Method for constructing milling force prediction model for milling variable-curvature part based on RIME-SVM

Abstract

The invention relates to the technical field of mechanical cutting machining, and discloses a method for constructing a milling force prediction model for milling a variable-curvature part based on RIME-SVM, and the method comprises the following steps: S1, obtaining prediction model data; s2, building an RIME-SVM milling force prediction model based on a support vector machine; s3, constructing a cutting force prediction model for machining a conventional straight surface by the end mill; s4, verifying the precision of the cutting force prediction model of the end mill for processing the conventional straight surface; s5, constructing a cutting force prediction model for machining different geometrical characteristics of the end mill; and S6, verifying the precision of the cutting force prediction model for processing different geometrical characteristics by the end mill. The RIME-SVM model combines the advantages of SVM processing nonlinear regression and the high efficiency of the RIME optimization process. According to the RIME-SVM model, the prediction precision is improved, the experiment cost is reduced, the generalization ability is high, unseen data can be accurately predicted, and the method is suitable for practical engineering application.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical cutting processing, and in particular relates to a method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM. Background Art

[0002] There is a complex nonlinear relationship between milling force and milling parameters (such as cutting speed, feed rate, cutting depth, etc.) and the geometric characteristics of the part. The SVM and GWO-SVM models can effectively capture these nonlinear relationships, thereby improving the accuracy of the prediction. Through the SVM and GWO-SVM models, a prediction model with strong generalization ability can be established, which means that the model can not only perform well on the training data, but also accurately predict unseen data, which is crucial for practical engineering applications. The performance of the milling force prediction model depends largely on the selection of model parameters. The SVM and GWO-SVM models automatically select the optimal parameters through the optimization algorithm, thereby improving the prediction performance of the model. By establishing an accurate prediction model, the number of samples required in the actual milling experiment can be reduced, thereby reducing the experimental cost.

[0003] However, the traditional SVM model may not be able to effectively handle the complex nonlinear relationships in the milling process, especially when there are multiple interactions between milling parameters and milling forces. Although GWO-SVM has improved the performance of SVM to a certain extent, it may still be difficult to fully capture these complex relationships, resulting in an inefficient optimization process.

[0004] Although the SVM and GWO-SVM models may have good computational efficiency in the optimization process, they may not have higher computational efficiency when dealing with large-scale data and complex optimization problems, and may not have better generalization capabilities, especially when facing unknown data or different working conditions. The SVM and GWO-SVM models usually require the selection of appropriate parameters (such as C, γ, etc.), which may require a lot of experiments to determine, while the RIME-SVM model can automatically select these parameters through the optimization algorithm, reducing the need for manual adjustment. In view of this, we propose a method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM to solve the above problems. Summary of the invention

[0005] The present invention aims to solve the technical problem that although SVM and GWO-SVM in the above-mentioned prior art may have good computational efficiency when processing optimization problems, they may not have higher computational efficiency when processing large-scale data and complex optimization problems, and may not have better generalization ability.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM, comprising the following steps:

[0008] S1. Obtain prediction model data: design experimental parameters, conduct milling experiments, and collect cutting force data as sample data;

[0009] S2. Constructing RIME-SVM milling force prediction model based on support vector machine: Use RIME algorithm to optimize the parameters of SVM penalty factor C and gamma in Gaussian kernel function to construct RIME-SVM prediction model;

[0010] S3. Construct a cutting force prediction model for end mills used in machining conventional straight surfaces: select part of the experimental data as training data and construct a RIME-SVM model for prediction;

[0011] S4. Verify the accuracy of the cutting force prediction model for machining conventional straight surfaces using end mills: compare the prediction results in step 3 with the experimental values ​​and calculate the error;

[0012] S5. Construct a cutting force prediction model for end mills used to process different geometric features: Take curvature as a variable and select relevant experimental data as training data to construct a RIME-SVM model for prediction;

[0013] S6. Verify the accuracy of the cutting force prediction model for end mills used to process different geometric features: Compare the prediction results in step 5 with the experimental values ​​and calculate the error.

[0014] As a preferred embodiment, in step S1, different spindle speeds n are designed to be 1200r / min-2700r / min, and milling width a p 0.7mm-1.2mm, milling width a e 0.5mm-3mm, feed speed v f The experimental parameters are 700mm / min-1200mm / min.

