1. Introduction
Inconel 718 has excellent properties such as high temperature resistance, oxidation resistance, and corrosion resistance. It is commonly used in aerospace parts manufacturing, but its cutting performance is poor. In the cutting process, it has the characteristics of a large milling force [
1], serious tool wear, and poor surface quality. With the development of the aerospace field, the cutting performance and surface quality of Inconel 718 are increasingly demanded. Therefore, it is an urgent problem to explore ways to improve the cutting performance and surface quality of Inconel 718.
Ultrasonic vibration machining is a machining method that applies ultrasonic waves to a cutting tool in a regular manner, allowing the tool to perform ultrasonic frequency vibration in a special direction and mode. Ultrasonic vibration machining is widely used in the fields of grinding [
2,
3], boring [
4], surface rolling [
5,
6], milling [
7,
8], drilling [
9,
10], and turning [
11]. Compared with CM, ultrasonic vibration milling has many advantages, such as effectively improving the surface characteristics of parts [
12] and residual stress, reducing tool wear [
13], suppressing tool chatter, reducing the milling force [
14,
15], and extending tool life [
16].
Most ultrasonic milling tools can be classified as one-dimensional ultrasonic vibration tools and two-dimensional ultrasonic vibration tools. In the field of one-dimensional ultrasonic vibration, Ni et al. [
17] designed a one-dimensional longitudinal ultrasonic milling tool and conducted comparative milling experiments on Ti-6Al-4V for CM and ultrasonic milling. It was concluded that ultrasonic milling had significant effects on reducing the milling force, improving the surface quality, and suppressing burrs. Chen et al. [
18] designed a one-dimensional longitudinal milling tool and compared the traditional helical milling and ultrasonic helical milling of Ti-6Al-4V alloy. By analyzing the two processing techniques, it was concluded that the aperture error and surface roughness of the ultrasonic helical milling hole were smaller than those in helical milling, and the subsurface hardness and surface residual compressive stress of the processed hole were significantly improved. Chang et al. [
19] proposed a one-dimensional longitudinal ultrasonic milling tool. CM and ultrasonic vibration milling experiments of GH4169 superalloy were carried out. The results showed that ultrasonic vibration milling could produce finer grains, higher residual stress, and reduce the occurrence of tool chatter. The milling force was significantly reduced, thereby improving the wear resistance, strength, and fatigue life of the material. Long et al. [
20] designed an exponential horn based on a one-dimensional wave equation and equivalent circuit theory. After the addition of ultrasonic vibration, the tool could produce torsional vibration. The resonance frequency and torsional amplitude were measured, and the results showed that the measurement results were consistent with the theoretical results, providing a guiding role for the development of a torsional ultrasonic horn.
However, a one-dimensional ultrasonic milling tool only vibrates in the axial or tangential direction, while a two-dimensional ultrasonic milling tool can vibrate in the tangential and axial directions, forming a circular or elliptical motion trajectory so that its cutting effect is better than that of a one-dimensional ultrasonic milling tool.
The methods for producing the longitudinal–torsional vibration mode are as follows. A double excitation vibration device is adopted, that is, a tangentially polarized piezoelectric ceramic sheet and a longitudinal vibration piezoelectric ceramic sheet are designed to generate composite vibration. The principle of this method is to change the longitudinal vibration and the torsional vibration by changing the sound speed of the longitudinal vibration and the torsional vibration so that the transducer resonates at the same frequency in the longitudinal–torsional vibration. However, the manufacturing technology of a tangentially polarized piezoelectric ceramic sheet is not perfect, which makes it difficult to satisfy the demands of high-power processing, so it is not widely used. The second method is to use a single excitation vibration device by setting a modal conversion structure on the horn or transducer so that the single longitudinal vibration generated by the transducer is converted into longitudinal–torsional vibration. This method has the advantages of a simple structure and convenient use, and it overcomes the shortcomings of a double excitation vibration device.
