A method and model for calculating a single-track cross-sectional profile of laser cladding

Abstract

The application discloses a kind of laser cladding single pass section profile calculation method and calculation model, belong to laser cladding process technical field.For the low precision of existing single pass cladding section profile, the problem that the quality control of multiple cladding is difficult, first, laser power, scanning speed and powder feeding rate are as key input variables, the mathematical model of the geometric structure parameter of elliptic function and single pass section profile model are constructed;Then the above model is substituted into the multiple cladding overlap rate model, and the optimal cladding layer overlap rate is calculated;Finally, the reliability of single pass section profile model is verified by detecting the quality of multiple cladding.Compared with the prior art, the present application has the following beneficial effects:(1) strong model applicability;(2) high calculation accuracy;(3) low production cost;(4) good product quality.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of laser cladding process, and particularly relates to a calculation method and a calculation model for a single-track cross-section profile of laser cladding. BACKGROUND

[0002] As an advanced surface additive deposition technology, laser cladding technology forms a high-quality cladding layer with good metallurgical bonding on the surface of a substrate through the simultaneous melting of metal powder and a thin layer of metal on the surface of the substrate by high-energy-density laser beam radiation, under the action of convection, heat transfer, mass transfer, crystallization and phase evolution.

[0003] The single-track cross-section profile model of laser cladding can be characterized by the geometric structure parameters of a suitability function, which mainly includes a parabolic function, a circular arc function and an elliptical function, etc. However, the models constructed by using the two functions have the following disadvantages: (1) the calculation accuracy significantly decreases with the increase of the cladding passes; (2) the cumulative error leads to a large deviation between the calculation results of the model and the experimental results, making it difficult to optimize the multi-track cladding overlap rate; and (3) the forming quality of the cladding layer is low, and the microstructure and mechanical properties are difficult to guarantee. SUMMARY

[0004] In view of the low precision of the single-track cladding cross-section profile and the difficulty in controlling the quality of multi-track cladding, the application provides a calculation method and a calculation model for the single-track cross-section profile of laser cladding.

[0005] To achieve the above-mentioned purpose, the application adopts the following technical solutions:

[0006] A calculation method for the single-track cross-section profile of laser cladding comprises the following steps:

[0007] S1: select n laser cladding process parameters, determine the range of each process parameter and m levels, design an orthogonal test scheme with n factors and m levels, perform single-track laser cladding test, and complete cladding layer cross-section image acquisition;

[0008] S2: use MATLAB software to machine process and automatically identify the cladding layer cross-section image, extract the cladding layer cross-section profile curve, digitize the single-track cladding layer cross-section profile features and fit them into a curve model;

[0009] Further, the profile feature extraction process is divided into 9 steps, which are (a) original image import; (b) gray scale transformation; (c) gray scale adjustment; (d) median noise reduction; (e) image sharpening; (f) binary processing; (g) profile thinning; (h) edge detection; (i) smoothing processing;

[0010] S3: Geometric modeling of single-channel cross-section profile of laser cladding;

[0011] Further, a Cartesian rectangular coordinate system is established with the horizontal boundary line of the cladding layer and the base body as the X-axis and the vertical symmetry axis of the cladding layer as the Y-axis.

[0012] S4: Obtain coordinate data of test points of the cross-section profile curve by using image measurement software;

[0013] Further, considering that the distribution density of test points increases with the increase of the curve curvature, in order to retain the cross-section profile features to the greatest extent and reduce the data error caused by software discrete measurement to ensure the accuracy of subsequent fitting, the test points are selected at equal intervals according to the X coordinate.

[0014] S5: According to the distribution characteristics of the cross-section profile curve of the cladding layer within the single-channel cladding process parameter range, an elliptic function is selected for fitting processing of the test points:

[0015] Elliptic function: ,

[0016] Wherein, a, b and c are all geometric structure parameters of the elliptic function.

