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Fabrication of a Peristome Surface Structure of Nepenthes alata by Elliptical Vibration Cutting

  • Dongyue Wang
  • Xiangyu Zhang
  • Deyuan Zhang
Original Articles
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Abstract

The phenomenon of continuous directional water transport on the peristome surface of Nepenthes alata (N. alata) has been found to be of great significance to the applications of microfluids, anti-adhesion surface texture, lubrication and so on. Various methods are used to fabricate the bionic structure of the peristome surface. However, the size of processing area and the fabrication material are limited in the previous methods, which results in the limitation of the bionic structure applications. In order to solve the remained problems of small-scale and limited materials, the mechanical machining is creatively applied to the fabrication of bionic structure of peristome surface of N. alata in this paper. An elliptical vibration cutting system (EVC) driven by mechanical structure is designed and built to satisfy the size requirements of the bionic structure. The surface topographies corresponding to the tool trajectories of cutting and extrusion are obtained, respectively. The results demonstrate that both the two methods can realize the fabrication of bionic inclined microcavities while few defects can be seen on the extruded surface. According to the measured structure dimensions, it can be found the EVC system keeps a superior machining repeatability. As a consequence, the availability of the newly proposed method for the large-area fabrication of the bionic structure is verified.

Keywords

Elliptical vibration cutting Bioinspired microcavity structure Cutting Extrusion Nepenthes alata 

Abbreviations

x

Tool displacement along cutting direction, μm

y

Tool displacement along direction of depth of cut, μm

A

Tool vibration amplitude in cutting direction, μm

B

Tool vibration amplitude in direction of depth of cut, μm

v

Cutting velocity, μm/s

φ

Phase shift between vibrations of x-axial and y-axial directions, rad

f

Tool vibration frequency, Hz

t

Time, s

θ

Instantaneous direction angle of the tool motion, rad

α

Nominal clearance angle of tool, rad

β

Wedge angle of tool, rad

L

Cutting length, μm

hmax

Maximum cutting depth, μm

1 Introduction

Recently, the phenomenon of continuous directional water transport on the peristome surface of Nepenthes alata (N. alata) has received considerable attention. As depicted in Fig. 1a, the peristome surface exhibits a unique structural feature of two-order hierarchy of parallel microgrooves. Duck-billed microcavities are regularly distributed along the microgrooves. The vertical section through the peristome, depicted in Fig. 1b, shows that the top of the microcavities is closed. The microcavities are slightly slanted and have arch-shaped open sharp edges [1]. This unique structure generates a top-closed capillary rise and long-distance unidirectional spreading properties on the peristome surface [2, 3]. This phenomenon has potential applications in various filed, such as microfluidic devices, self-lubrication, and anti-adhesion surface texture [4]. Thus, many recent studies have focused on the fabrication of the peristome-mimetic surface. Chen et al. made artificial peristome using a polydimethylsiloxane (PDMS) replica moulding method [5]. Chen et al. fabricated the bioinspired unidirectional liquid spreading surface through two-step inclined UV exposure photolithography [3, 6]. Li et al. combined lithography and deep reactive ion etching (DRIE) to fabricate topological liquid diode [7]. Li et al. used high-resolution stereo-lithography to make a peristome-mimicking structure [8]. Yu et al. obtained the peristome surface through a designed 3D printing and replicating way [9]. Although the bioinspired peristome surface has been obtained through these methods, they were fabricated in small-scale and workpiece materials are limited. In order to realize the applications of the bionic peristome surface structure in engineering fields, the remained problems of small-scale and limited materials need to be overcome.
Fig. 1

Surface features of the peristome of N. alata a the structure of the peristome surface; b the vertical section through the peristome [1]

Mechanical machining is the most common large-area processing method and has a wide range of machining materials. In mechanical machining field, specialized surface texture can be fabricated through elliptical vibration cutting (EVC), which was proposed by Shamoto and Moriwaki [10]. In this method, the tool motion path can be implemented on workpiece surface [11, 12]. By controlling the depth of cut, cutting direction and vibration amplitude of EVC, the desired surface topography can be obtained. EVC is usually used in fabrication of ultra-precision micro/nano-structures, freedom surfaces and optical glass parts [13, 14, 15, 16]. In general, the EVC system is driven by piezoelectric (PZT) actuators, in which the amplitude is not more than 100 μm [17]. When the size of structure is larger than the amplitude, the PZT-driven EVC system is obviously not applicable.

