A method for predicting time-varying coupling of drilling axial force and workpiece deformation

Abstract

The application discloses a kind of drilling axial force-workpiece deformation time-varying coupling prediction method, belong to machining and drilling hole making technical field.This method will drilling axial force, workpiece deformation and tool actual drilling depth as interrelated time-varying variable, establish "drilling axial force-workpiece deformation-actual drilling depth-drilling axial force" closed loop coupling solution process.In each calculation time step, by drilling axial force prediction model and workpiece deformation calculation model coupling iteration, through workpiece deformation correction tool actual drilling depth and update drilling axial force, and set preconceived convergence condition and adaptive relaxation process realizes stable iterative solution.This application overcomes the prediction deviation under traditional rigid assumption, can accurately reflect the force-deformation dynamic relationship in drilling process, for low stiffness, thin-walled, weak support and laminated workpiece drilling process optimization and low-damage hole making provides reliable basis.

Description

Technical Field

[0001] This invention relates to the fields of machining and drilling technology, and in particular to a time-varying coupling prediction method for drilling axial force and workpiece deformation. Background Technology

[0002] Drilling is widely used in aerospace, rail transportation, automotive manufacturing, and composite material component assembly, and is a crucial process for machining mechanical connection holes. With the widespread application of thin-walled structures, lightweight structures, and composite / metal laminated structures, workpieces often exhibit low stiffness, weak support, or localized suspension during drilling. Such workpieces are prone to flexural deformation under drilling axial forces, leading to a discrepancy between the theoretical feed distance and the actual drilling depth. This alters the contact state between the cutting edge and the workpiece, affecting the variation of drilling axial force and the hole quality. Therefore, there is a significant dynamic coupling relationship between drilling axial force, workpiece deformation, and the actual drilling depth.

[0003] In existing technologies, methods for predicting axial force during drilling of composite / metal laminated structures have established prediction models from the perspectives of tool cutting edge micro-element stress, drilling stage division, and dynamic feed rate correction. For example, CN107832546B, "A Method and System for Predicting Axial Force in Drilling of Laminated Structures," considers the additional feed rate caused by the deformation of a single layer and applies it to predict the axial force during the entire drilling process of laminated structures; CN105912868B, "A Method for Predicting Instantaneous Axial Force in Full-Cycle Drilling of Fiber-Reinforced Composite Materials / Metal Laminated Structures," achieves instantaneous axial force prediction throughout the entire cycle of laminated structures through cutting edge micro-elementization and drilling stage division. While these methods can model and predict drilling axial force, they primarily focus on the calculation process of the drilling axial force itself and have not yet incorporated the drilling axial force, workpiece deformation, and actual tool drilling depth as interrelated state variables for time-step closed-loop coupling solution. On the other hand, for workpiece deformation and drilling damage, existing methods have introduced deformation factors into the calculation of critical axial force or damage criteria. For example, CN110188446B, "A Calculation Method for Critical Axial Force in Drilling Delamination of Composite Material Plates Considering Deformation," considers the influence of bending deformation of composite material plates on drilling delamination and is used to calculate the critical axial force generated by delamination defects. This type of method helps analyze the influence of workpiece deformation on damage formation, but its focus is on calculating critical loads or damage criteria; it has not yet established a time-varying coupled prediction model for the drilling process, relating drilling axial force, workpiece deformation, and actual tool penetration depth.

[0004] Current technologies lack a time-varying coupled prediction method that can simultaneously consider the interaction between drilling axial force, workpiece deformation, and actual tool penetration depth. There is an urgent need to establish a time-varying coupled prediction method for drilling axial force and workpiece deformation. This method would dynamically predict the drilling axial force and workpiece deformation during drilling by iteratively updating the drilling axial force, workpiece deformation, and actual tool penetration depth, providing a basis for optimizing drilling process parameters and achieving low-damage hole making. Summary of the Invention

[0005] The purpose of this invention is to provide a time-varying coupled prediction method for drilling axial force and workpiece deformation. This method acquires parameters of the workpiece to be drilled, drilling tool parameters, and drilling process parameters; calibrates the cutting force model parameters; and establishes a drilling axial force prediction model and a workpiece deformation calculation model. Within each calculation time step of the drilling process, the initial drilling axial force is obtained based on the tool feed distance. This drilling axial force is then substituted into the workpiece deformation calculation model to obtain the workpiece deformation. The workpiece deformation is used to correct the actual drilling depth of the tool, and the corrected actual drilling depth is then substituted back into the drilling axial force prediction model to update the drilling axial force. By iteratively updating the drilling axial force, workpiece deformation, and actual drilling depth, the time-varying coupled prediction results of the drilling axial force and workpiece deformation throughout the entire drilling process are obtained.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides a time-varying coupled prediction method for drilling axial force and workpiece deformation, characterized by the following steps: S1. Initialize the basic parameters, obtain the parameters of the workpiece to be drilled, the parameters of the drilling tool and the drilling process parameters, and determine the parameters of the cutting force model to be calibrated for establishing the drilling axial force prediction model. S2, Based on the drilling axial force experimental data, the parameters of the cutting force model to be calibrated are calibrated to obtain the calibrated cutting force model parameters; the calibrated cutting force model parameters are used for the calculation of drilling axial force in the subsequent drilling axial force prediction model; S3, based on the calibrated cutting force model parameters, load the drilling axial force prediction model and the workpiece deformation calculation model; wherein, the drilling axial force prediction model is used to calculate the drilling axial force according to the actual drilling depth of the tool, and the workpiece deformation calculation model is used to calculate the workpiece deformation according to the drilling axial force. S4. Based on the drilling process parameters, workpiece thickness, and tool geometry parameters, the drilling process is divided into multiple calculation time steps, and the calculation time step number is initialized. S5, determine whether all calculation time steps have been traversed; if not, proceed to step S6 for the coupled solution process of drilling axial force and workpiece deformation in the current calculation time step; if all calculation time steps have been traversed, proceed to step S15 for the result output process. S6, within the current calculation time step, calculate the tool feed distance based on the feed rate and drilling time. The expression for this is: in, The tool feed distance for the current calculation time step. The feed rate of the tool. This refers to the drilling time corresponding to the current calculation time step. S7, using the current tool feed distance as the initial tool penetration depth, initializes the drilling axial force of the current calculation time step using the drilling axial force prediction model, the expression of which is: in, The initial drilling axial force for the current calculation time step. This is a functional representation of the drilling axial force prediction model; S8, substitute the current drilling axial force into the workpiece deformation calculation model to calculate the workpiece deformation at the current calculation time step. The expression is: in, This represents the deformation of the workpiece. This is the workpiece deformation response function; S9 calculates the actual drilling depth of the tool based on the current feed distance and workpiece deformation. The expression for this is: S10, Substitute the actual drilling depth of the tool into the drilling axial force prediction model to calculate the updated drilling axial force, the expression of which is: in, The drilling axial force is updated based on the actual drilling depth of the tool; S11, determine whether the drilling axial force and workpiece deformation in the current iteration step meet the preset convergence conditions; if the drilling axial force and workpiece deformation meet the preset convergence conditions, proceed to step S13; if the drilling axial force and / or workpiece deformation do not meet the preset convergence conditions, proceed to step S12. S12, perform adaptive relaxation processing on the updated drilling axial force to obtain the corrected drilling axial force, and return the corrected drilling axial force as a new input to step S8 to recalculate the workpiece deformation, actual drilling depth, and updated drilling axial force; wherein, the adaptive relaxation processing expression is: in, Let be the drilling axial force in the k-th iteration. This is the updated drilling axial force calculated based on the current actual drilling depth of the tool. To adapt the axial force of drilling after relaxation treatment, It is an adaptive relaxation factor, and 0 < ≤1, decrease in the early stages of iteration. To ensure stability, increase the value as the calculation approaches convergence. To speed up calculations; S13, update the drilling axial force state and workpiece deformation state of the current calculation time step, and store the drilling axial force and workpiece deformation that meet the preset convergence conditions as the coupling prediction results of the current calculation time step. S14, update the calculation time step number, and return to step S5 to determine whether all calculation time steps have been traversed; if not all calculation time steps have been traversed, recalculate the current feed distance for the next calculation time step, and continue to perform the coupled solution of drilling axial force and workpiece deformation; if all calculation time steps have been traversed, proceed to step S15. S15 outputs the drilling axial force and workpiece deformation corresponding to each calculation time step during the drilling process, and obtains the time-varying coupling prediction results of drilling axial force and workpiece deformation.

