A Damage Modeling Method for CFRP Cutting Structures Based on Mechanothermal Coupling Energy Evolution

Abstract

This invention relates to the field of composite material machining technology, specifically to a method for modeling CFRP (Composite Material Reinforced Plastic) cutting structure damage based on force-thermal coupling energy evolution. This method first collects cutting force and temperature data for a group of CFRP workpieces under different cutting parameters. Then, it calculates the structural response variables under the corresponding cutting parameters based on the cutting force and temperature data for each group. Next, a semi-analytical cutting structure damage prediction model is established. Then, based on the semi-analytical method, the initial porosity and initial fractal dimension of the CFRP workpiece under test, as well as the structural response variables under different cutting parameters, the measured porosity change, and the measured fractal dimension after cutting, are used to calibrate the preset weighting coefficients and the calibration coefficients of the semi-analytical cutting structure damage prediction model, obtaining the final cutting structure damage prediction model. This model can achieve accurate quantitative evaluation of the evolution of the internal pore structure of the CFRP workpiece after cutting under any cutting parameters.

Description

Technical Field

[0001] This invention relates to the field of composite material machining technology, and in particular to a method for modeling damage in CFRP cutting structures based on force-thermal coupling energy evolution. Background Technology

[0002] Carbon fiber reinforced resin matrix composites (CFRP) have been widely used in the aerospace field due to their advantages such as high specific strength, high specific modulus, and outstanding fatigue resistance.

[0003] In extreme service environments such as aerospace, CFRP structural components, such as engine fan blades, need to withstand strong thermal loads and high-frequency vibrations for extended periods, placing extremely stringent requirements on their dimensional accuracy, surface quality, and structural integrity. However, CFRP machining, a crucial step in CFRP applications, is prone to microscopic damage due to the multiphase, anisotropic, and low thermal conductivity polymer matrix. The strong thermal loads during machining can lead to microscopic defects such as fiber breakage, matrix cracking, and interface debonding. These defects extend and connect along the cutting path, evolving into more severe damage forms such as interlayer delamination and porosity accumulation. This damage evolution from microscopic to macroscopic caused by machining not only weakens the load-bearing capacity of CFRP structural components, leading to early fatigue failure, but also causes structural integrity degradation, severely reducing the service life and reliability of CFRP as a component and directly threatening its service safety under extreme conditions.

[0004] Therefore, existing technologies typically aim to fundamentally reveal the generation and cross-scale evolution mechanisms of damage, and establish corresponding quantifiable damage prediction models based on the characteristics of CFRP. The goal is to predict damage during the machining of CFRP structural components, and based on the prediction results, actively control and ultimately eliminate these machining damages as much as possible, thereby achieving high-quality and efficient machining of CFRP components. However, most current predictions of CFRP machining damage largely follow the paradigm of surface damage analysis for metals. Considering the specific characteristics of CFRP, they merely equate machining damage with macroscopic surface defects such as delamination and burrs, paying little attention to the overall machining evolution laws of internal structural defects in the material.

[0005] Because the CFRP cutting process itself involves significant thermal loads and high-frequency vibrations, it inevitably leads to microstructural evolution, such as the expansion of internal pores. These microstructural defects caused by force-thermal coupling have a far greater impact on the service performance of CFRP than surface defects. Therefore, there is an urgent need for a method to predict CFRP cutting structural damage, quantitatively assessing the evolution of the internal microstructure of CFRP caused by force-thermal coupling during cutting. This would further assist in adjusting machining parameters, thereby achieving effective control of CFRP cutting damage and improving machining quality. Summary of the Invention

[0006] Therefore, it is necessary to provide a CFRP cutting structure damage modeling method based on force-thermal coupling energy evolution to address the above-mentioned technical problems. The method uses force-thermal coupling input energy as the driving force and porosity fractal dimension evolution as the response to construct a cutting structure damage prediction model. This model can quantitatively predict and evaluate the porosity change and fractal dimension of the CFRP workpiece under any cutting parameters.

