A method for optimizing multi-objective process parameters of abrasive belt grinding based on improved NSGA-II algorithm

Abstract

The application discloses a kind of based on the improved NSGA-II algorithm abrasive belt grinding multi-objective process parameter optimization method, first establish the mathematical model of carbon emission, surface roughness and material removal rate of abrasive belt grinding process, then according to the improved NSGA-II algorithm multi-objective optimization model is established, and using the improved NSGA-II algorithm multi-objective optimization is realized the intelligent optimization of process parameter of grinding process.The method of the application fully considers the mutual influence between each process parameter in the process of abrasive belt grinding difficult-to-machine material, the improved NSGA-II algorithm proposed uses new sequencing method, improves the population diversity of algorithm, so that the algorithm has better solution set uniformity, and the searching ability of improved NSGA-II to global optimal solution is stronger, under the same condition, the number of Pareto optimal solution of improved NSGA-II algorithm is more than NSGA-II and MOPSO algorithm, which means that improved NSGA-II algorithm can find out better global optimal solution.

Description

Technical Field

[0001] This invention belongs to the field of mechanical manufacturing technology, specifically relating to a method for optimizing multi-objective process parameters in belt grinding based on an improved NSGA-II algorithm. Background Technology

[0002] Titanium alloys, nickel-based alloys, and other difficult-to-machine materials are key components of crucial core parts in aerospace propulsion systems, and their machining quality significantly impacts engine performance and lifespan. Due to their low thermal conductivity and low elastic modulus, these materials have high specific grinding energy. The grinding process not only involves substantial carbon emissions from energy consumption and pollution, but also, because of their low thermal conductivity, grinding heat is difficult to dissipate, easily generating extremely high localized instantaneous temperatures, which can burn the surface of the parts. Furthermore, the production volume of typical parts such as titanium alloy blades is enormous. Therefore, finding reasonable process parameters for low-carbon, high-efficiency grinding of these parts is crucial. Solving these problems is of significant value for energy conservation and emission reduction for relevant manufacturing enterprises. In the belt grinding process of these difficult-to-machine alloy materials, selecting appropriate grinding process parameters can effectively improve machining quality and reduce carbon emissions. However, belt grinding of these alloys is a complex process, and different process parameters (belt linear speed, workpiece feed rate, and depth of cut) will have different effects on the target values ​​(carbon emissions, surface roughness, and material removal rate) of the alloy grinding process. Typically, due to the interaction between different process parameters, it is difficult to simultaneously optimize all target values ​​of the grinding process; achieving the optimal value for one target often comes at the expense of deterioration in other target values. Therefore, optimizing multi-objective process parameters in belt grinding is crucial.

[0003] CN113919101A discloses a method for optimizing process parameters in ball-end grinding wheel machining based on response surface methodology and particle swarm optimization (PSO). The method employs response surface methodology to conduct grinding experiments on the workpiece and uses the experimental data to establish mathematical models for workpiece surface roughness and material removal rate. These mathematical models are then used as objective functions, and the PSO algorithm is employed to find the global optimum, yielding the optimal grinding process parameters. This method reduces the surface roughness of the machined workpiece while improving machining efficiency. However, this method only has two objective functions: surface roughness and material removal rate. The optimization effect on higher-dimensional objectives needs further verification. Furthermore, the PSO multi-objective optimization algorithm is prone to premature convergence and getting trapped in local optima, resulting in poor multi-objective optimization performance. CN114995319A discloses a method for optimizing process parameters in camshaft surface grinding quality control. Using surface roughness and material removal rate as optimization objectives, a second-generation non-dominated fast sorting genetic algorithm is used to find the optimal combination of process parameters, improving both surface grinding quality and machining efficiency. The drawback of this method is that although the second-generation non-dominated fast sorting genetic algorithm introduces a crowding-based sorting selection method to improve the uniformity of the solution set, this selection method deletes all individuals with high crowding at once, resulting in poor population diversity and requiring further improvement in optimization performance. CN113065630A discloses a method for optimizing process parameters in belt grinding, aiming at machining accuracy and efficiency, and achieving intelligent optimization of belt grinding process parameters. The NSGA-II algorithm is an improved version of NSGA proposed by Deb et al. in 2000. NSGA-II adopts fast non-dominated sorting and a crowding distance strategy. Due to its advantages in speed and effectiveness, it is widely used in engineering strategy optimization. The existing NSGA-II algorithm selects individuals from the last layer of non-dominated solutions in the parent generation to enter the offspring generation based on crowding distance, deleting all individuals with small crowding distances at once, resulting in an uneven distribution of the solution set and low population diversity.