[0007] Furthermore, the aforementioned time-varying coupling prediction method for drilling axial force-workpiece deformation is characterized in that, in step S1: the workpiece is a low-stiffness workpiece, a thin-walled workpiece, a weakly supported workpiece, or a laminated workpiece; the laminated workpiece is one of composite material and metal laminated workpiece, metal-metal laminated workpiece, or composite material and composite material laminated workpiece; the tool is a tool with axial feed motion and capable of establishing a drilling axial force prediction model, and is a twist drill, step drill, reamer, or composite drill; the parameters of the workpiece to be drilled include the material parameters of the workpiece, the geometric parameters of the workpiece, and the clamping boundary conditions of the workpiece; the drilling tool parameters include the tool geometric parameters; the drilling process parameters include at least one of spindle speed, feed rate, and drilling time parameters; the cutting force model parameters to be calibrated are used in the drilling axial force prediction model to calculate the drilling axial force based on the drilling tool parameters, the drilling process parameters, and the contact state between the tool and the workpiece.

[0008] Furthermore, the drilling axial force-workpiece deformation time-varying coupling prediction method is characterized in that, in step S3: the construction of the drilling axial force prediction model is as follows: firstly, the axial load action of the tool during the drilling process is divided into one or more axial force contribution units; the axial force contribution unit includes at least one of the cutting edge cutting action unit and the chisel edge squeezing action unit; each axial force contribution unit is activated, superimposed, or deactivated according to the real-time contact state between the tool and the workpiece to obtain the total drilling axial force at the current actual drilling depth of the tool.

[0009] Furthermore, the drilling axial force-workpiece deformation time-varying coupling prediction method is characterized in that, in step S3: the process of obtaining the axial force of the cutting edge cutting action unit is as follows: the cutting edge is discretized into micro-elements; for each cutting edge micro-element, the micro-element cutting force is calculated based on the cutting thickness, cutting width, tool geometry angle and calibrated cutting force model parameters, and the micro-element cutting force is decomposed into tangential force, radial force and axial force, and then the axial force components of each cutting edge micro-element are summed or integrated to obtain the axial force corresponding to the cutting edge cutting action unit; the process of obtaining the axial force of the chisel edge extrusion action unit is as follows: it is calculated based on the chisel edge indentation area, workpiece material hardness and chisel edge extrusion correction coefficient.

[0010] Furthermore, the drilling axial force-workpiece deformation time-varying coupling prediction method is characterized in that, in step S3: when the tool is a stepped drill, the axial force contribution unit includes a chisel edge squeezing action unit, a first stepped main cutting edge cutting action unit, and a second stepped main cutting edge cutting action unit; wherein, the chisel edge squeezing action unit is used to characterize the axial squeezing action of the stepped drill's chisel edge on the workpiece, and the first stepped main cutting edge cutting action unit and the second stepped main cutting edge cutting action unit are respectively used to characterize the material removal action of different stepped main cutting edges of the stepped drill on the workpiece; the drilling axial force prediction model enables, superimposes, or stops the chisel edge squeezing action unit, the first stepped main cutting edge cutting action unit, and the second stepped main cutting edge cutting action unit according to the contact state between the stepped drill and the workpiece at different actual drilling depths of the tool, so as to obtain the total drilling axial force in the current calculation time step.

[0011] Furthermore, the aforementioned time-varying coupling prediction method for drilling axial force-workpiece deformation is characterized in that, in step S3: different workpiece deformation calculation models are selected according to different workpiece deformation states. The workpiece deformation calculation model equates the drilling axial force to a concentrated load acting on the drilling position, and establishes a workpiece deformation response function between the drilling axial force and the workpiece deformation amount based on the workpiece's elastic modulus, cross-sectional dimensions, thickness, drilling position, and clamping boundary conditions; wherein, the workpiece deformation state is determined based on the ratio of the workpiece deformation amount to the workpiece thickness. When the ratio is not greater than a preset nonlinear deformation threshold, the workpiece deformation response function includes at least a linear bending stiffness term; when the ratio is greater than the preset nonlinear deformation threshold, the workpiece deformation response function also includes an additional stiffness term caused by geometric nonlinearity.

