Study on the tool wear of 3-D elliptical vibration cutting

As always, the rapid wear of tools was one of the key factors limiting the precise turning of difficultto-machine materials with diamond tool. 3-D elliptical vibration cutting has inherited many advantages of elliptical vibration cutting, such as the intermittent cutting property and friction reverse property. However, studies on the tool wear of three-dimensional elliptical vibration cutting has not been reported yet. The formation principle of 3-D cutting elliptical trajectory was analysed and a prediction model of tool wear was established in the present work. Besides, a self-developed three-dimensional elliptical vibration device was employed to conduct turning experiment. Compared with the proposed model, the experimental results showed a great agreement with the proposed prediction model. This work may provide a reference for the further optimization of the 3-D elliptical vibration cutting parameters.


Introduction
Since elliptical vibration cutting (EVC) was proposed by Shamoto and Moriwaki (1994), it has been considered as the most potential processing method and has received widespread attention of scholars.A large number of reports have shown that EVC has advantages over many aspects, such as improving the machinability of materials, suppressing the cutting chatter, reducing cutting force, extending tool life and improving the surface uniformity (Jung et al., 2016;Zhou et al., 2016;Zhang et al., 2015Zhang et al., , 2016;;Li et al., 2015).To date, the studies on EVC are mainly focused on the following aspects: (1) EVC devices, (2) machinability of different materials, (3) EVC cutting force model, (4) tool wear condition.
According to the different driving methods of EVC devices, it can be divided into resonant type and non-resonant type.The resonant type of EVC machining device was developed by E. Shamoto et al. and others (Moriwaki and Shamoto, 1995;Shamoto et al., 2002Shamoto et al., , 2005;;Suzuki, et al., 2003).Driving signals with phase difference were utilized to excite its resonant mode, and an elliptical trajectory could be formed at the tool tip.The machining performance, cutting force model and tool wear resistance of hard and brittle materials were studied in their research.Besides, they pro-posed a 3-D EVC device in 2005.Liu et al. (2004) started to study the resonant type EVC device in 2004.They studied the machinability, ductile-brittle transition model and the effect of tool nose radius on cemented carbide using their proposed device (Ma et al., 2006;Nath et al., 2009a, b).Sathyan et al. studied the resonant EVC device and they also conducted some investigations on chip formation, vibration mark trace and tool wear during the machining process (Ahmed and Sathyan, 2010).
The first non-resonant EVC device was developed by Brehl et al. (1999) Aiming at obtaining the advantage of the developed non-resonant EVC device, they conducted some investigations on the maximum chip thickness, cutting force model, tool wear, and surface quality and so on (Brehl and Dow, 1999).Kim and Loh (2007) studied on non-resonant EVC device since 2007.PCD tool was used to carry out the cutting experiment.A series of structures, such as micro grooves and the pyramid structure, were machined with various elliptical trajectory (Kim and Loh, 2007).In our previous work, an improved memetic algorithm was proposed to achieve nonlinear identification for a 3-D EVC system (Lu et al., 2014).
The analysis of tool wear mechanism for EVC is still limited to 2-D EVC so far.3-D EVC is developed to satisfy the requirements of cutting surfaces with various shapes and ma-Published by Copernicus Publications.Elliptical vibration cutting has a limitation to turn the complex surfaces.So the 3-D EVC was proposed to address this problem.The principle of 3-D EVC is shown in Fig. 2, ellipse 1 is the projection of tool trajectory on plane YOZ.Take the long axis of ellipse 1 as a rotation axis, the ellipse 2 can be obtained by ellipse 1 rotates a β angle.The projection of ellipse 2 on plane XOY and YOZ both are ellipses.And the projection of ellipse 2 on plane XOZ is a straight line.Take the short axis of ellipse 1 as a rotation axis, the ellipse 3 can be obtained by ellipse 1 rotates a α angle.The projection of ellipse 3 on plane YOZ and XOZ both are ellipses.The elliptical motion trajectory of arbitrary position can be obtained by adjusting the value of angle α and β.In addition, angle  α and β are two important parameters during the modelling process.

