Methods for predicting drilling axial forces in composite laminates

Abstract

This invention discloses a method for predicting the axial force during drilling of composite laminates, comprising the following steps: discretizing the main cutting edge of the drill bit into m micro-cutting edges; for each micro-cutting edge, using finite element simulation technology to simulate and obtain the axial force at multiple cutting angles within the range of 0° to 180° under a given feed rate; based on the obtained axial force, fitting and determining the axial force fluctuation equation f for each of the m micro-cutting edges. i (t); The axial force fluctuation equation f for each segment of the m-segment micro-cutting edge. i (t) and the corresponding dynamic contact length L i Multiplying (t) together, we obtain the axial force F of each of the m micro-cutting edges. i ; Calculate the time t it takes for each of the m micro-cutting edges to reach the drilling depth of the drill bit, and apply the axial force F at that time t. i Integrate to obtain the axial force F i Response over time; axial force F for each segment of the m-segment micro-cutting edge. i Summing them up yields the drilling axial force.

Description

Technical Field

[0001] This invention relates to the field of composite material cutting, and more specifically to a method for predicting the axial force during drilling of composite laminates. Background Technology

[0002] Carbon fiber reinforced resin matrix composites (CFRP) have excellent properties such as high specific strength, high specific modulus, corrosion resistance, and fatigue resistance. Their usage in the new generation of large civil aircraft is increasing year by year. Currently, they are being used from secondary load-bearing components to primary load-bearing components. The use of composite material components to replace traditional metal material components has become the mainstream trend in the civil aircraft manufacturing industry.

[0003] Drilling (or hole making) is a crucial step in assembly, and the quality of the holes directly affects aircraft operational safety. Exit delamination is the most important indicator in hole quality evaluation. Studies show that the magnitude of the axial force load during drilling significantly influences exit delamination damage; therefore, controlling exit delamination damage requires controlling the magnitude of the axial force load during hole making. However, with the increasing use of thick composite material structural components, the required hole diameters are also increasing. Optimizing large-diameter hole making through extensive trial-and-error process experiments would significantly increase costs, while optimizing hole making process parameters and cutting tools through simulation would greatly reduce costs. Summary of the Invention

[0004] To address the aforementioned problems, this invention proposes a method for predicting the axial drilling force of composite laminates, the method comprising the following steps:

[0005] The main cutting edge of the drill bit is discretized into m micro-cutting edges.

[0006] For each micro-cutting edge segment, the axial force at multiple cutting angles within the range of 0° to 180° under a given feed rate is simulated using finite element simulation technology.

[0007] Based on the obtained axial force, the axial force fluctuation equation f for each of the m micro-cutting edges is fitted and determined. i (t), where f i (t)=Asin(θ i (t))+B, (i=(1,2,…,m)), θ i Let θ be the cutting angle. i (t)=ω×t=2πn×t, where n is the drill bit rotation speed;

[0008] The axial force fluctuation equation f for each segment of the m-segment micro-cutting edge i (t) and the corresponding dynamic contact length L i Multiplying (t) together, we obtain the axial force F of each of the m micro-cutting edges.ii Among them, the dynamic contact length L i (t) is calculated according to the following formula: in, v is the tip angle of the drill bit. f denoted as axial feed rate, and f is the feed rate of the micro-cutting edge per revolution of the drill bit.

[0009] Calculate the time t it takes for each of the m micro-cutting edges to reach the drill bit's penetration depth, and apply the axial force F at that time t. i Integrate to obtain the axial force F ii In response to time, among which, h is the depth the drill bit penetrates, and d is the diameter of the drill bit;

[0010] Axial force F for each segment of the m-segment micro-cutting edge i Summing them up yields the drilling axial force. The method described in this embodiment reduces the simulation workload, shortens the simulation calculation time, and improves the simulation calculation efficiency, enabling the prediction of drilling axial force under arbitrary hole diameter and different material thicknesses.

[0011] According to one embodiment of the present invention, the plurality of cutting angles are the main cutting edges of the drill bit at 0°, 45°, 90°, 135°, and 180° relative to the fiber extension direction, respectively. The method of this embodiment utilizes five typical angles to comprehensively reflect the overall law of cutting force, and the axial force fluctuation equation can be obtained more accurately through fitting.

[0012] According to one embodiment of the present invention, the composite laminate is made of carbon fiber reinforced resin matrix composite material. The method of this embodiment solves a typical problem in predicting the drilling axial force of carbon fiber reinforced resin matrix composite materials commonly used in aircraft.

[0013] According to one embodiment of the present invention, the process of obtaining the axial force by simulating using finite element simulation technology includes: establishing a simulation geometric model composed of a drill bit, fiber, resin and an equivalent homogeneous body, wherein the equivalent homogeneous body is wrapped around the resin, wherein the drill bit is generated as a tetrahedral mesh in a free manner, and the fiber, resin and equivalent homogeneous body are generated as a hexahedral mesh in a swept manner.