[0004] The above methods only consider the optimization of two objective parameters and do not take into account the impact of process parameters on carbon emissions during grinding. In addition, the optimization effect of multi-objective optimization algorithms needs to be improved. Summary of the Invention

[0005] To address the aforementioned technical problems and improve the optimization effect of multi-objective process parameters in belt grinding, this invention proposes a multi-objective process parameter optimization method for belt grinding based on an improved NSGA-II algorithm. This method can effectively reduce carbon emissions generated by titanium alloy blades during the grinding process while ensuring that the material removal rate and surface roughness remain unchanged, thereby achieving the goal of high efficiency and low carbon emissions for belt grinding of difficult-to-machine materials.

[0006] The technical solution adopted in this invention is: a method for optimizing multi-objective process parameters in belt grinding based on an improved NSGA-II algorithm, the specific steps of which are as follows:

[0007] S1. Establish mathematical models for carbon emissions, surface roughness, and material removal rate in the belt grinding process;

[0008] S2. Establish a multi-objective optimization model based on the improved NSGA-II algorithm;

[0009] S3. Using the improved NSGA-II algorithm for multi-objective optimization, intelligent optimization of process parameters in the grinding process is achieved.

[0010] Furthermore, step S1 is specifically as follows:

[0011] S11. Establish a carbon emission model;

[0012] The carbon emissions from belt grinding of titanium alloy blades can be categorized into three main sources: resource consumption, processing, and waste disposal. These three sources respectively generate carbon emissions from material consumption, electricity consumption, and waste disposal.

[0013] Carbon emissions from material consumption :

[0014] (1)

[0015] in, , These represent the mass of grinding fluid and abrasive belt consumed during the grinding process, respectively. , These represent the carbon emission factors of the production of grinding fluid and abrasive belt, respectively.

[0016] Power plants generate carbon emissions during the process of producing electricity. The corresponding carbon emission values ​​are obtained based on the local electricity emission factor.

[0017] (2)

[0018] in, This indicates the carbon emissions indirectly generated during the grinding process. This represents the electrical energy consumed by the machine tool during the grinding process. This indicates the region's electricity emission factor.

[0019] The working states of a belt grinding machine can be divided into three states: startup, no-load, and cutting. These three states constitute one grinding cycle. The power of the machine tool in each of the three working states is denoted as the machine tool startup power. Machine tool no-load power Machine tool cutting power Analyzing the power composition of a grinding machine tool during cutting, we can conclude that:

[0020] (3)

[0021] in, This represents the effective grinding power. The electrical energy consumed by the machine tool in one grinding cycle can be calculated as follows:

[0022] (4)

[0023] in, , , These represent the running time of the machine tool in the start-up state, no-load state, and cutting state, respectively. This represents one grinding cycle. This indicates the power loss due to the additional load. This represents the time-dependent variable of machine tool operation. In actual machining processes, it refers to the machine tool's starting power during each machining cycle. Machine tool no-load power Additional load power loss It is essentially constant and can be measured by a power meter. Effective cutting power. It can be obtained from equation (5):

[0024] (5)

[0025] in, Indicates the tangential grinding force of the abrasive belt. This indicates the linear velocity of the abrasive belt. The value needs to be obtained by constructing a belt grinding force model:

[0026] (6)

[0027] in, Indicates the workpiece feed rate. Represents the proportionality coefficient. Indicates the depth of grinding. This indicates the contact area between a single abrasive grain and the workpiece. This represents the average contact strength between the abrasive grains and the workpiece, and its magnitude is directly proportional to the material hardness. This represents the dynamic friction coefficient between the workpiece and the abrasive grains. This represents the static grinding ratio coefficient. Indicates the static grinding coefficient. This indicates the diameter of the abrasive belt wheel.

[0028] Equation (7) represents the carbon emissions generated from waste treatment:

[0029] (7)

[0030] in, Indicates the quality of titanium alloy grinding chips. This indicates the carbon emission factor of recycled titanium alloy grinding debris. This indicates the quality of the grinding fluid waste. This indicates the carbon emission factor of recycled grinding fluid waste. Indicates the quality of the discarded sand belt. This indicates the carbon emission factor of the waste sand belt.

