A parameterized modeling method for ESRB uniform linear spraying distribution

Abstract

This invention proposes a model to characterize the coating thickness distribution under uniform motion of an electrostatic spraying rotary bell (ESRB), and establishes the mathematical relationship between this model and the atomizer parameters and trajectory parameters, ultimately forming a parameterized distribution model characterized by spraying parameters. This parameterized model aims to provide guidance for selecting spraying parameters in offline programming and trajectory planning processes in the coating industry using ESRB. First, based on the coating accumulation characteristics of uniform linear spraying with ESRB, a novel feature point fitting distribution model is constructed. This model can intuitively reflect the coating accumulation contour characteristics compared to traditional representation methods. Second, a multi-level, multi-factor orthogonal experiment is designed for the electrostatic rotary bell spraying process to establish a composite function model of each feature value changing with the parameters. Then, according to the spraying process requirements, objective functions are constructed for indicators such as coating thickness in each region, and solved using a genetic algorithm to determine the ESRB spraying parameters. Finally, two simulation experiments verify the effectiveness of the proposed model, showing that it has high prediction accuracy and can be effectively applied to ESRB spraying systems.

Description

Technical Field

[0001] This invention relates to the field of automated painting robot technology, specifically to a parametric modeling method for paint distribution models used in ESRB painting and its application in offline programming and trajectory planning. Background Technology

[0002] In high-end manufacturing fields such as automotive painting, ESRB is widely used due to its high transfer efficiency and excellent film quality. To achieve automation and intelligence in the painting process, offline programming of the painting robot trajectory is required, and an accurate paint distribution model is one of its core foundations.

[0003] Existing spraying models are mostly based on idealized mathematics (such as Gaussian distribution, beta distribution, etc.), often neglecting the dynamic influence of actual spraying parameters (such as flow rate, forming air, height, speed, etc.) on the distribution pattern. Therefore, when process parameters are adjusted, the model's prediction accuracy decreases, resulting in poor trajectory planning performance, requiring repeated trial and error, and increasing costs.

[0004] In addition, some scholars, based on the physical principles of ESRB, are dedicated to constructing computer simulation models using simulation methods such as computational fluid dynamics (CFD) (e.g., using FLUENT and OpenFOAM software). These studies have deeply analyzed the spray deposition process, droplet trajectory, and film thickness formation at the microscopic mechanism level, and attempted to establish mathematical models encompassing multiple factors such as flow rate and voltage to reveal the principle of spray pattern formation. However, these first-principles-based simulation models generally suffer from structural complexity and long computation time, and their accuracy is highly dependent on a large number of input parameters that are difficult to obtain precisely, as well as the still incomplete physical understanding of sub-processes such as atomization and charging. Therefore, although such research has significant theoretical value, its low computational efficiency and uncertain results make it difficult to meet the practical engineering needs of offline programming and thickness simulation systems for spraying robots, which have extremely high requirements for real-time performance and reliability. Summary of the Invention

[0005] This invention proposes a parameterized model to represent the coating thickness distribution generated by an ESRB atomizer under uniform motion. This model can establish a quantitative relationship between spraying process parameters and coating distribution characteristics, enabling rapid prediction of the distribution model and optimization of spraying parameters, thereby improving the accuracy and efficiency of offline programming and providing guidance for the selection of spraying parameters in offline programming and trajectory planning in the coating industry using ESRB.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A parameterized model for representing the coating thickness distribution generated by an ESRB atomizer under uniform motion, the parameterization process of its dynamic deposition distribution model is as follows:Figure 1 The invention is characterized by the following steps:

[0008] (1) Based on the coating thickness distribution profile obtained by ESRB spraying at a constant speed along a straight line on a plane, five characteristic parameters are extracted: the thickness value t at the central axis. c The thickness value t at the double peaks on both sides of the model p , t p The corresponding x-coordinate r p , t p Width at half thickness w 50 and a quarter of a t p Width of thickness w 25 ;

[0009] (2) Based on the aforementioned characteristic parameters, a piecewise function-form uniform linear distribution model is constructed. The central region is described using a cubic polynomial, and the two lateral regions are described using a Gaussian-like function, ensuring that the function is continuously differentiable at the connection points, such as... Figure 2 As shown;

[0010] (3) Through multi-factor and multi-level orthogonal spraying experiments, the measured data of each characteristic parameter under different combinations of spraying parameters were obtained;

[0011] (4) Establish a mathematical relationship model between the spraying process parameters and each characteristic parameter, and finally determine that the independent variables in the spray gun model include spraying height H, spraying speed S, spray gun flow rate Q, and shaping air N1 and N2.