[0015] Preferably, in step S1, an R1 carbide end mill with a diameter of 20 mm is used in the milling experiment to mill three geometric features, namely, a straight surface of geometric feature 1 with a curvature of 0, a concave surface of geometric feature 2 with a curvature of 1 / 341, and a convex surface of geometric feature 3 with a curvature of 1 / 835.

[0016] Preferably, in step S1, a KISTLER 9257B cutting force test system is used to collect cutting forces in three directions of X, Y, and Z, and the collected milling force data are filtered to extract the root mean square value of the milling force in each direction, and each group of experimental cutting force test results consisting of each processing parameter of each geometric feature and the root mean square value of the milling force in three directions are obtained as sample data.

[0017] Preferably, in step S2, the steps of constructing a RIME-SVM milling force prediction model based on a support vector machine are as follows:

[0018] First, a training sample set is given;

[0019] Then, support vector machine is used for regression. The fitting problem is transformed into an optimization problem by introducing slack variables, which is converted into Lagrangian form using the duality principle, and then the regression function of the support vector machine is obtained by solving it.

[0020] Next, the Gaussian kernel function is used as the kernel function;

[0021] Then, the RIME algorithm is used to optimize the parameters of the penalty factor C of SVM and the gamma in the Gaussian kernel function. The RIME algorithm simulates the soft frost and hard frost growth process of ice crystals, constructs a soft frost search strategy and a hard frost punching mechanism, and continuously updates the population to achieve optimization and find the optimal solution.

[0022] Finally, the RIME-SVM code is output.

[0023] As a preference, in step S2, given a sample set D = {(x i ,y i )|i=1,2,...l}, where x i ∈R n is an n-dimensional input sample, y i ∈R is the output sample. The basic theory of support vector machine for regression algorithm is to fit the relationship between input sample and output sample through training sample and regression function f(x)=w·x+b, where w is the weight vector, which is used to indicate the importance or contribution of the feature, x is the feature vector of the input sample, and b is the offset, which is used to adjust the offset of decision function f(x) to different regression functions, and introduce non-negative relaxation factor ξ. i ,ξ i *, transform the function fitting problem into the following optimization problem:

[0024]

[0025] y i -w·x i -b≤ε+ξ i

[0026] STw·x i +by i ≤ε+ξ i

[0027]

[0028] ε>0 indicates the required fitting accuracy, which is related to the noise level. C>0 controls the degree of penalty for samples exceeding the error ε. Using the duality principle of the optimization method, it can be converted into the following form:

[0029]

[0030] α i , α j and For different Lagrange multipliers, the support vector machine fitting function can be obtained as:

[0031]

[0032] in Represents the kernel function, and the kernel function inner product operation is used in high-dimensional feature space to solve the nonlinear regression problem.

[0033] As a preference, a Gaussian kernel function is used as the kernel function of the support vector machine, which is in the form of:

[0034]

[0035] The RIME algorithm is used to optimize the parameters of SVM penalty factor C and gamma in Gaussian kernel function.

[0036] As a preferred method, RIME is an efficient optimization algorithm based on the physical phenomenon of frost and ice. The RIME algorithm simulates the soft frost and hard frost growth process of ice crystals, constructs a soft frost search strategy and a hard frost punching mechanism, and continuously updates the population to achieve optimization and find the optimal solution. The RIME optimization algorithm process is as follows:

[0037] (1) Initialize the population: randomly generate a group of ice crystals, each of which represents a potential solution;

[0038] (2) Soft frost search mechanism: Inspired by the growth of soft frost, a soft frost search strategy is proposed by taking advantage of the strong randomness and coverage of frost. The condensation process of each particle is simulated according to the five motion characteristics of frost particles. The calculation formula is:

[0039]

[0040] in, To update the new position of the particle, i and j represent the jth particle of the i-th frost factor; R bestj is the jth particle with the best frost factor in the frost population R. The parameter r1∈(-1,1) is a random number. r1 and cosθ control the direction of particle movement. At the same time, cosθ will change with the number of iterations as shown in the formula β is the environmental factor, which follows the number of iterations as shown in the formula h is the adhesion, which is used to control the center distance between two frost particles; Ub ij and Lb ij are the upper and lower bounds of the search space, respectively, limiting the effective area of ​​particle movement; E is the attachment coefficient, which affects the condensation probability of the frost factor and increases with the number of iterations as shown in the formula The random number of parameter r2∈(-1,1) controls together with E whether the particles condense, that is, whether to update the particle position;

[0041] Where t is the current iteration number, T is the maximum iteration number of the algorithm; w is 5, which is used to control the number of segments of the step function;

[0042] (3) Hard frost ice puncture mechanism: By simulating the hard frost growth process, a hard frost punching mechanism is proposed for the replacement between frost ice particles. The calculation formula is:

[0043]

[0044] Among them, r3∈(-1,1); F normr (S i ) represents the normalized value of the current frost factor fitness value;

[0045] (4) Positive greedy selection mechanism: optimal position R bestj It is determined by a positive greedy selection mechanism, where the fitness of the agent after the update is compared with the fitness of the agent before the update.

