A simulation of chip formation mechanism in elliptical vibration assisted cutting of nickel-based superalloy Inconel 718

Abstract

This article reveals the chip formation and the reducing of cutting force mechanisms of nickel-based superalloy Inconel 718 under elliptical vibration cutting using finite element analysis software. The results are compared with traditional cutting methods. The elliptical motion trajectory of the tool in elliptical vibration cutting machining is analyzed, and a two-dimensional finite element elliptical vibration cutting model is established. The effects of dynamic impact on the elliptical vibration cutting of Inconel 718 were discussed in terms of the surface morphology, chip formation mechanism, and cutting force reduced mechanism. The simulation results show that (1) compared with traditional cutting, the surface morphology of the workpiece machined by elliptical vibration cutting is better, and the machined surface has obvious elliptic indentation; (2) in traditional cutting, sawtooth chips are formed through shear slip, while in elliptical vibration cutting, the faster relative cutting speed $v_{\mathrm{c}}$ , higher tool-tip temperature, and smaller material removal cross-sectional area cause a more prominent thermal softening effect in the chip formation process than that in traditional cutting, which leads to the plastic flow to be dominant in the material removal process, resulting in the strip chips; and (3) compared with traditional cutting, the normal cutting force and the tangential cutting force in elliptical vibration cutting are separately reduced about 51.4% and 60.8%.

Introduction

Nickel-based high-temperature alloy Inconel 718 is known for its excellent physical and chemical properties. Compared with other metals, Inconel 718 maintains its strength and corrosion resistance better at temperatures higher than 700 °C. Therefore, Inconel 718 is widely used in the high-temperature working parts of aviation and aerospace gas engines. However, due to the low thermal conductivity, high work-hardening, and high chemical affinity characteristics of this alloy during machining, the machining is prone to high temperatures, high cutting forces, and adherence to the tool, resulting in difficulty in ensuring the quality of the machined surface, and causing serious tool wear, thus the machinability of this alloy is relatively poor, and it is regarded as a typical difficult-to-machine material.^1–3 The chemical composition and mechanical properties of Inconel 718 are shown in Tables 1 and 2, ⁴ respectively. Machined surface integrity is critical to the service life and service performance of nickel-based high-temperature alloy components in aerospace and other fields. Surface integrity is closely related to chip morphology, cutting temperature, and cutting force during machining. For this reason, chip morphology and its fracture mode have received intensive attention in the field of machining. Zhang et al. ⁵ found that when the free surface of the chip has a typical serrated morphology, folds can be observed on the back of the chip, and the mechanism is attributed to the formation of serrated chips due to the large strain caused by high-speed cutting. In addition, the strong sliding behavior between the backside of the chip and the tool caused the debris of the ceramic tool to adhere to the chip, resulting in adhesive wear of the tool. A study by Ming et al. ⁶ found that the clogging of chips leads to severe scratching and change in the color of the hole surface, which also contributes to the occurrence of defects on the surface of the hole and nanocrystalline microstructure transformation. Therefore, chip morphology has a significant impact on the integrity of the drilled hole surface. In order to obtain a better-machined surface quality, it is necessary to thoroughly investigate the chip formation mechanism and its evolution during the machining of nickel-based superalloys.

Table 1.

Chemical composition of Inconel 718 alloy (wt.%).

Element	Ni	Cr	Nb	Mo	Ti	Al	Co	Si	Mn	Cu	C	P	Fe
wt.%	53.4	18.8	5.27	2.99	1.02	0.50	0.17	0.12	0.07	0.07	0.03	0.01	Bal

Table 2.

Mechanical properties of Inconel 718 alloy.

