Milling force model calibration method for variable helix angle milling cutter based on force patch area maximization

Abstract

The present application relates to the technical field of milling force prediction, and provides a variable helix angle milling cutter milling force model calibration method based on force pocket area maximization, which comprises the following steps: according to the principle of cutting mechanics, a linear average milling force model can be established; a loss function of minimizing the simulation cutting force F S and the experimental cutting force F M error is obtained, and each group of cutting force coefficients of the variable helix angle milling cutter is obtained. The tool radial runout effect is integrated, the accuracy of the variable helix angle cutter cutting force model is improved, the cutting-in phase matching of the experimental force and the simulation force is completed based on the force pocket area maximization principle, the cutting force coefficient identification accuracy is improved, in addition, the L2 regularization parameter is introduced to further ensure the stability and reasonableness of the cutting force coefficients, and the occurrence of the ill-conditioned solution is avoided. The present application is used for accurately identifying the multiple groups of cutting force coefficients and the tool runout parameters of the variable helix angle milling cutter, so as to improve the cutting force prediction accuracy of the variable helix angle milling cutter, and provides a basis for accurately judging the stability of the machining process.

Description

Technical Field

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

[0002] With the increasing demands for precision and efficiency in machining complex, weakly rigid parts for high-end equipment in fields such as aerospace, variable helix angle end mills have been increasingly used. Due to their unique helical groove structure design, variable helix angle end mills can generate cutting motions with different phases in different axial cutting layers. The rational utilization of this characteristic significantly reduces the possibility of regenerative chatter during milling, and research on their chatter stability has gradually become a hot topic.

[0003] Accurate identification of the milling force model for variable helix angle end mills is a prerequisite for accurate stability assessment of the machining process of this type of tool. Reference 1, "Budak, E., Altintas, Y. & Armarego, EJ. A. Diction of Milling Force Coefficients From Orthogonal Cutting Data. J. Manuf. Sci. Eng. 118, 216–224 (1996)," proposes a classic method for calibrating milling force coefficients for general cylindrical end mills. This method establishes a linear milling force model related to the cutting force coefficients. By fixing the axial cutting depth and gradually changing the feed per tooth, several sets of slot milling experiments are conducted to obtain milling force data corresponding to different feed per tooth. Finally, the cutting force coefficients are obtained using linear regression. The calibration has good robustness, but the cost is slightly high and it cannot calibrate tool runout parameters.

[0004] Reference 2, "Guo, Q., Zhao, B., Zhang, M., Jiang, Y. & Zhang, Y. Assemble-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 cutting force coefficients of variable helix angle cutters that considers the tool runout effect. This method incorporates the tool runout effect into the cutting force coefficients, achieving an accurate approximation of the experimental force data to the simulated force curve. However, since the tool runout parameters are not explicitly present in the force model equations, the calibration results cannot provide the tool runout parameters.

[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," presents a method for calibrating the cutting force coefficient of a variable helix milling cutter capable of synchronously outputting tool runout parameters. This method obtains the average cutting force coefficient through linear regression based on milling experiments, and then uses a trust domain reflection algorithm to iteratively determine the cutting force coefficient and tool runout parameters. However, this method is based on the assumption that the cutting force coefficient is equal on each cutting edge of the variable helix milling cutter, and is mainly suitable for cases where the differences in helix angle between different cutting edges are small.

[0006] Patent 1, "Identification Method of Cutting Force Coefficient of Variable Helix Angle Milling Cutters Based on Data Sliding Matching," proposes a method for calibrating the cutting force coefficient of variable helix angle milling cutters based on data sliding matching. Considering that different helix edges of variable helix angle milling cutters exhibit different shearing and plowing effects when cutting workpiece materials, this method introduces a sliding factor to synchronize the simulated force with the experimental force. Then, it uses the least squares method to construct matrix expressions for multiple sets of cutting force coefficients. Finally, an optimization algorithm is used to quickly calibrate multiple sets of cutting force coefficients and tool runout parameters for different helix angle edges. However, during numerical optimization, there is a high probability of encountering the problem of excessively large matrix condition numbers, which may lead to ill-conditioned solutions for the calibrated cutting force coefficients. Summary of the Invention

[0007] This invention primarily addresses the technical challenges of accurately identifying multiple cutting force coefficients and runout parameters of variable helix angle end mills in existing technologies, as well as the need for rapid phase matching between simulated and experimental forces and the potential for ill-conditioned solutions in multi-parameter calibration. It proposes a milling force model calibration method for variable helix angle end mills based on maximizing the force lobe area. This method accurately identifies multiple milling force coefficients and runout parameters of variable helix angle end mills and, based on the L2 regularization principle, ensures that the obtained cutting force coefficients are within a reasonable range.