[0046] Compared with the prior art, the technical effects and advantages of the present invention are: the method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM, SVM is a powerful machine learning algorithm, especially for regression problems, which minimizes classification errors by finding an optimal segmentation plane while maintaining sufficient generalization ability. In milling force prediction, SVM is used to capture the complex nonlinear relationship between milling parameters and milling forces. In order to deal with nonlinear problems in high-dimensional feature space, SVM uses kernel functions to map data to a higher-dimensional space and find the optimal segmentation plane in the space. The Gaussian kernel function is used because it performs well in dealing with nonlinear problems and has a wide convergence domain. RIME is an optimization algorithm based on physical phenomena, which constructs a search strategy by simulating the soft frost and hard frost growth process of ice crystals. RIME continuously updates the population through a soft frost search mechanism and a hard frost punching mechanism to achieve optimization and find the optimal solution. RIME can improve the generalization ability and prediction accuracy of the SVM model.

[0047] The RIME-SVM model can better capture the complex nonlinear relationship between milling parameters and milling forces through the optimization capability of the RIME algorithm, thereby improving the accuracy of the prediction. RIME-SVM automatically selects the parameters of the SVM model through the optimization algorithm, reducing the need for manual adjustments, which is very beneficial in practical applications. An accurate prediction model can reduce the number of samples required in actual milling experiments, thereby reducing experimental costs. The RIME-SVM model has a stronger generalization ability, meaning that the model can not only perform well on the training data, but also accurately predict unseen data, which is crucial for practical engineering applications. Although the SVM and GWO-SVM models may have good computational efficiency in the optimization process, RIME-SVM may perform better in these aspects, especially when dealing with large-scale data and complex optimization problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a structural schematic diagram of the cemented carbide end mill of the present invention;

[0049] Figure 2 It is a schematic diagram of the structure of the experimental piece of the present invention;

[0050] Figure 3 A schematic diagram of the milling trajectory of the milling cutter of the present invention;

[0051] Figure 4 The RIME algorithm optimization flow chart of the present invention;

[0052] Figure 5 It is a schematic diagram of the prediction error of the milling geometric feature 1Fx of the present invention;

[0053] Figure 6 This is a schematic diagram of the prediction error of the milling geometric feature 1Fy of the present invention;

[0054] Figure 7 This is a schematic diagram of the prediction error of the milling geometric feature 1Fz of the present invention;

[0055] Figure 8 This is a schematic diagram of the prediction error of milling different curvatures Fx according to the present invention;

[0056] Fig. 9 This is a schematic diagram of the prediction error of milling different curvatures Fy according to the present invention;

[0057] Fig.10 Schematic diagram of the prediction error of milling different curvatures Fz according to the present invention.

[0058] In the figure: 100, carbide end mill; 200, experimental piece. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] The following is combined with Figure 1-10 To further explain this application in detail,

[0061] The embodiment of the present application discloses a method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM, comprising the following steps:

[0062] S1. Obtain prediction model data

[0063] The experimental parameters are shown in Table 1. The spindle speed n is 1200r / min~2700r / min, the milling width a is p 0.7mm~1.2mm, milling width a e 0.5mm~3mm, feed speed v f The experimental parameters are 700 mm / min to 1200 mm / min. p 、a e 、v f A total of 24 single-factor experiments with 6 levels were designed.

[0064] Table 1 Milling experiment parameters

[0065]

[0066]

[0067] Use Figure 1 The R1 carbide end mill 100 with a diameter of 20 mm is used to mill three geometric features, namely, a straight surface of geometric feature 1 with a curvature of 0, a concave surface of geometric feature 2 with a curvature of 1 / 341, and a convex surface of geometric feature 3 with a curvature of 1 / 835. The experimental piece 200 and the milling trajectory of the milling cutter are shown in FIG. Figure 2 , Figure 3 shown.

