Variable helical angle milling cutter milling force model calibration method based on maximization of force lobe area

Abstract

The invention relates to the technical field of milling force prediction, and provides a variable helical angle milling cutter milling force model calibration method based on maximization of a force lobe area, and the method comprises the steps: building a linear average milling force model according to a cutting mechanics principle; and minimizing a loss function of an error between the simulated cutting force FS and the experimental cutting force FM to obtain each group of cutting force coefficients of the variable helical angle milling cutter. The radial run-out effect of the cutter is integrated, and the accuracy of the cutting force model of the variable helical angle cutter is improved; on the basis of a force lobe area maximization principle, cut-in phase matching of experimental force and simulation force is completed, and the cutting force coefficient identification accuracy is improved; in addition, the stability and rationality of a cutting force coefficient are further ensured by introducing an L2 regularization parameter, and occurrence of a ill-conditioned solution is avoided. The method is used for accurately identifying multiple groups of cutting force coefficients and cutter run-out parameters of the variable helical angle milling cutter so as to improve the cutting force forecasting precision of the variable helical angle milling cutter, and a basis is provided for accurate stability judgment in the machining process.

Description

Technical Field

[0001] The present invention relates to the technical field of milling force prediction, and in particular to a method for calibrating a cutting force model of a variable helix angle milling cutter. Background Art

[0002] With the continuous improvement of the requirements for machining precision and efficiency of weak rigidity complex parts in high-end equipment in fields such as aerospace, variable helix angle milling cutters have been increasingly used. Due to the unique spiral groove structure design, different axial cutting layers of variable helix angle milling cutters can produce cutting motions with different phases. The rational use of this feature significantly reduces the possibility of regenerative vibration during milling. Research on its vibration stability has gradually become a hot topic.

[0003] Accurately identifying the milling force model for variable helix angle cutters is a prerequisite for accurately determining the stability of such tool processing. Reference 1, "Budak, E., Altintas, Y. & Armarego, E. J. A. Prediction of Milling Force Coefficients From Orthogonal Cutting Data. J. Manuf. Sci. Eng. 118, 216–224 (1996)," proposes a classic milling force coefficient calibration method for general cylindrical end mills. This method establishes a linear milling force model for the cutting force coefficient. Several slot milling experiments are conducted by fixing the axial cutting depth and gradually varying the feed per tooth to obtain milling force data corresponding to different feed per tooth rates. Finally, the cutting force coefficient is derived using linear regression analysis. This method offers good calibration robustness, but is somewhat costly and cannot calibrate tool runout parameters.

[0004] Reference 2, "Guo, Q., Zhao, B., Zhang, M., Jiang, Y. & Zhang, Y. A separate-edge force coefficients' calibration method using specific condition for cutters with variable helix and pitch angles combining the runout effect. Int. J. Adv. Manuf. Technol. 93, 1737–1749 (2017)," proposes a calibration method for the cutting force coefficients of variable helix cutters that considers the runout effect. This method incorporates the tool runout effect into the cutting force coefficients, achieving an accurate approximation of the simulated force curve to the experimental force data. However, because the tool runout parameter does not appear explicitly in the force model equation, the calibration result cannot provide the tool runout parameter.

[0005] Reference 3, "Niu JB, Ding Y, Zhu LM, Ding H. Mechanics and multi-regenerative stability of variable pitch and variable helix milling tools considering runout. Int J Mach Tools Manuf 2017;123:129–145," proposes a method for calibrating the cutting force coefficient of variable helix milling cutters that can simultaneously output tool runout parameters. This method uses a linear regression method based on slot milling experiments to determine the average cutting force coefficient. It then uses a trust region reflection algorithm to iteratively determine the cutting force coefficient and tool runout parameters. However, this method assumes that the cutting force coefficient on each cutting edge of a variable helix milling cutter is equal, making it primarily suitable for situations where the helix angles of different cutting edges vary slightly.