[0014] According to one embodiment of the present invention, in the simulation geometric model, the fiber is defined as a transversely isotropic material along the fiber length direction, the resin is defined as an isotropic elastoplastic material, and the equivalent homogeneous body is regarded as an orthotropic linear elastic material.

[0015] According to one embodiment of the present invention, in the simulation geometric model, binding constraint relationships are established between the outer surface of the fiber and the inner surface of the resin, and between the outer surface of the resin and the inner surface of the equivalent homogeneous body. In the contact properties, the tangential behavior adopts a penalty function, the friction coefficient between the drill bit and the fiber is 0.8, the friction coefficient between the drill bit and the resin is 0.3, and the normal behavior is defined as hard contact.

[0016] According to one embodiment of the present invention, the method further includes: actually measuring the geometric angle of each micro-cutting edge segment, and based on the length of each micro-cutting edge segment and the cutting speed of the drill bit, simulating the axial force of each micro-cutting edge segment at cutting angles of 0°, 45°, 90°, 135°, and 180° in a simulation geometric model.

[0017] According to one embodiment of the present invention, the given feed rate is the feed rate of the micro-cutting edge when the main cutting edge rotates one revolution.

[0018] According to one embodiment of the present invention, the drill bit includes two main cutting edges.

[0019] Based on common knowledge in the field, the above-mentioned preferred conditions can be combined arbitrarily to obtain various preferred embodiments of the present invention.

[0020] The method of this invention microscopically analyzes the drilling process of a macroscopic drill bit by discretizing the main cutting edge of the drill bit into multiple micro-cutting edges. It analyzes the variation law of axial force, simulates the axial force at multiple discrete angles, and calculates the macroscopic drilling axial force using the axial force fluctuation equation and dynamic contact length. This method is simple, low in cost, and can be easily implemented using existing simulation software and calculation tools. It reduces the simulation workload, shortens the simulation calculation time, and improves the simulation calculation efficiency. It can predict the drilling axial force for arbitrary hole diameters and different material thicknesses. Attached Figure Description

[0021] To better understand the above and other objects, features, advantages, and functions of the present invention, reference can be made to the preferred embodiments shown in the accompanying drawings. The same reference numerals in the drawings refer to the same parts. Those skilled in the art should understand that the drawings are intended to schematically illustrate preferred embodiments of the invention and do not limit the scope of the invention in any way; the parts in the drawings are not drawn to scale.

[0022] Figure 1 This is a schematic diagram illustrating the transformation of the macroscopic drilling process into a microscopic cutting process using micro-cutting edges.

[0023] Figure 2 This represents the constitutive relation of the resin matrix.

[0024] Figure 3 This is a schematic diagram of the micro-cutting simulation when the fiber cutting angle is 0°.

[0025] Figure 4 This is a simulation diagram of micro-cutting edge cutting when the fiber cutting angle is 45°.

[0026] Figure 5 This is a simulation diagram of micro-cutting edge cutting when the fiber cutting angle is 90°.

[0027] Figure 6 This is a simulation diagram of micro-cutting edge cutting when the fiber cutting angle is 135°.

[0028] Figure 7 This is a schematic diagram of the axial force fluctuation curve fitted during the first micro-cutting edge cutting.

[0029] Figure 8 The simulation results show the macroscopic drilling axial force prediction results for the first micro-cutting edge.

[0030] Figure 9 The results are simulation predictions of the macroscopic drilling axial force of composite laminates.

[0031] Figure reference numerals: 1-micro-cutting edge; 2-fiber; 3-resin; 4-equivalent homogeneous body; Vc-cutting speed. Detailed Implementation

[0032] Composite materials consist of a matrix and a reinforcement. Typically, the matrix material includes metallic and non-metallic materials. Metallic matrices include, for example, aluminum, magnesium, copper, titanium, and their alloys, while non-metallic matrices include, for example, polymers, resins, rubber, ceramics, graphite, and carbon. Reinforcing materials are categorized into fibers, particles, and whiskers, such as oxide particles, glass fibers, carbon fibers, boron fibers, aramid fibers, silicon carbide fibers, asbestos fibers, and metal whiskers. The geometry of the reinforcement includes particles, fibers, and plates. Based on this, composite materials are classified as particle-reinforced, discontinuous fiber-reinforced, continuous fiber-reinforced, and plate-reinforced.