[0012] Furthermore, the drilling axial force-workpiece deformation time-varying coupling prediction method is characterized in that: in step S3: the actual drilling depth of the tool is determined based on the tool feed distance and workpiece deformation amount of the current calculation time step: under the action of the drilling axial force, the workpiece undergoes flexural deformation along the tool feed direction, causing the actual drilling depth of the tool relative to the workpiece to be less than the current tool feed distance, and the actual drilling depth of the tool is obtained by subtracting the workpiece deformation amount from the tool feed distance of the current calculation time step.

[0013] Furthermore, the aforementioned time-varying coupling prediction method for drilling axial force and workpiece deformation is characterized in that, in step S11: the preset convergence conditions include a drilling axial force convergence condition and a workpiece deformation convergence condition; wherein, the drilling axial force convergence condition is used to determine whether the change in drilling axial force obtained from two adjacent iterations is less than a preset drilling axial force convergence threshold, and the workpiece deformation convergence condition is used to determine whether the change in workpiece deformation obtained from two adjacent iterations is less than a preset workpiece deformation convergence threshold; when the change in drilling axial force is less than the preset drilling axial force convergence threshold, and the change in workpiece deformation is less than the preset workpiece deformation convergence threshold, it is determined that the coupling solution of drilling axial force and workpiece deformation in the current calculation time step has converged; otherwise, iterative updates of drilling axial force and workpiece deformation continue.

[0014] Furthermore, the aforementioned time-varying coupled prediction method for drilling axial force-workpiece deformation is characterized in that, in step S2, the calibration step of the cutting force model parameters includes: conducting a drilling calibration experiment under the reference support condition where workpiece deformation is suppressed or the influence of workpiece deformation is negligible, and collecting drilling axial force experimental data during the drilling process; determining the participation interval of each axial force contribution unit in the drilling axial force prediction model based on the drilling tool parameters, drilling process parameters, and the contact state between the tool and the workpiece; selecting the drilling axial force experimental data corresponding to the participation interval as the fitting basis, and aiming to satisfy the preset fitting condition between the predicted drilling axial force output by the drilling axial force prediction model and the drilling axial force experimental data, calibrating the cutting force model parameters to obtain the calibrated cutting force model parameters.

[0015] The beneficial effects of this invention are as follows: The time-varying coupled prediction method for drilling axial force and workpiece deformation proposed in this invention couples the drilling axial force, workpiece deformation, and actual drilling depth of the tool as interrelated time-varying variables for solution. The actual drilling depth is corrected in real time by adjusting the workpiece deformation, and the drilling axial force is further updated. This reflects the dynamic feedback relationship between the drilling axial force and workpiece deformation during the drilling process, avoiding prediction errors caused by directly equating the theoretical feed distance with the actual drilling depth under the traditional rigidity assumption. Furthermore, this invention achieves stable iterative solutions for the drilling axial force and workpiece deformation within each calculation time step through preset convergence conditions and adaptive relaxation processing. This provides a basis for drilling process analysis, parameter selection, and machining quality control of low-stiffness workpieces, thin-walled workpieces, weakly supported workpieces, and laminated workpieces. Attached Figure Description

[0016] Figure 1 This is a flowchart for predicting the time-varying coupling of drilling axial force and workpiece deformation; Figure 2 This is a schematic diagram of a drilling tool structure, where (a) is a schematic diagram of the overall structure of the drilling tool, (b) is a schematic diagram of the partial structure of the drill tip and stepped cutting edge, and (c) is a schematic diagram of the chisel edge structure at the end of the drill bit. In the diagram, R1 is the radius of the first step of the tool, R2 is the radius of the second step of the tool, L1 is the length of the first step of the tool, L2 is the effective cutting section length of the tool, and L3 is the total length of the tool. β 0 represents the helix angle. κ t1 The first step apex angle of the cutting tool. κ t2 The second step apex angle of the cutting tool. ψ c For the horizontal cutting edge angle, w 0 represents the length of the transverse blade. w101 is the width of the transverse cutting edge, 102 is the rake face, 103 is the first step of the tool, and 103 is the second step of the tool. Figure 3 This is a schematic diagram illustrating the deformation calculation of a workpiece under the action of axial force during drilling. In the diagram, L represents the workpiece length, B represents the workpiece width, and H represents the workpiece thickness. This refers to the deformation of the workpiece. Figure 4 This is a schematic diagram of a drilling axial force and workpiece deformation measuring device. In the diagram, (a) is the force measurement mode, and (b) is the force and deformation coupled measurement mode. In the diagram, 201 is the workpiece to be drilled, 202 is the fixture, 203 is the stepped drill bit, 204 is the rigid support plate, 205 is the reflector, 206 is the laser displacement sensor, 207 is the force gauge, 208 is the data acquisition system, 209 is the optical control unit, and 210 is the computer. Figure 5 The figures show the verification results of the coupling between CFRP drilling axial force and workpiece deformation in a CFRP / Ti laminated structure. (a) is a comparison of the experimental and theoretical values ​​of the axial force during the first-step drilling, (b) is a comparison of the experimental and theoretical values ​​of the workpiece deformation during the first-step drilling, (c) is a comparison of the experimental and theoretical values ​​of the axial force during the second-step drilling, and (d) is a comparison of the experimental and theoretical values ​​of the workpiece deformation during the second-step drilling. The tool parameters are defined as "first-step tool diameter - first-step tool length - second-step tool diameter". Figure 6 The figures show the verification results of the coupling between Ti drilling axial force and workpiece deformation in a CFRP / Ti laminated structure. (a) is a comparison of the experimental and theoretical values ​​of the axial force during the first-step drilling, (b) is a comparison of the experimental and theoretical values ​​of the workpiece deformation during the first-step drilling, (c) is a comparison of the experimental and theoretical values ​​of the axial force during the second-step drilling, and (d) is a comparison of the experimental and theoretical values ​​of the workpiece deformation during the second-step drilling. The tool parameters are "first-step tool diameter - first-step tool length - second-step tool diameter". Figure 7 The figures show the coupled verification results of the drilling axial force and workpiece deformation over time in CFRP / Ti stacked structures using a 3-3-6 stepped tool. (a) shows the CFRP drilling axial force over time; (b) shows the CFRP workpiece deformation over time; (c) shows the Ti drilling axial force over time; and (d) shows the Ti workpiece deformation over time. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer and to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be noted that the technical solutions claimed by the present invention include, but are not limited to, the following embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0018] like Figure 1 As shown, this embodiment provides a time-varying coupled prediction method for drilling axial force and workpiece deformation. This method couples the drilling axial force, workpiece deformation, and actual tool penetration depth during the drilling process as interrelated time-varying variables. The drilling axial force acts on the workpiece, causing it to flex along the tool feed direction. The workpiece deformation further changes the actual tool penetration depth relative to the workpiece, and this change in actual tool penetration depth alters the contact state between the tool and the workpiece, further affecting the drilling axial force output by the drilling axial force prediction model. Therefore, this embodiment obtains the time-varying coupled prediction results of drilling axial force and workpiece deformation during the drilling process by iteratively updating the drilling axial force, workpiece deformation, and actual tool penetration depth within each calculation time step.

