Machining Strategy and Experimental Study of Ultrasonic-Assisted Bidirectional Progressive Spiral Milling of Carbon Fiber Holes

Abstract

Carbon fiber-reinforced composites (CFRP) are widely used in aerospace structural holes due to their superior mechanical properties. However, fiber pulling, delamination, burr and other defects often occur in the parts, which seriously affect the accuracy and service life of the products. The traditional cylindrical milling cutter is easy to lead to the exit delamination defects due to the large axial force at the bottom edge, concentrated wear at the periphery edge, and weak rigid constraint at the exit machining position. Therefore, this paper proposed a new hole machining strategy, analyzed the kinematic law of the tapered progressive spiral milling hole, studied the cutting mechanism of the four stages of the tapered spiral bidirectional milling hole, explored the material removal force state of the ultrasonic augment-assisted progressive milling hole, and established the prediction of the layered axial force of the ultrasonic progressive milling hole. Finally, combined with the material removal mechanism of ultrasonic vibration, the self-designed bidirectional progressive spiral milling cutter was used to verify the mechanism of material removal by progressive milling, in which the axial force could be effectively reduced. After 60 and 90 holes were processed, the axial force was about 18.5 and 23.3 N, respectively, the critical force of delamination could be improved, and the hole quality could be guaranteed without obvious burr and delamination phenomena.

1. Introduction

CFRP (carbon fiber-reinforced polymers) are widely used in the manufacturing of some complex large aircraft components such as the wing, frame, beam and other structural parts because of its superior mechanical properties such as high strength, light weight, corrosion resistance, strong design ability and good fatigue resistance [1]. These structural parts need a large number of connecting holes for assembly or connection, and the quality of connecting holes will directly affect the bearing capacity and service life of the aerospace equipment; thus, the aerospace industry has high quality requirements for aircraft connecting holes [2]. Due to the physical characteristics of heterogeneous and anisotropic CFRP, as well as the characteristics of small fracture strain and low interlaminar bonding strength, fiber pulling, matrix tearing, delamination, burr and other defects often occur during the machining of holes [3,4], which seriously affect the accuracy and service life of the products [5] and sometimes even increase the secondary processing of the deburring process, greatly reducing processing efficiency and making the processing quality costly and difficult to control. Additive manufacturing is a powerful tool for the aerospace industry. Therefore, how to create an efficient, high-quality and low-cost hole machining of composite materials is one of the hot spots and difficulties in research at home and abroad.

Helical milling is also known as orbital drilling or spiral milling; its working principle is to set the eccentric position of the tool and to integrate the composite spiral cutting technology of the axial feed and circumferential feed movement to complete the machining of the hole parts larger than the tool diameter. This way of eccentric processing improves the heat dissipation of the cutting tool and chip removal condition, and it can significantly reduce the process of the axial cutting force [6]. The tool periodically mobilizes and speeds up the hole wall and air heat exchanger, effectively reducing the occurrence of mechanical and thermal damage [7,8] and improving the processing quality of the hole. This leads to inhibition of the layered composite materials, which prolongs the service life of the cutting tools, and which is suitable for a variety of apertures. It also has other advantages and is widely used in CFRP hole technology.

Domestic and foreign researchers mainly focus on the cutting mechanism, cutting force modeling and hole quality control. Among them, B. Denkena [9] and Brinksmeier E. et al. [10] showed, through kinematic analysis of the spiral milling holes, that the end cutting edge and the peripheral edge of the milling cutter participate in the cutting of workpiece materials at the same time. In addition, the peripheral edge of the milling cutter cuts intermittently, and the processing form is similar to that of the peripheral milling. The end cutting edge cuts continuously, and the processing form and insert milling are similar. At the same time, the calculation of the undeformed cutting parameters and material removal volume ratio of the milling cutter edge and the end cutting edge shows that, when the machining aperture and tool diameter are determined, the ratio of material volume of the peripheral edge and end cutting edge is constant and is not affected by the machining parameters [11]. Traditional spiral milling holes often adopt the cylindrical milling cutter, material removal is mostly conducted by the bottom edge, a weak blade is the main part that completes the processing of the hole wall [12,13], and the material removal in the process of the cutting tool’s weak blade is the focus. It is difficult to guarantee the product quality requirements, as the bottom edge material removal volume is larger, and the axial force is big, which is greater than the critical force of delamination, leading to delamination defects in the hole [14]. Therefore, the finishing processes such as reaming or deburring are required. Based on this, Wei [15] and Chen et al. [16] successively proposed the processing strategy of two-way spiral milling. In the process of reverse cutting, the material itself was used as support to enhance the constraint rigidity, and a two-way milling cutter was designed to enrich the experimental study of the reverse spiral hole and to verify the feasibility of the cutting process of a bidirectional progressive spiral milling hole.

