High reliability model of mechanical response in drilling of CFRP/Al stacks

CFRP/Al laminate material is widely used in aerospace due to its advantages of light weight and high machinability. For assembling, crowded assembly holes need to be drilled for CFRP/Al laminate products. However, the damages of burr, delamination, and tearing appear frequently in drilling without precise guidance by mechanical response model. In order to reduce the machining damages, in this paper, a high-reliability mechanical response model is established for each stage in laminate materials drilling to ascertain the matching method between materials, tools, and cutting parameters. The theoretical expression of drilling thrust based on the thin plate theory is established considering the influence of cutting parameters, and further corrected with the cutting parameter correction terms to predict drilling thrust force, and further guiding the optimization of drilling parameters. According to the experimental results, the proposed model has a reliability greater than 97.3% and a prediction deviation lower than 13.2% in CFRP/Al laminate material drilling thrust force prediction. In the cutting with optimized parameters from the proposed model, the inlet orifice of the laminated material has no flanging burr, and the CFRP layer exit orifice has no defects as burr, delamination, or tearing.


Introduction
Carbon fiber reinforced resin matrix composites/aluminum alloys (CFRP/Al) laminates have attracted much attention in the aerospace due to their high specific strength, high corrosion resistance, and designable mechanical properties [1,2]. The CFRP/Al laminate material needs to make a large number of assembly holes to assembly. The laminated materials holes are drilled in two ways: (1) drilling from the carbon fiber layer to the aluminum alloy layer; (2) drilling from the aluminum alloy layer to the carbon fiber layer. The probability of outlet burrs, delamination, tearing, and other defects is higher when drilling from the aluminum alloy layer, due to the anisotropic mechanical properties of CFRP and the low interlayer bonding strength [3,4]. But it is unavoidable to make holes from the aluminum alloy layer to CFRP because of the limitation of part structure.
The drilling load (drilling thrust and torque) affects the formation of hole defects in laminated materials greatly [5]. The thrust, related to the tool structure, the materials, and the processing parameters, directly affects the processing damage as tearing and delamination on the composite material outlet and the delamination of the composite material/ metal connection layer [6]. Therefore, the drilling thrust force is used as the link between the process parameters, tool structure and machining quality to analyze the drilling process. The force prediction models thus established step by step by the scholars to improve the drilling quality.
There are many research reports of the drilling thrust prediction models from both theoretical and experimental aspects to reduce the drilling defects in laminated material. In response to the above problems, scholars have studied the theoretical prediction model of drilling thrust from both theoretical and experimental aspects. The studies on thrust models for drilling aluminum alloys are reported earlier while those for CFRP are reported later. Tsao [7] proposed an empirical equation-based method to predict the thrust force generated during drilling of composite materials.
Isbilir [8] established a three-dimensional LaGrange finite element analysis model and used the simulation model to predict the thrust and torque of drilling aluminum alloys. Elhachimi and Paris et al. [9,10] improved thrust force prediction model based on the previous research considering the influence of drill bit geometry and cutting conditions on the axial force. On this basic, Hui Chenget al. [11] developed a thrust force dynamic analysis model for drilling of CFRP/ AL stack. Xiao et al. [12] established a thrust prediction model for the full fiber cutting angle of CFRP, considering the influence of fiber orientation when milling CFRP. The earlier research focus on single material, not suitable for the laminated material drilling.
In order to further study the laminated material drilling and improve the accuracy of the prediction model for thrust force, scholars proposed many classical theoretical models: S. Jain [13] established the critical axial thrust model of multiphase based on the research of single-phase material hole making thrust. Cheng H [14] focused on the cutting force for DC machining of CFRP-Al stacks, developed a novel cutting force model, which can represent the dynamic cutting force at any time of the DC process. Hocheng [15] established a critical thrust calculation formula for evaluating the initial delamination damage based on G IC (the interlaminar I-type fracture energy). Liu [16] established the material displacement equation via the classical laminate theory, and analytically calculated the delamination critical thrust using the energy balance equation. Matsumura [17] established a three-dimensional thrust prediction model for multiphase materials based on chip flow theory, and introduced a cutting coefficient to correct the model. P. Rahme [18] et al. converted the concentrated load of hole-making into uniform and triangular distributed loads, and established the critical thrust model of the outlet by load superposition. The classical mechanical prediction model is mainly carried out from two aspects: Firstly, the theoretical thrust force of hole making is studied based on the material and mechanical principles; secondly, the relationship between the cutting parameters and the thrust force is fitted based on the experimental results. Both research methods have their own advantages in thrust prediction, but the thrust is a centralized feedback result of tool structure, manufacturing objects, and machining parameters. So, it is difficult to model universally from a single theoretical study or numerical fitting.
Therefore, an exceptionally reliable theoretical drilling thrust prediction model for laminated materials is established in this paper, aiming to optimize the drilling parameters. The theoretical expression of drilling axial force considering the influence of drilling parameters is established based on the thin plate theory and corrected via the cutting parameter correction term. The influence of cutting parameters on the thrust and the optimal cutting parameters of each component phase in laminated material drilling are obtained. Experiments verified the reliability and accuracy of the theoretical model and the progressiveness of the optimal parameters. An effective theoretical model and method are provided for the optimization of cutting parameters.