[0007] This invention provides a damage modeling method for CFRP cutting structures based on force-thermal coupling energy evolution, comprising the following steps:

[0008] S1. Collect data from the CFRP workpiece to be tested. Data on cutting force and cutting temperature under different cutting parameters. ;

[0009] S2. Calculate the structural response variables under the corresponding cutting parameters based on each set of cutting force and cutting temperature data;

[0010] Calculating the structural response variables under corresponding cutting parameters based on a set of cutting force and cutting temperature data includes the following steps:

[0011] Calculate the total input energy during the cutting process based on the cutting force and cutting speed;

[0012] The total input energy is decomposed into mechanical energy and thermal energy through the energy distribution coefficient;

[0013] Mechanical energy and thermal energy are combined into effective destructive energy according to preset weighting coefficients;

[0014] Establish a temperature window function to calculate the nonlinear modulation coefficient of thermal energy based on the cutting temperature;

[0015] Calculate the structural response variables based on the nonlinear modulation coefficients of effective destructive energy and thermal energy;

[0016] S3. A semi-analytical damage prediction model for cutting structures is established using the change in porosity and the fractal dimension after cutting as damage prediction indicators.

[0017] S4. Based on the semi-analytical method, utilizing the initial porosity and initial fractal dimension of the CFRP workpiece under test, and The structural response variables under different cutting parameters, the measured porosity change, and the measured fractal dimension after cutting are used to calibrate the preset weighting coefficients and the coefficients to be calibrated in the semi-analytical cutting structure damage prediction model. After calibration, the final cutting structure damage prediction model is obtained.

[0018] In one embodiment, the semi-analytical cutting structure damage prediction model is as follows:

[0019] ,

[0020] ,

[0021] In the formula, This indicates the change in porosity. Indicates porosity after cutting. Indicates the initial porosity. Indicates the damage coefficient. This represents the structural response variable after the cutting process is completed. This represents the total specific surface area of ​​the CFRP workpiece under test per unit volume. This represents the fractal dimension after the cutting process is completed. Denotes the initial fractal dimension. Represents the coupling constant. Indicates the critical porosity. This represents the average cutting temperature during the cutting process. This represents the cutting temperature acceleration factor during the cutting process. Indicates the reference temperature. , and These are the coefficients to be calibrated for the semi-analytical cutting structure damage prediction model.

[0022] In one embodiment, the total input energy is calculated as follows:

[0023] ,

[0024] In the formula, This represents the total input energy. express Cutting force at any moment Indicates cutting speed. Indicates the cutting time. .

[0025] In one embodiment, the energy distribution coefficient is calculated as follows:

[0026]

[0027] In the formula, express Energy distribution coefficient at time, express Instantaneous cutting temperature at any given moment. Indicates the ambient temperature of the cutting environment. This represents the highest temperature value during the entire cutting process;

[0028] The formula for calculating mechanical energy is:

[0029]

[0030] In the formula, Represents mechanical energy;

[0031] The formula for calculating thermal energy is:

[0032]

[0033] In the formula, It represents thermal energy.

[0034] In one embodiment, the effective destruction energy is used to characterize the force-thermal coupling effect, and the effective destruction energy is calculated as follows:

[0035]

[0036] In the formula, Indicates effective destructive energy. and All represent preset weighting coefficients. , , .

[0037] In one embodiment, the temperature window function is in the form of a Gaussian function, and the expression of the temperature window function is:

[0038]

[0039] In the formula, express The nonlinear modulation coefficient of thermal energy at time t. This indicates the critical temperature of the CFRP material for thermism. Indicates the modulation interval. and All results were determined using differential scanning calorimetry.

[0040] In one embodiment, the integral value of the product function of the effective damaging energy and the nonlinear modulation coefficient of thermal energy during the cutting time is calculated as the structural response variable for quantifying the internal structural damage state of the CFRP workpiece under test; the formula for calculating the structural response variable is:

[0041] .

[0042] In one embodiment, the final cutting structure damage prediction model in step S4 is used to predict the porosity change and fractal dimension of the CFRP workpiece under arbitrary cutting parameters after cutting.

