Experimental and Scale-span Numerical Investigations in Conventional and Longitudinal Torsional Coupled Rotary Ultrasonic Assisted Drilling of CFRPs

Longitudinal torsional coupled rotary ultrasonic assisted drilling (LTC-RUAD) technology is introduced to improve the surface roughness of the hole wall and solve the tear, burr and delamination of carbon fiber reinforced polymers (CFRPs) induced by large thrust force and torque during conventional drilling (CD). An experiment and scale-span numerical investigation of drilling CFRPs was presented for both CD and LTC-RUAD process in this study. A drilling experimental platform using LTC-RUAD was built via a novel independently designed and manufactured LTC-RUAD vibration actuator, while the drilling experiments involving T700S-12K/YP-H26 CFRPs specimens with different process parameters were carried out by adopting the different ultrasonic vibration amplitude (UVA) in the longitudinal and torsional directions. Then, a three-dimensional (3D) scale-span FE simulation model of CD and LTC-RUAD which applied the different UVA using tapered drill-reamer (TDR) are developed to find more details about the effects of machining quality of the holes. Experimental and simulation results revealed that the maximum average thrust force reduction is observed to be as high as 30% under certain drilling conditions, and the maximum average thrust force and the delamination factor of the drilled hole shows a "concave" trend with the increase of the UVA. The quality at the exit of the drilled hole is the best when adopting S r =2000rpm, S f =0.01mm/rev, A lon =7.02 μ m and A tor =9. 29μm in LTC-RUAD. The delamination factor is only 0.054. The damage factors are reduced by 69.67% compared with CD.


