A cutting force vector regulation method based on micro-element blade method

Abstract

The application discloses a kind of cutting force vector regulation and control methods based on micro-element blade method, it is related to metal processing field.The main implementation method includes: first, milling coefficient is solved, fixed tool parameters and the rest milling parameters except every tooth feed rate, carries out multiple sets of orthogonal experiments and records the average milling force value of each group of experiments and corresponding every tooth feed rate, and obtains milling coefficient by linear regression of least square method;Then based on micro-element blade method, first, milling cutter is divided into multiple discrete micro-elements along the axial direction, then the actual spiral contact angle of each micro-element is calculated and whether it is actually involved in milling is judged, then the milling force model of each micro-element is established, every blade of milling cutter is integrated along the axial direction, then the milling force of each blade is summed to obtain the magnitude of the cutting force of the whole milling cutter;Finally, milling parameters are optimized by NSGA-II algorithm, aiming at studying the influence of every tooth feed rate and axial depth of cut on cutting force, the constructed milling force model is used as objective function, the input value is axial depth of cut and every tooth feed rate, the target is the average axial milling force of a period, the maximum axial milling force and material one rate, a group of optimized Pareto solution is obtained by multiple crossover mutation.The method can quickly obtain a group of more optimal milling parameters according to the cutting force model and optimization algorithm, and can effectively regulate and control the size of cutting force vector and the part relief deformation, to provide guidance for optimizing processing parameters.

Description

Technical Field

[0001] This invention relates to a cutting force vector control method based on the micro-element cutting tool method, belonging to the field of metal cutting. Background Technology

[0002] Milling technology, with its high precision, excellent machining quality, and superior economic benefits, plays a crucial role in fields such as aerospace and precision mold making. One of the challenges of this technology lies in the fact that milling is a complex dynamic process involving intermittent contact between the cutting edge and the workpiece. During this process, milling forces significantly influence tool wear, tool life, and part deformation. Therefore, accurate prediction and active control of milling forces have become core elements for optimizing processes and achieving high-quality machining.

[0003] Existing milling force control methods mostly rely on empirical trial and error or single-objective optimization, making it difficult to achieve an effective balance between multiple objectives such as minimizing cutting force, maximizing material removal rate, and minimizing tool wear. Especially when dealing with thin-walled or flexible parts, axial cutting forces can easily cause tool deformation. Without effective vector control methods, this severely limits the achievement of high-precision machining. Therefore, there is an urgent need for a milling force control method that can accurately model the milling force vector and achieve multi-objective collaborative optimization to improve the control accuracy and machining effect of the machining process. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the technical problem to be solved by this invention is to provide a cutting force vector control method based on the infinitesimal cutting edge method. This method, by infinitesimalizing the cutting problem and integrating it to obtain the total cutting force, can accurately predict the cutting force value under specific working conditions. Furthermore, by optimizing the algorithm, a better combination of cutting parameters can be obtained, thereby achieving precise control of the cutting force vector.

[0005] The solution adopted by this invention to solve the above-mentioned technical problem is: a cutting force vector control method based on the micro-element cutting edge method, comprising the following steps:

[0006] Step 1: Conduct multiple sets of experiments and process the data;

[0007] With all cutting parameters except feed per tooth fixed, multiple orthogonal experiments were conducted, and the average milling force of each experiment was recorded. With the corresponding feed rate c, establish the average milling force equation system. Through linear regression, establish the normal equation system to obtain the milling force coefficient and the cutting edge force coefficient.

[0008] Step 2: Construct a milling force model;

[0009] Establish a milling cutter coordinate system, discretize the tool into several micro-elements along the axial direction based on the micro-element method, calculate the actual contact angle of each micro-element and determine whether it participates in milling, then establish a milling force model for each micro-element and integrate it along the axial direction to obtain the milling force of each cutting edge, and sum the milling forces of each edge to obtain the total milling force of the tool.

[0010] Step 3: Optimize milling parameters using the NSGA-II algorithm:

[0011] The constructed milling force model is used as the objective function, and the input is the axial depth of cut a. p With feed per tooth c, the target is the average axial force Fz. avg Maximum axial force Fz max The material removal rate (MRR) is used to continuously obtain new solutions through crossover mutation. Each solution is assigned to a different Pareto front through non-dominated sorting. The crowding distance between solutions within the same front is calculated. Finally, the crossover mutant individuals and parent individuals are sorted according to the principle of prioritizing those with higher front levels and those with larger crowding distances within the same front level to obtain a new generation population. Step 3 is repeated until the cutting parameters are optimized.

