Nanomanufacturing and Metrology

, Volume 1, Issue 4, pp 268–276 | Cite as

Cutting Mechanism Investigation in Vibration-Assisted Machining

  • Wanqun Chen
  • Lu Zheng
  • Xiangyu Teng
  • Kai Yang
  • Dehong Huo
Original Articles


In the process of vibration-assisted machining, high-frequency and small-amplitude vibration is superimposed to the motion of either the tool or the workpiece, which leads to a dramatic change of cutting mechanics. This paper investigates the cutting mechanism of vibration-assisted micro-machining by using finite element simulations and experiments. A finite element model of vibration-assisted milling process is established using the Johnson–Cook material and damage models. Cutting mechanism, in terms of chip formation, stress distribution, cutting force and burr formation, between the vibration-assisted machining and the conventional machining is compared, and the machining experiments are conducted to verify the simulation results.


Vibration-assisted machining Micro-milling Cutting mechanism Chip formation Burr formation 

1 Introduction

Vibration-assisted machining is a machining process which introduces external energy to conventional machining process and produces high-frequency and small-amplitude vibration to the tool or workpiece. As the cutting and vibration parameters are set properly, the tool and uncut materials will lose contact periodically. The average machining forces and thinner chips can be generated, leading to a high processing efficiency [1, 2, 3], longer tool life [4], better surface quality and form accuracy and burr generation reduction in the cutting process [1, 2, 3, 4, 5, 6, 7]. When refers to hard to machine materials such as titanium alloy, ceramic and optical glass, it also has been found to increase the cutting depth in ductile-regime cutting mode, which can improve cutting performance and reduce the unnecessary post-process when produce components with complex shape features [8].

Vibration-assisted machining was first reported in 1950s for wood drilling and speeded up in 1990s due to techniques development in piezoelectric-driven stages and linear motors, which help in achieving machining tool nanometer-scale control. Currently, more and more researchers are paying attention to its advantages and several cutting processes such as turning, drilling and milling, which have been applied in this technique successfully to meet the increasing demands in high-precision components made by hard and brittle materials [9]. Lin el al. [10] developed an elliptical vibration turning system by applying the hybrid flexure hinge connection structure on cutting tool side and the feasibility of the whole system has been validated by using finites element analysis. Tooltip kinematical analysis and performance test have been done, and surface topography can be generated in the cutting results. Chen et al. [11] proposed a non-resonant vibration-assisted micro-milling system and produced two types of surface textures—wave and fish scale. By combining different vibration and machining parameters, the machined surface topography can be controlled, which in turn changes the surface wettability. Azarhoushang et al. [12] investigated the influence of ultrasonic vibration on drilling holes quality. The experiment results show that surface roughness and tool wear are reduced dramatically by adding tool axis direction high-frequency vibration to drilling process. Ultrasonic vibration-assisted grinding process is studied by Ding et al. [13]. They found that grinding forces variation has a connection with the vibration parameters and its results reflected on the grinded surface roughness. Moreover, matching performance of the grinding and vibration parameters determines the effect of ultrasonic vibration on grinding process directly. A 2D ultrasonic vibration-assisted grinding system was developed by Peng et al. [14], and results show that it is an effective method for the high-efficiency machining of hard brittle polysilicon material. To solve the diamond tool high tool wear issue when turning die steel, Zou et al. [15] applied 1D ultrasonic vibration-assisted to the turning process. The machining results indicate that the orthogonal ultrasonic vibration to the direction of workpiece can reduce the tool wear by indirectly and directly decreasing the friction coefficient between the tool and the workpiece. Similar results have been obtained by Adnan et al. [16], they proposed an ultrasonic turning system and validated it by processing AL-2024, besides studying the influence of vibration on surface roughness and cutting forces, and they also studied the effect of vibration on chips formation. Chen et al. [17] investigated the burr formation process in vibration-assisted slot milling. They found that the both slot side burrs are reduced when vibration assistance is applied in the feed direction and this is due to up-milling and down-milling which takes place periodically on both cutting-in and cutting-out sides.