Tool wear predictive model of 3-D EVC
Before the prediction model of tool wear is proposed, it is necessary to introduce the tool wear condition during the elliptical vibration cutting.As shown in Fig. 3a, tool tip pass the point P1, P2 and P3.At point P2, tool tip reaches the maximum depth of cut a p .The value of contact area between tool and workpiece is the maximum at this moment.It is assumed that the vibration period of one elliptical vibration cutting is T .Then the contact time of tool and workpiece is t = a p T / (2a).In this paper, we take it as a severe wear zone when tool tip contact with workpiece at time 2t/3, t , and marked it as region I. Similarly, we take it as a moderate wear zone and mild wear zone when tool tip contact with workpiece at time t/3, 2t/3 and time 0, t/3 , and marked it as region II and region III, respectively.We can see from Fig. 3 that tool tip A contact with workpiece at point P1 and P3.The contact marginal point between tool and workpiece turns  As shown in Fig. 4a, the 3-D ellipse trajectory can be obtained by the 2-D ellipse trajectory by a shift of angle α and β.Point P 1 , P 3 are donate to the cut in point and cut out point, respectively.Point P 2 is the tool tip position relative to workpiece when the depth of cut reaches the maximum value.Angle α mainly affects the position of tool wear.The region of tool wear locates at the right side of tool nose arc when α > 0. On the contrary, the region of tool wear located at the left side of tool nose arc when α < 0. We assume that positive clockwise and negative anti-clockwise.Angle β mainly affects the shift speed of contact marginal points between tool and workpiece and the region of tool wear.Thus angle α and β have significant influences on tool wear conditions of 3-D EVC.
It is assumed that the tool vibration frequency of 3-D EVC is f .Then the tool vibration period is T = 1/f .The time to reach the maximum depth of cut is T a p / (2b) during cutting.The wrap angle of the maximum tool wear on the one side of tool tip can be obtained as follows: On the basis of the arc length formulae L = ϕr, the shift speed of contact marginal points between tool and workpiece can be obtained as follows:

Figure 3 .
Figure 3. Wear regions of elliptical vibration cutting.

Figure 4 .
Figure 4. Diagrams of vibration tool trajectory of 3-D EVC and shift of contact marginal points.

Figure 6 .
Figure 6.SEM micrographs of tool wear.(a) SEM micrographs of tool using 2-D EVC.(I) Top view of tool tip.(II) Partial enlarged detail of tool tip.(III) Front view of tool.(b) SEM micrographs of tool using 3-D EVC.(I) Top view of tool tip.(II) Partial enlarged detail of tool tip.(III) Front view of tool.
2)Within the same time T a p /(2b), the moving distance of the contact arc central point between tool and workpiece is L = βr.Then the shift speed of the contact arc central point between tool and workpiece can be expressed as follows,T L = 2bβr T a p (3) We analyzed the various tool wear region of 3-D EVC from the following three cases when α < 0. When T L = C L , β = ϕ = arccos r − a p /r .The moving speed of the contact arc central point between tool and workpiece is equal to the shift speed of the contact marginal points.That means the contact arc central point A is coincide with the contact marginal point C of right side as shown in Fig. 4b.The contact marginal point B of left side is moving at speed of 2T L .The tool wear zone was divided into three regions according to the time of tool tip contact with the workpiece.The region 0, 2β/3 of the left side of tool tip is the severe wear region I.The region 2β/3, 3, 4β/3 is the moderate wear region II, and 4β/3, 2β is the mild wear region III.When T L > C L , β > ϕ = arccos r − a p /r .The moving speed of the contact arc central point between tool and workpiece is larger than the shift speed of the contact marginal points.That means the contact marginal point C of right side is shifting to the left slowly from the tool arc central point.The moving speed is T L − C L .The moving speed of the contact marginal point B of left side to the left is T L + C L .As shown in Fig. 4c, the contact marginal point C of right side is located at the left of tool tip when tool reaches to the maximum depth of cut a p .The central angle is β − ϕ at this moment.The tool wear zone is divided into three regions according to the time of tool tip contact with the workpiece.The region