[0008] This invention provides a method for calibrating a milling force model for a variable helix angle end mill based on maximizing the force lobe area, comprising the following steps:

[0009] Step 1: Based on the principles of cutting mechanics, the linear average milling force model can be established as follows:

[0010]

[0011] in, Let N be the average milling force along the x, y, and z axes, respectively, and let N be the angle divided into N parts. p f is the axial depth of cut of the tool. t For the feed rate, ψ st ψ ex K represents the cutting approach angle and cutting exit angle. tc K rc K ac These are the tangential, radial, and axial shear force coefficients, respectively; K te K re K ae These are the cutting edge force coefficients for the tangential, radial, and axial directions, respectively.

[0012] Step 2: Conduct multiple slot milling experiments using a variable helix angle end mill. For each experiment, fix the spindle speed, axial depth of cut, and radial depth of cut, and change the feed per tooth. Use a three-component force gauge to obtain the average milling force in the three directions at different feed rates.

[0013] Step 3: Assuming that the cutting force coefficients of the variable helix angle end mills are the same for each group of different helical edges, and using the linear average milling force model in Step 1 to perform linear regression analysis, the average milling force coefficient of the variable helix angle end mills is obtained.

[0014] Step 4: A side milling experiment was conducted using a variable helix angle milling cutter under single-tooth meshing conditions between the cutter and the workpiece. The instantaneous milling force at different cutting moments was measured using a three-component force gauge.

[0015] Step 5: From the instantaneous milling force data measured in Step 4, arbitrarily select the experimental force data for one cycle;

[0016] Step 6: Assign the cutting force coefficient group to be identified N of the variable helix angle end mill t One blade;

[0017] Step 7: Based on the geometric parameters, runout parameters, cutting force coefficients, and cutting mechanics principles of the variable helix angle end mill, establish an instantaneous cutting force model and predict multi-cycle cutting force data using the micro-element cutting force modeling method.

[0018] Step 8: Determine the time interval between 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; based on the cutting angle of the corresponding blade 1 in Step 5, set the phase angle of the cutting start point of blade 1 in the simulation program, and calculate the simulation force data for one cycle based on the instantaneous milling force model established in Step 7.

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

[0020] Step 10: Minimize the simulated cutting force F S With experimental cutting force F M The loss function of the inter-error is used to obtain the cutting force coefficients of each group of variable helix angle end mills.

[0021] Furthermore, step 3 includes:

[0022] Assuming that the cutting force coefficients of the variable helix angle end mill are the same for each set of different helix cutting edges. That is, K i =K j (i≠j);

[0023] Since it is assumed that the cutting force coefficients are the same for all groups, in this case we have:

[0024] in, These represent the average tangential, radial, and axial shear force coefficients of a variable helix angle end mill, respectively. These represent the average tangential, radial, and axial cutting edge force coefficients of a variable helix angle end mill, respectively.

[0025] Using the experimental average milling force obtained in step 2, a linear regression analysis was performed on the linear average milling force model from step 1, yielding the following average milling force coefficient for the variable helix angle end mill:

[0026]

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

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

[0029]

[0030] t θi =T·θ i，0 / 2π (4)

[0031] In the formula, T is the time required for the tool to rotate one revolution, R is the tool radius, and a e β is the radial depth of cut of the tool. i Let θ be the helix angle of blade i. i，0 Let be the tooth angle between blade i and blade i+1 at the free end of the tool;

[0032] Step 502: Calculate the area of ​​all blade force lobes with a data point in the intercepted periodic experimental force as the starting point of blade 1's cutting:

[0033]

[0034] In the formula, t0 is the time corresponding to the assumed starting data point when blade 1 cuts into the workpiece, and t l =t(k),k=1, 2,...,n;

[0035] Step 503: Determine the experimental data point that maximizes the accumulated force flap area as the true starting point data point for blade 1 to cut into the workpiece.