As discussed in the above paragraph, vibration-assisted machining presents a huge potential in producing textured surface and processing performance improvement. However, most of the previous studies are based on the experimental analysis. Only a few studies focus on the cutting mechanism of vibration-assisted machining and it is still not clear, which limits the further expansion of the application. Therefore, this paper simulates and analyzes the process of vibration-assisted machining based on the finite element modeling method, which gives a deeper understanding of the benefits of the vibration-assisted machining in the cutting mechanism level. The influence of the vibration-assisted machining on shear angle, stress distribution, chip formation, cutting force and burr generation is studied from the perspective of FE simulation. It will also provide meaningful suggestions for processing parameters optimization.

2 Finite Element Simulation

2.1 Finite Element Modeling

To investigate the influence of the vibration on the machining mechanism in vibration-assisted machining, a 2D finite element (FE) model is established using ABAQUS/Explicit commercial finite element software as shown in Fig. 1. Magnesium alloy is selected as the workpiece material. Johnson–Cook (JC) material model and JC damage model are used to describe the workpiece material behavior. The details of the material parameters can be found in Table 1.
Fig. 1

FE model of 2D vibration-assisted machining

Table 1

Mechanical properties and materials constant in J–C model for magnesium matrix [18]



Density (ton/mm3)

1378 × 10−12

Young’s modulus (MPa)


Poisson’s ratio


T melt (K)


T transition (K)


Thermal expansion (K−1)

25 × 10−6

Thermal specific heat (mJ/ton K)

914 × 106

Conductivity (mW/mm K)


A (MPa)


B (MPa)








d 1


d 2


d 3


d 4


d 5


As the large deformation and deformation rate in the workpiece are involved in the cutting process, arbitrary Lagrangian–Eulerian (ALE) formulation with the advancing front algorithm is used to provide the mesh distortion control in every analysis increment to avoid excessive mesh distortion, and analytical rigid body was assigned to the cutting tool and move in the cutting direction with a predefined speed. This model is meshed with four-node quad-dominated element (CPE4R). The average mesh size is 5 µm. The Coulomb friction model is used to define the surface-to-surface contact condition between the tool and workpiece interface. The friction coefficient is defined to be 0.2 in this work. The machining parameters used in the simulation are shown as follows: The cutting speed is 2.1 m/s; cutting depth is 50 μm; and the cutting edge radius is 1 μm. The workpiece is fixed with all degree of freedom, the vibrations in x and y directions are applied on the tool with the given frequency and amplitude, and the phase of the two vibration signal is set as π/2.

The relative motion of tooltip to workpiece in vibration-assisted cutting is
$$\left\{ {\begin{array}{*{20}l} {x\left( t \right) = vt + A\cos \left( {2\pi ft} \right)} \hfill \\ {z\left( t \right) = B\sin \left( {2\pi ft} \right)} \hfill \\ \end{array} } \right.$$
where A and B are the vibration amplitudes in x and z directions, respectively, f is the vibration frequency and v is the cutting speed.

3 Materials Removal Mechanism in Vibration-Assisted Micro-Milling

3.1 Shear Angle

The shear angle is an important indicator to describe the cutting process. A larger shear angle improves cutting process such as reduction in deformed chip thickness which finally results in the decrease in tool–chip contact length and power consumption [19, 20]. Therefore, the influence of the vibration on shear angle is studied. The shear angle graphs extracted from ABAQUS software and the generated shear bands are obtained, respectively. Figure 2 illustrates the shear angle of the conventional cutting and vibration-assisted cutting. It can be noted that the shear angle in conventional cutting is around \(\theta = 40^\circ\). When the 6 kHz elliptical vibrations applied in the machining process, it can be noted that the shear angle increased to \(\theta^{{\prime }} = 45^\circ\). These results show that the vibration-assisted machining is useful to increase the shear angle, which will be useful to improve the machining property during the machining process.
Fig. 2

Shear angle. a Conventional cutting; b vibration-assisted cutting

3.2 Stress Distribution

To study the stress distribution on vibration-assisted machining process, the simulation was carried out on magnesium alloy and the frequency and amplitude are set to 30 kHz and 5 µm, respectively. Apparently, in vibration-assisted machining the maximum stress is larger than that in conventional machining. Figure 3 shows the cutting stress result of point “A” changes with the cutting time and an obvious stress fluctuation can be noted in vibration-assisted machining. Moreover, the stress of the point “A” is larger than its fracture stress even though the tool has not been cut to this point at time “t,” which means the crack is generated before the cutting point and results in the decrease in the cutting force.
Fig. 3

