An adaptive method for grinding process parameters based on changes in normal contact force

Abstract

The present invention provides a method for adaptively adjusting grinding process parameters based on changes in normal contact force. The method comprises the following steps: step 1, designing an orthogonal central combination experiment; step 2, using a depth partial least squares algorithm to establish a prediction model for grinding process parameters, surface roughness, and material removal depth; step 3, constructing an improved Archimedean optimization algorithm; step 4, establishing a target optimization function that meets grinding requirements and determining the values ​​of K1 and K2; and step 5, using the improved Archimedean optimization algorithm to calculate the optimal results for each process parameter under different normal contact forces. The method, based on a four-factor, three-level orthogonal central combination experiment, employs a partial least squares algorithm to establish a prediction model for grinding process parameters, surface roughness, and material removal depth, achieving high prediction accuracy. For areas where normal contact force is difficult to control during actual grinding, the method can ensure consistency in surface roughness and material removal depth during machining.

Description

Technical Field

[0001] The present invention relates to a manufacturing technology of an aero-engine blade, and in particular to a grinding process parameter self-adaptation method based on a change in normal contact force. Background Art

[0002] As a strategic high-tech product, the manufacturing technology of aircraft engines reflects a country's comprehensive strength. Blades are one of the key components of aircraft engines, and their manufacturing technology has always been the primary technical problem to be solved in the development of new-generation aircraft engines. After precision milling, the surface of the blades has residual cutting height and cutting marks. The consistency of its surface accuracy and surface roughness has a great impact on the service life and dynamic performance of aircraft engines under high temperature and high pressure conditions. Grinding and polishing processes are usually used to ensure the blade surface accuracy (±0.03mm) and surface roughness (Ra≤0.4um). Special CNC machine tools and manual grinding methods are commonly used at home and abroad to grind blades. Polishing, special CNC machine tools are expensive and have low applicability, while manual grinding not only has a harsh environment, high labor intensity, and low grinding efficiency, but also the consistency of the surface roughness and profile accuracy of the blade is difficult to ensure; in recent years, due to the advantages of industrial robots such as good flexibility, strong applicability, low cost, and simple equipment and good processing quality of sanding belt machines, flexible grinding and polishing equipment composed of industrial robots and sanding belt machines has begun to be used in blade grinding. At the same time, many technical difficulties have emerged and need to be solved urgently. At present, the research on robotic belt grinding focuses on robot force control technology, grinding trajectory planning technology, surface roughness prediction modeling and optimization, material removal rate and material removal depth modeling and optimization, etc.

[0003] Surface roughness and material removal depth are two important indicators for judging the quality of blade grinding. Domestic and foreign researchers have conducted a lot of in-depth research on them. For example, Chen used the response surface method to establish a blade surface roughness model and optimize the grinding process parameters. The optimized parameters were used in the experiment to obtain a significant reduction in the surface roughness of the blade. Huai Wenbo et al. used the response surface method to analyze the relationship between process parameters and surface roughness when polishing blades with an emery wheel. At the same time, the influence of process parameters on the surface roughness ratio before and after grinding was also considered. The CNN network established a prediction model for material removal depth and significantly improved the prediction accuracy. These studies mainly revolved around the single goal of surface roughness or material removal depth in the grinding process. In blade grinding, not only the surface roughness must be guaranteed to meet the process requirements, but also the dimensional accuracy of the profile must be considered. Some studies used gray correlation to convert the multi-objective optimization problem of surface roughness and material removal rate in blade grinding into a single goal, and used RBF neural network to establish a mapping relationship between process parameters and gray correlation, and then used FA algorithm to obtain the optimal process parameters.

[0004] Force control technology, a key technology in robotic belt grinding, is used to control the normal contact force between the abrasive belt and the workpiece. The surface roughness and material removal depth of the blade after grinding are closely related to the normal contact force. Zhu Dahu et al. proposed a force control strategy for robotic blade grinding. They compared and analyzed the changing trends of blade surface roughness with and without force control. The study showed that the normal contact force has a significant impact on the surface roughness and dimensional accuracy of the blade after grinding. Yan Sijie et al. analyzed the relationship between material removal depth and normal contact force during grinding and found that the change in normal contact force during the cut-in / cut-out phase causes overcutting / undercutting on the workpiece surface, affecting the final surface quality of the workpiece. Xu Xiaohu et al. considered the elastic deformation of the contact wheel and the workpiece and the change in blade curvature and proposed an improved residual height model to evaluate the surface roughness of the blade grinding process. The study showed that different process parameters have different effects on the blade surface roughness. These works studied the effect of normal contact force on surface roughness or material removal depth, but few literature considers how to ensure the consistency of surface roughness and material removal depth when the normal contact force changes during grinding. Summary of the Invention