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

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

[0038] Step 701: Discretize the axial cutting depth into q infinitesimal elements using the discretization method. Any axial infinitesimal element is represented by the index k, where k∈[1,q].

[0039] Step 702: Considering the impact of tool runout, adjust the angle at which the helix end mill enters and exits the workpiece.

[0040]

[0041]

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

[0043] Step 703: Using the infinitesimal cutting force modeling method, based on the linear cutting force model, the simulation formula for the instantaneous cutting force of the variable helix angle end mill is obtained as follows:

[0044]

[0045] in:

[0046]

[0047] In the above formula, Δz is the thickness of each infinitesimal element, and W i，k (t) is a switching function used to determine whether the helical blade i participates in cutting; ψ i，k (t) represents the position angle of the i-th blade on the k-th infinitesimal element at time t; h i，k (t, p) is the instantaneous undeformed shear thickness equation containing jumps; h i，k (t) represents the actual instantaneous undeformed cut thickness including the jump; The hysteresis angle of the first edge on the k-th infinitesimal element; θ i→1，k The tooth angle between the first and i-th edges on the k-th infinitesimal element;

[0048] Step 704: Using the method of separation of variables, the instantaneous cutting force in step 703 is expressed as the product of the position matrix Θ and the cutting force coefficient vector K. Based on the infinitesimal cutting force model, the instantaneous milling force data is predicted as follows:

[0049]

[0050] in:

[0051]

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

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

[0054]

[0055] in:

[0056]

[0057] In the above formula, t1, ..., t d ... t n This refers to the sampling time point of one revolution of the tool in the simulated force data. The sampling time point in the experimental force data is the time point at which the tool rotates one revolution, starting from the moment of entry.

[0058] Step 902: Based on formula (8) in step 901, calculate the vector expression of the cutting force coefficient group using the least squares method (LSM).

[0059]

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

[0061] Step 1001: Calculate the simulated cutting force F S With experimental cutting force F M The L2 norm of the interval error yields the error loss function Δ1(λ, ρ):

[0062]

[0063] in, It is a function of the tool runout parameters λ and 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) for the L2 regularization parameter ε as follows:

[0069]

[0070] Step 1004: Using a dual-objective optimization method, simultaneously consider the objective function Δ2(ε) and the rearranged error loss function Δ1(λ, ρ, ε), adjust the weights between the objective function and the error loss function, and optimize the values ​​of the runout angle λ and 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] This invention provides a calibration method for the milling force model of variable helix angle end mills based on maximizing the force lobe area. It integrates the radial runout effect of the tool, improving the accuracy of the cutting force model for variable helix angle end mills. Based on the principle of maximizing the force lobe area, it achieves phase matching between experimental and simulated forces, enhancing the accuracy of cutting force coefficient identification. Furthermore, the introduction of an L2 regularization parameter further ensures the stability and rationality of the cutting force coefficients, avoiding ill-conditioned solutions. This invention is used to accurately identify multiple sets of cutting force coefficients and tool runout parameters for variable helix angle end mills, improving the accuracy of cutting force prediction and providing a foundation for accurate stability assessment during machining. Attached Figure Description

[0072] Figure 1 This is a flowchart illustrating the implementation of the multi-group cutting force coefficient identification method for variable helix angle end mills provided by the present invention.

[0073] Figure 2 This is a schematic diagram showing the starting point of the intervention and the location where the experimental force data was collected;

[0074] Figures 3(a)-(d) are schematic diagrams of the force flap surface accumulation process and the determination of the maximum area. Detailed Implementation

[0075] To make the technical problems solved by this invention, the technical solutions adopted, and the technical effects achieved 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 of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings, not all of them.