[0017] S6: Select an exponential regression model as the basic component, combine a polynomial function and a trigonometric function model to perform multivariate nonlinear fitting on a plurality of groups of data, introduce a standard simplex hill climbing method and a general global optimization method to determine the optimal parameters of the model, and apply MATLAB software to realize one-step optimization of the model parameters, to obtain the objective function model of the geometric structure parameters-process parameters of the elliptic function:

[0018] a = 0.39261 (p 0.27230 v 0.00369 v f -0.40507 ) + 2.31260 sin (v f + 0.12452) - 3.35727,

[0019] b = 6.12358 x 10 3 (p -0.72213 v -0.61507 v f 0.18576 ) - 0.46651 cos (p + 1.99589) - 0.95726,

[0020] c = -9.26016 × 10 -5 (p -0.15465 v 2.34145 v f 0.02714 )-0.24563cos(v+0.11984)-0.28974cos(2p-963.25493)-7.69138×10 -7 v 3 +3.82432×10 -4 pv f 2 -6.91820×10 -8 p 2 +1.73812,

[0021] In the formula, p, v, v f These are all laser cladding process parameters, namely laser power, scanning speed, and powder feeding rate;

[0022] S7: Use diagnostic plots of the geometric structure parameters a, b, and c of the elliptic function to verify the fitting accuracy of the objective function to the data;

[0023] Furthermore, diagnostic charts mainly include residual distribution charts and charts showing the relationship between experimental and predicted values;

[0024] S8: Based on the elliptic function model and the objective function model of its geometric structure parameters, calculate the optimal overlap rate of multi-pass cladding, conduct multi-pass cladding tests, and verify the reliability of the laser cladding single-pass cross-sectional profile model by detecting the macroscopic and three-dimensional morphology of the surface of the multi-pass cladding layer.

[0025] A calculation model for the profile of a single cross-section in laser cladding, wherein the calculation model is as follows:

[0026] ,

[0027] a = 0.39261 (p 0.27230 v 0.00369 v f -0.40507 )+2.31260sin(v f +0.12452)-3.35727,

[0028] b = 6.12358 × 10 3 (p -0.72213 v -0.61507 v f 0.18576 )-0.46651cos(p+1.99589)-0.95726,

[0029] c = -9.26016 × 10 -5 (p-0.15465 v 2.34145 v f 0.02714 -0.24563 cos(v+0.11984) -0.28974 cos(2p-963.25493) -7.69138 x 10 -7 v 3 +3.82432 x 10 -4 pv f 2 -6.91820 x 10 -8 p 2 +1.73812,

[0030] wherein p, v, v f are laser power, scanning speed and powder feeding rate respectively.

[0031] Compared with the prior art, the present application has the following advantages:

[0032] (1) The elliptical model has strong adaptability. The elliptical model can automatically match the corresponding relationship of the long axis, the short axis and the X and Y axes according to the single-track cross-sectional profile, and can adapt to the requirement of large changes in the cross-sectional profile generated by different parameter combinations.

[0033] (2) The elliptical model has high calculation accuracy. The elliptical model successfully maps the process parameters such as laser power, scanning speed and powder feeding rate, has high calculation accuracy and small error.

[0034] (3) The elliptical model has flexibility and comprehensive controllability. The calculation process is simple, has high universality, does not require a large amount of experimental data, saves pre-test time and cost, consumes less energy and has low production cost.

[0035] (4) The product quality is good. Based on the single-track profile elliptical model, the multi-track cladding layer is constructed, the surface flatness is high, the boundary is not smooth and the powder residue phenomenon is effectively alleviated, and the composite interface is good. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 is a flow chart for extracting a single-track cross-sectional profile of laser cladding;

[0037] Figure 2 is a schematic diagram of automatic recognition result of image processing of a single-track cross-sectional profile of laser cladding; (a) is an original image; (b) is a gray scale conversion; (c) is a gray scale adjustment; (d) is a median noise reduction; (e) is an image sharpening; (f) is a binary processing; (g) is a contour thinning; (h) is an edge detection; (i) is a smoothing processing;

[0038] Figure 3 is a schematic diagram of geometric modeling of a single-track cross-sectional profile of laser cladding;

[0039] Figure 4 Schematic diagram for selecting test points of single-channel cross-section profile curve of laser cladding

