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Micro-/Nano-texturing by Ultrasonic-Assisted Grinding

  • Masayoshi Mizutani
  • Shaolin Xu
  • Keita Shimada
  • Tsunemoto Kuriyagawa
Living reference work entry

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Part of the Micro/Nano Technologies book series (MNT, volume 1)

Abstract

In this chapter, a novel ultrasonic-assisted micro-/nano-texturing method was proposed and developed. A new 3D ultrasonic vibration spindle was developed for carrying out the proposed processes. The texturing mechanisms were analyzed by mathematically calculating the cutting loci and establishing the surface generation modeling processes. Finally, the tool design principles were proposed and experimentally verified. The experimental results and theoretical analysis proved that the proposed method can rapidly and precisely fabricate tailored surface textures at micrometer and nanometer scales.

Keywords

Micro-/nano-texturing Ultrasonic assisted grinding Texured surface Functional surface 

1 Introduction

1.1 Micro-/Nano-texturing Technologies

Methods for fabricating textured surfaces comprising micro-/nanostructures have been exploited in many industries (Masuzawa 2000).

Conventional diamond machining processes, including turning, cutting, milling, microgrinding, and fly cutting, produce surface textures by removing the material using mechanical forces. These methods are capable of machining ultraprecise microstructures (Brinksmeier et al. 2012; Denkena et al. 2010), which are usually fabricated on mold inserts when replicating structures on polymer or glass materials or are directly fabricated on engineering components. There are no specific material requirements for the machining objects because diamond has the highest hardness in nature. On the other hand, tool wear can be an issue, especially when machining ferrous metals. The reason for this is that the high machining temperature usually results in graphitization of the diamond by the ferrous metals (Shimada et al. 2004), which greatly accelerates tool wear and deteriorates surface quality. Surface textures at the submicrometer scale are also difficult to obtain using conventional diamond machining because the radius of the cutting edge is limited and cutting burrs on the edges of the microstructures are usually difficult to prevent or remove (Yan et al. 2009).

Besides using mechanical energy, optical energy and electrical energy are popularly utilized in the current industry, for example, laser beam machining (LBM) (Dubey and Yadava 2008) and electrical discharge machining (EDM) (Ho and Newman 2003; Abbas et al. 2007). Both methods provide optical or electrical energy to the work material, which is locally removed via melting and evaporation. Laser beam or electrical discharge can easily provide heat that exceeds the boiling point of any material. However, in practice, certain materials with low optical absorbance or low electrical conductivity cannot be processed by such methods; therefore, it is very difficult to obtain highly precise structures and surfaces using these methods. The heat-affected zone on the machined surface is also an inevitable problem. However, with the development of the excimer laser and femtosecond laser, ultrashort laser pulses can be used to remove the material by vaporization; this mitigates the melting phase, which can help in obtaining high dimensional accuracy and fewer heat defects (Liu et al. 1997; Cheng et al. 2013). On the other hand, the machining efficiency is usually lower than that of LBM or EDM.

The micro-fabrication methods used in the microelectromechanical system (MEMS) field, including lithography, chemical etching, plasma etching, electron (or ion) beam etching, and oxidation, are capable of the fabrication of very complex structures at the micrometer and nanometer scales (Lyshevski 2002); these are widely used in the semiconductor industry. However, these methods do exhibit certain problems, such as the limitations of the machinable materials, complicated fabrication processes, and costly equipment. In addition, the fabrication processes are usually carried out in a direction perpendicular to the workpiece surfaces, which also restricts the machinable structures.

Replication processes (Hansen et al. 2011), including molding and embossing (or imprinting), can be used to fabricate microstructures at a relatively low cost and high efficiency. The textural patterns are directly reproduced from those of a die or a mold. However, the materials used for the dies must possess high-temperature strength, thus limiting the range of potential materials. A molding process is typically used when fabricating textures on glass, polymeric, or metal materials, which are melted and then solidified into a mold to replicate the structure. Only metals that exhibit good ductility and are softer than the die/mold materials can be used for the embossing process. A major problem with replication processes is the loss of shape accuracy.

