Experimental research on new hole-making method assisted with asynchronous mixed frequency vibration in TiBw/TC4 composites

With the gradual promotion and the application of difficult-to-machine materials such as titanium matrix composites in the aerospace field, high-quality hole-making technology has become a major demand in aviation manufacturing. In order to improve the hole-making quality of TiBw/TC4 composites, asynchronous mixed frequency vibration-assisted hole-making (AMFVAHM) method is proposed. The process consists of two steps: ultrasonic vibration-assisted drilling (UVAD) base hole and low-frequency torsional vibration-assisted helical milling (LFTVAHM) target hole. Based on this process, the cutting trajectory modeling is established, and the hole-making experiment on TiBw/TC4 composites is conducted. The experimental data show that during the hole expansion stage, the maximum XY-plane average milling force decreases by 30.96% and the maximum axial average milling force decreases by 24.49% compared with conventional helical milling (HM) when the torsional vibration frequency and the milling frequency are the same in LFTVAHM. The hole-making experiment shows that AMFVAHM can reduce the chip size, tool wear, and some other defects such as entrance/exit burrs, scratches, and fractures of the hole wall. Comparing with HM and UVAD, the verticality of hole wall increases by 71.43% and 86.21%, the inlet damage decreases by 27.98% and 31.60%, the outlet damage decreases by 2.80% and 14.47%, the hole wall roughness (Ra) decreases by 36.29% and 63.43%, and the maximum white layer thickness decreases by 19.99% and 67.66%. Meanwhile, AMFVAHM process not only reduces the cutting force and cutting temperature but also improves the hole-making quality due to the fretting friction effect of LFTVAHM in secondary hole expansion, which meets the need for high-quality hole-making of difficult-to-machine materials in practical engineering applications.

D 1 Base hole diameter (mm) d 1 Twist drill diameter (mm) r 1 Twist drill radius (mm) ρ 1 Ultrasonic vibration range (μm) A 1 Ultrasonic vibration amplitude (μm) f 1 Ultrasonic vibration frequency (Hz) t Time (s) D 2 Target hole diameter (mm) R 2 Target hole radius (mm) d 2 End mill diameter (mm) r 2 End mill radius (mm) ρ 2 Low-frequency torsional vibration angle (rad) A 2 Low-frequency torsional vibration amplitude (rad) f 2 Low-frequency torsional vibration frequency (Hz) O T X T Y T Z T UVAD 3D cutter coordinate system n 1 Rotation speed of twist drill (r/min) θ Rotation angle of twist drill (rad) f v Feed speed of twist drill (mm/min) r Radius from point O T to point A 1 (mm) O W X W Y W LFTVAHM 2D workpiece coordinate system O C X C Y C LFTVAHM 2D cutter coordinate system e End mill eccentricity (mm) α Angle of rotation of point B relative to O C X-C Y C without torsional vibration (rad) β The angle of O C X C Y C relative to O W X W Y W revolution without torsional vibration (rad)