[0040] Figure 5 Diagnostic diagram for geometric structure parameters a, b and c of elliptical model; wherein: (a), (c) and (e) are residual distribution diagrams of geometric structure parameters a, b and c respectively; (b), (d) and (f) are relationship diagrams of test values and predicted values of geometric structure parameters a, b and c respectively

[0041] Figure 6 Macroscopic morphology of multi-channel cladding layer

[0042] Figure 7 Three-dimensional microscopic morphology of multi-channel cladding layer DETAILED DESCRIPTION

[0043] In order to better explain the process technical solution of the present application, the present application will be described in detail through specific embodiments in combination with the drawings in the embodiments of the present application. A calculation method of single-channel cross-section profile of laser cladding, the base material is 27SiMn steel, and the cladding layer material is GS-Fe01 alloy powder, which comprises the following steps:

[0044] S1: select laser power, scanning speed and powder feeding rate and other three laser cladding process parameters, determine the range and level of each process parameter, design a 3-factor 4-level orthogonal test scheme, perform single-channel laser cladding test and complete cladding layer cross-section image acquisition. The results are shown in Tables 1 and 2.

[0045] Table 1 Process parameter range and level

[0046]

[0047] Table 2 3-factor 4-level orthogonal test scheme

[0048]

[0049] S2: In order to digitize the single-channel cross-section profile characteristics of the cladding layer and fit them into a curved surface model, MATLAB software is used to machine process and automatically identify the cladding layer cross-section image to extract the profile curve.

[0050] As Figure 1As shown, the profile feature extraction process is divided into 9 steps, (a) original image import: import the original image into the software as the source and basis for machine recognition. (b) gray scale conversion: the RGB value of each pixel needs to be obtained to convert it to a gray scale value using a gray scale algorithm, and the gray scale value replaces the corresponding position of the RGB value. (c) gray scale adjustment: mainly adjust the gray scale range of the gray scale image. (d) median noise reduction: in order to preserve the profile edge features of the cladding layer while reducing the surrounding noise, nonlinear median filtering is used to complete image noise reduction and achieve good results. (e) image sharpening: after performing two-dimensional Fourier transform to obtain frequency domain information, generate a second-order Butterworth filter grid coordinate and complete the system function point multiplication image frequency spectrum transform, and then perform Fourier inverse transform again to obtain the sharpened filtered image. (f) binary processing: according to the image gray scale characteristics, the inter-class variance of the background and target is maximized to ensure that the best adaptive threshold is found as the basis for segmentation. (g) profile thinning: here, the precise thinned profile boundary is obtained by controlling the number of morphological erosion and expansion. (h) edge detection: mainly apply Gaussian filtering to ensure the accuracy and accuracy of the detection to calculate the gradient amplitude and gradient direction of the gray scale value, while suppressing the non-maximum value of the gradient amplitude, and connecting the detected edge points through double threshold processing to obtain the complete edge. (i) smoothing processing: remove errors in the single-channel forming and machine recognition process to ensure that the cladding layer profile curve is smooth and meets the subsequent fitting requirements. The recognition and processing results of each step are shown in Figure 2 .

[0051] S3: Geometric modeling of the single-channel cross-sectional profile features of laser cladding.

[0052] A Cartesian coordinate system is established with the horizontal dividing line of the cladding layer and the substrate as the X-axis and the vertical symmetry axis of the cladding layer as the Y-axis, as shown in Figure 3 . The O point is the coordinate origin, the O' point is the center of the ellipse, the cladding layer width is W, and the cladding layer height is H.

[0053] S4: Obtain the coordinate data of the single-channel cross-sectional profile curve test points using image measurement software.

[0054] Considering that the distribution density of test points increases with the increase of curve curvature, in order to preserve the cross-sectional profile features to the greatest extent and reduce the data errors caused by software discrete measurement to ensure the accuracy of subsequent fitting, the test points are selected at equal intervals of X coordinates, as shown in Figure 4 .

[0055] S5: Select an elliptic function to fit the test points according to the distribution characteristics of the cross-sectional profile curves of several groups of samples within the single-channel cladding parameter range.