1.Introduction
Carbon fiber reinforced polymers (CFRPs) are being widely used in aerospace industry and automobile industries and several other structural applications owing to their superior mechanical and physical properties [1,2]. Through a near-net shape process is usually for CFRPs components, but additional machining operations are often required to facilitate furtherly installation of rivets or bolted joints. For any mechanical fastening, conventional drilling (CD) process is extensively used for producing CFRPs holes. However, different to drill metal materials, various mechanical damage in terms of delamination, poor surface integrity, fiber pullout, fiber breakage and burr usually occur due to the heterogeneous and anisotropic nature of CFRPs laminates during drilling [3,4]. These undesirable drilling-induced damages not only directly deteriorate the surface finish and assembly tolerance, but also reduce the hole strength against fatigue, thus the load-carrying capacity of CFRPs structure is affected [5]. To overcome the aforementioned problems, a need for a less invasive drilling technique capable to mitigate damage in drilling CFRPs structural components is recognized.
A hybrid non-traditional process, known as "rotary ultrasonic assisted drilling (RUAD)", has been successfully extended to the area of CFRPs drilling owing to its remarkable improvement in machinability for machining difficult-to-machine metal material in the last few years [6,7]. In RUAD, high frequency vibrations, typically in the range of 20kHz, generated by a piezoelectric transducer are superimposed on a rotating standard tool in the axial direction or rational direction to improve the machining process. Fundamentally, RUAD is a completely different process from CD, and the tool-workpiece interaction is intermittent with significantly higher deformation rates. Nonetheless, the cutting process is continuous in CD. Compared with CD, RUAD is shown to be beneficial for drilling holes in brittle materials [8] and has many documented advantages, for instance, reduction in thrust force, improved surface finish, better hole quality, elimination of burrs and lower tool wear [9].
In the literature, some researchers have conducted RUAD experiments to investigate the effect of different drill bit geometries, different process parameters on damage defects of the drilled holes. Sadek et al. [10] investigated the RUAD process to reduce thermal and mechanical defects associated with drilling of CFRPs, the results revealed that the optimized RUAD condition can reduce the machining temperature by 50%, the thrust force by 40% and produce delamination-free holes, without affecting productivity. Cong et al. [11] employed the similar RUAD method to drill CFRPs laminate to prevent clog and improve the hole's quality. Wang et al. [12,13] also successfully extended RUAD method in which vibration is applied along the tool axis to improve the machining of the CFRPs surfaces, whereas the risk of delamination damage increases since the cooling fluid with a certain pressure is pumped through core drill. Thomas et al. [14] investigated the drill bit's vibrational characteristic, the experimental and simulation results showed that there are several well-documented advantages of RUAD over CD techniques such as reduction in thrust forces and torque, better surface finish, low tool wear and elimination/reduction in burr formation. Makhdum et al. [15] conducted an extensive experiment by using high-frequency vibration to excite a drill bit during its standard operation to study the effect of RUAD on CFRPs, the research results showed that adopting RUAD technique had a significant improvement to improve the drilling quality compared with CD. Asami et al. [16] developed a LTC vibration device for the ultrasonic machining of brittle materials with an abrasive slurry. Compared with the one-dimensional longitudinal vibration drilling, the LTC vibration was discovered to improve the machining efficiency. These above studies showed that there are several advantages of RUAD over CD such as reduction in drilling forces and torque, better surface finish, low tool wear and elimination in burr formation.
Although experimental efforts have been done about the use of RUAD in the drilling of CFRPs, still some considerable works remain so that this strategy can be industrialized, efficiently. Accordingly, finite element (FE) simulation is a helpful approach to evaluate this machining process in detail [17]. Expect for few literatures reported by Phadnis et al. [18,19] in simulation of cutting forces in RUAD, there are not any corresponding research representing burr formation, delamination generation, as well as tool movement in the simulation of vibration drilling owing to the complexity involved in modeling of such processes and the extent of computational resources required. In the aforementioned studies, they indicated that the average thrust force in RUAD was reduced as high as 30% compared to CD of CFRPs.
Furthermore, it was noted that the predicted results were in good agreement with experimental results.
However, in the numerical analysis for CFRPs drilling using RUAD, almost all of them used macro-mechanics theories (Tsai-Wu [20], Hashin [21,22], Puck [23] and Chang-Chang [24], etc.) although they were capable to determine the damage modes by regarding composite as homogeneous material, where some real damage defects are impossible to be simulated, such as burr, etc. In addition, CFRPs is a kind of multiphase material with macro-micro characteristic, whereas these theories did not consider the influence of local stress difference caused by different mechanical performances of constituent fiber and matrix, which are related to the behaviors of CFRPs at macroscale. For the drilling FE model, the stress and strain of the CFRPs laminate in the direction of thickness, which is lacked of considering in these macro-mechanics theories, should be considered in particular. If the micro-scale modeling method of the CFRPs FE model is adopted, which is limited by computing power and efficiency in a high-performance workstation.
Meanwhile, as one of the two major variables of RUAD, ultrasonic vibration amplitude (UVA) in the longitudinal and torsional direction plays a dominate role in the longitudinal torsional coupled rotary ultrasonic assisted drilling (LTC-RUAD) process. The influence of machining quality of the holes is not researched furtherly as the change of the UVA. Plentiful studies are major focused on "abrasive drilling" in terms of optimizing the process parameters, whereas the drilling and grinding coupled process in the drilling of CFRPs is not researched further. For instance, a tapered drill-reamer (TDR) or step drill bit are adopted in the LTC-RUAD process for CFRPs drilling. from the perspectives of the thrust force and torque, burr and delamination at the hole exit. In addition, the correlative factors affecting the hole making quality, hole making defects and cutting force of CFRPs to optimize the process parameters and LTC parameters, which is conducive to achieve high-precision drilling.

LTC-RUAD test system and calibration
The LTC-RUAD experimental instruments used in this paper is attributed to be independently designed and manufactured by Nanjing University of Aeronautics and Astronautics. The whole LTC-RUAD test system consists of a BT40 LTC ultrasonic vibration holder, a labview controller, a power supply and the corresponding voltage amplifier. LTC ultrasonic vibration holder majorly comprises of longitudinal torsional coupler, electrode slice, piezoelectric ceramic piece and amplitude amplifier pole, etc.
The actual parts and connection relationship of each parts are shown in Fig.1.   the frequency is about 19.6 kHz, as shown in Fig.2(a). Simultaneously, the amplitude of longitudinal vibration and torsional vibration shows a semi-linear relationship at the resonant frequency, and it's different from the original design which is supposed to be linear, as shown in Fig.2(b). The primary reason for such errors is that the piezoelectric ceramic piece has hysteresis and creep properties, etc.

