Study on the mechanism affecting the quality of micro-hole in ultrasonic-assisted drilling of high-speed circuit boards

High-speed circuit boards are created to meet the high-speed signal transmission requirements of 5G communication technology, but the non-polar resins, flat glass fibers, and multiple and hard fillers used for this purpose have posed new challenges to their micro-hole processing. The quality of micro-hole has always been a decisive factor in board performance. Therefore, this paper aims at proposing a new processing method for improving the micro-hole drilling quality of high-speed circuit boards. By establishing an ultrasonic-assisted drilling tool motion model, analyzing the changes in drilling method, material deformation, chip breakage, and chip removal during ultrasonic-assisted drilling of printed circuit boards, the influence mechanism on micro-hole quality during ultrasound-assisted drilling is studied prudently. Besides, an experimental platform for ultrasonic-assisted drilling is designed and built, and single-factor experiments for verification of ultrasonic effects, optimization of drilling parameters, and orthogonal experiments for ultrasonic-assisted drilling of high-speed circuit boards are conducted on this platform. The experimental results show that the loading of ultrasonic vibration has made an obvious improvement on several machining defects including hole wall roughness, entrance burr, and nail head in micro-hole drilling of high-speed circuit boards. In addition, the influence order of each processing parameter and a better combination of them are discovered, which provides a theoretical research basis and instructions for the improvement of micro-hole quality of high-speed circuit boards.


Introduction
Printed circuit boards (PCBs) generally rely on metallized micro-holes for electrical connection of different line layers, so it is necessary to drill the required size of micro-hole on PCBs through mechanical processing, and then plating conductive copper layer on the insulating hole wall by copper plating process to achieve the purpose of metallization conduction.
In order to meet the high-speed signal transmission requirements of 5G communication technology, a highspeed circuit board with lower dielectric constant (Dk) and dielectric loss (Df) values than ordinary printed circuit board has come into being. However, changes in the material of this high-speed circuit board have raised new challenges to micro-hole processing. Therefore, it is an important issue to study the micro-hole drilling for high-speed circuit boards and to ensure that their processing quality can meet the emerging requirements as the 5G communication technology is developing.
PCBs generally rely on metallized micro-hole to electrically connect different circuit layers, so the quality of micro-hole has always been the focus of scholars' attention. Zhu [1] summarized the technology development direction of high-speed circuit boards and the current status of raw material selection and application, which provides the basis for the processing mechanism research of high-speed circuit boards. Ko, Chang [2] centered their research on micro-hole burrs and proved through experiments that the step drill is effective in improving the generation of micro-hole burrs. Bhandari, Hong [3] designed an experiment (DOE) technique which based on the Taguchi method and figured out the most significant drilling parameter affecting burr height.
The results show that the drill diameter makes a statistically significant contribution to burr-height variation. Song, Fu [4] found that tool wear also reduces the hole accuracy of PCB drilling, which eventually leads to an increase in burr height and nail head. Hidehito et al. [5] experimentally verified the correlation between the radial runout of the drill and the micro-hole quality. Sahoo, Thakur [6] applied finite element analysis (FEA) in deformation and stress simulation to obtain the effect of feed rate on various parameters of micro-hole quality during PCB drilling. Other scholars have studied from the perspective of drills, such as Wang, Zou [7] who developed their own Ti-based cermet micro-drills for PCB hole processing. With the development of communication technology, high-frequency and high-speed circuit boards are taking up an increasing share of the market. [8] Therefore, many scholars also begin to study the processing of high-speed circuit boards. Yan Bing et al. [9], aiming at the characteristics of the chip morphology of high-speed circuit board, which is short curved and long spiral, increased the drilling angle of the micro drill to reduce the first rear angle, and finally effectively reduced tool wear and hole wall roughness, so as to improve the quality of the micro-hole. However, the drill is a processing consumable, and the way to enhance its cost to improve the hole quality is not as good as improving the processing method in terms of economic benefits. In addition, the research on high-speed circuit board processing is still relatively scattered and needs to be further improved.
Ultrasonic-assisted machining technology is a kind of processing technology in which the force is acted regularly in the form of high frequency pulse [10]. This kind of processing method has a relatively good technological effect, so many scholars have conducted in-depth research on it, in order to guide the application of various processing and molding [11]. As early as the twentieth century, Junichiro Kumabe [12] discovered that this technology has a relatively excellent process effect because the cutting edge is periodically separated from the workpiece during machining, and there is also a static effect (displacement does not change with time) and rigidity effect of the drill bit (the pulse force improves the drill's ability to resist bending deformation). Zhang and Wang [13] also made significant contributions to the machining mechanism by experimentally demonstrating that vibratory drilling can also result in local chip breakage under certain conditions in zero phase difference and its neighborhood. The study of Brehl and Dow [14] helped to explain the basic kinematic relationships of vibratory tool trajectories and described how intermittent cutting mechanisms can reduce machining temperatures and extend tool life. Ma [15] explained the variable speed cutting, variable thickness cutting, variable angle cutting, and separation impact characteristics of the vibratory drilling process. In terms of applied research, Mikhailova, Onawumi [16] applied ultrasound-assisted technology to marble drilling, and it is found to reduce part damage due to machining. Baraheni and Amini [17] applied it to drilling of glass fiber reinforced plastics, and studied and improved drilling parameters. Shao, Jiang [18] applied it to carbon fiber composite material drilling and found that it can effectively improve the processing quality of drilling. MA, Kang [19] et al. also applied ultrasound-assisted technology to the processing of carbon fiber composites and investigated the effect of load on tool vibration amplitude. All these studies proved that ultrasonic-assisted drilling technology can improve the quality of drilling. Other scholars have taken another approach, Yuan, Wei [20] placed the ultrasonic vibration process after machining and used a tool head loaded with ultrasonic vibration to remove the burrs generated in deep holes, blind holes, cross holes, and other machining locations. Liu, Chen [21], on the other hand, used electrolytic rotary ultrasonic-magnetic composite machining technique to remove burrs from the hole edges of TC4 titanium alloy, and the hole roughness was also significantly reduced. It can be seen that ultrasonicassisted drilling in a single material and common size hole processing has a strong research base, but the field of PCB processing has a special nature, the impact of micro-hole, composite materials, and size effect on ultrasonic-assisted processing need further research.
The non-polar resin, flat glass fiber, and multiple and hard fillers used in high-speed circuit boards have all led to a more difficult micro-hole processing. Therefore, this paper conducts a study with the aim of improving the micro-hole quality of high-speed circuit boards and proposes a new processing method for the poor micro-hole drilling quality of high-speed circuit boards by applying ultrasonic-assisted drilling technology to PCB micro-hole processing. The specific research includes the mechanistic study and experimental study of ultrasonic-assisted drilling of high-speed circuit boards, discovers the influence mechanism of each processing parameter on the quality of micro-hole processing, and provides theoretical guidance for the actual processing of high-speed circuit boards.