Content	Density $\rho ({\mathrm{k}}_{\mathrm{g}}/{\mathrm{m}}^3)$	Yield strength ${\sigma }_{0.2}(\mathrm{MPa})$	Tensile strength ${\sigma }_b(\mathrm{MPa})$	Elongation ${\sigma }_5(\text{\%})$	Shrinkage $\psi (\text{\%})$	Toughness $a_k(\mathrm{J}/{\mathrm{cm}}^2)$
Value	8280	1620	1430	24	40	40

Elliptical vibration cutting (EVC) $(\le 16\mathrm{kHz})$ technology, as a new non-traditional machining method, is typically characterized by tools with intermittent cutting behavior. A large number of studies have shown that EVC can effectively improve the machined surface quality, reduce the cutting force, ⁷ effectively inhibit the formation of chip tumors, and improve the tool life. ⁸ In addition, the EVC method has been proven to be beneficial for removing burrs ⁹ and obtaining a mirror-like surface finish, ¹⁰ which has a great potential to be applied in machining difficult-to-machine materials. ¹¹ It was shown that when vibration-assisted drilling of carbon fiber reinforced polymer/Al co-cured material was applied, ¹² the thickness of undeformed chips is discontinuous, resulting in a superior chip breakage effect, which reduces the surface scratches on the hole wall and thus improves the drilling accuracy. In the cutting of 7050-T7451 aluminum alloy, the cutting forces under ultrasonic elliptical vibratory cutting (UEVC) conditions were reduced by about 40% with better surface quality and reduced tool wear. ¹³ In dry ultra-precision machining of Ti-6Al-4V, the UEVC method can produce the continuous chips and easy to form shorter, regular, and friable chips, which in turn reduces the burrs and flash, and enhances the surface quality of the machined surface. ¹⁴ In addition, ultrasonic vibration precision turning of titanium alloys also effectively improves the machined surface quality. ¹⁵ The aforementioned studies used experimental methods to find out that vibration-assisted cutting better controls the chip shape, reduces the chip force, and improves the machined surface quality. However, due to the EVC-induced changes in tool cutting motion trajectory, stress changes, and thermal softening phenomenon, these factors interact with each other and comprehensively determine the chip formation process and machining surface quality, so the study of the effect of vibration on chip shape and its evolution law is necessary to be further investigated.

Finite element analysis (FEA) has been reported extensively in cutting technology research. Compared with the experimental study, the FEA method is economic. ¹⁶ In the FEA of UEVC cutting Inconel 718 machining, it was found that ultrasonic vibration resulted in an increase of the shear angle in the cutting region, leading to a lower chip thickness than conventional turning. ¹⁷ Additionally, Babitsky et al. ¹⁸ found that more regular chips were produced in ultrasonic vibration-assisted turning and the chips produced in conventional turning had distinctive shear bands using electron scanning microscopy, and the equivalent plastic strain in the cutting region was simulated using FEA. However, the reasons for the formation of more continuous chips in ultrasonic vibration-assisted turning and the formation of chips with distinct shear bands in conventional turning, as well as their evolutionary processes, which should be further investigated. In the simulation of UEVC cutting TiC-particle reinforced titanium matrix composites machining, compared with traditional cutting (TC), it was found that the cutting speed became larger and the cutting force became smaller at the instant of the tip contacting the substrate, which in turn caused the material deformation to be small, reduced the machined surface roughness, and formed a better-machined surface. ¹⁹ The above studies show that, as an economic method, FEA has been widely used in the simulation research of machining, and is beneficial in presenting the dynamic evolution of chips and machined surfaces during machining.

Therefore, EVC technology has better machining performance than TC. In order to expand the application of EVC technology in the field of nickel-based high-temperature alloy machining, this article investigated the chip formation mechanism and cutting force reduction mechanism of Inconel 718 under EVC machining, established a two-dimensional (2D) EVC finite-element model of Inconel 718 by using ABAQUS software and conducted simulation to the deformation behavior of the cutting layer and the dynamic evolution of the chip process of Inconel 718 under EVC machining. The effects of the intermittent cutting behavior of the tool and the cyclic dynamic impact of elliptical vibration on the machined surface morphology, contact zone stress, cutting force, and tip temperature were comparatively investigated.