[0031] In summary, based on equations (1), (2), and (7), the total carbon emissions from the grinding of titanium alloy blades using abrasive belts can be calculated. The model:

[0032] (8)

[0033] S12. Establish a surface roughness model;

[0034] Surface roughness is modeled and quantified. After considering the influencing factors in the grinding process, the relationship between grinding process parameters and surface roughness is obtained. The empirical formula between them is shown in equation (9), from which the surface roughness model can be obtained:

[0035] (9)

[0036] in, The constant is obtained by substituting the experimental data into equation (9), and the actual roughness is measured by a surface roughness measuring instrument.

[0037] S13. Establish a material removal rate model;

[0038] The material removal rate (MRR) in grinding processes can be obtained from the workpiece feed rate and grinding depth, resulting in a material removal rate model:

[0039] (10)

[0040] Furthermore, step S2 is specifically as follows:

[0041] S21. Improved NSGA-II algorithm;

[0042] When selecting individuals from the last layer of non-dominated solutions to enter the next generation, the solution space is divided into several congruent triangles. The positions of the non-dominated solutions are determined and marked in the corresponding triangles. After all non-dominated solutions are assigned to the triangles, they are sorted according to the number of non-dominated solutions in each triangle region. The specific process is as follows:

[0043] Let the origin be a point, and shift the values ​​of each objective function so that the minimum value of the objective function lies at the origin, and then normalize the values ​​of each objective function:

[0044] (11)

[0045] in, Represents a vector of decision variables. Represents the objective function value. This represents the minimum value of the objective function in the solution set. This represents the maximum value of the objective function in the solution set, which yields the normalized objective function value. .

[0046] After normalization, the solution space is obtained, and the values ​​of the objective function will all fall within the first quadrant of the coordinate axes. , , Connecting three points forms a triangle, which is then divided into several congruent triangles, each numbered. Solutions to the objective function will fall into these triangles. The triangles are sorted by the number of solutions to the objective function within each triangle. The selection rules for advancing the next generation of the appropriate population are as follows:

[0047] Sort the triangular regions according to the sparse to dense distribution of solutions within them, and then sequentially select individuals according to the sorting priority. Each time, select one individual from each triangular region to enter the next generation population, and then remove that individual from the triangular region. Repeat this process until the number of individuals in the next generation population reaches the required number of individuals in the next generation population.

[0048] S22. Establish a multi-objective optimization model;

[0049] Multi-objective optimization of the belt grinding process for titanium alloy blades aims to minimize carbon emissions per unit time, minimize surface roughness, and maximize grinding efficiency, with belt linear speed as the primary factor. Workpiece feed rate Grinding depth These are decision variables.

[0050] Constraints are imposed on decision variables in multi-objective optimization models:

[0051] (12)

[0052] in, These represent the minimum values ​​of the belt linear speed, workpiece feed rate, and grinding depth, respectively. These represent the maximum values ​​of the belt linear speed, workpiece feed speed, and grinding depth, respectively.

[0053] In summary, the multi-objective optimization model for belt grinding of titanium alloy blades is as follows:

[0054] (13)

[0055] in, This represents the optimal solution of the optimization function. , , The three objective functions are carbon emissions, surface roughness, and material removal rate.

[0056] Furthermore, step S3 is specifically as follows:

[0057] S31. Comparison of solution set uniformity;

[0058] The improved NSGA-II, NSGA-II, and MOSPO algorithms were used to solve the problem, and the results of the three algorithms were compared to verify the effectiveness of the improved NSGA-II algorithm in solving the multi-objective optimization problem in belt grinding. The parameters of the three algorithms were set, and the population size was [value missing]. The maximum number of iterations is .

[0059] First, initialize the population by randomly generating populations within a set range. The algorithm iterates through the population of individuals, using a normal distribution to generate offspring through crossover, randomly selecting mutated gene loci, calculating the objective function value using the existing individuals, sorting the objective function values ​​accordingly, and then selecting individuals to enter the next generation population. This process is repeated until the number of iterations is reached, and finally the optimal process parameters corresponding to the objective are obtained from the solution set of the algorithm.

[0060] The uniformity of the solution set distribution of each algorithm is evaluated using the spatial evaluation index SP proposed by Schott. The calculation formula is as follows:

[0061] (14)

[0062] in, Represents an individual To other individuals The minimum sum of the differences of distances in corresponding dimensions is used to find the distance in space. Recent individual ,and . Representing different objective functions, , Let represent the objective functions corresponding to individuals in the population. Indicates all The average value, Indicates population size, This indicates the number of optimization objectives.

[0063] S32. Comparison of optimization results;

[0064] The improved NSGA-II algorithm, the NSGA-II algorithm, and the MOSPO algorithm were used to optimize the process parameters of the titanium alloy belt grinding process, and the results were compared with those before optimization to verify the improvement effect of the improved NSGA-II algorithm.

