Design method of annular scanning laser welding process

Abstract

The invention discloses an annular scanning laser welding process design method, and belongs to the technical field of annular scanning laser welding. According to the method, through optimization of experimental design and simulation calculation, the problems that traditional laser welding assembly clearance tolerance is poor, experimental cost is high, and production efficiency is low are solved. The method comprises the steps of determining process design parameters and levels, selecting experimental design types, determining welding seam forming characteristic parameters, designing an experimental matrix, carrying out a process reference experiment and a simulation reference experiment, correcting an energy coefficient of a simulation model, completing simulation calculation of remaining experimental schemes, and optimizing parameter combinations through data analysis. Compared with a traditional method, the method has the advantages that the experiment frequency and cost are reduced, the production efficiency is improved, good universality and adaptability are achieved, welding process parameters can be rapidly designed, and the method is suitable for welding application of thin-wall workpieces made of different materials and with different thicknesses.

Description

Technical Field

[0001] The invention relates to a circular scanning laser welding weld process design method, which belongs to the technical field of circular scanning laser welding. Background Art

[0002] The concentrated energy density of laser welding can significantly improve the heat affected zone and joint structure of thin-walled workpieces, but its assembly gap tolerance is poor, the pre-welding process preparation time is long, and the production efficiency is low. Annular scanning laser welding realizes rapid welding forming in a large range through the joint coordination of the Z-axis focusing axis and the XY motion axis, which can effectively solve the problems of poor assembly gap tolerance and low production efficiency of traditional laser welding. It is one of the most promising welding methods. Compared with traditional laser welding, there are many process parameters in annular scanning laser welding, such as laser power, welding speed, defocus, laser scanning frequency, scanning amplitude, scanning direction, etc., which brings challenges to the process design of annular scanning laser welding. If the process parameters are not designed reasonably, the melting ratio and molten pool morphology of the weld are unreasonable, which will cause various forming defects. Due to the large number of annular scanning laser welding process parameters, the use of traditional experimental methods requires more manpower, material and financial resources, which to a certain extent increases the process cost and reduces production efficiency. The above problems restrict the large-scale application of annular scanning laser welding in thin-walled workpieces. Summary of the invention

[0003] In order to solve the problems of high cost and low production efficiency of circular scanning laser welding experiments, the present invention proposes a circular scanning laser welding weld process design method.

[0004] The present invention adopts the following technical solution: a circular scanning laser welding process design method, comprising the following steps:

[0005] Step 1: Determine process design parameters and levels

[0006] Determine the process design parameters and levels based on the factors that affect weld formation;

[0007] Step 2: Select the experimental design type

[0008] Select the appropriate experimental design type based on the number and complexity of the process design parameters selected by the user;

[0009] Step 3: Determine the response variable

[0010] Determine a response variable, wherein the response variable is a characteristic parameter of weld formation;

[0011] Step 4: Design the Experimental Matrix

[0012] Generate an experimental matrix based on the experimental design type described in step 2 and the process design parameters and levels described in step 1;

[0013] Step 5: Conduct process benchmark experiments

[0014] In the experimental matrix, 2 to 4 groups of experimental schemes are randomly selected to carry out process benchmark experiments for correcting the simulation calculation model, and obtain characteristic parameters of weld formation;

[0015] Step 6: Conduct simulation benchmark experiments

[0016] The simulation benchmark experiment process is as follows:

[0017] (1) Based on the same experimental scheme as the process benchmark experiment, simulation calculation is performed to obtain the characteristic parameters of the new weld formation;

[0018] The simulation calculation process is as follows:

[0019] 1) Input the process parameters in the experimental plan;

[0020] 2) Calculate the motion trajectory of the laser beam center;

[0021]

[0022] Where x0 and y0 are the coordinates of the beam starting point, D is the scanning amplitude, f is the scanning frequency, and v W is the welding speed, t is the welding time;

[0023] 3) Calculate the instantaneous laser energy distribution on the workpiece

[0024]

[0025] Where η is the energy coefficient, P is the laser power, r0 is the spot radius, x(t) and y(t) are the laser beam centers, and Δt is the time step;

[0026] 4) Update the surface and internal temperature of the workpiece

[0027] T n+1 =f S (f D (f A (T n ))) (3)