Kinematics analysis of EVC

Elliptical vibrational motion is a synthesis of two simple harmonic motions in the plane of the same frequency, in directions perpendicular to each other and with a certain phase difference, ²⁰ assuming that the equations of motion in both directions are

$$\begin{array}{c}\{\begin{array}{c}X(t)=A\cos (2\pi f+\beta )\\ Y(t)=B\sin (2\pi f)\end{array}\end{array}$$

(1)

where A is the X-direction amplitude, B is the Y-direction amplitude, f is the elliptic vibration frequency, $\beta$ is the phase difference between X and Y, the trajectory is a positive ellipse when the phase difference between them $\beta =90\circ$ , the trajectory equation is as follows:

$$\begin{array}{c}\{\begin{array}{c}X(t)=A\cos (2\pi f)\\ Y(t)=B\sin (2\pi f)\end{array}\end{array}$$

(2)

Consider the phase difference in the workpiece feeding direction, so that the motion trajectory to form an elliptical vibration motion trajectory, the trajectory equation of motion is

$$\begin{array}{c}\{\begin{array}{c}X(t)=A\cos (2\pi f)+v*t\\ Y(t)=B\sin (2\pi f)\end{array}\end{array}$$

(3)

The above equation is derived to obtain the expression of the tool velocity:

$$\begin{array}{c}\{\begin{array}{c}{v}_x(t)=2\pi fA\sin (2\pi ft)+v\\ v_y(t)=2\pi fA\cos (2\pi ft)\end{array}\end{array}$$

(4)

In the process of EVC, it can be roughly divided into three stages, ²¹ each of which is explained in detail below in conjunction with Figure 1.

Figure 1.

Schematic diagram of the principle of a single elliptical vibration trajectory.

The first stage is an a-b stage, which has the maximum removal efficiency in this stage. The second stage is the b-c stage, in which the front tool face reverses the chip direction, which can effectively inhibit the germination of chip tumors, thus improving the tool life and forming better processing quality. ²² The third stage is the c-d stage, in which the tool is not in contact with the workpiece and the tool begins to cold cut.

Finite element simulation

Finite element simulation is a set of mathematical linear equations that transforms an infinite degree-of-freedom problem in the continuous domain into a finite-degree-of-freedom problem to be solved in the discrete domain and is suitable for the study of complex physical phenomena in machining processes, such as the simulation of stress and temperature fields. The contact process between the tool and the workpiece during the machining presents material and geometric nonlinearities. ABAQUS simulation software is powerful in processing and simulating complex nonlinear problems in the machining process, so ABAQUS/Explicit was used to simulate EVC cutting of Inconel 718.

Establishment of 2D model

The workpiece length is 5 mm and the height is 2.5 mm. The simplified model is shown in Figure 2. Due to the simulation process is a 2D EVC cutting Inconel 718 thermodynamic coupled processing, planar quadrilateral continuous elements (CPE4RT) ²³ was used for the workpiece mesh, and the mesh element removal technology was used to realize the separation of chip and workpiece. In order to eliminate tool deformation and wear during EVC cutting, the tool is set to a rigid body to facilitate better analysis of the workpiece chip evolution mechanism during machining. The reference point RP was set on the upper right of the tool and the cutting speed to the reference point RP was set as 400 mm/s. In the simulation, the tool vibration frequency is 5000 Hz, and the amplitude is A = 0.3 mm, B = 0.25 mm. In order to improve the simulation efficiency, the height of the undeformed layer was set to 0.6 mm and refined. The refined cell mesh size is 0.025 mm × 0.025 mm, and the matrix part of the material model is 0.225 mm × 0.025 mm. In addition, constraints are applied at the bottom of the workpiece to ensure that the workpiece is fixed, and the predefined field temperature of the EVC cutting model is set to 20 °C. According to the existing research results, ²⁴ CBN tools have obvious advantages in processing nickel-based superalloys, such as high thermal conductivity, endurance, and good compressive strength, so CBN tools are selected in this article. The rake angle and the clearance angle of the CBN tool are 0° and 15°, respectively, and the radius of the tool tip is 0.05 mm.

Figure 2.