[0006] Patent 1, "Method for Identifying the Cutting Force Coefficient of a Variable Helix Angle Cutter Based on Data Sliding Matching," proposes a method for calibrating the cutting force coefficient of a variable helix angle cutter based on data sliding matching. Taking into account the different shearing and plowing effects of different helical edges of a variable helix angle cutter when cutting the workpiece material, this method achieves phase synchronization between the simulated force and the experimental force by introducing a sliding factor. The method then uses the least squares method to construct matrix expressions for multiple sets of cutting force coefficients. Finally, an optimization algorithm is used to rapidly calibrate multiple sets of cutting force coefficients and tool runout parameters for different helix angle edges. However, during the numerical optimization process, there is a high probability that the matrix condition number will be too large, resulting in the possibility that the calibrated cutting force coefficient may be an ill-conditioned solution. Summary of the Invention

[0007] The present invention mainly solves the technical problems that the existing technology is difficult to accurately identify multiple sets of cutting force coefficients and runout parameters of variable helix angle milling cutters, as well as the possible pathological solutions of fast matching of simulation force and experimental force cutting phase and multi-parameter calibration that need to be solved in the identification process. A milling force model calibration method for variable helix angle milling cutters based on maximizing the force petal area is proposed, which can accurately identify multiple sets of milling force coefficients and runout parameters of variable helix angle milling cutters, and based on the L2 regularization principle, the obtained cutting force coefficients are within a reasonable range.

[0008] The present invention provides a milling force model calibration method for a variable helix angle milling cutter based on maximizing the force petal area, comprising the following steps:

[0009] Step 1: According to the principle of cutting mechanics, the linear average milling force model can be established as follows:

[0010]

[0011] in, is the average milling force in the x-axis, y-axis, and z-axis directions, N is the angle divided into N parts, a p is the axial cutting depth of the tool, f t is the feed speed, ψ st , ψ ex Indicates the cutting entry angle and cutting exit angle, K tc , K rc , K ac are the tangential, radial and axial shear force coefficients respectively; K te , K re , K ae are the tangential, radial and axial edge force coefficients, respectively;

[0012] Step 2: Use a variable helix angle milling cutter to conduct multiple slot milling experiments. In each experiment, the spindle speed, axial cutting depth, and radial cutting depth are fixed, and the feed per tooth is changed. The average milling force in the three directions of slot milling at different feed speeds is obtained using a three-component dynamometer.

[0013] Step 3: Assuming that the cutting force coefficients of each group of variable helix angle milling cutters corresponding to different spiral edges are the same, a linear regression analysis is performed using the linear average milling force model of step 1 to obtain the average milling force coefficient of the variable helix angle milling cutter;

[0014] Step 4: Use a variable helix angle milling cutter to conduct a side milling experiment under the condition of tool-workpiece single tooth meshing, and use a three-component dynamometer to measure the instantaneous milling force at different cutting moments;

[0015] Step 5: randomly select one cycle of experimental force data from the instantaneous milling force data measured in step 4;

[0016] Step 6: Assign cutting force coefficient groups to be identified N to variable helix angle milling cutter t A blade;

[0017] Step 7: Based on the geometric parameters, runout parameters, cutting force coefficients, and cutting mechanics principles of the variable helix angle milling cutter, a microelement cutting force modeling method is used to establish an instantaneous cutting force model and predict multi-cycle cutting force data;

[0018] Step 8: Determine the time interval of the simulation force data points so that the number of simulation force data points in a single cycle is equal to the number of experimental force data points; according to the cutting angle of the corresponding blade 1 in step 5, set the phase angle of the cutting starting point of the simulation program blade 1, and calculate the simulation force data of one cycle based on the instantaneous milling force model established in step 7;

[0019] Step 9: Construct an equivalent relationship between the experimental cutting force and the simulated cutting force at different time points within a cycle to obtain a vector expression of the cutting force coefficient group;

[0020] Step 10: Minimize the simulated cutting force F S and experimental cutting force F M The loss function of the time error is used to obtain the cutting force coefficients of each group of variable helix angle milling cutters.

[0021] Furthermore, the step 3 includes:

[0022] Assuming that the cutting force coefficients of each group of variable helix angle milling cutters corresponding to different helical edges are the same K i =K j (i≠j);

[0023] Because it is assumed that the cutting force coefficients of each group are the same, in this case:

[0024] in, represent the average tangential, radial, and axial shear force coefficients of the variable helix angle milling cutter, respectively; represent the average tangential, radial and axial edge force coefficients of the variable helix angle milling cutter respectively;

[0025] Using the experimental average milling force obtained in step 2, a linear regression analysis is performed on the linear average milling force model in step 1, and the average milling force coefficient of the variable helix angle milling cutter is obtained as follows:

[0026]

[0027] Furthermore, the step 5 includes the following steps 501 to 504:

[0028] Step 501: Calculate the time difference t between the cutting out and the cutting into the workpiece by any edge i of the variable helix angle milling cutter. i The time difference t between the adjacent cutting edges and the cutting edge θi :

[0029]

[0030] t θi =T·θ i，0 / 2π (4)

[0031] Where T is the time required for the tool to rotate one circle, R is the tool radius, and a e is the radial cutting depth of the tool, β i is the helix angle of blade i, θ i，0 is the tooth angle between edge i and edge i+1 at the free end of the tool;

[0032] Step 502: Calculate all blade force lobe areas with a certain data point in the intercepted periodic experimental force as the cutting starting point of blade 1:

[0033]

[0034] Where t0 is the time corresponding to the starting point of the assumed blade 1 cutting into the workpiece, t l =t(k),k=1, 2,...,n;

[0035] Step 503: Determine the experimental data point that maximizes the accumulated force petal area as the actual starting point of the blade 1 cutting into the workpiece;

[0036] Step 504: Output one cycle of experimental force data using the starting point as the initial sampling point.

[0037] Furthermore, the step 7 includes the following steps 701 to 704:

[0038] Step 701: Discretize the axial cutting depth into q units using a discretization method. Any axial unit is represented by an index k, where k∈[1,q].

[0039] Step 702: Considering the influence of tool runout, modify the angle of the helix angle milling cutter entering and cutting out the workpiece;

[0040]

[0041]

[0042] Where: st，i，k Indicates the angle at which the variable helix angle milling cutter cuts into the workpiece during down milling, ψ ex，i，k Indicates the angle at which the variable helix angle milling cutter cuts the workpiece during down milling, ψ st，i，k Indicates the angle at which the variable helix angle milling cutter cuts into the workpiece during reverse milling, ψ ex，i，k represents the angle of the workpiece cut by the variable helix angle milling cutter during up-milling; ρ is the tool runout, λ is the tool runout angle; t p Cut previous edge i for current edge i p The time interval between milling the material left at the same workpiece surface position; p is the difference in the numbers of the two cutting edges that mill the same workpiece surface position successively; f i，k (t p ) is t p The feed rate of the milling cutter during the time interval; R i，k is the actual milling radius of the i-th blade on the k-th infinitesimal element; R is the geometric radius of the milling cutter;

[0043] Step 703: Using the micro-element cutting force modeling method and based on the linear cutting force model, the simulation formula of the instantaneous cutting force of the variable helix angle milling cutter is obtained as follows:

[0044]

[0045] in:

[0046]

[0047] In the above formula, Δz is the thickness of each microelement, W i，k (t) is the switching function used to determine whether the spiral blade i is involved in cutting; ψ i，k (t) is the position angle of blade i on element k at time t; h i，k (t, p) is the instantaneous undeformed thickness equation including runout; h i，k (t) is the actual instantaneous undeformed cut thickness including runout; The lag angle of the first edge on the kth infinitesimal element; θ i→1，k is the tooth-to-tooth angle between the first and i-th edges on the k-th element;

[0048] Step 704: Use the separation of variables method to write the instantaneous cutting force in step 703 into the form of the product of the position matrix Θ and the cutting force coefficient vector K. Based on the micro-element cutting force model, the instantaneous milling force data is predicted as follows:

[0049]

[0050] in:

[0051]

[0052] Furthermore, the step 9 includes the following steps 901 to 902:

[0053] Step 901: Let the experimental cutting force vector obtained in step 5 be equal to the simulated cutting force vector obtained in step 8, and obtain the identity equation for the force coefficient group K:

[0054]

[0055] in:

[0056]

[0057] In the above formula, t1, ..., t d ,...,t n is the sampling time point when the tool rotates one circle in the simulation force data. It is the sampling time point of the tool rotating one circle with the cutting moment as the starting point in the experimental force data;

[0058] Step 902: According to formula (8) in step 901, the least square method (LSM) is used to calculate the vector expression of the cutting force coefficient group:

[0059]

[0060] Furthermore, the step 10 includes the following steps 1001 to 1004:

[0061] Step 1001: Calculate the simulated cutting force F S and experimental cutting force F M The second norm of the error between the two, the error loss function Δ1(λ, ρ) is obtained:

[0062]

[0063] in, is a function of tool runout parameters λ, ρ;

[0064]

[0065] Where I is the identity matrix;