At the same time, based on the basic principle of spiral hole milling, some researchers introduced an ultrasonic generator to output ultrasonic oscillation, and found that the effective cutting time of the tool in vibration cutting is shorter than that of ordinary cutting time [15], and the periodic separation of the tool and the workpiece leads to the periodic change of cutting speed and cutting depth [17]. Regarding changing the cutting mechanism in the cutting process, ultrasonic machining compared with the traditional machining method has a huge advantage. Takeyama [18] and Makhdum [19] successively conducted ultrasound-assisted carbon fiber drilling, and they found that the cutting force was significantly reduced and the quality of the parts was greatly improved. Zhang Liaoyuan [20], Hu Erjuan [21], and Zhang et al. [22] established the theoretical model of cutting force of ultrasonic vibration cutting CFRP and compared it with the experimental results, and they found that the theoretical prediction and the measured results are in good agreement. Under the same cutting parameters, the average axial force can be reduced by 20–30% [20], and the cutting stress is more concentrated, which is beneficial to the shear fracture of the fiber [21] and improves the machining efficiency [22]. Zhang Deyuan [23] further proposed a new process method of ultrasonic vibration sheath–reaming–shaving, and researched and realized high-quality, efficient, and low-cost processing to meet the requirements of precision assembly manufacturing.

From what has been discussed above, spiral milling technology still cannot solve the machining defects of carbon fiber holes such as burr and delamination. There are still technical problems to be solved in the process of carbon fiber holes, such as a high-quality removal mechanism and a high-performance cutting tool design. Therefore, this paper puts forward four stages of a bidirectional progressive spiral milling material removal method to further study the mechanism of ultrasonic milling and the self-designed bidirectional progressive milling cutter, which were used to verify the mechanism of material removal and state of axial force. This study can effectively fill the gap of high-quality processing technology of carbon fiber composites, can solve the technical problems caused by excessive axial force in the process of aerospace carbon fiber processing, and can enrich the technical field of carbon fiber composite processing tool design.

2. Analysis of Material Removal Rule of Bidirectional Progressive Spiral Milling Hole

2.1. Geometric Relation between Periphery Cutting Zone and End Cutting Zone of Taper Spiral Progressive Milling Cutter

The mechanism of hole removal by the progressive taper spiral milling is different from that of a traditional cylindrical milling cutter. In order to accurately express its kinematic law, a bidirectional progressive taper spiral milling cutter with a certain taper ($\mathsf{\phi }$) is used to carry out kinematic research on material removal under the premise of the same cutting depth and eccentricity. As shown in Figure 1, the cutting diameter of each position of the progressive taper spiral milling cutter is different. The movement of the taper spiral milling hole is compounded by the revolution, rotation and axial feed movement of the conical milling cutter. The movement track of the tool center is the spiral line.

In Figure 1, n_g is the revolution speed; n_z is the spindle speed; D_R (mm) is the maximum diameter at the top of the peripheral edge, namely, the nominal diameter; D_Ri (mm) is the diameter of any point on the peripheral edge; D_r (mm) is the diameter of the end milling edge; D_h (mm) is the diameter of the milling hole; a_p is the depth of the axial cutting; the distance between the tool axis and the axis of the hole is the eccentricity e (mm), and the rotary diameter D_e of the tool center track can be expressed as:

$$D_h=D_R+2e$$

(1)

$$D_e=D_h-D_R$$

(2)

$$a_p=tan\theta ·l_R$$

(3)

$${\theta }_{min}=arctan\frac{a_p}{2\pi ·R_{imax}}$$

(4)

$${\theta }_{max}=arctan\frac{a_p}{2\pi ·R_{imin}}=90°$$

(5)

where R_i is the cutting radius of any point on the peripheral edge, and $R_{imax}=\frac{D_R}{2}$, $R_{imin\to 0}$.

However, the spiral milling requires the participation of the peripheral edge and the end cutting edge, and the total cutting depth is a_p. According to the cutting perimeter at each position of the cutting edge, as shown in Figure 1, it can be known that:

$$\frac{h_r}{l_r}=\frac{a_p}{l_R}$$

(6)

$$h_r+h_R=a_p$$

(7)

where $h_r$ is the axial cutting depth with end cutting edge rotates once; $l_r$ is the cutting perimeter with the end cutting edge rotated once; $l_R$ is the cutting perimeter with the peripheral edge rotated once; $h_R$ is the axial cutting depth with the peripheral edge rotated once.