LTC-RUAD experimental procedure of drilling CFRPs laminate
A corresponding CFRPs with a thickness of 5.76 mm (32 layers) was used for conducting the drilling experiments in this study. The CFRPs were made using unidirectional prepregs supplied by GW composite Co, Ltd, and the model of prepregs was T700S-12K/YP-H26. The curing process mainly followed the literature [25]. The fiber volume fraction after curing was approximately 59%. The entire curing process was performed in the composite material forming laboratory of Nanjing University of Aeronautics and Astronautics. After curing, the CFRPs were made into the dimension of the drilling specimen via waterjet cutting, for which the length and width of specimens were 180 mm and 120 mm, respectively.
The entire schematic diagram of the experimental setup and the specific experimental setup are illustrated in Fig.3 and Fig.4. It mainly consists of an LTC-RUAD system and a data acquisition system. The CFRPs were mounted on a dynamometer using a special fixture on the table of a XK7124 CNC machining center, and the TDR bit which is installed on the LTC-RUAD handle was fed into the CFRPs.
Drilling experiments were carried out on CFRPs using a diameter Φ 6 mm cemented carbide TDR bit. Experiments were conducted without coolant. The thrust force during drilling was measured by using a piezo-electric dynamometer (type Kistler 9257B). The charge amplifier (type Kistler 5407A) converted the resulting charge signals, which were proportional to the force, to voltage and managed the experiment through the data acquisition system (type NI DAQ).

Fig.3 Schematic diagram of LTC-RUAD experimental setup
A full factorial design of experiments with two factors based on the initial process parameters was adopted in this study [26]. Three levels of spindle feed rate and their corresponding spindle rotation speed were employed. According to the amplitude of the calibration curve which is shown in Fig.2, the torsional UVA and longitudinal UVA were corresponding to each other under the same voltage owing to the resonance amplitude was inspired by the same piezoelectric ceramic piece. Therefore, the different UVA generated under different voltages were adopted according to the optimal resonant frequency of the LTC-RUAD handle. The integrated machining scheme is shown in Tab.1. Experiments of each machining parameter were repeated 3 times to obtain a satisfactory measured dataset. All the experiments were carried out on the LTC-RUAD handle. For instance, the voltage was 0 V in CD. In addition, a new TDR bit was employed for the sake of removing the influence of tool wear during drilling.
All process experiments were performed using three laminates. Finally, as shown in

Principle of the LTC-RUAD process of CFRPs using TDR
The structure of TDR mainly contains three parts: chisel edge, first cutting edge and secondary cutting edge [27]. The cutting process of the bit is rotary and the feed motion is located at the axial direction in the CD of CFRPs, respectively. The first cutting edge is the drilling process that is mainly to achieve material removal, while the second cutting edge is the grinding process which would achieve the role of reaming. The thrust force is mainly determined by chisel edge owing to the chisel edge squeezes the workpieces during drilling, and the torque is generated by the first and secondary cutting edge according to the cutting thickness of the single rotary.
In LTC-RUAD, the LTC vibration of the TDR bit for hole drilling of the CFRPs is applied. Fig.5(a) shows the kinematic view of the LTC-RUAD. Clearly, a polar coordinate is defined on the TDR bit end face. The moving trajectory of position r from the center of the TDR can be written as follows.
where L, R and Z denote the kinematic position of the drilling. Ator and Alon denote the UVA of torsional vibration and longitudinal vibration, respectively. The parameter f denotes the ultrasonic frequency, t denotes the time, r denotes the displacement from the center of the TDR, Sr denotes rotational speed due to the TDR ration, and Sf denotes the feed rate of the TDR. Simultaneously, as showed in Fig.5(b), the circumferential angular displacement β of the TDR can be written as.
The displacements at each point in TDR can be expressed as where x, y and z denote the displacement in rectangle coordinate, respectively. owing to the torsional vibration and longitudinal vibration of the tool. There are reciprocating effects in the axial and rotational directions when adopts the LTC-RUAD process, which means that the tool will lift and do not contact the material within a rotation period. The cure also indicates that the chip thickness of the cutting edge is not uniform, while the fibers can be cut off more quickly in the cutting direction. Besides, the softening of resin is promoted due to the reciprocating microscopic cutting, so that the surface topography of the hole may appear the obvious ironing phenomenon. Thus, the moving trajectory difference of the TDR in CD and LTC-RUAD would highly affect the corresponding machining performances.