[0065] The beneficial effects of this invention are as follows: First, the method of this invention establishes a mathematical model of carbon emissions, surface roughness, and material removal rate in the belt grinding process. Then, based on the improved NSGA-II algorithm, a multi-objective optimization model is established. The improved NSGA-II algorithm is used for multi-objective optimization to achieve intelligent optimization of the grinding process parameters. This invention fully considers the mutual influence between various process parameters in the belt grinding of difficult-to-machine materials. The proposed improved NSGA-II algorithm adopts a new sorting method, improving the population diversity of the algorithm and giving it better solution set uniformity. Furthermore, the improved NSGA-II has a stronger ability to search for the global optimum. Under the same conditions, the improved NSGA-II algorithm has more Pareto optimal solutions than the NSGA-II and MOPSO algorithms, meaning that the improved NSGA-II algorithm can find a better global optimum. Attached Figure Description

[0066] Figure 1 This is a flowchart of a method for optimizing multi-objective process parameters in belt grinding based on an improved NSGA-II algorithm, according to the present invention.

[0067] Figure 2 This is a flowchart of the improved NSGA-II algorithm in an embodiment of the present invention.

[0068] Figure 3 This is a segmentation diagram of the non-dominated solution front of the improved NSGA-II algorithm in an embodiment of the present invention.

[0069] Figure 4 This is the solution space graph of the improved NSGA-II algorithm after normalization in this embodiment of the invention.

[0070] Figure 5 This is a comparison chart of the solution set uniformity between the improved NSGA-II algorithm and the existing NSGA-II / MOPSO algorithm in this embodiment of the invention.

[0071] Figure 6 This is a comparison diagram of the Pareto front solution set distribution between the improved NSGA-II algorithm and the existing NSGA-II / MOPSO algorithm in this embodiment of the invention.

[0072] Figure 7This is a comparison chart of the optimization results of the improved NSGA-II algorithm and the existing NSGA-II / MOPSO algorithm in the embodiments of the present invention. Detailed Implementation

[0073] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0074] like Figure 1 The flowchart of a multi-objective process parameter optimization method for belt grinding based on an improved NSGA-II algorithm is shown below. The specific steps are as follows:

[0075] S1. Establish mathematical models for carbon emissions, surface roughness, and material removal rate in the belt grinding process;

[0076] S2. Establish a multi-objective optimization model based on the improved NSGA-II algorithm;

[0077] S3. Using the improved NSGA-II algorithm for multi-objective optimization, intelligent optimization of process parameters in the grinding process is achieved.

[0078] In this embodiment, step S1 is specifically as follows:

[0079] S11. Establish a carbon emission model;

[0080] In establishing the carbon emission model for titanium alloy belt grinding in this embodiment, the sources and influencing factors of carbon emissions are fully considered. The carbon emission sources generated by belt grinding of titanium alloy blades are divided into three main aspects: resource consumption, processing, and waste disposal. These three parts respectively generate carbon emissions from material consumption, electricity consumption, and waste disposal.

[0081] Carbon emissions from material consumption :

[0082] (1)

[0083] in, , These represent the mass of grinding fluid and abrasive belt consumed during the grinding process, respectively. , These represent the carbon emission factors of the production of grinding fluid and abrasive belt, respectively.

[0084] The grinding process of titanium alloy blades does not directly generate carbon emissions, but rather indirectly generates them by consuming electrical energy. Power plants generate a certain amount of carbon emissions during the production of electricity, and the corresponding carbon emission values ​​can be obtained based on the local electricity emission factor.

[0085] (2)

[0086] in, This indicates the carbon emissions indirectly generated during the grinding process. This represents the electrical energy consumed by the machine tool during the grinding process. This indicates the region's electricity emission factor.

[0087] The working states of a belt grinding machine can be divided into three states: startup, no-load, and cutting. These three states constitute one grinding cycle. The power of the machine tool in each of the three working states is denoted as the machine tool startup power. Machine tool no-load power Machine tool cutting power Analyzing the power composition of a grinding machine tool during cutting, we can conclude that:

[0088] (3)

[0089] in, This represents the effective grinding power. The electrical energy consumed by the machine tool in one grinding cycle can be calculated as follows:

[0090] (4)

[0091] in, , , These represent the running time of the machine tool in the start-up state, no-load state, and cutting state, respectively. This indicates the power loss due to the additional load. This represents the time-dependent variable of machine tool operation. In actual machining processes, it refers to the machine tool's starting power during each machining cycle. Machine tool no-load power Additional load power loss It is essentially constant and can be measured by a power meter. Effective cutting power. It can be obtained from equation (5):