Finite element model in elliptical vibration cutting (EVC).

The material properties of workpieces and tools are shown in Table 3. ²⁵

Table 3.

Material properties of Inconel 718 alloy and CBN tool.

Material property	Inconel 718	CBN
Young's modulus (MPa)	206,000	706,000
Poisson's ratio	0.3	0.15
Density $(\mathrm{kg}\cdot {\mathrm{m}}^{-3})$	8280	3450
Specific heat $(\mathrm{J}\cdot {\mathrm{kg}}^{-1}{{\hspace{0.17em}}^{\circ }\mathrm{C}}^{-1})$	435	670

Determination of material parameters

Material constitutive equation

In the simulation process, the constitutive equation of the workpiece material plays a crucial role in capturing the relationship between material flow equivalent stress, equivalent stress, equivalent strain rate, and temperature. The J-C (Johnson-Cook) model is commonly employed to represent this constitutive relationship. The J-C model incorporates three essential effects: strain hardening, strain rate hardening, and thermal softening. It is particularly suitable for describing the stress-strain behavior of metal materials under high strain rate conditions. The expression of the J-C model is as follows: ²⁶ (5) where ${\sigma }_s$ is the material flow stress, $\epsilon$ is the equivalent plastic strain, $\dot{\epsilon }$ is the equivalent plastic strain rate, $T_m$ is the melting temperature, $T_w$ is the room temperature, $T_w$ is the material temperature, A, B, C, n, and m are the material intrinsic parameters. The intrinsic parameters of the Inconel 718 ²⁷ are shown in Table 4.

Chip separation criteria

The chip separation criterion can be categorized into two types: the physical separation criterion and the geometric separation criterion. In this study, the physical separation criterion is adopted, which means that the chip is generated when a specific physical quantity reaches a predetermined threshold value. To simulate the damage of metal materials accurately, the J-C damage evolution model is employed. In this model, when the damage parameter exceeds 1, the material is considered to have failed. The expression of the J-C damage evolution model is as follows: ²⁷

$$\begin{array}{c}\omega =\sum _{j=1}^n\left({\displaystyle \frac{\mathrm{\Delta }\overline{{\epsilon }^{pl}}}{\overline{{\epsilon }_f^{pl}}}}\right)\end{array}$$

(6)

where $\omega$ is the ratio of the equivalent plastic strain at the element integral point to the critical equivalent plastic strain, $\mathrm{\Delta }\overline{{\epsilon }^{pl}}$ is the increment of the equivalent plastic strain rate, and $\overline{{\epsilon }_f^{pl}}$ is the material failure equivalent plastic strain, it is expressed as: ²⁸ (7)

Table 4.

Coefficients for Johnson-Cook (J-C) stress flow model of Inconel 718.

A $({\mathrm{MP}}_{\mathrm{a}})$	B $({\mathrm{MP}}_{\mathrm{a}})$	C	n	m	$T_m({\hspace{0.17em}}^{\circ }\mathrm{C})$	$T_w({\hspace{0.17em}}^{\circ }\mathrm{C})$
985	949	0.01	0.4	1.61	1320	20

where p is the compressive stress, q is the equivalent stress, $\overline{{\epsilon }^{pl}}$ is the plastic strain rate, and $d_1,d_2,d_3,d_4,d_5$ are the failure parameters of the material. The failure parameters of Inconel 718 ²⁸ are shown in Table 5.

In ABAQUS simulation, the damage evolution of metal chip separation can be characterized using both energy separation and displacement separation criteria. In this study, the displacement separation rule is selected as the criterion for chip separation. The expression for the displacement separation criterion is as follows:

$$\begin{array}{c}D={\displaystyle \frac{\overline{u^{pl}}}{\overline{\overline{u_f^{pl}}}}={\displaystyle \frac{\overline{u^{pl}}}{\overline{\overline{{\epsilon }_f^{pl}L}}}}}\end{array}$$

(8)

where $\overline{u^{pl}}$ is the equivalent plastic displacement, $\overline{\overline{u_f^{pl}}}$ is the failure equivalent plastic displacement, L is the unit feature length, $\overline{{\epsilon }_f^{pl}}$ is the equivalent plastic strain at material failure. When $D\ge 1$ , the unit of the material fails.