[0033] Finite element simulation (FEM) is an effective method for predicting axial force loads during drilling. In recent years, many scholars have used this technology to conduct simulation studies on the drilling process of composite materials and predict axial force loads. In 2012, Phadnis et al. published "Drilling in carbon / epoxy composites: Experimental investigations and finite element implementation" in the journal "Composite: Part A". Based on the 3D Hashin failure criterion and Cohesive elements, they established a macroscopic drilling simulation model of composite materials and achieved prediction of axial force loads for drilling with a thickness of 2 mm and a hole diameter of 3 mm. The average computation time of the simulation model was 72 hours. In 2012, Isbilir et al. published "Finite Element Analysis of Drilling of Carbon Fiber Reinforced Composites," which used two-dimensional continuous shell elements to model composite materials and cohesive elements to embed the interlayer interfaces. The damage evolution of the composite material was based on the 2D Hashin failure criterion. A macroscopic drilling simulation model with a hole diameter of 12 mm and a plate thickness of 4.16 mm was established, achieving simulation prediction of axial forces during the drilling process. The simulation calculation time was 4 months. While the above simulation calculation time is acceptable for drilling small-diameter holes in thin plates, the simulation calculation time for drilling axial force loads in large-diameter, thick composite laminates is too long, resulting in low computational efficiency that fails to meet the requirements for simulation efficiency.

[0034] This invention addresses the problems of high computational load and low simulation efficiency in macroscopic simulation of large-diameter hole drilling in thick composite laminates. It proposes a method for predicting axial force during drilling of composite laminates based on microscopic cutting simulation. This method analyzes and predicts the variation law of axial force from the perspective of composite drilling mechanism, and realizes this prediction through simulation, thus shortening the simulation calculation time and improving the simulation efficiency. It can predict the axial force of holes of any diameter.

[0035] In this disclosure, a composite laminate refers to a laminated structure (or layered structure) in which the reinforcement extends in one direction and is arranged in the matrix, such as a continuous fiber reinforced type or a plate-like reinforced type. This disclosure uses carbon fiber reinforced resin matrix composite material as an example to introduce the concept of the invention, wherein the matrix is ​​resin and the reinforcement is carbon fiber, but it is not limited thereto. The inventive concept of this disclosure can also be applied to other types of composite materials.

[0036] Now, with reference to the accompanying drawings, specific embodiments of the present invention will be described in detail. The embodiments described herein are merely preferred embodiments of the invention; those skilled in the art can conceive of other ways to implement the invention based on these preferred embodiments, and such other ways also fall within the scope of the invention.

[0037] See Figure 1 This invention illustrates the conversion of macro-drilling by a drill bit into micro-cutting. During macro-drilling, the drill bit's motion includes a feed motion (i.e., axial movement) toward the surface of the composite laminate and a rotational motion of the drill bit at the depth of feed. The rotational speed of the drill bit is significantly greater than the feed rate. This disclosure analyzes the axial drilling forces that occur as the drill bit moves in the feed direction (i.e., the axial direction of the drill bit) while simultaneously rotating and cutting the material. The drill bit typically includes two primary cutting edges, each of which cuts and removes the solid material it contacts as the drill bit rotates into the composite laminate.

[0038] like Figure 1 As shown, the drill bit's apex angle is The rotational speed is n, the diameter is d, the feed per revolution of the drill bit is f, and the depth to which the drill bit completely penetrates the material is h. Since the fiber extends in one direction, the angle between each main cutting edge and the fiber's extension direction changes periodically as the drill bit rotates; this angle is called the cutting angle or fiber cutting angle. Specifically, taking an initial cutting angle of 0° between each main cutting edge and the fiber when the drill bit is stationary as an example, the cutting angle changes from 0° to 360° during one revolution or full rotation of the drill bit. That is, the cutting angle changes from 0° to 180° for every half revolution of the drill bit. This disclosure studies the drilling axial force of each main cutting edge using the periodic variation range of the cutting angle from 0° to 180° as the unit.

[0039] The overall idea of ​​this invention is that, since the entire drilling process is a periodic repetition and superposition of the cutting process of each main cutting edge within the cutting angle range of 0° to 180°, this invention only simulates the cutting force within the 180° cutting angle range to obtain the axial force fluctuation equation. This equation reflects the axial force law of the main cutting edge during rotational motion. Then, the axial force fluctuation equation is multiplied by the dynamic contact length of the main cutting edge to obtain the drilling axial force. The dynamic contact length reflects the gradually changing dynamic contact length between the main cutting edge and the material during axial feed. Therefore, the product obtained by multiplication reflects the motion and the superposition and fusion of forces in the feed direction and rotation direction.

[0040] This prediction method starts from the essence of the drilling mechanism of composite materials, discretizes the main cutting edge of the drill bit into multiple micro-cutting edges, and uses finite element simulation technology to establish micro-cutting simulation models of the micro-cutting edges under five typical fiber cutting angles. Then, by combining the five micro-simulation models, the axial force response relationship between the drill bit micro-cutting edges and the workpiece (i.e., composite laminate or carbon fiber reinforced resin matrix composite) is obtained. Finally, the drilling axial force of the drill bit micro-cutting edges is integrated and summed to obtain the overall macro-drilling axial force of the drill bit.