[0019] The drilling axial force-workpiece deformation time-varying coupling prediction method described in this embodiment includes basic parameter initialization, cutting force model parameter calibration, loading of drilling axial force prediction model and workpiece deformation calculation model, time step division of drilling process calculation, coupling solution of drilling axial force and workpiece deformation, and prediction result output.

[0020] First, basic parameters are initialized to obtain the parameters of the workpiece to be drilled, the drilling tool parameters, and the drilling process parameters. The parameters of the cutting force model to be calibrated for establishing the drilling axial force prediction model are also determined. The workpiece can be a low-stiffness workpiece, a thin-walled workpiece, a weakly supported workpiece, or a laminated workpiece. The laminated workpiece can be one of a composite material and metal laminated workpiece, a metal-to-metal laminated workpiece, or a composite material-to-composite material laminated workpiece. The tool is a tool with axial feed motion capable of establishing a drilling axial force prediction model, such as a twist drill, step drill, reamer, or composite drill. The parameters of the workpiece to be drilled include the workpiece's material parameters, geometric parameters, and clamping boundary conditions. The drilling tool parameters include the tool's geometric parameters. The drilling process parameters include at least one of the spindle speed, feed rate, and drilling time parameters. The parameters of the cutting force model to be calibrated are used in the drilling axial force prediction model to calculate the drilling axial force based on the drilling tool parameters, the drilling process parameters, and the contact state between the tool and the workpiece.

[0021] After initializing the basic parameters, the cutting force model parameters to be calibrated are determined based on the drilling axial force experimental data to obtain calibrated cutting force model parameters. These calibrated parameters are used for calculating the drilling axial force in the subsequent drilling axial force prediction model. The calibration steps for the cutting force model parameters include: conducting drilling calibration experiments under reference support conditions where workpiece deformation is suppressed or its influence is negligible, and collecting drilling axial force experimental data during the drilling process; determining the participation interval of each axial force contribution unit in the drilling axial force prediction model based on the drilling tool parameters, drilling process parameters, and the contact state between the tool and the workpiece; selecting the drilling axial force experimental data corresponding to the participation interval as the fitting basis, and aiming to satisfy a preset fitting condition between the predicted drilling axial force output by the drilling axial force prediction model and the drilling axial force experimental data, calibrating the cutting force model parameters to obtain calibrated cutting force model parameters.

[0022] Based on the calibrated cutting force model parameters, a drilling axial force prediction model and a workpiece deformation calculation model are loaded; wherein, the drilling axial force prediction model is used to calculate the drilling axial force according to the actual drilling depth of the tool, and the workpiece deformation calculation model is used to calculate the workpiece deformation based on the drilling axial force.

[0023] In one embodiment, the drilling axial force prediction model first divides the axial load on the tool during the drilling process into one or more axial force contribution units. Each axial force contribution unit includes at least one of a cutting edge cutting action unit and a chisel edge pressing action unit. Each axial force contribution unit is activated, superimposed, or deactivated based on the real-time contact state between the tool and the workpiece to obtain the total drilling axial force at the current actual drilling depth.

[0024] like Figure 2 As shown, this embodiment uses a stepped drill as the drilling tool for illustration. Figure 2 Image (a) shows the overall structure of the drilling tool. Figure 2 (b) shows the partial structure of the drill tip and stepped cutting edge, showing the positions of the rake face 101, the first step of the tool 102, and the second step of the tool 103, respectively; Figure 2(c) shows the chisel edge structure at the drill bit end. When the drilling tool is a stepped drill, the axial force contribution unit includes a chisel edge squeezing action unit, a first stepped main cutting edge cutting action unit, and a second stepped main cutting edge cutting action unit. The chisel edge squeezing action unit characterizes the axial squeezing effect of the stepped drill's chisel edge on the workpiece, while the first and second stepped main cutting edge cutting action units characterize the material removal effect of different stepped main cutting edges on the workpiece. The drilling axial force prediction model activates, superimposes, or deactivates the chisel edge squeezing action unit, the first stepped main cutting edge cutting action unit, and the second stepped main cutting edge cutting action unit based on the contact state between the stepped drill and the workpiece at different actual drilling depths, to obtain the total drilling axial force within the current calculation time step.

[0025] Specifically, the drilling axial force corresponding to the chisel edge extrusion unit can be calculated based on the chisel edge indentation area, the workpiece material hardness, and the chisel edge extrusion correction coefficient, and its expression can be expressed as: In the formula, This refers to the axial drilling force corresponding to the chisel edge extrusion unit. This is the correction factor for transverse blade extrusion. The area of ​​the horizontal blade indentation. The hardness of the workpiece material is given. The indentation area of ​​the chisel edge can be determined based on the length and width of the chisel edge, the actual drilling depth of the tool, and the contact state between the chisel edge and the workpiece.

[0026] The drilling axial force of the first-step main cutting edge is obtained by summing the contributions of the drilling axial force generated by each micro-cutting edge on the first-step main cutting edge. Its expression is as follows: In the formula, The drilling axial force generated by the first-step main cutting edge. The number of infinitesimal elements obtained by discretizing the first-order main cutting edge. Let z be the infinitesimal axial force at the cutting edge position z, and a be the effective integral length of the first step main cutting edge participating in the cutting; coefficient 2 indicates that the stepped drill has two symmetrical main cutting edges.