[0076] like Figure 1 As shown in the figure, the milling force model calibration method for variable helix angle end mills based on maximizing the force lobe area provided by the present invention includes the following process:

[0077] Step 1: Based on the principles of cutting mechanics, the linear average milling force model can be established as follows:

[0078]

[0079] in, Let N be the average milling force along the x, y, and z axes, respectively, and let N be the angle divided into N parts. p f is the axial depth of cut of the tool. t For the feed rate, ψ st ψ ex K represents the cutting approach angle and cutting exit angle. tr K rc K ac These are the tangential, radial, and axial shear force coefficients, respectively; K te K re K ae These are the cutting edge force coefficients for the tangential, radial, and axial directions, respectively.

[0080] Step 2: Conduct multiple slot milling experiments using a variable helix angle end mill. For each experiment, fix the spindle speed, axial depth of cut, and radial depth of cut, and change the feed per tooth. Use a three-component force gauge to obtain the average milling force in the three directions at different feed rates.

[0081] Specifically, the three-component force gauge can be the KISTLER 9257 general-purpose three-component force gauge.

[0082] Step 3: Assuming that the cutting force coefficients of the variable helix angle end mills are the same for each group of different helical edges, and using the linear average milling force model from Step 1 to perform linear regression analysis, the average milling force coefficient of the variable helix angle end mills is obtained.

[0083] Specifically, it is assumed that the cutting force coefficients for each set of different helical cutting edges of the variable helix angle end mill are the same. That is, K j =K j (i≠j).

[0084] Since it is assumed that the cutting force coefficients of each group are the same, which is the concept of average cutting force coefficient, in this case we have: in, These represent the average tangential, radial, and axial shear force coefficients of a variable helix angle end mill, respectively. These represent the average tangential, radial, and axial cutting edge force coefficients of a variable helix angle end mill, respectively.

[0085] Using the experimental average milling force obtained in step 2, a linear regression analysis was performed on the linear average milling force model from step 1, yielding the following average milling force coefficient for the variable helix angle end mill:

[0086]

[0087] Step 4: A side milling experiment was conducted using a variable helix angle milling cutter under single-tooth meshing conditions between the cutter and the workpiece. The instantaneous milling force at different cutting moments was measured using a three-component force gauge.

[0088] Specifically, a side milling experiment was conducted using a variable helix angle end mill under the condition of single tooth meshing between the cutter and the workpiece (i.e., at any given cutting moment, at most one tooth of the cutter participates in the cutting work). The instantaneous milling force at different cutting moments was measured using a three-component force gauge. 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, arbitrarily select the experimental force data for one cycle.

[0090] This invention considers the most general case: that is, when the first data point is not the entry point of a certain edge of the variable helix angle cutter. Figure 2 Based on the principle of maximizing the force lobe area, the starting point of the cutting edge in the periodic experimental force is found, and the experimental force data for one period is output using this starting point as the initial sampling point. Step 5 includes the following steps 501 to 504:

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

[0092]

[0093] In the formula, T is the time required for the tool to rotate one revolution, R is the tool radius, and a e β is the radial depth of cut of the tool. i Let θ be the helix angle of blade i. i，0 Let be the tooth angle between blade i and blade i+1 at the free end of the tool.

[0094] Step 502: Calculate the area of ​​all blade force lobes with a data point in the intercepted periodic experimental force as the starting point of blade 1's cutting ( Figure 3a ):

[0095]

[0096] In the formula, t0 is the time corresponding to the assumed starting data point when blade 1 cuts into the workpiece, and t l =t(k),k=1, 2,...,n.

[0097] Step 503: Determine the experimental data point that maximizes the accumulated force flap area as the true starting point data point for blade 1 to cut 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 lobe areas within these specific time ranges, special experimental data points are obtained to maximize the accumulated force lobe area, as shown in Figure 3(d). This experimental data point is the actual starting point data point for blade 1 to cut into the workpiece.

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

[0100] Step 6: Assign the cutting force coefficient group to be identified N of the variable helix angle end mill t One blade;

[0101] Step 7: Based on the geometric parameters, runout parameters, cutting force coefficients, and cutting mechanics principles of the variable helix angle end mill, establish an instantaneous cutting force model and predict multi-cycle cutting force data using the infinitesimal cutting force modeling method; Step 7 includes the following steps 701 to 704:

[0102] Step 701: Discretize the axial cutting depth into q infinitesimal elements using the discretization method. Any axial infinitesimal element is represented by the index k, where k∈[1,q].

