Cutting force prediction modeling method related to rigidity characteristics of workpiece

Abstract

The invention discloses a cutting force prediction modeling method related to workpiece rigidity characteristics. The method includes: designing a thin-wall test piece considering workpiece thickness; a cutting experiment scheme is formulated by considering the weak rigidity characteristic of the workpiece and the influence of milling cutter parameters and cutting parameters; carrying out a thin-wall test piece cutting machining experiment and data preprocessing; carrying out cutting force influence factor range analysis, and carrying out necessity dimensionality reduction on parameters based on an influence degree analysis result; solving the first-order inherent frequency of the workpieces with different thicknesses based on modal simulation; and a cutting force index regression model related to the machining parameters and the inherent frequency is constructed. According to the method, the rigidity is represented by the workpiece thickness, an experimental scheme is designed in combination with a response surface method and an orthogonal method, and parameter dimension reduction is realized by using range analysis; the cutting force index regression model is constructed by adopting the first-order inherent frequency representation rigidity of the workpiece, the precision and reliability of cutting force prediction are remarkably improved, and the technical problem that the rigidity characteristic of the workpiece is not considered in a traditional model is solved.

Description

Technical Field

[0001] This invention belongs to the field of cutting technology, specifically relating to a cutting force prediction modeling technique that considers the influence of weak workpiece rigidity. This technique designs a thin-walled test piece cutting experiment with workpiece thickness as the rigidity characterization parameter, and constructs a cutting force exponential regression prediction model with natural frequency as the rigidity characterization parameter. This improves the accuracy and generalization ability of the prediction model, and provides an accurate and reliable model basis for machining deformation calculation and process optimization. Background Technology

[0002] In modern manufacturing, machining, as a core process for part forming, is widely used in high-end fields such as aerospace, automotive manufacturing, and precision instruments. Cutting forces cause elastic deformation (such as chatter and tool deflection) in the machine tool-tool-workpiece system, directly affecting the dimensional accuracy and surface roughness of the parts. For example, in the machining of thin-walled titanium alloy parts in the aerospace field, excessive cutting forces can easily cause workpiece deformation, leading to a higher scrap rate. By predicting cutting forces and optimizing process parameters, the deformation can be controlled within the micrometer level, meeting high-precision requirements. Existing cutting force prediction methods mainly include finite element simulation, machine learning, and empirical formula methods. Among them, the finite element simulation method is based on continuum mechanics and plastic deformation theory, establishing a three-dimensional finite element model of the tool and workpiece to simulate the material flow, stress field, and temperature field evolution during the cutting process, and then calculating the cutting force through simulation. This method can intuitively present the cutting mechanism; however, the simulation process depends on the precise setting of the material constitutive model and friction model, making it difficult to guarantee prediction accuracy. Furthermore, fine mesh generation results in a single simulation taking several hours to several days, leading to low computational efficiency. Machine learning methods leverage the advantages of big data and intelligent algorithms, using models such as neural networks, random forests, and deep learning to learn nonlinear mapping relationships from historical cutting data to predict cutting forces. This method does not require a pre-defined mechanistic model and can handle multivariate coupling problems, but it still suffers from significant dependence on data quality and poor predictive generalization ability. Empirical formula methods, based on extensive cutting experimental data, establish correlation formulas between cutting forces and process parameters (cutting speed, feed rate, depth of cut) through regression analysis (such as linear regression or nonlinear fitting). These methods offer advantages such as fast calculation speed and simple form, but current research has not yet considered the influence of workpiece rigidity characteristics.

[0003] However, in high-end manufacturing fields such as aerospace and new energy equipment, many parts exhibit weak stiffness characteristics such as thin walls, slenderness, and complex curved surfaces due to lightweight design requirements. The stiffness of these parts is typically only 1 / 5 to 1 / 20 of that of ordinary rigid workpieces. Weak stiffness structural parts have the following characteristics under cutting forces: ① Deformation sensitivity, i.e., small cutting forces easily lead to large deformations; ② Dynamic deformation and cutting force feedback coupling effect, i.e., under the action of cutting forces, workpiece deformation changes the cutting depth and cutting angle, which in turn affects the magnitude and distribution of cutting forces, and may even cause chatter; ③ Multi-region stiffness differences, i.e., the deformation of different regions of the structural part under the same machining path can vary by 2 to 3 times, resulting in significant spatial heterogeneity of cutting force distribution. Therefore, in order to improve the accuracy, speed, and generalization ability of the prediction model, this patent focuses on weak stiffness structural parts, using the empirical formula method as the basic implementation approach, introducing workpiece rigidity characteristics to design cutting experiments, and constructing a cutting force index regression model, forming a new method for predicting cutting forces related to weak workpiece rigidity. Summary of the Invention