[0028] Among them, T n Represents the temperature at the current moment, T n+1 represents the temperature at the next moment, f A Represents the convection term update:

[0029]

[0030] in, is the melt pool flow velocity, which is obtained by the following equation:

[0031]

[0032] in, is the partial differential operator, T is the transpose operation, is the divergence operator, is the gradient operator, t is the welding time, is the flow velocity of the molten pool, ρ and μ are the density and viscosity of the material respectively, p is the molten pool pressure, It is the source of internal strength;

[0033] f D Representative diffusion item update:

[0034]

[0035] Among them, ρ is the density of the material, C is the specific heat capacity of the material, and λ is the thermal conductivity of the material;

[0036] f S Represents source item update:

[0037]

[0038] 6) Extract new characteristic parameters of weld formation

[0039] According to the isotherms of the material melting point, new weld formation characteristic parameters are extracted;

[0040] (2) Correction of energy coefficients in simulation models

[0041] The characteristic parameters of the weld formation obtained by the process benchmark experiment are compared with the characteristic parameters of the new weld formation obtained by the simulation benchmark experiment. According to the comparison results, the energy coefficient in formula (2) is corrected to make the simulation benchmark experiment results consistent with the process benchmark experiment results. Finally, the average value of the corrected energy coefficients of each group of the simulation benchmark experiment is calculated as the final energy coefficient.

[0042] Step 7: Execute the remaining experiments in the experimental matrix

[0043] Repeat the simulation calculation in step 6 according to the process parameters and the corrected energy coefficients in the remaining experimental schemes in the experimental matrix, and record the response variable value of each experimental scheme;

[0044] Step 8: Data Analysis and Optimization

[0045] Use statistical analysis methods to analyze experimental data, establish a relationship model between process design parameters and response variables, and optimize parameters based on the established model to find the optimal parameter combination and complete the process design.

[0046] Furthermore, in the first step, the process design parameters include laser power, welding speed, defocus, laser scanning frequency, and scanning amplitude; the level refers to a reasonable design range of the process design parameters, which is related to the material, laser, and workpiece thickness.

[0047] Furthermore, in the second step, the experimental design types include full factorial design, fractional factorial design, and Taguchi design.

[0048] Furthermore, in the third and fifth steps, the characteristic parameters of the weld formation include weld width and weld depth.

[0049] Furthermore, in the fourth step, the experimental matrix is ​​a series of experimental schemes composed of different process design parameters, and each experimental scheme provides the process parameters required for carrying out circular scanning laser welding.

[0050] Furthermore, in the sixth step, the characteristic parameters of the new weld formation include weld width and weld depth.

[0051] Furthermore, in the sixth step, It is the internal force source, which includes the thermal buoyancy, thermal capillary force and recoil pressure exerted on the molten pool.

[0052] Furthermore, in the eighth step, the statistical analysis methods include ANOVA and regression analysis.

[0053] Compared with the existing method, the advantages of the present invention are as follows:

[0054] (1) Low experimental cost. The traditional method requires a large number of process experiments, which consumes a lot of manpower, material resources and financial resources. This method only requires a small number of experiments to modify the prediction model to complete the process design;

[0055] (2) High production efficiency. The traditional method requires many experiments and a long experimental cycle, which reduces production efficiency. However, this method only requires a small number of experiments, has a short experimental cycle, and has high production efficiency.

[0056] (3) Good versatility. Traditional methods rely on materials and workpiece thickness. If the materials and workpiece thickness change, relevant experiments need to be carried out again. However, this method only needs to modify the input parameters to complete the process design, which has good versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 The invention is a process flow chart of a circular scanning laser welding process design method.

[0058] Figure 2 It is a schematic diagram of the motion trajectory of the laser beam center.

[0059] Figure 3 It is a schematic diagram of the instantaneous laser energy distribution on the plate.

[0060] Figure 4 It is a schematic diagram of extracting new weld forming characteristic parameters from the isotherms of the material melting point.

[0061] Figure 5 Schematic diagram of the response surface of weld depth-to-width ratio under different scanning amplitudes and scanning frequencies obtained based on the response surface methodology.