[0012] (5) Based on the uniform linear distribution model described in step (2) and the mathematical relationship model described in step (4), the characteristic parameter expression obtained in step (4) is substituted into the uniform linear distribution model in step (2) to obtain the final expression of the parameterized model. Given the spraying parameters, the coating distribution profile is predicted according to the parameterized model for spraying trajectory planning and thickness simulation verification.

[0013] ESRB model parametric modeling

[0014] For the uniform linear distribution model, this invention employs a piecewise function, with the normal intercept of the spray trajectory as the x-axis and the central axis of symmetry as x=0. Within the abscissa interval [0, r...],... p Within [the area], a cubic polynomial function is used to describe the thickness t from the center. c to peak thickness t p The outline; where the x-coordinate is greater than r p The region uses r p As the axis of symmetry, passing through (w) 50 ,t p / 2 ), (w 25 ,t p / 4The Gaussian function at the constraint point describes the descending edge of the profile; the cubic polynomial function and the Gaussian function at the connection point (r) p ,t p The first derivatives of both are equal and continuous at x < 0. When x < 0, the thickness is f(x) = f(-x). Its expression is as shown in equation (1):

[0015] (1)

[0016] For a cubic polynomial, let (0,t) c ) and (r p ,t p The derivative at point () is 0;

[0017]

[0018] Substituting into formula (1), we get:

[0019]

[0020] For the Gaussian function, let x = r p Point A is the axis of symmetry of the Gaussian function, and the Gaussian distribution coefficient A = t is obtained. p Expected value µ=r p To ensure that the Gaussian function strictly passes through (0.5w) 50 0.5t p ) and (0.5w 25 0.25t p The standard deviation σ needs to be continuously changed at this point. When the axis of symmetry and peak value of the Gaussian distribution are fixed (x=r...), the distribution's standard deviation σ needs to be continuously changed. p A=t p (0.5w) 50 0.5t p ) and (0.5w 25 0.25t p Each point uniquely determines σ 50 σ 25 Therefore, as the x-coordinate moves along the x-axis, σ continuously changes as follows:

[0021]

[0022] Substituting equations (2) and (3) into equation (1), we obtain the ESRB uniform linear distribution model in piecewise function form, as shown in equation (4):

[0023]

[0024] In the above formula, xdata represents the x-coordinate of a point on the cross-sectional profile, xi represents the centerline coordinate of the corresponding cross-sectional profile i, and rmax represents the maximum range of the given spraying, which is usually considered to be between 300 and 400 mm, and is 350 mm by default unless otherwise specified.

[0025] Orthogonal experimental design

[0026] To reduce the number of experiments, this invention employs orthogonal experiments with seven factors: rotational speed, internal forming air, external forming air, paint flow rate, voltage, height, and moving speed. To better reflect the influence of these parameters on the distribution model, the number of levels for each factor should not be too small; conversely, to reduce the number of experiments and save costs, the number of levels for each factor should not be too large. The parameters to be changed are tested with five different levels, and orthogonal spraying experiments are conducted. To ensure a uniform distribution of parameter combinations, at least 49 sets of experiments are required for the seven-factor, five-level experiment. The number of parameters remains large. An interaction effect was observed between height and spraying parameters in the trajectory parameters, while the moving speed is much slower than the spraying deposition rate. Therefore, the interaction experiment between moving speed and other factors was ignored, and a single-factor experiment on moving speed was conducted. In summary, this invention requires at least 25 sets of experiments with 6 factors and 5 levels. , and 5 single-factor experiments.