For the determination of $h_r$ and $h_R$, Equation (6) is used in Equation (7).

$$h_r=\frac{l_r}{l_R} ·a_p$$

(8)

$$h_R=\left(1-\frac{l_r}{l_R}\right)·a_p$$

(9)

At the same time, there is a certain relationship between the cutting perimeter corresponding central angle of the bottom edge and the peripheral edge, namely:

$$\frac{l_r}{2\beta }=\frac{l_R}{2\pi }$$

(10)

where $\beta$ is entering the angle for spiral interpolation and represents half of the central angle corresponding to the cutting path from entry to exit at any point of the edge, as shown in Figure 1. According to different entry angles $\beta$_i, the cutting perimeters of the end edge and the peripheral edge can be expressed as:

$$l_r=\frac{l_R}{\pi }·{\beta }_i$$

(11)

Thus, the axial cutting depth of the end edge and the peripheral edge can be expressed as:

$$h_{ri}=\frac{l_r}{l_R} ·a_p=\frac{{\beta }_i}{\pi }·a_p$$

(12)

$$h_{Ri}=a_p\left(1-\frac{{\beta }_i}{\pi }\right)$$

(13)

According to the relationship of the angle parameters in the figure, it can be known that [8]:

$${\beta }_i=arcsin\left(\sqrt{{\left(\frac{D_{Ri}}{2}\right)}^2-{\left(\frac{R_{\beta i}{}^2-{\left(\raisebox{1ex}{$D_{Ri}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}^2-{\left(\frac{D_h-D_{Ri}}{2}\right)}^2}{D_h-D_{Ri}}\right)}^2}/R_{\beta i}\right)$$

(14)

where $R_{\beta i}$ is the entry angle radius, and it is different according to the entry angle of spiral interpolation.

For the determination of $h_{ri}$ and $h_{Ri}$, Equation (14) is used in Equations (12) and (13).

$$h_{ri}=\frac{a_p}{\pi }·arcsin\left(\sqrt{{\left(\frac{D_{Ri}}{2}\right)}^2-{\left(\frac{R_{\beta i}{}^2-{\left(\raisebox{1ex}{$D_{Ri}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}^2-{\left(\frac{D_h-D_{Ri}}{2}\right)}^2}{D_h-D_{Ri}}\right)}^2}/R_{\beta i}\right)$$

(15)

$$h_{Ri}=a_p\left(1-\frac{1}{\pi }arcsin\left(\sqrt{{\left(\frac{D_{Ri}}{2}\right)}^2-{\left(\frac{R_{\beta }{}^2-{\left(\raisebox{1ex}{$D_{Ri}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}^2-{\left(\frac{D_h-D_{Ri}}{2}\right)}^2}{D_h-D_{Ri}}\right)}^2}/R_{\beta i}\right)\right)$$

(16)

The cutting diameters of the peripheral edge are different, resulting in D_Ri, which is different, as $D_r<D_{Ri}\le D_R$. In the process of taper spiral milling, the end cutting edge will exit the prefabricated hole milling process earlier than the peripheral edge, and the actual hole wall morphology is formed by the peripheral edge reaming, and finally the semi-finishing is completed through the top edge of the peripheral edge. Here, chip thickness h_i, chip width b_i, and chip area A_i can be expressed as:

$$b_i=f_z·sin{\alpha }_i$$

(17)

$$A_i=b_i·h_i$$

(18)

where $f_z$ is the feed per tooth (mm); ${\alpha }_i$ is the engagement angle u for the periphery cut.

The volume at different positions of the peripheral edge can be expressed as ($V_{Ri}$) [8]:

$$V_{Ri}=2\pi \int R_i·d{R}_i·h_{Ri}$$

(19)

$$V_{Ri}=A_{Ri}·a_p$$

(20)

$$V_{Ri}=\pi ·{\left(\frac{D_h-D_{Ri}}{2}\right)}^2·a_p$$

(21)

The volume of the end cutting edge can be expressed as ($V_{ri}$):

$$V_{ri}=a_p·\int l_{ri}·d{r}_i$$

(22)

$$V_{ri}=A_{ri}·a_p$$

(23)

$$V_{ri}=\pi ·{\left(\frac{D_r}{2}\right)}^2·a_p$$

(24)

2.2. Research on the Material Removal Mechanism in Bidirectional Taper Spiral Progressive Milling

The bidirectional progressive spiral milling hole is mainly divided into four stages, and the cutting conditions of the end cutting edge and the periphery edge are different in each stage. The undeformed cutting parameters produced by this method can be expressed by cutting width and cutting depth, as shown in Figure 2.