[0056] Elliptic function: ,

[0057] Wherein: a, b, c are all elliptic function geometry structure parameters.

[0058] S6: The calculation method of elliptic function geometry structure parameters a, b, c:

[0059] Select the exponential regression model as the basic component, combine the polynomial function and the triangular function model to carry out multivariate nonlinear fitting on several groups of data, introduce the standard simplex hill climbing method and the general global optimization method to determine the optimal parameters of the model, apply MATLAB software to realize the one-time optimization of the model multi-parameters, and obtain the objective function model of the elliptic function geometry structure parameters-process parameters:

[0060] a = 0.39261 (p 0.27230 v 0.00369 v f -0.40507 + 2.31260sin(v f + 0.12452)-3.35727,

[0061] b = 6.12358 × 10 3 (p -0.72213 v -0.61507 v f 0.18576 - 0.46651cos(p+1.99589)-0.95726,

[0062] c = -9.26016 × 10 -5 (p -0.15465 v 2.34145 v f 0.02714 - 0.24563cos(v+0.11984)-0.28974cos(2p-963.25493)-7.69138 × 10 -7 v 3 + 3.82432 × 10 -4 pv f 2 - 6.91820 × 10 -8 p 2 + 1.73812,

[0063] In the formula, p, v, v f are laser power, scanning speed and powder feeding rate respectively.

[0064] S7: Through the diagnostic graph of geometry structure parameters a, b, c, the fitting accuracy of the above objective function on several groups of data is tested, wherein the diagnostic graph mainly includes residual distribution graph and test value and predicted value relationship graph.

[0065] For example Figure 5As shown, all residual data points randomly fall within a horizontal band within the range of (-0.1, 0.1), containing no systematic distribution trends or predictable information, perfectly satisfying the normality property, indicating that the model fits the data well. Furthermore, the coefficient of determination R0 for both predicted and measured values ​​is [not specified]. 2 The values ​​are all much greater than 0.9, which also proves that the error between the experimental value and the predicted value is small and the correlation is good.

[0066] S8: Based on the elliptic function model and the objective function model of its geometric structure parameters, calculate the optimal overlap rate of multi-pass cladding, conduct multi-pass cladding tests, and verify the reliability of the laser cladding single-pass cross-sectional profile model by detecting the macroscopic morphology and three-dimensional microscopic morphology of the surface of the multi-pass cladding layer.

[0067] Based on an optimal combination of process parameters for single-pass laser cladding, namely a laser power of 744W, a scanning speed of 233mm / min, a powder feeding rate of 1.2r / min, and a spot diameter of 2.5mm, a multivariate nonlinear mathematical model constructed with elliptic function coefficients a, b, and c as target response indices is used to effectively predict the geometric structural parameters of the elliptic function of the single-pass cladding cross-section profile.

[0068] Then, the width of a single cladding layer is calculated: The precise information regarding the height of a single cladding layer: H = bc.

[0069] Substituting the above parameters into the multi-pass overlapping model of controllable laser cladding process parameters ;

[0070] Where, η c The critical overlap rate for multi-pass cladding is given by d, where d is the distance between the centers of any two adjacent cladding layers. The optimal critical overlap rate of 26% is then obtained by solving for the best combination of process parameters applicable to single-pass cladding.

[0071] Multi-pass cladding tests were conducted under the condition of an optimal critical overlap rate of 26% for adjacent passes, and macroscopic and three-dimensional morphology inspections were performed, such as... Figure 6 , Figure 7 As shown. The results indicate that the metal material in the overlapping area of ​​the cladding layer basically fills the depression in the remelting expansion area completely; the overall forming height of the cladding layer remains basically consistent; there are no obvious grooves between each pass, and the surface is smooth and flat.

[0072] The details of the application not described herein are considered known to those skilled in the art. Although the foregoing description of the application has been described in some detail for the purposes of clarity and the understanding of the application, it should be apparent that certain changes and modifications can be practiced within the scope of the application as defined by the appended claims.