[0004] The purpose of this invention is to propose a cutting force prediction modeling method related to the weak rigidity characteristics of workpieces. To facilitate experimental design, the thickness of thin-walled test pieces is used as a characterization parameter of workpiece rigidity to carry out cutting experiments. In the modeling stage, in order to improve the generalization ability of the model, the first-order natural frequency is used as a rigidity characterization parameter to construct a cutting force exponential regression model. This provides a model foundation and technical guarantee for accurate and rapid prediction of cutting force, thereby realizing machining deformation analysis and process optimization.

[0005] This invention is achieved using the following technical means:

[0006] (1) Consider the workpiece thickness to design thin-walled test pieces: In order to simulate workpieces with different rigidity characteristics, design thin-walled test pieces with different thicknesses, so that their length-to-thickness ratio or width-to-thickness ratio is ≥20; the workpiece thickness reflects the weak rigidity of the workpiece, which can facilitate the quantification of the experimental stress level.

[0007] (2) Considering the weak rigidity of the workpiece, the influence of milling cutter parameters, and cutting parameters, a cutting experiment scheme was formulated: This invention adopts a strategy combining response surface methodology (RSM) and orthogonal experimental design to systematically study the influence of workpiece stiffness on the cutting process. A set of thin-walled test pieces with the same length and width but different thicknesses were prepared to simulate the range of stiffness variation of structural parts in actual machining. For each type of test piece, nine sets of cutting parameter combinations were designed for testing. The experiment used a rotary force-measuring tool holder for core data acquisition. This device is directly integrated into the spindle-tool system and can measure the three-dimensional cutting forces (Fx, Fy, Fz) in real time during the cutting process, effectively avoiding the interference signals introduced by the vibration of the workpiece-fixture system in traditional pedestal-type force gauges. All force signals were recorded synchronously at a high sampling frequency of 2.5kHz to ensure accurate capture of the dynamic characteristics of the cutting process and provide a reliable data foundation for constructing a high-precision cutting force model.

[0008] (3) Conducting machining experiments and data preprocessing for thin-walled test pieces: The machining experiment described in this invention refers to machining test pieces of various specifications one by one according to the above experimental scheme, and collecting three-dimensional dynamic cutting force data in real time during the cutting process through a force-measuring tool holder. Each set of parameters is repeated three times to eliminate random errors.

[0009] (4) Perform range analysis on the factors affecting cutting force, and perform necessary dimensionality reduction on the parameters based on the results of the influence degree analysis: Based on the multi-parameter dataset obtained from the cutting force experiment, the range analysis method is used to rank the factors affecting cutting force. Calculate the average range R of the cutting force index of each factor (including spindle speed, feed per tooth, depth of cut, cutting width, and workpiece thickness) at different levels, and determine the order of importance of the factors according to the size of the range. On this basis, perform necessary dimensionality reduction on the parameters: retain the key influencing factors with large ranges as core modeling variables; eliminate secondary factors (such as speed changes within a specific range) whose range values ​​are less than a set threshold (e.g., accounting for <10% of the total range), thereby effectively reducing the parameter dimensionality while ensuring model accuracy, and simplifying the complexity and computational load of the subsequent cutting force prediction model.

[0010] (5) Solving the first-order natural frequencies of workpieces with different thicknesses based on modal simulation: The thickness of the workpiece (i.e., rigidity characteristics) has a significant impact on the milling force. However, in practical applications, the geometric shapes and structural complexities of workpieces vary. If the thickness is directly used to characterize the rigidity of the workpiece, the constructed prediction model lacks the ability to be generalized to different structural components. The dynamic characteristics of a structural component are a comprehensive manifestation of its rigidity in a dynamic environment. The core parameters of the dynamic characteristics include natural frequencies, mode shapes, damping ratios, etc., which describe the response law of the structure to dynamic excitation. Therefore, in order to construct a cutting force prediction model related to workpiece rigidity and machining parameters, and to have the ability to generalize the model, this study uses the natural frequency values ​​of the structural component to characterize the rigidity characteristics. This patent uses ABAQUS finite element software to perform modal simulation analysis of thin-walled parts, solves the first-order natural frequencies of test pieces with different thicknesses, and uses these frequency values ​​as the key indicators for quantitatively characterizing the rigidity of the workpiece. The higher the first-order natural frequency, the better the rigidity of the workpiece structure, and vice versa. This method effectively establishes the mapping relationship between thickness, frequency, and workpiece rigidity through simulation.