Self-assembling methods like chemical vapor deposition (CVD) and physical vapor deposition (PVD) can be used for producing structures at micrometer and nanometer scales (e.g., nanotubes and nanowire) (Stupp et al. 1997; Shimomura and Sawadaishi 2001). However, these methods are limited to specific materials and are usually time-consuming and costly.

For the generation of geometrically defined surface textures, diamond machining methods have strong merits, including high form accuracy, high flexibility, and high productivity (Denkena et al. 2010). In recent decades, hybrid diamond machining processes, such as laser-assisted machining and ultrasonic-assisted machining, have been developed for improving diamond machining performance. For example, the laser-assisted turning process has been proved to have a higher material removal rate (Rozzi et al. 2000a, b) and to potentially suppress the generation of cutting burrs. The elliptical vibration-assisted cutting process has been proved applicable to machine brittle materials in the ductile regime, helping to decrease tool wear and improve surface quality (Shamoto and Moriwaki 1994; Moriwaki and Shamoto 1995).

1.2 Rotary Ultrasonic Texturing

Rotary ultrasonic machining has been widely used in grinding, drilling, and milling operations to fabricate flat surfaces, holes, and various surface structures (Brehl and Dow 2008). To study the effect of ultrasonic vibration on improvements in surface quality in the 1D ultrasonic-assisted grinding process, K. Shimada (2012) established a theoretical calculation model for predicting the grinding forces and roughness of finished surfaces and found that some micro- and nanostructures could be fabricated using the ultrasonic-assisted slant-feed grinding (UASG) method.

The combination of ultrasonic vibration, tool rotation, and workpiece feed motion can lead to a high-frequency periodic change of the cutting locus of every cutting edge on the grinding wheel. The texturing principle is to fabricate surface textures at the micrometer/nanometer scale by intentionally controlling the cutting locus; the periodic features of the cutting locus can be of micrometer or submicrometer dimensions under appropriate experimental conditions. Until now, only one paper has reported the fabrication of micro-textures using 1D rotary ultrasonic machining with the principle mentioned above – D. Xing (2013) (Xing et al. 2013) studied the kinematics of cutting edges in a 1D ultrasonic-assisted milling process and fabricated a micrometer-scale scaly textured surface on aluminum alloy by controlling the high-frequency periodic change of the cutting locus. There has been no report on the fabrication of surface textures using a 3D rotary ultrasonic machining process, except for the previous work reported by the authors of the present dissertation (Xu et al. 2013, 2014).

In this chapter, a novel ultrasonic-assisted micro-/nano-texturing method that uses diamond grinding wheels or one-point diamond tools, referred to as the rotary ultrasonic texturing (RUT) method, is proposed and developed. A new 3D ultrasonic vibration spindle was firstly developed for carrying out the RUT processes. The surface generation processes were analyzed by mathematically calculating the cutting loci under different vibration modes. The material removal mechanisms were studied by analyzing the relationship between the geometry of the cutting edges and the related textural features. Then, the geometrically defined diamond tools were designed and manufactured for the RUT process, and surface generation models for the use of these tools were established for predicting the 3D surface textures.

2 Development of Equipment for Rotary Ultrasonic Texturing

The vibration mode depends on the structure of the ultrasonic vibrator. There are typically two types of ultrasonic vibrator, magnetostrictive and piezoelectric (Thoe et al. 1998). The resonant piezoelectric vibrator was selected for manufacturing the 3D ultrasonic vibration spindle in the present study. The vibrator is resonated by exciting several combined piezoelectric plates, which are sandwiched between metal cylindrical horns, with high-frequency electrical signals; this system is generally referred to as a bolt-clamped Langevin-type transducer (BLT) (Kurosawa et al. 1998). The high-frequency electrical energy is converted into mechanical vibration via the resonant piezoelectric transducer (PZT). The horn/tool assembly is used to amplify the vibration amplitude of the tool because the oscillation amplitude at the face of the piezoelectric transducer is too small to achieve a reasonable cutting rate.