Research on machining difficulties and defects of high-speed circuit board
High-speed circuit board compared to the ordinary plate has a lower Dk, Df, and printed circuit board Dk, Df values are generally around to reduce the resin system, packing system, glass fiber system and copper foil system is improved, the main characteristics can be summarized as low profile of the copper foil, nonpolar resin, flat glass fiber, and more hard packing, the influence of each material on processing is analyzed as follows.

Resin
The insulation part of PCB substrate contains resin and glass fiber cloth, and the Dk value of glass fiber is generally high. Therefore, in order to obtain a low Dk value of the plate, the resin material with low Dk should be selected. Resin material Dk, Df values mainly by its molecular structure, purity, and water absorption rate of these three aspects, one of the polarity of the molecular structure is the most critical factors, so the design or selection has less polar groups, low polarity chemical bonds, with large volume of polymer and highly symmetrical structure of the resin is a common way to reduce the Dk, Df. Commonly used in Dk, Df resin structure polytetrafluoroethylene (PTFE), cyanate (CE), and polyphenyl ether (PPO), etc., its comparison with ordinary sheet is shown in the following table (Table 1). Although these resin materials improve the transmission performance of the circuit board, their low activity makes the resin reaction and degluing more difficult, and also brings difficulties to drilling. This type of resin tensile degree is low, and by the impact of drilling heat, so the chip has greater adhesion; on the one hand, it is easy to adhere to the wall of the micro-hole, after the completion of drilling cooling formation of drilling dirt, resulting in the rise of the rough wall of the hole. On the other hand, it is easy to mix with copper foil chip, broken glass fiber, resulting in chip winding defects, but also lead to chip removal difficulties, and even the occurrence of micro-hole blockage.

