Defect tolerance design-oriented impact pit depth size calculation method

Abstract

The invention relates to a defect tolerance design-oriented impact pit depth size calculation method. The method comprises the following steps of 1, reading surface point cloud data of a pit defect-containing sample; step 2, performing point cloud data segmentation to obtain point cloud data in an area near the center of the bottom of the pit and surface data of an unimpacted area near the pit; step 3, carrying out outlier detection and processing on pit data and unimpacted surface data; 4, filtering the pit data and the unimpacted surface data to obtain a pit without roughness components and an unimpacted surface profile; step 5, performing size and shape spherical surface fitting to obtain coordinates of a center point of a fitting spherical surface; and 6, carrying out surface shape plane fitting to obtain a plane equation, and calculating the depth of the pit. According to the impact pit contour obtained by the method, interference of roughness and roughness contour extreme values can be avoided, and the influence of roughness components on pit depth measurement values can be eliminated.

Description

Technical Field

[0001] The present invention belongs to the field of structural strength, relates to a calculation method and algorithm for the depth of a low-speed impact pit, and specifically relates to a method for calculating the depth size of an impact pit oriented to defect tolerance design. Background Art

[0002] Typically, the service life of mechanical load-bearing structural components is determined using the safe life method. This method assumes that the structure is in an ideal, defect-free state. However, in reality, structural components may develop defects during the entire process from raw materials to manufacturing and use. These defects can significantly reduce the service life of the structure and endanger its safety.

[0003] The defect-tolerant safe life design method is a fatigue strength design approach based on the safe life design method and takes into account defects and damage during manufacturing and service. Defect-tolerant safe life design takes into account service defects and damage, making it more reliable than the safe life method.

[0004] The main defect types considered in defect tolerance design include impact, scratches, corrosion, and combined defects. Impact defects are primarily caused by dropped tools during machining and repair, resulting in impact pits on the part surface. Impact pits can cause localized residual stress and stress concentration effects. Under fatigue loading, the local stress field caused by stress concentration and the residual stress field combine to determine the stress state at the pit location and control the fatigue life of the material.

[0005] The stress concentration effect of an impact crater depends on the local curvature radius of the impacting object and the impact depth. Material-grade specimens are often impacted using a spherical or hemispherical impactor with a specified radius. The impactor is often made of a material with a higher modulus than the object being impacted to ensure that the impactor does not significantly deform during the impact. Therefore, the local radius of the impact crater can be assumed to be equal to the local radius of the impactor. The key to determining the size of the impact crater lies in determining its depth.

[0006] Existing impact pit measurement methods fall into two categories: contact and non-contact. Contact methods, such as step profilers, cannot guarantee that the contact path will pass through the pit's center, resulting in a measured depth that is path-dependent. Furthermore, these methods inevitably cause some damage to the surface being measured. Non-contact methods, such as white-light interferometry, can obtain the three-dimensional topography of the surface being measured, but the measured topography inevitably includes roughness, waviness, and shape profiles. Therefore, they cannot directly provide shape profile information, nor can they directly determine the pit depth, which requires shape profile information. Summary of the Invention

[0007] In response to the shortcomings of the existing technology, the present invention aims to provide a method for calculating the depth size of impact pits for defect tolerance design. This method can process the pit surface point cloud data obtained by non-contact measurement methods, exclude the pit surface roughness and waviness information, and thus extract and determine the pit size profile and depth.

[0008] The present invention is achieved through the following technical solutions.

[0009] A method for calculating the depth of an impact pit for defect tolerance design includes the following steps:

[0010] Step 1: Read the surface point cloud data of the sample containing pit defects;

[0011] Step 2: Segment the point cloud data to obtain point cloud data of the area near the center of the pit bottom (hereinafter referred to as pit data) and surface data of the unimpacted area near the pit (hereinafter referred to as unimpacted surface data);

[0012] Step 3: Detect and process outliers in pit data and unimpacted surface data;

[0013] Step 4: Filter the pit data and the unimpacted surface data to obtain the pit and unimpacted surface profiles without roughness components;

[0014] Step 5: Perform spherical fitting of size and shape to obtain the coordinates of the center point of the fitting sphere;

[0015] Step 6: Perform surface shape plane fitting, obtain the plane equation, and calculate the pit depth.

[0016] Specifically, the surface point cloud data described in step 1 is the spatial three-dimensional coordinates of the detection point. There is no need to specify the coordinate origin, but the default height direction is the Z direction, the unimpacted surface is the XY plane, and the point cloud data is recorded as z(x,y).