Figure 1 shows two types of PZT system for generating the two basic ultrasonic vibration modes, the longitudinal vibration (LV) mode and the bending vibration (BV) mode. In the LV mode, the tool vibrates along the axial (Z) direction, whereas in the BV mode, the tool vibrates in the transverse (XY) plane perpendicular to the axis. To produce the LV mode, the PZT comprises only one round piezoelectric plate, as shown in Fig. 1a. When a sinusoidal voltage is applied to the transducer, the piezoelectric plate expands and contracts so that the vibrator is resonated and the tool tip attached to the end of the horn vibrates in the LV mode along the Z axis. The vibration amplitude depends on the applied voltage, the material properties of the PZT, and the spindle structure. The vibration amplitude is magnified by the horns and is maximized at the tool tip. The 1D ultrasonic vibration spindle is widely used in the rotary ultrasonic processes. In Fig. 1b, if two half-round piezoelectric plates are placed on the PZT and two sinusoidal voltages with a 180-degree phase difference are applied to the piezoelectric plates, the two piezoelectric plates will expand and contract alternately. Ultimately, the tool attached to the end of the horn vibrates with the bending mode in the XY plane.
Fig. 1

Two types of PZT system for generating the two basic ultrasonic vibration modes: (a) LV mode and (b) BV mode (Xu et al. 2017)

Various ultrasonic vibrators can be developed by combining the two basic PZT systems mentioned above. Figure 2 shows a type of ultrasonic vibrator that is capable of generating 2D vibration in the transverse (XY) plane. Four piezoelectric plates with the same resonant frequency are placed on the ultrasonic actuator. Thus, the specific shape of the vibration locus depends on the vibration amplitudes and phase difference of the applied sinusoidal voltages. If sinusoidal voltages with a 180-degree phase difference are applied to each pair of opposite piezoelectric plates, two BV modes can be generated simultaneously. With a certain phase difference of the two BVs, an elliptical or circular vibration mode can be generated in the transverse (XY) plane. For instance, by applying 0-, 90-, 180-, and 270-degree phase-shifted sinusoidal signals with the same amplitude in the clockwise direction on the four piezoelectric plates, a circular vibration (CV) can be generated.
Fig. 2

PZT systems for generating elliptical or circular vibration in the transverse plane (Xu et al. 2017)

In the present work, the PZT systems shown in Figs. 1a and 2 were further combined into one ultrasonic vibrator, as shown in Fig. 3, and a new 3D hybrid ultrasonic vibrator was designed and manufactured. The circular vibration was tuned by modulating the parameters mentioned above for this vibrator. Therefore, by implementing the LV and CV modes simultaneously, the 3D ultrasonic vibrator can generate the LV mode along the axis (Z direction) of the spindle, the CV mode on the transverse (XY) plane, and 3D hybrid vibration (HV) in the 3D space. Figure 4 schematically shows the construction of the ultrasonic vibration spindle. As such, the main spindle is rotationally driven by a motor, the resonant ultrasonic vibrator controlled by an ultrasonic oscillator is arranged coaxially to the spindle, step horns are integrally connected to the ultrasonic vibrator, and then, a tool (such as a grinding wheel or cutting tool) is mounted at the tip end of the horn.
Fig. 3

PZT system used for manufacturing the 3D rotary ultrasonic spindle (Xu et al. 2017)

Fig. 4

Schematic of the construction of the 3D rotary ultrasonic spindle (Xu et al. 2017)