Therefore, to solve the remained problems of small-scale and limited machining materials, the mechanical machining is creatively applied to the fabrication of bionic structure of peristome surface of N. alata in this paper. An EVC system driven by mechanical structure is designed and built to satisfy the size requirement of the bionic structure. The rest of this paper is organized as follows. The tool trajectories of cutting and extrusion are determined in Sect. 2. Composition of the EVC system and construction of experiment platform are introduced in Sect. 3. The surface topographies obtained by the EVC are analysed and the actual machining contours are compared with the theoretical ones in Sect. 4. Finally, the conclusions are given in Sect. 5.

2 Elliptical Vibration Machining Mechanism

In EVC, the tool vibrates in the cutting direction and the direction of depth of cut simultaneously [18]. The inclination of the elliptical trajectory of the tool is controlled by changing the phase shift between the motion trajectory components of these two directions. Thus, the cutting tool motion trajectory can be defined as follows [17]:
$$ \left\{ {\begin{array}{*{20}l} {x = A\sin \left( {2\pi ft + \varphi } \right) + vt} \hfill \\ {y = B\sin \left( {2\pi ft} \right)} \hfill \\ \end{array} } \right. $$
(1)
According to the duck-billed microcavity structure of N. alata, the tool motion trajectories of cutting and extrusion are determined, respectively. Figure 2a shows the tool cutting trajectory, in which the tool gets engaged into the workpiece at M1 and continues to cut till the position of maximum uncut chip thickness (M2), then reverses to the top of the microcavity (M3) till the position where the tool separates from the workpiece (M4). The noncutting duration is from M4 to M5 in one vibration cycle. Similarly, the tool extrusion trajectory is shown in Fig. 2b. The extrusion process starts at M1, and the tool gradually moves towards the top of microcavity (M2) till the position of maximum extrusion depth (M3). Subsequently, the tool turns to disengage from the workpiece and ultimately separates at P. The noncutting duration in one vibration cycle is the same as that of the tool cutting trajectory.
Fig. 2

Schematics of the tool trajectories a the trajectory of cutting, without flank face interference; b the trajectory of extrusion, with flank face interference

During EVC process, the instantaneous direction angle of the tool motion varies with time due to the tool vibration and it can be defined as follows [18]:
$$ \tan \theta = \frac{{\frac{{{\text{d}}y}}{{{\text{d}}t}}}}{{\frac{{{\text{d}}x}}{{{\text{d}}t}}}} = \frac{{2\pi fB\cos \left( {2\pi ft} \right)}}{{2\pi fA\cos \left( {2\pi ft + \varphi } \right) + v}} $$
(2)

As depicted in Fig. 2a, the tool clearance angle is larger than the instantaneous direction angle at M1. As the tool cuts into the workpiece, the distance between the flank face and the machined surface gradually increases. When the tool separates from the workpiece at M4, the sum of wedge angle and the clearance angle is smaller than the instantaneous direction angle. Therefore, there is no interference between the tool rake face and the machined surface. Different from the cutting process, the fabrication of the final surface topographies completely relies on the flank face interference in the extrusion method. As clear from Fig. 2b, the sum of the wedge angle and the clearance angle is smaller than the instantaneous direction angle at M1. The flank face maintains contact with the workpiece until the tool clearance angle is equal to the instantaneous direction angle after the largest extruded area is obtained. Then, the tool separates from the workpiece, and the structure is fabricated.

The centres of the two elliptical vibration trajectories are located on the unmachined workpiece surface. The cutting length and the maximum uncut chip thickness are determined according to the length and maximum depth of the duck-billed microcavities of the peristome surface of N. alata. The position of the top of microcavity can be controlled by the phase shift between the vibration trajectories in x-axial and y-axial directions. To avoid the interference in the trajectories of adjacent cycles, an important condition that the distance at which tool moves in one cycle in the x-axial direction must be larger than the actual cutting length needs to be satisfied, and it is given by:
$$ vT \ge M_{1} M_{4} \left( {PM_{1} } \right) $$
(3)
In this paper, the cutting length between the adjacent tool trajectories is 400 μm, and the maximum uncut chip thickness is 100 μm. The frequency of the vibration is set as 3/4 Hz to ensure the stability of tool movement. And the cutting velocity is set as 400 μm/s to satisfy Eq. 3. In order to obtain the microcavity structure through the method of cutting, the necessary condition is calculated as follows:
$$ \left\{ {\begin{array}{*{20}l} {\tan \alpha \ge \tan \theta_{{M_{1} }} = \frac{2\pi fB}{2\pi fA\cos \varphi + v}} \hfill \\ {\tan \left( {\alpha + \beta } \right) \le \tan \theta_{{M_{4} }} = \frac{2\pi fB\cos \pi }{{2\pi fA\cos \left( {\pi + \varphi } \right) + v}}} \hfill \\ \end{array} } \right. $$
(4)
Therefore, the phase shift between the motions in two directions is defined as \( - {\pi \mathord{\left/ {\vphantom {\pi 9}} \right. \kern-0pt} 9} \). The final cutting trajectory equation is thereafter given as follows:
$$ \left\{ {\begin{array}{*{20}l} {x = 200\sin \left( {\frac{3}{2}\pi t - \frac{\pi }{9}} \right) + 400t} \hfill \\ {y = - 100\sin \left( {\frac{3}{2}\pi t} \right)} \hfill \\ \end{array} } \right. $$
(5)
As for the extrusion method, the condition needs to be satisfied is:
$$ \tan \left( {\alpha + \beta } \right) \le \tan \theta_{{M_{1} }} = \frac{2\pi fB}{2\pi fA\cos \varphi + v} $$
(6)
The phase shift between the motions in two directions is defined as \( {\pi \mathord{\left/ {\vphantom {\pi 3}} \right. \kern-0pt} 3} \). Therefore, the final tool trajectory of extrusion is given as follows:
$$ \left\{ {\begin{array}{*{20}l} {x = 200\sin \left( {\frac{3}{2}\pi t + \frac{\pi }{3}} \right) + 400t} \hfill \\ {y = - 100\sin \left( {\frac{3}{2}\pi t} \right)} \hfill \\ \end{array} } \right. $$
(7)