[0092] (5)

[0093] in, Indicates the tangential grinding force of the abrasive belt. This indicates the linear velocity of the abrasive belt. The value is relatively easy to obtain. The value needs to be obtained by constructing a belt grinding force model:

[0094] (6)

[0095] in, Indicates the workpiece feed rate. Represents the proportionality coefficient. Indicates the depth of grinding. This indicates the contact area between a single abrasive grain and the workpiece. This represents the average contact strength between the abrasive grains and the workpiece, and its magnitude is directly proportional to the material hardness. This represents the dynamic friction coefficient between the workpiece and the abrasive grains. This represents the static grinding ratio coefficient. Indicates the static grinding coefficient. This indicates the diameter of the abrasive belt wheel.

[0096] During the belt grinding process of titanium alloys, the titanium alloy is separated from the workpiece in the form of grinding chips. After the grinding process is completed, the grinding chips and grinding fluid waste generated need to be recycled or treated to avoid environmental pollution. The carbon emissions generated in this part are collectively referred to as carbon emissions from waste treatment. The carbon emission value generated from waste treatment is expressed by equation (7):

[0097] (7)

[0098] in, Indicates the quality of titanium alloy grinding chips. This indicates the carbon emission factor of recycled titanium alloy grinding debris. This indicates the quality of the grinding fluid waste. This indicates the carbon emission factor of recycled grinding fluid waste. Indicates the quality of the discarded sand belt. This indicates the carbon emission factor of the waste sand belt.

[0099] In summary, based on equations (1), (2), and (7), the total carbon emissions from the grinding of titanium alloy blades using abrasive belts can be calculated. The model:

[0100] (8)

[0101] S12. Establish a surface roughness model;

[0102] To ensure the surface quality of grinding, surface roughness needs to be modeled and quantified. Many factors influence the surface roughness of ground surfaces, such as grinding parameters, abrasive belt parameters, and the number of strokes in sparkless grinding. After considering these influencing factors during the grinding process, the relationship between grinding process parameters and surface roughness is derived. The empirical formula between them is shown in equation (9), from which the surface roughness model can be obtained:

[0103] (9)

[0104] in, The constant is obtained by substituting the experimental data into equation (9), and the actual roughness is measured by a surface roughness measuring instrument.

[0105] S13. Establish a material removal rate model;

[0106] The material removal rate (MRR) in grinding processes can be obtained from the workpiece feed rate and grinding depth, resulting in a material removal rate model:

[0107] (10)

[0108] In this embodiment, step S2 is specifically as follows:

[0109] S21. Improved NSGA-II algorithm;

[0110] The implementation process of the improved NSGA-II algorithm proposed in this embodiment is as follows: Figure 2 As shown, the following improvements were made compared to the NSGA-II algorithm: A new fitness sharing strategy was proposed, namely, when selecting individuals from the last layer of non-dominated solutions to enter the next generation, the solution space was divided into 25 congruent triangles, as shown below. Figure 3 As shown, the location of non-dominated solutions is determined and marked in the corresponding triangle. After all non-dominated solutions are assigned to the triangles, they are sorted according to the number of non-dominated solutions in each triangle region. Individuals in triangle regions with fewer non-dominated solutions have a higher probability of being selected for the next generation. This effectively improves population diversity and helps the algorithm find the global optimum.

[0111] The specific process is as follows:

[0112] Let the origin be a point, and shift the values ​​of each objective function so that the minimum value of the objective function lies at the origin, and then normalize the values ​​of each objective function:

[0113] (11)

[0114] in, Represents a vector of decision variables. Represents the objective function value. This represents the minimum value of the objective function in the solution set. This represents the maximum value of the objective function in the solution set, which yields the normalized objective function value. .

[0115] After normalization, we get the following: Figure 4 The solution set space is shown. At this point, the values ​​of the objective function will all fall within the first quadrant of this coordinate axis. , , Connecting three points forms a triangle, which is then divided into 25 congruent triangles, each numbered. The solutions to the objective function will fall into these 25 triangles. These triangles can then be sorted by the number of solutions in each triangle. When selecting the appropriate population to advance to the next generation, the selection rules are as follows:

[0116] The triangular regions are sorted from sparse to dense in terms of solution distribution. Individuals are then selected sequentially according to this sorting priority. Each time, an individual is chosen from each triangular region to enter the next generation population, and then removed from the region. This process is repeated until the next generation population reaches the required number of individuals. This operation ensures that individuals from sparsely distributed triangular regions are given high priority for selection into the next generation, thus preventing the algorithm from getting trapped in local optima and improving population diversity.