[0005] Based on the above background, the purpose of the present invention is to provide a method for adaptively adjusting grinding process parameters based on the change of normal contact force, which is used to improve the problems of blade roughness and inconsistent material removal rate during complex surface grinding, thereby improving the blade surface dimensional accuracy, overall engine performance, and engine life.

[0006] This paper proposes a method for adaptively adjusting parameters in robotic belt grinding based on variations in normal contact force. First, an orthogonal center coordinate combination (CCD) experiment is designed, and a depth-based partial least squares algorithm is used to establish a predictive model linking grinding process parameters with surface roughness and material removal depth. Second, the predictive model of normal contact force, surface roughness, and material removal depth measured by sensors is combined with an improved Archimedean optimization algorithm to determine the adaptive process parameters. This method ensures consistency in surface roughness and material removal depth during robotic belt grinding, even with variations in normal contact force.

[0007] The method for adaptively adjusting the parameters of a robot belt grinding according to the present invention comprises the following steps:

[0008] Step 1: Design a Cross-Central Composite (CCD) Experiment

[0009] In the orthogonal center combination (CCD) test, the main process parameters affecting the surface roughness and material removal depth in robotic belt grinding include: belt linear speed vs (m / s), feed speed vf (mm / s), normal contact force Fn (N), belt grit P (#), etc. Based on the single-factor experimental design, a 4-factor 3-level orthogonal center combination table was used for the test. Five points were measured in the direction perpendicular to the grinding path and the average value was taken as the final surface roughness Ra; the depth value h (mm) at three points on the grinding path was measured and the average value was taken as the material removal depth MRD;

[0010] Step 2: Use the deep partial least squares algorithm to establish a prediction model of grinding process parameters, surface roughness and material removal depth

[0011] Use the data obtained in step 1 to train the deep partial least squares model and establish a prediction model for process parameters, surface roughness, and material removal depth. Use process parameters (P, Fn, vs, vf) as the input array of the deep partial least squares model, and surface roughness Ra and material removal depth MRD as the output array of the model.

[0012] Step 3: Construct the improved Archimedean optimization algorithm (NSAOA). The specific implementation process is as follows:

[0013] (1) Initialize the population: Randomly generate the initial position x of each individual in the current population P in the search space of the objective function i , individual density den i Volume i , and acceleration acc i , the initial value calculation method is repeated as follows:

[0014] P i,j =low j +rand(up j -low j )

[0015] Where i = 1, 2, 3, ..., N, N is the number of populations, j = 1, 2, ..., D, D is the dimension of the independent variable of the function to be sought, up j and low j They represent the preset x i 、den i 、vol i 、acc i The maximum and minimum values ​​in the constraint range, rand is a random number randomly distributed in [0,1];

[0016] (2) Self-update: At the beginning of each iteration, the density and volume of the current individual are randomly updated. The update formula is as follows:

[0017] den i t+1 =den i t+1 +rand(den best -den i t )

[0018] vol i t+1 =vol i t+1 +rand(vol best -vol i t )

[0019] where den i t+1 and vol i t+1 represents the density and volume of the i-th individual at the t+1th iteration.

[0020] (3) Calculation of migration factor and density factor: AOA is divided into two stages: global search and local development, depending on whether the objects immersed in the fluid collide. The migration factor TF is mainly used to switch between the global search stage and the local development stage. Its calculation method is as follows:

[0021]

[0022] Where t is the current iteration number, t max is the maximum number of iterations, exp represents the exponential function with e as the base, and TF will gradually increase to 1 as the number of iterations increases. t+1 is a density factor that decreases with the increase of the number of iterations. It can help transition from the global search phase to the local development phase. It is calculated as follows:

[0023]

[0024] (4) Search and development phase: When TF≤0.5, it indicates that a collision has occurred between objects. A global search is performed and a body Mr is randomly selected. The individual acceleration is updated as follows:

[0025]

[0026] where den Mr 、vol Mr and acc Mr To randomly select the density, volume and acceleration of an individual. When TF>0.5, there is no collision between objects, local development is performed, and the individual acceleration is updated as follows:

[0027]

[0028] where den best 、vol best and acc best is the density, volume and acceleration of the current optimal individual. In addition, the acceleration is normalized:

[0029]

[0030] Where u and l are constants 0.9 and 0.1;

[0031] (5) Optimal neighborhood perturbation strategy: The optimal neighborhood perturbation strategy is introduced to increase the search for nearby areas, helping the algorithm to escape the local optimum during global search. The process of neighborhood perturbation of the optimal position is as follows:

[0032]

[0033] in is the position generated after perturbation, x t is the updated individual position after global search, r1, r2 are random numbers between 0 and 1. At the same time, for the neighborhood position after disturbance, a greedy algorithm is needed to determine whether the result needs to be retained. The calculation process of the greedy algorithm is as follows:

[0034]

[0035] in is the optimal position obtained by the greedy algorithm, and f(x) is the fitness value corresponding to the x position;

[0036] (6) Individual position update: When TF <= 0.5, it is in the search phase, and when TF > 0.5, it is in the development phase. An individual Mr is randomly selected, and the individual position is updated as follows:

[0037]

[0038] Where T = c3 × TF, p = 2 × rand - c4, c1, c2, c3, and c4 are fixed constants. F is the direction factor used to determine the iterative position update. When p ≤ 5, F is 1, and when p > 0.5, F is -1.

[0039] (7) Stagnation perturbation strategy: A stagnation perturbation strategy based on Lévy flight is introduced to perturb the population position in order to expand the search area and increase the diversity of the population. The method for generating a random step size s that obeys the Lévy distribution is as follows:

[0040]

[0041] Among them, u and v obey the normal distribution. v~N(0,1), and:

[0042]

[0043] When the fitness value of the historical optimal position in the group does not change for five consecutive iterations, it means that the search has stagnated. At this time, the Lévy flight strategy is used to perturb the position of individuals in the group to help the algorithm jump out of the local optimum. The individual update method of the stagnant perturbation strategy based on Lévy flight is as follows:

[0044]

[0045] Where α is the scale factor, rn represents a random number that obeys the standard normal distribution;

[0046] (8) Save the optimal fitness value: Use the objective function to evaluate and select the position x of the individual with the optimal fitness in the current iteration best 、densityden best Volume best and acceleration acc best ;

[0047] Step 4: Establish a target optimization function that meets the grinding requirements. The specific function is as follows:

[0048] Min(f)=K1(y Ra -E Ra ) 2 +K2(y MRD -E MRD ) 2

[0049] Among them E Ra and E MRD is the desired surface roughness and material removal depth, y MRD and y Ra This is the prediction result of the material removal depth and surface roughness prediction model established by the deep partial least squares algorithm. K1 and K2 are the weight coefficients of surface roughness and material removal depth, respectively. K1 and K2 are limited to between 0 and 1, and their sum is 1. The higher the weight coefficient, the closer the requirements of the relevant items are to the expectations.

[0050] Step 5: Use the improved Archimedean optimization algorithm to calculate the optimal result curve of each process parameter under different normal contact forces. The specific optimization steps are described as follows:

[0051] ① Read training data and test data and normalize them;

[0052] ② Determine the search range of the four parameters P, Fn, vs, and vf, and randomly initialize the initial positions of the process parameters P, Fn, vs, and vf in the solution space;

[0053] ③ Input each individual in the population into the deep partial least squares model trained in step 2 to obtain the surface roughness Ra and material removal depth MRD values ​​corresponding to each individual;

[0054] ④ Calculate the fitness value of each individual in the current population of NSAOA through the optimization function established in step 4, and record the position x of the individual with the best fitness best 、densityden best Volume best and acceleration acc best ;

[0055] ⑤ Repeat the steps ③ and ④ according to the NSAOA algorithm and iterate continuously to finally obtain the optimal process parameter value under the current normal vector force;

[0056] ⑥ Repeat process ⑤ for different grinding method normal vector contact forces, and plot the data results into a function curve to guide the changes of various process parameters during actual grinding.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] (1) Based on the orthogonal central composite test with 4 factors and 3 levels, a prediction model of grinding process parameters, surface roughness and material removal depth was established using the deep partial least squares algorithm. The determination coefficient of the regression model showed that the model had high prediction accuracy.