[0062] Figure 6 Schematic diagram comparing weld morphology using unoptimized process parameters and optimized process parameters. DETAILED DESCRIPTION

[0063] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0064] Combination Figure 1 The circular scanning laser welding process design method of the present invention comprises the following steps:

[0065] Step 1: Determine process design parameters and levels

[0066] Determine the process design parameters and levels based on the factors that affect weld formation. The process design parameters may include laser power, welding speed, defocus, laser scanning frequency, and scanning amplitude; the level refers to the reasonable design range of process design parameters, which is related to the material, laser, and workpiece thickness.

[0067] Step 2: Select the experimental design type

[0068] According to the number and complexity of the process design parameters selected by the user, an appropriate experimental design type is selected, including full factorial design, fractional factorial design, Taguchi design, etc.

[0069] Step 3: Determine the response variable

[0070] The response variables in the present invention are characteristic parameters of weld formation, including weld width and weld depth.

[0071] Step 4: Design the Experimental Matrix

[0072] According to the experimental design type selected by the user in the second step and the process design parameters and levels in the first step, an experimental matrix is ​​generated. The experimental matrix is ​​a series of experimental schemes composed of different process design parameters, and each experimental scheme provides the process parameters required for circular scanning laser welding.

[0073] Step 5: Conduct process benchmark experiments

[0074] In the experimental matrix, 2 to 4 groups of experimental schemes are randomly selected to carry out process benchmark experiments (for correcting the simulation calculation model), and obtain characteristic parameters of weld formation, including weld width and depth.

[0075] Step 6: Conduct simulation benchmark experiments

[0076] The simulation benchmark experiment process is as follows:

[0077] (1) Based on the same experimental scheme as the process benchmark experiment, simulation calculations are performed to obtain new characteristic parameters of weld formation, including weld width and depth.

[0078] The simulation calculation process is as follows:

[0079] 1) Input the process parameters in the experimental plan;

[0080] 2) Calculate the motion trajectory of the laser beam center;

[0081]

[0082] Where x0 and y0 are the coordinates of the beam starting point, D is the scanning amplitude, f is the scanning frequency, and v W is the welding speed and t is the welding time.

[0083] 3) Calculate the instantaneous laser energy distribution on the workpiece

[0084]

[0085] Where η is the energy coefficient (initial value is 1), P is the laser power, r0 is the spot radius, x(t) and y(t) are the laser beam centers, and Δt is the time step.

[0086] 4) Update the surface and internal temperature of the workpiece

[0087] T n+1 =f S (f D (f A (T n ))) (3)

[0088] Among them, T n Represents the temperature at the current moment, T n+1 represents the temperature at the next moment, f A Represents the convection term update:

[0089]

[0090] in, is the melt pool flow velocity, which is obtained by the following equation:

[0091]

[0092] in, is the partial differential operator, T is the transpose operation, is the divergence operator, is the gradient operator, t is the welding time, is the flow velocity of the molten pool, ρ and μ are the density and viscosity of the material respectively, p is the molten pool pressure, Internal force sources include thermal buoyancy, thermal capillary force, and recoil pressure on the molten pool.

[0093] f D Representative diffusion item update:

[0094]

[0095] Among them, ρ is the density of the material, C is the specific heat capacity of the material, and λ is the thermal conductivity of the material.

[0096] f S Represents source item update:

[0097]

[0098] 7) Extract new characteristic parameters of weld formation

[0099] According to the isotherms of the material melting point, new weld formation characteristic parameters are extracted, including weld width and depth.

[0100] (2) Correction of energy coefficients in simulation models

[0101] The characteristic parameters of weld formation obtained from the process benchmark experiment are compared with the characteristic parameters of new weld formation obtained from the simulation benchmark experiment. According to the comparison results, the energy coefficient in formula (2) is corrected to make the simulation benchmark experiment results consistent with the process benchmark experiment results. Finally, the average value of the corrected energy coefficients of each group of the simulation benchmark experiment is calculated as the final energy coefficient.

[0102] Step 7: Execute the remaining experiments in the experimental matrix

[0103] According to the process parameters and the corrected energy coefficients in the remaining experimental schemes in the experimental matrix, the simulation calculation in step 6 is repeated, and the response variable value of each experimental scheme is recorded.

[0104] Step 8: Data Analysis and Optimization

[0105] Use statistical analysis methods such as ANOVA and regression analysis to analyze experimental data, establish a relationship model between process design parameters and response variables, optimize parameters based on the established model, find the optimal parameter combination, and complete process design.