On the basis of the proposed design principle described above, a 3D ultrasonic vibration spindle (SC-450SP-H24) was successfully manufactured by Taga Electric Co., Ltd. The rotary ultrasonic texturing processes were carried out using this spindle. Picture showing the 3D ultrasonic vibration spindle is shown in Fig. 5. Two types of tool, with the specifications shown in Fig. 6, were used. The specific parameters of the 3D ultrasonic spindle using the two types of tool are presented in Table 1.
Fig. 5

3D ultrasonic vibration spindle

Fig. 6

Specifications of the two types of tool used in the work described in this chapter

Table 1

Specifications of the 3D ultrasonic vibration spindle

3D ultrasonic vibration spindle (SC-450SP-H24)

Rotation speed

0–4000 rpm (stable at 0–3000 rpm)

Vibrator type

Bolt-clamped Langevin-type transducer (BLT)

Synchronizing system

Microcomputer-controlled phased-locked loop-type automatic synchronization system

Protruding length of tools/total tool length

15/35 mm

12/28 mm

Clamping torque of bolt

12.5 Nm

Vibration frequency (LV mode)

25.0 ± 3.0 kHz

Vibration frequency (CV mode)

19.0 ± 2.0 kHz

Vibration amplitude (LV mode)

1.5 μm (L)

3 μm (H)

Vibration amplitude (CV mode)

10 × 10 μm2 (L)

15 × 15 μm2 (H)

A four-axis (XYZC) computer numerical control (CNC) precision machine tool (TRIDER-X) produced by the NEXSYS Corporation (as shown in Fig. 7) was used. The 3D ultrasonic vibration spindle is mounted to this machine tool to carry out the RUT process.
Fig. 7

Equipment used for the RUT process: an ultrasonic vibration spindle mounted on a CNC machine

3 Proposed UASG Method

In the UASG method, the combination of ultrasonic vibration, rotation, and feed motion can lead to a high-frequency periodic cutting locus of each diamond abrasive on the grinding wheel. The cutting loci have periodic features at the micrometer/nanometer scales; these can be actively controlled for micro-/nano-texturing. However, the traditional UASG process does not possess such features, as will be explained in the next section. Therefore, the UASG method shown in Fig. 8 was proposed. Here the diamond grinding wheel rotates and vibrates at an ultrasonic frequency, with the feed direction slanted with respect to the horizontal direction (Y axis).
Fig. 8

Schematic of the UASG process (Xu et al. 2017)

3.1 The Calculation of the Cutting Loci

To determine the texturing mechanisms of the UASG technique, the kinematic motion of the diamond cutting abrasives should first be analyzed. The vibration loci in the LV, CV, and HV modes can be calculated by Eqs. (1), (2), and (3), respectively, as follows.

$$ z(t)={A}_l\, \sin \left(2\pi {f}_lt+{\varphi}_l\right) $$
(1)
$$ \left\{\begin{array}{c}x(t)={A}_c\, \sin \left(2\pi {f}_ct+{\varphi}_c\right)\\ {}y(t)={A}_c\, \cos \left(2\pi {f}_ct+{\varphi}_c\right)\end{array}\right. $$
(2)
$$ \left\{\begin{array}{c}x(t)={A}_c\, \sin \left(2\pi {f}_ct+{\varphi}_c\right)\\ {}y(t)={A}_c\, \cos \left(2\pi {f}_ct+{\varphi}_c\right)\\ {}z(t)={A}_l\, \sin \left(2\pi {f}_lt+{\varphi}_l\right)\end{array}\right. $$
(3)
where subscripts l and c represent the LV and CV modes, respectively, and A, f, and φ are the amplitude, frequency, and initial phase angle of vibration, respectively. If the initial phase angles are assumed to be 0, the vibration loci in the LV, CV, and HV modes can be drawn as shown in Figs. 9, 10, and 11, respectively. The two-bending vibration pair in Fig. 10 has a 90-degree phase difference; therefore, a circular vibration locus is generated, as explained in section “Development of Equipment for Rotary Ultrasonic Texturing.” The vibration frequencies of the LV and CV modes are different; therefore, no periodic features can be observed in the vibration locus of the HV mode, as shown in Fig. 11.
Fig. 9