• Stage I:

$$1\le i\le i_{h1},i_{h1}=\frac{h1}{a_p},.$$

where h₁ is the thickness of the CFRP. The end cutting edge and the peripheral edge start to participate in the cutting, and the end cutting edge does not exit the stage, as shown in Figure 2. The material removal analysis of the peripheral edge is shown in Figure 2, where the cutting width is b_Ri, and the cutting thickness is h_Ri, and the two parameters change from large to small as the engagement angle for the periphery cut changes. Meanwhile, the material removal rule of the end cutting edge is shown in Figure 2, where the cutting depth is h_ri, and the diameter at the cutting edge is Dr.

Thus, the cutting volume of peripheral edge ($V_{Ri}$) is:

$$V_{Ri}=V_i-V_{i-1}-V_{ri}$$

(25)

$$V_{Ri}=\frac{i}{3}\pi \left(R_i^2+R_i·r_i+r_i^2\right)·a_p-\frac{i-1}{3}\pi \left(R_{i-1}^2+R_{i-1}·r_{i-1}+r_{i-1}^2\right)a_p-i·\pi r_i^2·a_p$$

(26)

where i is the cutting level number; $V_{Ri}$ is the removal volume of the peripheral edge during cutting level i; $R_i$ is the maximum cutting radius of the peripheral edge in cutting level i; $r_i$ is the cutting radius of the end of the cutting edge in cutting level i.

When $1\le i\le i_{h1},r_i=r$, then:

$$V_{Ri}=\frac{i}{3}\pi \left[\left(R_i^2-R_{i-1}^2\right)+\left(R_i-R_{i-1}\right)r\right]a_p+\frac{1}{3}\pi \left(R_{i-1}^2+R_{i-1}·r+r^2\right)a_p-i\pi r^2{a}_p$$

(27)

where $R_i=r_i+tan\left(\frac{\phi }{2}\right)·i·a_p$, which makes $k_{\phi }=tan\left(\frac{\phi }{2}\right)$, called the taper coefficient. Then,

$$R_i=r_i+k_{\phi }·i·a_p$$

(28)

Thus, the removal volume of the peripheral edge in cutting level one (${\Delta }_1$) is:

$${\Delta }_1=\frac{1}{3}\pi \left(R_1^2+R_1·r+r^2\right)a_p$$

(29)

The uniform increment by progressive spiral milling of the peripheral edge in level i (${\Delta }_i$) is:

$${\Delta }_i=\frac{i}{3}\pi \left[\left(R_i^2-R_{i-1}^2\right)+\left(R_i-R_{i-1}\right)r\right]a_p-i\pi r^2{a}_p$$

(30)

The removed volume of the end cutting edge in cutting level i ($V_{ri}$) is:

$$V_{ri}=i\pi r^2{a}_p$$

(31)

It can be seen that the material removal mechanism of the conical milling cutter is equivalent to the superposition drilling bottom hole and the progressive spiral milling holes when the end cutting edge enters into stage I.

Therefore, the material removal of the end edge of the bidirectional progressive spiral milling cutter is about 0.44 that of a conventional cylindrical spiral milling cutter. (The tool parameters of the experimental part are applied.)

• Stage II:

The end cutting edge has withdrawn from the state, and the top edge of the peripheral edge has not participated in the cutting stage, as shown in Figure 3, $i_{h1}<i\le i_{h2},i_{h2}=\frac{h_2}{a_p}$, where h₂ is the axial length of the peripheral edge.