In the field of two-dimensional ultrasonic vibration, Ma et al. [
21] proposed a single-excitation LTUM tool that set a spiral slot structure on the conical surface of a horn to achieve longitudinal–torsional conversion. A surface roughness Ra of 0.5 μm was achieved in the milling of BK0 optical glass, and this process also showed great advantages in fast chip removal. However, the horn with a spiral slot structure had many parameters affecting frequency resonance, and the model was difficult to establish. Ying et al. [
22] designed a single-excitation LTUM tool for titanium alloy milling. By designing spiral grooves on the conical surface of the horn to realize longitudinal and torsional transformation, the tool could improve the compressive stress and fatigue resistance design performance of titanium alloy, laying a foundation for the study of compressive stress and fatigue resistance of titanium alloy. However, the spiral groove structure was set at the conical end of the horn, which increased the spiral groove parameters and made design optimization more difficult. Geng et al. [
23] proposed a dual-excitation ultrasonic milling tool for CFRP processing. Two sets of piezoelectric ceramic plates were used to generate bending vibration at the end of the tool. Compared with traditional grinding, the surface integrity of ultrasonic machining was better, and the tool life was increased by 1.98 times. The surface after traditional grinding exhibited fiber pull-out, irregular tool feed marks, and higher roughness. However, the use of two sets of piezoelectric ceramic plates in this tool greatly increased the manufacturing cost, and the design and processing process were complex. Zheng et al. [
24] proposed a single-excitation oblique longitudinal–torsional ultrasonic milling tool, which realized longitudinal–torsional conversion by machining chutes on the milling tool. The rotation axis of the tool was slightly tilted, and the tilt angle was about 15 °, which could form a good microstructure surface morphology on the simulated aircraft wing and biomedical metal surface. The fish-scale microstructure was prepared on the curved surface structure of the implant. Compared with CM, it avoided the phenomenon of secondary back cutting. However, this ultrasonic tool required the design of a chute structure on the milling tool, which was difficult to manufacture, and the types of milling tools suitable for clamping were limited. Du et al. [
25] developed an ultrasonic milling tool with longitudinal bending vibration mode. When the same voltage was applied, the PZT ceramics on the transducer became thicker and thinner respectively, thus forming bending vibration. The innovation of this tool is that it could achieve both an impact ironing effect and intermittent cutting effect at the same time, so as to achieve high-precision milling. Compared with traditional milling and one-dimensional longitudinal ultrasonic milling, this tool reduced the milling force by 85.2% and 54.5%, respectively, reduced the surface roughness, and effectively suppressed the generation of burrs. However, the tool was not innovative in structure.
Based on the above research, a single-excitation LTUM tool is designed, which is more compact. The chute is set at the cylindrical end, and the structure realizes longitudinal–torsional conversion. The structure is simple and easy to manufacture. First, the motion characteristics of LTUM are analyzed and designed. The single excitation ultrasonic horn is optimized with Abaqus finite element analysis software. Then, the impedance analysis experiment and amplitude test experiment are carried out on the designed LTUM tool to verify the performance parameters of the designed ultrasonic tool. Finally, milling experiments are carried out on the difficult-to-cut material Inconel 718. It is concluded that the LTUM tool can effectively reduce the milling force and tool wear, improve the surface quality, inhibit the generation of burrs, and improve the chip breaking ability when milling Inconel 718. The feasibility of the LTUM tool design is proven, which provides guidance for the development of LTUM tools and verifies that LTUM technology can significantly improve the machining performance of Inconel 718 material.
2. Design of LTUM Tool
2.1. Motion Characteristic Analysis of LTUM
LTUM couples the vibration of the torsional vibration along the rotation direction of a tool and the ultrasonic longitudinal vibration along the longitudinal direction of the tool, with the tool as the vibration carrier, and the ultrasonic vibration output is uniform and stable.
Figure 1 shows the LTUM model. The tool cutting edge motion is composed of the tool rotation motion, ultrasonic longitudinal vibration, ultrasonic torsional vibration, and feed motion.
When the tool is subjected to ultrasonic vibration for cutting, the motion path of the tool becomes very complicated. In ultrasonic milling, the trajectory of the cutting edge affects the machining efficiency and work efficiency. Therefore, it is necessary to establish the trajectory equation of the milling edge. In the CM process, the trajectory equation of the milling edge is as follows:
LTUM is based on CM, and longitudinal–torsional vibration is applied to the tool at the same time. The path of motion equation of the milling edge is as follows:
where
m is the feed rate, where
m =
wszfz/60;
w is the speed of the main spindle;
fz is the feed per tooth;
L is the supersonic frequency;
d is the ultrasonic longitudinal amplitude;
e is the ultrasonic torsional amplitude;
u is the tool radius; and
θ1 and
θ2 are the initial phases of ultrasonic longitudinal vibration and torsional vibration, respectively.
Figure 2 shows their trajectories.