Vibration locus of the LV mode (f l  = 25 kHz and A l  = 3 μm)

Fig. 10

Vibration locus of the CV mode (f c  = 19 kHz and A c  = 10 × 10 μm2)

Fig. 11

Vibration locus of the HV mode during four LV periods (f l  = 25 kHz, A l  = 3 μm, f c  = 19 kHz, and A c  = 10 × 10 μm2)

In the tool-in-hand coordinate system shown in Fig. 8, the cutting locus of every diamond abrasive in the UASG process can be mathematically calculated using Eqs. (4), (5), and (6) in the LV, CV, and HV modes, respectively, where v fy and v fz are the feed speeds in the y and z directions, D is the tool diameter, h p is the protrusion height of the diamond cutting abrasive, n t is the rotational frequency of the diamond tool, and φ r is the initial phase of the rotational motion.

$$ \left\{y=\begin{array}{c}x=\left(\frac{D}{2}+{h}_p\right)\sin \left(\frac{2\pi {n}_tt}{60}+{\varphi}_r\right)\\ {}\left(\frac{D}{2}+{h}_p\right)\cos \left(\frac{2\pi {n}_tt}{60}+{\varphi}_r\right)+{v}_{\mathrm{fy}}t\\ {}z={A}_l\, \sin \left(2\pi {f}_lt+{\varphi}_l\right)+{v}_{\mathrm{fz}}t\end{array}\right. $$
(4)
$$ \left\{\begin{array}{c}x=\left(\frac{D}{2}+{h}_p\right)\sin \left(\frac{2\pi {n}_tt}{60}+{\varphi}_r\right)+{A}_c\, \sin \left(2\pi {f}_ct+{\varphi}_c\right)\\ {}y=\left(\frac{D}{2}+{h}_p\right)\cos \left(\frac{2\pi {n}_tt}{60}+{\varphi}_r\right)+{A}_c\, \sin \left(2\pi {f}_ct+{\varphi}_c\right)+{v}_{\mathrm{fy}}t\\ {}z={v}_{\mathrm{fz}}t\end{array}\right. $$
(5)
$$ \left\{\begin{array}{c}x=\left(\frac{D}{2}+{h}_p\right)\sin \left(\frac{2\pi {n}_tt}{60}+{\varphi}_r\right)+{A}_c\, \sin \left(2\pi {f}_ct+{\varphi}_c\right)\\ {}y=\left(\frac{D}{2}+{h}_p\right)\cos \left(\frac{2\pi {n}_tt}{60}+{\varphi}_r\right)+{A}_c\, \sin \left(2\pi {f}_ct+{\varphi}_c\right)+{v}_{\mathrm{fy}}t\\ {}z={A}_l\, \sin \left(2\pi {f}_lt+{\varphi}_l\right)+{v}_{\mathrm{fz}}t\end{array}\right. $$
(6)

3.2 Conventional Grinding and Slant-Feed Grinding

Figure 12 schematically shows the difference between the conventional grinding (CG) and slant-feed grinding (SG) processes. In the SG process, the feed direction is slanted with respect to the Y axis, whereas in the CG process, the feed direction is horizontal along the Y axis.
Fig. 12

Schematics of the (a) CG process and (b) SG process (Xu et al. 2017)

The diamond abrasives on the grinding wheels are generally randomly distributed. The protrusion height of each abrasive on the surface of a grinding wheel determines its participation in the material removal process. Each abrasive removing material from the workpiece will create a cut track on the workpiece during the grinding process. To explain the differences between the CG and SG procedures, the term “effective cut track” is defined as the cut tracks remaining on the finished surface. The rotation speed of the tool during the grinding process is usually very high; therefore, it is reasonable to assume that only diamond abrasives with the maximum protrusion height on the cross section of a grinding wheel, e.g., the red diamond abrasive shown in Fig. 13a, will leave an effective cut track on the finished surface. Each diamond abrasive shown in Fig. 13b is assumed to be the highest in the cross section and able to produce effective cut tracks on the finished surface when using the CG process. Each diamond abrasive is fed linearly along the horizontal feed direction. Therefore, the cut tracks produced during each wheel rotation period are partially overlapped by the following cut tracks; as such, linear grooves along the horizontal feed direction can be generated, as shown in Fig. 13c.
Fig. 13