Introduction
TiBw/TC4 titanium matrix composites are one of the most crucial groups of metal materials for aviation, aerospace, and automobile industries, benefit from their high specific stiffness, high specific strength, excellent mechanical properties at high temperatures, and wear resistance [1]. However, 70% of fatigue failures of composite components are caused by defects in hole-making which contain cracks, burrs, scratches and other defects for the anisotropy of TiBw/TC4 composites [2], and it is also accompanied by drastic wear of the tool which affects the performances, production costs, and the wide application of composite components [3]. Scholars have found that under specific cutting conditions, the surface quality of metal matrix composites in wet cutting is worse than that in dry cutting due to higher matrix strength. During wet cutting, the reinforcing phase is easily removed by fracture or extraction, thus leaving more micro-holes, micro-cracks, and other defects on the machined surface [4]. Therefore, the theory and technology of hole-making under dry cutting conditions have received a lot of attention from scholars. Currently, there are four main methods of dry cutting hole-making for metal matrix composites: (1) Conventional drilling is the most commonly used hole-making method in the manufacturing field due to its high productivity and low cost and its ability to meet most of the machining requirements of the parts in terms of selecting tools and optimizing machining parameters, while it is difficult to avoid delamination defects effectively by conventional drilling because the critical axial force required for delamination defects during conventional drilling is low [5,6]. (2) Core drilling provides a more efficient method for machining bigger deeper holes compared to conventional drilling by optimizing the process parameters and the performance parameters of the brazed diamond core drill. This method reduces the required drilling force and provides better surface finish and less drill wear. While the core drill cannot achieve efficient continuous processing due to its dynamic unbalance and stopping dedusting [7,8].
(3) Special machining technologies consist of three main methods: EDM machining [9], laser machining [10], and ultrasonic machining [11]. These methods are mainly used for processing micro-holes or microstructures, but their efficiency for processing composite holes with diameters between several millimeters to dozens of millimeters is low. (4) Helical milling process is a new type of hole-making technology also known as "milling instead of drilling." During the helical milling process, the tool proceeds through a helical path while rotates around its own axis. Due to the flexible kinematics of the tool, helical milling mainly removes material through side edges, which reduce cutting temperature and cutting force and solve the problem of interlayer delamination of composite materials for better surface quality [12], while the side edges of the milling cutter are highly susceptible to wear when applied to highspeed machining [13,14].
To further improve the quality of hole-making and reduce tool wear, scholars have adopted a novel machining process called vibration-assisted machining and found that it is an effective method to solve the machining problems of high-quality holes and small-diameter deep holes in composite materials. In recent years, ultrasonic vibration-assisted hole-making has developed rapidly. Feng Y. et al. [15] analyzed the law of axial force by conducting experiments on hole wall integrity of UVAD of TiBw/TC4 composites. The results show that UVAD can reduce the hole wall residual stress, white layer thickness, and hole wall roughness by 4.67 ~ 16.31%, 42.48%, and 5.98 ~ 29.27% respectively compared to conventional drilling. The number and size of hole wall defects are also significantly reduced. Amini S. et al. [16] experimentally investigated the performance of longitudinal-torsional vibration in ultrasonic assisted drilling of Al 7075-T6 with HSS tool. The results show that the increase in rotational speed reduces the maximum torque and thrust force by 36% compared to conventional drilling, and the increase in feed rate intensifies the maximum torque and force values by 35%. This method also improves the surface quality of holes. Chen G. et al. [17] conducted a comparative study for geometrical topography and surface integrity of Ti-6Al-4 V alloy by helical milling and ultrasonic vibration helical milling (UVHM) to investigate the geometric and mechanical behavior of their machined holes. The experimental results show that the compressive residual stress of hole surface increases more than 63.5% by UVHM compared with helical milling, and the hole-diameter error and surface roughness are reduced, while the impact effect between the cutting edge and machined surface makes the tool wear larger. Through comparative experiments on fiber removal, Liu J. et al. [18] modeled the cutting trajectory, velocity, acceleration, and the effective rake angle of peripheral cutting edge in the processes of helical milling, axial ultrasonic vibration helical milling(A-UVHM), and longitudinal and torsional ultrasonic vibration helical milling (LT-UVHM) according to kinematics and metal cutting principles. The study shows that the axial forces of A-UVHM and LT-UVHM are reduced by 9.0 ~ 35.7% compared to helical milling. This is caused by the axial longitudinal and torsional vibration helping to fracture fibers and generate better surface quality. Low-frequency vibration-assisted hole-making is another emerging hole-making method. Yang H. et al. [19] proposed a novel analytical model that predicts the low-frequency vibration-assisted drilling (LFVAD) thrust force and torque by incorporating the vibration amplitude and frequency correction, drill working angle, drilling forces within different cutting lip positions, and their transformation into thrust force and torque. The drilling experiments on Ti-6Al-4 V titanium alloy show that, the prediction error of maximum thrust force, maximum torque, mean thrust force, and mean torque can reach 12%, 9%, 6.5%, and 10.1% respectively. Hou Y. J. et al. [20] proposed a new process for the fabrication of a Ti-6Al-4 V-alloy trapezoidal thread using low-frequency torsional vibration extrusion (LTVE) through a forming tap and established a semi-analytical model of torsional vibration extrusion with friction. The total amounts are determined quantitatively by studying the influence of low-frequency torsional vibration on the form tapping torque. The above studies show that vibration-assisted machining technology is an effective method for highquality machining of composite components, which significantly reduces surface roughness, cutting force, and cutting temperature; in comparison, the intermittent cutting method with no separation of tool and workpiece during low-frequency torsional vibration-assisted machining makes chip breaking and chip removal more effective, which helps alleviate tool wear and remove workpiece burrs.
The above researches show that ultrasonic axial vibration-assisted machining can remove most of the processing material and ensure the processing efficiency; low-frequency torsional vibration-assisted machining can make the chip size smaller and effectively solve the problem of tool wear and tip ablation due to the pulse-type transient alternating characteristics of the cutting force. This paper concludes that the combination of base hole drilling assisted with ultrasonic vibration and hole expansion by helical milling assisted with low-frequency torsional vibration will suppress the hole-making defects of the reinforcement and the matrix material. Therefore, AMFVAHM technology is proposed as shown in Fig. 1. Currently, few studies have been conducted on LFTVAHM and AMFVAHM. The lack of theoretical model and experimental study cannot guide the optimization of process parameters. In this paper, we conduct theoretical and experimental research on the AMFVAHM process to investigate its hole-making mechanism and process effect which can provide theoretical guidance and basic data for the development and application of new materials and new processes.