Progressive failure theories of the scale-span model of CFRPs
Since the integrate FE analysis process is clearly explained in previous studies [28], the main points are only briefly reviewed to the scale-span analysis method in this study. The adopted modeling method in this paper is based on the implementation of the dynamic micromechanics of failure (MMF) criterion of CFRPs. The kernel of this method consists of establishing the damage-failure constitutions of fiber and matrix under dynamic loading conditions and realizing damage-failure information interaction between the representative volume element (RVE) model which includes fiber and matrix and the macroscopic drilling FE model of CFRPs. According to the scale-span FE drilling schematic diagram which is shown in Fig.7, the whole simulation process is mainly divided into three steps: Step (1): The components of CFRPs are simplified as idealized multi-directional pre-set lay-up sequence structure which includes multilayer UD-CFRPs. It is assumed that the structure of multi-directional CFRPs (MD-CFRPs) is flawless and that the fibers and matrix are tightly bonded during curing. Some minor defects in the material are overlook, such as voids and micro-crack, which is shown in Fig.7 (c). Meanwhile, the drilling bit FE model is also required to be established according to the actual drilling conditions, which is shown in Fig.7 (a).
Step (2): The corresponding RVE model is also established via the basic parameter of CFRPs, such as the diameter of the filament fiber and the fiber volume fraction of CFRPs, etc. which is shown in Fig.7 (b). The stress-strain relationship of the damage element of the macroscopic FE model of CFRPs will be transferred to the RVE model via SAFs when the bit is in contact with CFRPs. These elements of fiber and matrix in RVE model will be secondary analyzed through the MMF criterion of CFRPs, including element failure judgement, stiffness degradation and deletion, etc.
In addition, if the elements are not deleted in the current increment, the element with reduced stiffness will be homogenized in macroscopic drilling FE model, and the macroscopic elastic properties of elements are characterized by the scale-span prediction method [29], which is used for analysis in the next iteration step.
Step (3): The macroscopic elastic properties of elements which have different degrees of damage will be assigned to the corresponding macroscopic elements with different lay-up sequence structure of CFRPs. Then, the next iteration analysis of the macroscopic drilling FE model will be carried out, and the scale-span simulation process of drilling CFRPs will be end if the pre-set increments is reached.   process. The reference point of the TDR was also assigned with a single node mass and rotary inertia element, where the axial velocity and rotations were loaded. A refined mesh was used in the immediate vicinity of the model volume to be drilled and a coarse mesh was used to discretize the volume away from the drilling zone for the sake of ensuring that the prediction of thrust force was more accurate and maximized utilization of the available computing resources during drilling. The CFRPs were modeled using the C3D8R 8-node, 3D brick reduced integration elements. The cohesive-zone was modeled using the COH3D8 0-thickness CEs.
Analogously, the TDR was modeled with the C3D10M 10-node, 3D discrete rigid Based on the aforementioned settings, jobs were created and the corresponding calculation input file was output to check for errors. The mass scaling factor was set to 10 3 according to the reference [30] to improve computational efficiency on the premise of ensuring accuracy through many attempts. The complete computation of a job required approximately 192 hours on a high-performance computer with two 48 core 8160 platinum processors and 128 GB RAM. All simulations were performed at the high-performance computing facility at Nanjing University of Aeronautics and Astronautics.

4.Results and discussion
For the sake of allowing a better comparison of the experimental and simulated thrust force, torque and the damage in entrance, hole-wall and exit of the performed hole using CD and LTC-RUAD, a typical feed rate of Sf=0.03mm/rev was chosen from the experimental feed data with a spindle speed Sr=2000rpm. Meanwhile, the LTC-RUAD experimental results of other process parameters were also adopted to further evaluate the correctness of the simulation results from the maximum average thrust force, torque and delamination factor, etc.  Alon=11.21μm, as shown in Fig.9(b).   Amongst these is the use of a more realistic friction model, inclusion of thermal effects and accounting for TDR wear effects.