[0066] Step 1002: Introduce the L2 regularization parameter ε and rearrange the error loss function:

[0067]

[0068] Step 1003: Construct the objective function Δ2(ε) related to the L2 regularization parameter ε as follows:

[0069]

[0070] Step 1004: Use the dual-objective optimization method to simultaneously consider the objective function Δ2(ε) and the rearranged error loss function Δ1(λ, ρ, ε), adjust the weight between the objective function and the error loss function, and optimize the values ​​of the runout angle λ and the runout amount ρ through iterative optimization of the genetic algorithm until the optimal solution is reached, and obtain the most matching cutting force coefficient group K, runout angle λ, runout amount ρ and regularization parameter ε.

[0071] The present invention provides a method for calibrating the milling force model of a variable helix angle milling cutter based on maximizing the force petal area. This method integrates the radial runout effect of the tool and improves the accuracy of the cutting force model of the variable helix angle cutter. Based on the principle of maximizing the force petal area, the method achieves phase matching between the experimental force and the simulation force, thereby improving the accuracy of identifying the cutting force coefficient. In addition, the introduction of the L2 regularization parameter further ensures the stability and rationality of the cutting force coefficient and avoids the occurrence of pathological solutions. The present invention is used to accurately identify multiple sets of cutting force coefficients and tool runout parameters of variable helix angle milling cutters, thereby improving the cutting force prediction accuracy of variable helix angle milling cutters and providing a basis for accurate stability judgment of the machining process. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 This is a flow chart for implementing the method for identifying multiple groups of cutting force coefficients of a variable helix angle milling cutter provided by the present invention;

[0073] Figure 2 It is a schematic diagram of the cutting starting point and the interception position of the experimental force data;

[0074] Figure 3(a)-(d) is a schematic diagram of the force petal area accumulation process and the determination of the maximum area. DETAILED DESCRIPTION

[0075] To make the technical problems solved, the technical solutions adopted, and the technical effects achieved by the present invention more clearly apparent, the present invention is 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 of the present invention and are not intended to limit the present invention. It should also be noted that, for ease of description, the accompanying drawings only illustrate portions relevant to the present invention, rather than all of the contents.

[0076] like Figure 1 As shown, an embodiment of the present invention provides a method for calibrating a milling force model of a variable helix angle milling cutter based on maximizing the force petal area, comprising the following steps:

[0077] Step 1: According to the principle of cutting mechanics, the linear average milling force model can be established as follows:

[0078]

[0079] in, is the average milling force in the x-axis, y-axis, and z-axis directions, N is the angle divided into N parts, a p is the axial cutting depth of the tool, f t is the feed speed, ψ st , ψ ex Indicates the cutting entry angle and cutting exit angle, K tr , K rc , K ac are the tangential, radial and axial shear force coefficients respectively; K te , K re , K ae are the tangential, radial and axial edge force coefficients, respectively.

[0080] Step 2: Use a variable helix angle milling cutter to conduct multiple slot milling experiments. In each experiment, the spindle speed, axial cutting depth, and radial cutting depth are fixed, and the feed per tooth is changed. The average milling force in the three directions of slot milling at different feed speeds is obtained using a three-component dynamometer.

[0081] Specifically, the three-component dynamometer is, for example, a 9257 universal three-component dynamometer produced by KISTLER.

[0082] Step 3: Assume that the cutting force coefficients of each group of variable helix angle milling cutters corresponding to different spiral edges are the same, and use the linear average milling force model in step 1 to perform linear regression analysis to obtain the average milling force coefficient of the variable helix angle milling cutter.

[0083] Specifically, it is assumed that the cutting force coefficients of each group of different helical edges of the variable helix angle milling cutter are the same K j =K j (i≠j).

[0084] Because it is assumed that the cutting force coefficients of each group are the same, it is the concept of average cutting force coefficient. In this case, there are: in, represent the average tangential, radial, and axial shear force coefficients of the variable helix angle milling cutter, respectively; Represent the average tangential, radial and axial edge force coefficients of the variable helix angle milling cutter, respectively.

[0085] Using the experimental average milling force obtained in step 2, a linear regression analysis is performed on the linear average milling force model in step 1, and the average milling force coefficient of the variable helix angle milling cutter is obtained as follows:

[0086]

[0087] Step 4: Use a variable helix angle milling cutter to conduct a side milling experiment under the condition of tool-workpiece single tooth meshing, and use a three-component dynamometer to measure the instantaneous milling force at different cutting moments.