Process method of AMFVAHM
AMFVAHM technology includes ultrasonic vibrationassisted drilling (UVAD) base hole and low-frequency torsional vibration-assisted helical milling (LFTVAHM) target hole. The process is illustrated in Fig. 1.
Firstly, the base hole with a diameter of D 1 is drilled at the rotation speed n 1 , and the feed speed f v by twist drill with a diameter of d 1 under the assistance of ultrasonic axial vibration with a vibration frequency of f 1 and an amplitude of A 1 . Variation of the amplitude of ultrasonic axial vibration ρ 1 with time can be expressed as Eq. (1), where A 1 is the ultrasonic vibration amplitude, f 1 is the ultrasonic vibration frequency, and t is the time.
Then, the helical hole-milling process with an eccentric distance of e is carried out by the end mill with a diameter of d 2 and is assisted with low-frequency circumferential torsional vibration under a vibration frequency of f 2 and amplitude of A 2 . Technological parameters employed are the cutter rotation speed of n 2 , a revolution speed of N, and a lead pitch of a p . Finally, the target hole with a diameter of D 2 can be machined. The low-frequency torsion vibration angle ρ 2 of the workpiece changes with time following the rules as shown in Eq. (2), where A 2 is the amplitude of low-frequency torsional vibration and f 2 is the frequency of low-frequency torsional vibration.

Kinematics of base hole drilling assisted with ultrasonic vibration
Compared with conventional drilling (CD), the UVAD process superposes the ultrasonic axial vibration based on the rotary motion and the feed motion of the conventional drilling process.
To facilitate the analysis of the motion trajectory of the drilling process, it is assumed that the workpiece is a fixed part, and the twist drill tip is taken as the origin to establish the cutter coordinate system (O T X T Y T Z T ), as shown in Fig. 2. The cutting edges of the twist drill include the chisel edge and the main cutting edge, while point A of the outer edge of the main cutting edge is selected for motion analysis.
As shown in Fig. 2, it is assumed that the rotation angle of point A relative to the Y T axis is θ. Then, the relationship between the rotation angle θ and time t can be expressed as Eq. (3).
Assuming that the initial value of the axial coordinate (Z-direction) of point A is 0, the motion equation of point A at the outer edge of the main cutting edge in conventional drilling can be expressed as Eq. (4).
Since the UVAD process superimposes ultrasonic axial vibration on conventional drilling, the motion equation of point A on the outer edge of the main cutting edge during the UVAD process can be expressed as Eq. (5).