[0041] Specifically, this method considers the cutting mechanism inherent in composite material drilling and establishes a microscopic cutting simulation finite element model based on ABAQUS finite element simulation software, including the drill bit, fiber, resin, and equivalent homogeneous body. The model defines the mechanical constitutive properties of each phase of the fiber, matrix, and equivalent homogeneous body. Combining actual boundary conditions, the contact method between the drill bit and the material, and appropriate mesh generation, the microscopic axial force of the drill bit's micro-cutting edge is simulated and calculated at fiber cutting angles of 0°, 45°, 90°, 135°, and 180°. To characterize the constraint effect of the surrounding material on the workpiece material, the surrounding material is simplified to an equivalent homogeneous body, which constrains the microscopic workpiece. Then, the microscopic axial force of the micro-cutting edge is imported into MATLAB for fitting a wave equation. The fitted wave equation is multiplied by the dynamic contact length, and the product is integrated and summed using a program written in MATLAB, thus predicting the macroscopic axial force during composite material drilling. This method can be used to simulate and predict the axial force during drilling materials of different thicknesses.

[0042] In general, the method includes the following steps.

[0043] Step 1: The main cutting edge of the drill bit is uniformly discretized into m micro-cutting edges. The geometric angles of each micro-cutting edge of the drill bit (such as rake angle, clearance angle, principal cutting edge angle, secondary cutting edge angle, inclination angle, secondary clearance angle, etc.) are measured by a tool measuring instrument. The macroscopic drilling process of the drill bit is transformed into the microscopic cutting of the micro-cutting edges. During the process of the drill bit rotating one revolution or one circle, each micro-cutting edge undergoes a periodic change in fiber cutting angle from 0° to 180°.

[0044] Step 2: As Figures 3 to 6As shown, based on the cutting characteristics of the drill bit during actual macroscopic drilling, geometric models 1 (micro-cutting edge), 2 (mesoscopic fiber), 3 (resin), and 4 (equivalent homogeneous body geometric model 4) of the uncut area are established. All established geometric models are three-dimensional variable entities. The geometric angles of the micro-cutting edge are determined using a tool measuring instrument. The length of the main cutting edge is the cutting length per tooth, and the width of the drill bit is the feed width per tooth. Here, "each tooth" represents each main cutting edge, and the feed width per tooth refers to the radial distance of the cutting length of each main cutting edge to the drill bit's central axis, i.e., the axial projection distance of the cutting length of each main cutting edge onto the workpiece surface. The diameter of a single fiber is D1, and its length is L1. The thickness of the fiber layup is H1. The geometric dimensions of the resin matrix (i.e., resin) are determined based on the fiber volume fraction to ensure uniform fiber distribution within the resin. The equivalent homogeneous body surrounds the matrix.

[0045] Step 3: Mesh the drill bit 1, fiber 2, resin matrix 3, and equivalent homogeneous body 4 respectively. Drill bit 1 is generated as a tetrahedral mesh using a free method, with 10-node modified quadratic tetrahedral elements. Fiber 2, resin 3, and equivalent homogeneous body 4 are all generated as hexahedral meshes using a swept method, with 8-node linear hexahedral reduced integral elements. Element deletion is set for fiber 2 and resin 3, using the default hourglass control and stiffness degradation methods. Element deletion is not set for the equivalent homogeneous body.

[0046] Step 4: Assign material properties to each part of the finite element simulation model: In the microscopic cutting simulation model, the fiber is defined as a transversely isotropic material along the fiber length direction, using engineering constants, and has no plastic stage. Before damage occurs, the fiber follows linear elastic material behavior, and the maximum principal stress criterion is used to determine the damage evolution of the material. When the maximum principal stress at the Gaussian integration point reaches the fiber's tensile strength limit or the minimum principal stress reaches the compressive strength limit, the fiber fails, the relevant element loses its load-bearing capacity, and the relevant element is deleted. The maximum principal stress criterion is shown in formula (1):

[0047]

[0048] In the formula Tensile strength along the fiber length direction. Compressive strength along fiber length

[0049] The resin matrix is ​​defined as an isotropic elastoplastic material. The elastic stage is characterized by the elastic modulus and Poisson's ratio, and the plastic stage is characterized by isotropic yield hardening and the Miss yield criterion. Figure 2 The constitutive relationship of the resin matrix is ​​shown, with strain on the x-axis and stress on the y-axis. E is the elastic modulus, σ0 is the stress at the onset of plastic strain, and σ b For ultimate strength, This represents the plastic strain at failure.

[0050] Formula (2) is used to determine the initial damage to the material:

[0051]

[0052] In the formula ω D The cumulative plastic strain state variable is given by p, where p is the compressive stress and q is the Mises equivalent stress. These are the equivalent plastic strain, equivalent plastic strain rate, and initial damage plastic strain, respectively. When a material is damaged, its stiffness degrades. The linear stiffness degradation method is used to characterize this degradation, as shown in formula (3).