[0012] Furthermore, the experiment described in step 1 is as follows:

[0013] The specimen is subjected to full-contact milling. Under these conditions, the angle of entry φ of the milling cutter is... st =0, tangent angle φ ex =π, using a three-dimensional force gauge to measure the cutting forces Fx, Fy, and Fz in three directions, while keeping other cutting parameters constant, changing the feed per tooth c, and measuring and recording the values ​​for each experimental group. And the feed per tooth, c.

[0014] Furthermore, the set of equations for the average milling force described in step 1 is as follows:

[0015]

[0016] In the formula, N is the number of teeth on the milling cutter, a p λ is the axial depth of cut (mm), and c is the feed per tooth (mm / tooth). K represents the average milling force (N) measured in each experiment. tc K rc K ac Milling force coefficient (N / mm) 2 K represents the force generated by shearing, which is proportional to the chip area. te K re K ae The cutting edge force coefficient (N / mm) represents the force generated by the extrusion and friction of the tool cutting edge, and is proportional to the cutting width.

[0017] Furthermore, the normal equations described in step 1 are as follows:

[0018]

[0019] In the formula K qc K qe These represent the slope and intercept of the objective linear equation, respectively. Let c be the average cutting force of the i-th experiment of the target linear equation. i Let be the feed per tooth in the i-th experiment.

[0020] Furthermore, the process of constructing the milling force model in step 2 is as follows:

[0021] Step 2.1: Establish the milling cutter coordinate system. The feed direction of the flat-end mill is the positive X-axis, the spindle direction is the positive Z-axis, the Y-axis direction is determined by the right-hand screw rule, and the tool rotation angle is φ.

[0022] Step 2.2: Discretize the tool along the axial direction into several micro-elements, each with a thickness of d. z The milling force acting on the infinitesimal element can be decomposed into tangential force, radial force, and axial force, which can be expressed as:

[0023]

[0024] Where φ i The actual contact angle of the infinitesimal element can be expressed as: Where φ p The angle between the teeth of the cutting tool. β is the helix angle of the cutting tool; h i For real-time chip thickness, h i =csinφ i (z); g(φ) i ) is the step function used to determine whether the infinitesimal element participates in the cutting process, g(φ) i The following is represented:

[0025]

[0026] Where φ st For the angle of entry, In the formula a e Radial cut width; φ ex For the tangent angle, φ ex =π.

[0027] Step 2.3: Decompose the infinitesimal force element into the X, Y, and Z directions of the milling cutter coordinate system through coordinate transformation. The decomposed expression is as follows:

[0028]

[0029] Step 2.4: Integrate the infinitesimal element along the axial direction to obtain the milling force of each cutting edge. Sum the milling forces of each cutting edge to obtain the total milling force of the entire milling cutter. The milling force of each cutting edge is expressed as follows:

[0030]

[0031] The integral yields:

[0032]

[0033] The cutting force acting on the entire milling cutter can be expressed as:

[0034]

[0035] Furthermore, step 3 is as follows:

[0036] Step 3.1: Initialize the population by randomly generating an initial population Pop with N individuals. Individual characteristics include the independent variable axial depth of cut ap, feed per tooth c, and the target value average axial force Fz. avg Maximum axial force Fz max Material removal rate (MRR), individual frontier rank (Rank), set of other individuals dominated by an individual (DominationSet[]), number of times an individual is dominated (DominatedCount), and crowding distance of an individual on its respective frontier (CrowdingDistance).

[0037] Step 3.2: Perform non-dominated sorting on the initial population to obtain the non-dominated set:

[0038] Step 3.3: Calculate the crowding distance between individuals in the same non-dominated set.

[0039] Step 3.4: Sort the initial population according to the principle of prioritizing individuals at the frontier level, and prioritizing individuals with greater crowding distance at the same frontier level.

[0040] Step 3.5: Set the genetic algorithm parameters, perform crossover and mutation operations on the parent population, and obtain the crossover set Pop. c and the mutated set of individuals Pop m .

[0041] Step 3.6: Combine the parent population Pop and the crossover set Pop. c and the mutated set of individuals Pop m Merge the populations and then perform a non-dominated sorting on the merged populations to obtain a new non-dominated set: Then, calculate the crowding distance between individuals in the same non-dominated set, sort the population according to the principles described in step 3.4, and retain the top N individuals to generate a new population. Before reaching the maximum number of iterations (iter...),... max Repeat step 3 until an optimized Pareto front is obtained.