Fig. 2 O T X T Y T Z T coordinate system
Point A of the cutter's outer edge of the main cutting edge in two machining technologies is selected for kinematic simulation. The motion trajectory of point A in CD is a helical line shown in Fig. 3a, while the one in UVAD is shown in Fig. 3b, which is formed by the superposition of the helical line and sinusoidal curve.

Kinematics of hole expansion by helical milling assisted with low-frequency torsional vibration
The workpiece coordinate system (O W X W Y W ) and the cutter coordinate system (O C X C Y C ) shown in Fig. 4 are used to character ize the related parameters. The end mill tip, point B, is selected for the motion analysis.
The eccentric distance between the center of the end mill and the center of the target hole is denoted as e. The eccentric distance of the end mill based on the geometric relations is shown in Eq. (6).
The end mill revolution speed based on the operation relation is shown in Eq. (7).
The axial feed speed of the end mill is shown in Eq. (8).
It is assumed that the initial value of the axial coordinate (Z-direction) of point B is zero and the cutter point B starts to machine the workpiece from the Y W axis and Y C axis at the initial position. The angle between BO C and Y C axis (i.e., the rotation angle during the period of 0 ~ t) is denoted as α, and the angle between O C O W and Y W axis (i.e., the revolution angle during 0 ~ t) is denoted asβ, as shown in Eq. (9).
The motion equation of point B of conventional helical end mill in the cutter coordinate system O C X C Y C can be expressed as Eq. (10).
Since LFTVAHM is superimposed with circumferential vibration assistance based on conventional helical milling, the relative position of cutter coordinate system O C X C Y C to the workpiece coordinate system O W X W Y W is shown in Eq. (11).
After coordinate transformation, the motion equation of point B in the workpiece coordinate system O W X W Y W during LFTVAHM is shown in Eq. (12).  3 Experimental procedure

Material preparation
The TiBw/TC4 composite material is synthesized by adding the reinforced phases into the titanium alloy matrix by employing powder metallurgy and in situ synthesis [21]. In this study, TC4 powder of 85 ~ 125 μm (with an average particle size of 110 μm) is selected to prepare the TiBw/TC4 composite material at volume fraction of 8.5%. The composition information of the composite material is provided in Table 1.

Workpiece preparation
As shown in Fig. 6, the columnar TiBw/TC4 composite material with a diameter of 142 mm (Fig. 6a) is cut into cuboid-like bulk workpieces with dimensions of 130 mm (length) * 30 mm (width) * 8 mm (thickness) (Fig. 6c) by a wire cutting machine (Fig. 6b). The spacing between the base points of the hole machining axis is 20 mm to avoid defect fields and mutual influence of high-temperature cutting heat during hole machining.

The experimental device
The experimental devices of AMFVAHM are shown in Fig. 7. The main machining platform is VMC-C30 five-axis CNC machining center. The ultrasonic vibration handle is installed on the spindle of the machine tool, and SZ12 ultrasonic vibration control device is externally connected. The K-thermocouple encapsulated by a ceramic tube is embedded in the TiBw/ TC4 workpiece through the temperature measuring groove. The installation position is shown in Fig. 8. The hole-making temperature is collected in real-time by DH5922N dynamic signal analysis device. The workpiece is fastened to the custom-made low-frequency torsional vibration platform by a vise. The vibration platform can achieve low-frequency torsional vibration of 0 ~ 33 Hz through servo control, and the torsional angle accuracy can reach ± 0.029°. The workpiece, vice, and vibration platform are jointly installed on Kistler9272force sensor, and the cutting force of drilling base holes and expanding holes obtained by milling are measured in real-time by the Dynoware software.
The experimental conditions and process parameters are shown in Tables 2 and 3, respectively.

Temperature calibration experiment
As shown in Fig. 9a, the workpiece is heated by an external intelligent heating table according to experimental conditions, and the temperature of the workpiece is measured (at the indoor temperature of 5 °C). The temperature is measured when the heat exchange becomes stable. Linear fitting is carried out according to the voltage value corresponding to the sampling point, and linear rules between the voltage and temperature are obtained by fitting as shown in Fig. 9b. Finally, we get the voltage-temperature equation as shown in Eq. (15).