[0088] Specifically, a variable helix angle milling cutter was used to carry out side milling experiments under the condition of single-tooth engagement between the tool and the workpiece (that is, at most one tooth of the tool was involved in the cutting work at any cutting moment). The instantaneous milling force at different cutting moments was measured using a three-component dynamometer. The cutting time was no less than 20 spindle rotation cycles, and the number of milling force data points in each cycle was n.

[0089] Step 5: From the instantaneous milling force data measured in step 4, randomly select one cycle of experimental force data.

[0090] The present invention considers the most general situation: when the first data point is not the cutting starting point of a certain blade of the variable helix angle cutter ( Figure 2 ), based on the principle of maximizing the force petal area, find the starting point of the cutting of any blade in the periodic experimental force, and output the experimental force data of one cycle with the starting point of the cutting as the initial sampling point. Step 5 includes the following steps 501 to 504:

[0091] Step 501: Calculate the time difference t between the cutting out and the cutting into the workpiece by any edge i of the variable helix angle milling cutter. i (i.e. the time width of the blade i force flap) and the time difference t between the adjacent blades (blade i and blade i+1) cutting into the workpiece θi:

[0092]

[0093] Where T is the time required for the tool to rotate one circle, R is the tool radius, and a e is the radial cutting depth of the tool, β i is the helix angle of blade i, θ i，0 is the tooth angle between edge i and edge i+1 at the free end of the tool.

[0094] Step 502: Calculate the area of ​​all blade force petals ( Figure 3a ):

[0095]

[0096] Where t0 is the time corresponding to the starting point of the assumed blade 1 cutting into the workpiece, t l =t(k),k=1, 2,...,n.

[0097] Step 503: Determine the experimental data point that maximizes the accumulated force petal area as the actual starting point data point at which the blade 1 cuts into the workpiece.

[0098] Specifically: Repeat steps 501 and 502 continuously, t l =t(1), t(2), ..., t(n), until the entire cycle is covered, as shown in Figure 3(a)-(c). By comparing the accumulated force petal areas within these specific time ranges, a special experimental data point is obtained to maximize the accumulated force petal area, as shown in Figure 3(d). This experimental data point is the actual starting point data point of blade 1 cutting into the workpiece.

[0099] Step 504: Output one cycle of experimental force data using the starting point as the initial sampling point.

[0100] Step 6: Assign cutting force coefficient groups to be identified N to variable helix angle milling cutter t A blade;

[0101] Step 7: Based on the geometric parameters, runout parameters, cutting force coefficients, and cutting mechanics principles of the variable helix angle milling cutter, a microelement cutting force modeling method is used to establish an instantaneous cutting force model and predict multi-cycle cutting force data. Step 7 includes the following steps 701 to 704:

[0102] Step 701: Discretize the axial cutting depth into q units using a discretization method. Any axial unit is represented by an index k, where k∈[1,q].

[0103] Step 702: Considering the influence of tool runout, modify the angle of the helix angle milling cutter entering and cutting out the workpiece;

[0104]

[0105] Where: st，i，k Indicates the angle at which the variable helix angle milling cutter cuts into the workpiece during down milling, ψ ex，i，k Indicates the angle at which the variable helix angle milling cutter cuts the workpiece during down milling, ψ st，i，k Indicates the angle at which the variable helix angle milling cutter cuts into the workpiece during reverse milling, ψ ex，i，k represents the angle of the workpiece cut by the variable helix angle milling cutter during up-milling; ρ is the tool runout, λ is the tool runout angle; t p Cut previous edge i for current edge i p The time interval between milling the material left at the same workpiece surface position; p is the difference in the numbers of the two cutting edges that mill the same workpiece surface position successively; f i，k (t p ) is t p The feed rate of the milling cutter during the time interval; R i，k is the actual milling radius of the i-th blade on the k-th infinitesimal element; R is the geometric radius of the milling cutter;

[0106] Step 703: Using the micro-element cutting force modeling method and based on the linear cutting force model, the simulation formula of the instantaneous cutting force of the variable helix angle milling cutter is obtained as follows:

[0107]

[0108]

[0109] in:

[0110]