[0042] Beneficial effects:

[0043] 1. This invention constructs a model that can accurately predict milling forces by inputting tool parameters and cutting parameters and using the micro-element cutting method, thereby improving the accuracy of the cutting force vector description. Furthermore, it innovatively combines this model with the NSGA-II multi-objective optimization algorithm to achieve synergistic optimization of average axial force, maximum axial force, and material removal rate, and automatically generates a set of excellent Pareto solutions.

[0044] 2. The cutting parameter adjustment method provided by this invention can effectively suppress workpiece deformation while taking into account machining efficiency. It provides a complete solution from accurate modeling to intelligent parameter optimization, which surpasses the traditional methods that rely on experience trial and error or single-objective optimization in terms of efficiency and cost. Attached Figure Description

[0045] Figure 1 This is a flowchart of the program of the present invention;

[0046] Figure 2 This is a regression diagram of the milling force parameters of the present invention;

[0047] Figure 3 This is a diagram of the milling cutter coordinate system of the present invention;

[0048] Figure 4 This is a milling force prediction diagram for the present invention;

[0049] Figure 5 The images show a comparison of material removal rate versus average axial force and a comparison of material removal rate versus maximum axial force, as presented in this invention. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for explaining the invention and are not intended to limit the invention.

[0051] A cutting force vector control method based on the infinitesimal cutting edge method includes the following steps:

[0052] Step 1: Conduct multiple sets of experiments and process the data.

[0053] Step 1.1: Perform full contact milling (slot milling) on ​​the specimen. Under these conditions, the cutter's angle of entry φ...st =0, tangent angle φ ex =π, using a three-dimensional force gauge to measure the cutting forces Fx, Fy, and Fz in three directions, while keeping other cutting parameters constant, changing the feed per tooth c, and measuring and recording the values ​​for each experimental group. And the feed per tooth, c.

[0054] Step 1.2: Establish the following set of average milling force equations:

[0055]

[0056] In the formula, N is the number of teeth on the milling cutter, a p λ is the axial depth of cut (mm), and c is the feed per tooth (mm / tooth). K represents the average milling force (N) measured in each experiment. tc K rc K ac Milling force coefficient (N / mm) 2 ), K te K re K ae This is the cutting edge force coefficient (N / mm).

[0057] Step 1.3: Perform regression using the least squares method. The regression method is as follows:

[0058] Taking the X direction as an example, the sum of squared errors, In the formula Let m be the average milling force in the X direction measured in the i-th experiment, and K be the number of experiments. xc K xe These are the slope and intercept of the objective linear equation, respectively.

[0059] Pair E with K respectively xc and K xe Taking partial derivatives, we obtain the normal equation system as follows:

[0060]

[0061] Therefore, we can conclude that:

[0062]

[0063] The Y and Z directions can be solved using a similar method. Based on this, the cutting force coefficient and the cutting edge force coefficient are obtained as follows:

[0064]

[0065] Based on this method, a regression model was established, and the results are as follows: Figure 3 As shown.

[0066] Step 2: Construct a milling force model.

[0067] Step 2.1: Establish the end mill coordinate system. The feed direction of the flat end mill is the positive X-axis, the spindle direction is the positive Z-axis, and the Y-axis direction is determined by the right-hand rule. The tool rotation angle is φ. The specific details of the end mill coordinate system are as follows: Figure 3 As shown.

[0068] Step 2.2: Discretize the tool along the axial direction into several micro-elements, each with a thickness of d. z The milling force acting on the infinitesimal element can be decomposed into tangential force, radial force, and axial force, which can be expressed as:

[0069]

[0070] Where φ i The actual contact angle of the infinitesimal element can be expressed as: Where φ p The angle between the teeth of the cutting tool. β is the helix angle of the cutting tool; h i For real-time chip thickness, h i =csinφ i (z); g(φ) i ) is the step function used to determine whether the infinitesimal element participates in the cutting process, g(φ) i The following is represented:

[0071]

[0072] Where φ st For the angle of entry, In the formula a e Radial cut width; φ ex For the tangent angle, φ ex =π.

