Titanium alloy die forging processing parameter optimization method based on dynamic weight

Abstract

This invention discloses a method for optimizing machining parameters of titanium alloy forgings based on dynamic weights, belonging to the field of metal cutting and intelligent optimization technology. Addressing the problem that existing methods struggle to simultaneously optimize multiple objectives such as tool life, material removal rate, surface roughness, and workpiece deformation, and are prone to getting trapped in local optima, this invention proposes the following solution: Machining data is collected, and four objective functions and constraints are established; an improved NSGA-II algorithm is used for solving the problem. This algorithm introduces a dynamic weight adjustment mechanism in the form of a sine function to achieve phased optimization with emphasis, and employs an adaptive mutation strategy to maintain population diversity; the Pareto optimal solution set is classified into efficiency-first, quality-first, and comprehensive balance schemes for on-site selection. This invention effectively prevents premature convergence through the synergistic effect of dynamic weights and adaptive mutation, and the optimization results balance machining efficiency, quality, and tool life, reducing trial cutting costs. It is suitable for the efficient and high-quality machining of complex parts such as aerospace titanium alloy forgings.

Description

Technical Field

[0001] This invention belongs to the field of metal cutting and intelligent optimization control technology, specifically a method for optimizing the processing parameters of titanium alloy forgings based on dynamic weights. Background Technology

[0002] Titanium alloys are widely used in the manufacture of aerospace structural components due to their high strength, good corrosion resistance, and long fatigue life. Titanium alloy forgings are typically characterized by thin walls, complex shapes, and uneven allowances, making it difficult to achieve continuous and stable machining.

[0003] In machining, process parameters such as cutting speed, feed rate, and depth of cut have a significant impact on tool life, machining efficiency, workpiece surface roughness, and deformation. While the Non-Dominated Sorting Genetic Algorithm (NSGA-II) exhibits good performance in multi-objective optimization, its use of fixed weight coefficients for fitness evaluation prevents dynamic adjustment of the focus on different optimization objectives. This leads to the algorithm easily getting trapped in local optima in the early stages and a decrease in convergence speed in later stages. Furthermore, it fails to consider actual machining constraints (such as lower limits for tool life and upper limits for surface quality), making it difficult to meet the comprehensive optimization requirements under complex working conditions of titanium alloys. Traditional cutting parameter optimization methods have the following shortcomings: 1. Methods such as orthogonal experimental design and response surface methodology can usually only optimize a single cutting parameter and are difficult to simultaneously consider multiple machining performance indicators such as surface roughness Ra, tool life T, material removal rate Q, and part deformation D. 2. Static weighted multi-objective optimization methods (such as fixed-weight NSGA-II, PSO, GA, etc.) obtain local optima under fixed weights and cannot dynamically respond to changes in processing conditions, resulting in limited optimization accuracy and stability. 3. The lack of a systematic multi-objective parameter optimization method leads to high on-site processing and trial cutting costs and low efficiency. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a method for optimizing the processing parameters of titanium alloy forgings based on dynamic weights. This method can simultaneously optimize four conflicting objectives: tool life, material removal rate, surface roughness, and workpiece deformation. By dynamically adjusting the weights of each objective during the algorithm evolution process and introducing an adaptive mutation strategy and a process constraint handling mechanism, a balance between global search and local convergence is achieved, thereby improving the process feasibility of the optimization results.

[0005] The technical solution adopted by this invention to solve its technical problem is a method for optimizing the processing parameters of titanium alloy forgings based on dynamic weights, comprising the following steps: Step 1: Data acquisition. Collect data on cutting force, tool wear, cutting temperature, surface roughness, and workpiece deformation during the machining process of titanium alloy forgings. Step 2: Establish objective functions and constraints. Based on the data collected in Step 1, establish four objective functions: maximize tool life T, maximize material removal rate Q, minimize surface roughness Ra, minimize workpiece deformation D, and set process parameter constraints. Step 3: Solve using the improved NSGA_Ⅱ algorithm. The objective function of Step 2 is solved using an improved non-dominated sorting genetic algorithm to obtain the Pareto optimal solution set. The improved non-dominated sorting genetic algorithm includes: introducing a dynamic weight adjustment mechanism, which periodically adjusts the weight coefficients of each objective function through a sine function during the algorithm iteration process; and introducing an adaptive mutation strategy, which adaptively increases the mutation probability as the population diversity decreases. Step 4: Parameter Recommendation and Application. The Pareto optimal solution set obtained in Step 3 is classified and organized to generate various process parameter schemes, including efficiency-first, quality-first, and comprehensive balance schemes, for on-site processing selection.