[0111] In the above formula, Δz is the thickness of each microelement, W i，k (t) is the switching function used to determine whether the spiral blade i is involved in cutting; ψ i，k (t) is the position angle of blade i on element k at time t; h i，k (t, p) is the instantaneous undeformed thickness equation including runout; h i，k (t) is the actual instantaneous undeformed cut thickness including runout; The lag angle of the first edge on the kth infinitesimal element; θ i→1，k is the tooth-to-tooth angle between the first and i-th edges on the k-th element;

[0112] Step 704: Use the separation of variables method to write the instantaneous cutting force in step 703 into the form of the product of the position matrix Θ and the cutting force coefficient vector K. Based on the micro-element cutting force model, the instantaneous milling force data is predicted as follows:

[0113]

[0114] in:

[0115]

[0116] Step 8. Determine the time interval of the simulation force data points so that the number of simulation force data points in a single cycle is equal to the number of experimental force data points, that is, the number of simulation milling force data points in each cycle is n; according to the cutting angle of blade 1 corresponding to step 5, set the phase angle of the cutting starting point of blade 1 in the simulation program, and calculate the simulation force data of one cycle based on the instantaneous milling force model established in step 7.

[0117] Step 9: Construct an equivalent relationship model between the experimental cutting force and the simulated cutting force at different time points within a cycle to obtain a vector expression of the cutting force coefficient group; Step 9 includes the following steps 901 to 902:

[0118] Step 901: Let the experimental cutting force vector obtained in step 5 be equal to the simulated cutting force vector obtained in step 8, and obtain the identity equation for the force coefficient group K:

[0119]

[0120] in:

[0121]

[0122] In the above formula, t1, ..., t d ,…,t n is the sampling time point when the tool rotates one circle in the simulation force data. It is the sampling time point when the tool rotates one circle starting from the cutting moment in the experimental force data.

[0123] Step 902: According to formula (8) in step 901, the least square method (LSM) is used to calculate the vector expression of the cutting force coefficient group:

[0124]

[0125] Step 10: Minimize the simulated cutting force F S and experimental cutting force F M The loss function of the time error is used to obtain the cutting force coefficients of each group of variable helix angle milling cutters;

[0126] Step 1001: Calculate the simulated cutting force F S and experimental cutting force F M The second norm of the error between the two, the error loss function Δ1(λ, ρ) is obtained:

[0127]

[0128] in, is a function of tool runout parameters λ, ρ.

[0129]

[0130] Where I is the identity matrix.

[0131] Step 1002: Introduce the L2 regularization parameter ε and rearrange the error loss function:

[0132]

[0133] This step introduces the L2 regularization parameter ε and rearranges the error loss function, which can avoid the condition number of the cutting force coefficient being too large during the numerical optimization process and avoid the occurrence of overfitting.

[0134] Step 1003: Construct the objective function Δ2(ε) related to the L2 regularization parameter ε as follows:

[0135]

[0136] In this step, the objective function Δ2(ε) related to the L2 regularization parameter ε is constructed so that the ratio of the shear force coefficient to the edge force coefficient in the cutting force coefficient in the same direction is consistent with the ratio of the corresponding coefficients in the average cutting force coefficient, avoiding the occurrence of pathological solutions in the subsequent numerical optimization of the cutting force coefficient.

[0137] Step 1004: Using a dual-objective optimization method, the objective function Δ2(ε) and the rearranged error loss function Δ1(λ, ρ, ε) are simultaneously considered, the weight between the objective function and the error loss function is adjusted, and the values ​​of the run-out angle λ and the run-out amount ρ are optimized through iterative optimization of the genetic algorithm until the optimal solution is reached, thereby obtaining the most matching cutting force coefficient set K, run-out angle λ, run-out amount ρ, and regularization parameter ε;

[0138] This step adjusts the weights between the objective function and the error loss function, for example, 0.7:0.3. Through iterative optimization using a genetic algorithm, the values ​​of the runout angle λ and the runout amount ρ are optimized until an optimal solution is reached. This allows the model to have both good generalization performance and a relatively low error level.