Theoretical mechanical model for thrust of laminated materials
The theoretical mechanical model for thrust of laminated materials is established with many unique problems. The drilling process of laminated materials is quite different from that of single material. In addition to the cutting processes of the two materials, there are simultaneous cutting of two-phase materials. Moreover, CFRP is a typical brittle material whose material characteristic is quite different from that of aluminum alloy.

Theoretical model of thrust of CFRP layer
The theoretical model is based on the basic assumptions of the mechanical model analysis for the CFRP composite material plate: the contact form of the drill bit and the workpiece is uniform contact; thus, the thrust is evenly distributed on the chisel edge and the two main cutting edges. The drilling area is simplified to an axisymmetric circular thin plate to analyze the drilling force model of CFRP hole making, as shown in Fig. 1. Based on the above assumptions, the cutting mechanics model of carbon fiber composites is established. According to the thin plate theory in elastic mechanics, the equilibrium differential equation during hole making is: The contact area between the drill bit and the workpiece is axisymmetric and the stress/strain relationship is expressed as: In Eq. (2), M xx , M xy , and M yy are the bending moments in different directions, q is the thrust, D ij is the stiffness matrix, and w is the displacement function.
According to the classical laminate theory of composite materials, the stiffness matrix of a single-layer board can be expressed equations: where Z k is the thickness of the kth layer of the composite laminate, Q ij is the inverse matrix of Q ij , further: Here the T is: The carbon fiber material is an orthotropic material: so D 16 = D 26 = D 61 = D 62 =0, and: where E 1 is the longitudinal elastic modulus of the fiber, E 2 is the transverse elastic modulus of the fiber, 21 is the Poisson's ratio, and G 12 is the shear modulus.
Equation (2) and Eq. (6) are substituted into differential Eq. (1), and simplified as: According to the deflection theorem: According to the principle of virtual displacement and linear elastic fracture mechanics, the total virtual work of the external force is equal to the total virtual strain energy of the deformable body when, when a small virtual displacement is given to a deformable body in equilibrium under the action of external force. Hence, during hole drilling, the total work done by the uniform load q to the composite panel is equal to the elastic strain energy of the material and the failure energy of the material when it is damaged, which can be expressed as follows: Among them, δW is the total virtual work done by the uniform load q, δU is the elastic strain energy of the material, and U d is the failure energy when the material is damaged. δU is approximately equal to the crack propagation energy per unit area and reflects the essence of the material's ability to resist damage. Therefore, the crack propagation energy is equivalent to the failure energy of the material.
Considering Eq. (9) to Eq. (11), the total work done by the uniform load q to the composite material is: According to the material mechanics that when the composite material is drilled, the total elastic strain energy of the composite material laminate is: As known from the mechanics of composite materials, the crack propagation energy can be expressed as: (10) x = r cos y = r sin where G Ic is the crack propagation energy type I of the composite materials.
Therefore, by substituting Eq. (15), Eq. (17), and Eq. (19) into Eq. (13), the following equation could be derived: According to Eq. (20), the drilling force of the composites drilling can be predicted as the following equation: The model above considers the influence of the material properties on the thrust, but in machining, the cutting parameters also influence the thrust. Therefore, the cutting parameter correction coefficient K is introduced to correct the above equation based on the above model.