[0006] Furthermore, the specific mathematical expressions for the four objective functions are as follows: 2.1 Tool Life Objective Function :

[0007] in, Tool life, in minutes; These are constants related to the tool material and the workpiece material; These are the exponential coefficients for cutting speed, feed per tooth, and depth of cut, respectively. This refers to the cutting speed, expressed in m / min. This refers to the feed per tooth, expressed in mm / z. This refers to the depth of cut, in mm. 2.2 Objective function for material removal rate :

[0008] in, This refers to the number of teeth on the cutting tool. The unit is mm³ / min; 2.3 Objective function for surface roughness :

[0009] in, Surface roughness, in μm; These are the regression coefficients; 2.4 Objective function for part deformation :

[0010] in, This is the shape correction factor. Characteristic overhang length, in mm. This refers to the elastic modulus, with units of MPa. The moment of inertia of the cross section is expressed in mm. 4 ; and All are regression coefficients; all regression coefficients were determined by fitting experimental data.

[0011] Furthermore, the solution process of the improved non-dominated sorting genetic algorithm in step 3 includes the following sub-steps: 3.1 Initializing the Population: Multiple sets of cutting parameters are randomly generated as the initial population. Each set of parameters includes the cutting speed. Feed per tooth Depth of cut ; 3.2 Fast non-dominated sorting: Based on the calculated objective function value, the individuals in the initial population are stratified, and individuals that cannot dominate each other are divided into the same Pareto front. 3.3 Objective function value normalization: For each individual in the initial population, the original objective function values ​​are normalized to the [0,1] interval using the following formula:

[0012] in, Let be the original calculated value of the i-th objective function (i=1,2,3,4 corresponding to T, Q, Ra, D respectively). and These are the minimum and maximum values ​​of the target in the current population, respectively; for the target that needs to be minimized, i.e., surface roughness... and workpiece deformation After normalization, take This unifies all objectives into a maximization form; 3.4 Dynamic weight adjustment: When calculating fitness in each generation, the current weight of each objective is determined, and a weighted sum is calculated based on the normalized objective values ​​as the fitness of the individual. 3.5 Adaptive Crossover and Mutation: Crossover probability It decreases linearly with the number of iterations: ,in The initial crossover probability, This represents the current iteration number. This represents the maximum number of iterations. Mutation probability Adaptive adjustment: ,in The initial mutation probability, For adjustment coefficients, Let the standard deviation be the population objective function. This represents the current average fitness of the population. 3.6 Merging Parent and Offspring: Merging the current parent population with the offspring population generated through crossover and mutation; 3.7 Crowding Calculation and Next Generation Parent Selection: Perform a fast non-dominated sort on the merged population, sort the individuals in the same frontier from largest to smallest crowding, and select the individuals with the highest crowding to form the next generation parent population. 3.8 Determine if the maximum number of iterations has been reached: If not, return to step 3.2 to continue iterating; if reached, output the current Pareto front as the optimal solution set.

[0013] Furthermore, in the dynamic weight adjustment mechanism, for the i-th objective function, its weights... Adjust according to the following sine function form:

[0014] in, The total number of objective functions in this method ; This represents the weight fluctuation range, with a value ranging from 0.1 to 0.4. This represents the current iteration number; This represents the maximum number of iterations. Let be the phase difference of the i-th objective function.

[0015] Furthermore, the objective function includes four objectives, whose phase differences are respectively set as follows: material removal rate Q corresponds to Surface roughness Ra corresponds to The workpiece deformation D corresponds to Tool life T corresponds to This allows the algorithm to achieve phased optimization, focusing on material removal rate in the early stage of iteration, surface quality and deformation control in the middle stage, and tool life in the later stage.