[0068] The KISTLER 9257B cutting force test system was used to collect the cutting forces in the X, Y, and Z directions. The collected milling force data were filtered to extract the root mean square values ​​of the milling forces in each direction. The experimental cutting force test results of each group, which consisted of the machining parameters of each geometric feature and the root mean square values ​​of the milling forces in three directions, were obtained as sample data as shown in Table 2.

[0069] Table 2 Cutting force test results of each group of experiments

[0070]

[0071]

[0072] S2. Constructing RIME-SVM milling force prediction model based on support vector machine Given a sample set D = {(x i ,y i )|i=1,2,...l}, where x i ∈R n is an n-dimensional input sample, y i ∈R is the output sample. The basic theory of support vector machine for regression algorithm is to fit the relationship between input sample and output sample with regression function f(x)=w·x+b through training sample. w is the weight vector, which is used to indicate the importance or contribution of the feature. x is the feature vector of the input sample. b is the offset, which is used to adjust the offset of decision function f(x) to different regression functions. Introduce non-negative relaxation factor ξ i ,ξ i *, transform the function fitting problem into the following optimization problem:

[0073]

[0074] y i -w·x i -b≤ε+ξ i

[0075] STw·x i +by i ≤ε+ξ i

[0076]

[0077] ε>0 indicates the required fitting accuracy, which is related to the noise level, and c>0 controls the degree of penalty for samples exceeding the error ε. Using the duality principle of the optimization method, it can be converted into the following form:

[0078]

[0079] α i , α j and For different Lagrange multipliers, the support vector machine fitting function can be obtained from formulas 3 to 4:

[0080]

[0081] in Represents the kernel function. The kernel function inner product operation is used in high-dimensional feature space to solve nonlinear regression problems. The Gaussian kernel function can adapt well to low-dimensional, high-dimensional, small sample, large sample, etc., and has a wide convergence domain. It is currently the most widely used kernel function. Therefore, the Gaussian kernel function is used as the kernel function of the support vector machine, in the form of:

[0082]

[0083] Support vector machines are suitable for small sample data and can handle nonlinear problems. They have good robustness and interpretability. In contrast, neural networks require large sample data and have poor model interpretability. Therefore, support vector machines are used to build prediction models. Existing optimized support vector machine algorithms, such as the Grey Wolf Optimization (GWO) algorithm, improve the ability of support vector machines to handle nonlinear problems and overcome the problem of falling into local optimal solutions. However, they are sensitive to initial parameter settings and the accuracy is difficult to guarantee.

[0084] The RIME algorithm is used to optimize the parameters of the SVM penalty factor C and the gamma in the Gaussian kernel function. RIME is an efficient optimization algorithm based on the physical phenomenon of frost and ice. The RIME algorithm simulates the soft frost and hard frost growth process of ice crystals, constructs a soft frost search strategy and a hard frost punching mechanism, and continuously updates the population to achieve optimization and find the optimal solution.

[0085] The use of RIME to optimize the support vector machine improves the generalization ability of the model and has a higher accuracy in predicting multiple-input and single-input problems. The prediction of milling force belongs to the multiple-input and single-output problem, so RIME-SVM is used to build a milling force prediction model.

[0086] like Figure 4 The RIME algorithm optimization flow chart shown in the figure shows that the RIME optimization algorithm process is as follows:

[0087] The RIME optimization algorithm process is as follows:

[0088] (1) Initialize the population: randomly generate a group of ice crystals (candidate solutions), each of which represents a potential solution.

[0089] (2) Soft frost search mechanism: Inspired by the growth of soft frost, a soft frost search strategy is proposed by taking advantage of the strong randomness and coverage of frost. The condensation process of each particle is simulated according to the five motion characteristics of frost particles. The calculation formula is:

[0090]

[0091] in, To update the new position of the particle, i and j represent the jth particle of the i-th frost factor; R bestjis the jth particle with the best frost factor in the frost population R. The parameter r1∈(-1,1) is a random number. r1 and cosθ control the direction of particle movement. At the same time, cosθ will change with the number of iterations as shown in Equation (8); β is an environmental factor, which follows the number of iterations as shown in Equation (9); h is the adhesion, which is used to control the center distance between two frost particles; Ub ij and Lb ij are the upper and lower bounds of the search space, respectively, limiting the effective area of ​​particle movement; E is the attachment coefficient, which affects the condensation probability of the frost factor and increases with the number of iterations as shown in formula (10). The random number of parameter r2∈(-1,1) controls whether the particles condense together with E, that is, whether to update the particle position.