[0027] The spraying experiment process is as follows Figure 3 , 4 As shown. The experimental procedure was as follows: 1) Select a metal plate identical to the vehicle body substrate, clean and dry it; 2) Fix the metal plate on the experimental table (production line), ensuring good grounding; 3) Have the painting robot spray the well-grounded aluminum plate twice, according to the values ​​of each experimental group, with the starting point, turning point, and ending point of the spraying all outside the flat aluminum plate; 4) Remove the sprayed metal plate, dry it, and record the experimental parameters; 5) Use a thickness gauge to measure the thickness at different locations on it, and take the average value after multiple measurements; 6) Observe the characteristic values ​​of each set of data and record them. There are two purposes for doing this: first, only the stable segment of the uniform straight line is retained on the flat plate, while the unstable segment is performed outside the flat plate; second, spraying twice can increase the paint film thickness and eliminate the error caused by the left-right asymmetry of the model due to the direction of movement. The spraying robot used in the experiment was the ABB IRB5400 spraying robot, and the rotary cup used was the ABB RB 1000-SSD_BOC-BOC electrostatic rotary cup. The experimental equipment and materials included aluminum plate specimens, Fischer Iso Scope FMP30 thickness gauge, electric thermostatic drying oven, electronic weighing scale, and water-based metallic topcoat.

[0028] Modeling the mapping relationship between spraying process parameters and feature parameters

[0029] The relationship model between the spraying parameters and the characteristic parameters is fitted using a polynomial or power function. The fitting coefficients are determined based on orthogonal experimental data using the least squares method, including:

[0030] (1) Peak value t p The peak value, or the highest value of the distribution model, represents the cumulative thickness of the entire coating model. Orthogonal experimental data shows that the peak value t... p It is related to paint flow rate, internal forming air flow rate, and spraying height, and is unrelated to or has a very small correlation with rotational speed, voltage, and external forming air flow rate.

[0031] To accurately fit the coating flow rate Q to the peak value t p To assess the influence of the initial parameters, a quadratic polynomial is used for least-squares fitting. The coefficients a1 and b1 are calculated from the boundary mean to reflect their changing trend; the constant term c1 is calculated from the initial conditions to obtain a curve that better matches the initial parameters, as expressed in equation (5):

[0032]

[0033] Based on the internal forming airflow parameter N1 and peak value t p The relationship is fitted using a power function, and its expression is shown in equation (6):

[0034]

[0035] Where b2 is the power exponent and a2 is the coefficient.

[0036] Similarly, the influence of the height parameter H is also represented by a power function, as shown in equation (7):

[0037]

[0038] Where b3 is the exponent and a3 is the coefficient.

[0039] By using the boundary mean of orthogonal experiments and least squares fitting, the fitting coefficients of each formula can be obtained. Substituting these coefficients with the initial parameter conditions, the corresponding eigenvalues ​​can be calculated.

[0040] (2) Peak coordinates r p Peak coordinate r p The value represents the width between the two peaks. Through orthogonal experimental data, it can be seen that the peak coordinates are related to the rotational speed, the internal forming airflow, and the height, while they are unrelated to or have little influence on other factors.

[0041] Because the height generally remains constant during the actual spraying process, the internal forming airflow rate N1 is taken as the main influencing factor. First, the peak coordinate r under the set internal forming airflow rate is determined. p To most accurately fit the internal shaping airflow N1 to the peak coordinate r p To account for the influence of the polynomial, this invention uses a quadratic polynomial for calculation, the expression of which is shown in equation (8):

[0042]

[0043] Where a4 and b4 are coefficients, and c2 is a constant.

[0044] Next, based on the height H and the peak coordinate r p To calculate the peak value, this invention uses a polynomial for fitting and calculating the peak coordinates. Its expression is shown in equation (9):

[0045]

[0046] Where a5 and b5 are coefficients, and c3 is a constant.

[0047] By using the boundary mean of orthogonal experiments and least squares fitting, the fitting coefficients of each formula can be obtained. Substituting these coefficients with the initial parameter conditions, the corresponding eigenvalues ​​can be calculated.

[0048] (3) Center thickness t c Center thickness t c This is the cumulative thickness value at the axis of symmetry of the distribution model, reflecting the thickness fluctuation between the two peaks of the entire spraying model. Through orthogonal experimental data, it can be known that the center thickness t... c It is related to paint flow rate, internal forming air flow rate, and height.