Effect of process parameters on axial force of UVAD
Through the orthogonal experimental scheme provided in Table 4, the maximum axial force surface is obtained, where the maximum axial force is taken from the maximum average drilling axial force after filtering as shown in Fig. 10. The influence rules of the drill rotation speed n 1 and the drill feed speed f v on the axial drilling force are then analyzed. As shown in Fig. 11a, when the drill rotation speed is constant, the axial drilling force increases with the drill feed speed. The main reason is that with the increase of the drill feed speed, the cutting quantity of the cutting edge per unit time increases, which increases the axial force   with the increase of the feed speed. As shown in Fig. 11c, when the drill feed speed is constant, the drilling force shows a decreasing trend with an increase in the drill rotation speed.

Effect of process parameters on drilling temperature of UVAD
Combined with the temperature nominal curve shown in Fig. 9b, the temperature curves during UVAD under different process parameters can be obtained. The influence rules of rotation speed n 1 and feed speed f v on drilling temperature are then analyzed. As shown in Fig. 12, the change of temperature curve shows an increasing trend similar to the inverse tangent curve. For a constant drill rotation speed, the higher the drill feed speed, the higher the drilling temperature. When the drill feed speed is constant, the higher the drill rotation speed, the higher the drilling temperature.

Effect of process parameters on cutting force of LFTVAHM
Through the orthogonal experiment shown in Table 5, we obtained their milling force curves, Fig. 13 as one of them, which compared experimentally measured cutting forces of LFTVAHM and HM under the same processing parameters during the same period. Figure 13a shows the curves of the measured cutting forces during conventional helical milling under the process parameters of n 2 = 300 r/min, f t = 0.03 mm, and a p = 0.3 mm. Figure 13b shows the curves of the measured cutting forces during LFTVAHM under the process parameters of n 2 = 300   r/min, f t = 0.03 mm, a p = 0.3 mm, A 2 = 0.38°, and f 2 = 25 Hz. It can be concluded that, compared with conventional helical milling, in the LFTVAHM process, an air cutting phenomenon occurs due to the periodic separation between the cutter and the workpiece. Therefore, the instantaneous cutting thickness is zero, resulting in an instantaneous cutting force of 0, which intuitively manifests as the decline of the force in the X/Y direction to the zero scale line, as shown in Fig. 13b2. The cutting force may fluctuate greatly due to the existence of low-frequency torsional vibration, while it is found that the low-frequency torsional vibration can effectively reduce the average cutting force peak under the same process parameters according to the analysis of the filtering results as shown in Fig. 13a2, b2. The maximum milling force surface is experimentally obtained via the orthogonal experimental scheme provided in Table 5. The maximum XY-plane (the resultant force of Xand Y-direction forces) and axial (Z-direction) average milling force surfaces are shown in Figs. 13b and 14b. The influence rules of tangential feed per tooth f t and lead pitch a p on XYplane and axial milling force are then analyzed. As shown in Figs. 14a and 15a, when the lead pitch is constant, the XYplane and axial milling force increases with the tangential feed per tooth because larger tangential feed per tooth lead to higher cutting amount of end mill side edge per unit time. As shown in Figs. 14c and 15c, when the tangential feed per tooth is constant, the XY-plane and axial milling force increases with the lead pitch. An increase in the lead pitch increases the chip thickness of the single-tooth side edge of the end mill, thus increases the milling force in all directions.
In order to further analyze the influences of the characteristic frequency f 2 of low-frequency torsional vibration on the XY-plane milling force, four groups of interpolation experiment are applied. As shown in Table 5, a low-frequency torsional vibration frequency of 0, 15, 20, and 25 Hz is set for each experiment, respectively. The tangential feed per tooth The variation curves of milling force under different torsional vibration frequencies are obtained after analysis and filtering. The maximum XY-plane (XY-plane direction) and axial (Z-direction) average milling forces are obtained after extracting the peak value of resultant force of X-and Y-direction forces and the peak value of Z-direction force, as shown in Fig. 16.
It can be concluded that the low-frequency torsional vibration effectively reduces the XY-plane milling force. The decrement of the XY-plane milling force is the largest when synchronous frequency torsional vibration is applied, which effectively reduce the milling force by 30.96% compared to when there is no torsional vibration. However, the low-frequency torsional vibration has a minor influence on the axial milling force, and the axial milling force under the synchronous frequency torsional vibration decreases by 24.49% compared to when there is no torsional vibration.