[0017] Specifically, the specific process of step 2 is as follows:

[0018] The extreme value search function is used to obtain the point with the minimum Z value and its coordinates in the point cloud data; according to the diameter of the impact head, with the minimum Z value point as the center of the circle, the point cloud data is segmented using functions such as the neighborhood query function or the conditional search function to obtain the pit data and the unimpacted surface data.

[0019] Specifically, the specific process of step 3 is as follows:

[0020] The outlier detection function is used to detect and process outliers / anomalies on the pit data and the unimpacted surface data.

[0021] Specifically, the specific process of step 4 is as follows:

[0022] Three-dimensional robust Gaussian filtering is used to filter the pit data and plane data;

[0023] Furthermore, the three-dimensional robust Gaussian filter is a Gaussian filter using a robust weight function. The three-dimensional Gaussian filter can be expressed as follows:

[0024]

[0025] Where α is a constant, which can be determined by the wavelength pass rate / amplitude transmission rate of the filter. λ cξ ,λ cη are the filter cutoff wavelengths in two orthogonal directions ξ and η, respectively, ξ and η are the independent variables of the Gaussian function;

[0026] Furthermore, the robust weight function refers to the robust weight function determined by the M estimation method in the robustness theory, such as Tukey, Hampel, IGGI and QC weight functions, where ρ(v) represents the weight function and ν is the residual error iteratively solved in the filtering process;

[0027] Then, the three-dimensional robust Gaussian filtering process can be expressed as:

[0028]

[0029] Where w(x, y) is the low-frequency signal of the pit surface obtained after filtering, that is, the pit surface profile without roughness components, and ρ(ξ, η) is the robust weight function.

[0030] Specifically, the specific process of step 5 is as follows:

[0031] Construct the optimization objective function and use the optimization method to perform spherical fitting on the pit contour data w(x,y);

[0032] Furthermore, the optimization objective function can be expressed in the optimization field as a given function f:A→R, where A is a set of real numbers and R is a field of real numbers, and x0∈A is found, and for x∈A, f(x0)≤f(x). The optimization objective function can be linear or nonlinear depending on the optimization method used;

[0033] Furthermore, the optimization method may be a linear or nonlinear optimization method, such as a gradient method, a simplex method, etc.;

[0034] Furthermore, the spherical equation used for spherical fitting is:

[0035] (xx c ) 2 +(yy c ) 2 +(zz c ) 2 =r2

[0036] Where x c ,y c , z c are the coordinates of the center of the sphere, and r is the radius of the sphere.

[0037] Specifically, the specific process of step 6 is as follows:

[0038] The optimization method is used to perform plane fitting on the unimpacted surface data to obtain the plane equation. The X and Y coordinates of the sphere center are substituted into the plane equation to obtain the plane height value corresponding to the sphere center. The impact pit depth is obtained by subtracting the plane height value from the impact ball radius.

[0039] Furthermore, the optimization objective function can be expressed in the optimization field as a given function f:A→R, where A is a set of real numbers and R is a field of real numbers, and x0∈A is found, and for x∈A, f(x0)≤f(x). The optimization objective function can be linear or nonlinear depending on the optimization method used;

[0040] Furthermore, the optimization method may be a linear or nonlinear optimization method, such as a gradient method, a simplex method, etc.;

[0041] Furthermore, the plane equation used for plane fitting is: z=ax+by+c

[0042] Where a, b, and c are the coefficients and constants of the three-dimensional plane equation;

[0043] Let the plane equation obtained be z=a t x+b t y+c t , where a t ,b t ,c t are the coefficients and constants of the plane equation obtained by optimization method;

[0044] Substitute the X and Y coordinate values ​​of the sphere center into the plane equation to obtain the plane height value z corresponding to the sphere center. h =a t x c +b t y c +c t The pit depth D = r-(z c -z h ).

[0045] Compared with existing technologies, the present invention has the following advantages: it can process the surface point cloud data of pits obtained by non-contact measurement methods, eliminating information about the surface roughness of the pits, thereby extracting and determining the pit size profile and depth. The impact pit profile obtained by the present invention avoids interference from roughness and extreme values ​​of the roughness profile, eliminating the influence of roughness components on the measured pit depth. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flow chart of a method for calculating the depth of an impact pit according to the present invention;

[0047] Figure 2 This is a diagram of a three-dimensional Gaussian filter function used in an embodiment of the present invention;

[0048] Figure 3 This is a point cloud image of the surface of a material containing impact defects provided by an embodiment of the present invention;