[0053] E=(1-d s E0 (3)

[0054] In the formula, E is the initial stiffness of the material, E0 is the stiffness of the material after degradation, and d s The damage variable is obtained through formulas (4) and (5):

[0055]

[0056]

[0057] In the formula L c The element feature length, the size of which depends on the mesh type. G is the equivalent plastic deformation at failure. f The fracture energy per unit area, σ b This represents the actual load stress at the time of failure.

[0058] The equivalent homogeneous body is considered as an orthotropic linear elastic material, defined by nine engineering constants, without considering the material's damage evolution.

[0059] Material property parameters for each constituent phase are assigned through established cross-sectional properties. The mechanical constitutive relation of the fiber is defined using subroutines written in Fortran, with state variables within these subroutines controlling the deletion of components. The fiber's material properties are defined using a local material coordinate system, specifying material orientation. Figures 3 to 6 In the diagram, the material coordinate system represented by numbers 1, 2, and 3 is shown on the left. Direction 1 is along the fiber length, direction 2 is perpendicular to direction 1 in the same plane, and direction 3 is perpendicular to both directions 1 and 2, consistent with the fiber stacking direction. The material orientation of the equivalent homogeneous body is defined the same as that of the fiber, and will not be elaborated further.

[0060] Step 5: Import the geometric model consisting of the drill bit, fiber, resin, and equivalent homogeneous body into the assembly module for assembly. Use commands such as offset and rotation to ensure the positional relationship between the drill bit and the workpiece. Select the tool tip to establish a reference point and create a set of reference points to lay the foundation for the output of axial force.

[0061] Step 6: Create a dynamic analysis step, set the analysis step time, set the axial force curve output in the historical variables and the cloud map output of the required physical quantities in the field edge quantities, and the output interval of the historical variables and field edge quantities should be appropriate.

[0062] Step 7: Define the constraints and contact methods between the cutting tool (i.e., the drill bit) and the workpiece, as well as between the various components of the workpiece. First, since the geometric deformation of the cutting tool is not considered in the simulation model, the cutting tool element is bound to the reference point set as a rigid body. Second, establish the binding constraints between the outer surface of the fiber and the inner surface of the resin matrix, and between the outer surface of the resin and the equivalent homogeneous inner surface. Then, define the surface-point contacts between the cutting tool and the fiber, and between the cutting tool and the matrix. In the contact properties, the tangential behavior uses a penalty function, the friction coefficient between the cutting tool and the fiber is 0.8, and the friction coefficient between the cutting tool and the matrix is ​​0.3. The normal behavior is defined as hard contact. Finally, since the fiber undergoes large deformation during the calculation, self-contact of the fiber is defined, with a friction coefficient of 0.8. Self-contact is not defined for the resin, as its deformation during the simulation is minimal.

[0063] Step 8: Define model boundary conditions. First, define the cutting speed at the tool reference point. Then, apply completely fixed constraints to the base body and the upper and lower surfaces of the equivalent homogeneous body, constraining six degrees of freedom:

[0064] U1=U2=U3=UR1=UR2=UR3=0 (6)

[0065] Where U represents translational displacement and UR represents rotational displacement.

[0066] Finally, symmetry constraints are applied to the front and back faces of the equivalent homogeneous body, namely:

[0067] U1=UR2=UR3=0 (7)

[0068] Step 9: Submit the job and calculate the axial force simulation cutting results for five typical fiber direction angles (i.e., the fiber cutting angle formed by the main cutting edge of the drill bit relative to the fiber extension direction) of 0°, 45°, 90°, 135°, and 180°.

[0069] Step 10: Fit the axial force fluctuation equation for each micro-cutting edge segment. First, calculate the length l of each micro-cutting edge segment in the microscopic simulation. i The length of the micro-cutting edge l i Calculated using formula (8):

[0070]

[0071] In the formula f z The feed per tooth. The point angle of the drill bit is denoted by , and the feed per tooth represents the axial feed of each micro-cutting edge segment when each main cutting edge rotates once.

[0072] Next, the average value of the steady-state stage of the simulated axial force curve under five fiber cutting angles was taken as the axial force at that fiber cutting angle, and the magnitude of the axial force on each micro-cutting edge under five typical fiber cutting angles was calculated. Finally, the magnitude of the axial force on each micro-cutting edge was imported into MATLAB, and the fluctuation equation of the axial force on each micro-cutting edge with the fiber cutting angle was obtained by fitting. The fitted axial force fluctuation equation is shown in formula (9):

[0073] f i (t)=Asin(θ i (t))+B(i=(1,2,…,m)) (9)

[0074] In the formula f i Let θ be the axial force on each micro-cutting edge segment, A and B be the parameters to be fitted, and θ be the axial force on each micro-cutting edge segment. i Let be the fiber cutting angle, which is obtained by formula (10):

[0075] θ i (t)=ω×t=2πn×t (10)

[0076] In the formula, n is the drill bit rotation speed.