Copper
The choice of copper foil material in high-speed circuit board will also affect its performance. This is mainly due to high speed signal transmission with extremely fast switching frequency signal, which can make the wire produced electromagnetic induction, in particular, the center conductor cross section position of the inductance is larger, as shown in Fig. 1, which greatly reduce the throughput of signal or in the center of the current, and through a wire transfer or current signal, most has focused on the conductor of the skin. This phenomenon is called "skin effect," also called "epidermal effect." The skin effect causes the actual thickness of the skin used for transmission to become very thin, increasing the resistance and ultimately leading to increased losses. Therefore, in order to reduce the signal loss, low profile copper foil should be selected, that is, the roughness Rz should be particularly low; less than 2.0 μm low rough copper foil can meet the requirements.
Low profile copper foil itself does not have a great impact on drilling processing, but its binding force with resin layer is poor. In addition to common poor processing phenomena in PCB processing, such as burr and nail head, it is easier to produce inter-layer separation defects, and even inner interconnect failure (ICD). Therefore, the use of low profile copper foil will indirectly cause the decline of the quality of micro-hole processing.

Fiberglass cloth
Although fiberglass cloth has become a "drag" in terms of Dk and Df values, changing its content and type can also change the performance of the overall board. In the traditional FR-4 plate, non-alkali glass fiber E-glass is used, and then a new type of NE-glass is developed to improve its performance. The Dk value drops to 4.6, and the Df value drops to 0.0007. This type of glass fiber has been used in batches. In addition, according to different needs can also choose different glass fiber cloth such as Q-glass, quartz fiber, polymer polypropylene, etc. (Fig. 2). The polarity is low, the drilling and milling glue slag is difficult to remove, and the halo is large In general, the glass fibers used in high-speed circuit boards tend to be thinner and thinner, so flat glass fibers are used to compress their thickness. The flat glass fiber has a higher load level, reduces the friction between the resin, and increases the viscosity, but because of its stability, the drilling resistance is increased, that is, the cutting resistance is increased, which will accelerate the wear of the micro drill. The wear of the micro drill will lead to the decline of its processing performance, so that its processing ability of glass fiber becomes weaker and more burrs appear, or indirectly affect the hole wall roughness and hole position accuracy.

Packing
In addition to this, there are many changes in packing in high-speed circuit boards. The first is the rise of its weight ratio, up to 60 ~ 70%. Secondly, the shape and structure of the filler changed, and the superfine and spherical filler particles appeared. Then there are changes in packing types, such as the use of inorganic packing can get better heat dissipation performance, the Dk value is also smaller. High-speed circuit board commonly used filler aluminum hydroxide, silicon powder, talcum powder, and so on.
The biggest impact of filler on drilling processing is for micro drilling, because the number of filler increases and the hardness increases, so micro drilling is more likely to wear when drilling high-speed plate. When the edge of micro drilling decreases, the subsequent processing of micro-holes will appear more burr, nail head, hole wall rough, and other processing defects.
Above all, high-speed circuit board in the resin, copper foil, glass fiber and filler have changed, which makes the high-speed PCB drilling difficulty increases; the pore defects summary is shown in Fig. 3; the specific number of burr, burr and nail head length increases, the chip winding and microporous congestion frequency increases, tool wear faster, easier to ICD. Therefore, in order to improve the quality of micro-hole processing of high-speed printed circuit boards, these problems need to be solved.