[0027] The drilling axial force of the second-step main cutting edge is obtained by summing the contributions of the axial forces generated by each micro-element cutting edge on the second-step main cutting edge. Its expression is as follows: In the formula, The drilling axial force generated by the second-step main cutting edge. The number of infinitesimal elements obtained by discretizing the second-order main cutting edge. Let be the axial force of the micro-element located at position z of the cutting edge, and b be the effective integral length of the second-step main cutting edge participating in the cutting; the coefficient 2 indicates that the stepped drill has two symmetrical main cutting edges. For each micro-element of the cutting edge, the micro-element cutting force is calculated based on the cutting thickness, cutting width, tool geometry angle, and calibrated cutting force model parameters. The micro-element cutting force is then decomposed into tangential force, radial force, and axial force. The axial force components of each micro-element of the cutting edge are then summed or integrated to obtain the axial force corresponding to the cutting edge cutting action unit.

[0028] By adding the axial force contributions from the chisel edge, the first-step main cutting edge, and the second-step main cutting edge, the total drilling axial force applied to the step drill can be obtained. Since the drilling axial force is related to the drill depth, for ease of subsequent coupled solution, the total drilling axial force is denoted as: In the formula, This represents the total axial force during drilling. Let z be the axial force prediction function for drilling, and z be the drilling depth of the tool relative to the workpiece.

[0029] In actual drilling, whether the chisel edge, the first-step main cutting edge, and the second-step main cutting edge participate in cutting depends on the actual drilling depth of the tool relative to the workpiece. As the actual drilling depth changes, each axial force contribution unit is activated, superimposed, or deactivated based on the real-time contact state between the tool and the workpiece. That is, when the corresponding cutting edge or chisel edge participates in drilling, its axial force is included in the total drilling axial force; when the corresponding cutting edge or chisel edge has not entered the workpiece or has exited the workpiece, its axial force is not included in the total drilling axial force.

[0030] In the time-varying coupled prediction process of this invention, the drilling depth z in the drilling axial force calculation formula is not always equal to the theoretical tool feed distance, but is the actual drilling depth after correction based on the workpiece deformation. Therefore, within any calculation time step, the drilling axial force prediction model is further expressed as: In the formula, z_actual represents the actual drilling depth of the tool relative to the workpiece. This form couples the drilling axial force prediction model with the workpiece deformation calculation model, allowing the reverse influence of workpiece deformation on the actual cutting state of the tool and the drilling axial force to be incorporated into the calculation process.

[0031] like Figure 3 As shown, the workpiece deformation calculation model is used to calculate the workpiece deformation based on the drilling axial force. Figure 3In this context, L represents the workpiece length, B represents the workpiece width, H represents the workpiece thickness, and δ represents the workpiece deformation. In one embodiment, the drilling axial force is equivalent to a concentrated load acting at the drilling location, and based on the workpiece's elastic modulus, cross-sectional dimensions, thickness, drilling location, and clamping boundary conditions, a workpiece deformation response function is established between the drilling axial force and the workpiece deformation. The workpiece deformation calculation model can be expressed as: In the formula, δ is the workpiece deformation, F is the drilling axial force, and W is the workpiece deformation response function determined by the workpiece material parameters, workpiece geometric parameters, and clamping boundary conditions.

[0032] In one embodiment, different workpiece deformation calculation models are selected based on different workpiece deformation states. The workpiece deformation state is determined based on the ratio of workpiece deformation to workpiece thickness. When the ratio of workpiece deformation to workpiece thickness is not greater than a preset nonlinear deformation threshold, the workpiece deformation response function includes at least a linear bending stiffness term; when the ratio of workpiece deformation to workpiece thickness is greater than the preset nonlinear deformation threshold, the workpiece deformation response function also includes an additional stiffness term caused by geometric nonlinearity. In this case, the relationship between the drilling axial force and the workpiece deformation can be expressed as: In the formula, It is the linear bending stiffness coefficient. δ is the additional stiffness coefficient for geometric nonlinearity, and δ is the workpiece deformation. and The coefficients are determined by the workpiece's elastic modulus, cross-sectional dimensions, thickness, clamping boundary conditions, and load location. For multilayer workpieces, the linear bending stiffness coefficient and geometric nonlinear additional stiffness coefficient can be determined based on the equivalent elastic modulus, equivalent cross-sectional stiffness, or layered calculation results of each material layer.

[0033] For a workpiece that is fixed at both ends and subjected to a concentrated load at the center, in one specific embodiment, the relationship between the drilling axial force and the workpiece deformation can be expressed in the following form: In the formula, E is the elastic modulus of the workpiece material, I is the moment of inertia of the workpiece section, A is the cross-sectional area of ​​the workpiece, L is the effective span of the workpiece, and δ is the workpiece deformation. It should be noted that the above expression is only a preferred embodiment. For different workpiece structures or clamping boundary conditions, beam models, plate models, finite element models, or experimental fitting models can also be used to establish workpiece deformation calculation models.

[0034] After establishing the drilling axial force prediction model and the workpiece deformation calculation model, the drilling process is discretized into multiple calculation time steps based on the drilling process parameters, workpiece thickness and tool geometry parameters, and the calculation time step number i=1 is initialized.

[0035] For the i-th calculation time step, based on the feed rate v and the current time... Calculate the current feed distance of the tool: In the formula, Let v be the tool feed distance in the i-th calculation time step, and v be the tool feed rate. Let be the drilling time corresponding to the i-th calculation time step.

[0036] Then it determines whether all calculation time steps have been traversed. If not, it proceeds to the coupled solution process of drilling axial force and workpiece deformation for the current calculation time step; if all calculation time steps have been traversed, it proceeds to the result output process.

[0037] Within the current computation time step, first, based on the current tool feed distance... As the initial tool penetration depth, the drilling axial force at the current computation time step is initialized using the drilling axial force prediction model: in, The initial drilling axial force for the current calculation time step. This is a functional representation of the drilling axial force prediction model.

[0038] Then, the current drilling axial force Substitute the workpiece deformation calculation model into the calculation model to calculate the workpiece deformation at the current calculation time step: in, This represents the workpiece deformation at the current calculation time step. This is the workpiece deformation response function.

[0039] Under the action of axial force during drilling, the workpiece undergoes deflection along the tool feed direction, causing the actual drilling depth of the tool relative to the workpiece to be less than the current tool feed distance. Therefore, the actual drilling depth is calculated based on the tool feed distance at the current calculation time step and the workpiece deformation. in, This represents the actual drilling depth of the tool at the current calculation time step.

[0040] Subsequently, the actual drilling depth of the tool was determined. Substitute the values ​​into the drilling axial force prediction model and calculate the updated drilling axial force: in, This refers to the drilling axial force updated based on the actual drilling depth of the tool.