[0016] Furthermore, the process parameter constraints in step 2 include at least the following: cutting speed. Range, feed per tooth range, depth of cut The range, the lower limit of tool life, and the upper limit of surface roughness.

[0017] Furthermore, in step 3, the penalty function method or the feasibility priority strategy is used to deal with individuals that violate the constraints. For individuals that violate the constraints, a penalty term is applied to their fitness value, making them disadvantaged in the non-dominated ranking, thereby guiding the search to converge toward the feasible region.

[0018] The beneficial effects of this invention are: 1. Traditional cutting parameter optimization methods typically only optimize a single performance index, while in actual machining, there are strong conflicts between the four objectives: tool life, machining efficiency, surface quality, and workpiece deformation. This invention, for the first time, incorporates these four conflicting objectives into a unified optimization framework, solving them simultaneously using a non-dominated sorting genetic algorithm, outputting a set of Pareto optimal solutions for flexible selection based on different production needs. Compared to single-objective optimization, this invention achieves a comprehensive balance in machining performance.

[0019] 2. This invention continuously collects real-time data such as cutting force, tool wear, and cutting temperature through a machine tool monitoring system. When a significant change in the machining state is detected, the optimization algorithm can be triggered to resolve the problem. The objective function model is incrementally updated or refitted using the newly added data, thereby achieving dynamic closed-loop optimization of machining parameters. This feature enables the invention to adapt to complex, time-varying machining environments, and it is particularly suitable for long-cycle, high-requirement machining scenarios such as aerospace titanium alloy forgings. Attached Figure Description

[0020] Figure 1 This is a flowchart of the present invention; Figure 2 This is a diagram illustrating the initialization parameters. Figure 3 This is a schematic diagram of objective function value normalization; Figure 4 This is a schematic diagram of the phase difference of four targets.

[0021] Figure 5 This is the output image of the Pareto results. Detailed Implementation

[0022] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0023] Figure 1 The specific process of this invention is illustrated.

[0024] Step 1: Data Collection

[0025] This embodiment takes the milling of the rib features of a certain type of titanium alloy forging (material TC4) as an example. During the machining process, different cutting speeds are collected by the machine tool's built-in sensors and external force gauges, infrared thermal imagers, surface roughness testers, and coordinate measuring machines. Feed per tooth Depth of cut Cutting force Tool wear, cutting temperature, and surface roughness after machining. and the deformation of key features Each set of experimental parameters was repeated three times, and the average value was taken as the final data, resulting in a total of 50 valid samples.

[0026] Step 2: Establish the objective function and constraints

[0027] 2.1 Tool Life Objective Function

[0028] Based on the extended Taylor tool life equation, we assume a power-law relationship between tool life and cutting parameters. Nonlinear regression is performed on the collected tool wear data to obtain the following fit:

[0029] In this embodiment, the least squares method is used to fit the result: , , , This function is used to maximize tool life.

[0030] 2.2 Objective function for material removal rate

[0031] According to the milling principle, the material removal rate is directly determined by the cutting parameters and the number of teeth on the cutting tool:

[0032] The number of teeth of the cutting tool This embodiment uses a four-tooth carbide-coated end mill. This function is used to maximize machining efficiency.

[0033] 2.3 Objective function for surface roughness

[0034] Using the quadratic response surface methodology, As the independent variable, for the experimentally measured Regression analysis was performed on the values, and the following results were obtained:

[0035] All coefficients in the formula are fitted using experimental data. The unit is μm. This function is used to minimize surface roughness.

[0036] 2.4 Objective function for part deformation

[0037] Part deformation is caused by elastic deformation due to cutting force Regression correction terms caused by complex factors such as thermo-mechanical coupling composition.

[0038] First, according to the cantilever beam mechanical model, the cutting force The calculation formula is:

[0039] The elastic deformation component is:

[0040] Where the shape correction coefficient Characteristic overhang length mm, elastic modulus GPa, moment of inertia of cross section mm 4 .

[0041] The regression correction term is:

[0042] Final total deformation The unit is μm. This function is used to minimize workpiece deformation.