[0043] Step S4 specifically includes the following steps:

[0044] S41, will Substituting the measured porosity change and structural response variable of the CFRP workpiece after cutting under the set of cutting parameters into the equation... Construct different computational formulas and combine multiple different computational formulas to construct a system of linear equations;

[0045] S42. Solve the linear equation system using the least squares method to determine the solution. , and Specific value;

[0046] S43. Using a semi-analytical cutting structure damage prediction model, establish a prediction formula for the fractal dimension after cutting under different cutting parameters. Based on the prediction formula for the fractal dimension after cutting under different cutting parameters and the measured fractal dimension after cutting, construct a nonlinear least squares optimization model.

[0047] The nonlinear least squares optimization model is as follows:

[0048]

[0049] In the formula, This represents the fractal dimension after the actual cutting is completed. This represents the fractal dimension predicted by the semi-analytical cutting structure damage prediction model after the cutting process is completed.

[0050] S44. Obtain the solution by solving the nonlinear least squares optimization model using a numerical optimization algorithm. and The specific value.

[0051] In one embodiment, obtaining the initial or measured porosity and fractal dimension of the CFRP workpiece to be tested in step S4 includes the following steps:

[0052] S51. The pore size distribution data and porosity of the CFRP workpiece under test are obtained by mercury porosimetry.

[0053] S52. The fractal dimension is obtained by fitting the aperture distribution data based on the fractal dimension model.

[0054] The beneficial effects of this invention are as follows: This invention innovatively uses porosity as the basic indicator of structural damage and fractal dimension as the core indicator for quantifying the evolution of porosity induced by cutting. By quantifying the allocation of mechanical energy and thermal energy in the total input energy, as well as the coupling and evolution of their contribution to damage, a cutting structure damage prediction model is constructed using a semi-analytical method. This cutting structure damage prediction model can quantitatively predict and evaluate the change in porosity and the fractal dimension of the CFRP workpiece after cutting under arbitrary cutting parameters. It realizes the accurate quantitative evaluation of the evolution of the internal microstructure of CFRP caused by the force-thermal coupling effect during the cutting process, and can further assist in adjusting the CFRP cutting process parameters to achieve machining quality optimization and damage control. Attached Figure Description

[0055] Figure 1 This is a flowchart illustrating a method for modeling damage in CFRP cutting structures based on force-thermal coupling energy evolution, as provided in an embodiment of the present invention.

[0056] Figure 2 This is a schematic diagram of the cutting and signal acquisition system provided in an embodiment of the present invention;

[0057] Figure 3 This is a flowchart illustrating the process of calculating the structural response variables under corresponding cutting parameters based on a set of cutting force and cutting temperature data, as provided in an embodiment of the present invention.

[0058] Figure 4 This is a schematic diagram of the DSC curve of the CFRP workpiece under test provided in an embodiment of the present invention;

[0059] Figure 5 A comparison chart of predicted and measured values ​​of the fractal dimension provided in an embodiment of the present invention;

[0060] Figure 6 The fractal dimension relative error distribution diagram provided in the embodiments of the present invention;

[0061] Figure 7 A comparison chart of the predicted and measured values ​​of the fractal dimension when using leave-one-out cross-validation, provided for an embodiment of the present invention;

[0062] Figure 8 The fractal dimension relative error distribution diagram provided for leave-one-out cross-validation in an embodiment of the present invention. Detailed Implementation

[0063] 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 illustrative and not intended to limit the invention.

[0064] Existing technologies indicate that for CFRP, micropores are the starting point for damage initiation. The CFRP cutting process itself is a process of strong thermal load coupled with dynamic driving and high-frequency vibration, which inevitably leads to the initiation and evolution of micropore structures within the material. This crucial bridge from physical driving to microstructural response has not yet been effectively constructed. To establish a predictive model that truly reflects the damage mechanism of CFRP cutting, it is necessary to go beyond the characterization of macroscopic defects and delve into the evolution of internal pores under the driving force-thermal coupling field.

[0065] This invention innovatively uses porosity as the primary indicator for measuring structural damage and further uses fractal dimension as the core indicator for quantifying cutting-induced porosity evolution. It constructs a quantitative cutting structural damage prediction model driven by mechanical-thermal coupling input energy and responding to the evolution of porosity fractal dimension, thereby enabling the prediction of porosity and fractal dimension variation trends under different cutting conditions. This effectively fills the theoretical gap in the field of CFRP cutting, from physical driving to microstructural damage evaluation.