[0103] Step 702: Considering the impact of tool runout, adjust the angle at which the helix end mill enters and exits the workpiece.

[0104]

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

[0106] Step 703: Using the infinitesimal cutting force modeling method, based on the linear cutting force model, the simulation formula for the instantaneous cutting force of the variable helix angle end mill is obtained as follows:

[0107]

[0108]

[0109] in:

[0110]

[0111] In the above formula, Δz is the thickness of each infinitesimal element, and W i，k (t) is a switching function used to determine whether the helical blade i participates in cutting; ψ i，k (t) represents the position angle of the i-th blade on the k-th infinitesimal element at time t; h i，k (t, p) is the instantaneous undeformed shear thickness equation containing jumps; h i，k (t) represents the actual instantaneous undeformed cut thickness including the jump; The hysteresis angle of the first edge on the k-th infinitesimal element; θ i→1，k The tooth angle between the first and i-th edges on the k-th infinitesimal element;

[0112] Step 704: Using the method of separation of variables, the instantaneous cutting force in step 703 is expressed as the product of the position matrix Θ and the cutting force coefficient vector K. Based on the infinitesimal cutting force model, the instantaneous milling force data is predicted as follows:

[0113]

[0114] in:

[0115]

[0116] Step 8: Determine the time interval between 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, i.e., the number of simulation milling force data points in each cycle is n; according to the cutting angle of the corresponding cutting edge 1 in Step 5, set the phase angle of the cutting start point of the simulation program cutting edge 1, 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 equal relationship model between experimental cutting force and simulated cutting force at different time points within a cycle, and obtain the vector expression for the cutting force coefficient group; Step 9 includes the following steps 901 to 902:

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

[0119]

[0120] in:

[0121]

[0122] In the above formula, t1, ..., t d 、…、t n This refers to the sampling time point of one revolution of the tool in the simulated force data. This refers to the sampling time point in the experimental force data, which is the time when the tool rotates one revolution, starting from the moment of entry.

[0123] Step 902: Based on formula (8) in step 901, calculate the vector expression of the cutting force coefficient group using the least squares method (LSM).

[0124]

[0125] Step 10: Minimize the simulated cutting force F S With experimental cutting force F M The loss function of the inter-helix error is used to obtain the cutting force coefficients of each group of variable helix angle end mills;

[0126] Step 1001: Calculate the simulated cutting force F S With experimental cutting force F M The L2 norm of the interval error yields the error loss function Δ1(λ, ρ):

[0127]

[0128] in, It is a function of the tool runout parameters λ and 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 reorganizes the error loss function, which can avoid the condition number of the cutting force coefficient being too large during the numerical optimization process and prevent overfitting.

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

[0135]

[0136] This step constructs an objective function Δ2(ε) for the L2 regularization parameter ε, such that the ratio of the shear force coefficient to the cutting edge force coefficient in the cutting force coefficients in the same direction is consistent with the ratio of the corresponding coefficient in the average cutting force coefficient, thus avoiding ill-conditioned solutions in the subsequent numerical optimization of the cutting force coefficients.

[0137] Step 1004: Using a dual-objective optimization method, simultaneously consider the objective function Δ2(ε) and the rearranged error loss function Δ1(λ, ρ, ε), adjust the weights between the objective function and the error loss function, and optimize the values ​​of the runout angle λ and runout amount ρ through iterative optimization of the genetic algorithm until the optimal solution is reached, and obtain the most matching cutting force coefficient set K, runout angle λ, runout amount ρ and regularization parameter ε;