[0043] 2.5 Constraints

[0044] Based on the machine tool performance, cutting tool and workpiece requirements, the following constraints are set:

[0045] Step 3: Solve using the improved NSGA-II algorithm

[0046] This embodiment employs the dynamic weight adaptive NSGA-II algorithm proposed in this invention, with a population size of... Maximum number of iterations Initial crossover probability Initial mutation probability Weight fluctuation range The specific solution process is as follows: 3.1 Initialize the population 100 sets of individual cutting parameters are randomly generated, each containing All three decision variables are uniformly distributed within their constraints. See also Figure 2 For example, the first individual: , , The second individual: , , And so on.

[0047] 3.2 Quick Non-Dominated Sort

[0048] For each individual in the current population, four target values ​​are calculated based on the objective function expression. Then perform a quick nondominated sort: Definition of dominance relationship: For two individuals and If the following conditions are met simultaneously: , , , If at least one inequality is strictly true, then it is called... Dominate .

[0049] Sorting process: Calculate each individual Dominated count and the dominating set .

[0050] All Individuals are placed in the first non-dominated layer. .

[0051] for Each individual in traversal Each individual ,Will Subtract 1, if If it becomes 0, then... Place in the next layer .

[0052] Repeat the above process until all individuals are stratified.

[0053] Finally, the frontier surface was obtained. ,in The individuals in the set do not dominate each other, forming the current optimal solution set.

[0054] 3.3 Normalization of Objective Function Values

[0055] Because the dimensions of each objective are different—for example, tool life is in minutes, material removal rate is mm³ / min, surface roughness is in μm, and deformation is in μm—the original values ​​need to be normalized. Interval. See also Figure 3 For each target :

[0056] in and These are the minimum and maximum values ​​of the objective in the current population, respectively. For the minimization objective ( and After normalization, take This unifies all objectives into a maximization form, facilitating subsequent weighted summation.

[0057] 3.4 Dynamic Weight Adjustment

[0058] When calculating fitness in each generation, the weights of each objective are calculated using a sine function:

[0059] See Figure 4 The phase differences of the four objective functions are set as follows: correspond , correspond , correspond , correspond The individual weighted fitness is then:

[0060] The weighted sum is used for subsequent selection. After non-dominated sorting, it can assist in selection when sorting by fitness within the same frontier. However, this invention still mainly uses non-dominated sorting, and the weighted sum is only used for constraint processing or auxiliary decision-making. In this embodiment, non-dominated sorting and crowding are used directly for selection, and the weighted fitness is used to record the optimal individual.

[0061] 3.5 Adaptive Crossover and Mutation

[0062] Crossover operation: Simulated binary crossover (SBX) is used, with crossover probability... Decreases linearly with algebraic variation:

[0063] In this embodiment, the first generation 150th generation The downward trend allows the algorithm to explore thoroughly in the early stages and retain excellent solutions in the later stages.

[0064] Mutation operation: Polynomial mutation is used, with mutation probability... Adaptive adjustment based on population diversity:

[0065] in Let be the standard deviation of the objective function values ​​for all individuals in the current population. For average fitness, the adjustment coefficient When the population tends to converge, that is... When it shrinks, It automatically increases in size to enhance diversity and prevent precocious puberty.

[0066] 3.6 Combining Parent and Offspring Generations

[0067] Let the current number be... The parent population of the generation is (Scale 100), through the analysis of Individuals in the population undergo crossover and mutation operations to generate offspring populations. (The size is also 100). Merge the two into... , with a scale of 200.

[0068] 3.7 Crowding Calculation and Parent Selection in the New Generation

[0069] To merge populations The 100 best individuals are selected as the parents of the next generation. Within the same non-dominated layer, it is necessary to further differentiate between superior and inferior qualities. The steps for calculating congestion are as follows: Initialize crowding for all individuals within the same non-dominated layer. .

[0070] For each objective ( Sort by objective function value in ascending order. Set the crowding degree of boundary individuals (minimum, maximum) to infinity (to ensure they are preserved).

[0071] For intermediate individuals Calculate the congestion increment:

[0072] in , The target value is the value of the adjacent individual, and the denominator is the difference between the maximum and minimum values ​​of the target within the layer.

[0073] Repeat the above steps for all four objectives, and sum them up to obtain the final crowding level for each individual. .