[0049] Observation shows that the center thickness t c Influencing factors and peak t p The influencing factors are basically the same. In order to accurately fit the influence of flow rate on peak value, this invention uses a polynomial to calculate it, and its expression is as shown in equation (10):

[0050]

[0051] Where a6 and b6 are coefficients, and c4 is a constant.

[0052] Next, based on the internal forming airflow N1 and the center thickness t... c To calculate the peak value of the relationship, this invention uses a power function for fitting, and its expression is shown in equation (11):

[0053]

[0054] Where b7 is a power function and a7 is a coefficient.

[0055] Similarly, the influence of the height parameter is also represented by a power function, as shown in equation (12):

[0056]

[0057] Where b8 is a power function and a8 is a coefficient.

[0058] By using the boundary mean of orthogonal experiments and least squares fitting, the fitting coefficients of each formula can be obtained. Substituting these coefficients with the initial parameter conditions, the corresponding eigenvalues ​​can be calculated.

[0059] (4) Model width w 50 In engineering, the width of 50% peak value is considered the spray pattern, serving as an indicator for evaluating spray width and reflecting its width. Orthogonal experimental data shows that, under the same conditions, the internal forming airflow parameter N1 significantly affects the width w. 50 The influence of the spraying distance is greatest, followed by the paint flow rate. Since the height H is a trajectory parameter, the influence of the spraying distance is considered last. Therefore, the width w is first determined under the set forming air flow rate parameter N1. 50 Next, based on the paint flow rate, height, and width w 50 Based on the relationship, calculate the final width w. 50 Their expressions are shown in equations (13), (14), and (15), respectively:

[0060]

[0061]

[0062]

[0063] Among them, a9, a 10 a 11 b9, b 10 b 11 c5, c6, and c7 are coefficients, while c5, c6, and c7 are constants.

[0064] By using the boundary mean of orthogonal experiments and least squares fitting, the fitting coefficients of each formula can be obtained. Substituting these coefficients with the initial parameter conditions, the corresponding eigenvalues ​​can be calculated.

[0065] (5) Model width w 25 Model width w 25 with w50 Similar, but it represents more the distribution on both sides of the edge, reflecting the downward trend on both sides of the sprayed model. Through orthogonal experimental data, it can be seen that the model width w 25 Influencing factors and model width w 50 Similar to the external forming airflow parameter, but more sensitive to the internal forming airflow parameter N1 for width w. Observations show that, all other things being equal, the internal forming airflow parameter N1 is more sensitive to the width w. 25 The effect is greatest on the coating flow rate Q and the external forming air flow rate parameter N2.

[0066] Since both the external forming airflow parameter N2 and the internal forming airflow parameter N1 are airflow factors, they are considered together. To most accurately fit the influence of flow rate on the peak value, a composite polynomial is used for calculation, and its expression is shown in equations (16) and (17):

[0067]

[0068]

[0069] Where a 12 a 13 b 12 b 13 b 11 c is a coefficient, and c8 and c9 are constants.

[0070] Based on paint flow rate Q and height H and width w 25 The relationship, calculate the width w 25 Its expression is as shown in equations (18) and (19):

[0071]

[0072]

[0073] Where a 14 a 15 b 14 b 15 c is the coefficient. 10 c 11 It is a constant.

[0074] By using the boundary mean of orthogonal experiments and least squares fitting, the fitting coefficients of each formula can be obtained. Substituting these coefficients with the initial parameter conditions, the corresponding eigenvalues ​​can be calculated.

[0075] The influence of the moving speed parameter on the model was investigated. Under the same conditions, the coating thickness t at different moving speeds S was obtained through single-factor experiments. c Experimental data. For example... Figure 5 As shown, with other factors remaining constant, the faster the moving speed, the less coating is deposited per unit area, and the thinner the thickness; conversely, the slower the speed, the more coating is deposited, and the thicker the thickness. In previous studies, the uniform linear distribution model was obtained by integrating the static deposition rate model, thus yielding formula (20):

[0076] (20)

[0077] Therefore, it can be seen that, with other parameters remaining constant, the thickness at each point is inversely proportional to the velocity v. In the uniform linear distribution model, the thickness is mainly determined by t. c and t p By definition, we obtain formula (21).