[0106] Tungsten inert gas welding is often used in the manufacture of bellows, connecting rings and other ducts for launch vehicle power systems. This method has a large heat-affected zone when welding thin-walled ducts, which can easily lead to problems such as coarse structure and reduced mechanical properties of the joints. Laser welding has concentrated energy density, which can significantly improve the heat-affected zone and joint structure of duct welding, but its assembly gap tolerance is poor. Annular scanning laser welding can achieve rapid welding forming in a large range, and can effectively solve problems such as poor assembly gap tolerance and large heat-affected zone. The following takes the scanning laser welding of 0.4mm thick 1Cr18Ni9Ti stainless steel flat plate as an example to illustrate the implementation process of the present invention.

[0107] Example

[0108] Step 1: Determine process design parameters and levels

[0109] According to process experience and relevant literature, the design parameters and levels of 1Cr18Ni9Ti stainless steel flat plate scanning laser welding process are determined, as shown in Table 1.

[0110] Table 1 Design parameters and levels of scanning laser welding process for 1Cr18Ni9Ti stainless steel flat plate

[0111] Serial number Process design parameters (unit) level 1 Laser power (kW) 0.5～2.0 2 Welding speed (m / min) 0.5～2.0 3 Defocus (mm) -10～10 4 Scanning width(mm) 0.5～3.0 5 Scanning frequency (Hz) 50～200

[0112] Step 2: Select the experimental design type

[0113] In order to better examine the influence of different process parameters, a 4-level design is used in this example. According to Table 1, the experimental design of this example is 5 factors and 4 levels. In order to reduce the number of experiments and improve design efficiency, this example adopts Taguchi design, and the experimental design table is shown in Table 2.

[0114] Table 21Cr18Ni9Ti stainless steel flat plate scanning laser welding experimental design table

[0115] factor name level A Laser power 0.5，1.0，1.5，2.0 B Welding speed 0.5，1.0，1.5，2.0 C Defocus -10，-3，3，10 D Scanning amplitude 0.5，1.0，2.0，3.0 E Scan frequency 50，100，150，200

[0116] Step 3: Determine the response variable

[0117] The response variables in the present invention are characteristic parameters of weld formation, including weld width and weld depth.

[0118] Step 4: Design the Experimental Matrix

[0119] According to Table 2 in the second step and the corresponding variables in the third step, the experimental matrix of this example is shown in Table 3.

[0120] Table 31Cr18Ni9Ti stainless steel flat plate scanning laser welding experimental matrix

[0121] Experimental protocol Laser power Welding speed Defocus Scanning amplitude Scan frequency Melt Width Melt Depth 1 0.5 0.5 -10 0.5 50 2 0.5 1.0 -3 1.0 100 3 0.5 1.5 3 2.0 150 4 0.5 2.0 10 3.0 200 5 1.0 0.5 -3 2.0 200 6 1.0 1.0 -10 3.0 150 7 1.0 1.5 10 0.5 100 8 1.0 2.0 3 1.0 50 9 1.5 0.5 3 3.0 100 10 1.5 1.0 10 2.0 50 11 1.5 1.5 -10 1.0 200 12 1.5 2.0 -3 0.5 150 13 2.0 0.5 10 1.0 150 14 2.0 1.0 3 0.5 200 15 2.0 1.5 -3 3.0 50 16 2.0 2.0 -10 2.0 100

[0122] Step 5: Conduct process benchmark experiments

[0123] In the experimental matrix (Table 3), 2 to 4 groups were randomly selected to carry out process benchmark experiments for correcting the simulation calculation model, and the characteristic parameters of weld formation, including weld width and depth, were obtained. The test plate was cut by a shearing machine, and the shearing burrs were facing upward during welding. The test plate specifications were 0.4mm×100mm×300mm. The surface of the material was cleaned with alcohol before welding, and the material was pressed with a piano key tooling. RAYCUS RFL-C6000W continuous fiber laser and KUKAKR30HA robot were used to carry out scanning laser welding process tests. The laser output wavelength was 1060~1070nm, the rated output power was 6000W, and the actual output power of the laser was controlled by analog quantity. The system is equipped with SCANLAB HURRYSCAN 30 two-dimensional scanning welding head, and the welding head is equipped with a lateral side blowing air curtain, which can realize conventional one-dimensional and two-dimensional scanning paths. The welding process uses two-way protective gas for side-axis tail protection and back protection. The shielding gas is argon with a purity of 99.99%, the tail shielding gas flow rate is 40-50 L / min, and the back shielding gas flow rate is 3-5 L / min.