[0066] The specific method of this invention is as follows:

[0067] In one embodiment, such as Figure 1 As shown in this embodiment, the CFRP cutting structure damage modeling method based on force-thermal coupling energy evolution includes the following steps:

[0068] S1. Collect data from the CFRP workpiece to be tested. Data on cutting force and cutting temperature under different cutting parameters. Specifically, the cutting force and cutting temperature data are obtained using, for example... Figure 2 The cutting process and signal acquisition system shown collects data. The cutting force data signal is acquired by a force measuring instrument, and the cutting temperature data signal is acquired by an infrared thermal imager. Both transmit the acquired data signals to a data acquisition unit or computer for processing.

[0069] S2. Calculate the structural response variables under the corresponding cutting parameters based on each set of cutting force and cutting temperature data;

[0070] like Figure 3 As shown, the structural response variables under corresponding cutting parameters are calculated based on a set of cutting force and cutting temperature data, including the following steps:

[0071] S21. Calculate the total input energy during the cutting process based on the cutting force and cutting speed.

[0072] Specifically, the formula for calculating the total input energy is:

[0073]

[0074] In the formula, This represents the total input energy. express Cutting force at any moment Indicates cutting speed. Indicates the cutting time. .

[0075] It should be noted that, since the cutting speed remains essentially constant throughout the entire cutting process, this invention assumes that the cutting speed remains consistent throughout the entire cutting process. Specifically, the cutting speed is the spindle speed of the cutting system. The product of the diameter of the cutting tool and the diameter of the cutting tool.

[0076] S22. The total input energy is decomposed into mechanical energy and thermal energy using the energy distribution coefficient. Mechanical energy is used to characterize mechanical action, and thermal energy is used to characterize thermal action.

[0077] Specifically, in this embodiment, the formula for calculating the energy distribution coefficient is as follows:

[0078]

[0079] In the formula, express Energy distribution coefficient at time, express Instantaneous cutting temperature at any given moment. Indicates the ambient temperature of the cutting environment. This indicates the highest temperature value during the entire cutting process.

[0080] Mechanical energy and thermal energy can be calculated using integrals. The formula for mechanical energy is:

[0081]

[0082] In the formula, It represents mechanical energy.

[0083] The formula for calculating thermal energy is:

[0084]

[0085] In the formula, It represents thermal energy.

[0086] S23. Combine mechanical energy and thermal energy into effective destructive energy according to a preset weighting coefficient.

[0087] The effective breaking energy is used to characterize the force-thermal coupling effect. It refers to the portion of the input energy in the cutting system that is used for increasing material damage. The formula for calculating the effective breaking energy is:

[0088]

[0089] In the formula, Indicates effective destructive energy. and All represent preset weighting coefficients. , , .

[0090] S24. Establish a temperature window function to calculate the thermal energy nonlinear modulation coefficient based on the cutting temperature. The thermal energy nonlinear modulation coefficient is used to nonlinearly modulate the contribution of thermal energy to reflect the degradation of CFRP material properties with increasing temperature.

[0091] In this embodiment, the temperature window function adopts the form of a Gaussian function, and the expression of the temperature window function is:

[0092]

[0093] In the formula, express The nonlinear modulation coefficient of thermal energy at time t. This indicates the critical temperature of the CFRP material for thermism. Indicates the modulation interval.

[0094] The critical temperature of CFRP material is the critical temperature at which the CFRP resin matrix begins to undergo a glass transition, and the modulation range is the temperature range from the starting point to the ending point of the glass transition of the CFRP resin.

[0095] The temperature window function is used to characterize the effective temperature range of thermally activated damage. Among them, and All results were determined based on differential scanning calorimetry (DSC), specifically by fitting the DSC curve of the CFRP resin matrix. For example, see attached... Figure 4 As shown, after baseline correction of the glass transition range data of CFRP resin, nonlinear least squares fitting was performed using a Gaussian function. The optimal parameters were finally obtained. = 166.0℃, = 20.5℃. This method ensures that the parameters of the temperature window function are directly derived from the intrinsic thermophysical properties of the material, giving the temperature window function a solid physical basis.