[0092]

[0093] Among them, t is the current iteration number and T is the maximum iteration number of the algorithm.

[0094]

[0095] The default value of w is 5, which is used to control the number of segments of the step function.

[0096]

[0097] (3) Hard frost ice puncture mechanism: By simulating the hard frost growth process, a hard frost perforation mechanism is proposed. It is used for the replacement between frost ice particles, and its calculation formula is:

[0098]

[0099] Among them, r3∈(-1,1); F normr (S i ) represents the normalized value of the current frost factor fitness value.

[0100] (4) Positive greedy selection mechanism: optimal position R bestj This can be determined by a positive greedy selection mechanism, that is, the fitness of the agent after the update is compared with the fitness of the agent before the update. If the fitness after the update is better than the fitness before the update, it will be replaced, and the positions of the two agents will also be exchanged. This operation ensures that the population evolves in a better direction at each iteration.

[0101] The RIME algorithm is used to optimize the parameters of SVM penalty factor C and gamma in Gaussian kernel function.

[0102] The RIME-SVM part code is as follows:

[0103]

[0104]

[0105] S3. Construct a cutting force prediction model for end mills used to process conventional straight surfaces

[0106] In order to construct a cutting force prediction model for end mills used in machining conventional straight surfaces, 80% of the data in the 24 groups of experiments in milling geometric features 1 in Table 2 were selected as training data sets, and the remaining 20% ​​were selected as test data sets. The 5th, 11th, 17th, and 23rd groups of data were selected as test data sets and numbered 1, 2, 3, and 4, respectively. p 、a e 、v f as input, the milling forces in each direction as output, the population size was set to 200, the maximum number of iterations was set to 20, and the RIME-SVM model was constructed.

[0107] S4. Verify the accuracy of the cutting force prediction model for machining conventional straight surfaces using end mills

[0108] The predicted values ​​of milling forces in each direction of SVM, GWO-SVM, and RIME-SVM were compared with the experimental values, and the errors were calculated (see Tables 3–5).

[0109] Table 3 Milling geometric features 1F x Comparison table of experimental values ​​and predicted values

[0110]

[0111]

[0112] Table 4 Milling geometric features 1F y Comparison table of experimental values ​​and predicted values

[0113]

[0114] Table 5 Milling geometric features 1F z Comparison table of experimental values ​​and predicted values

[0115]

[0116] According to the data in Tables 3 to 5, the error values ​​of milling forces in different directions in different prediction models when milling geometric feature 1 are plotted, as shown in Figures 5 to 7 shown.

[0117] From Tables 3 to 5 and Figures 5 to 7 It can be seen that SVM predicts F x The maximum error is 6.12%, the minimum error is 1.58%, and the mean square error is 4.64%. xThe maximum error is 3.67%, the minimum error is 0.89%, and the mean square error is 3.00%; RIME-SVM predicts F x The maximum error is 1.38%, the minimum error is 0.79%, and the mean square error is 1.01%. SVM predicts F y The maximum error is 15.47%, the minimum error is 0.59%, and the mean square error is 9.19%. y The maximum error is 14.25%, the minimum error is 1.34%, and the mean square error is 10.43%. y The maximum error is 1.38%, the minimum error is 0.83%, and the mean square error is 1.10%. SVM predicts F z The maximum error is 3.14%, the minimum error is 0.47%, and the mean square error is 1.70%. z The maximum error is 21.56%, the minimum error is 2.28%, and the mean square error is 12.02%; RIME-SVM predicts F z The maximum error is 3.21%, the minimum error is 1.02%, and the mean square error is 1.94%.

[0118] It can be seen that RIME-SVM is effective in predicting F x The root mean square error of RIME-SVM is 5.02% and 1.99% smaller than that of SVM and GWO-SVM. y The root mean square error is 8.09% and 9.33% smaller than that of SVM and GWO-SVM; SVM is more effective in predicting F z The root mean square error is 10.32% and 0.24% smaller than that of GWO-SVM and RIME-SVM. In summary, RIME-SVM has a more accurate prediction effect.

[0119] S5. Construct a cutting force prediction model for end mills to process different geometric features

[0120] The effect of variable curvature on milling force was studied, and the curvature was taken as a variable for prediction. The experimental data are shown in Table 6.