[0073] Step 2.3: Decompose the infinitesimal force element into the X, Y, and Z directions in the milling cutter coordinate system through coordinate transformation. The decomposed expression is as follows:

[0074]

[0075] Step 2.4: Integrate the infinitesimal element along the axial direction to obtain the milling force of each cutting edge. Sum the milling forces of each cutting edge to obtain the total milling force of the entire milling cutter. The milling force of each cutting edge is expressed as follows:

[0076]

[0077] The integral yields:

[0078]

[0079] The cutting force acting on the entire milling cutter can be expressed as:

[0080]

[0081] A milling force prediction model was established based on this method, and the results are as follows: Figure 4 As shown.

[0082] Step 3: Optimize the milling parameters using the NSGA-II algorithm.

[0083] Step 3.1: Initialize the population by randomly generating an initial population Pop with N individuals. Individual characteristics include the independent variables axial depth of cut ap and feed per tooth c, and target values ​​include the average axial force Fz. avg Maximum axial force Fz max Material removal rate (MRR), individual frontier rank (Rank), set of other individuals dominated by an individual (DominationSet[]), number of times an individual is dominated (DominatedCount), and crowding distance of an individual on its respective frontier (CrowdingDistance).

[0084] In order to ensure that the goal of all three objective quantities is to minimize them, the reciprocal of the material removal rate MRR, 1 / MRR, is taken as the actual objective.

[0085] Step 3.2: Perform non-dominated sorting on the initial population to obtain the non-dominated set:

[0086] In the non-dominated ranking, if individual A dominates individual B, then and n is the number of target features of an individual. When A dominates B, B is added to A's DominationSet[], and B's DominatedCount is incremented by one.

[0087] Step 3.3: Calculate the crowding distance between individuals in the same non-dominated set.

[0088] When calculating the crowding distance, the target needs to be normalized. Where f m For a given target value for an individual, the total crowding distance is:

[0089] Step 3.4: Sort the initial population according to the principle of prioritizing individuals at the frontier level, and prioritizing individuals with greater crowding distance at the same frontier level.

[0090] Step 3.5: Set the genetic algorithm parameters. In this embodiment of the invention, the crossover probability Pcrossover = 0.7, the number of offspring generated by crossover Ncrossover = N × Pcrossover, the proportion of individuals participating in mutation Pmutation = 0.4, the number of offspring generated by mutation Nmutation = N × Pmutation, the mutation probability Pmu = 0.02, and the mutation length sigma = 0.1 × (Var max -Var min ), where Var max and Var min Using the upper and lower bounds of individual independent variable characteristics, a crossover and mutation operation is performed on the parent population to obtain the crossover set Pop. c and the mutated set of individuals Pop m .

[0091] When performing crossover mutation, boundaries must be set [Var] min Var max If a variable exceeds the boundary, the variable value will be pulled to the boundary position. The operation method is x = max(VarMin, min(VarMax, x)).

[0092] Step 3.6: Combine the parent population Pop and the crossover set Pop. c and the mutated set of individuals Pop m Merge the populations and then perform a non-dominated sorting on the merged populations to obtain a new non-dominated set: Then, calculate the crowding distance between individuals in the same non-dominated set, sort the population according to the principles described in step 3.4, and retain the top N individuals to generate a new population. Before reaching the maximum number of iterations (iter...),... max Repeat step 3 until an optimized Pareto front is obtained.

[0093] Based on this method, the cutting parameters were optimized, and the optimization results are as follows: Figure 5 As shown.

[0094] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for controlling the cutting force vector based on the micro-element cutting edge method, characterized in that: Includes the following steps: Step 1: Conduct multiple sets of experiments and process the data. With all cutting parameters except feed per tooth fixed, multiple orthogonal experiments were conducted, and the average milling force of each experiment was recorded. With the corresponding feed rate c, establish the average milling force equation system. Through linear regression, establish the normal equation system to obtain the milling force coefficient and the cutting edge force coefficient. Step 2: Construct a milling force model. Establish a milling cutter coordinate system, discretize the tool into several micro-elements along the axial direction based on the micro-element method, calculate the actual contact angle of each micro-element and determine whether it participates in milling, then establish a milling force model for each micro-element and integrate it along the axial direction to obtain the milling force of each cutting edge, and sum the milling forces of each edge to obtain the total milling force of the tool. Step 3: Optimize the milling parameters using the NSGA-II algorithm. The constructed milling force model is used as the objective function, and the input is the axial depth of cut a. p With feed per tooth c, the target is the average axial force Fz. avg Maximum axial force Fz max The material removal rate (MRR) is used to continuously obtain new solutions through crossover mutation. Each solution is assigned to a different Pareto front through non-dominated sorting. The crowding distance between solutions within the same front is calculated. Finally, the crossover mutant individuals and parent individuals are sorted according to the principle of prioritizing those with higher front levels and those with larger crowding distances within the same front level to obtain a new generation population. Step 3 is repeated until the cutting parameters are optimized.