[0096] S25. Calculate the structural response variables based on the effective destructive energy and the nonlinear modulation coefficient of thermal energy.

[0097] Specifically, in step S25, the integral value of the product function of the effective damaging energy and the nonlinear modulation coefficient of thermal energy during the cutting time is calculated as the structural response variable for quantifying the internal structural damage state of the CFRP workpiece under test; the formula for calculating the structural response variable is:

[0098] .

[0099] S3. A semi-analytical damage prediction model for the cutting structure is established using the change in porosity and the fractal dimension after cutting as damage prediction indicators; the semi-analytical damage prediction model for the cutting structure is as follows:

[0100]

[0101]

[0102] In the formula, This indicates the change in porosity. Indicates porosity after cutting. Indicates the initial porosity. Indicates the damage coefficient. This represents the structural response variable after the cutting process is completed. This represents the total specific surface area of ​​the CFRP workpiece under test per unit volume. This represents the fractal dimension after the cutting process is completed. Denotes the initial fractal dimension. Represents the coupling constant. Indicates the critical porosity. This represents the average cutting temperature during the cutting process. This represents the cutting temperature acceleration factor during the cutting process. Indicates the reference temperature. , and These are the coefficients to be calibrated for the semi-analytical cutting structure damage prediction model. The reference temperature is used for temperature normalization.

[0103] in, The data was obtained from mercury intrusion porosimetry experimental data. The semi-analytical cutting structure damage prediction model in this embodiment quantifies the allocation of mechanical and thermal energy in the total input energy, and further couples the synergistic contribution of mechanical and thermal energy to damage and their evolution process. Using porosity as the fundamental indicator of structural damage and fractal dimension as the core indicator for quantifying cutting-induced porosity evolution, it can achieve accurate quantitative assessment of the internal structural damage evolution of CFRP caused by the force-thermal coupling effect during cutting.

[0104] S4. Based on the semi-analytical method, utilizing the initial porosity and initial fractal dimension of the CFRP workpiece under test, and The structural response variables under different cutting parameters, the measured porosity change, and the measured fractal dimension after cutting are used to calibrate the preset weighting coefficients and the coefficients to be calibrated in the semi-analytical cutting structure damage prediction model. After calibration, the final cutting structure damage prediction model is obtained.

[0105] It should be noted that the final cutting structure damage prediction model established based on a certain CFRP workpiece under test can only be used to predict the porosity change and fractal dimension of the CFRP workpiece under test after cutting. When predicting the porosity change and fractal dimension of other CFRP workpieces after cutting, a new corresponding cutting structure damage prediction model needs to be established.

[0106] In one embodiment, the final cutting structure damage prediction model in step S4 is used to predict the change in porosity and the fractal dimension after cutting of the CFRP workpiece under arbitrary cutting parameters.

[0107] Step S4 specifically includes the following steps:

[0108] S41, will Substituting the measured porosity change and structural response variable of the CFRP workpiece after cutting under the set of cutting parameters into the equation... Different computational formulas are constructed, and multiple different computational formulas are combined to construct a system of linear equations.

[0109] Before constructing different computational formulas, first analyze the structural response variables. The definition is further defined as follows:

[0110]

[0111] In the formula, This indicates the number of cutting parameter groups.

[0112] Then, by breaking down the integral into weighted inputs under different energies and performing the calculation, we can obtain:

[0113]

[0114] ;

[0115] but This can be further expressed as:

[0116] ;

[0117] The relationship between porosity change and structural response variables is as follows:

[0118] ;

[0119] We can further conclude that:

[0120] ;

[0121] Then Different calculation formulas are constructed by substituting the measured porosity change and structural response variables of the CFRP workpiece after cutting under the set of cutting parameters into the above formula.

[0122] In this embodiment, a system of linear equations constructed using multiple different computational formulas can be represented in matrix form, defined as follows:

[0123]

[0124]

[0125]

[0126] Multiple different computational formulas can be used to construct the matrix form of the linear equation system:

[0127]

[0128] In the formula, This is the residual term, used to characterize the deviation between model predictions and experimental data.

[0129] S42. Solve the linear equation system using the least squares method to determine the solution. , and Specific value;

[0130] Due to the experimental sample size, ,matrix It is reversible, thus the parameters can be stably solved using the least squares method. Solving using the least squares method... available , and Specific value.