Stress comparison with time domain

3.3 Chip Formation in Vibration-Assisted Micro-Milling

Figure 4 illustrates the elliptical vibration with frequency of 6 kHz and amplitude of 5 μm. The cracks can be found on the chip root at tool–workpiece contact zone. Figure 4a shows a crack initiation on the chips, with tool moving continuously, and another crack is generated on the chips. Then, the cracks start to grow and expanded under the impact and extrusion of the cutter, as shown in Fig. 4c, d. Finally, the cracks are located close to the rake face of the tool, which can be considered as the main reason to reduce the rake face wear and reduce the cutting force.
Fig. 4

Chip formation with elliptical vibration of 6 kHz

When the elliptical vibration frequency increases to 10 kHz, it can be noted that the cracks are generated along the shear angle. Figure 5a, b shows that an initial crack is found in the shear plane. Then, the cracks growth is initiated under the vibration impact of the cutting tool as shown in Fig. 5c. Finally, the chips fracture along the shear angle is observed resulting in block chips as shown in Fig. 5d.
Fig. 5

Chip formation with elliptical vibration of 10 kHz

The chips formation process with different vibration frequencies are compared, as shown in Fig. 6. It can be noted that the continuous chip is formed during the cutting process without vibration. With the elliptical vibration frequency increases from 6 to 30 kHz, the crack generated direction changes from nearly of rake face to shear plane and finally along the upfeed direction. The chip morphology gradually changes from continuous chips to broken ones.
Fig. 6

Chip formation with elliptical vibration and different vibration frequencies

From the perspective of energy conversion, the destruction of materials can be considered as a result of the impact stress exceeding its critical stress of the material. In the vibration cutting process, the material is naturally faster and easier to be destroyed with the increase in the tool vibration speed. The material destruction mechanism can be considered to be completed instantaneously under the action of high-speed impact loads, and the small impact per tooth will result in the plastic failure of the material.

3.4 Cutting Force Simulation in Vibration-Assisted Micro-Milling

It can be seen from Fig. 7 that the cutting force of ordinary cutting is about 3 N, while the cyclical fluctuation of cutting force is found when the vibration with frequency of 6 kHz is applied. The maximum cutting force is equivalent to the cutting force of ordinary cutting, but the average cutting force is significantly lower than the average cutting force obtained from ordinary cutting. With the cutting going on, the crack is continuously formed on the chip in contact with the rake face. Therefore, the peak cutting force sometimes is lower than the ordinary cutting. When the vibration frequency is increased to 10 kHz, the cutting force shows periodic fluctuation, but the amplitude of the cutting force fluctuates greatly. When the tool comes into contact with the workpiece suddenly, the peak cutting force is found to be approximately 3.5 N which is greater than the cutting force of ordinary cutting. This can be attributed to the impact of the tool when it is in contact with the workpiece. After that, as described above, the crack is continuously formed on the chip in shear plane; therefore, the peak cutting force of vibration cutting is reduced to nearly 2 N, which is significantly lower than the ordinary cutting force. When the vibration frequency is further increased to 60 kHz, the crack of material caused by the vibration of the cutting tool becomes more obvious. The effective cutting force interval becomes larger; thus, the average cutting force decreases to approximately 0.16 N. It should be noted that as the damage stress of the magnesium alloy is smaller than steel, cracks are easy to generate in the vibration-assisted machining process, and when the vibration frequency exceeding a certain value, the fluctuation frequency of the cutting force will be inconsistent with the vibration frequency.
Fig. 7

Cutting force comparison with different vibration frequencies

3.5 Burr Formation

To determine the influence of vibration on burr formation, a 3D simulation model in the slot milling process is established. The dimensions of the workpiece in the FE model are \(2 \times 1 \times 0.2\;{\text{mm}}^{3}\), and the minimum element size is set as 10 μm. A 1-mm-diameter tungsten carbide end mill with a 3 μm cutting edge radius is used in the simulation. The following machining parameters are used: tool rotational speed n = 40,000 rpm, feed per tooth fz = 15 μm, axial depth of cut ap = 50 μm. Vibration (frequency 5000 Hz, amplitude 10 μm) is applied to the workpiece in the feed direction. The Johnson–Cook (JC) material constitutive and damage models are used to model material plasticity and damage, respectively.