Thus, the removal volume of the peripheral edge during cutting level i ($V_{Ri}$) is:

$$V_{Ri}=V_i-V_{i-1}$$

(32)

$$V_{Ri}=\frac{i}{3}\pi \left(R_i^2+R_i·r_i+r_i^2\right)·a_p-\frac{i-1}{3}\pi \left(R_{i-1}^2+R_{i-1}·r_{i-1}+r_{i-1}^2\right)a_p$$

(33)

where

$$r_i=r+tan\left(\frac{\phi }{2}\right)·\left(i-i_{h1}\right)·a_p$$

(34)

$$R_i=r+tan\left(\frac{\phi }{2}\right)·i·a_p$$

Thus,

$$\begin{gathered} V_{Ri}=\frac{i}{3}\pi \left[\left(R_i^2+R_i·r_i+r_i^2\right)-\left(R_{i-1}^2+R_{i-1}·r_{i-1}+r_{i-1}^2\right)\right]a_p \\ +\frac{1}{3}\pi \left(R_{i-1}^2+R_{i-1}·r_{i-1}+r_{i-1}^2\right)a_p \end{gathered}$$

(35)

where $r_i=r+k_{\phi }·\left(i-i_{h1}\right)·a_p$; $R_i=r+k_{\phi }·i·a_p$.

Therefore, in stage II, only the peripheral edge is cutting, the material removal mechanism is equivalent to the expanding progressive hole based on the cutting level (i − 1), and the uniform increment by progressive spiral milling ${\Delta }_i$ is:

$${\Delta }_i=\frac{i}{3}\pi \left[\left(R_i^2+R_i·r_i+r_i^2\right)-\left(R_{i-1}^2+R_{i-1}·r_{i-1}+r_{i-1}^2\right)\right]a_p$$

(36)

At this stage, the bottom edge has been cut out and does not participate in material removal, $V_{ri}=0$.

Therefore, the ratio of the peripheral edge removal amount of the bidirectional progressive spiral milling cutter and the traditional cylindrical spiral milling cutter ($R^{\prime }$= 3) is 0.91 (the tool parameters of the experimental part are applied).

The cutting removal amount of the peripheral edge is relatively uniform and progressive. Finally, the hole wall is processed through the top of the peripheral edge.

• Stage III:

(1)

The top edge of the peripheral edge is cut in, not out, as shown in Figure 4.

$$i_{h2}<i<i_H, i_H=\frac{h_1+h_2}{a_p},\mathrm{so}$$

$$V_{Ri}=V_i-V_{i-1}$$

$$=\pi ·R_t^2·a_p+\frac{1}{3}\pi \left(R_t^2+R_t·r_i+r_i^2\right)·a_p-\frac{1}{3}\pi \left(R_{i-1}^2+R_{i-1}·r_{i-1}+r_{i-1}^2\right)a_p$$

where $r_i=r+tan\left(\frac{\phi }{2}\right)·\left(i·a_p-H\right)$; $R_{i-1}=r+tan\left(\frac{\phi }{2}\right)·\left(i-1\right)·a_p$.

Then:

$$V_{Ri}=\pi ·R_t^2·a_p+\frac{1}{3}\pi \left[\left(R_t^2+R_t·r_i+r_i^2\right)-\left(R_{i-1}^2+R_{i-1}·r_{i-1}+r_{i-1}^2\right)\right]·a_p$$

(37)

where $r_i=r+k_{\phi }·\left(i·a_p-H\right)$; $R_{i-1}=r+k_{\phi }·\left(i-1\right)·a_p$.

It can be seen that the top edge of the conical milling cutter perimeter edge begins to cut in and enters stage III. In this stage, the material removal of the perimeter edge is divided into two parts, including the top edge, which begins to semi-finish the hole wall, and the perimeter edge progressive spiral milling. The uniform increment by progressive spiral milling ${\Delta }_i$ is:

$${\Delta }_i=\frac{1}{3}\pi \left[\left(R_t^2+R_t·r_i+r_i^2\right)-\left(R_{i-1}^2+R_{i-1}·r_{i-1}+r_{i-1}^2\right)\right]·a_p$$

(38)

At the same time, the end cutting edge has been cut out and does not participate in material removal, $V_{ri}=0$.

(2)

The top of the peripheral edge begins to withdraw from the machining state, as shown in Figure 4, $i=i_H$, and then:

$$V_{Ri}=V_i-V_{i-1}$$

$$=\pi ·R_t^2·a_p-\frac{1}{3}\pi \left(R_t^2+R_t·r_i+r_i^2\right)·a_p$$

where $r_i=R_t-tan\left(\frac{\phi }{2}\right)·a_p$; thus,

$$V_{Ri}=\pi ·a_p·\left(R_t^2-\frac{1}{3}{R}_t^2-\frac{1}{3}{R}_t·r_i-\frac{1}{3}{r}_i^2\right)$$

$$V_{Ri}=\frac{1}{3}\pi ·a_p·\left(2R_t^2-R_t·r_i-r_i^2\right)$$

(39)

It is verified that the chip shape of the last cut of the material is similar to the volume of the flat cut hollow cone.