Theoretical equation of aluminum alloy thrust
In this paper, the polynomial form drilling thrust theoretical equation, considering the influence of single factor and coupling parameters, is used to calculate the thrust of aluminum alloy, because it has higher prediction accuracy [19][20][21][22][23]. The theoretical equation of aluminum alloy thrust is as follows:

Analysis of drilling process for laminated materials
It is difficult to establish a single CFRP (Al) hole-making axial force model to accurately reflect the mechanical response law of laminated material hole-making. So, in this paper, the mechanical response law is described by establishing the axial mechanical model of the laminated material hole making in the whole process in stages. The time-dependent changes of the CFRP/Al laminate during the drilling process are divided into five stages, as shown in Fig. 2.
According to the difference of cutting materials, the lamination material hole making is divided into five stages. As shown in Fig. 2, stage I represents Al drilling initial stage; stage II represents aluminum alloy drilling stable stage; stage III represents hybrid drilling stage; stage IV represents CFRP drilling stable stage; stage V represents CFRP drilling end stage. According to the above five stages, the hole-making mechanics model is established. The stages will be modeled as the following sections.

Model of material removal volume
The material removal rate is an important influencing factors of the drilling axial force. By establishing the material removal rate function, the axial mechanical response law of the drilling process can be described intuitively. According to the above-mentioned division stages of the laminated material hole-making process, the volume removal functions of the aluminum alloy material at each stage are established.
(1) Stage I: Al drilling initial stage In order to analyze the response relationship of the axial thrust of aluminum alloy, the aluminum alloy material removal rate function is established. On the basis of the tool structure, the material removal volume function during the drilling process of Al alloy is deduced as: Fig. 2 Hole-making process of laminated materials 1 3 where V f is feed rate, is drill radius, is drill tip angle, h 1 is thickness of aluminum alloy layer, and h 2 is thickness of CFRP layer. According to Eq. (25), the material removal rate function is: When drilling the aluminum alloy layer in the A-B stage (0 < t < t 1 ), the main cutting edge of the tool gradually drills into the aluminum alloy layer material until the main cutting edge is completely submerged into the aluminum alloy. The removal rate has a quadratic positive correlation with time, and the drilling thrust has a positive correlation with the material removal rate. Therefore, the drilling thrust force and time shows a quadratic positive correlation response at this stage.
The theoretical model expression at this stage can be expressed as follows: where F Al is stable drilling load for aluminum alloy layer. (2) Stage II: aluminum alloy drilling stable stage In the B-C stage (t 1 < t < t 2 ), the main cutting edge of the tool keeps cutting in the aluminum alloy layer stably. According to Eq. (26), the material removal rate is a constant related to the cutting parameters at this stage. So, the thrust basically shows a stable state. In the A-C stage (0 < t < t 2 ), the drilling process could be regarded as a pure aluminum alloy material cutting stage, and the stable hole-making axial force can be expressed by Eq. (24) (3) Stage III: hybrid drilling stage This stage is the key removal stage of the Al/CFRP laminated two-phase material, the model needs to analyze the drilling forces for both the aluminum block and the CFRP. The equation of the material volume removal rate of the Al alloy is shown in Eq. (28). The relationship between the material removal rate of the CFRP layer and the cutting time is deduced as follows: By taking the partial derivative with respect to time, the material removal rate function can be expressed as follows: From point C (time t 2 ), the drill begins to enter the lamination interface cutting area (C-D stage, t 2 < t < t 3 ). At this stage, part of the main cutting edge cuts the alu- minum alloy, and the material removal mechanism is mainly the plastic deformation of the aluminum alloy.
Other part of the main cutting edge cuts CFRP, and the material removal mechanism is mainly the brittle fracture of carbon fiber and fiber/resin separation. In the transition region, the proportion of the main cutting edge cutting Al gradually decreases from 100 to 0% with the progress of the cutting process. Equation (29) shows that the material removal rate at this stage is negatively correlated twice with time. So, the cutting thrust generated by cutting aluminum alloys is negatively correlated twice and gradually decreases. The proportion of CFRP cutting by the main cutting edge gradually increases from 0 to 100% with the drill tip submerging in the CFRP layer (stage C-D in Fig. 10).
Equation (29) shows that the CFRP removal rate is positively correlated with time at this time, so the drilling thrust force generated by drilling CFRP shows a quadratic positive correlation trend and gradually increases.
The cutting thrust in the C-D stage is the result combined action of aluminum alloy and CFRP. The thrust of aluminum alloy has a quadratic negative correlation with time, while the CFRP thrust has a quadratic positive correlation with time. In addition, the thrust of cutting aluminum alloy is greater than the thrust of cutting CFRP. So, the thrust first decreased and then increased at this stage.
According to the above analysis, in the hybrid hole making stage, the axial force of hole making can be expressed as follows: where F CFRP is stable drilling load for CFRP. (4) Stage IV: CFRP drilling stable stage In the D-E stage (t 3 < t < t 4 ), the main cutting edge of the tool keeps drilling stably the CFRP layer. The drilling at this stage can be regarded as the cutting stage of pure CFRP material. The main cutting mechanism at this stage is the brittle fracture of carbon fiber and fiber/resin separation under the action of the cutting edge of the tool and the thrust force tends to a constant value. At this stage, the stable hole-making axial force can be expressed by Eq. (23). In the E-F stage (t 4 < t < t 5 ), it is the CFRP drilling end stage. Equation (29) shows that the CFRP material removal rate in this stage has a quadratic negative correlation with time, so the drilling thrust force is quadratic with time until it comes to zero.
At this stage, the analysis shows that the axial force in the drilling stage can be expressed as the following equation: According to the above analysis, the cutting axial forces equations of each stage are established respectively. The axial force equation of the whole laminated material hole making can be expressed as follows:

Drilling experiment of laminated material
The correction coefficient K of the cutting parameters of the CFRP (Eq. (23)) and the polynomial coefficient of the aluminum alloy layer (Eq. (24)) needs to be calculated from experimental data. The thrust experiments under different parameters were carried out to obtain the thrust under variable drilling parameters, and the numerical fitting algorithm was used to obtain the theoretical thrust expression for laminated material drilling.

Setups of the experiments
The Al/CFRP laminate was used in the experiment. The CFRP layer is T800/epoxy LT-03A [24] multi-directional laminate with a thickness of 10.5 mm, a layup information of [0°/45°/90°/135°/0°] 6 s , and a total of 60 layers. The aluminum alloy layer is 7075-T7451 layer with a thickness of 8.3 mm. The hole-making direction is from the aluminum alloy to CFRP with single-feed drilling, and the size of the laminate material is shown in Fig. 3. The Swiss Mikron high-speed machining center with high precision, high dynamic performance, high stability, and high cutting speed is used in this experiment. And the Carbide twist drill used in this experiment has a diameter of 6.2 mm and a tip angle of 120°.The processing method is single-feed drilling. The Kister dynamometer with sampling frequency of 256 Hz is used to measure the cutting force. To reduce random errors, each experiment was repeated 6 times. The processing conditions are shown in Fig. 4.

Experiment matrix design
According to the processing experience, the spindle speed of the lamination material drilling is about 3000 ~ 5000 r/min, and the feed rate is about 80 ~ 160 mm/min. The orthogonal test method is used to design the test parameter matrix during the parameters boundary, as shown in the Table 1.    (22) is used to calculate the theoretical thrust force of T800 material and the results is 46.3 N. Based on the theoretical cutting axial force, the theoretical Eq. (33) of thrust of CFRP layer is fitted by nonlinear surface considering the influence of speed and feed cutting parameters.

Aluminum alloy thrust model
where V f is feed rate and S is spindle speed. The thrust models of the CFRP and aluminum alloy layers in the stable cutting stage were obtained by numerical fitting based on the experimental results.
According to the d cutting mechanics model establishment process above, Eq. (32) can be expressed as:

Thrust model validation
To further verify the reliability and correctness of the theoretical model, the model verification is carried out in the following two dimensions: goodness of fit and thrust experiments.

Goodness of fit calculation
The goodness of fit of the proposed model is calculated as the following equation: where SSR is the regression sum of squares between the model and the true value, while SSE is the residual sum of squares between the model and the true value. As a result for the proposed model, the goodness of fit is 97.7% for drilling thrust prediction of CFRP, and 97.3% for that of Al. The model has high prediction reliability.

Experiment verification
The reliability of the model is calculated by the goodness of fit. To further verify the correctness of the above theoretical equation, a thrust drilling experiment is carried out with a spindle speed of 3200 r/min and a feed rate of 90 mm/min, and other conditions are consistent with the experiments in Chapter 3. The thrust experiment results are shown in Fig. 7. The thrust force of CFRP layer drilling is 821.48 N, and the theoretical cutting thrust force from the proposed model is 712.54 N, resulting in an error value within 13.26%. The drilling thrust force of the Al layer was 234.51 N and the theoretical cutting thrust force value from the proposed model is 218.43 N, resulting in an error value of 6.85%. The theoretical model can accurately and effectively predict the drilling thrust force of each constituent phase of the laminated material.