3 Experimental Set-up

In order to satisfy the requirements of frequency and amplitude, a low-frequency EVC system driven by mechanical structure is built. As shown in Fig. 3a, different from the traditional PZT-driven method, the elliptical trajectory of tool can be obtained by the combination of simple harmonic motions provided by the rotations of eccentric shafts in x-axial and y-axial directions. The amplitudes are determined by the eccentricities of eccentric shafts which are 100 μm and 200 μm in x-axial and y-axial directions, respectively. The eccentric shafts are driven by the DC 24V motors. Because the vibration frequency is set as 3/4 Hz in Sect. 2, the rotary velocities of the two motors are set as 40 r/min by the motor governor. The phase shift between the vibration trajectories in x-axial and y-axial directions is controlled by the initial position of eccentric shafts which is set at the start of each experiment. Considered that the kinematic accuracies of tool are totally decided by the size and shape accuracy of eccentric shafts, the eccentric shafts are machined by precision grinding. The eccentric shafts need to keep in touch with sliding blocks to deliver simple harmonic motions to the tool, so grease is used for the purposes of lubrication and wear decreasing. Meanwhile, the materials of shafts and sliding blocks are steel and aluminium to make wear easier to occur on the sliding blocks to protect the eccentric shafts and obtain a better process repeatability.
Fig. 3

Experiment set-up a schematics of the elliptical vibration cutting device; b cutting platform

The micro-cutting tool is used to fabricate the inclined microcavities. The tool has a wedge angle of 15 degree and a tool nose radius of no larger than 50 μm. The clearance angles of cutting and extrusion method are different, which can be determined by Eqs. 4 and 6, respectively. Its value can be altered by changing the clamping position of tool fixture. Because the tooltip is too thin and easily damaged, soft workpiece materials are chosen. In the cutting process, workpiece material needs well plasticity to avoid the surface damage caused by the tool upward movement. As for the extrusion method, it requires less elastic recovery of the finishing surface. Accordingly, the experimental conditions are determined and shown in Table 1.
Table 1

Experimental conditions

Method

Cutting

Extrusion

Clearance angle (°)

20

13

Vibration frequency (Hz)

3/4

3/4

Amplitude in x-axial direction (μm)

200

200

Amplitude in y-axial direction (μm)

100

100

Phase shift (rad)

− π/9

π/3

Cutting velocity (μm/s)

400

400

Workpiece material

Polytetrafluoroethylene (PTFE)

Paraffin

The EVC experiment platform is set up as depicted in Fig. 3b. The EVC device, which is used to stimulate the cutting tool to perform elliptical vibration, is fixed inside the spindle of a milling machine (BV100, China). The cutting velocity (v) is set as 400 μm/s. The workpiece is fixed on the milling machine worktable. Then, the EVC system is used to fabricate the structure. The surface topographies are observed by a digital microscope (HIROX RH-2000, Japan). A vertical section of the structure is obtained by burying the workpiece in epoxy resin before a polishing process. The structure dimensions are measured by the built-in measuring software of digital microscope. All of the results will be discussed in the following section.