[0117] S22. Establish a multi-objective optimization model;

[0118] In this embodiment, the multi-objective optimization of the belt grinding process for titanium alloy blades aims to minimize carbon emissions per unit time, minimize surface roughness, and maximize grinding efficiency, with belt linear speed as the primary factor. Workpiece feed rate Grinding depth These are decision variables.

[0119] In actual grinding processes, the selection range of process parameters needs to be determined based on the type of grinding wheel and workpiece, as well as grinding experience. Therefore, in multi-objective optimization models, it is necessary to constrain the decision variables.

[0120] (12)

[0121] in, These represent the minimum values ​​of the belt linear speed, workpiece feed rate, and grinding depth, respectively. These represent the maximum values ​​of the belt linear speed, workpiece feed speed, and grinding depth, respectively.

[0122] In summary, the multi-objective optimization model for belt grinding of titanium alloy blades is as follows:

[0123] (13)

[0124] in, This represents the optimal solution of the optimization function. , , The three objective functions are carbon emissions, surface roughness, and material removal rate.

[0125] In this embodiment, step S3 is specifically as follows:

[0126] S31. Comparison of solution set uniformity;

[0127] The improved NSGA-II, NSGA-II, and MOSPO algorithms were used to solve the problem, and the results of the three algorithms were compared to verify the effectiveness of the improved NSGA-II algorithm in solving the multi-objective optimization problem in belt grinding. In this embodiment, the parameters of the three algorithms are set as follows: population size is 200, and the maximum number of iterations is 60.

[0128] First, the population is initialized by randomly generating 200 individuals within a set range. Then, iteration begins, using a normal distribution for crossover to produce offspring, randomly selecting mutated gene loci. The objective function value is calculated using the existing individuals, and these values ​​are sorted to select individuals for the next generation. This process is repeated until the desired number of iterations is reached. Finally, the optimal process parameters corresponding to the objective are obtained from the algorithm's solution set.

[0129] The uniformity of the solution set distribution of each algorithm is evaluated using the Spacing Metric (SP) proposed by Schott. The calculation formula is as follows:

[0130] (14)

[0131] in, Represents an individual To other individuals The minimum sum of the differences of distances in corresponding dimensions is used to find the distance in space. Recent individual ,and . Representing different objective functions, , Let represent the objective functions corresponding to individuals in the population. Indicates all The average value, Indicates population size, This indicates the number of optimization objectives.

[0132] As can be seen from the definition, SP mainly examines the uniformity of the overall solution set distribution by statistically analyzing the distance from each individual in the solution set to its nearest individual. The smaller the value of SP, the better the uniformity of the algorithm's solution set.

[0133] like Figure 5As shown in the figure, the comparison results of the solution set uniformity of the improved NSGA-II algorithm and the existing NSGA-II / MOPSO algorithm in this embodiment show that the improved NSGA-II algorithm has the smallest spatial evaluation index value, indicating that the improved NSGA-II algorithm has the best solution set distribution uniformity, followed by the NSGA-II algorithm, while the MOPSO algorithm performs poorly in comparison.

[0134] S32. Comparison of optimization results;

[0135] Figure 6 Figures (a), (b), and (c) show the Pareto fronts of the improved NSGA-II algorithm, the NSGA-II algorithm, and the MOPSO algorithm, respectively. From the solution set distribution of the three figures, it can be seen that, under the same conditions, the improved NSGA-II algorithm has more Pareto optimal solutions than the other two algorithms. This means that the improved NSGA-II has better population diversity and global search ability than NSGA-II and MOPSO.

[0136] To verify the improvement effect of the improved NSGA-II algorithm in this paper, the improved NSGA-II algorithm, the NSGA-II algorithm, and the MOSPO algorithm were used to optimize the process parameters of the titanium alloy belt grinding process, and the results were compared with those before optimization to verify the improvement effect of the improved NSGA-II algorithm.