Table 5.

Johnson-Cook (J-C) shear failure parameters of Inconel 718.

Material	$d_1$	$d_2$	$d_3$	$d_4$	$d_5$
Inconel 718	−0.239	0.456	0.3	0.07	2.5

Friction model

During the cutting process, the contact area between the tool and the workpiece gives rise to two types of friction regions: the adhesive region and the slip region. These friction regions are characterized using a modified Coulomb friction model in the simulation. The expression for the modified Coulomb friction model is as follows ²⁹ :

$$\begin{array}{c}{f}_s=\{\begin{array}{ccc}\mu {\sigma }_n& \mu {\sigma }_n<{\dot{\tau }}_{max}& (slipzone)\\ {\dot{\tau }}_{max}& \mu {\sigma }_n\ge {\dot{\tau }}_{max}& (adhesionzone)\end{array}\end{array}$$

(9)

where $f_s$ is the friction stress, ${\sigma }_n$ is the positive stress, $\mu$ is the friction factor, and ${\dot{\tau }}_{max}$ is the critical shear stress.

Simulation results and analysis

Surface topography

Figure 3 shows the stress contour plot of the machined surface, along with a magnified view of a specific region, both with and without EVC. Figure 3(a) is the surface machined by EVC, and Figure 3(b) is the surface machined by TC. It can be seen from Figure 3 that under EVC machining, the path of the tool on the workpiece surface is an elliptical path, and the cutting depth $a_p$ is periodically gradient changed from small to large. In comparison to TC methods, the machined surface achieved with EVC exhibits a relatively flat roughness profile. Notably, distinctive elliptical vibration track indentations are present, contributing to an overall improved surface finish.

Figure 3.

Comparison of surface morphology in the cutting process: (a) EVC; and (b) TC.

In addition, in TC machining, unexpected features, such as burrs and small defects, are observed on the machined surface, which is absolutely not allowed for the surface requirements of precision parts. Therefore, as mentioned above, the excellent surface quality obtained by EVC processing is further confirmed.

Traditional cutting force and chip formation process

Figure 4 is the variation of cutting force in TC with a depth of cut of 0.5 mm and a cutting speed is 24 m/min. As machining proceeds, the workpiece comes into contact with the tool. Under the extrusion of the tool, the material undergoes plastic deformation, and the value of the NCF (normal cutting force) increases dramatically, reaching a maximum value of about 380 N. Then, the cutting depth remains unchanged, the cutting enters a stable state, and the NCF decreases to a certain extent, and in this stage, the NCF value shows periodic changes, fluctuating around 200 N. When the tool leaves the surface of the workpiece, the contact surface of the extrusion is changed from the front face of the tool to the rear face, and the extrusion effect of the tool on the workpiece is weakened, and as a result, NCF decreases. When the tool completely leaves the surface of the workpiece, there is no extrusion between the tool and the workpiece, and the NCF decreases rapidly to 0, as shown in Figure 4(a).

Figure 4.

The force diagram in traditional cutting (TC): (a) normal force and tangential force; and (b) magnification of local tangential forces.

In a machining process, sawtooth chips are composed of multiple units of sawtooth chips after many single-toothed chips undergo adiabatic shear slip behavior. The evolution law of a single sawtooth chip is closely related to the change of cutting force. However, in the actual cutting process, the formation process of the chip is very fast, which is not easy to observe. In order to further reveal the evolution of a single sawtooth chip, a contrast analysis is conducted by employing the TCF (tangential cutting force) change curve (Figure 4(b)) and the simulated sawtooth chip cloud pictures (Figure 5).

Figure 5.

The formation process of single sawtooth debris: (a) 1.2 × 10⁻³s; (b) 1.35 × 10⁻³s; (c) 1.65 × 10⁻³s; (d) 1.95 × 10⁻³s; (e) 2.175 × 10⁻³s; and (f) 2.475 × 10⁻³s.