[0078] (twenty one)

[0079] Application and Optimization of ESRB Parametric Distribution Model

[0080] Based on the relationship between the distribution model and spraying parameters, this model is applied to offline planning. With coating thickness uniformity, thickness range, and deviation between the mean and target thickness as optimization objectives, a genetic algorithm is used to optimize and solve the spraying parameters. This includes:

[0081] (1) Obtain the values ​​of characteristic parameters and predict the coating distribution under given spraying parameters;

[0082] (2) Generate a raster-type spraying path and determine the trajectory spacing;

[0083] (3) Select an ideal thickness value within its allowable range as the target thickness T. t Establish an evaluation function Y1 representing the performance of matching the target thickness, the expression of which is shown in equation (20):

[0084] (20)

[0085] Where T mean The mean thickness is expressed as in equation (21):

[0086] (twenty one)

[0087] An evaluation function Y2 characterizing the color difference of the coating is established, and its expression is shown in equation (22):

[0088] (twenty two)

[0089] Establish an evaluation function Y3 that uses variance to represent thickness uniformity, and its expression is shown in equation (23):

[0090] (twenty three)

[0091] Where T i The thickness of the selected n sampling points.

[0092] A multi-objective processing strategy based on linear weighting is adopted, combining the three optimization objectives Y1, Y2, and Y3 into a single optimization objective according to their respective weights, thus transforming the problem into a constrained minimization problem. Weights are assigned to each objective function according to their importance. ,make ( The comprehensive optimization index is obtained, and its expression is shown in equation (24):

[0093] (twenty four)

[0094] For the optimization problem of minimizing multivariable parameters with a single objective, intelligent optimization algorithms can be used to solve it. Here, we choose to use a genetic algorithm for optimization calculation, select the objective function mentioned above as the fitness function, and set the value range of each optimization parameter according to the process. Its expression is as shown in equation (25):

[0095] (25)

[0096] Simulation verification of the ESRB parameterized distribution model

[0097] The steps for verifying the accuracy of the parameterized distribution model are as follows:

[0098] (1) Model prediction accuracy verification: Select multiple spraying process combinations with different parameters from the modeling experiment, and obtain the coating distribution profile by measuring the actual spraying experiment and predicting the parameterized distribution model. Compare the degree of agreement between the two on key feature parameters to verify the generalization ability and prediction accuracy of the model.

[0099] (2) Engineering application equivalence verification: The target coating thickness is set according to the process requirements of the actual spraying production line. The optimal combination of spraying parameters is obtained based on the parameterized distribution model and optimization algorithm. The optimization results are compared with the parameters determined by the engineer in actual production to verify their equivalence in meeting the process requirements, thereby proving the practical value of the model in the offline programming system.

[0100] The present invention provides a parameter simulation module for the offline programming system of the spraying robot, including a parameterized distribution model module, a trajectory planning module, a parameter optimization module, and a thickness simulation module, providing important tools from prediction of the spraying model, trajectory generation, parameter optimization to thickness verification.

[0101] The present invention has the following beneficial effects:

[0102] ① Strong parameter correlation: Through systematic experiments and modeling, an explicit mathematical relationship between the main spraying process parameters (flow rate, forming air, height, speed) and the geometric features of the distribution profile was established, and the model has strong adaptability to parameter changes.

[0103] ② High prediction accuracy: Based on parametric modeling of actual spraying data, it can accurately predict the unique "bimodal" distribution pattern of ESRB.

[0104] ③ Good engineering practicality: The model output is the thickness distribution under uniform linear motion, which can be directly used in the most common trajectory planning scenarios. It has high computational efficiency and meets the real-time requirements of offline programming systems.

[0105] ④ Optimization support: It provides a mathematical model basis for the automatic optimization of spraying parameters, which can reduce manual trial and error and improve spraying quality and material utilization. Attached Figure Description

[0106] The accompanying drawings are provided to further understand the technical solutions of the present invention and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the technical solutions of the present invention, and do not constitute a limitation on the technical solutions of the present invention.