Drilling parameter optimization
The relationship between cutting parameters and thrust was further studied on the basis of the theoretical thrust model above. The thrust is then taken as the optimization target to analyze the optimal machining parameters of each constituent phase of the laminated material.

Relationship between cutting parameters and thrust a) Analysis for CFRP cutting parameters and thrust
The fitted surface and contour lines are shown in Figs. 8 and 9, based on the fitted theoretical.
The influence of feed rate on thrust: when the spindle speed is constant, the drilling thrust force increases as feed rate increases, and t and the dependent relationship of feed rate to thrust is approximated linear. Thrust.
The influence of spindle speed on thrust: when the spindle speed is below 3500 r/min, the influence of spindle speed on the thrust is more significant, and the thrust is positively correlated to the spindle speed. When the spindle speed exceeds 3500 r/min, it effects the thrust little.
The law of influence of spindle speed and feed rate coupling effect on thrust: when the spindle speed is less than 3500 r/min, the spindle speed influences the thrust greater than the feed rate. On the contrary, the feed rate influences more when the spindle speed is greater than 3500 r/min. b) Al cutting parameters and thrust analysis The fitted surface and contour lines are shown in Figs. 10 and 11, based on the fitted theoretical.
The influence of feed rate on thrust: when the spindle speed is constant, the drilling thrust increases as feed speed increases, and the dependent relationship of feed rate to thrust is approximated as a cubic function relationship.
The influence of spindle speed on thrust has 5 conditions. When the feed rate is lower or equal 120 mm/min and the spindle speed is below 4000 r/min, the thrust and spindle speed are negatively correlated, while they are positively correlated when the spindle speed is greater than 4000 r/min. The thrust of the aluminum alloy layer is the smallest in the low-speed mode under the low feed condition. When the feed rate is greater than 120 mm/ min and the spindle speed is less than 3500 mm/min, the thrust is positively correlated with the spindle speed. When the spindle speed is greater than 3500 r/min and less than 4500 mm/min, the thrust is negatively correlated with the spindle speed. When the spindle speed exceeds 4500 r/min, thrust is positively correlated with the spindle speed.
Influence law of rotational speed and feed coupling effect on thrust: the spindle speed and feed rate influence the thrust as a cubic curve.

Analysis of hole making damage and relationship between thrust and hole damage
In the process of industrial application, it is difficult to make a comprehensive evaluation on the quality of each hole, but it is possible to obtain intuitive feedback on the drilling process by monitoring the change of drilling force. Therefore, the following is to explore the relationship between the drilling thrust and the hole quality, so as to provide a basis for the subsequent feedback of hole quality directly through the drilling thrust.
a) Relationship between thrust and hole damage of CFRP From the drill test, it can be seen that the main manifestations of CFRP hole making processing damage are tear and delamination. Therefore, in order to objectively evaluate the hole making damage of CFRP laminated materials, a twodimensional quantitative evaluation index of tear defects is introduced. Tear defect evaluation coefficient is s : where A sj is tear area of segment j, m is total number of tears, and A norm is the area of hole wall.
The delamination damage is three-dimensional damage and the delamination volume is very small at actual processing, So the volume based three-dimensional delamination damage factor is proposed: where t is the scanning layer depth, A Dj is delamination area of each layer. On the basis of the test results, the VK-X1000 shape measurement laser display system is used for burr and tear measurement, and SAM is used to scan the delamination volume. The fundamentals of the SAM can be described as follows. The transducer initially converts the electromagnetic pulses (EMP) into acoustic waves at a specific frequency. After leaving the transducer, the acoustic waves are focused on the sample through coupling medium (typically deionized water or absolute alcohol, etc.).The use of the coupling medium is to prevent the ultrasonic waves from rapid attenuation when they spread in sparse media. The sample is placed in a coupling medium and reflections occur as soon as the ultrasonic waves encounter the acoustic impedance interface caused by defects like porosity, voids, impurities or delamination on the surface or inside the sample. So as to detect delamination defects.
Measure the test piece by the above method. The test results are shown in Figs. 12 and 13.
It can be seen from the measurement results that the burr, tear defect, and delamination volume at the hole exit quality of CFRP layer are positively correlated with the thrust of hole making, indicating that the size of the axial force of hole making can indirectly feed back the hole making quality. b) Relationship between thrust and hole damage of Al At the same time, as the aluminum alloy material can be regarded as isotropic material, there is no tear, delamination in aluminum alloy drilling, only burr and     flanging defects. Therefore, the maximum defect height is used for aluminum alloy hole making quantitative evaluation: where A i is article i burr height.
Measure the test piece by the above method, the test results are shown in Figs. 14 and 15. It can be seen from the measurement results that the defect height at the hole exit quality of Al layer are positively correlated with the thrust of hole making, indicating that the size of the thrust of hole making can indirectly feed back the hole making quality.
Therefore, from the above test results, it can be seen that the hole making damage factor is positively related to the hole making thrust, which is intuitively reflected that the greater the hole making thrust is, the more serious the hole making damage is. Therefore, the