At the very beginning of contact between the tool and the workpiece, under the action of the impact load of the tool, the tool and the workpiece begin to extrude, and the material undergoes plastic deformation, as shown in (b) of Figure 5, resulting in a sharp increase in the TCF, which reaches about 73 N, point 2 in Figure 4(b), at which the value of the stress can be seen as $2.009{\mathrm{GP}}_{\mathrm{a}}$ from (b) in Figure 5. As the machining continues, the extrusion of the workpiece and the tool continues, the plastic deformation of the workpiece surface is further strengthened, and the TCF continues to increase, which is represented in the change of the force at point 3 in Figure 4(b), when the cutting force reaches 110 N. At the same time, the friction between the tool-tip and the surface of the workpiece begins to take place in Figure 5(c). At this point, the value of stress is $2.151{\mathrm{GP}}_{\mathrm{a}}$ . From the increase in stress values, it is clear that from point 2 to point 3, a large number of dislocations are accumulated due to the increase in plastic deformation after the tool is in contact with the workpiece. When the density of dislocations increases, the rheological stress increases, resulting in an increase in the plastic deformation resistance, which increases the hardness value of the material, so that the strain-hardening effect is prominent. After that, the accumulated protrudes sprout shear slip, as shown in Figure 5(e), and the cutting force begins to decline sharply, but there is a stage of rising cutting force value between 4–5 and 5–6, the main reason for the existence of this stage is the ductile fracture at the free surface of chips I, which requires a certain amount of energy (region I in Figure 6), so that the decline of cutting force has a certain rebound. Then, the shear slip continues, representing the completion of a shear slip, namely, point 6 in Figure 4(b), at which time the TCF value is about 40 N.

Figure 6.

Schematic diagram of the principle of sawtooth debris: (a) serrated chip schematic; and (b) schematic of a simulated sawtooth chip.

Through the above analysis, it can be found that the periodic change of cutting force value and the formation of sawtooth chips can be well corresponding. The cutting force value increases rapidly when the workpiece is initially squeezed by the tool. When the softening effect and strain strengthening effect reach a certain balance, the adiabatic shear slip condition is formed, ³⁰ then the shear slip is produced, and the cutting force value decreases rapidly.

Influence of elliptic vibration on chip morphology

In EVC machining, the variation curves of NCF and TCF are shown in Figure 7, where the frequency is 5000 Hz and the amplitude is 0.25 mm.

Figure 7.

The variation curves of NCF and TCF in the EVC: (a) Normal and tangential forces; (b) The partial enlarged curves of NCF and TCF.

Due to the evolution of chips in the machining process being rapid and not easy to be observed, the trends of NCF (Figure 7) and the simulation of chip morphology (Figure 8) were combined to analyze the evolutional process of chip morphology in a single EVC cycle. Figure 8(a), (c) and (e) correspond to points 1, 2, and 3 in the graph of Figure 7(b), respectively.

Figure 8.

The evolutional process of a chip in a single elliptical vibration cutting (EVC) cycle: (a) 1.2 × 10⁻³s; (b) 1.25 × 10⁻³s; (c) 1.3 × 10⁻³s; (d) 1.35 × 10⁻³s; and (e) 1.4 × 10⁻³s.