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

[0139] This invention provides a calibration method for the milling force model of variable helix angle end mills based on maximizing the force lobe area. This method integrates the radial runout effect of the tool, improving the accuracy of the cutting force model of variable helix angle end mills. Based on the principle of maximizing the force lobe area, it achieves phase matching between experimental and simulated forces, improving the accuracy of cutting force coefficient identification. In addition, the introduction of L2 regularization parameters further ensures the stability and rationality of the cutting force coefficients, avoiding the occurrence of ill-conditioned solutions. This invention is used to accurately identify multiple sets of cutting force coefficients and tool runout parameters of variable helix angle end mills, thereby improving the cutting force prediction accuracy of variable helix angle end mills and providing a foundation for accurate stability judgment in 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, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications to the technical solutions described in the foregoing embodiments, or equivalent substitutions for some or all of the technical features, do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calibrating the milling force model of a variable helix angle end mill based on maximizing the force lobe area, characterized in that, Includes the following processes: Step 1: Based on the principles of cutting mechanics, the linear average milling force model can be established as follows: ； in, To separate x axis, y axis, z Average milling force in the axial direction To divide the angle into share, The axial depth of cut of the tool. For feed rate, , Indicates the cutting approach angle and cutting exit angle. These are the shear force coefficients for the tangential, radial, and axial directions, respectively. These are the cutting edge force coefficients for the tangential, radial, and axial directions, respectively. Step 2: Conduct multiple slot milling experiments using a variable helix angle end mill. For each experiment, fix the spindle speed, axial depth of cut, and radial depth of cut, and change the feed per tooth. Use a three-component force gauge to obtain the average milling force in the three directions at different feed rates. ; Step 3: Assuming that the cutting force coefficients of the variable helix angle end mills are the same for each group of different helical edges, and using the linear average milling force model in Step 1 to perform linear regression analysis, the average milling force coefficient of the variable helix angle end mills is obtained. Step 4: A side milling experiment was conducted using a variable helix angle milling cutter under single-tooth meshing conditions between the cutter and the workpiece. The instantaneous milling force at different cutting moments was measured using a three-component force gauge. Step 5: From the instantaneous milling force data measured in Step 4, arbitrarily select the experimental force data for one cycle; Step 5 includes the following steps 501 to 504: Step 501: Calculate the arbitrary cutting edge of the variable helix angle end mill. Time difference between cutting out and cutting into the workpiece The time difference between the cutting edge and the adjacent cutting edge entering the workpiece : ； ； In the formula, The time required for the tool to rotate one revolution. For the tool radius, The radial depth of cut of the tool. For the blade The helix angle, For the blade Kajima The tooth angle at the free end of the cutting tool; Step 502: Calculate the area of ​​all blade force lobes with a data point in the intercepted periodic experimental force as the starting point of blade 1's cutting: ； In the formula, t0 is the time corresponding to the assumed starting point data point when blade 1 cuts into the workpiece. k = 1, 2, ..., n; Step 503: Determine the experimental data point that maximizes the accumulated force flap area as the true starting point data point for blade 1 to cut into the workpiece. Repeat steps 501 and 502 continuously. = t(1) t(2) t(n); until the entire cycle is covered, by comparing the accumulated force lobe area within these specific time ranges, special experimental data points are obtained to maximize the accumulated force lobe area. This experimental data point is the actual starting point data point for blade 1 to cut into the workpiece. Step 504: Output the experimental force data for one cycle, using the starting data point as the initial sampling point; Step 6: Assign the cutting force coefficient group to be identified To variable helix angle end mill One blade; Step 7: Based on the geometric parameters, runout parameters, cutting force coefficients, and cutting mechanics principles of the variable helix angle end mill, establish an instantaneous cutting force model and predict multi-cycle cutting force data using the micro-element cutting force modeling method. Step 8: Determine the time interval between 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; based on the cutting angle of the corresponding blade 1 in Step 5, set the phase angle of the cutting start point of blade 1 in the simulation program, and calculate the simulation force data for one cycle based on the instantaneous milling force model established in Step 7. Step 9: Construct the quantitative relationship between experimental cutting force and simulated cutting force at different time points within a cycle, and obtain the vector expression of the cutting force coefficient group; Step 10: Minimize the simulated cutting force With experimental cutting force The loss function of the inter-error is used to obtain the cutting force coefficients of each group of variable helix angle end mills.