2. The cutting force vector control method based on the micro-element cutting edge method as described in claim 1, characterized in that, The experiment described in step 1 is as follows: The specimen is subjected to full-contact milling. Under these conditions, the angle of entry φ of the milling cutter is... st =0, tangent angle φ ex =π, using a three-dimensional force gauge to measure the cutting forces Fx, Fy, and Fz in three directions, while keeping other cutting parameters constant, changing the feed per tooth c, and measuring and recording the values ​​for each experimental group. And the feed per tooth, c.

3. The cutting force vector control method based on the micro-element cutting edge method as described in claim 1, characterized in that, The average milling force equations described in step 1 are as follows: In the formula, N is the number of teeth on the milling cutter, a p λ is the axial depth of cut (mm), and c is the feed per tooth (mm / tooth). K represents the average milling force (N) measured in each experiment. tc K rc K ac Milling force coefficient (N / mm) 2 ), K te K re K ae This is the cutting edge force coefficient (N / mm).

4. The cutting force vector control method based on the micro-element cutting edge method as described in claim 1, characterized in that, The normal equations described in step 1 are as follows: In the formula K qc K qe These represent the slope and intercept of the objective linear equation, respectively. Let c be the average cutting force of the i-th experiment of the target linear equation. i Let be the feed per tooth in the i-th experiment.

5. The cutting force vector control method based on the micro-element cutting edge method as described in claim 1, characterized in that, The process of constructing the milling force model in step 2 is as follows: (1) Establish the milling cutter coordinate system. The feed direction of the flat end mill is the positive direction of the X-axis, the spindle direction of the milling cutter is the positive direction of the Z-axis, the Y-axis direction is determined by the right-hand screw rule, and the tool rotation angle is φ. (2) Discretize the tool along the axial direction into several micro-elements, the thickness of which is d. z The milling force acting on the infinitesimal element can be decomposed into tangential force, radial force, and axial force, which can be expressed as: Where φ i The actual contact angle of the infinitesimal element can be expressed as: Where φ p The angle between the teeth of the cutting tool. β is the helix angle of the cutting tool; h i For real-time chip thickness, h i =csinφ i (z); g(φ) i ) is the step function used to determine whether the infinitesimal element participates in the cutting process, g(φ) i The following is represented: Where φ st For the angle of entry, In the formula a e Radial cut width; φ ex For the tangent angle, φ ex =π. (3) The infinitesimal force is decomposed into the X, Y, and Z directions in the milling cutter coordinate system through coordinate transformation. The decomposed expression is as follows: (4) Integrate the infinitesimal element along the axial direction to obtain the milling force of each cutting edge, and sum the milling forces of each cutting edge to obtain the total milling force of the milling cutter. The milling force of each cutting edge is expressed as follows: The integral yields: Therefore, the cutting force acting on the entire milling cutter can be expressed as:

6. The cutting force vector control method based on the micro-element cutting edge method as described in claim 1, characterized in that, Step 3 is as follows: (1) Initialize the population by randomly generating an initial population Pop with N individuals. Individual characteristics include the independent variable axial depth of cut ap, feed per tooth c, and target value average axial force Fz. avg Maximum axial force Fz max Material removal rate (MRR), individual frontier rank (Rank), set of other individuals dominated by an individual (DominationSet[]), number of times an individual is dominated (DominatedCount), and crowding distance of an individual on its respective frontier (CrowdingDistance). (2) Perform non-dominated sorting on the initial population to obtain the non-dominated set: (3) Calculate the crowding distance between individuals in the same non-dominated set. (4) The initial population is sorted according to the principle of prioritizing individuals at the frontier level and prioritizing individuals with greater crowding distance at the same frontier level. (5) Set the genetic algorithm parameters, perform crossover and mutation operations on the parent population, and obtain the crossover set Pop. c and the mutated set of individuals Pop m . (6) Combine the parent population Pop and the crossover set Pop c and the mutated set of individuals Pop m Merge the populations and then perform a non-dominated sorting on the merged populations to obtain a new non-dominated set: Then, calculate the crowding distance between individuals in the same non-dominated set, sort the population according to the principle described in step 3 (4), and retain the top N individuals to generate a new population. Before reaching the maximum number of iterations, iter... max Repeat step 3 until an optimized Pareto front is obtained.

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