[0049] Figure 4 The pit point cloud image obtained through segmentation, outlier detection and processing provided by the embodiment of the present invention;

[0050] Figure 5 The unimpacted surface point cloud image obtained through segmentation, outlier detection and processing provided by an embodiment of the present invention;

[0051] Figure 6 is a pit contour map extracted after filtering provided by an embodiment of the present invention;

[0052] Figure 7 is a non-impacted surface contour map extracted after filtering provided by an embodiment of the present invention;

[0053] Figure 8 is a spherical surface image of a pit obtained by fitting according to an embodiment of the present invention;

[0054] Figure 9 It is a fitting plane diagram of the unimpacted surface obtained by fitting according to an embodiment of the present invention. DETAILED DESCRIPTION

[0055] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0056] This invention proposes a method for calculating the depth and size of low-velocity impact pits, designed for defect tolerance design. This method fully considers the composition of surface topography, particularly the importance of distinguishing roughness, waviness, and shape profiles within the topography for accurate pit depth measurement. It then establishes a method for processing impact pit point cloud data and measuring impact pit depth.

[0057] A method for calculating the depth of an impact pit for defect tolerance design includes the following steps:

[0058] Step 1: Read the surface point cloud data of the sample containing pit defects;

[0059] Step 2: Segment the point cloud data to obtain point cloud data of the area near the center of the pit bottom (hereinafter referred to as pit data) and surface data of the unimpacted area near the pit (hereinafter referred to as unimpacted surface data);

[0060] Step 3: Detect and process outliers in pit data and unimpacted surface data;

[0061] Step 4: Filter the pit data and the unimpacted surface data to obtain the pit and unimpacted surface profiles without roughness components;

[0062] Step 5: Perform spherical fitting of size and shape to obtain the coordinates of the center point of the fitting sphere;

[0063] Step 6: Perform surface shape plane fitting, obtain the plane equation, and calculate the pit depth.

[0064] Specifically, the surface point cloud data described in step 1 is the spatial three-dimensional coordinates of the detection point. There is no need to specify the coordinate origin, but the default height direction is the Z direction, the unimpacted surface is the XY plane, and the point cloud data is recorded as z(x,y).

[0065] Specifically, the specific process of step 2 is as follows:

[0066] The extreme value search function is used to obtain the point with the minimum Z value and its coordinates in the point cloud data; according to the diameter of the impact head, with the minimum Z value point as the center of the circle, the point cloud data is segmented using functions such as the neighborhood query function or the conditional search function to obtain the pit data and the unimpacted surface data.

[0067] Specifically, the specific process of step 3 is as follows:

[0068] The outlier detection function is used to detect and process outliers / anomalies on the pit data and the unimpacted surface data.

[0069] Specifically, the specific process of step 4 is as follows:

[0070] Three-dimensional robust Gaussian filtering is used to filter the pit data and plane data;

[0071] Furthermore, the three-dimensional robust Gaussian filter is a Gaussian filter using a robust weight function. The three-dimensional Gaussian filter can be expressed as follows:

[0072]

[0073] Where α is a constant, which can be determined by the wavelength pass rate / amplitude transmission rate of the filter. λ cξ ,λ cη are the filter cutoff wavelengths in two orthogonal directions ξ and η, respectively, ξ and η are the independent variables of the Gaussian function;

[0074] Furthermore, the robust weight function refers to the robust weight function determined by the M estimation method in the robustness theory, such as Tukey, Hampel, IGGI and QC weight functions, where ρ(v) represents the weight function and ν is the residual error iteratively solved in the filtering process;

[0075] Then, the three-dimensional robust Gaussian filtering process can be expressed as:

[0076]

[0077] Where w(x, y) is the low-frequency signal of the pit surface obtained after filtering, that is, the pit surface profile without roughness components, and ρ(ξ, η) is the robust weight function.

[0078] Specifically, the specific process of step 5 is as follows:

[0079] Construct the optimization objective function and use the optimization method to perform spherical fitting on the pit contour data w(x,y);

[0080] Furthermore, the optimization objective function can be expressed in the optimization field as a given function f:A→R, where A is a set of real numbers and R is a field of real numbers, and x0∈A is found, and for x∈A, f(x0)≤f(x). The optimization objective function can be linear or nonlinear depending on the optimization method used;

[0081] Furthermore, the optimization method may be a linear or nonlinear optimization method, such as a gradient method, a simplex method, etc.;

[0082] Furthermore, the spherical equation used for spherical fitting is:

[0083] (xx c ) 2 +(yy c ) 2 +(zz c ) 2 =r 2

[0084] Where x c ,y c , z c are the coordinates of the center of the sphere, and r is the radius of the sphere.