[0131] S43. Using a semi-analytical cutting structure damage prediction model, establish a predictive calculation formula for the fractal dimension after cutting under different cutting parameters. Based on the predictive calculation formula for the fractal dimension after cutting under different cutting parameters and the measured fractal dimension after cutting, construct a nonlinear least squares optimization model.

[0132] Specifically, under the i-th set of cutting conditions, the damage index predicted by the model can be expressed as:

[0133]

[0134] In the formula, This represents the critical pore volume increment, which is... and The product of.

[0135] To solve for the unknown parameters and The damage index measured in the experiment Compared with model predictions In comparison, the nonlinear least squares optimization model is established as follows:

[0136]

[0137] In the formula, This represents the fractal dimension after the actual cutting is completed. This represents the fractal dimension predicted by the semi-analytical cutting structure damage prediction model after the cutting process is completed.

[0138] S44. Obtain the solution by solving the nonlinear least squares optimization model using a numerical optimization algorithm. and The specific value is then determined. A nonlinear fitting of the least squares optimization model is performed using numerical optimization methods. This process can simultaneously utilize multiple sets of experimental data to constrain the parameters, ensuring the robustness of the fit.

[0139] In one embodiment, obtaining the initial or measured porosity and fractal dimension of the CFRP workpiece to be tested in step S4 includes the following steps:

[0140] S51. The pore size distribution data and porosity of the CFRP workpiece under test are obtained by mercury porosimetry.

[0141] S52. The fractal dimension is obtained by fitting the aperture distribution data based on the fractal dimension model.

[0142] Preferably, in this embodiment, a fractal model based on thermodynamic relationships is used to analyze the mercury intrusion porosimetry data to calculate the initial fractal dimension.

[0143] In a specific embodiment, taking the milling of CFRP laminate as an example, the method of the present invention will be further explained with reference to specific experimental data.

[0144] The CFRP laminate of this embodiment is composed of 28 layers of unidirectional carbon fiber woven fabric, using domestically produced T800 carbon fiber / epoxy resin as the raw material. The stacking sequence is [0° / +45° / 0° / -45°] 7s, and it is formed using an autoclave curing process. The physical properties of the CFRP laminate of this embodiment are as follows: after curing, the thickness of a single layer is (0.187±0.012) mm, and the density is (1.58±0.03) g / cm³. 3 The fiber volume fraction was 58 vol% ± 3 vol%, and the sample size for the milling test was 100 mm × 100 mm × 5 mm.

[0145] Specifically, in this embodiment, side milling is selected. The number of samples was 5. During the experiment, the axial depth of cut was kept constant. Different force-heat input conditions were constructed by adjusting the spindle speed, feed per tooth, and radial depth of cut. A total of six sets of samples were set up, including one static reference sample (A0, unmachined) and five sets of cutting conditions with different combinations of cutting parameters (A1-A5). The specific cutting parameters are detailed in Table 1.

[0146] Table 1 Cutting Parameter Table

[0147]

[0148] Cutting force and cutting temperature data of CFRP laminates under different cutting parameters were collected. Specifically, in this embodiment, the side milling cutting experiment was conducted in a dry environment using a five-axis machining center (model XKH800). During the cutting process, a Kistler 9272 rotary force gauge was used to record the changes in cutting force. To ensure the repeatability of the experiment, each set of parameters was cut twice to ensure the accuracy and stability of the cutting force measurement. The cutting tool was replaced after every three sets of cutting parameters to eliminate the influence of tool wear. After calibration, the cutting temperature was measured using a FOTRIC 220S infrared thermal imager. The emissivity of the CFRP composite material used in this embodiment was calibrated according to ASTM E1933-14 standard. This embodiment characterized the changes in the pore structure of CFRP material after cutting under different parameter conditions. The pore structure was measured using an AutoPore IV 9500 mercury porosimeter, with a test range of 0.003-360 μm.

[0149] Then, based on each set of cutting force and cutting temperature data, the structural response variables under the corresponding cutting parameters are calculated, a semi-analytical cutting structure damage prediction model is established, and preset weighting coefficients are applied. , and The final cutting structure damage prediction model of the CFRP laminate is obtained through calibration. It can be used to predict the porosity change and fractal dimension of the CFRP workpiece after cutting under any cutting parameters.

