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +a4xy+a5y<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +a6xy<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +a7x<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> y+a8x<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> +a9y<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> (1) a0~a9 are the fitting coefficients of each polynomial; in order to reduce the amount of calculation, the tensor product of Chebyshev polynomials is used to generate an orthogonal polynomial group as the basis function g i (x, y) to reconstruct formula (1) and obtain formula (2). The parameters t and s are determined by the neighborhood: In the neighborhood of the gear pixel-level edge ROI, the coefficients a0 to a9 are fitted using the least squares method. The partial derivative of the polynomial is taken at the center of the neighborhood to obtain the second-order Hessian matrix: Where: r xx ,r yy ,r xy is the corresponding second-order partial derivative of the polynomial; Suppose the unit eigenvector corresponding to the absolute value of the maximum eigenvalue of the Hessian matrix is ​​(n x ,n y ), then (n x ,n y ) is the unit normal vector of the gear edge contour; at a certain pixel point (x i ,y i ), the grayscale distribution function on the normal cross section is expanded by the second-order Taylor series, then the point on the cross section (x i +tn x ,y i +tn y ) is represented by the grayscale: Where, let N = (tn x ,tn y ), r x ,r y is the first-order partial derivative of the polynomial; The sub-pixel coordinate point of the gear profile is the point with the largest grayscale change rate, that is, the maximum value of the grayscale distribution function in the direction of the gradient vector. get: If tn x ,tn y Can satisfy both That is, the point where the first-order derivative is zero is located within the current pixel, and the sub-pixel coordinates of the gear profile are:

3. The method for obtaining gear overall error based on continuous segmented fitting Facet model according to claim 1 is characterized in that: Assume that the gear contour is divided into k segments, each segment has m data, and the coordinates of the i-th sub-pixel point on the j-th gear contour interval are expressed as Represented by, where i = 1, 2, ... m, j = 1, 2, ... k, the sub-pixel point set of each interval is but: g(x (j) ) is the gear profile sub-pixel point dataset S j The previous set of linearly independent basis functions, X j It's S j The data in the matrix generated by the basis function group, the coefficient ε is to be determined j There are n+1, X is The diagonal block matrix of The block matrix of , then the continuous least squares regression model of the gear profile multi-segment interval is expressed as: Establish the Lagrangian function L(ε,λ): L(ε,λ)=||Xε-y|| 2 +2min T Zé (9) λ is a column vector of length k-1. The regression coefficient ε can be obtained by taking the partial derivative of the Lagrangian function.

4. The method for obtaining gear overall error based on continuous segmented fitting Facet model according to claim 1 is characterized in that: Assume that there are n sub-pixel edge coordinate points of the center hole contour of the gear end section, and the coordinates of each point are (x i ,y i ), i = 1 ~ n; then the coordinates of the center of the gear center hole (x0, y0) and the radius r can be obtained by least squares fitting, and the optimization objective function of the square error can be expressed as: Let parameters b1 = -2x0, b2 = -2y0, The values ​​of parameters b1, b2, and b3 should minimize S, so b1, b2, and b3 should satisfy: After expanding and solving the equation group, the values ​​of b1, b2, and b3 can be obtained. Substitute them into the circular coordinate equation to find the center (x0, y0) and radius r of the gear center hole. The calculation of the pitch deviation is carried out in the following steps: First calculate the measuring circle with a diameter of d m The intersection point with the tooth profile, the actual tooth pitch P of the gear i The arc length formed by the intersection of the adjacent tooth profiles on the same side and the measuring circle, assuming the number of teeth is z, the theoretical tooth pitch is P = πd m / z, then the single pitch deviation of any adjacent gear teeth is f pi =P i -P, the cumulative pitch deviation of k teeth is Tooth profile deviation f at any point on the tooth profile evaluation segment f It is given by the following formula: (x m ,y m ) is a point on the actual tooth profile, (x,y) is the distance between (x m ,y m ) The foot of the perpendicular line to the theoretical involute tooth profile, tooth profile deviation f f It is necessary to judge whether it is positive or negative. When the actual tooth profile point is outside the tooth area surrounded by the theoretical left and right tooth profiles, it is positive, and when it is inside, it is negative.

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