[0085] Specifically, the specific process of step 6 is as follows:

[0086] The optimization method is used to perform plane fitting on the unimpacted surface data to obtain the plane equation. The X and Y coordinates of the sphere center are substituted into the plane equation to obtain the plane height value corresponding to the sphere center. The impact pit depth is obtained by subtracting the plane height value from the impact ball radius.

[0087] Furthermore, the optimization objective function can be expressed in the optimization field as a given function f:A→R, where A is a set of real numbers and R is a field of real numbers, and x0∈A is found, and for x∈A, f(x0)≤f(x). The optimization objective function can be linear or nonlinear depending on the optimization method used;

[0088] Furthermore, the optimization method may be a linear or nonlinear optimization method, such as a gradient method, a simplex method, etc.;

[0089] Furthermore, the plane equation used for plane fitting is: z=ax+by+c

[0090] Where a, b, and c are the coefficients and constants of the three-dimensional plane equation;

[0091] Let the plane equation obtained be z=a t x+b t y+c t , where a t ,b t ,c t are the coefficients and constants of the plane equation obtained by optimization method;

[0092] Substitute the X and Y coordinate values ​​of the sphere center into the plane equation to obtain the plane height value z corresponding to the sphere center. h =a t x c +b t y c +c t The pit depth D = r-(z c -z h ).

[0093] Example

[0094] This embodiment is the calculation of the pit depth of titanium alloy. Titanium alloy TC4 is a commonly used structural material in the aviation industry. Its application scenarios include aircraft and helicopter load-bearing components, aircraft engine fan and compressor blades, casings, etc. For these application scenarios, titanium alloy components have impact pits caused by service, maintenance, etc., and there are defect tolerance issues. Therefore, in this example, a titanium alloy sample containing impact pits is selected for the detailed description of the present invention. The impact pits are obtained by the drop hammer method, and the punch diameter is 6 mm. The programming language used in this example is MATLAB.

[0095] like Figure 1As shown, the method for calculating the depth of the titanium alloy impact pit provided by the embodiment of the present invention includes the following steps:

[0096] The measurement method includes the following steps:

[0097] Step 1. Obtain the three-dimensional point cloud data of the sample. TM -20 three-dimensional profilometer to characterize the surface of the sample and obtain point cloud data.

[0098] Step 2. Use the min() function to obtain the point with the minimum Z value and its coordinates in the point cloud data; according to the diameter of the impact head, with the minimum Z value point as the center of the circle, use the pdist() function to determine the data points falling within the pit area, realize the segmentation of the point cloud data, and obtain the pit data z pit (x, y) (hereinafter referred to as pit data) and unimpacted surface data z pln (x,y) (hereinafter referred to as plane data);

[0099] Step 3. Use dbscan() function to scan the pit data z pit (x,y) and plane data z pln (x,y) performs outlier detection and deletes outliers.

[0100] Step 4. Use three-dimensional robust Gaussian filtering to filter the pit data z pit (x,y) and plane data z pln (x,y) is filtered.

[0101] The three-dimensional robust Gaussian filter used is a Gaussian filter using the Tukey weight function. The three-dimensional Gaussian filter can be expressed as follows:

[0102]

[0103] Where α is a constant, which can be determined by the wavelength pass rate / amplitude transmission rate of the filter. λ cx ,λ cy are the filter cutoff wavelengths in the X and Y directions, respectively, with a value of 800 μm. x and y are the independent variables of the Gaussian function.

[0104] Tukey robust weight function is:

[0105]

[0106] Where ν = r / s is the iterative estimation residual in the filtering calculation process, where r is the observation error, that is, the difference between the filtered contour and the original contour data; s is the scale parameter, and the median absolute deviation (MAD) is selected as the scale parameter value, that is, s = MAD = median(r).

[0107] Then, the three-dimensional robust Gaussian filtering process can be expressed as:

[0108]

[0109] Where w(x, y) is the low-frequency signal of the pit surface obtained after filtering, that is, the pit surface profile without roughness components, and ρ(ξ, η) is the robust weight function.