Effect of process method on hole-making temperature of LFTVAHM, HM, and UVAD
In combination with the temperature nominal curve shown in Fig. 9b, the temperature curves of LFTVHM under different process parameters can be experimentally obtained.
The comparison results of the three processes are shown in Fig. 17. Due to the specificity of the helical milling process, the cutting temperature for LFTVAHM and HM is 94.2% lower than that for UVAD. The hole-making temperature for LFTVAHM is slightly higher than that for HM since the low-frequency circumferential torsional vibration in LFT-VAHM enhances the secondary friction in the meantime of hole-expanding, which results in a slightly higher instantaneous cutting temperature for LFTVAHM than the cutting temperature for HM.

Influence laws of different hole-making process on hole quality
In order to explore the influence laws of different holemaking process on hole quality and further analyze the hole-making effect of the asynchronous mixed frequency vibration hole-making process, we selected three processes to compare: asynchronous mixed frequency vibrationassisted hole-making (UVAD + LFTVAHM), conventional helical milling (UVAD + HM), and ultrasonic vibrationassisted drilling (UVAD). The specific processing parameters are shown in Table 6, in which the best drilling parameters of UVAD are used [15].

Tool wear and chip form
The tool wear after hole-making by the three processes is tested by a Navitar 12X optical microscope. As shown in Fig. 18, the wear of the main cutting edge of the drill during UVAD is very serious, and the maximum wear width reaches 0.634 mm. The wear width of the side edge of the end mill of LFTVHM (0.091 mm) is slightly smaller than that of HM (0.137 mm). The low-frequency torsional vibration achieves periodic contact/separation between the cutter and the workpiece, which improves the heat dissipation condition of the cutter and effectively avoids the cutter-sticking phenomenon.
Next, the chip morphology of the three hole-making processes is detected, as shown in Fig. 19, the chip size of LFTVHM is the smallest, and the chips have shapes of small debris with regular small serrated edges. For HM, the chips have shapes of large debris, and the chip edges have some tear fracture cracks. Chips generated by UVAD are mainly short and fine filamentous chips, while the enlarged chip unit shows a fan-shaped fold.

Hole shape and verticality of hole wall
The hole shape and entrance/exit burr of the three processes are also tested by the Navitar 12X optical microscope. As shown in Fig. 20, LFTVHM is characterized by the microfrictional effect, the hole circumference of AMFVAHM is smooth, and there is almost no burr at the hole entrance/exit. For conventional helical milling, the hole circumference is slightly broken, and there are some burrs at the local position of the entrance/exit. For UVAD, the hole circumference shows an obvious fracture morphology with a maximum A Hexagon Metrology trilinear coordinates measuring machine (CMM) is used to measure the verticality of hole-making along the hole wall for both the positive and negative sides. Figure 21 presents the hole-making verticality indices of the three processes. When detecting from the upper positioning plane, the hole-making verticality indices of LFTVHM, conventional helical milling, and UVAD are 0.018, 0.042, and 0.090 mm, respectively. When detecting from the lower positioning plane, the holemaking verticality indices are 0.012, 0.042, and 0.087 mm, respectively. In general, the assistance of low-frequency torsional vibration plays a role in friction leveling on the side wall with uneven verticality. Consequently, the holemaking verticality of the AMFVAHM process is optimal, i.e., it is increased by 71.43% and 86.21% compared with HM and UVAD.