[0041] Because the drilling axial force, workpiece deformation, and actual drilling depth are interdependent, the drilling axial force and workpiece deformation need to be iteratively updated within the same calculation time step. It is determined whether the drilling axial force and workpiece deformation in the current iteration step meet preset convergence conditions. These preset convergence conditions include a drilling axial force convergence condition and a workpiece deformation convergence condition. The drilling axial force convergence condition is used to determine whether the change in drilling axial force obtained from two adjacent iterations is less than a preset drilling axial force convergence threshold, and the workpiece deformation convergence condition is used to determine whether the change in workpiece deformation obtained from two adjacent iterations is less than a preset workpiece deformation convergence threshold.

[0042] When the drilling axial force and / or workpiece deformation in the current iteration step do not meet the preset convergence conditions, an adaptive relaxation process is performed on the updated drilling axial force to obtain a corrected drilling axial force. This corrected drilling axial force is then used as a new input to return to the workpiece deformation calculation model, recalculating the workpiece deformation, the actual drilling depth of the tool, and the updated drilling axial force. The adaptive relaxation process expression is: In the formula, Let be the drilling axial force in the k-th iteration. To update the drilling axial force calculated based on the current actual drilling depth of the tool. To adapt the axial force of drilling after relaxation treatment, It is an adaptive relaxation factor, and 0 < ≤1, decrease in the early stages of iteration. To ensure stability, increase the value as the calculation approaches convergence. To speed up the calculation.

[0043] When the drilling axial force and workpiece deformation in the current iteration step meet the preset convergence conditions, the drilling axial force state and workpiece deformation state of the current calculation time step are updated, and the drilling axial force and workpiece deformation that meet the preset convergence conditions are stored as the coupled prediction result of the current calculation time step. Subsequently, the calculation time step number is updated, and a check is performed to determine whether all calculation time steps have been traversed. If not, the current feed distance for the next calculation time step is recalculated, and the coupled solution of drilling axial force and workpiece deformation continues; if all calculation time steps have been traversed, the drilling axial force and workpiece deformation corresponding to each calculation time step during the drilling process are output, obtaining the time-varying coupled prediction result of drilling axial force and workpiece deformation.

[0044] The time-varying coupling prediction results can include curves showing the variation of drilling axial force with drilling time, drilling axial force with tool feed distance, workpiece deformation with drilling time, workpiece deformation with tool feed distance, and the actual drilling depth with drilling time or tool feed distance. These results allow for the analysis of the dynamic feedback relationship between drilling axial force and workpiece deformation under different drilling tool parameters, drilling process parameters, and workpiece clamping boundary conditions.

[0045] To further illustrate the implementation effect of the drilling axial force-workpiece deformation time-varying coupling prediction method described in this invention, the drilling process of a CFRP / Ti laminate structure is used as an example. In this embodiment, the CFRP laminate thickness is 2mm, the Ti layer is a Ti-6Al-4V titanium alloy with a thickness of 2mm; the drilling tool is a stepped drill with a helix angle of 30°, a chisel edge length of 0.2mm, and both the first and second step apex angles are 140°. The drilling process parameters are a spindle speed of 300r / min and a feed rate of 30mm / min. To verify the applicability of the method of this invention under different tool geometry parameters, stepped drills with first step diameters of 2mm, 3mm, 4mm, and 5mm were selected for prediction and experimental verification, and the second step diameter was 6mm for all drills with a step length of 3mm.

[0046] like Figure 4As shown in (a), before performing time-varying coupling prediction of drilling axial force and workpiece deformation, the cutting force model parameters in the drilling axial force prediction model are first calibrated in force measurement mode. In force measurement mode, the workpiece 201 to be drilled is fixed by the fixture 202, the stepped drill bit 203 drills the workpiece 201, a rigid support plate 204 is set at the bottom of the workpiece 201, and the drilling axial force signal is collected by the force measuring instrument 207. The data acquisition system 208 transmits the drilling axial force signal to the computer 210. Since the rigid support plate 204 supports the workpiece 201, it can suppress workpiece deflection or make the effect of workpiece deformation negligible. Therefore, this force measurement mode can be used to obtain the drilling axial force experimental data required for the calibration of the cutting force model parameters.

[0047] During the calibration of the cutting force model parameters, based on the stepped drill geometry parameters, feed rate, workpiece thickness, and the contact state between the tool and the workpiece, the participation intervals of the chisel edge extrusion unit, the first-step main cutting edge cutting unit, and the second-step main cutting edge cutting unit are determined. Experimental data on drilling axial force corresponding to these participation intervals are selected as the fitting basis. Based on the experimental data on drilling axial force obtained under different stepped drill structures, the cutting force coefficient, edge force coefficient, and chisel edge extrusion correction coefficient in the drilling axial force prediction model are fitted. After calibration, the calibrated cutting force model parameters are obtained and used for calculating the drilling axial force in the subsequent drilling axial force prediction model.

[0048] like Figure 4 As shown in (b), after the cutting force model parameters were calibrated, a coupling verification experiment of drilling axial force and workpiece deformation was conducted. In the force-deformation coupling measurement mode, the workpiece 201 to be drilled was fixed by the fixture 202, placing it in a low-rigidity clamping state; the stepped drill bit 203 drilled the workpiece 201; the force gauge 207 collected the drilling axial force during the drilling process; the reflector 205, laser displacement sensor 206, and optical control unit 209 were used to measure the workpiece deformation of the workpiece 201 during the drilling process; the data acquisition system 208 transmitted the drilling axial force signal and the workpiece deformation signal to the computer 210. Through this force-deformation coupling measurement mode, experimental data on the changes in drilling axial force and workpiece deformation with drilling time or tool feed distance under different stepped drill structure conditions can be obtained.