[0110] Step 5. Use the spherical equation to perform spherical fitting on the pit data. The spherical equation used is:

[0111] (xx c ) 2 +(yy c ) 2 +(zz c ) 2 =r 2

[0112] Where x, y, z are pit data points z pit (x,y) coordinates, x c ,y c ,z c is the coordinate of the center of the spherical pit, r = 3000um is the radius of the impact head

[0113] Construct the optimization objective function f:

[0114]

[0115] Where N is the pit data point z pit The number of (x,y)

[0116] Using the Nelder-Mead simplex algorithm to optimize the objective function, the coordinates of the sphere center x can be obtained c ,y c ,z c The coordinates of the center of the sphere are x c =1744.4,y c =2126.5,z c =3189.8

[0117] Step 6. Use the three-dimensional plane equation to perform plane fitting on the plane data. The three-dimensional plane equation used is:

[0118] z=ax+by+c

[0119] Where a, b, c are the coefficients and constants of the three-dimensional plane equation obtained by the optimization method.

[0120] Construct the optimization objective function g:

[0121]

[0122] Where N is the pit data point z pln The number of (x,y)

[0123] By using the nonlinear least squares method to optimize the objective function, we can obtain the coefficients and constants of the three-dimensional plane equation, which are denoted as a t ,b t ,c t

[0124] At this point, the three-dimensional plane equation is known, which is z = a t x+b t y+c t . After calculation a t =-0.0007041,b t =0.0007051,c t =499.2, then the equation of the plane is z=-0.0007041x+0.0007051y+499.2.

[0125] The coordinate value x of the center of the sphere c ,y c Substitute the plane equation to obtain the plane height z corresponding to the center of the sphere h =a t x c +b t y c +c t =499.4712, then the pit depth D is D = r-(z c -z h ), after calculation, the pit depth D=r-(z c -z h )=3000-(3189.8-499.4712)=309.6712, that is, the pit depth is 309.6712um.

[0126] The above description is only a preferred embodiment of the present invention and does not limit the implementation mode and protection scope of the present invention. For those skilled in the art, it should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the description and illustrations of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the depth of impact pits for defect tolerance design, characterized in that: The steps include: Step 1: Read the surface point cloud data of the sample containing pit defects; the surface point cloud data is the spatial three-dimensional coordinates of the detection point, there is no need to specify the coordinate origin, the default height direction is the Z direction, and the unimpacted surface is the XY plane; Step 2: segment the point cloud data to obtain the point cloud data in the area near the center of the bottom of the pit and the surface data of the non-impact area near the pit. The point cloud data in the area near the center of the bottom of the pit is referred to as pit data, and the surface data of the non-impact area near the pit is referred to as non-impact surface data. Specifically, the extreme value search function is used to obtain the point with the minimum Z value in the point cloud data and its coordinates; according to the diameter of the impact head, the neighborhood query function or the conditional search function is used to segment the point cloud data with the minimum Z value point as the center of the circle to obtain the pit data and the non-impact surface data; Step 3: Perform outlier detection and processing on the pit data and the unimpacted surface data; use the outlier detection function to perform outlier / anomaly detection and processing on the pit data and the unimpacted surface data; Step 4: Filter the pit data and the unimpacted surface data to obtain the pit and unimpacted surface profiles without roughness components; specifically, filter the pit data and the plane data using a three-dimensional robust Gaussian filter; The three-dimensional robust Gaussian filter is a Gaussian filter using a robust weight function; The three-dimensional Gaussian filter is expressed as follows: Where α is a constant, which can be determined by the wavelength pass rate / amplitude transmission rate of the filter. λ cξ ,λ cη are the filter cutoff wavelengths in two orthogonal directions ξ and η, respectively, ξ and η are Gaussian function independent variables; Then, the three-dimensional robust Gaussian filtering process is expressed as: Where w(x, y) is the low-frequency signal of the pit surface obtained after filtering, that is, the pit surface profile without roughness components, and ρ(ξ, η) is the robust weight function; Step 5: Perform spherical fitting of size and shape to obtain the coordinates of the center point of the fitted sphere; specifically: use a three-dimensional spherical function to fit the surface contour of the filtered pit, and the three-dimensional spherical function is: (x-x c ) 2 +(y-y c ) 2 +(z-z c ) 2 =r 2 In the formula, x c ,y c , z c is the coordinate of the center of the sphere, r is the radius of the sphere; Step 6: Perform surface shape plane fitting, obtain the plane equation, and calculate the pit depth; specifically: Use the three-dimensional plane equation to fit the filtered unimpacted surface profile, and the three-dimensional plane equation is: z=ax+by+c In the formula, a, b, c are the coefficients and constants of the three-dimensional plane equation; Substitute the X and Y coordinate values ​​of the center of the sphere into the plane equation to obtain the plane height value z corresponding to the center of the sphere h =a t x c +b t y c +c t ; pit depth D = r-(z c -z h ).

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