By comparing the cutting edge trajectories of CM and LTUM, the cutting edge trajectory of LTUM has a periodic fluctuation phenomenon. This is because LTUM generates periodic torsional vibration based on longitudinal vibration. This composite vibration leads to periodic contact and separation between the tool and the workpiece, so LTUM can produce intermittent cutting, while CM can only be processed continuously. LTUM can reduce the milling force and cutting heat, reduce the surface roughness, and improve the surface quality.
2.2. Design of Longitudinal-Torsional Ultrasonic Horn
The horn is an indispensable part of the whole LTUM tool; it has the functions of amplifying amplitude, matching impedance, and gathering energy [
26]. The horn model is designed in an ideal state, so it is necessary to ensure that each part of the horn is made of uniform material and mechanical loss is not considered. When the wavelength of the horn is greater than the cross-section size, it can be considered that the longitudinal wave spreads along the longitudinal direction of the horn. The displacement and stress of the particle on the cross-section of the horn should be evenly distributed. For simple harmonic motion, each section of the horn should satisfy the fluctuating equation. The longitudinal vibration equation of the horn is as follows [
27]:
where
s =
s(
x) is the cross-section area coefficient of the horn;
ξ =
ξ(
x) is the particle function; and
k =
ω/
c, where
k is the circular wave number.
ω is the angular frequency,
c is the sound velocity,
c = (
E/
ρ)
1/2,
E is young’s modulus, and
ρ is the material density.
The stepped horn has a simple structure and an easy design and manufacturing process. The conical horn has the advantages of good stability, no stress concentration, and a large amplification coefficient [
28]. The use of a conical composite stepped horn can also have the above advantages.
The large end of the horn should be connected to the transducer. Considering the diameter of the transducer, the diameter D of the large end of the horn is 30 mm and the diameter d of the small end is 15 mm.
The horn material is 20GrMnTi, and
Table 1 shows the material properties. The design frequency
f is 28 kHz, to facilitate the calculation,
L2 is set to 30 mm, and the design is shown in
Figure 3. The large end
L1 is set to
λ/4, and
λ is the wavelength. The horn was designed using the four-terminal network method, and the specific design equation is as follows:
Area coefficient: n = D/d.
Circular wave number: g = ω/c = 2πf/c.
Frequency equation:
where
n =
D/
d and
α = (
n − 1)/
nL2.
Table 1.
Material characteristics of the horn.
Table 1.
Material characteristics of the horn.
Material | Density (kg/m3) | Elastic Modulus (GPa) | Poisson’s Ratio σ |
---|
20GrMnTi | 7800 | 207 | 0.3 |
The horn flange is set at the junction of the large end and the cone end, and the flange thickness is 5 mm.
The longitudinal wave loses a large amount of energy in the air. Ignoring the influence of secondary refraction, only the reflected longitudinal wave and the reflected shear wave are considered. Shear waves can easily cause shear deformation, and gas and liquid cannot bear the shear force, so the shear waves can only propagate in the solid state. As shown in
Figure 4, the longitudinal wave is incident at an angle of α. When the longitudinal wave σ is reflected when it passes through the slanting slot position, a reflected longitudinal wave σ
1 with an angle of θ and a reflected transverse wave τ are generated. The reflected transverse wave vibrates along the circumferential direction of the horn to produce torsional vibration, and the reflected longitudinal wave vibrates along the axial direction of the horn to produce longitudinal vibration.
In summary, the slanting slot structure can make the longitudinal wave produce longitudinal–torsional waves and output these waves at the end of the horn.
Figure 5 shows the structure of the horn: there are four slanting slots evenly distributed along the circumferential direction at the small end of the horn, with an angle of 60°, a length of 10 mm, a width of 3 mm, and a depth of 4.5 mm.
2.3. FEM Analysis
The mode analysis of the horn was conducted with Abaqus software. Modal analysis is the basis of dynamic analysis, and the vibration characteristics of the workpiece can be determined by modal analysis. The three-dimensional model of the horn was imported into Abaqus software, and the fixed constraint was applied to the flange position of the horn.
Figure 6 is the simulation result. When the 12th-order modal resonance frequency is 29,798 Hz, the horn could achieve longitudinal vibration, and the displacement vector of each point was the longitudinal displacement.
Figure 7 is the simulation result. At 28,133 Hz, the displacement vector at the end of the horn had a torsional trend. The horn generated longitudinal–torsional vibration, which met the design frequency requirements.