[0121] Table 6 Milling forces in various directions when milling workpieces with variable curvature under different milling parameters

[0122]

[0123]

[0124]

[0125]

[0126] 80% of the 72 data sets in Table 6 are selected as training data sets, and 20% are selected as test data sets. That is, data sets 1 to 58 are selected as training data sets, and data sets 59 to 72 are selected as test data sets, which are numbered 1 to 14 in sequence. p 、a e 、v f as input, the milling forces in each direction as output, the population size was set to 200, the maximum number of iterations was set to 20, and the RIME-SVM model was constructed.

[0127] S6. Verify the accuracy of the cutting force prediction model for end mills used to process different geometric features

[0128] The predicted values ​​of milling forces in each direction of SVM, GWO-SVM, and RIME-SVM were compared with the experimental values, and the errors were calculated (see Tables 7–9).

[0129] Table 7 Milling different curvature F x Comparison table of experimental values ​​and predicted values

[0130]

[0131] Table 8 Milling different curvatures F y Comparison table of experimental values ​​and predicted values

[0132]

[0133]

[0134] Table 9 Milling different curvatures F z Comparison table of experimental values ​​and predicted values

[0135]

[0136]

[0137] From Tables 7 to 9 and Figures 8 to 10 It can be seen that SVM predicts F x The maximum error is 7.18%, the minimum error is 0.06%, and the mean square error is 4.83%. x The maximum error is 10.96%, the minimum error is 0.49%, and the mean square error is 6.65%; RIME-SVM predicts F x The maximum error is 1.30%, the minimum error is 0.06%, and the mean square error is 1.06%. SVM predicts F y The maximum error is 14.86%, the minimum error is 0.69%, and the mean square error is 9.01%. yThe maximum error is 15.30%, the minimum error is 2.46%, and the mean square error is 10.85%. y The maximum error is 1.65%, the minimum error is 0.51%, and the mean square error is 1.32%. SVM predicts F z The maximum error is 33.19%, the minimum error is 5.13%, and the mean square error is 16.23%. z The maximum error is 2%, the minimum error is 3.55%, and the mean square error is 20.65%; RIME-SVM predicts F z The maximum error is 2.94%, the minimum error is 1.27%, and the mean square error is 2.24%.

[0138] It can be seen that RIME-SVM is effective in predicting F x The root mean square error of RIME-SVM is 3.77% and 5.59% smaller than that of SVM and GWO-SVM. y The root mean square error of RIME-SVM is 7.69% and 9.53% smaller than that of SVM and GWO-SVM. z The root mean square error is 13.99% and 18.41% smaller than that of SVM and GWO-SVM. In summary, RIME-SVM has a more accurate prediction effect.

[0139] The method of constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM verifies the superiority of the RIME-SVM model in milling force prediction through experimental data, especially when dealing with milling force prediction of variable curvature parts. The experimental results show that the RIME-SVM model not only improves the prediction accuracy, but also reduces the number of required training samples, thereby reducing the experimental cost.

[0140] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM, characterized in that: The steps include: S1. Obtain prediction model data: design experimental parameters, conduct milling experiments, and collect cutting force data as sample data; S2. Constructing RIME-SVM milling force prediction model based on support vector machine: Use RIME algorithm to optimize the parameters of SVM penalty factor C and gamma in Gaussian kernel function to construct RIME-SVM prediction model; S3. Construct a cutting force prediction model for end mills used in machining conventional straight surfaces: select part of the experimental data as training data and construct a RIME-SVM model for prediction; S4. Verify the accuracy of the cutting force prediction model for machining conventional straight surfaces using end mills: compare the prediction results in step 3 with the experimental values ​​and calculate the error; S5. Construct a cutting force prediction model for end mills used to process different geometric features: Take curvature as a variable and select relevant experimental data as training data to construct a RIME-SVM model for prediction; S6. Verify the accuracy of the cutting force prediction model for end mills used to process different geometric features: Compare the prediction results in step 5 with the experimental values ​​and calculate the error.

2. The method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM according to claim 1, characterized in that: In step S1, the spindle speed n is designed to be 1200r / min-2700r / min and the milling width a p 0.7mm-1.2mm, milling width a e 0.5mm-3mm, feed speed v f The experimental parameters are 700mm / min-1200mm / min.