[0077] Step 11: Predict the macroscopic axial force curve. The axial force generated by each micro-cutting edge of the drill bit is determined by the product of the dynamic contact length between each micro-cutting edge and the workpiece material and the axial force fluctuation equation of each micro-cutting edge. The dynamic contact length is:

[0078]

[0079] In the formula, n is the drill bit rotation speed, and v f Let f be the axial feed rate, and f be the feed rate of the micro-cutting edge per revolution of the drill bit. This refers to the apex angle of the drill bit.

[0080] Therefore, the equation for the change of axial force of each micro-cutting edge with time is:

[0081] F i =f i (t)×L i (t) (12)

[0082] By calculating the time t it takes for each micro-cutting edge to fully penetrate the workpiece material, the variation curve of the drilling axial force over time can be predicted and plotted in MATLAB. The time t for each micro-cutting edge to fully penetrate the workpiece material is determined by the following formula:

[0083]

[0084] In the formula, h is the drilling depth, d is the drill bit diameter, n is the drill bit rotation speed, and f is the feed rate per revolution. This refers to the apex angle of the drill bit.

[0085] Therefore, the axial force during the drilling process at the entry point is:

[0086]

[0087] Step 12: Program in MATLAB to predict and output the simulation results of axial force during the drilling process.

[0088] The specific implementation of the present invention will be described in detail below with reference to specific examples.

[0089] This invention, based on ABAQUS finite element simulation software and MATLAB software, takes a drilling diameter of 20 mm, a composite material thickness of 10 mm, a drill bit speed of 2400 r / min, and a feed per tooth of 0.015 mm as an example. The specific steps of the method for predicting the macroscopic axial force of composite laminate based on mesoscopic cutting simulation are as follows:

[0090] Step 1: As Figure 1 As shown, with m=10, the main cutting edge of the drill bit is discretized into 10 micro-cutting edges. The tool angle of each micro-cutting edge is measured by a tool measuring instrument. The measured tool angle results are shown in Table 1.

[0091] Table 1

[0092]

[0093] Step 2: Based on the cutting characteristics of the drill bit during actual macroscopic drilling, establish geometric models for the micro-cutting edge, micro-fiber, resin, and the equivalent homogeneous body of the uncut area. All combined models are three-dimensional variable entities. The geometric angles of the micro-cutting edge are as shown in Table 1. The length of each micro-cutting edge segment is 30 μm, and the drill bit width is 26 μm per tooth feed width. The diameter of a single fiber is 7 μm, and its length is 150 μm. The carbon fiber layer consists of three layers, with 30 carbon fibers per layer. The fibers are uniformly distributed within the resin matrix, with a fiber volume fraction of 60%. The equivalent homogeneous body surrounds the resin matrix.

[0094] Step 3: Mesh the tool, fiber, resin matrix, and equivalent homogeneous body respectively. Tool 1 is generated as a tetrahedral mesh using a free-form method, with 10-node modified quadratic tetrahedral elements. Fiber, resin, and equivalent homogeneous body are all generated as hexahedral meshes using a swept-form method, with 8-node linear hexahedral reduced-integral elements. Element deletion is set for fiber and resin, using the default hourglass control and stiffness degradation methods. Element deletion is not set for the equivalent homogeneous body.

[0095] Step 4: Assign material properties to each component in the finite element simulation model. Material property parameters for each constituent phase are assigned through the established section properties. The mechanical constitutive relation of the fiber is defined using subroutines written in Fortran, and the deletion of control units is controlled by state variables within these subroutines. The material properties of the fiber are defined using a local material coordinate system to define the material orientation, such as... Figures 3 to 6 As shown, the material coordinate system represented by numbers 1, 2, and 3 is shown on the left. Direction 1 is along the fiber length direction, direction 2 is perpendicular to direction 1 in the same plane, and direction 3 is perpendicular to both directions 1 and 2, consistent with the fiber stacking direction. The material direction of the equivalent homogeneous body is defined the same as that of the fiber and will not be repeated. The material properties of the fiber and the equivalent homogeneous body are shown in Tables 2 and 3, respectively.

[0096] Table 2

[0097]

[0098] Table 3

[0099]

[0100] The material constitutive relation of the resin is as follows Figure 2 As shown in Table 4. The elastic stage is characterized by the elastic modulus E and Poisson's ratio V. The initial plastic damage of the material is determined by formula (2). When the material reaches the tensile limit, it enters the damage stage. The stiffness degradation of the material is calculated by formulas (3)-(5). The material properties of the resin are shown in Table 4.