[0059] (2) The NSAOA algorithm is used to solve the adaptive process parameter change curve that ensures the consistency of material removal depth and surface roughness when the normal contact force changes. Therefore, for areas where the normal contact force is difficult to control, this method can be used to ensure the consistency of surface roughness and material removal depth during the processing process. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flow chart of the entire steps of the present invention.

[0061] Figure 2 It is a schematic diagram of the deep partial least squares model. DETAILED DESCRIPTION

[0062] The present invention will be further illustrated by the following examples.

[0063] Figure 1It is a flowchart of the entire step implementation of the present invention. Data is obtained through orthogonal center combination experiments, and then the projection matrix and prediction matrix are obtained using deep partial least squares method, which are added to the improved Archimedean optimization algorithm process to iterate the optimal model parameters, where max_EFS is the maximum number of iterations, Fn is the current normal contact force, which will increase automatically with each cycle, and Fn_max is the set upper limit of the polishing contact force, so that the optimal parameters under different forces can be obtained.

[0064] Step 1: Design an orthogonal central combination (CCD) experiment. The specific process is as follows:

[0065] The robotic grinding system consists of an industrial robot and control cabinet, a six-dimensional force sensor, a belt sander and 3M Jinta sanding belts, a test workpiece and a fixture. The industrial robot is model HSR-JR605, with a rated load of 5kg, a maximum working radius of 746mm, and a repeatability of ±0.02mm. An HPS-FT060E six-dimensional force sensor is installed at the end of the robot to sense the contact force during the blade grinding and polishing process. The force sensor has an XY-axis force measurement range of ±600N and an accuracy of ±0.2N, and a Z-axis force measurement range of ±1000N and an accuracy of ±0.4N. The belt sander is model HS-R10-2600, with a power of 2.2KW and a maximum linear speed of 3 The speed is 0 m / s. The contact wheel diameter and width are 60 mm and 10 mm, respectively. The inner layer of the contact wheel is composed of a 50 mm diameter aluminum core and an outer layer of 5 mm thick, HRC3035 hardness rubber. The belt tension is precisely adjusted by a pressure valve. The abrasive is a pyramid-shaped abrasive belt made of 237AA alumina sand from 3M Company in the United States. This type of abrasive belt offers high cutting efficiency and low grinding temperatures, ensuring excellent grinding results. The workpiece material is TC11 (Ti-6.5Al-3.5Mo-1.5Zr0.3Si) titanium alloy, widely used in the aviation industry for its excellent oxidation resistance at high temperatures and hot and cold working properties.

[0066] In the orthogonal center combination (CCD) test, the main process parameters affecting the surface roughness and material removal depth in robotic belt grinding are: belt linear speed vs (m / s), feed speed vf (mm / s), normal contact force Fn (N), belt particle size P (#), etc. According to the single-factor experimental design, a 4-factor 3-level orthogonal center combination table was used and the experiment was carried out. The surface roughness of the workpiece was measured with a Mitutoyo (SJ210) surface roughness meter. The sampling length in the measurement was 0.8mm and the evaluation length was 4mm. Five points were measured in the direction perpendicular to the grinding path and the average value was taken as the final surface roughness Ra; the grinding depth of the workpiece was measured with a Keyence (LJ-X8020) line laser sensor. The measurement accuracy of the line laser sensor in the Z direction is 2.5um. The depth values ​​h (mm) of three points on the grinding path were measured and the average was taken as the material removal depth MRD. Through orthogonal center combination experiments, the horizontal distribution of each grinding factor is as follows: abrasive belt particle size 120#, 180#, 240#, normal contact force 10N, 15N, 20N, abrasive belt linear speed 4m / s, 7m / s, 10m / s, feed speed 3mm / s, 6mm / s, 9mm / s, and finally 30 sets of different data were obtained.

[0067] Step 2: Use the deep partial least squares algorithm to establish a prediction model of grinding process parameters, surface roughness and material removal depth. The specific process is as follows:

[0068] The 30 sets of data obtained in step 1 are used to train the deep partial least squares model and establish a prediction model for process parameters, surface roughness, and material removal depth. During the training process, the 30 sets of process parameters (P, Fn, vs, vf), surface roughness Ra, and material removal depth MRD are used as input arrays for the deep partial least squares model. After all projection matrices and prediction matrices are determined, the training is completed. Next, the process parameters (P, Fn, vs, vf) are input to obtain the corresponding prediction results.