3. The method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM according to claim 2, characterized in that: In step S1, an R1 carbide end mill with a diameter of 20 mm is used in the milling experiment to mill three geometric features, namely, a straight surface of geometric feature 1 with a curvature of 0, a concave surface of geometric feature 2 with a curvature of 1 / 341, and a convex surface of geometric feature 3 with a curvature of 1 / 835.

4. The method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM according to claim 3, characterized in that: In step S1, the KISTLER 9257B cutting force test system is used to collect cutting forces in the X, Y, and Z directions. The collected milling force data are filtered to extract the root mean square value of the milling force in each direction, and each group of experimental cutting force test results consisting of the processing parameters of each geometric feature and the root mean square value of the milling force in three directions are obtained as sample data.

5. The method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM according to claim 1, characterized in that: In step S2, the steps of constructing the RIME-SVM milling force prediction model based on the support vector machine are as follows: First, a training sample set is given; Then, support vector machine is used for regression. The fitting problem is transformed into an optimization problem by introducing slack variables, which is converted into Lagrangian form using the duality principle, and then the regression function of the support vector machine is obtained by solving it. Next, the Gaussian kernel function is used as the kernel function; Then, the RIME algorithm is used to optimize the parameters of the penalty factor C of SVM and the gamma in the Gaussian kernel function; The RIME algorithm simulates the soft frost and hard frost growth process of ice crystals, constructs a soft frost search strategy and a hard frost punching mechanism, updates the population, and finds the optimal solution; Finally, the RIME-SVM code is output.

6. The method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM according to claim 5, characterized in that: In step S2, given a sample set D = {(x i ,y i )|i=1,2,...l}, where x i ∈R n is an n-dimensional input sample, y i ∈R is the output sample, and the regression function f(x) = w·x+b is used to fit the relationship between the input sample and the output sample, where w is the weight vector, indicating the importance or contribution of the feature, x is the feature vector of the input sample, and b is the offset. The offset of the decision function f(x) to the regression function is adjusted, and a non-negative relaxation factor ξ is introduced. i ,ξ i *, transform the function fitting problem into the following optimization problem: ε>0 indicates the required fitting accuracy, C>0 controls the degree of penalty for samples exceeding the error ε. Using the duality principle of the optimization method, it can be converted into the following form: Lagrange multiplier α i , Lagrange multipliers Lagrange multiplier α j and Lagrange multipliers The support vector machine fitting function is obtained as follows: in Represents the kernel function.

7. The method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM according to claim 6, characterized in that: The Gaussian kernel function is used as the kernel function of the support vector machine, which is in the form of: The RIME algorithm is used to optimize the parameters of SVM penalty factor C and gamma in Gaussian kernel function.

8. The method for constructing a milling force prediction model for milling variable curvature parts based on RIME-SVM according to claim 7, characterized in that: The RIME optimization algorithm process is as follows: (1) Initialize the population: randomly generate a group of ice crystals, each of which represents a potential solution; (2) Soft frost search mechanism: Utilizing the strong randomness and coverage of frost, a soft frost search strategy is proposed; According to the five motion characteristics of frost particles, the condensation process of each particle is simulated; the calculation formula is: in, To update the new position of the particle, i and j represent the jth particle of the i-th frost factor; R bestj is the jth particle with the best frost factor in the frost population R, and the parameter r1∈(-1,1) is a random number. r1 and cosθ control the direction of particle movement, and cosθ will change with the number of iterations as shown in the formula β is the environmental factor, following the number of iterations as shown in the formula h is the adhesion, which is used to control the center distance between two frost ice particles; Ub ij and Lb ij are the upper and lower bounds of the search space respectively; E is the attachment coefficient, which affects the condensation probability of the frost factor and increases with the number of iterations as shown in the formula The random number of parameter r2∈(-1,1) controls whether the particles condense together with E, indicating whether to update the particle position; Among them, t is the current iteration number, and T is the maximum iteration number of the algorithm; w is 5, which is used to control the number of segments of the step function; (3) Hard frost ice puncture mechanism: By simulating the hard frost growth process, a hard frost punching mechanism is proposed for the replacement between frost ice particles. The calculation formula is: Among them, r3∈(-1,1); F normr (S i ) represents the normalized value of the current frost factor fitness value; (4) Positive greedy selection mechanism: Determine the optimal position R through the positive greedy selection mechanism bestj , which means that the fitness of the agent after the update is compared with the fitness of the agent before the update.

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