• Stage IV:

The reverse cutting edge takes part in the cutting, spiraling upward along the axial direction to finish the hole wall. As shown in Figure 5, the recommended cutting allowance at this stage is less than or equal to 0.5 mm.

3. Analysis of the Cutting Principle of Ultrasonic-Assisted Progressive Milling

Ultrasonic-assisted conical spiral milling is a machining strategy that uses a conical milling cutter for bidirectional spiral milling CFRP. Ultrasonic-assisted machining changes the motion trajectory of the cutting edge, specifically involving the end cutting edge, the periphery edge, and the reverse cutting edge, which causes a periodic pulse effect on the tool motion trajectory in different cutting stages and improves the machining quality of the hole wall.

(1) As shown in Figure 6, the end cutting edge begins to participate in the cutting during stage I, which is equivalent to a hammer with high frequency vibration, and which is assumed to have numerous micro-element cutting edges. The trajectory length is lw in an ultrasonic vibration cycle, and we can obtain [19]:

$$l_w={{\displaystyle \int }}_0^{\frac{1}{f}}{\left[{\left(\frac{\pi nr}{30}\right)}^2+{\left(2\pi fz·cos\left(2\pi f\right)\right)}^2\right]}^2{d}_t$$

(40)

where r is the radius of any cutting position of a milling cutter; z is the amplitude of the ultrasonic vibration; f is the frequency of the ultrasonic vibration.

In one ultrasonic vibration cycle, material removal volume V_c of the end cutting edge cutting element in the ultrasonic milling process can be expressed as:

$$V_c=S_w·l_w$$

(41)

where S_w is the cross sectional area of the cutting edge element.

If the number of elements involved in the cutting at the end cutting edge of the tool is N, then according to the material removal, the amount is:

$$M_w=\rho N{V}_c=\rho N{S}_w·l_w$$

(42)

where $\rho$ is the density of the carbon fiber composites (g/cm³); M_w is the total amount of removal during a period vibration by ultrasonic milling.

It can be seen from the equation that, on the premise of the same nominal diameter, the diameter of the bottom edge of the traditional cylindrical milling cutter is different from that of the conical milling cutter, and the relationship is as follows:

$$D_R=D_r+2tan\left(\frac{\phi }{2}\right)·h_2$$

(43)

$$D_R={Dr}^{\prime }={Dr}^{\prime }$$

(44)

where $D_R$ is the diameter of the top edge of the peripheral edge, the nominal diameter; $D_r$ is the diameter of the top edge of the end of the cutting edge (mm); $\phi$ is the cone angle (°); $h_2$ is the axial length of the peripheral edge (mm); ${Dr}^{\prime }$ is the nominal diameter of the cylindrical milling cutter (mm); ${Dr}^{\prime }$ is the diameter of the bottom edge of the cylindrical milling cutter (mm).

It can be seen that compared with a traditional cylindrical milling cutter, the amount of material out of an ultrasonic spiral milling cutter is smaller in the cutting stage of the bottom edge, which will significantly affect the chip deformation and create a small change. It has a positive effect on the reduction of axial force.

The fracture of the carbon fiber composite element is mainly a shear fracture. According to Reference [19], the shear force Fτ of the cutting edge cutting fiber bundle can be expressed as:

$$F_{\tau }=\frac{4·E·{\left(N_c·b\right)}^{1/2}·H^{3/2}}{3\left(1-v^2\right)}$$

(45)

where E is the axial modulus of elasticity (GPa); N_c is the number of broken fibers; b is the radius of the fiber element (um); H is the cutting edge length of fiber bundle cut (um); v is the Poisson’s coefficient.

Therefore, different cutting lengths of the fiber bundle require different shear forces. For cylindrical and conical milling cutters with the same nominal diameters, the bottom edge relationship is as follows:

$${Dr}^{\prime }-D_r=2k_{\phi }·h_2$$

(46)

The length of the cutting fiber bundle is different, and the shear force required by the tapered milling cutter is less than that of the cylindrical milling cutter in the cutting stage of the bottom edge. Therefore, the bottom edge of the tapered milling cutter reduces the cutting axial force to a great extent. At the same time, due to the small amount of material removal, the reserved material allowance can be used as support to enhance the material rigidity of the subsequent milling hole.