[0069] Figure 2 is a schematic diagram of the deep partial least squares model. represents a dataset of observed variables, and is the predictor variable dataset, where n is the sample size, m is the number of observed variables, and d is the number of predictor variables. Figure 2 middle represents the output of the first nonlinear mapping layer. Let φ represent This is a nonlinear mapping method that maps X to a high-dimensional nonlinear space H (1) =φ(X). During the training phase, the output of the nonlinear mapping layer is trained by partial least squares. and predictor variables [y1,y2,…,y m] to conduct cross-modeling. The main step of cross-modeling is to find Map to The projection matrix And the prediction matrix using U to predict Y It is worth noting that k1 should not be greater than the rank of X. The final output of the first layer is The same steps are followed to increase the depth of the model. In a deep PLS model, the final estimate of Y is determined only by the top layer (i.e. Figure 2 The latent variable prediction of the prediction layer on the right.

[0070] Step 3: Construct the improved Archimedean optimization algorithm (NSAOA). The specific implementation process is as follows:

[0071] (1) Initialize the population: Randomly generate the initial position x of each individual in the current population P in the search space of the objective function i , individual density den i Volume i , and acceleration acc i , the initial value calculation method is repeated as follows:

[0072] P i,j =low j +rand(up j -low j )

[0073] Where i = 1, 2, 3, ..., N, N is the number of populations, j = 1, 2, ..., D, D is the dimension of the independent variable of the function to be sought, up j and low j They represent the preset x i 、den i 、vol i 、acc i The maximum and minimum values ​​in the constraint range, rand is a random number randomly distributed in [0,1];

[0074] (2) Self-update: At the beginning of each iteration, the density and volume of the current individual are randomly updated. The update formula is as follows:

[0075] den i t+1 =den i t+1 +rand(den best -den i t )

[0076] vol i t+1 =voli t+1 +rand(vol best -vol i t )

[0077] where den i t+1 and vol i t+1 represents the density and volume of the i-th individual at the t+1th iteration.

[0078] (3) Calculation of migration factor and density factor: AOA is divided into two stages: global search and local development, depending on whether the objects immersed in the fluid collide. The migration factor TF is mainly used to switch between the global search stage and the local development stage. Its calculation method is as follows:

[0079]

[0080] Where t is the current iteration number, t max is the maximum number of iterations, exp represents the exponential function with e as the base, and TF will gradually increase to 1 as the number of iterations increases. t+1 is a density factor that decreases with the increase of the number of iterations. It can help transition from the global search phase to the local development phase. It is calculated as follows:

[0081]

[0082] (4) Search and development phase: When TF≤0.5, it indicates that a collision has occurred between objects. A global search is performed and a body Mr is randomly selected. The individual acceleration is updated as follows:

[0083]

[0084] where den Mr 、vol Mr and acc Mr To randomly select the density, volume and acceleration of an individual. When TF>0.5, there is no collision between objects, local development is performed, and the individual acceleration is updated as follows:

[0085]

[0086] where den best 、vol best and acc best is the density, volume and acceleration of the current optimal individual. In addition, the acceleration is normalized:

[0087]

[0088] Where u and l are constants 0.9 and 0.1;

[0089] (5) Optimal neighborhood perturbation strategy: The optimal neighborhood perturbation strategy is introduced to increase the search for nearby areas, helping the algorithm to escape the local optimum during global search. The process of neighborhood perturbation of the optimal position is as follows:

[0090]

[0091] in is the position generated after perturbation, x t is the updated individual position after global search, r1, r2 are random numbers between 0 and 1. At the same time, for the neighborhood position after disturbance, a greedy algorithm is needed to determine whether the result needs to be retained. The calculation process of the greedy algorithm is as follows:

[0092]

[0093] in is the optimal position obtained by the greedy algorithm, and f(x) is the fitness value corresponding to the x position;

[0094] (6) Individual position update: When TF <= 0.5, it is in the search phase, and when TF > 0.5, it is in the development phase. An individual Mr is randomly selected, and the individual position is updated as follows:

[0095]

[0096] Where T = c3 × TF, p = 2 × rand - c4, c1, c2, c3, and c4 are fixed constants. F is the direction factor used to determine the iterative position update. When p ≤ 5, F is 1, and when p > 0.5, F is -1.