[0107] Figure 1 A flowchart for parameterizing a dynamic sedimentation distribution model.

[0108] Figure 2 Fitting curves for dynamic sediment distribution models.

[0109] Figure 3 Experiments on ESRB planar linear spraying on an automobile production line.

[0110] Figure 4 Data collection for topcoat thickness during spraying experiments.

[0111] Figure 5 This is the positive integral of the static deposition rate model.

[0112] Figure 6 The results of the spraying experiment with different spraying parameters are compared with the results of the simulation.

[0113] Figure 7The coating flow rate was 168.830 cc / min, and the internal forming air flow rate was 201.478 Nl / min. (Spraying results)

[0114] Figure 8 The coating result was achieved with a paint flow rate of 173.799 cc / min and an internal forming air flow rate of 205.327 Nl / min. Detailed Implementation

[0115] To further understand the invention's content, features, and effects, the following embodiments are provided, along with detailed descriptions in conjunction with the accompanying drawings:

[0116] (1) Proof of the accuracy of the model for predicting spray distribution

[0117] Several sets of reasonable spraying parameters were designed, and these parameters were substituted into the ESRB parametric distribution model to obtain the predicted distribution results. Spraying experiments were conducted to obtain the experimental test results. The accuracy and effectiveness of the algorithm were verified by comparing the predicted distribution of the established parametric model with the actual measured distribution. The parametric model prediction results and experimental measurement results are as follows: Figure 6 As shown.

[0118] By observing the experimental measurement results and simulation results, it can be demonstrated that the algorithm proposed in this invention has high prediction accuracy. Therefore, this model has high practical value and can be applied to ESRB spraying trajectory planning and thickness simulation.

[0119] (2) Application of parameterized distribution model in offline programming

[0120] By applying a parametric model to adjust the spraying parameters and comparing them precisely with the actual spraying parameters calibrated by engineers, the model's important role in offline programming and spraying parameter setting is demonstrated. To verify the accuracy of the parametric distribution model and the practicality of the planning method, the actual spraying parameters of a car factory production line were compared with the computer-optimized results. The production line is for automotive topcoat spraying, with a target thickness of 12 μm. Because the spraying process involves four robots completely spraying two coats over the car body, the target thickness for a single spray is 6 μm. The flow rate q and the shape air p were optimized, while other parameters remained consistent with actual production. These parameters were: rotation speed 50.0 kr / min, shape air 500 Nl / min, voltage -70 kV, and spraying height 200 mm.

[0121] The weight parameter ω in the optimization objective iDifferent choices of parameters will lead to different optimization results. Under the conditions of ω1=0.5, ω2=0.5, and ω1=0, 10 sets of reasonable spraying experiments were designed, and 10 sets of optimization results were obtained. Under these conditions, the optimization results focus more on the satisfaction level of the target thickness and the magnitude of the range, but neglect the uniformity of its distribution. By comparing the weighted summation of the objective function values, q=168.830 cc / min and p=201.478 Nl / min are the optimal choices. Figure 7 The coating results are as follows: paint flow rate is 168.830 cc / min, and internal forming air flow rate is 201.478 Nl / min.

[0122] Under the conditions of ω1=0.8, ω2=0.1, and ω1=0, the previous 10 sets of optimization results were used. Under these conditions, the optimization results prioritized the satisfaction of the target thickness, while considering the magnitude of the range and the uniformity of the distribution. The optimal choice was determined by comparing the weighted summation of the objective function values: q=173.799 cc / min, p=205.327 Nl / min. Figure 8 The coating results are as follows: paint flow rate is 173.799 cc / min, and internal forming air flow rate is 205.327 Nl / min.

[0123] By comparing the calculation results under various optimized parameters, all are basically consistent with the actual spraying parameters used in the production line: q=160cc / min, p=200Nl / min, and all meet the spraying requirements. This proves that the parameterized distribution model is accurate and reliable, and has important application value in offline programming systems.