[0137] Figure 7 The results show the multi-objective optimization of the titanium alloy belt grinding process using three algorithms. Figure 7 (a) Comparison of carbon emissions per minute during grinding under the same surface roughness and material removal rate. The figure shows that the process parameters optimized by the three algorithms have improved the carbon emissions generated during the process, and the improvement effect of the improved NSGA-II algorithm is the most obvious. Figure 7 (b) Comparison of surface roughness while keeping carbon emissions and material removal rates the same. Figure 7 (c) Comparison of material removal rates while maintaining the same carbon emissions and surface roughness. As can be seen from the figure, the improved NSGA-II algorithm outperforms both the MOPSO and NSGA-II algorithms in improving both surface roughness and material removal rate. Therefore, the improved NSGA-II algorithm proposed in this invention significantly improves the optimization of process parameters in belt grinding.

[0138] S33. Practical Applications;

[0139] To verify the practical guiding significance of the improved NSGA-II algorithm proposed in this embodiment for selecting process parameters in the belt grinding of titanium alloy blades, the algorithm was used to solve for the optimal process parameters for the grinding process of titanium alloy blades (requiring a removal of 10g of workpiece mass). The obtained process parameters were used to process titanium alloy blades, and the results were compared with those of existing processing methods. Table 1 shows a comparison between the grinding results optimized by the improved NSGA-II algorithm and the grinding results of the traditional processing method.

[0140] Table 1

[0141]

[0142] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A method for optimizing multi-objective process parameters in belt grinding based on an improved NSGA-II algorithm, the specific steps of which are as follows: S1. Establish mathematical models for carbon emissions, surface roughness, and material removal rate in the belt grinding process; The process of establishing the carbon emission model is as follows: The carbon emissions from belt grinding of titanium alloy blades can be categorized into three main sources: resource consumption, processing, and waste disposal. These three sources respectively generate carbon emissions from material consumption, electricity consumption, and waste disposal. Carbon emissions from material consumption : （1）； in, , These represent the mass of grinding fluid and abrasive belt consumed during the grinding process, respectively. , These represent the carbon emission factors for producing grinding fluid and abrasive belts, respectively. Power plants generate carbon emissions during the process of producing electricity. The corresponding carbon emission values ​​are obtained based on the local electricity emission factor. （2）； in, This indicates the carbon emissions indirectly generated during the grinding process. This represents the electrical energy consumed by the machine tool during the grinding process. This indicates the region's electricity emission factor; The working states of a belt grinding machine can be divided into three states: startup, no-load, and cutting. These three states constitute one grinding cycle. The power of the machine in each of the three working states is recorded as the machine startup power. Machine tool no-load power Machine tool cutting power Analyzing the power composition of a grinding machine tool during cutting, we can conclude that: （3）； in, This represents the effective grinding power; the electrical energy consumed by the machine tool in one grinding cycle can be obtained as follows: （4）； in, , , These represent the running time of the machine tool in the start-up state, no-load state, and cutting state, respectively. This represents one grinding cycle. This indicates the power loss due to the additional load. This represents the time variable of machine tool operation; in actual machining processes, it refers to the machine tool's starting power during each machining cycle. Machine tool no-load power Additional load power loss The effective cutting power is essentially constant and can be measured by a power meter. It can be obtained from equation (5): （5）； in, Indicates the tangential grinding force of the abrasive belt. Indicates the linear velocity of the abrasive belt; The value needs to be obtained by constructing a belt grinding force model: （6）； in, Indicates the workpiece feed rate. Represents the proportionality coefficient. Indicates the depth of grinding. This indicates the contact area between a single abrasive grain and the workpiece. This represents the average contact strength between the abrasive grains and the workpiece, and its magnitude is directly proportional to the material hardness. This represents the dynamic friction coefficient between the workpiece and the abrasive grains. This represents the static grinding ratio coefficient. Indicates the static grinding coefficient. Indicates the diameter of the abrasive belt wheel; Equation (7) represents the carbon emissions generated from waste treatment: （7）； in, Indicates the quality of titanium alloy grinding chips. This indicates the carbon emission factor of recycled titanium alloy grinding debris. This indicates the quality of the grinding fluid waste. This indicates the carbon emission factor of recycled grinding fluid waste. Indicates the quality of the discarded sand belt. Indicates the carbon emission factor of waste sand belts; In summary, based on equations (1), (2), and (7), the total carbon emissions from the grinding of titanium alloy blades using abrasive belts can be calculated. The model: （8）； S2. Establish a multi-objective optimization model based on the improved NSGA-II algorithm; S3. Using the improved NSGA-II algorithm for multi-objective optimization, intelligent optimization of process parameters in the grinding process is achieved.