Claims

1. A method for calculating the profile of a single cross-section in laser cladding, characterized in that, Includes the following steps: S1: Select n laser cladding process parameters, determine the range of each process parameter and m levels, design an n-factor m-level orthogonal experimental scheme, conduct a single-pass laser cladding test, and complete the acquisition of cross-sectional images of the cladding layer; S2: MATLAB software is used to process and automatically identify the cross-sectional image of the cladding layer to extract the cross-sectional contour curve of the cladding layer, and the contour features of the single cladding layer are digitized and fitted into a curve model. S3: Geometric modeling of the single-pass cross-sectional profile of laser cladding; S4: Use image measurement software to obtain the coordinate data of the test points of the cross-sectional profile curve; S5: Based on the distribution characteristics of the cross-sectional profile curve of the cladding layer within the range of single-pass cladding process parameters, an elliptic function is selected to fit the test points. S6: The exponential regression model is selected as the basic component. Multivariate nonlinear fitting is performed on several sets of data by combining polynomial function and trigonometric function models. The standard simple surface climbing method and the general global optimization method are introduced to determine the optimal parameters of the model. MATLAB software is used to achieve the optimization of multiple parameters of the model in one go, and the objective function model of elliptic function geometric structure parameters - process parameters is obtained. S7: Verify the fitting accuracy of the objective function to the data using diagnostic plots of the elliptic function's geometric structure parameters a, b, and c; S8: Based on the objective function of the elliptic function model and its geometric structural parameters, calculate the optimal overlap rate of multi-channel cladding and conduct multi-channel cladding tests.

2. The method for calculating the profile of a single laser cladding cross section according to claim 1, characterized in that, The contour feature extraction process in step S2 consists of nine steps: (a) importing the original image; (b) grayscale transformation; (c) grayscale adjustment; (d) median denoising; (e) image sharpening; (f) binarization; (g) contour thinning; (h) edge detection; and (i) smoothing.

3. The method for calculating the profile of a single laser cladding cross section according to claim 1, characterized in that, Step S3: Geometric modeling of the single-pass cladding cross-sectional profile, specifically, involves the following operations: A Cartesian coordinate system is established with the horizontal boundary between the cladding layer and the substrate as the X-axis and the vertical axis of symmetry of the cladding layer as the Y-axis.

4. The method for calculating the profile of a single laser cladding cross section according to claim 1, characterized in that, In step S4, the test points are selected at equal intervals according to the X coordinate.

5. The method for calculating the profile of a single laser cladding cross section according to claim 1, characterized in that, The elliptic function in step S5 is: Elliptic functions: , Where a, b, and c are all geometric structure parameters of the elliptic function.

6. The method for calculating the profile of a single laser cladding cross section according to claim 1, characterized in that, The objective function model for the elliptic function geometric structure parameters-process parameters in step S6 is: a=0.39261(p 0.27230 v 0.00369 v f -0.40507 )+2.31260sin(v f +0.12452)-3.35727, b=6.12358×10 3 (p -0.72213 v -0.61507 v f 0.18576 )-0.46651cos(p+1.99589)-0.95726, c=-9.26016×10 -5 (p -0.15465 in 2.34145 in f 0.02714 )-0.24563cos(v+0.11984)-0.28974cos(2p-963.25493)-7.69138×10 -7 in 3 +3.82432×10 -4 pv f 2 -6.91820×10 -8 p 2 +1.73812, In the formula, p, v, v f These are laser power, scanning speed, and powder feeding rate, respectively.

7. The method for calculating the profile of a single laser cladding cross section according to claim 1, characterized in that, The diagnostic graph in step S7 includes a residual distribution graph and a graph showing the relationship between experimental and predicted values.

8. The method for calculating the profile of a single laser cladding cross section according to claim 1, characterized in that, In step S8, the optimal overlap rate of multi-pass cladding is calculated based on the objective function of the elliptic function model and its geometric structural parameters. Multi-pass cladding tests are carried out, and the reliability of the single-pass cross-sectional profile model of laser cladding is verified by detecting the macroscopic and three-dimensional morphology of the surface of the multi-pass cladding layer.

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