Study on the tool trajectory variation of ultrasonic-assisted drilling
In order to solve the processing difficulties of high-speed circuit board and improve its micro-hole quality, this paper innovatively introduces ultrasonic vibration-assisted technology into the drilling of printed circuit board. In order to clarify the improvement effect of ultrasonic vibration assistance technology on drilling, it needs to be studied from the theoretical aspect first. The principle of ultrasonic-assisted drilling is to load high-frequency ultrasonic vibration on the drill or workpiece so that the drilling process becomes a compound motion of high-speed rotary motion of the drill, feed motion, and ultrasonic high-frequency vibration. Therefore, this paper takes the trajectory change of micro-drilling as the starting point for in-depth study by establishing the motion model of the tool.
A point on the micro-drill blade is selected as the object for analysis (Fig. 4), and the displacement of the point in the z-direction relative to the workpiece after adding the ultrasonic vibration term to the conventional model is: where fr is the feed rate (mm/r), n is the micro-drilling speed (r/min), A is the ultrasonic amplitude (mm), and f is the ultrasonic vibration frequency (Hz).
Let the angular velocity of the micro-drill's own rotational motion during ultrasonic vibration drilling be ω(rad/s), then the relationship between the angular velocity and time t is: where θ is the angular displacement (rad).
After eliminating the time t by coupling (1) and (2), the expression for the displacement z of the analyzed point on the tool with respect to the workpiece becomes: By expanding the coordinates of the analyzed points in a three-dimensional coordinate system Fig. 5), the equation of the trajectory of a point on the micro-drill blade is finally obtained: where r is the micro-drilling radius (mm).
After substituting r = 0.15 mm, Eq. (4) is plotted in MATLAB, and the trajectory diagram of the analysis point relative to the workpiece during ultrasonic-assisted drilling can be obtained, and similarly, the trajectory diagram of the point during ordinary drilling can be obtained by removing the ultrasonic term, and a comparison of the two is shown in Fig. 6. It can be seen that the cutting path of the tool during ultrasonic vibration-assisted drilling is not a monotonic curve as in ordinary drilling, and the tool is not pressed against the workpiece and fed all the time, but does axial reciprocating motion with high frequency.
Combined with the structural analysis of the micro-drill, it is known that within the microscopic scale, the main cutting edge and the cross-edge of the drill are in contact and then separated from the workpiece periodically all the time, cutting with a pulsating separation intermittent motion. This tiny amplitude vibration impact strengthens Fig. 4 Ultrasonic-assisted drilling motion model the cutting ability of the main cutting edge and cross-edge, especially the cross-edge which will only press the workpiece tightly during ordinary drilling, and after loading ultrasonic vibration, it will continuously impact the part of the material that is not removed. With the high-speed rotation of the micro-drill also plays a role in drilling, it eventually makes the material removal easier. On the other hand, the sub-cutting edge of the micro-drill also scrapes the hole wall reciprocally all the time because of the high-frequency axial vibration, and plays a plowing role under the high-speed rotation, which is equivalent to the secondary processing of the hole wall and has a positive impact on the improvement of micro-hole quality.

Study on the variation of effective cutting angle of ultrasonic-assisted drilling tools
The loading of ultrasonic vibration also has an effect on the effective cutting angle of the tool. If the ultrasonic vibration drilling tool trajectory in Fig. 6 is expanded laterally, the sine curve shown in Fig. 5 can be obtained. It can be seen that the effective front angle α and effective back angle γ of the tool change with the tool trajectory during ultrasonicassisted drilling. Number 1 to 4 in Fig. 7 represent the tool cutting the workpiece at different angles with ultrasonic vibration. In one vibration cycle, the effective front angle α of the micro-drill cutting edge increases and then decreases in the cutting-in phase (when moving in the feed direction) until it is the same as that in ordinary cutting, and then first decreases and later increases in the cutting-out phase (when moving in the opposite direction from the feed) before finally entering the next cycle; while the changing trend of the effective rear angle γ is always opposite to the effective front angle. In contrast, the trajectory of the main cutting edge in ordinary drilling can be regarded as a straight line in a certain time, and the front and rear angles of the tool do not change.
According to the M.E. Merchant cutting equation, the formula for the shear angle can be obtained by the principle of minimum combined force: And the degree of deformation of the workpiece material during cutting can be measured by the relative slip ε and the deformation coefficient ξ. As shown in Fig. 8, when the cut material is squeezed and slid to OM by the tool, the distance of shear surface slip should be △y. Considering that the value of △y is very small when micro cutting, it can be considered that if the material slip occurs on the shear surface, then the slip amount should be △s.
The relative slip ε is mainly used to reflect the degree of slip deformation in the deformed zone during cutting, and the deformation coefficient ξ is mainly used to measure the change in the generated chip geometry. The expressions of both are: Combined with the analysis of Fig. 8, Eqs. (5), (6), and (7), it can be seen that when the micro-drill vibrates toward the feeding direction, the increase of the effective front angle α leads to the increase of the shear angle φ, and the increase of both makes the relative slip ε and the deformation coefficient ξ decrease. In other words, the deformation and friction of the cut material by extrusion are reduced. The chips are more easily discharged by flowing into the spiral groove along the cutting edge, which finally leads to the reduction of the cutting force of ultrasonic-assisted drilling. When the micro-drill vibrates in the direction opposite to the feeding direction, although the effective front angle α increases at this time, the micro-drill cutting edge is in the cut-out stage, gradually moving away from the workpiece material, and the material being cut keeps decreasing, even stopping the machining with empty cutting in a relatively short period of time. This law of change in the effective angle of the tool, coupled with the fact that the micro-drilling cutting edge is cutting in a pulsed separation intermittent motion, makes ultrasonic-assisted drilling technology conducive to the reduction of the average drilling force and drilling temperature.
In summary, the reduced deformation of the material being cut during ultrasonic-assisted drilling results in reducing drilling force and temperature and bringing a smoother material removal process, which has a very positive impact on the quality of micro-hole drilling.