When the tool is not in contact with the workpiece, there is no squeezing action and the cutting force is 0 N, namely, point 1 in the diagram of Figures 7(b) and 8(a). At the beginning of EVC machining, the tool enters the material removal stage, corresponding to stages (a) to (c) in Figure 8. When the tip of the tool comes in contact with the workpiece, with the squeezing action of the tool, the contact zone undergoes plastic deformation. From Figure 8(a) to (c), it can be seen that the stress value increases from $1.336\mathrm{to}1.705{\mathrm{GP}}_{\mathrm{a}}$ . At this stage, the area of the chip removed gradually increases resulting in the resistance of plastic deformation of the workpiece increasing as well, which ultimately leads to an increase in the NCF from 0 N to about 360 N, namely, point 2 in the graph of Figure 7(b). When the chip starts to separate from the rake face of the tool, due to the intermittent cutting behavior of EVC, the extrusion of the tool on the workpiece slowly decreases, leading to the weakening of the plastic deformation of the material. From Figure 8(c) to (e), it can be seen that the stress value decreases from $1.705\mathrm{to}1.285{\mathrm{GP}}_{\mathrm{a}}$ . At this stage, the NCF is rapidly reduced from about 360 to 0 N, corresponding to point 3 in Figure 7(b). When a single EVC vibration cycle is finished, the chip morphology is a strip chip which is different with the sawtooth chip formed in CT machining.

There are three reasons for producing this type of chip: firstly, in EVC, the cutting speed $v_{\mathrm{c}}$ is a combination of the tool vibration speed $v_{\mathrm{f}}$ , and the cutting speed $v_{\mathrm{s}}$ , so compared with TC, the $v_{\mathrm{c}}$ is greater than $v_s$ , which can be illustrated in Figure 9. In addition, in EVC, the distance path S1 is longer than path S2. As the cutting speed increases, the contact pressure between the tool and the workpiece increases, resulting in the plastic deformation of the workpiece and the friction in the tool-workpiece contact area become more intense, and ultimately the cutting heat increases. The temperature change during the material removal stage is shown in Figure 10, the temperature of the tool-tip was increased from 246.2 °C to 261.2 °C.

Figure 9.

Tool travel path diagram.

Figure 10.

Temperature cloud map during material removal phase in elliptical vibration cutting (EVC): (a) 1.85 × 10⁻³s; and (b) 1.9 × 10⁻³s.

Secondly, in the cutting process, the heat generated is carried away by chips, workpieces, tools and coolants. Since the coolant factor is not considered in the simulation cutting process, the dispersion of cutting heat can be illustrated in Figure 11, where Q_t1 and Q_w1 are expressed as the heat into the CBN tool and the machined surface, respectively; Q_c1 and Q_w2 are expressed as the heat into the chip and the workpiece to be machined, respectively; and Q_c2 and Q_t2 are expressed as the heat into the chip and the workpiece, respectively; h₁ and h₂ are the chip thicknesses under the two machining methods.

Figure 11.

Schematic diagram of heat dispersion: (a) EVC; (b) TC.

Finally, the material removal diagram of TC and EVC is shown in Figure 12(a) is the cross-section area of the material removed by a single elliptical cycle tool under EVC machining, representing the enlargement of the blue box in Figure 12(b), and the cutting depth $a_p$ presents a periodic gradient change from small to large, and is smaller than the cutting depth $a_p$ in TC. The cross-sectional area of material removal in EVC gradients with increasing depth of cut $a_p$ , and the maximum cross-sectional area is removed when the depth of cut $a_p$ reaches the maximum. At the same time, the continuous friction between the tool-tip and the workpiece makes the changing trend of the tool-tip temperature consistent with the change of the material cross-section area, namely, the tool-tip temperature is the highest when the cross-section area is the largest. Figure 12(d) is the chip of material removed by the tool within a specified time under TC processing, and which is formed by the continuous accumulation of a single sawtooth chip in Figure 12(c). The material removal volume of TC was kept within a fixed range due to the cutting depth $a_p$ constant. As can be seen in Figure 11, compared with TC, the chip width formed in EVC is narrower, namely, h₂ is larger than h₁ (Figure 11).

Figure 12.

Chip formation: (a) and (b) EVC; and (c) and (d) TC.