[0011] (6) Construct a cutting force exponential regression model related to machining parameters and natural frequency: Based on experimental data, establish an exponential relationship model between cutting force and machining parameters (including spindle speed, feed per tooth, depth of cut, and width of cut) and workpiece natural frequency.

[0012] (7) Perform model validation and optimization: calculate the root mean square error (RMSE) and coefficient of determination (R²). 2 ) and Mean Absolute Percentage Error (MAPE), when the model has high accuracy on the training set and low accuracy on the test set (i.e., R... 2 If the difference is greater than 0.1, further refine the experimental level, optimize the experimental plan, and improve the model prediction accuracy by supplementing experimental data. When the accuracy of both the model training set and the test set is low, verify the dataset, remove data noise, and rebuild the model.

[0013] The invention is characterized by its innovative approach to proposing a cutting force prediction modeling method that considers the weak rigidity of the workpiece. This method uses workpiece thickness to characterize rigidity, combines response surface methodology and orthogonal method for experimental design, and uses range analysis to reduce parameter dimensionality. It also uses the first-order natural frequency of the workpiece to characterize rigidity and constructs an exponential regression model for cutting force, which significantly improves the accuracy and reliability of cutting force prediction and solves the technical problem of traditional models not considering the rigidity characteristics of the workpiece. Attached Figure Description

[0014] Figure 1 It is a tool holder type force gauge and milling cutter.

[0015] Figure 2 It is a test piece.

[0016] Figure 3This is the interface for acquiring cutting force data.

[0017] Figure 4 It is ABAQUS modal analysis.

[0018] Figure 5 It is an analysis of influencing factors. Detailed Implementation

[0019] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The objective of the present invention focuses on the influence mechanism of workpiece rigidity characteristics on cutting force, in order to obtain high-precision cutting force prediction characteristics while ensuring machining quality.

[0020] This invention implements a cutting force prediction modeling and parameter optimization method based on the rigidity characteristics of the workpiece. The implementation of this invention will be described in detail below with reference to the accompanying drawings.

[0021] The specific steps of the cutting force prediction modeling and parameter optimization method based on workpiece rigidity characteristics are as follows:

[0022] Step (1), experimental equipment and rigidity measurement

[0023] Rectangular thin-walled test specimens with dimensions of 150mm × 100mm were prepared using ZL114A aluminum alloy, with thickness gradients of 3.0mm, 3.5mm, 4.0mm, 4.5mm, and 5.0mm. A HOMAG XHS630 five-axis machining center was used for milling. A three-tooth end mill with a diameter of 5mm, a rake angle of 12°, and a helix angle of 45° was selected as the cutting tool. A RAISE rotary force measuring device was used. Modal simulation analysis was performed on the test specimens of each thickness using ABAQUS finite element software to obtain their first-order natural frequencies. The first-order natural frequencies of the test specimens for each thickness are shown in the table below.

[0024] Table 1 First-order natural frequencies of the test specimen

[0025]

[0026] Step (2), multi-parameter cutting experiment

[0027] This invention employs a hybrid strategy combining Response Surface Methodology (RSM) and orthogonal experimental design to systematically study the influence of workpiece stiffness characteristics on cutting dynamics. Specific experimental parameter combinations and collected data are shown in Table 2. For each test piece with different thicknesses, nine representative cutting parameter combinations were selected for testing. A total of 30 sets of valid experimental data were collected, and each experiment was repeated three times under the same conditions.

[0028] Table 2 Cutting parameters and results

[0029]

[0030] Step (3), Range analysis of factors affecting cutting force

[0031] Range analysis was performed on the three cutting force components. Based on orthogonal experimental design, the range analysis calculated the average response of each factor (workpiece thickness A, spindle speed B, cutting width C, feed rate D, and depth of cut E) at three levels, and then calculated the range (R = maximum average - minimum average). A larger range indicates a more significant impact of that factor on the cutting force.