2. The method for optimizing multi-objective process parameters in belt grinding based on the improved NSGA-II algorithm according to claim 1, characterized in that, The mathematical model for surface roughness and material removal rate is as follows: 1) Establish a surface roughness model; Surface roughness is modeled and quantified. After considering the influencing factors in the grinding process, the relationship between grinding process parameters and surface roughness is obtained. The empirical formula between them is shown in equation (9), from which the surface roughness model can be obtained: （9）； in, The constant obtained by substituting the experimental data into equation (9) represents the actual roughness, which is measured by a surface roughness measuring instrument. 2) Establish a material removal rate model; The material removal rate (MRR) in grinding processes can be obtained from the workpiece feed rate and grinding depth, resulting in the following material removal rate model: （10）。 3. The method for optimizing multi-objective process parameters in belt grinding based on the improved NSGA-II algorithm according to claim 1, characterized in that, Step S2 is as follows: S21. Improved NSGA-II algorithm; When selecting individuals from the last layer of non-dominated solutions to enter the next generation, the solution space is divided into several congruent triangles. The positions of the non-dominated solutions are determined and marked in the corresponding triangles. After all the non-dominated solutions are assigned to the triangles, they are sorted according to the number of non-dominated solutions in each triangle region. The specific process is as follows: Let the origin be a point, and shift the values ​​of each objective function so that the minimum value of the objective function lies at the origin, and then normalize the values ​​of each objective function: （11）； in, Represents a vector of decision variables. Represents the objective function value. This represents the minimum value of the objective function in the solution set. This represents the maximum value of the objective function in the solution set, which yields the normalized objective function value. ; After normalization, the solution space is obtained, and the values ​​of the objective function will all fall within the first quadrant of the coordinate axes. , , Connecting three points forms a triangle, which is then divided into several congruent triangles, each numbered. Solutions to the objective function will fall into these triangles. The triangles are sorted by the number of solutions to the objective function within each triangle. The selection rules for advancing the next generation of the appropriate population are as follows: Sort the triangular regions according to the sparse to dense distribution of solutions within them, and then sequentially select individuals according to the sorting priority. Each time, select one individual from each triangular region to enter the next generation population, and then remove that individual from the triangular region. Repeat this process until the number of individuals in the next generation population reaches the required number of individuals in the next generation population. S22. Establish a multi-objective optimization model; Multi-objective optimization of the belt grinding process for titanium alloy blades aims to minimize carbon emissions per unit time, minimize surface roughness, and maximize grinding efficiency, with belt linear speed as the primary factor. Workpiece feed rate Grinding depth For decision variables; Constraints are imposed on decision variables in multi-objective optimization models: （12）； in, These represent the minimum values ​​of the belt linear speed, workpiece feed rate, and grinding depth, respectively. These represent the maximum values ​​of the belt linear speed, workpiece feed rate, and grinding depth, respectively. In summary, the multi-objective optimization model for belt grinding of titanium alloy blades is as follows: （13）； in, This represents the optimal solution of the optimization function. , , The three objective functions are carbon emissions, surface roughness, and material removal rate.

4. The method for optimizing multi-objective process parameters in belt grinding based on the improved NSGA-II algorithm according to claim 1, characterized in that, Step S3 is as follows: S31. Comparison of solution set uniformity; The improved NSGA-II, NSGA-II, and MOSPO algorithms were used to solve the problem, and the results of the three algorithms were compared to verify the effectiveness of the improved NSGA-II algorithm in solving the multi-objective optimization problem in belt grinding. The parameters of the three algorithms were set, and the population size was [value missing]. The maximum number of iterations is ; First, initialize the population by randomly generating populations within a set range. The population consists of individuals, and then the iteration begins. Offspring are generated by crossover using a normal distribution. The mutated gene loci are randomly selected. The objective function value is calculated using the existing individuals. The objective function values ​​are sorted accordingly, and individuals are selected to enter the next generation population. This process is repeated until the number of iterations is reached. Finally, the optimal process parameters corresponding to the objective are obtained from the solution set of the algorithm. The uniformity of the solution set distribution of each algorithm is evaluated using the spatial evaluation index SP proposed by Schott. The calculation formula is as follows: (14)； in, Represents an individual To other individuals The minimum sum of the differences of distances in corresponding dimensions is used to find the distance in space. Recent individual ,and ; Representing different objective functions, , Let each represent the objective function corresponding to an individual in the population; Indicates all The average value, Indicates population size, Indicates the number of optimization objectives; S32. Comparison of optimization results; The improved NSGA-II algorithm, the NSGA-II algorithm, and the MOSPO algorithm were used to optimize the process parameters of the titanium alloy belt grinding process, and the results were compared with those before optimization to verify the improvement effect of the improved NSGA-II algorithm.

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