[0124] Step 6: Conduct simulation benchmark experiments

[0125] The simulation benchmark experiment process is as follows:

[0126] (1) Based on the same experimental scheme as the process benchmark experiment, simulation calculations are performed to obtain new characteristic parameters of weld formation, including weld width and depth.

[0127] The simulation calculation process is as follows:

[0128] 1) Input the process parameters in the experimental plan;

[0129] 2) Calculate the motion trajectory of the laser beam center;

[0130]

[0131] Where x0 and y0 are the coordinates of the beam starting point, D is the scanning amplitude, f is the scanning frequency, and v W is the welding speed, t is the welding time. The motion trajectory of the laser beam center is as follows Figure 2 shown.

[0132] 3) Calculate the instantaneous laser energy distribution on the plate

[0133]

[0134] Where η is the energy coefficient (initial value is 1), P is the laser power, r0 is the spot radius, x(t) and y(t) are the laser beam centers, and Δt is the time step. The instantaneous laser energy distribution on the plate is as follows: Figure 3 shown.

[0135] 4) Update the surface and internal temperature of the workpiece

[0136] T n+1 =f S (f D (f A (T n ))) (3)

[0137] Among them, T n Represents the temperature at the current moment, T n+1 represents the temperature at the next moment, f A Represents the convection term update:

[0138]

[0139] in, is the melt pool flow velocity, which is obtained by the following equation:

[0140]

[0141] in, is the partial differential operator, T is the transpose operation, is the divergence operator, is the gradient operator, t is the welding time, is the flow velocity of the molten pool, ρ and μ are the density and viscosity of the material respectively, p is the molten pool pressure, Internal force sources include thermal buoyancy, thermal capillary force, and recoil pressure on the molten pool.

[0142] f D Representative diffusion item update:

[0143]

[0144] Among them, ρ is the density of the material, C is the specific heat capacity of the material, and λ is the thermal conductivity of the material.

[0145] f S Represents source item update:

[0146]

[0147] 8) Extract new characteristic parameters of weld formation

[0148] According to the isotherms of the material melting point, new weld formation characteristic parameters are extracted, including weld width and depth, such as Figure 4 shown.

[0149] (2) Correction of energy coefficients in simulation models

[0150] The characteristic parameters of weld formation obtained from the process benchmark experiment are compared with the characteristic parameters of new weld formation obtained from the simulation benchmark experiment. According to the comparison results, the energy coefficient in formula (2) is corrected to make the simulation benchmark experiment results consistent with the process benchmark experiment results. Finally, the average value of the corrected energy coefficients of each group of the simulation benchmark experiment is calculated as the final energy coefficient.

[0151] Step 7: Execute the remaining experiments in the experimental matrix

[0152] According to the process parameters and the corrected energy coefficients in the remaining experimental schemes in the experimental matrix, the simulation calculation in step 6 is repeated, and the response variable values ​​of each experimental scheme are recorded, as shown in Table 4.

[0153] Table 41Cr18Ni9Ti stainless steel flat plate scanning laser welding experimental matrix

[0154]

[0155]

[0156] Step 8: Data Analysis and Optimization

[0157] Use statistical analysis methods such as ANOVA, regression analysis, response surface method, etc. to analyze experimental data, establish a relationship model between process design parameters and response variables, optimize parameters based on the established model, find the optimal parameter combination, and complete process design. Figure 5 Shown is a schematic diagram of the response surface of the weld depth-to-width ratio (ratio of weld depth to weld width) at different scanning amplitudes and scanning frequencies obtained based on the response surface method. Figure 5 The scanning amplitude and scanning frequency corresponding to the highest point of the corresponding surface in the image are the scanning amplitude and scanning frequency for obtaining the best aspect ratio. Figure 6 This is a schematic diagram comparing the weld morphology using unoptimized process parameters and optimized process parameters. The optimized weld has a smooth surface and a full shape.