[0032] Table 3. Range Analysis of Cutting Force Fx

[0033]

[0034] Table 3 shows that the depth of cut (E) has the greatest impact on F (range 7.02 N), followed by the cutting width (C) and feed rate (D). Fx increases significantly with increasing E, C, and D, indicating that the increased material removal rate leads to enhanced resistance in the x-direction. The spindle speed (B) is lowest at 6000 r / min, and increasing the workpiece thickness (A) slightly reduces Fx.

[0035] Table 4. Range Analysis of Cutting Force Fy

[0036]

[0037] Table 4 shows that the depth of cut (E) remains the dominant factor (range 6.24 N), followed by the width of cut (C) and feed rate (D). Fy increases with increasing E, C, and D, reflecting the sensitivity of lateral force to cutting parameters. Fy is lowest at spindle speed (B) of 6000 r / min, and increasing workpiece thickness (A) can slightly reduce lateral force.

[0038] Table 5. Range Analysis of Cutting Force Fz

[0039]

[0040] Table 5 shows that the depth of cut (E) has the most significant impact on Fz (range 9.44 N), followed by the width of cut (C) and feed rate (D). Fz increases sharply with increasing E, C, and D, indicating that the vertical force is highly sensitive to the material removal rate. Fz is lowest at a spindle speed (B) of 6000 r / min, and Fz decreases slightly with increasing workpiece thickness (A).

[0041] Step (4), construction and solution of the exponential model

[0042] Based on the aforementioned experimental data, the specific process for constructing the prediction model is as follows: First, the first-order natural frequencies of workpieces of different thicknesses under clamping constraints are calculated through simulation. Using the first-order natural frequencies and various machining parameters as inputs, and the three-dimensional cutting forces as outputs, a dataset is formed. This dataset is divided into two groups: an experimental group and a model validation group. The experimental group (groups 1-27) covers the measurement results of cutting forces under different combinations of cutting parameters and serves as the core dataset for establishing a cutting force and cutting heat prediction model. The model validation group (groups 28-30) is strictly independent of the model construction process and is used to quantitatively evaluate the accuracy, generalization ability, and reliability of the finally established cutting force prediction model. This grouping strategy ensures the independence of model training and validation, which helps to objectively evaluate the performance of the established model.

[0043] To more comprehensively and accurately describe the relationship between milling force and various influencing factors, considering the effects of the first-order natural frequency of the test piece (characterizing rigidity), tool parameters, and cutting parameters, a milling force exponential regression model is constructed as follows:

[0044]

[0045] In the formula, B represents the first-order natural frequency of the workpiece, C represents the spindle speed, D represents the cutting width, E represents the feed per tooth, and E represents the depth of cut.

[0046] Based on the 27 sets of data in the experimental table, exponential regression models for milling heat were constructed. This involved data fitting using the least squares method, and the parameters of the model were calculated and determined through an iterative algorithm, as shown below:

[0047]

[0048] Step (5), Model Validation

[0049] In the model validation section, the cutting force prediction model constructed in this study exhibits good generalization ability and prediction accuracy. The coefficient of determination R² for the training set reaches 0.9555, and the R² for the test set is 0.9024, with a difference of less than 0.1 (only 0.0531), indicating that the model does not exhibit overfitting and has high reliability. Validation using test set data (as shown in Table 1) shows that the model's error percentage is mostly below 2% in predicting feed force Fx, radial force Fy, and axial force Fz, with only a few data points showing slightly higher errors (e.g., the Fx error in group 2 is 5.03%), but the overall predicted values ​​are in good agreement with the measured values. The current model accuracy meets the requirements of engineering applications. If, in the future, there is a significant difference in performance between the training and test sets (e.g., R² difference > 0.1) or an overall decrease in accuracy, the model's predictive ability can be further improved by refining the experimental level, optimizing the experimental scheme, supplementing data, or removing noise.