[0139] The present invention provides a method for calibrating the milling force model of a variable helix angle milling cutter based on maximizing the force petal area. This method integrates the radial runout effect of the tool, improving the accuracy of the cutting force model of the variable helix angle cutter. Based on the principle of maximizing the force petal area, the cutting phase of the experimental force and the simulation force is matched, thereby improving the accuracy of the identification of the cutting force coefficient. In addition, the introduction of the L2 regularization parameter further ensures the stability and rationality of the cutting force coefficient and avoids the occurrence of pathological solutions. The present invention is used to accurately identify multiple sets of cutting force coefficients and tool runout parameters of a variable helix angle milling cutter, thereby improving the cutting force prediction accuracy of the variable helix angle milling cutter and providing a basis for accurate stability judgment of the machining process.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications to the technical solutions described in the above embodiments, or equivalent replacement of some or all of the technical features therein, do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A milling force model calibration method for a variable helix angle milling cutter based on maximizing the force petal area, characterized in that: The following processes are included: Step 1: According to the principle of cutting mechanics, the linear average milling force model can be established as follows: in, is the average milling force in the x-axis, y-axis, and z-axis directions, N is the angle divided into N parts, a p is the axial cutting depth of the tool, f t is the feed speed, ψ st , ψ ex Indicates the cutting entry angle and cutting exit angle, K tc , K rc , K ac are the tangential, radial and axial shear force coefficients respectively; K te , K re , K ae are the tangential, radial and axial edge force coefficients, respectively; Step 2: Use a variable helix angle milling cutter to conduct multiple slot milling experiments. In each experiment, the spindle speed, axial cutting depth, and radial cutting depth are fixed, and the feed per tooth is changed. The average milling force in the three directions of slot milling at different feed speeds is obtained using a three-component dynamometer. Step 3: Assuming that the cutting force coefficients of each group of variable helix angle milling cutters corresponding to different spiral edges are the same, a linear regression analysis is performed using the linear average milling force model of step 1 to obtain the average milling force coefficient of the variable helix angle milling cutter; Step 4: Use a variable helix angle milling cutter to conduct a side milling experiment under the condition of tool-workpiece single tooth meshing, and use a three-component dynamometer to measure the instantaneous milling force at different cutting moments; Step 5: randomly select one cycle of experimental force data from the instantaneous milling force data measured in step 4; Step 6: Assign cutting force coefficient groups to be identified N to variable helix angle milling cutter t A blade; Step 7: Based on the geometric parameters, runout parameters, cutting force coefficients, and cutting mechanics principles of the variable helix angle milling cutter, a microelement cutting force modeling method is used to establish an instantaneous cutting force model and predict multi-cycle cutting force data; Step 8: Determine the time interval of the simulation force data points so that the number of simulation force data points in a single cycle is equal to the number of experimental force data points; according to the cutting angle of the corresponding blade 1 in step 5, set the phase angle of the cutting starting point of the simulation program blade 1, and calculate the simulation force data of one cycle based on the instantaneous milling force model established in step 7; Step 9: Construct an equivalent relationship between the experimental cutting force and the simulated cutting force at different time points within a cycle to obtain a vector expression of the cutting force coefficient group; Step 10: Minimize the simulated cutting force F S and experimental cutting force F M The loss function of the time error is used to obtain the cutting force coefficients of each group of variable helix angle milling cutters.

2. The method for calibrating the milling force model of a variable helix angle milling cutter based on maximizing the force petal area according to claim 1, characterized in that: The step 3 comprises: Assuming that the cutting force coefficients of each group of variable helical angle milling cutters corresponding to different helical edges are the same K i =K j (i≠j); Because it is assumed that the cutting force coefficients of each group are the same, in this case: in, represent the average tangential, radial, and axial shear force coefficients of the variable helix angle milling cutter, respectively; represent the average tangential, radial and axial edge force coefficients of the variable helix angle milling cutter respectively; Using the experimental average milling force obtained in step 2, a linear regression analysis is performed on the linear average milling force model in step 1, and the average milling force coefficient of the variable helix angle milling cutter is obtained as follows:

3. The milling force model calibration method of a variable helix angle milling cutter based on force petal area maximization according to claim 2, characterized in that: The step 5 includes the following steps 501 to 504: Step 501: Calculate the time difference t between the cutting out and the cutting into the workpiece by any edge i of the variable helix angle milling cutter. i The time difference t between the adjacent cutting edges and the cutting edge θi : Where, T is the time required for the tool to rotate one circle, T is the tool radius, and a e is the radial cutting depth of the tool, β i is the helix angle of blade i, θ i，0 is the tooth angle between edge i and edge i+1 at the free end of the tool; Step 502: Calculate all blade force lobe areas with a certain data point in the intercepted periodic experimental force as the cutting starting point of blade 1: Where t0 is the time corresponding to the starting point of the assumed blade 1 cutting into the workpiece, t l =t(k),k=1, 2,...,n; Step 503: Determine the experimental data point that maximizes the accumulated force petal area as the actual starting point of the blade 1 cutting into the workpiece; Step 504: Output one cycle of experimental force data using the starting point as the initial sampling point.