[0049] In the prediction calculation process, the tool feed distance for the current calculation time step is first calculated based on the feed rate and the drilling time corresponding to the current calculation time step. Then, the current tool feed distance is used as the initial tool penetration depth and substituted into the drilling axial force prediction model to obtain the initial drilling axial force for the current calculation time step. This drilling axial force is then substituted into the workpiece deformation calculation model to calculate the workpiece deformation for the current calculation time step. Since the workpiece undergoes deflection along the tool feed direction under the action of the drilling axial force, the actual tool penetration depth relative to the workpiece is less than the current tool feed distance. Therefore, the actual tool penetration depth is corrected based on the difference between the current tool feed distance and the workpiece deformation. Subsequently, the corrected actual tool penetration depth is substituted back into the drilling axial force prediction model to obtain the updated drilling axial force, and it is determined whether the changes in drilling axial force and workpiece deformation obtained in two adjacent iterations meet the preset convergence conditions. If the preset convergence condition is not met, the updated drilling axial force is adaptively relaxed, and the workpiece deformation, actual drilling depth, and drilling axial force are iteratively updated. If the preset convergence condition is met, the current iteration result is used as the coupled prediction result for that calculation time step. After completing all calculation time steps, the time-varying coupled prediction results of drilling axial force and workpiece deformation throughout the drilling process can be obtained.

[0050] like Figure 5 As shown, the verification results of the CFRP drilling process in the CFRP / Ti laminated structure include comparisons between experimental and theoretical values ​​of axial force during the first-step drilling, comparisons between experimental and theoretical values ​​of workpiece deformation during the first-step drilling, comparisons between experimental and theoretical values ​​of axial force during the second-step drilling, and comparisons between experimental and theoretical values ​​of workpiece deformation during the second-step drilling. Figure 6 As shown, the verification results of the Ti drilling process in the CFRP / Ti laminate structure include comparisons between experimental and theoretical values ​​of the axial force during the first-step drilling, the experimental and theoretical values ​​of the workpiece deformation during the first-step drilling, the experimental and theoretical values ​​of the axial force during the second-step drilling, and the experimental and theoretical values ​​of the workpiece deformation during the second-step drilling. The curves showing the changes in drilling axial force and workpiece deformation over time during the drilling process are shown below. Figure 7 As shown, the experimental and predicted values ​​of the drilling axial force and workpiece deformation over time are compared for the CFRP drilling stage and the Ti drilling stage. The verification results show that under different stepped drill structure conditions, the method of this invention can predict the changing trends of drilling axial force and workpiece deformation well. By comparing the peak values ​​of drilling axial force and workpiece deformation, the maximum relative error of drilling axial force is 10.09%, and the maximum relative error of workpiece deformation is 14.12%, indicating that the predicted results of drilling axial force and workpiece deformation are in good agreement with the experimental results.

[0051] The method of this invention can effectively consider the interaction between drilling axial force, workpiece deformation and actual drilling depth of the tool, and avoid the problem of ignoring workpiece deformation feedback when predicting drilling axial force based solely on the assumption of a rigid workpiece. It can more accurately characterize the coupling behavior of drilling axial force and workpiece deformation during the drilling process of low-rigidity workpieces.

[0052] As can be seen from the above embodiments, the drilling axial force-workpiece deformation time-varying coupling prediction method of the present invention can not only output the drilling axial force prediction results corresponding to each calculation time step in the drilling process, but also simultaneously obtain the workpiece deformation prediction results. Furthermore, it achieves a closed-loop coupling solution between the drilling axial force and the workpiece deformation by correcting for the actual drilling depth. Therefore, this method can be used for the drilling process analysis of low-stiffness workpieces, thin-walled workpieces, weakly supported workpieces, and laminated workpieces, providing a predictive basis for the selection of drilling process parameters, the evaluation of drilling tool parameters, and the control of hole-making quality.

Claims

1. A time-varying coupled prediction method for drilling axial force and workpiece deformation, characterized in that, Specifically, the steps include the following: S1. Initialize the basic parameters, obtain the parameters of the workpiece to be drilled, the parameters of the drilling tool and the drilling process parameters, and determine the parameters of the cutting force model to be calibrated for establishing the drilling axial force prediction model. S2, Based on the drilling axial force experimental data, the parameters of the cutting force model to be calibrated are calibrated to obtain the calibrated cutting force model parameters; S3, based on the calibrated cutting force model parameters, load the drilling axial force prediction model and the workpiece deformation calculation model; wherein, the drilling axial force prediction model is used to calculate the drilling axial force according to the actual drilling depth of the tool, and the workpiece deformation calculation model is used to calculate the workpiece deformation according to the drilling axial force. S4. Based on the drilling process parameters, workpiece thickness, and tool geometry parameters, the drilling process is divided into multiple calculation time steps, and the calculation time step number is initialized. S5, determine whether all calculation time steps have been traversed; if not, proceed to step S6 for the coupled solution process of drilling axial force and workpiece deformation in the current calculation time step; if all calculation time steps have been traversed, proceed to step S15 for the result output process. S6, within the current calculation time step, calculate the tool feed distance based on the feed rate and drilling time. The expression for this is: in, The tool feed distance for the current calculation time step. The feed rate of the tool. This refers to the drilling time corresponding to the current calculation time step. S7, using the current tool feed distance as the initial tool penetration depth, initializes the drilling axial force of the current calculation time step using the drilling axial force prediction model, the expression of which is: in, The initial drilling axial force for the current calculation time step. This is a functional representation of the drilling axial force prediction model; S8, substitute the current drilling axial force into the workpiece deformation calculation model to calculate the workpiece deformation at the current calculation time step. The expression is: in, This represents the deformation of the workpiece. This is the workpiece deformation response function; S9 calculates the actual drilling depth of the tool based on the current feed distance and workpiece deformation. The expression for this is: S10, Substitute the actual drilling depth of the tool into the drilling axial force prediction model to calculate the updated drilling axial force, the expression of which is: in, The drilling axial force is updated based on the actual drilling depth of the tool; S11, determine whether the drilling axial force and workpiece deformation in the current iteration step meet the preset convergence conditions; if the drilling axial force and workpiece deformation meet the preset convergence conditions, proceed to step S13; if the drilling axial force and / or workpiece deformation do not meet the preset convergence conditions, proceed to step S12. S12, perform adaptive relaxation processing on the updated drilling axial force to obtain the corrected drilling axial force, and return the corrected drilling axial force as a new input to step S8 to recalculate the workpiece deformation, actual drilling depth, and updated drilling axial force; wherein, the adaptive relaxation processing expression is: in, Let be the drilling axial force in the k-th iteration. This is the updated drilling axial force calculated based on the current actual drilling depth of the tool. To adapt the axial force of drilling after relaxation treatment, It is an adaptive relaxation factor, and 0 < ≤1, decrease in the early stages of iteration. To ensure stability, increase the value as the calculation approaches convergence. To speed up calculations; S13, update the drilling axial force state and workpiece deformation state of the current calculation time step, and store the drilling axial force and workpiece deformation that meet the preset convergence conditions as the coupling prediction results of the current calculation time step. S14, update the calculation time step number, and return to step S5 to determine whether all calculation time steps have been traversed; if not all calculation time steps have been traversed, recalculate the current feed distance for the next calculation time step, and continue to perform the coupled solution of drilling axial force and workpiece deformation; if all calculation time steps have been traversed, proceed to step S15. S15 outputs the drilling axial force and workpiece deformation corresponding to each calculation time step during the drilling process, and obtains the time-varying coupling prediction results of drilling axial force and workpiece deformation.