[0101] Table 4

[0102]

[0103] Step 5: Import the simulation geometric models of the cutting tool, fiber, resin, and equivalent homogeneous body into the assembly module for assembly, such as... Figures 3 to 6 As shown, the right side consists of an assembly coordinate system composed of X, Y, and Z. By using commands such as offset and rotation, the positional relationship between the tool and the workpiece is ensured so that the depth of cut of the tool is 15μm per tooth. The tool endpoint is selected to establish a reference point, and a set of reference points is established.

[0104] Step 6: Create a dynamic analysis step, set the analysis step time to 5E-5s, set the axial force curve output of the reference point set in the history variables, and set the output frame count to 800 frames. Set the stress and strain output in the field edge quantities, and set the output frame count to 800 frames.

[0105] Step 7: Define the constraints and contact methods between the tool and the workpiece, as well as between the various components of the workpiece. First, since the geometric deformation of the tool is not considered in the simulation model, the tool element is bound to the reference point set as a rigid body. Second, establish the binding constraints between the outer surface of the fiber and the inner surface of the resin matrix, and between the outer surface of the resin and the equivalent homogeneous inner surface. Then, define the surface-point contacts between the tool and the fiber, and between the tool and the matrix. In the contact properties, the tangential behavior uses a penalty function, the friction coefficient between the tool and the fiber is 0.8, and the friction coefficient between the tool and the matrix is ​​0.3. The normal behavior is defined as hard contact. Finally, since the fiber undergoes large deformation during the calculation, self-contact is defined for the fiber, with a friction coefficient of 0.8. Self-contact is not defined for the resin, as its deformation during the simulation is minimal.

[0106] Step 8: Define the model boundary conditions. First, define the cutting speed of the tool reference point. The cutting speed of the tool is 150.72 m / min (i.e., the linear speed of the drill bit). Second, apply completely fixed constraints to the base body and the upper and lower bottom surfaces of the equivalent homogeneous body. Finally, apply symmetrical constraints to the front and back surfaces of the equivalent homogeneous body.

[0107] Step 9: Establish simulation models for different fiber cutting angles, such as... Figure 3 , Figure 4 , Figure 5 , Figure 6 As shown, the submitted assignments calculate the axial force simulation cutting results for each fiber direction angle (i.e., the fiber cutting angle formed by the main cutting edge of the drill bit relative to the fiber extension direction) at five typical fiber direction angles: 0°, 45°, 90°, 135°, and 180°.

[0108] Step 10: Fit the axial force fluctuation equation on each micro-cutting edge segment. Taking the first micro-cutting edge segment of a main cutting edge of the drill bit as an example, fit the axial force fluctuation equation of the first micro-cutting edge segment. The same principle applies to the other nine segments, so it will not be repeated here. First, calculate the length of the first micro-cutting edge segment in the micro-simulation as 30μm using formula (8). Calculate the simulation results of five axial forces on the micro-cutting edge segment at fiber cutting angles of 0°, 45°, 90°, 135°, and 180°. That is, the five axial forces are simulated based on the geometric angle of each micro-cutting edge segment, the length of each micro-cutting edge segment, and the cutting speed of the drill bit (i.e., the cutting speed of each micro-cutting edge segment). The five axial forces obtained from the simulation were imported into MATLAB to fit the axial forces on the micro-cutting edge, and the axial force fluctuation equation (9) was finally determined. Then, the dynamic contact length was calculated by formula (11), and the axial force response between the micro-cutting edge and the workpiece was obtained by substituting it into formula (12). The contact time was calculated according to formula (13) to obtain the axial force response of the first segment of the micro-cutting edge. Similarly, the axial force response of the remaining nine segments of the micro-cutting edge was calculated, and the axial force of the entire drill cutting edge was obtained by integrating and summing by substituting it into formula (14). Among them, the axial force fluctuation equation represents the dynamic change of the axial force on each segment of the micro-cutting edge, which is a sinusoidal variation law. The axial force is related to the tool (e.g., the tool's geometric angle, cutting length, cutting speed, etc.) and the composite material. Different composite materials have different mechanical properties and different interaction forces with the tool. Therefore, the axial force fluctuation equation is also different.

[0109] Figure 7 The figure shows the axial force fluctuation curve in the range of 0° to 180° during the first micro-cutting edge cutting. The curve is a sine curve, which is fitted by five axial forces obtained from simulation at fiber cutting angles of 0°, 45°, 90°, 135° and 180°, reflecting the periodic sinusoidal variation law of axial force during rotation. Figure 8 The simulation prediction results of the macroscopic drilling axial force of the first micro-cutting edge are shown. It can be seen that as the micro-cutting edge gradually feeds axially and drills into the workpiece, the dynamic contact length with the workpiece continuously increases, and the axial force gradually increases. During the simultaneous execution of feed motion and rotational motion, the axial force of the micro-cutting edge generally increases gradually, and the specific form of the force is a sine curve. Figure 9 The simulation results of the macroscopic axial force of the composite laminate are shown. Its shape consists of three segments: an ascending segment, a stable segment, and a descending segment. The ascending segment indicates that the axial force gradually increases as the drill bit gradually penetrates into the workpiece. The stable segment is a relatively constant flat straight line segment, indicating that the drill bit is fully penetrated into the workpiece and cutting the workpiece smoothly. At this time, the axial force remains basically constant. The descending segment indicates that the axial force gradually decreases as the drill bit gradually removes the material from the workpiece and drills out of the workpiece, eventually reaching zero. As mentioned above, in this process, the axial force is specifically represented in the form of a sine curve.