4 Results and Discussions

The surface topographies of the cutting and extrusion experiments are demonstrated in Fig. 4. It can be confirmed that the bioinspired inclined microcavities array can be machined successfully by these two methods. Figure 4a shows the PTFE surface topography by cutting, in which the surface defects can be observed. The chips produced in the cutting process are difficult to be peeled off from the workpiece surface due to the preferable plasticity of PTFE. As clearly seen from Zone 1, the burr is formed near the microcavities, which leads to an easy-broken structure when the burr is removed. In addition, the upward movement of the tool from M2 to M4 in Fig. 2a will result in the workpiece surface protruding, or even breaking as Zone 2 shows. In contrast, neither of these two phenomena occurs in the extrusion method. As depicted in Fig. 4b, there are no obvious burrs on the finishing paraffin surface, and the microcavity structures can remain intact.
Fig. 4

Surface topographies a the PTFE surface topography by cutting, the length of structure is defined as l1. Zone 1: a burr formed during the cutting process. And Zone 2: a broken top of microcavity by the cutting tool; b the paraffin surface topography by extrusion, the length of structure is defined as l1; c a vertical section taken at the A–A position in panel (a), the depth of the microcavity is defined as l2; d a vertical section taken at the B–B position in panel (b), the depth of the microcavity is defined as l2

The vertical sections of the cutting and extrusion methods are illustrated in Fig. 4c, d, respectively. It can be seen that the two methods both can fabricate the inclined microcavities. In order to analyse the experiment results more clearly, the actual profiles demonstrated in Fig. 4c, d are extracted to compare with the theoretical profiles which are depicted in Fig. 5. Figure 5a shows the great distinction between the theoretical profile and the actual one when using the cutting method. Zone 3 is defined as the elastic recovery zone where an elastic recovery of the workpiece material occurs on the finishing surface. The workpiece surface uplift caused by the upward movement of the tool can lead the actual tool clearance angle to decrease. Thus, Eq. 4 is not satisfied and the flank face interference occurs as shown in Zone 4 where the material is extruded and the actual length of structure is greater than the theoretical one. As for the extrusion method depicted in Fig. 5b, the actual profile machined by the extrusion method keeps a higher consistency with the theoretical profile than that made by cutting method.
Fig. 5

Schematics of comparisons between the actual and the theoretical profiles a the comparison between the actual and the theoretical profiles of the cutting method. Zone 3: the workpiece elastic recovery region on the machined surface. And Zone 4: the flank face interference region on the finishing surface due to the surface protruding resulted from the upward movement of the tool and the decrease in the real tool clearance angle; b the comparison between the actual and the theoretical profiles of the extrusion method

For these two methods of cutting and extrusion, the length of the structure (l1) and the depth of the microcavity (l2) in five different locations are measured, respectively, to evaluate the machining accuracy and repeatability of the EVC system. In every position, the values are measured at least five times to calculate the uncertainty which is shown by the standard deviation. The error bars indicate the standard deviations in Fig. 6. In this experiment, tool setting error exists due to the limitation of experimental conditions. As depicted in Fig. 6, the actual depth of microcavity obtained by both methods is higher than the theoretical value under the influence of tool setting error and machining error of the eccentric shaft. But for the cutting method shown in Fig. 6a, the uplift caused by the upward movement of tool also has an effect on the actual depth of the microcavity which leads to a greater deviation between the actual and the theoretical value. Because the length of structure increases with the depth, the actual length value is larger than the theoretical one. Considered that the clearance angle of extrusion method is smaller than the one of cutting method, the structure length is more sensitive to the variation of depth. So a larger actual length of structure is obtained by the extrusion method demonstrated in Fig. 6b. Although there is a large deviation between the actual value and the theoretical value, the five sets of measured data make a small difference, which indicates the EVC system keeps a superior processing repeatability.
Fig. 6

Schematics of comparisons between the actual structure dimension and the theoretical value, the length of structure (l1) and the depth of microcavity (l2) in five different locations are measured by the built-in measuring software of digital microscope. The error bars indicate the standard deviations from at least five measurements in every position. a the comparisons between the actual and the theoretical value of cutting method; b the comparison between the actual and the theoretical value of extrusion method

5 Conclusions

A low-frequency EVC system driven by mechanical structure is designed and built to fabricate the bionic structure of peristome surface of N. alata in this paper. The tool trajectories of cutting and extrusion are determined by controlling the tool vibration amplitudes, phase shift and geometric parameters. The results demonstrate that both two methods can realize the fabrication of the bioinspired inclined microcavities while few defects can be seen on the extruded surface. And the EVC system keeps a superior processing repeatability. Therefore, the EVC provide the possibility of large-scale manufacturing of bionic structure. But due to the limitation of experimental conditions, the existence of experimental error makes a great influence on the machining precision. The study needs to continue to improve the experimental conditions and processing accuracy.

Notes

Acknowledgements

The authors would like to thank the 4th CIRP Conference on Surface Integrity (CSI) Organizing Committee for the support of this research.

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Copyright information

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

Authors and Affiliations

  1. 1.School of Mechanical Engineering and AutomationBeihang UniversityBeijingChina

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