2. The drilling axial force-workpiece deformation time-varying coupling prediction method according to claim 1, characterized in that, In step S1: the parameters of the workpiece to be drilled include the material parameters of the workpiece, the geometric parameters of the workpiece, and the clamping boundary conditions of the workpiece; the parameters of the drilling tool include the geometric parameters of the tool; and the parameters of the drilling process include at least one of the spindle speed, feed rate, and drilling time parameters. The parameters of the cutting force model to be calibrated are used in the drilling axial force prediction model to calculate the drilling axial force based on the drilling tool parameters, the drilling process parameters, and the contact state between the tool and the workpiece.

3. The drilling axial force-workpiece deformation time-varying coupling prediction method according to claim 2, characterized in that, In step S3: the construction of the drilling axial force prediction model: firstly, the axial load of the tool during the drilling process is divided into one or more axial force contribution units; the axial force contribution unit includes at least one of the cutting edge cutting action unit and the chisel edge squeezing action unit; each axial force contribution unit is activated, superimposed or stopped according to the real-time contact state between the tool and the workpiece to obtain the total drilling axial force at the current actual drilling depth of the tool.

4. The drilling axial force-workpiece deformation time-varying coupling prediction method according to claim 3, characterized in that, In step S3: the process of obtaining the axial force of the cutting edge cutting action unit: the cutting edge is discretized into infinitesimal elements; For each micro-element of the cutting edge, the micro-element cutting force is calculated based on the cutting thickness, cutting width, tool geometry angle, and calibrated cutting force model parameters. The micro-element cutting force is then decomposed into tangential force, radial force, and axial force. The axial force components of each micro-element of the cutting edge are then summed or integrated to obtain the axial force corresponding to the cutting edge cutting action unit. The axial force of the chisel edge extrusion action unit is obtained by calculating based on the chisel edge indentation area, workpiece material hardness, and chisel edge extrusion correction coefficient.

5. The drilling axial force-workpiece deformation time-varying coupling prediction method according to claim 4, characterized in that, In step S3: when the tool is a stepped drill, the axial force contribution unit includes a chisel edge squeezing action unit, a first stepped main cutting edge cutting action unit, and a second stepped main cutting edge cutting action unit; wherein, the chisel edge squeezing action unit is used to characterize the axial squeezing action of the stepped drill's chisel edge on the workpiece, and the first stepped main cutting edge cutting action unit and the second stepped main cutting edge cutting action unit are respectively used to characterize the material removal action of different stepped main cutting edges of the stepped drill on the workpiece; the drilling axial force prediction model enables, superimposes, or stops the chisel edge squeezing action unit, the first stepped main cutting edge cutting action unit, and the second stepped main cutting edge cutting action unit according to the contact state between the stepped drill and the workpiece at different actual drilling depths of the tool, so as to obtain the total drilling axial force in the current calculation time step.

6. The drilling axial force-workpiece deformation time-varying coupling prediction method according to claim 1, characterized in that, In step S3: different workpiece deformation calculation models are selected according to different workpiece deformation states. The workpiece deformation calculation model equates the drilling axial force to a concentrated load acting on the drilling position, and establishes a workpiece deformation response function between the drilling axial force and the workpiece deformation amount based on the workpiece's elastic modulus, cross-sectional dimensions, thickness, drilling position, and clamping boundary conditions. The workpiece deformation state is determined based on the ratio of the workpiece deformation amount to the workpiece thickness. When the ratio is not greater than a preset nonlinear deformation threshold, the workpiece deformation response function includes at least a linear bending stiffness term. When the ratio is greater than the preset nonlinear deformation threshold, the workpiece deformation response function also includes an additional stiffness term caused by geometric nonlinearity.

7. The drilling axial force-workpiece deformation time-varying coupling prediction method according to claim 1, characterized in that: In step S3: the actual drilling depth of the tool is determined based on the tool feed distance and workpiece deformation in the current calculation time step. Under the action of the drilling axial force, the workpiece undergoes flexural deformation along the tool feed direction, causing the actual drilling depth of the tool relative to the workpiece to be less than the current tool feed distance. The actual drilling depth of the tool is obtained by subtracting the workpiece deformation from the tool feed distance in the current calculation time step.

8. The drilling axial force-workpiece deformation time-varying coupling prediction method according to claim 1, characterized in that, In step S11: the preset convergence conditions include the drilling axial force convergence condition and the workpiece deformation convergence condition; wherein, the drilling axial force convergence condition is used to determine whether the change in drilling axial force obtained in two adjacent iterations is less than the preset drilling axial force convergence threshold, and the workpiece deformation convergence condition is used to determine whether the change in workpiece deformation obtained in two adjacent iterations is less than the preset workpiece deformation convergence threshold; when the change in drilling axial force is less than the preset drilling axial force convergence threshold, and the change in workpiece deformation is less than the preset workpiece deformation convergence threshold, it is determined that the coupling solution of drilling axial force and workpiece deformation in the current calculation time step has converged; otherwise, the iterative update of drilling axial force and workpiece deformation continues.

9. The drilling axial force-workpiece deformation time-varying coupling prediction method according to claim 3, characterized in that, In step S2, the calibration step of the cutting force model parameters includes: conducting a drilling calibration experiment under the reference support condition where workpiece deformation is suppressed or the influence of workpiece deformation is ignored, and collecting drilling axial force experimental data during the drilling process; determining the participation interval of each axial force contribution unit in the drilling axial force prediction model based on the drilling tool parameters, drilling process parameters, and the contact state between the tool and the workpiece; selecting the drilling axial force experimental data corresponding to the participation interval as the fitting basis, and aiming to satisfy the preset fitting condition between the predicted drilling axial force output by the drilling axial force prediction model and the drilling axial force experimental data, calibrating the cutting force model parameters to obtain the calibrated cutting force model parameters.

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