Claims

1. A parametric modeling method for an ESRB uniform linear distribution model, characterized in that, Includes the following steps: (S1) For the paint thickness distribution profile formed by the ESRB spraying at a constant speed along a straight line on a plane, a set of feature parameters defining its geometry is extracted. The extracted feature parameter set is [t c t p r p w 50 w 25 ]; (S2) Based on the aforementioned characteristic parameters, a piecewise function mathematical model is constructed to describe the thickness distribution profile of the coating. The piecewise function is continuous. At the segmentation points, the first derivative of the piecewise function is equal and continuous. (S3) Design multi-factor, multi-level orthogonal spraying experiments and single-factor experiments to obtain actual thickness distribution data under different combinations of spraying process parameters. Then, perform least squares fitting on the obtained data to obtain the fitting coefficients of the formula, thereby establishing a mapping relationship model from spraying process parameters to characteristic parameters.

2. The method according to claim 1, characterized in that, The five feature parameters in the feature parameter set in step (S1) are: the thickness value t at the central axis. c The thickness value t at the double peaks on both sides of the model p , t p The corresponding x-coordinate r p , t p Width at half thickness w 50 and a quarter of a t p Width of thickness w 25 The unit of thickness is micrometers (mm), and the unit of coordinates is millimeters (mm). The actual geometric meaning of these characteristic values ​​is as follows: (1) t c and t p This represents the thickness level of the core region in the middle of the model; (2)r p This represents the width of the thicker, middle section; (3) w 50 and w 25 This indicates the downward trend on both sides of the model.

3. The method according to claim 2, characterized in that, The piecewise function mathematical model constructed in step (S2) is as follows: With the normal section of the spray trajectory as the x-axis and the central axis of symmetry at x=0, the x-coordinate interval is [0, r]. p Within [the area], a cubic polynomial function is used to describe the thickness t from the center. c to peak thickness t p The outline; When the x-coordinate is greater than r p The region uses r p As the axis of symmetry, passing through (w) 50 ,t p / 2 ), (w 25 ,t p / 4 The Gaussian function of the constraint points describes the descending edge of the profile; The cubic polynomial function and the Gaussian function mentioned above are connected at the point (r) p ,t p The two are continuous at point (), and their first derivatives are equal and continuous.

4. When x < 0, the thickness is f(x) = f(-x).

5. The method according to claim 1, characterized in that, The spraying process parameters in step (S3) include at least: paint flow rate Q, in cc / min; internal forming air N1, in NL / min; external forming air N2, in NL / min; spraying height H, in mm; and moving speed S, in mm / s.

6. The method according to claim 1, characterized in that, In step (S3), data were obtained by combining orthogonal experiments and single-factor experiments. In addition, five single-factor experiments were conducted for the factor of movement speed.

7. The orthogonal experiment is designed for six key influencing factors: paint flow rate, internal forming air, external forming air, electrostatic voltage, rotary cup speed and spraying height. Five levels are selected for each factor, and at least 25 sets of experiments are completed to efficiently obtain regular data on the influence of parameters.

8. The experiment involved a spraying robot performing two uniform linear spraying operations on a grounded aluminum plate to ensure that stable and symmetrical coating samples were obtained in each set of experiments. Subsequently, a thickness gauge was used to measure the thickness distribution and extract the feature values ​​of each set of experimental data.

9. The method according to claim 1, characterized in that, The feature parameter distribution model generated by the parametric modeling method is integrated into the offline programming system of the spraying robot for coating distribution prediction, spraying parameter optimization, or coating thickness simulation verification.

10. The method according to claim 6, characterized in that, The optimization of spraying parameters refers to: using at least one of the evaluation functions Y1 (the difference in the target thickness of the coating), Y2 (the difference in the color difference of the target thickness of the coating), or Y3 (the variance of the target thickness of the coating) as the optimization objective, and using the spraying process parameters as the optimization variables, and employing a genetic algorithm to solve for the optimal combination of spraying parameters.

11. The method according to claim 6, characterized in that, The coating thickness simulation verification includes model prediction accuracy verification and engineering application equivalence verification; The model prediction accuracy verification is conducted by comparing the model prediction results with experimental measurement results under multiple sets of new parameters to evaluate the model's generalization ability and prediction accuracy. The engineering application equivalence verification compares the spraying parameters obtained by the model optimization with the actual engineering application parameters to verify its ability to meet the same process requirements, thereby proving the practical value of the model.

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