Surface morphology
According to the research works by Cheng et al. [31], the micro-scale damage mechanism of UD-CFRPs is different when the different fiber cutting angles are adopted at microscopic, which is shown in Fig.12(b). Yet, in the drilling FE model, it can only show that the stress of the corresponding element is greater in the fiber orientation or elements are deleted because of the limitation of mesh size, which is shown in Fig.12(c) and Fig.13. Meanwhile, the hole-wall surface also appears different phenomena since the different lay-up angle, such as pits, tears, lateral extrusion and delamination, etc. However, as shown in Fig.13, due to the effect of repeated vibration ironing using LTC-RUAD, the surface of the drilled hole is smoother than that using CD, and there are only some slight cracks according to the analysis of the cutting process at the micro-scale level. Since the damage of the scale-span FE model can only achieve material removal through element deletion or the corresponding stress value become larger, the elements that is located in the contact areas can be deleted quickly under the TDR of high-frequency vibration, namely, the fibers can be cut off quickly.
Similarly, the elements of the FE model do not reach the maximum damage variable in CD, which promotes most of them are retained, whereas the corresponding stress is larger, especially in the bottom layers of CFRPs, which is shown in Fig.12(c). which is shown in Fig.14(a). Unfortunately, it is difficult to quantify the burr and tear damage owing to the fiber arrangement in species is random, and some initial damage may be existed in the species during preparing, such as microcrack, etc. Meanwhile, in the scale-span FE model that adopts the LTC-RUAD process, the hole-wall precision of the prefabricated hole has been improved obviously, and only minor tearing damage and delamination damage have appeared, which is shown in Fig.14(b). along the fiber direction. The height of the delamination region is higher than the rest CFRPs [32]. In order to evaluate the simulation results of the scale-span FE model accurately and the delamination damage can inhibit the delamination using LTC-RUAD, a quantitative analysis of delamination factor at the exit of the hole is adopted in this study. According to Fig.15(b), the peripheral damage area is assumed as fan-shaped. It is defined as the ratio of the total peripheral damage area to the nominal hole area.
where Ad denotes the total area of the delamination zone, Anom denotes the nominal diameter area.  Fig.15(c). For the scale-span FE model, the ratio of total number of CEs before and after the drilling simulation was calculated using an ABAQUS-Python code script, which is shown in Fig.16(c). According to the collected average experimental results and the simulation results from different process parameters and UVA, the corresponding delamination factor of drill exit and these absolute percentage deviations [2] are listed in Fig.17. The dominant cause is that there is a material property deviation between the scale-span drilling FE model and experiments under the same machining parameters, followed by the deviation of the measurement devices. In addition, the other important reason is that the thermodynamic failure of elements in the drilling process is not taken into account in the established progressive failure theories model.
Although the deviation of the obtained simulation results is not regular, whereas the influence of the UVA for the suppression of the delamination is almost consistent via the analysis of the simulation results. The delamination factor shows a "concave" trend with the increase of UVA, especially at high rotational speed and low feed rate.
The reasons for this case are consistent with the maximum average thrust force, the UVA within the range of 7μm can be cut off the fiber quickly in the case of the high-frequency owing to it is equivalent to the diameter size of fiber. At the same time, it is also verified that the maximum average thrust force is the main factor causing the delamination [32].

5.Conclusion
In this study, an experiment and scale-span numerical study of drilling in a T700S-12K/YP-H26 CFRPs was presented for both CD and LTC-RUAD process. (1) The predicted the thrust force and torque by the scale-span drilling FE model is reasonable accuracy when compared to experimental results, and the maximum deviation are only 3.43% and 7.69%. And the maximum thrust force and torque that adopts LTC-RUAD is greater than that adopts CD. Nevertheless, the maximum average thrust force reduction was observed to be as high as 30% under certain drilling conditions.
(2) Different kinds of damage behavior of holes can be simulated truly in drilling of CFRP laminates using the TDR, such as the tear damage at drill entry, pits or lateral extrusion damage at drill surface and burr, tear and delamination at drill exit. The maximum thrust force and the delamination factor of the drilled hole shows a "concave" trend with the increase of the UVA. The corresponding parameters reaches the minimum value when the longitudinal UVA is approximately 7~9μm.
(3) In LTC-RUAD using the TDR, the quality at the exit of the drilled hole is the best when adopting Sr=2000rpm, Sf=0.01mm/rev, Alon=7.02μm and Ator=9.29μm in LTC-RUAD. The delamination factor is only 0.054. The damage factors are reduced by 69.67% compared with CD. In addition, the scale-span FE model was shown to replicated the drilling process effectively.     Defect suppression mechanism of the drilling hole using the TDR bit  Illustration of LTC-RUAD using TDR Figure 6 Moving trajectory of TDR Figure 7 Scale-span FE drilling schematic diagram Comparison of the thrust force using CD and LTC-RUAD Figure 10 Setup showing the FE model of drilling CFRPs using LTC-RUAD Figure 11 Comparison of the maximum average thrust force and deviation     Comparison of the delamination and deviation