[0097] (7) Stagnation perturbation strategy: A stagnation perturbation strategy based on Lévy flight is introduced to perturb the population position in order to expand the search area and increase the diversity of the population. The method for generating a random step size s that obeys the Lévy distribution is as follows:

[0098]

[0099] Among them, u and v obey the normal distribution. v~N(0,1), and:

[0100]

[0101] When the fitness value of the historical optimal position in the group does not change for five consecutive iterations, it means that the search has stagnated. At this time, the Lévy flight strategy is used to perturb the position of individuals in the group to help the algorithm jump out of the local optimum. The individual update method of the stagnant perturbation strategy based on Lévy flight is as follows:

[0102]

[0103] Where α is the scale factor, rn represents a random number that obeys the standard normal distribution;

[0104] (8) Save the optimal fitness value: Use the objective function to evaluate and select the position x of the individual with the optimal fitness in the current iteration best 、densityden best Volume best and acceleration acc best ;

[0105] Step 4: Design the optimization objective function according to the grinding requirements. The specific function is as follows:

[0106] Min(f)=K1(y Ra -E Ra ) 2 +K2(y MRD -E MRD ) 2

[0107] Among them E Ra and E MRD For the desired surface roughness and material removal depth, the values ​​are set to 0.69 and 0.059 mm in this example. MRD and y Ra This is the output of the material removal depth and surface roughness prediction model established using the deep partial least squares algorithm. K1 and K2 are weight coefficients for surface roughness and material removal depth, respectively. K1 and K2 are limited to between 0 and 1, and their sum is 1. A higher weight coefficient indicates that the requirements of the relevant items are closer to the expected value. Different correlation coefficient ratios can be set for different stages of the grinding process, such as rough grinding, semi-finishing grinding, and finishing grinding. In this example, K1 and K2 are set to 0.1 and 0.9, respectively, to balance the requirements of the finishing stage.

[0108] Step 5: Use the improved Archimedean optimization algorithm to calculate the optimal result curve of each process parameter under different normal contact forces. The specific optimization steps are described as follows:

[0109] ① Read training data and test data and normalize them;

[0110] ② Determine the search range of the four parameters P, Fn, vs, and vf, and randomly initialize the initial positions of the process parameters P, Fn, vs, and vf as well as 50 groups of density, volume, and acceleration in the solution space;

[0111] ③ Input each individual in the population into the deep partial least squares model trained in step 2 to obtain the surface roughness Ra and material removal depth MRD values ​​corresponding to each individual;

[0112] ④ Evaluate the fitness value of each individual in the contemporary NSAOA population through the optimization function established in step 4, and select the individual with the best fitness;

[0113] ⑤ Repeat the steps ③ and ④ according to the NSAOA algorithm for 1000 times to finally obtain the optimal process parameter value under the current normal vector force;

[0114] ⑥Fix the normal vector contact force and repeat process ⑤ from 10N to 20N with a step size of 0.1N. Plot the data results into a function curve to guide the changes of various process parameters during actual grinding.