[0074] Selection strategy: First, select from low to high non-dominated levels ( Individuals are selected; if not all individuals in a certain layer can be selected, individuals within that layer are selected in descending order of crowding until the population size is reached. Individuals with high crowding density are preferentially preserved around sparse areas to maintain a uniform distribution on the Pareto front.

[0075] 3.8 Iteration Termination Judgment

[0076] After completing the above steps, determine the current iteration number. Has the maximum number of iterations been reached? If it is not achieved, then... and the new parent population Return to step 3.2 and continue iterating; if the target has been reached, output the final value. All individuals on the frontier are considered as the Pareto optimal solution set, as shown in the following results. Figure 5 As shown.

[0077] Step 4: Parameter Recommendation and Application

[0078] The final Pareto optimal solution set (which typically contains dozens of sets of non-dominated cutting parameters) is then categorized and organized: Efficiency-first approach: Select material removal rate The highest-scoring solutions are suitable for rough processing or mass production.

[0079] Quality-first approach: Select surface roughness and workpiece deformation The smallest set or of solutions is suitable for finishing or thin-walled features.

[0080] Comprehensive balancing scheme: Select the solution where all four objective values ​​are at a moderate level, which is suitable for general processing conditions.

[0081] In this embodiment, a typical set of comprehensive balance parameters is output as follows: m / min, mm / z, mm. Under this parameter, tool life... min, material removal rate mm³ / min, surface roughness μm, workpiece deformation μm. Compared to empirical solutions ( The material removal rate was increased by 10.5%, the roughness was reduced by 9.6%, the deformation was reduced by 10.4%, and the tool life was extended by 20.2%, which verified the superiority of the present invention.

[0082] On-site operators can select the corresponding solution from the recommended library according to actual processing needs (such as urgent orders that require increased efficiency or precision machining that requires guaranteed quality), and directly call the cutting parameters in the CNC program, thus avoiding the high cost of trial cutting based on experience.

[0083] Constraint Handling Instructions

[0084] During the iteration process in step 3, for violations of constraints (such as tool life) min or surface roughness For individuals with a fitness level of μm, this invention employs a penalty function method: a large penalty term is applied to their fitness value (or rank in the non-dominated ranking), causing these individuals to be automatically ranked after all feasible solutions during ranking, thereby guiding the search towards convergence to the feasible region. Specifically, before the non-dominated ranking, if an individual violates any constraint, the objective value in its dominance relation is replaced with a range value (e.g., the lifetime is set to negative infinity and the roughness to positive infinity), ensuring that it is dominated by all feasible solutions.

[0085] The embodiments described herein are preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for optimizing processing parameters of a titanium alloy die forging based on dynamic weights, characterized in that, Includes the following steps: Step 1: Data acquisition. Collect data on cutting force, tool wear, cutting temperature, surface roughness, and workpiece deformation during the machining process of titanium alloy forgings. Step 2: Establish objective functions and constraints. Based on the data collected in Step 1, establish four objective functions: maximize tool life T, maximize material removal rate Q, minimize surface roughness Ra, minimize workpiece deformation D, and set process parameter constraints. Step 3: Solve using the improved NSGA_Ⅱ algorithm. The objective function of Step 2 is solved using an improved non-dominated sorting genetic algorithm to obtain the Pareto optimal solution set. The improved non-dominated sorting genetic algorithm includes: introducing a dynamic weight adjustment mechanism, which periodically adjusts the weight coefficients of each objective function through a sine function during the algorithm iteration process; and introducing an adaptive mutation strategy, which adaptively increases the mutation probability as the population diversity decreases. Step 4: Parameter Recommendation and Application. The Pareto optimal solution set obtained in Step 3 is classified and organized to generate various process parameter schemes, including efficiency-first, quality-first, and comprehensive balance schemes, for on-site processing selection.