Optimal cutting parameters based on minimum thrust
The optimal cutting parameters of CFRP layer are calculated by the theoretical model with an optimization goal of minimum thrust. The optimal spindle speed is 9496.58 r/min and the feed rate is 37.97 mm/min for CFRP drilling. The optimal spindle speed is 2689 (2597) r/min and the feed rate is feed 28.7 (16.8) mm/min for aluminum drilling. In actual drilling, the optimal spindle speed is 9500 r/min and the feed rate is 40 mm/min for CFRP drilling. The optimal spindle speed is 2700 r/min and the feed rate is feed 30 mm/min for aluminum drilling.
Parameter optimization verification experiment According to the optimization results, the optimal drilling parameters of CFRP and aluminum alloy are very different. Obviously, in order to obtain better hole-making quality, variable parameter drilling is a feasible and effective way. To further verify the optimal cutting parameters of each constituent phase for the laminated material, the test of the layered variation parameters of the laminated material was carried out, as shown in Fig. 16. The spindle speed of the CFRP layer drilling is 9500 r/min, and the feed rate is 40 mm/min. The spindle speed of the aluminum alloy layer is 2700 r/min, and the feed rate is 30 mm/min.
The result of the verification experiment is shown in Fig. 17. The maximum thrust of the aluminum alloy drilling is 53.61 N, and the maximum thrust of CFRP drilling is 51.37 N. The error with the model prediction value is within 11.12%.
The drilled laminated material was observed in the microscope, as shown in Figs. 18 and 19. Compared with the laminated material drilled by conventional parameters, the quality of the aluminum alloy inlet orifice is better, the processing defects as flanging burrs, and

Conclusion
Conventional single material-oriented models cannot solve the thrust prediction and process parameter optimization of CFRP/Al laminates because of big differences between the CFRP and aluminum alloy. To improve the drilling quality of CFRP/Al laminated materials and reduce the drilling thrust, this paper proposed a theoretical mechanical model for thrust of laminated materials drilling, which is further corrected by numerical fitting. The model can effectively and accurately predict the thrust force in the drilling of laminated materials, available for guiding the optimization of process parameters based on the minimum thrust force. The verification experimental results show that the proposed theoretical model has high accuracy in thrust force prediction, and the proposed optimized parameters effectively reduce the cutting force and improve the machining quality of the laminated material drilling. The following conclusions were drawn from this research: (1) The theoretical model of CFRP/Al laminated material is established, and the drilling process is divided into five relatively independent stages. The mapping relationship between the process parameters and the drilling thrust force of each stage is modeled, which is further corrected by numerical fitting. The experimental results show that the error of the predicted thrust is within 13.26%, which can effectively predict the laminated materials drilling thrust and guide the optimization of drilling parameters.
(2) The drilling thrust is obtained through experiments with 25 sets of conventional machining parameters. Based on the theoretical thrust, the cutting mechanics prediction models of CFRP and Al stable drilling stages are fitted with a nonlinear surface to correct the theoretical expression of the thrust forces. Experiments shows the modified model has a reliability greater than 97.3%. (3) In the cutting with optimized parameters from the proposed model, the error between the experimental thrust and the theoretical thrust is 11.12% or less. For processing quality, the inlet orifice of the laminated material drilling with the optimized parameters has no flanging burr, and the CFRP layer exit orifice has no defects as burr, delamination, or tearing.
Funding The work is supported by National Natural Science Foundation of China (No. 51975288).

Data availability Not applicable.
Code availability Not applicable.

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Ethical approval The work contains no libelous or unlawful statements, does not infringe on the rights of others, or contains material or instructions that might cause harm or injury.

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Fig. 19
Hole exit delamination of CFRP