2. The method for calibrating the milling force model of a variable helix angle end mill based on maximizing the force lobe area according to claim 1, characterized in that, Step 3 includes: Assuming that the cutting force coefficients of the variable helix angle end mill are the same for each set of different helix cutting edges. ,Right now ; Since it is assumed that the cutting force coefficients are the same for all groups, in this case we have: ; in, These represent the average tangential, radial, and axial shear force coefficients of a variable helix angle end mill, respectively. These represent the average tangential, radial, and axial cutting edge force coefficients of a variable helix angle end mill, respectively. Using the experimental average milling force obtained in step 2, a linear regression analysis was performed on the linear average milling force model from step 1, yielding the following average milling force coefficient for the variable helix angle end mill: 。 3. The method for calibrating the milling force model of a variable helix angle end mill based on maximizing the force lobe area according to claim 2, characterized in that, Step 7 includes the following steps 701 to 704: Step 701: Discretize the axial cutting depth using the discretization method. Each infinitesimal element, with any axial infinitesimal element indexed. k express, ; Step 702: Considering the impact of tool runout, adjust the angle at which the helix end mill enters and exits the workpiece. During climb milling: ; During reverse milling: ; in: This indicates the angle at which the variable helix angle end mill cuts into the workpiece during climb milling. This indicates the angle at which the variable helix angle end mill cuts the workpiece during climb milling. This indicates the angle at which the variable helix angle end mill cuts into the workpiece during conventional milling. This indicates the angle at which the variable helix angle end mill cuts the workpiece during conventional milling; This is the tool runout. This refers to the tool runout angle; For the current blade i Cut off the previous blade The time interval between milling the material left at the same position on the surface of the workpiece; p This represents the difference in the numbering of two cutting edges used to mill the same workpiece surface at different positions. for The feed rate of the milling cutter during the time interval; For the first i The blade in the k The actual milling radius on a micro element; R Let be the geometric radius of the milling cutter; Step 703: Using the infinitesimal cutting force modeling method, based on the linear cutting force model, the simulation formula for the instantaneous cutting force of the variable helix angle end mill is obtained as follows: ； in: ； In the above formula, The thickness of each micro-element, This is a switching function used to determine the helical blade. Whether it participates in cutting; for time On the micro-yuan The position angle of the blade; Equation for instantaneous undeformed shear thickness with jump The actual instantaneous undeformed cut thickness includes the jump; 1,k→0 No. The hysteresis angle of the first edge on a micro element; For the first The first blade and the second blade on the infinitesimal element The tooth angle between each cutting edge; Step 704: Use the method of separation of variables to write the instantaneous cutting force in step 703 as a position matrix. and cutting force coefficient vector Based on the infinitesimal cutting force model, the product form predicts the instantaneous milling force data as follows: ； in: 。 4. The method for calibrating the milling force model of a variable helix angle end mill based on maximizing the force lobe area according to claim 3, characterized in that, Step 9 includes the following steps 901 to 902: Step 901: Set the experimental cutting force vector obtained in step 5 to the simulated cutting force vector obtained in step 8, and obtain the force coefficient set. The identity: ； in: ； In the above formula, This refers to the sampling time point of one revolution of the tool in the simulated force data. The sampling time point in the experimental force data is the time point at which the tool rotates one revolution, starting from the moment of entry. Step 902: Based on formula (8) in step 901, calculate the vector expression of the cutting force coefficient group using the least squares method. : 。 5. The method for calibrating the milling force model of a variable helix angle end mill based on maximizing the force lobe area according to claim 4, characterized in that, Step 10 includes the following steps 1001 to 1004: Step 1001: Calculate the simulated cutting force With experimental cutting force The L2 norm of the interval error is used to obtain the error loss function. : ； in, , is the tool runout parameter The function; ； in, It is the identity matrix; Step 1002: Introduce L2 regularization parameters And rearrange the error loss function: ； Step 1003: Construct parameters related to L2 regularization objective function as follows: ； Step 1004: Simultaneously consider the objective function using a dual-objective optimization method. and the reorganized error loss function The weights between the objective function and the error loss function are adjusted, and the jump angle is optimized through iterative optimization using a genetic algorithm. and bounce The value is calculated until the optimal solution is reached, thus obtaining the best-matching set of cutting force coefficients. Jump angle bounce and regularization parameters .

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