[0115] The above description merely represents the preferred embodiments of the present invention, and while the description is relatively specific and detailed, it should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make various modifications, improvements, and substitutions without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A method for adaptively adjusting grinding process parameters based on changes in normal contact force, characterized by: The following steps are involved: Step 1: Design orthogonal central combination test: The main process parameters affecting surface roughness and material removal depth in robotic belt grinding in the orthogonal center combination test are: belt linear speed vs, feed speed vf, normal contact force Fn, and belt grit P. Based on the single-factor experimental design, a 4-factor 3-level orthogonal center combination table was used for the test. Five points were measured perpendicular to the grinding path and the average value was taken as the final surface roughness Ra. The depth value h at three points on the grinding path was measured and the average value was taken as the material removal depth MRD. Step 2: Use the deep partial least squares algorithm to establish a prediction model of grinding process parameters, surface roughness and material removal depth: The data obtained in step 1 are used to train the depth partial least squares model, and a prediction model of process parameters, surface roughness and material removal depth is established. 、 、 Surface roughness Ra and material removal depth MRD are used as input arrays of the depth partial least squares model. After all projection matrices and prediction matrices are solved, the predicted values ​​of surface roughness Ra and material removal depth MRD can be obtained by inputting process parameters. Step 3: Design the optimization objective function according to the grinding requirements. The specific function is as follows: ； in and For the desired surface roughness and material removal depth, and Output of the material removal depth and surface roughness prediction model established by the deep partial least squares algorithm. and is the weight coefficient of surface roughness and material removal depth, where The value is limited to 0-1 and the sum is 1; Step 4: Use the improved Archimedean optimization algorithm NSAOA to calculate the optimal result curve of each process parameter under different normal contact forces; The specific steps of step 4 optimization are described as follows: ① Read training data and test data and normalize them; ②Determine P, 、 、 The search range of the four parameters, randomly initialize the process parameters P, 、 、 The initial position of ③ Input each individual in the population into the deep partial least squares model trained in step 2 to obtain the surface roughness Ra and material removal depth MRD values ​​corresponding to each individual; ④ Using the optimization function established in step 3, calculate the fitness value of each individual in the current population of NSAOA and record the position of the individual with the best fitness. ,density ,volume and acceleration ; ⑤ Repeat the steps ③ and ④ according to the improved Archimedean optimization algorithm and iterate continuously to finally obtain the optimal process parameter value under the current normal vector force; ⑥ Repeat process ⑤ for different grinding method normal vector contact forces, and plot the data results into a function curve to guide the changes of various process parameters during actual grinding; Improving the Archimedean optimization algorithm includes the following steps: Step 1: Initialize the population: Randomly generate the initial position x of each individual in the current population P in the search space of the objective function i , individual density den i Volume i , and acceleration acc i , the initial value calculation method is repeated as follows: ； Where i=1,2,3,…,N, N is the number of populations, j=1,2,…,D, D is the dimension of the independent variable of the function to be sought, and They represent the preset 、 、 、 The maximum and minimum values ​​in the constraint range, rand is a random number randomly distributed in [0,1]; Step 2: Self-update: At the beginning of each iteration, the density and volume of the current individual are randomly updated. The update formula is as follows: ； ； in and Indicates the Iteration No. Density and volume of individual entities; Step 3: Calculate the migration factor and density factor: AOA is divided into two stages: global search and local development according to whether the objects immersed in the fluid collide. The migration factor It is mainly used to switch between the global search phase and the local development phase. Its calculation method is as follows: ； in is the current iteration number, is the maximum number of iterations, exp represents the exponential function with e as the base, It will gradually increase to 1 as the number of iterations increases. is the density factor, which decreases with the increase of the number of iterations and helps to transition from the global search phase to the local development phase. It is calculated as follows: ； Step 4: Search and development phase: When TF ≤ 0.5, it indicates that a collision has occurred between objects. A global search is performed. At this time, a body Mr is randomly selected and the individual acceleration is updated as follows: ； in 、 and To randomly select the density, volume, and acceleration of an individual, when TF > 0.5, there is no collision between objects, and local development is performed. The update of the individual acceleration is as follows: ； in 、 and is the density, volume and acceleration of the current optimal individual. In addition, the acceleration is normalized: ； in and are constants 0.9 and 0.1; Step 5: Optimal Neighborhood Perturbation Strategy: Introduce the optimal neighborhood perturbation strategy to increase the search of nearby areas, helping the algorithm to escape the local optimum during global search. The process of neighborhood perturbation of the optimal position is as follows: ； in is the position generated after perturbation, is the individual position updated after global search, , , is a random number between 0 and 1. At the same time, the greedy algorithm is needed to determine whether the result needs to be retained for the disturbed neighborhood position. The calculation process of the greedy algorithm is as follows: ； in is the optimal position obtained by the greedy algorithm, for The fitness value corresponding to the position; Step 6: Individual position update: When TF <= 0.5, it is in the search phase, and when TF > 0.5, it is in the development phase. A random individual Mr is selected, and the individual position is updated as follows: ； in , , 、 、 ,and is a fixed constant, F is the direction factor used to determine the iterative position update, when hour for , When F is ; Step 7: Stagnation perturbation strategy: Introduce the stagnation perturbation strategy based on Lévy flight to perturb the population position in order to expand the search area and increase the diversity of the group. The method to generate a random step size s that obeys the Lévy distribution is as follows: ； in 、 Obey the normal distribution, , ,and: ； When the fitness value of the historical optimal position in the group does not change for five consecutive iterations, it means that the search has stagnated. At this time, the Lévy flight strategy is used to perturb the position of individuals in the group to help the algorithm jump out of the local optimum. The individual update method of the stagnant perturbation strategy based on Lévy flight is as follows: ； in is the scale factor, represents random numbers that follow a standard normal distribution; Step 8: Save the optimal fitness value: Use the objective function to evaluate and select the position of the individual with the best fitness in the current iteration ,density ,volume and acceleration .

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