Micromorphology of entrance/exit and hole surface
Keyence VK-X100 shape measurement laser microscope is used to detect the microscopic morphology of hole entrance/exit after hole-making via three processes. As shown in Fig. 22 and 31.60%, respectively, and its hole exit damage is reduced by 2.80% and 14.47%, respectively. Next, the micromorphology and surface roughness of the hole wall after hole-making by the three technological processes are measured. As shown in Fig. 23, the roughness values by asynchronous mixed-frequency vibration hole-making are R a = 0.892 μm and R q = 1.123 μm, respectively. Compared with conventional helical milling, the roughness values decrease by 36.29% and 36.27%, respectively. Lastly, the same values are decreased by 63.43% and 60.68%, respectively, compared with UVAD.

White layer thickness of hole surface
The white layer [22] thickness of the hole wall under the three technological conditions is measured by a JSM-6360LV scanning electron microscope (SEM) and a GENESIS2000XMS60 energy dispersive spectrum analyzer (EDS). As shown in Fig. 24, the white layer obtained by UVAD is the thickest and discontinuous, with a maximum thickness of 33.43 μm. The white layer obtained by conventional helical milling is thinner and continuous, with maximum thickness of 13.51 μm. Due to the assistant effect of low-frequency torsional vibration, the motion state of periodic contact/separation between the cutter and the workpiece improves the heat dissipation condition. Furthermore, the white layer obtained by LFTVHM is the thinnest and discontinuous, with a maximum thickness of only 10.81 μm. The thickness of this layer decreases by 67.66% and 19.99%, respectively, compared with the maximum thickness values of the other two processes.

Conclusions
In this study, we theoretically analyzed two steps of asynchronous mixed-frequency vibration holemaking (AMFVAHM): ultrasonic vibration-assisted dr illing (UVAD) and low frequency torsional vibration-assisted helical milling (LFTVAHM). Three different hole-making processes of TiBw/TC4 composites are examined experimentally. Experimental studies on the hole-making process of TiBw/TC4 composites are carried out for three different processes. The main conclusions are as follows.  (1) According to the kinematic mechanism, the cutting trajectory models of UVAD and LFTVAHM are established, which clearly shows the hole-making mechanism and the special form of movement of AMFVAHM. (2) In the process of LFTVAHM, the tool and the workpiece have the motion state of cutting and separating due to the unique motion characteristics of low-frequency torsional vibration, which leads to the situation that the X/Y direction milling force is instantaneously zero during the milling process.
(3) In the process of AMFVAHM, a large number of materials are removed during UVAD for basic hole, making the cutting force of the LFTVAHM decreased greatly. LFTVAHM effectively reduce the XY-plane milling force in the process of helical milling, when the torsional vibration frequency is the same as the cutting frequency of the tool, the XY-plane milling force is reduced by 30.96%, and the axial milling force is reduced by 24.49% compared with helical milling without torsional vibration. (4) In the secondary hole expansion process of AMFVAHM, the chip size is further reduced, and there is reciprocating friction movement between the tool and the hole  wall which have the effect of secondary grinding to a certain extent due to the unique motion characteristics of low-frequency torsional vibration. At the same time, it also helps to reduce the burr defects, scratches, tears, and crushing of the hole wall, and tool wear. Compared with the HM process and UVAD process, the verticality is improved by 71.43% and 86.21%, the maximum height at entrance edge is decreased by 27.98% and 31.60%, the maximum height at exit edge is decreased by 2.80% and 14.47%, the maximum thickness of white layer is decreased by 19.99% and 67.66%, and the roughness (R a ) is decreased by 36.29% and 63.43%.
Author contribution All authors contributed to the study conception and design. All authors read and approved the final manuscript. Data availability The datasets generated during and/or analyzed during the current study are not publicly available, but are available from the corresponding author on reasonable request.

Code availability
The code that supports the findings of this study is available from the corresponding author upon request.

Declarations
Consent to participate All authors agreed to participate in the submission. Written informed consent was obtained from all the participants prior to the enrollment (or for the publication) of this study.

Consent for publication
All authors approved the final manuscript and the submission to this journal.

Competing interests
The authors declare no competing interests.