Claims

1. A circular scanning laser welding process design method, characterized in that: The steps include: Step 1: Determine process design parameters and levels Determine the process design parameters and levels based on the factors that affect weld formation; Step 2: Select the experimental design type Select the appropriate experimental design type based on the number and complexity of the process design parameters selected by the user; Step 3: Determine the response variable Determine a response variable, wherein the response variable is a characteristic parameter of the weld formation; Step 4: Design the Experimental Matrix Generate an experimental matrix based on the experimental design type described in step 2 and the process design parameters and levels described in step 1; Step 5: Conduct process benchmark experiments In the experimental matrix, 2 to 4 groups of experimental schemes are randomly selected to carry out process benchmark experiments for correcting the simulation calculation model, and obtain characteristic parameters of weld formation; Step 6: Conduct simulation benchmark experiments The simulation benchmark experiment process is as follows: (1) Based on the same experimental scheme as the process benchmark experiment, simulation calculation is performed to obtain the characteristic parameters of the new weld formation; (2) Correction of energy coefficients in simulation models The characteristic parameters of the weld formation obtained by the process benchmark experiment are compared with the characteristic parameters of the new weld formation obtained by the simulation benchmark experiment. According to the comparison results, the energy coefficient in formula (2) is corrected to make the simulation benchmark experiment results consistent with the process benchmark experiment results. Finally, the average value of the corrected energy coefficients of each group of the simulation benchmark experiment is calculated as the final energy coefficient. Step 7: Execute the remaining experiments in the experimental matrix Repeat the simulation calculation in step 6 according to the process parameters and the corrected energy coefficients in the remaining experimental schemes in the experimental matrix, and record the response variable value of each experimental scheme; Step 8: Data Analysis and Optimization Use statistical analysis methods to analyze experimental data, establish a relationship model between process design parameters and response variables, and optimize parameters based on the established model to find the optimal parameter combination and complete the process design.

2. The method according to claim 1, characterized in that In the first step, the process design parameters include laser power, welding speed, defocus, laser scanning frequency, and scanning amplitude; the level refers to the reasonable design range of the process design parameters, which is related to the material, laser, and workpiece thickness.

3. The method according to claim 1, characterized in that In the second step, the experimental design types include full factorial design, fractional factorial design, and Taguchi design.

4. The method according to claim 1, characterized in that In the third and fifth steps, the characteristic parameters of the weld formation include weld width and weld depth.

5. The method according to claim 1, characterized in that In the fourth step, the experimental matrix is ​​a series of experimental schemes composed of different process design parameters, and each experimental scheme provides the process parameters required for carrying out circular scanning laser welding.

6. The method according to claim 1, characterized in that In the sixth step, the characteristic parameters of the new weld formation include weld width and weld depth.

7. The method according to claim 1, characterized in that In the sixth step, the simulation calculation process is as follows: 1) Input the process parameters in the experimental plan; 2) Calculate the motion trajectory of the laser beam center; Where x0 and y0 are the coordinates of the beam starting point, D is the scanning amplitude, f is the scanning frequency, and v W is the welding speed, t is the welding time; 3) Calculate the instantaneous laser energy distribution on the workpiece Where η is the energy coefficient, P is the laser power, r0 is the spot radius, x(t) and y(t) are the laser beam centers, and Δt is the time step; 4) Update the surface and internal temperature of the workpiece T n+1 =f S (f D (f A (T n ))) (3) Among them, T n Represents the temperature at the current moment, T n+1 represents the temperature at the next moment, f A Represents the convection term update: in, is the melt pool flow velocity, which is obtained by the following equation: in, is the partial differential operator, T is the transposition operation, is the divergence operator, is the gradient operator, t is the welding time, is the flow velocity of the molten pool, ρ and μ are the density and viscosity of the material respectively, p is the molten pool pressure, It is the source of internal strength; f D Representative diffusion item update: Among them, ρ is the density of the material, C is the specific heat capacity of the material, and λ is the thermal conductivity of the material; f S Represents source item update: 5) Extract new characteristic parameters of weld formation According to the isotherms of the material melting point, new weld formation characteristic parameters are extracted.

8. The method according to claim 7, characterized in that It is the internal force source, which includes the thermal buoyancy, thermal capillary force and recoil pressure exerted on the molten pool.

9. The method according to claim 1, characterized in that In the eighth step, statistical analysis methods included ANOVA and regression analysis.

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