Study on the chip thickness variation of ultrasonic-assisted drilling
Continuing the analysis on the basis of the tool motion model in the previous sections, chip generation and fracture can also be studied. The micro-drill used for PCB microhole machining in this study makes a double-edged. All the expression about the displacement of the analysis point in Eq. (3) is written as Z 1 , then in symmetrically selected analysis point on the other edge, the displacement of which is written as Z 2 , the expression is mm.
So in ultrasonic vibration drilling, the two edges of the tool are alternately cutting the workpiece, then it can be deduced that the cutting thickness during processing should be: The size of the chip thickness determines whether the chip can be generated or not. When the chip thickness becomes zero or even negative, it indicates that geometrically the trajectories of the two edges of the micro-drill are intersecting and the chip is fractured.
As shown in Fig. 9, the dynamic axial cutting thickness curve is drawn according to Eq. (9). According to the previous section, in a certain time, the trajectory of the main cutting edge can be regarded as a straight line during ordinary drilling, so its cutting thickness will not change, and the material to be cut will move along the spiral groove of the micro-drill for a certain distance before a fracture occurs, so the long spiral type chips will account for a large part of ordinary drilling. However, the cutting thickness changes dynamically during ultrasonic-assisted drilling, and there will be both mechanical chip breakage and geometric chip breakage in the actual processing, and the proportion of short spiral type, ribbon type, and broken block type in the chips will increase significantly. Moreover, as the drilling depth increases, the long spiral type chips appearing in ordinary drilling will be subject to the joint action of the front tool surface of the micro-drill, the inner wall of the spiral groove and the hole wall, and may be bent and folded due to extrusion, which is more unfavorable to discharge out of the hole, and even blockage of the hole will occur. On the contrary, ultrasonic-assisted drilling is not only favorable to the improvement of the chip breaking ability, but also easier to generate and discharge more easily banded and broken type chips, which will have a positive impact on the chip discharge, improving the chip removal ability and reducing the risk of plugging.

Experimental materials and apparatus
The drill bit selected in this study is a double-edged, singlegroove micro-drill with a diameter of 0.3 mm, and the specific structural parameters are shown in the table below (Table 2). There are two kinds of PCBs selected in the study, among which the lead-free and halogen-free medium Tg circuit board is used in the single-factor experiment; the high-speed board S1000 is used in the orthogonal experiment, whose dielectric loss Df value is 0.009 and belongs to the medium Tg, low Z-axis thermal expansion coefficient board, and its main components are copper foil, glass fiber, and brominated epoxy resin combination, etc.
The ultrasonic-assisted drilling experimental platform used in this experiment is designed and built based on the existing single-axis vertical drilling machine for PCB drilling, and its structural design is shown in Fig. 10. The experimental platform as a whole is placed under the pneumatic spindle and consists of three parts: the bakelite plate at the bottom, the ultrasonic vibration plate, and the ultrasonic transducer. The bottom bakelite plate is completely fixed with the marble table of the machine tool as the base plate; the ultrasonic vibration plate plays the role of bearing the workpiece and conducting vibration, which is fixed in the rectangular groove of the bakelite plate by a large number of small tabs, and is not locked with bolts to ensure its vibration performance, and only restricts its movement in the plane, and the vibration in the vertical direction is not constrained; the ultrasonic transducer is welded on the middle line of the ultrasonic vibration plate, and leads to the wire. The ultrasonic transducer is welded to the center line of the ultrasonic vibration plate, and leads to the wire connected to the external 20 kHz automatic frequency sweep type ultrasonic generator of the machine tool; the role of these two is to generate ultrasonic signals and converted into mechanical vibration.
After the experimental platform was built, the amplitude of the loaded vibration plate was also measured. The actual amplitude of the workpiece at different power levels is shown in Table 3.

Experimental methods
The specific flow of the experiment is shown in Fig. 11:   Figure 11a shows the physical ultrasonic-assisted drilling experimental platform built, and Fig. 11b shows the external ultrasonic generator. After completing the drilling experiment of the printed circuit board on this platform, samples were taken to make PCB micro slices, and the final products are demonstrated in Fig. 11d.
The quality of micro-hole processing is evaluated by observing the images of PCB micro-slice collected through the ultra-deep field microscope in Fig. 11e, and measuring and recording the micro-hole roughness, burr, and nail head. The images of the three defects in the ultra-deep field microscope are presented in Fig. 12a, b, c, and d.
The experiments in this study are divided into two parts as shown in Fig. 13: single-factor experiments and orthogonal experiments. The purpose of the single-factor experiments is to demonstrate the improvement effect of ultrasonic assistance on micro-hole processing quality and to provide more reasonable experimental factor levels for the subsequent orthogonal experiments. Then orthogonal experiments were conducted to study the significance level and the order of influence of each parameter on the microporous quality so as to figure out a better combination of processing parameter levels.
The processing parameters used in the single-factor experiments are shown in the table below, and the initial parameters are selected from the parameter recommendation table of the micro-drill manufacturer (Table 4).