4. The method for calibrating the milling force model of a variable helix angle milling cutter based on maximizing the force petal area according to claim 3, characterized in that: The step 7 includes the following steps 701 to 704: Step 701: Discretize the axial cutting depth into q elements using a discretization method. Any axial element is represented by an index k, k∈[1,q]. Step 702: Considering the influence of tool runout, modify the angle of the helix angle milling cutter entering and cutting out the workpiece; Climb milling: When reverse milling: Where: st，i，k Indicates the angle at which the variable helix angle milling cutter cuts into the workpiece during down milling, ψ ex，i，k Indicates the angle at which the variable helix angle milling cutter cuts the workpiece during down milling, ψ st，i，k Indicates the angle at which the variable helix angle milling cutter cuts into the workpiece during reverse milling, ψ ex，i，k represents the angle of the workpiece cut by the variable helix angle milling cutter during up-milling; ρ is the tool runout, λ is the tool runout angle; t p Cut previous edge i for current edge i p The time interval between milling the material left at the same workpiece surface position; p is the difference in the numbers of the two cutting edges that mill the same workpiece surface position successively; f i，k (t p ) is t p The feed rate of the milling cutter during the time interval; R i，k is the actual milling radius of the i-th blade on the k-th infinitesimal element; R is the geometric radius of the milling cutter; Step 703: Using the micro-element cutting force modeling method and based on the linear cutting force model, the simulation formula of the instantaneous cutting force of the variable helix angle milling cutter is obtained as follows: in: In the above formula, Δz is the thickness of each microelement, W i，k (t) is the switching function used to determine whether the spiral blade i is involved in cutting; ψ i，k (t) is the position angle of blade i on element k at time t; h i，k (t, p) is the instantaneous undeformed thickness equation including runout; h i，k (t) is the actual instantaneous undeformed cut thickness including runout; The lag angle of the first edge on the kth infinitesimal element; θ i→1，k is the tooth-to-tooth angle between the first and i-th edges on the k-th element; Step 704: Use the separation of variables method to write the instantaneous cutting force in step 703 into the form of the product of the position matrix Θ and the cutting force coefficient vector K. Based on the micro-element cutting force model, the instantaneous milling force data is predicted as follows: in:

5. The method for calibrating the milling force model of a variable helix angle milling cutter based on maximizing the force petal area according to claim 4, characterized in that: The step 9 includes the following steps 901 to 902: Step 901: Let the experimental cutting force vector obtained in step 5 be equal to the simulated cutting force vector obtained in step 8, and obtain the identity equation for the force coefficient group K: in: In the above formula, t1, ..., t d ,…,t n is the sampling time point of one revolution of the tool in the simulation force data, t l ,…,t l-1 +t d ,…,t l-1 +t n It is the sampling time point of the tool rotating one circle with the cutting moment as the starting point in the experimental force data; Step 902: According to formula (8) in step 901, the least square method (LSM) is used to calculate the vector expression of the cutting force coefficient group:

6. The method for calibrating the milling force model of a variable helix angle milling cutter based on maximizing the force petal area according to claim 5, characterized in that: The step 10 includes the following steps 1001 to 1004: Step 1001: Calculate the simulated cutting force F S and experimental cutting force F M The second norm of the error between the two, the error loss function Δ1(λ, ρ) is obtained: in, is a function of tool runout parameters λ, ρ; Where I is the identity matrix; Step 1002: Introduce the L2 regularization parameter ε and reorganize the error loss function: Step 1003: Construct the objective function Δ(ε) related to the L2 regularization parameter ε as follows: Step 1004: Use the dual-objective optimization method to simultaneously consider the objective function Δ2(ε) and the rearranged error loss function Δ1(λ, ρ, ε), adjust the weight between the objective function and the error loss function, and optimize the values ​​of the runout angle λ and the runout amount ρ through iterative optimization of the genetic algorithm until the optimal solution is reached, and obtain the most matching cutting force coefficient group K, runout angle λ, runout amount ρ and regularization parameter ε.

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