2. The method for optimizing machining parameters of titanium alloy forgings based on dynamic weights according to claim 1, characterized in that, The specific mathematical expressions for the four objective functions are as follows: 2.1 Tool Life Objective Function : in, Tool life, in minutes; These are constants related to the tool material and the workpiece material; These are the exponential coefficients for cutting speed, feed per tooth, and depth of cut, respectively. This refers to the cutting speed, expressed in m / min. This refers to the feed per tooth, expressed in mm / z. This refers to the depth of cut, in mm. 2.2 Material removal rate objective function : wherein is the number of teeth of the tool, in mm3 / min; 2.3 Surface roughness objective function : wherein Rq is the surface roughness in μm; R is the regression coefficient; 2.4 Part deformation objective function : in, This is the shape correction factor. Characteristic overhang length, in mm. This refers to the elastic modulus, with units of MPa. The moment of inertia of the cross section is expressed in mm. 4 ; and All are regression coefficients; all regression coefficients were determined by fitting experimental data.

3. The method for optimizing processing parameters of a titanium alloy die forging based on dynamic weight according to claim 1, characterized in that, The solution process of the improved non-dominated sorting genetic algorithm in step 3 includes the following sub-steps: 3.1 Initializing the Population: Multiple sets of cutting parameters are randomly generated as the initial population. Each set of parameters includes the cutting speed. Feed per tooth Depth of cut ; 3.2 Fast non-dominated sorting: Based on the calculated objective function value, the individuals in the initial population are stratified, and individuals that cannot dominate each other are divided into the same Pareto front. 3.3 Objective function value normalization: For each individual in the initial population, the original objective function values ​​are normalized to the [0,1] interval using the following formula: in, Let be the original calculated value of the i-th objective function, where i = 1, 2, 3, 4 correspond to T, Q, Ra, and D respectively. and These are the minimum and maximum values ​​of the target in the current population, respectively; for the target that needs to be minimized, i.e., surface roughness... and workpiece deformation After normalization, take This unifies all objectives into a maximization form; 3.4 Dynamic weight adjustment: When calculating fitness in each generation, the current weight of each objective is determined, and a weighted sum is calculated based on the normalized objective values ​​as the fitness of the individual. 3.5 Adaptive Crossover and Mutation: crossing probability with iteration algebraic linear descent: wherein is an initial crossing probability, is a current iteration number, is a maximum iteration number; Mutation probability Adaptive adjustment: wherein is the initial mutation probability, is the adjustment coefficient, is the standard deviation of the population objective function, is the current population average fitness; 3.6 Merging Parent and Offspring: Merging the current parent population with the offspring population generated through crossover and mutation; 3.7 Crowding Calculation and Next Generation Parent Selection: Perform a fast non-dominated sort on the merged population, sort the individuals in the same frontier from largest to smallest crowding, and select the individuals with the highest crowding to form the next generation parent population. 3.8 Determine if the maximum number of iterations has been reached: If not, return to step 3.2 to continue iterating; if reached, output the current Pareto front as the optimal solution set.

4. The method for optimizing processing parameters of a titanium alloy die forging based on dynamic weight according to claim 3, characterized in that, In the dynamic weight adjustment mechanism, for the ith objective function, its weight is adjusted in the following sinusoidal function form: wherein, is the total number of objective functions, ; is the weight fluctuation range, and the value range is 0.1-0.4; is the current iteration number; is the maximum iteration number; is the phase difference of the i-th objective function.

5. The method for optimizing processing parameters of a dynamically weighted titanium alloy swage part according to claim 4, characterized in that, The objective function includes four objectives, whose phase differences are respectively set as follows: material removal rate Q corresponds to Surface roughness Ra corresponds to The workpiece deformation D corresponds to Tool life T corresponds to This allows the algorithm to achieve phased optimization, focusing on material removal rate in the early stage of iteration, surface quality and deformation control in the middle stage, and tool life in the later stage.

6. The method for optimizing processing parameters of a dynamically weighted titanium alloy swage part according to claim 1, characterized in that, The process parameter constraints in step 2 include at least the following: cutting speed. Range, feed per tooth range, depth of cut The range, the lower limit of tool life, and the upper limit of surface roughness.

7. The method for optimizing processing parameters of a dynamically weighted titanium alloy swage part according to claim 1, characterized in that, In step 3, the penalty function method or the feasibility priority strategy is used to deal with individuals that violate the constraints. For individuals that violate the constraints, a penalty term is applied to their fitness value, which puts them at a disadvantage in the non-dominated ranking, thereby guiding the search to converge toward the feasible region.

Images