Single-factor experiment for ultrasound effect validation
The independent variable of the single-factor experiment for ultrasonic effect verification was ultrasonic intensity. In order to prove the applicability of ultrasonic, three levels of feed rate were also used to repeat the experiment separately after fixing the spindle speed to 110 krpm. These three sets of experiments were observed and analyzed separately. The experimental results were observed in an ultra-field depth microscope as shown in Fig. 14.
The single-factor experimental data for the ultrasonic effect validation were counted and plotted as two-dimensional line graphs of the results for micro-hole roughness, entrance burr, and exit burr respectively. Figure 15 shows the results of the average micro-hole roughness measurements for the repeated experiments with three different drilling parameters. It can be seen that the micro-hole roughness values show an overall decreasing trend after loading ultrasonic vibration at different drilling parameters, but at a certain level of ultrasonic intensity, the micro-hole roughness values show a slight increase again at some of the parameters because the micro-hole roughness of the PCB is determined by the processing of the copper foil layer and the resin-glass fiber layer together. Copper foil is a plastic material, ultrasonic vibration not only enhances the cutting effect of the main cutting edge of the micro-drill on the copper foil material, but also causes the secondary cutting edge to rework the fracture of the copper foil material at the hole wall under high frequency reciprocal vibration, which makes the ductile fracture of the copper foil protruding from the hole wall occur again. However, glass fiber composites with anisotropy will fracture in different ways depending on the angle between the cutting direction and the fiber direction. When the amplitude of ultrasonic vibration increases to a certain level, the resin softened by the high temperature inside the hole will be deformed as the micro-drill pulls on the glass fiber supporting it, causing the micro-hole roughness to rise slightly. Regardless of the ultrasonic intensity, the micro-hole roughness values are smaller under different drilling parameters than for ordinary drilling, which is sufficient to prove that the ultrasonic-assisted technology has an improved effect on the micro-hole quality of PCBs.
In addition to the micro-hole roughness, ultrasonicassisted drilling also has a good improvement on the burr generation. Figure 16 below shows the average entrance burr length measurement results for the repeated experiments with three different drilling parameters.
The entrance burr is formed when the copper foil material at the edge of the hole is squeezed during drilling and the   micro-drill moves the deformed material upwards a small distance when it is retired. Therefore, the burr is actually a plastic flow deformation of the copper foil material that has not been removed and turned into chips. From the previous mechanistic study, it is clear that the effective front-toback angle of the cutting edge changes periodically during ultrasonic-assisted drilling, which reduces the force on the residual material in the direction of the workpiece when the cutting edge cuts into the workpiece and weakens the burr formation. In addition, the high-frequency vibration of the micro-drill in the feed direction causes the edge of the copper foil material at the entrance of the hole to be constantly scraped by the side of the micro-drill. The sub-cutting edge of the micro-drill also cuts the material around the hole in the feed direction due to the high-frequency vibration in the axial direction when drilling and retracting the tool, which has the effect of smoothing the burr. Figure 17 below shows a line graph of the average exit burr lengths measured from repeated experiments with three different drilling parameters.
The exit burr is also caused by the plastic flow deformation of the copper foil material. But for the exit part of the material, the contact time with the micro-drill blade is only for a short moment when it drills through and then immediately retires. Therefore, the scraping and plowing effect of the micro-drill on the exit burr is very limited. While the improvement effect due to the effective front angle and the change of the cutting thickness still exists, so it can still be seen that the exit burr length is smaller after loading ultrasound than when it is not loaded.
In summary, ultrasonic-assisted vibration drilling has improved the micro-hole roughness, entrance burr, and exit burr defects of printed circuit boards, proving the effectiveness of ultrasonic vibration drilling.