[0150] To verify the prediction accuracy of the final cutting structure damage prediction model for CFRP laminates of this invention, this embodiment conducted actual measurements of the structural damage of sample groups under different cutting parameters, measuring the porosity and fractal dimension after cutting, and comparing them with the predicted values ​​of the final cutting structure damage prediction model. Table 2 details the comparison between the measured and predicted values ​​of the porosity and fractal dimension of CFRP laminates after cutting under different cutting parameters. A comparison of the predicted and measured values ​​of the fractal dimension is also provided. Figure 5 As shown, the relative error distribution of the fractal dimension predicted by the final cutting structure damage prediction model of the CFRP laminate is as follows: Figure 6 As shown.

[0151] Table 2 Comparison of measured and predicted values ​​of porosity and fractal dimension after cutting

[0152]

[0153] As shown in Table 2, compared with the measured values, the predicted values ​​for samples A1 to A5 have a relative error of less than or equal to 4.83% in porosity and a relative error of less than or equal to 0.98% in fractal dimension, proving that the final cutting structure damage prediction model for the CFRP laminate of this invention has high prediction accuracy. Furthermore, from... Figure 5 It can be seen that the error between the predicted and measured values ​​of the fractal dimension is small. Figure 6 As can be seen from the data, the goodness of fit R of the prediction model for the final cutting structure damage of the CFRP laminate to the predicted fractal dimension is... 2 =0.9933, and the root mean square error (RMSE) is 0.0147, indicating that the final cutting structure damage prediction model of the CFRP laminate of this invention has a high degree of fit and a low prediction error.

[0154] This embodiment further employs leave-one-out cross-validation to assess the generalization ability of the final cutting structure damage prediction model. In leave-one-out cross-validation, one set of sample parameters is removed from all parameters at each step, and the remaining set is used to evaluate the preset weighting coefficients. , and After calibration, the fractal dimension of the excluded groups is predicted. The leave-one-out cross-validation results are as follows: Figure 7 and 8 As shown. By Figure 7 and Figure 8 It can be seen that the errors between the predicted and measured values ​​of the fractal dimension of each sample are within a reasonable range, and the predicted and measured values ​​maintain a high degree of consistency. R 2 = 0.9788, RMSE is 0.0262. Although the fitting accuracy of the model decreased slightly compared to the calibration of all parameters, the residuals remained stable within ±0.04, and the error fluctuation range was controlled between ±3% and 5%, indicating that the established final cutting structure damage prediction model has excellent generalization ability.

[0155] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for damage modeling of CFRP cutting structures based on force-thermal coupling energy evolution, characterized in that, Includes the following steps: S1. Collect data from the CFRP workpiece to be tested. Data on cutting force and cutting temperature under different cutting parameters. ; S2. Calculate the structural response variables under the corresponding cutting parameters based on each set of cutting force and cutting temperature data; Calculating the structural response variables under corresponding cutting parameters based on a set of cutting force and cutting temperature data includes the following steps: Calculate the total input energy during the cutting process based on the cutting force and cutting speed; The total input energy is decomposed into mechanical energy and thermal energy using an energy distribution coefficient. The mechanical energy and thermal energy are combined into effective destructive energy according to a preset weighting coefficient; Establish a temperature window function to calculate the nonlinear modulation coefficient of thermal energy based on the cutting temperature; Calculate the structural response variables based on the nonlinear modulation coefficients of effective destructive energy and thermal energy; S3. A semi-analytical damage prediction model for cutting structures is established using the change in porosity and the fractal dimension after cutting as damage prediction indicators. S4. Based on the semi-analytical method, utilizing the initial porosity and initial fractal dimension of the CFRP workpiece under test, and The pre-set weighting coefficients and the coefficients to be calibrated of the semi-analytical cutting structure damage prediction model are calibrated by the structural response variables under different cutting parameters, the measured porosity change, and the measured fractal dimension after cutting. After calibration, the final cutting structure damage prediction model is obtained. The semi-analytical cutting structure damage prediction model is as follows: ， ， In the formula, This indicates the change in porosity. Indicates porosity after cutting. Indicates the initial porosity. Indicates the damage coefficient. This represents the structural response variable after the cutting process is completed. This represents the total specific surface area of ​​the CFRP workpiece under test per unit volume. This represents the fractal dimension after the cutting process is completed. Denotes the initial fractal dimension. Represents the coupling constant. Indicates the critical porosity. This represents the average cutting temperature during the cutting process. This represents the cutting temperature acceleration factor during the cutting process. Indicates the reference temperature. , and These are the coefficients to be calibrated for the semi-analytical cutting structure damage prediction model.