According to the above analysis, under the same test parameters, the relative cutting speed $v_{\mathrm{c}}$ in EVC is greater than the cutting speed $v_{\mathrm{s}}$ in TC, which generates more heat. When the heat reaches a certain degree, the surface structure of the workpiece is recrystallized and the grain is refined. Figure 13 shows the plastic strain cloud diagram during EVC machining, from which it can be seen that after grain refinement, the hardness and strength of the workpiece decreases, and the plasticity increases, with its value rising from 1.051 to 1.085, resulting in a weakening of the work-hardening effect. In addition, the intermittent cutting behavior of the tool during the material removal process in EVC results in smaller chips being produced on the workpiece removal surface, which undergoes a rubbing-ploughing-chip formation process in each cycle (Figure 14). Therefore, at higher temperatures and smaller removal cross-sectional areas, thermal softening is prominent in the process of chip generation. The above two reasons lead to the fact that in EVC, the removal of material is dominated by plastic flow, resulting in the formation of strip chips.

Figure 13.

Plastic strain components at different stages: (a) 1.85 × 10⁻³s; and (b) 1.9 × 10⁻³s.

Figure 14.

The rubbing-ploughing-chip formation schematic in elliptical vibration cutting (EVC).

Reducing mechanism of cutting force under elliptical vibration

Due to the simple harmonic characteristics of EVC, it is evident, from Figure 7(a), that the cutting force curves of EVC present periodic changes. Under EVC, the average NCF is 124.5 N and the average TCF is 22.7 N. As shown in Figure 4, the average NCF and TCF of TC are 256.1 and 57.9 N, respectively. Compared with TC, the average NCF of EVC is reduced by proximately 51.4% and the average TCF is reduced by about 60.8%.

Compared with TC machining, the reduction mechanism of cutting force in EVC is explained from the following three aspects: firstly, in EVC, the depth of cut $a_p$ varies from small to large periodic gradient variation, and its maximum depth of cut $a_p$ is smaller than the depth of cut $a_p$ in TC. Therefore, the resistance of the workpiece to the tool is weakened; secondly, the material removal area is constant because the depth of cut $a_p$ remains constant in TC. While in EVC, the tool in the high-frequency vibration, the material removal area is a crescent-shaped part, as shown in the red box in Figure 15, and its material removal cross-sectional area is smaller than the material removal cross-sectional area in TC, the reduction of material removal cross-sectional area, resulting in a smaller cutting force; Finally, in EVC, due to the increase in the relative cutting speed and the increase in the tool travel path, the workpiece and the tool friction in the contact area is more intense, resulting in a higher average temperature of the tool-tip (Figure 16), and the increased temperature increases the plasticity of the material and reduces the hardness of the material. Under the combined influence of the above three aspects, the average cutting force becomes smaller.

Figure 15.

Schematic diagram of material removal in elliptical vibration cutting (EVC).

Figure 16.

Tool-tip temperature curve: (a) temperature curve in TC; and (b) temperature curve in EVC.

Conclusion

In this article, Inconel 718 machined by EVC method was simulated by using ABAQUS finite element software, and the chip formation and the reducing of cutting force mechanisms in the cutting process with or without EVC was analyzed, and the conclusions can be found by comparison and discussions:

Through comparative analysis, it is found that in EVC, the machined surface shows a higher overall finish without burrs and small defects, while in TC, burrs and small defects appear, which indicates that in EVC, the surface quality is higher than that of the machined surface in TC.

In the case of TC, the chip evolution mechanism is the combination of strain hardening effect and heat softening effect to form an adiabatic shear slip region, and finally, shear slip occurs to form a sawtooth chip. In EVC, due to greater relative cutting speed $v_{\mathrm{c}}$ and longer tool travel S₁, the tool-tip temperature is higher than that in TC, and higher tool-tip temperature combined with a smaller chip cross-sectional area further cause a prominent heat softening effect which resulting in the plastic flow intensified in the material removal process, as a result, the strip chips is formed.

Due to the machining characteristics of EVC, the average cutting force in EVC is lower than that in TC. On the conditions presented in this article, the average NCF is reduced from 256.1 to 124.5 N, a reduction of about 51.4%. The average TCF is reduced from 57.9 to 22.7 N, a reduction of about 60.8%.

In the future, the effect of thermal softening and strain hardening of ultrasonic vibration-assisted machining on the evolution of micro-structures of machined surfaces should be further investigated.