[0110] The method of this invention microscopically analyzes the drilling process of a macroscopic drill bit by discretizing the main cutting edge of the drill bit into multiple micro-cutting edges. It analyzes the variation law of axial force, simulates the axial force at multiple discrete angles, and calculates the macroscopic drilling axial force using the axial force fluctuation equation and dynamic contact length. This method is simple, low in cost, and can be easily implemented using existing simulation software and calculation tools. It reduces the simulation workload, shortens the simulation calculation time, and improves the simulation calculation efficiency. It can predict the drilling axial force for arbitrary hole diameters and different material thicknesses.

[0111] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these are merely illustrative examples, and the scope of protection of the present invention is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but all such changes and modifications fall within the scope of protection of the present invention.

Claims

1. A method for predicting the axial force during drilling of composite laminates, characterized in that, The method includes the following steps: Discretize the main cutting edge of the drill bit into infinitesimal elements. Micro-cutting edge; For each micro-cutting edge segment, the axial force of the micro-cutting edge at multiple cutting angles within the range of 0° to 180° under a given feed rate is simulated using finite element simulation technology. Based on the obtained axial force, the axial force fluctuation equation for each of the m micro-cutting edges is fitted and determined. ,in, i=1,2,…,m The cutting angle, , This refers to the drill bit rotation speed; The axial force fluctuation equation for each segment of the m-segment micro-cutting edge. With the corresponding dynamic contact length Multiplying these together yields the axial force of each of the m micro-cutting edges. Among them, dynamic contact length Calculate using the following formula: ,in, The tip angle of the drill bit. This refers to the axial feed rate. This represents the feed rate of the micro-cutting edge per revolution of the drill bit; Calculate the time it takes for each of the m micro-cutting edges to reach the drill bit's penetration depth. and at that time Axial force Integrate to obtain the axial force. In response to time, among which, , This represents the depth to which the drill bit penetrates. The diameter of the drill bit; right Axial force in each segment of the micro-cutting edge Summing them up yields the drilling axial force. .

2. The method for predicting drilling axial force in composite laminates as described in claim 1, characterized in that, The multiple cutting angles are the main cutting edges of the drill bit at 0°, 45°, 90°, 135°, and 180° relative to the fiber extension direction, respectively.

3. The method for predicting drilling axial force in composite laminates as described in claim 1, characterized in that, Composite laminates are made of carbon fiber reinforced resin matrix composites.

4. The method for predicting drilling axial force in composite laminates as described in claim 2, characterized in that, The process of obtaining the axial force by simulating using finite element simulation technology includes: establishing a simulation geometric model composed of a drill bit, fiber, resin and an equivalent homogeneous body, with the equivalent homogeneous body surrounding the resin. The drill bit is generated as a tetrahedral mesh in a free manner, while the fiber, resin and equivalent homogeneous body are generated as a hexahedral mesh in a swept manner.

5. The method for predicting drilling axial force in composite laminates as described in claim 4, characterized in that, In the simulation geometric model, fibers are defined as transversely isotropic materials along the fiber length direction, resins are defined as isotropic elastoplastic materials, and equivalent homogeneous bodies are regarded as orthotropic linear elastic materials.

6. The method for predicting drilling axial force in composite laminates as described in claim 5, characterized in that, In the simulation geometric model, binding constraints are established between the outer surface of the fiber and the inner surface of the resin, and between the outer surface of the resin and the inner surface of the equivalent homogeneous body. In the contact properties, the tangential behavior adopts a penalty function, the friction coefficient between the drill bit and the fiber is 0.8, the friction coefficient between the drill bit and the resin is 0.3, and the normal behavior is defined as hard contact.

7. The method for predicting drilling axial force in composite laminates as described in claim 4, characterized in that, The method further includes: actually measuring the geometric angle of each micro-cutting edge segment, and based on the length of each micro-cutting edge segment and the cutting speed of the drill bit, simulating the axial force of each micro-cutting edge segment at cutting angles of 0°, 45°, 90°, 135°, and 180° in a simulation geometric model.

8. The method for predicting drilling axial force in composite laminates as described in claim 1, characterized in that, The given feed rate is the feed rate of the micro-cutting edge when the main cutting edge rotates one revolution.

9. The method for predicting drilling axial force in composite laminates as described in claim 1, characterized in that, The drill bit consists of two main cutting edges.

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