Orthogonal experiment of ultrasonic-assisted drilling of high-speed circuit board
Before the orthogonal experiments, single-factor experiments for parameter optimization were also conducted in Fig. 16 Entrance burrs of ultrasonic-assisted drilling in different feed rate this paper. The parameters and results are shown in the following table (Table 5).
To facilitate comparison and get more intuitive analysis results, the data results of micro-hole roughness and entrance burr cases are plotted as the following surface plots to study respectively, and the surface distribution is the data results in micrometer.
Analysis of Fig. 18 shows that although increasing the feed speed can also suppress the burr formation to some extent, this effect can be confused with the improvement of burr by ultrasonic vibration assistance. Increasing the feed speed also leads to a rise in hole roughness, so the range of feed speed is adjusted downward during parameter optimization. Analysis of Fig. 19 shows that the best value of microhole roughness occurs at a lower spindle speed, and the trend of the effect of speed on burr is not obvious in this group of experimental data, and the value of burr length fluctuates with the change of feed speed at a lower spindle speed.  The optimization results of the machining parameters under ultrasonic-assisted vibration drilling were obtained as shown in Table 6.
Finally, an orthogonal experimental design was performed based on this parameter. Since it was found that the ultrasonic-assisted technique also had an improvement effect on the generation of nail head (circuit board copper layer thickness of 30 μm) when drilling high-speed circuit boards, the nail head was also included in the evaluation criteria for micro-hole quality, and a three-index L9(3 3 ) orthogonal experimental design was conducted. Table 7 was obtained after compiling the results.
First, the results of the orthogonal experiments were analyzed by polar difference analysis. The polar difference (R) indicates the magnitude of the change of the experimental index within the range of the value of the factor. The larger the R value is, the greater the influence of the level change of the factor on the experimental index. The results of the analysis for microporous roughness, entrance burr, and nail head are shown in Tables 8, 9, and 10, respectively.
The results show that the most influential factor on the micro-hole roughness results is the ultrasonic power, and the feed rate and spindle speed have a similar influence. From the derived better levels of each factor, the lowest micro-hole roughness values can be obtained at the spindle speed of 160 krpm, feed speed of 27 mm/s, and ultrasonic intensity of 25%. When the feed speed is reduced to 27 mm/s during ultrasonic vibration, the high frequency vibration and feed motion of the micro-drill pulls less on the glass fiber inside the hole, and the ultrasonic plowing effect on it is very good. While the trend of the ultrasonic power part is similar to the results of the previous single-factor test, when the ultrasonic amplitude is too high, the hole wall quality is slightly reduced. Thus, loading 25% intensity of ultrasonic vibration can get the best results, reducing 50.8%.
The results show that the most influential factor on the entrance burr length is still the ultrasonic power, followed by the spindle speed. From the derived better levels of each factor, the smallest entrance burr length is obtained at the spindle speed of 100 krpm, feed rate of 33 mm/s, and ultrasonic intensity of 25%. The trend in the spindle speed and feed rate sections is not quite the same as the micro-hole roughness because the entrance burr is mainly formed by the flow plastic deformation of the copper foil material at the edge of the hole, while the micro-hole roughness is determined by the processing condition of the material inside the hole. The higher feed rate affects the processing quality of the material inside the hole, but the copper foil at the orifice still has a better processing quality under ultrasonic vibration. The ultrasonic power also gives the smallest burr length at 25%, but in fact, it can be seen from the calculated ki value that the difference between the level of 25% and 45% is only 7.2%, while the difference with and without ultrasonic loading is 47.1%, which is enough to prove the improvement effect of ultrasonic vibration loading on the entrance burr.
The results show that the most influential factor on the nail head length remains the ultrasonic power, followed by the spindle speed. From the resulting optimal level of each factor, the smallest nail head length was obtained at a  spindle speed of 100 krpm, a feed rate of 27 mm/s, and an ultrasonic intensity of 25%. This is because the nail head is actually a flow plastic deformation of the copper foil layer material, but it only occurs in the hole. The principle of its generation is very similar to that of the entrance burr.
The ultrasonic vibration loading has a similar principle of their improvement. The improvement effect of the spindle speed is still very obvious. Since the optimal combinations obtained from the extreme difference analysis of the three influencing factors are not exactly the same, they also need to be judged by comparing the order of their influences. As shown in Table 11, there is no doubt that the ultrasonic power (factor C) has the greatest influence, with a better level of 25% for both. The spindle speed (factor A), which has the second influence on both the entrance burr and the nail head, is only 5.7% different from the feed speed and spindle speed as calculated in the micro-hole roughness extreme difference analysis, so the spindle speed is taken as the second criterion in the combination of the better process parameters, and the first level, i.e., 100 krpm, is selected as the best value for both the entrance burr and the nail head. It can be concluded that the best combination of parameters for ultrasonic vibration-assisted drilling to achieve the best overall drilling quality is the spindle speed of 100 krpm, feed rate of 27 mm/s, and ultrasonic intensity of 25%.   In addition, the effect of ultrasonic vibration-assisted drilling can also be demonstrated by the change of chip morphology. Combined this with the conclusion given in the previous theoretical study of ultrasonic-assisted drilling process, it is concluded that ultrasonic vibration increases the proportion of short continuous chips, ribbon chips, and broken chips in the chips as shown in Fig. 20, which leads to the improvement of material removal and chip discharge in the hole. This is finally reflected in the processing quality of micro-hole.
Then, the results of the orthogonal experiments were also analyzed by analysis of variance (ANOVA), and the results of the analysis of the three influencing factors were tallied into the ANOVA table shown below (Tables 12, 13 and 14).
According to the analysis of the results of the significance test, after excluding the influence caused by random errors, the significant level of ultrasonic intensity is still the highest. All three ANOVAs show that ultrasonic intensity has a significant effect on the machining quality of micro-hole, while the significance of spindle speed ranks second and the significance level of feed speed is lower. But three of them have an effect on machining quality, and the most obvious effect is on the entrance burr situation.
In summary, the ultrasonic-assisted technology has a very obvious improvement on several machining defects such as micro-hole roughness, entrance burr, and nail head cases. They have the same effect when the ultrasonic intensity is changed, and the spindle speed and feed rate have less obvious effect on machining quality than the ultrasonic power, but still a better combination of parameters can be obtained by extreme difference analysis. More importantly, the research method is not only applicable to PCBs in experiments, but provides a way to obtain the primary and secondary order and optimal level combinations of the effects of each parameter on the quality of micro-hole.