[0050] Table 6 Prediction Error

[0051]

Claims

1. A method for predicting and modeling cutting forces related to workpiece rigidity characteristics, characterized in that: Includes the following steps, Step 1: Design a thin-walled test specimen considering the workpiece thickness; Step 2: Considering the weak rigidity of the workpiece, the milling cutter parameters, and the cutting parameters, formulate a cutting process experiment plan; Step 3: Conduct machining experiments on thin-walled test pieces and perform data preprocessing; Step 4: Perform a range analysis of the factors affecting cutting force, and perform necessary dimensionality reduction of the parameters based on the results of the influence analysis. Step 5: Solve for the first-order natural frequencies of workpieces with different thicknesses based on modal simulation: The workpiece thickness, i.e., the rigidity characteristic, has a significant impact on the milling force. However, in practical applications, the workpiece geometry and structural complexity vary. If the thickness is directly used to characterize the workpiece rigidity, the constructed prediction model lacks the ability to be generalized to different structural components. The dynamic characteristics of a structural component are the comprehensive performance of its rigidity in a dynamic environment. The core parameters of the dynamic characteristics include natural frequency, mode shape, and damping ratio, which describe the response law of the structure to dynamic excitation. The natural frequency value of the structural component is used to characterize the rigidity characteristics. Modal simulation analysis of thin-walled parts was performed using ABAQUS finite element software to solve the first natural frequency of test pieces with different thicknesses. This frequency value was used as a key indicator to quantitatively characterize the rigidity of the workpiece. The higher the first natural frequency, the better the rigidity of the workpiece structure, and vice versa. The mapping relationship between thickness, frequency and workpiece rigidity was effectively established through simulation. Step 6: Construct an exponential regression model of cutting force related to machining parameters and natural frequency: Establish an exponential relationship model between cutting force and machining parameters and workpiece natural frequency based on experimental data; machining parameters include spindle speed, feed per tooth, depth of cut, and width of cut; Step 7: Perform model validation and optimization.

2. The method for predicting and modeling cutting forces related to workpiece rigidity characteristics according to claim 1, characterized in that: In step 1, in order to simulate workpieces with different rigidity characteristics, thin-walled test pieces with different thicknesses are designed so that their length-to-thickness ratio or width-to-thickness ratio is ≥20; the thickness of the workpiece is used to reflect the weak rigidity of the workpiece and to quantify the experimental stress level.

3. The method for predicting and modeling cutting forces related to workpiece rigidity characteristics according to claim 1, characterized in that: In step 2, a strategy combining response surface methodology (RSM) and orthogonal experimental design is adopted to systematically study the influence of workpiece stiffness on the cutting process. A set of thin-walled test pieces with the same length and width but different thicknesses were prepared to simulate the range of stiffness variation of structural parts in actual machining. For each type of test piece, nine sets of cutting parameter combinations were designed for testing. The experiment used a rotary force-measuring tool holder for core data acquisition. The rotary force-measuring tool holder was directly integrated into the spindle-tool system to measure the three-dimensional cutting forces (Fx, Fy, Fz) in real time during the cutting process. All force signals were recorded synchronously at a high sampling frequency of 2.5kHz.

4. The method for predicting and modeling cutting forces related to workpiece rigidity characteristics according to claim 1, characterized in that: In step 3, the cutting experiment refers to processing test pieces of various specifications one by one according to the above experimental plan, and collecting three-dimensional dynamic cutting force data in real time during the cutting process through a force measuring tool holder; each set of parameters is repeated three times to eliminate random errors.

5. The method for predicting and modeling cutting forces related to workpiece rigidity characteristics according to claim 1, characterized in that: In step 4, based on the multi-parameter dataset obtained from the cutting force experiment, the range analysis method is used to rank the factors affecting the cutting force by significance. The average range R of the cutting force index at different levels is calculated for each factor, including spindle speed, feed per tooth, depth of cut, cutting width, and workpiece thickness. The order of importance of the factors is determined according to the size of the range. Necessary dimensionality reduction of the parameters is performed: key influencing factors with large ranges are retained as core modeling variables; secondary factors with ranges less than a set threshold are eliminated. While ensuring the accuracy of the model, the dimensionality of the parameters is reduced, simplifying the complexity and computation of the subsequent cutting force prediction model.

6. The method for predicting and modeling cutting forces related to workpiece rigidity characteristics according to claim 1, characterized in that: In step 7, the root mean square error (RMSE) and the coefficient of determination (R²) are calculated. 2 And the mean absolute percentage error (MAPE), when the model has high accuracy on the training set and low accuracy on the test set, i.e., R 2 If the difference is greater than 0.1, refine the experimental level, optimize the experimental plan, and improve the model prediction accuracy by supplementing experimental data. When the accuracy of both the model training set and the test set is low, examine the dataset, remove data noise, and rebuild the model.

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