To ensure that the horn could efficiently transmit ultrasonic vibration to the tool during milling, a clamping method needed to be considered. The commonly used clamping methods are hot assembly connection and thread connection. The hot assembly connection structure is simple and the connection is tight, but it is not easy to disassemble and change the tool. Thread connection can reduce the loss of ultrasonic transmission, but processing is difficult and the cost is high. With comprehensive consideration, the spring chuck and the screw nut were used to connect the milling tool, as shown in
Figure 8a. This connection method ensured the reliability of the clamping and the clamping of different straights. As shown in
Figure 8b, after clamping the milling tool on the horn, the overall frequency reached 19,773 Hz.
Transient dynamic analysis is based on modal analysis to obtain the time of the tip output at a certain point at a fixed frequency. As shown in
Figure 9a, a displacement excitation of 1 μm was applied to the large end cylinder of the horn, and the analysis frequency was 20–40 kHz. Transient dynamics analysis was carried out, and part of the outlet displacement curve was fitted. The vibration-cutting trajectory in three-dimensional space was obtained at the resonance frequency. At 21,042 Hz, the longitudinal vibration excitation y (t) = 0.001 × sin (2π × 21,042 × t) was applied to the large end of the horn to obtain the time displacement of the tool tip in the x-, y-, and z-directions. As shown in
Figure 9a, the torsional amplitude was small, so it could be regarded as the bending amplitude in the y-direction.
The displacement in the x-, y-, and z-directions was combined to obtain a three-dimensional elliptical trajectory, as shown in
Figure 9b. From the diagram, it can be seen that the elliptical trajectory synthesized by the tip in the x-, y-, and z-directions was regular, and the amplitudes were 6.9 µm and 1 µm.
2.4. Optimization of Ultrasonic Milling Tool
It can be seen from the discussion in the previous section that the parameters of the slanting slots affect the magnitude of the amplitude, that is, the torsional–longitudinal ratio of the torsional amplitude to the longitudinal amplitude. Additionally, the magnitude of the torsional–longitudinal ratio in the milling process determines the quality of the machined surface. To better match the horn to the 21 kHz transducer, some parameters of the horn needed to be optimized. The resonance frequency and torsional–longitudinal ratio of the horn affect the machining performance of the milling tool. The length of the small end of the horn and the parameters of the slanting slots affect the resonance frequency and torsional–longitudinal ratio. Through Abaqus simulation analysis, the end size and chute parameters of the horn were optimized, so that the frequency of the horn was closer to 21 kHz. At the small end of the horn, the slanting slots were evenly distributed along the axial direction. Considering the structure of the output end of the horn, the slanting slots were set to be 10 mm long, 3 mm wide, 4 mm deep, and 4 mm away from the connection between the cone and the small end. The slanting slot angle, slot depth, and the length of the small end of the horn were adjustable. The temporary slanting slot angle was 45°, the slot depth was 5 mm, and the length of the small end of the horn was 38 mm.
The single-factor method was used to change the length of the small end of the horn as well as the angle and depth of the slanting slots of the horn, and the parameters were kept unchanged. The resonance frequency of the horn at approximately 21 kHz was found, and the flange of the horn was guaranteed to be located at the node position. The changes in the resonance frequency f and the torsional–longitudinal ratio
e of the horn are shown in
Figure 10.
Figure 10a,b show the influences of the slanting slot angle on the resonance frequency and
e. The resonance frequency
f increased with the increase in the slanting slot angle, and the frequency was close to 21 kHz at approximately 55°. The ratio
e first increased and then was reduced with the increase in the slanting slot angle, and the ratio reached the maximum at 55°.
Figure 10c,d show the influences of the depth of the slanting slot on the resonance frequency
f and
e. The resonance frequency decreased slowly with the increase in the depth of the slanting slot, and when the slanting slot depth was approximately 5 mm, the resonance frequency
f was close to 21 kHz. The ratio
e increased as the depth of the slanting slot increased.
Figure 10e,f show the influences of the
L3 length on the resonance frequency
f and
e.
Figure 10e shows the influence of
L3 on the resonance frequency. With the increase in the length of
L3, the resonance frequency
f was reduced and was close to 21 k Hz at about 35 mm.
Figure 10f shows the influence of
L3 on
e. With the increase in
L3 length,
e first increased and then was reduced, reaching the maximum at about 35 mm. Therefore, considering the resonance frequency
f and
e, the slanting slot parameters were set to be 10 mm long, 3 mm wide, and 4 mm deep.