2. The CFRP cutting structure damage modeling method based on force-thermal coupling energy evolution according to claim 1, characterized in that, The formula for calculating the total input energy is: ， In the formula, This represents the total input energy. express Cutting force at any moment Indicates cutting speed. Indicates the cutting time. .

3. The CFRP cutting structure damage modeling method based on force-thermal coupling energy evolution according to claim 2, characterized in that, The formula for calculating the energy distribution coefficient is: ， In the formula, express Energy distribution coefficient at time, express Instantaneous cutting temperature at any given moment. Indicates the ambient temperature of the cutting environment. This represents the highest temperature value during the entire cutting process; The formula for calculating the mechanical energy is: ， In the formula, Represents mechanical energy; The formula for calculating the thermal energy is: ， In the formula, It represents thermal energy.

4. The CFRP cutting structure damage modeling method based on force-thermal coupling energy evolution according to claim 3, characterized in that, The effective destructive energy is used to characterize the force-thermal coupling effect, and the formula for calculating the effective destructive energy is: ， In the formula, Indicates effective destructive energy. and All represent preset weighting coefficients. , , .

5. The CFRP cutting structure damage modeling method based on force-thermal coupling energy evolution according to claim 4, characterized in that, The temperature window function adopts the form of a Gaussian function, and the expression of the temperature window function is: ， In the formula, express The nonlinear modulation coefficient of thermal energy at time t. This indicates the critical temperature for the thermistor of CFRP material. Indicates the modulation interval. and All results were determined using differential scanning calorimetry.

6. The CFRP cutting structure damage modeling method based on force-thermal coupling energy evolution according to claim 5, characterized in that, The integral value of the product function of the effective damage energy and thermal energy nonlinear modulation coefficients during the cutting time is used as the structural response variable to quantify the internal structural damage state of the CFRP workpiece under test. The formula for calculating the structural response variable is: 。 7. The CFRP cutting structure damage modeling method based on force-thermal coupling energy evolution according to claim 6, characterized in that, The final cutting structure damage prediction model in step S4 is used to predict the porosity change and fractal dimension of the CFRP workpiece under arbitrary cutting parameters after cutting. Step S4 specifically includes the following steps: S41, will Substituting the measured porosity change and structural response variable of the CFRP workpiece after cutting under the set of cutting parameters into the equation... Different computational formulas are constructed, and multiple different computational formulas are combined to construct a system of linear equations. S42. Solve the linear equation system using the least squares method to determine the solution. , and Specific value; S43. Using a semi-analytical cutting structure damage prediction model, establish a prediction formula for the fractal dimension after cutting under different cutting parameters. Based on the prediction formula for the fractal dimension after cutting under different cutting parameters and the measured fractal dimension after cutting, construct a nonlinear least squares optimization model. The nonlinear least squares optimization model is as follows: ， In the formula, This represents the fractal dimension after the actual cutting is completed. This represents the fractal dimension predicted by the semi-analytical cutting structure damage prediction model after the cutting process is completed. S44. Obtain the solution by solving the nonlinear least squares optimization model using a numerical optimization algorithm. and The specific value.

8. The CFRP cutting structure damage modeling method based on force-thermal coupling energy evolution according to claim 1, characterized in that, Step S4 involves obtaining the initial or measured porosity and fractal dimension of the CFRP workpiece to be tested, which includes the following steps: S51. The pore size distribution data and porosity of the CFRP workpiece under test are obtained by mercury porosimetry. S52. The fractal dimension is obtained by fitting the aperture distribution data based on the fractal dimension model.

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