Figure 8 shows the simulation results for conventional micro-milling and vibration-assisted micro-milling, respectively. It can be seen from Fig. 8a that the burr size in down-milling side is larger than that in the up-milling side in conventional micro-milling. However, on the slot edges machined by vibration-assisted milling, small-amplitude high-frequency vibration in the feed direction induces alternating change in the relative direction of movement between the workpiece and the tool on both sides of the slot. Chip formation on both sides of the slot then becomes similar as shown in Fig. 8b. Compared with those in conventional micro-milling, the burr size on the down-milling side of the slot is greatly reduced and becomes similar to those on the up-milling side when vibration is added.
Fig. 8

Slot micro-milling simulation results: a conventional and b vibration-assisted

4 Machining Experiments

The machining experiments are carried out on a precision micro-milling machine (Nanowave MTS5R) with a high-speed spindle (maximum speed 80,000 rpm) as shown in Fig. 9. A homemade 2D vibration stage with maximum vibration frequency of 10 kHz and the maximum vibration amplitude of 5 μm is installed on the machine to realize the vibration of the workpiece. A 1-mm-diameter milling cutter with two flutes and 1 μm cutting edge radius is used in the experiments.
Fig. 9

Vibration-assisted micro-milling setup

Conventional and vibration-assisted micro-milling experiments were performed on a workpiece of magnesium alloy using the same machining parameters as for the FE simulation, set out in Sect. 3.5. As shown in Fig. 10a, for conventional micro-machining burrs of different sizes are formed on each side of the slot. It can be seen that more and larger burrs are formed on the down-milling side. For the slots machined by vibration-assisted micro-milling, the burr height on the down-milling side is significantly reduced as shown in Fig. 10b.
Fig. 10

Burr formation test results. a Conventional micro-milling and b vibration-assisted micro-milling

Figure 11 illustrates the generated chips with conventional micro-milling and vibration-assisted milling with 6 kHz and 10 kHz, respectively. The vibration is applied in the feed and cross-feed direction, with the phase difference of π/2. The vibration amplitude is 2 μm, and the machining parameters are as follows: Cutting depth is 50 μm, spindle speed is 40,000 rpm, and feed per tooth is 5 μm. It can be found that the chip generated from conventional micro-milling is smooth and continuous. Significant cracks on the chips could be clearly observed after vibration frequency of 6 kHz is applied. When the vibration frequency of 10 kHz is applied, block chips appeared, which are in good agreement with the simulation results. The correctness of the simulation analysis is verified.
Fig. 11

Chips with different vibration frequencies

5 Conclusion

This paper investigated the cutting mechanism in the vibration-assisted machining, and the shear angle, chip and burr formation process of the vibration-assisted machining is studied. Finite element simulation and machining experiments are conducted, and the following conclusions can be drawn:
  1. 1.

    In conventional machining, the material removal is a continuous process, and the shear angle is a fixed value, while in the vibration-assisted machining, the shear angle is changing due to the changes of the contact state between the workpiece and the tool. The maximum shear angle with vibration is found larger than the conventional machining, and it is found that the shear angle increases with the increase in the vibration frequency.

  2. 2.

    Compared with conventional machining, more cracks generated in the cutting region with vibration-assisted machining result in the decrease in the cutting force.

  3. 3.

    Vibration frequency has a significant influence on the machining mechanism. With the increase in the vibration frequency, the crack initiation direction is gradually shifted to the cutting direction. Thus, the cutting force is further reduced and block chips are generated.

  4. 4.

    Vibration-assisted machining has the advantage to reduce the burr formation, and it is extremely important for forming a high-precision machined surface without deburring process.




The authors gratefully acknowledge the financial support of the Engineering and Physical Sciences Research Council (EP/M020657/1) and the National Natural Science Foundation of China (Grant No. 51505107).


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Copyright information

© International Society for Nanomanufacturing and Tianjin University and Springer Nature 2018

Authors and Affiliations

  1. 1.Mechanical Engineering, School of EngineeringNewcastle UniversityNewcastle upon TyneUK
  2. 2.Centre for Precision EngineeringHarbin Institute of TechnologyHarbinPeople’s Republic of China
  3. 3.Army Aviation InstituteBeijingPeople’s Republic of China

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