(2) As the peripheral edge enters the cutting stage, the fiber rebounds and minimal material allowance removal requirements may occur, as most of the allowance has been removed in the first and second stages. After the introduction of ultrasonic-assisted processing, the movement direction of the cutting edge without an ultrasonic trajectory is an angle between the direction of the delta in a vibration cycle, which changes over time; thus, the impact of the cutting edge effect on the material changes direction. The theoretical trajectory is shown, and the ultrasonic vibration caused by the impact of the F_m, is as follows:

$$F_m=-m{\pi }^2·f^2·z·sin\left(2\pi ft\right)$$

(47)

where $m$ is the quality of the cutting edge elements; t is the time.

After the ultrasonic vibration is applied in the vertical direction of the fiber axis, the resultant force $F_p$ of the tangential force and radial force of the cutting edge can be expressed as:

$$F_p=F_t·sin\mu +F_r·cos\mu$$

(48)

where $F_t$ is the tangential force (N); $F_r$ is the radial force (N); $\mu$ is the angle between the cutting edge movement direction and carbon fiber parts.

Then, the fiber bundle at the aperture begins to fracture, and the force applied meets the relationship:

$$F_c=F_p+F_m·cos\delta \ge F_{\tau }$$

(49)

It can be seen that the ultrasonic vibration processing accumulates the ultrasonic impact effect in the cutting process, which makes it easier to cut the carbon fiber and to fracture the material, thus improving the processing efficiency. As shown in Figure 6, in this stage, until the top of the edge gradually exits the hole wall milling and when the exit may face the burr removal processing requirements, considering the cumulative effect of the ultrasonic vibration, the cutting edge will increase in impact force, making it easier to cut the carbon fiber, thus improving the surface quality and processing efficiency.

(3) In the final hole finishing stage of the reverse cutting edge, the material removal is small. With the aid of ultrasonic vibration, the tool movement relative to the workpiece is not unidirectional in the axial upward direction, but the cyclic reciprocating movement is. Therefore, after the machined surface formation, and through the reverse cutting edges along the axis of forward, backward and forward for the repeat ironing effect, the essence of the ultrasonic vibration cutting process under the reverse action consists of the combination of cutting and ironing, which can significantly improve the quality of the processing surface. It is also suitable for reverse cutting with a certain allowance. This process is shown in Figure 7: the dotted line is the route of the ironing, and the solid line is the cutting direction of the feed path identification.

In conclusion, the ultrasonic movement of the reverse cutting edge can enhance the effect of extrusion and ironing; thus, the reverse cutting process is a combined action process of cutting, extrusion and grinding.

4. Experimental Analysis

In this paper, experimental research was carried out to explore the cutting mechanism and the influence of ultrasonic vibration on the cutting force of the ultrasonic-assisted bidirectional cone spiral incremental milling hole. The VDL-1000E high speed milling NC machining center produced by Dalian Machine Tool Plant was used in the test. The spindle speed range was 45–8000 rpm, and the feed speed range was 1–10,000 r/min⁻¹. The ultrasonic vibration equipment used in the test was USBT40ER32, an inductive rotary ultrasonic vibration processing tool handle independently developed by Tianjin University. The piezoelectric force sensor Kistler 9139AA three-way dynamometer was used to collect and record the milling force. Figure 8 shows the test site. After the hole-making process was completed, a dust mask is worn and a vacuum cleaner is used to vacuum the powder-like chips generated during the cutting process.

• Test tool

In this test, a bi-directional conical ultrasonic milling cutter was selected, and a reverse milling structure was added, as shown in Figure 9a. That is, a reverse cutting edge with gradual deformation was added at the top of the milling cutter edge for reverse finishing of the hole wall of the carbon fiber composite materials. The tool base material is a YG8-type hard alloy with a diamond coating. The diameter of the bottom edge is 4 mm, the maximum diameter of the top diameter of the peripheral edge is 6 mm, the axial length of the edge is 10 mm, the number of teeth is 6, the rake is 6°, the relief angle is 12°, the spiral angle is 30°, and the taper is 11.4°.

2.

Experimental material

In this test, a one-way CFRP sheet was used for ultrasonic vibration spiral milling. The type of carbon fiber composite was T700, and the matrix material was epoxy resin. The selected sheet sizes were 200 mm in length, and 110 mm in width and in height. The cutting parameters are as follows in

Table 1. Single factor test parameters of helix milling with ultrasonic-assisted vibration.

Cutting Direction	Rotation Speed (rpm)	Feed per Tooth fz (mm/z)	ap (mm)	f (KHz)	A(μm)	Dh
downward	4000	0.2	0.2	30	5	7.8
upward	4500	0.1	0.2	30	5	8

.