Conclusions
In this paper, a new method of ultrasonic-assisted drilling of high-speed circuit boards is proposed for the challenges of micro-hole quality of high-speed circuit boards. The impact   mechanism of ultrasonic assistance on the drilling method, material deformation, drilling force, chip breaking, and chip removal of high-speed circuit boards is analyzed through the tool motion model. Then, the ultrasonic-assisted drilling experimental platform is designed and built to carry out experiments on ultrasonic effect verification, drilling parameter optimization, and optimal parameter level combination analysis. The conclusions are as follows.
1. The major difference between ordinary drilling and ultrasonic drilling is the difference in tool trajectory. The main cutting edge and the cross edge of micro-drill are cutting with pulsed separation intermittent motion during ultrasonic-assisted drilling, and the secondary cutting edge is scraping the hole wall reciprocally, which improves the cutting ability of micro-drill and the quality of micro-hole. 2. The chip deformation formula is deduced, and the results show that the effective cutting angle and cutting thickness of the ultrasonic-assisted drilling tool will change periodically, resulting in a reduction of the deformation of the processed material, which is conducive to the reduction of drilling force, and has a positive impact on chip breaking and chip removal, ultimately contributing to the improvement of micro-hole quality. 3. Ultrasonic vibration loading on high-speed circuit boards has a significant improvement on processing defects including micro-hole roughness, entrance burr, nail head. In particular, when the ultrasonic intensity was 25%, the micro-hole roughness was reduced by 50.8%, and the lowest value was 4.737 μm. The entrance burr length decreased by 47.1%, and the lowest value was 5.488 μm. The length of nail head decreased by 24.1% to the lowest value of 37.56. Ultrasonic power being too high will lead to a small decline in the quality of micro-hole processing. But compared to ordinary drilling of micro-hole quality, there is still a relatively obvious improvement. 4. When ultrasonic-assisted drilling of S1000 printed circuit boards, a better combination of parameters is the spindle speed of 100 krpm, feed rate of 27 mm/s, and ultrasonic intensity of 25%. At the same time, a method that can obtain the primary and secondary order and the optimal level combination of the influence of each parameter on the micro-hole quality is provided. The mechanism of the influence of micro-hole quality of ultrasonic-assisted drilling of PCBs is investigated in a comprehensive theoretical and experimental way, which provides a theoretical research basis and processing guidance for high-speed circuit board drilling.

Authorship contribution
None of the material has been published or is under consideration for publication elsewhere. All authors hereby confirm that this manuscript is their original work, and the citations have been marked with references. Authors' contributions are as follows: Zhisen Gao: investigation, data curation, writing-original draft; Hongyan Shi: supervision, funding acquisition, conceptualization, methodology, writing-review and editing, validation; Sha Tao and Xianwen Liu: investigation, data curation; Tao Zhu and Zhuangpei Chen: investigation, validation. All authors agreed to submit this manuscript to IJAMT.