3.

Analysis of cutting force

The cutting force curve can be obtained through the test. As shown in Figure 10, F_x and F_y gradually increase as the cutting tool enters the cutting state and as it enter the first stage of stable cutting, at which the bottom edge and the peripheral edge participate in cutting. The cutting length of the peripheral edge gradually increases, and the cutting force gradually reaches the peak. The bottom edge is then out of the cutting process, cutting into the second stage. At this time, only the edge participates in the cutting, with the edge axial downward feed, the cutting volume gradually reduced, and the cutting force also monotonically changing with a decreasing trend. When the top of the peripheral edge exits the cutting process, the cutting force drops to the lowest point, which is the third stage. At this time, the cutting force is not zero, because there is a pressure foot in the experimental system. In the process of reverse cutting, the material removal is small, which verifies that during the above mechanism analysis, there may be an elastic rebound, burr and other processing allowance, under the action of reverse cutting edge extrusion, ultrasonic ironing, and the finishing machining.

In Figure 11, it is clearly reflected that the changing state of F_z at the beginning of the cutting, the cutting force mutation with the bottom edge, and the edge begin to participate in the cutting, ultrasonic-assisted vibration generated by the impact force, which makes the cutting force fall to stable, where the cutting becomes light and enters into stable cutting, stage I. As the bottom edge exits the milling process, it can be seen from the curvature of the falling axial force that the cutting removal amount is small and falls in a uniform decreasing way. The reason is that the peripheral edge gradually cuts uniformly downward, the cutting removal is gradually reduced, and at the same time, the top cutting edge involved in the cutting removal is small, which indicates stage II. As the top cutting edge of the peripheral edge exits and the third stage begins, the cutting force is reduced to a minimum.

In the fourth stage of reverse cutting, the main fiber fracture mode is changed from extrusion to cutting and rolling, the material removal and deformation are low, and the axial force is lower than the critical value of the interlayer binding force; however, there are some jump points in the figure, which are caused by fiber rebound or burr in the hole wall position and by the cutting force mutation.

According to the analysis in Figure 12, it can be seen that with the increase in the number of hole makings, Fx and Fy increased by 30.27% and 22.26%, respectively, with the increase in the number of processed holes at 90, which leads to an increase in tool wear, and which makes it difficult for the tool to remove the material, leading to a gradual increase in cutting force [24]. However, in the aspect of axial force, under the ultrasonic vibration impact, the cutting becomes easy and fast, and the axial force is still at a relatively low level. After 60 holes were processed, the axial force was about 18.5 N, which was reduced by 48% compared with the reference; after 90 holes were machined, the axial force was only 23.3 N, almost equal to the axial force level recorded in the reference in the initial machining state [25], which effectively avoids the tearing of carbon fiber materials, and no obvious delamination defects occurred in the holes.

5. Conclusions

In this paper, based on the kinematic characteristics of a cone spiral milling hole, the material removal characteristics of forward and reverse cone spiral milling holes were analyzed, and the ultrasonic milling mechanism was introduced to reveal the material removal law of the ultrasonic enhanced progressive cone spiral milling holes, which made it possible to achieve both machining efficiency and quality. The following conclusions were obtained through experimental verification.

The main contributions of this study can be summarized as follows:

• Based on the research of the material removal mechanism, it is verified that taper progressive spiral milling can realize integral processing of drilling and reaming shaving. For the bottom edge drilling and edge reaming hole to carry out rough machining, the application of the top edge to complete semi-finishing, and of the reverse cutting edge to complete finishing, the material removal of the end edge is about 0.44 that of a conventional cylindrical spiral milling cutter, which greatly reduces the axial force and improves the cutting efficiency and quality of the parts.
• The ultrasonic vibration-assisted progressive cone-spiral milling strategy changes the material removal mechanism, making the bottom edge beat the impact material at high frequency, the peripheral edge gradually impact the material, and the reverse cutting edge shear and rolling remove the material, making the cutting more brisk with a lower cutting force.
• Based on the plate and shell theory and linear elastic fracture mechanics, ultrasonic vibration-assisted progressive cone spiral milling can effectively increase the rigidity of the parts, improve the critical force of delamination, and reduce the axial force. With the increase in the number of milling holes, after 90 holes were machined, the axial force was only 23.3 N, which was still at a relatively low level, which improves the surface quality of the holes, and no obvious delamination defects were found in the parts.