Schematics of (a) a cross section of a diamond grinding wheel, (b) diamond abrasives for fabricating effective cut tracks, (c) surface textures fabricated by the CG process, and (d) surface textures fabricated by the SG process (Xu et al. 2013)

In contrast, during the SG process, the cut track produced during each rotation period is individually duplicated on the surface of the workpiece with no (or minimal) overlap along the slanted feed direction. Only diamond abrasives with a larger protrusion height than that of adjacent diamond abrasives (e.g., the diamond abrasives labeled 1, 2, 3, and 4 in Fig. 13b) will leave obvious effective cut tracks on the finished surface. Therefore, the surface textures shown in Fig. 13d were generated using the SG method. The length of each cut track along the slant feed direction is determined by the protrusion height and distribution of the diamond cutting abrasives.

3.3 Surface Texturing Mechanisms

Without consideration of the radial motion of the tool, all of the cut tracks shown in Fig. 13c, d are assumed to be linear grooves on the YZ plane. When the LV mode is used, the linear grooves will be transformed to sinusoidal grooves. Figure 14 shows the cutting loci of one diamond abrasive during three rotation periods of the CG and SG processes in the LV mode. In the CG process, the sinusoidal loci overlap one by one along the horizontal feed direction. In contrast, the sinusoidal loci are distributed along the slant feed direction in the SG process, and the distance between two adjacent sinusoidal loci can be controlled by adjusting the machining conditions. This sinusoidal cutting locus can be actively controlled for fabricating surface micro-/nano-textures.
Fig. 14

Cutting loci of one diamond abrasive during three rotation periods of (a) the CG process (v fy = 3 mm/min) and (b) the SG process (v fy = v fz = 3 mm/min) in the LV mode (Xu et al. 2017)

When the CV mode is used, the linear grooves are transformed to continuous 2D curves in the XY plane, as shown in Fig. 15. The same transformations of the cutting loci can be observed, i.e., the 2D curves for the three rotation periods overlap one by one in the CG process, whereas they distribute along the slant feed direction without any overlap in the SG process. With this 2D cutting locus, the cutting abrasive intermittently comes into contact with the workpiece; thus, micro-concave textures can be fabricated on the surface of the workpiece.
Fig. 15

Cutting loci of a diamond abrasive during three rotation periods in (a) the CG process (v fy = 3 mm/min) and (b) the SG process (v fy = v fz = 3 mm/min) in the CV mode

When the HV mode is used, much more complicated cutting loci are generated. Figure 16 shows the cutting loci for three rotation periods of the SG process in the HV mode. Because the vibration frequencies of the LV and CV modes are different, no periodic features can be observed in these cutting loci. In the HV mode, the UASG process is expected to fabricate random-like surfaces.
Fig. 16

Cutting loci of one diamond abrasive during three rotation periods of the SG process (v fy = v fz = 3 mm/min) in the HV mode (Xu et al. 2017)

4 Experimental Verification and Discussion

4.1 Experimental Conditions

Electroplated diamond grinding wheels were used to carry out the ultrasonic-assisted grinding processes. Figure 17 shows the surface topography of a 600-mesh-size diamond grinding wheel. It can be observed that the diamond abrasives are randomly distributed on the surface of the grinding wheel and that the shapes of the diamond abrasives are irregular. All samples were pre-machined on a precision machine by successive use of 1000- and 3000-mesh-size diamond grinding wheels. Subsequently, the UASG processes were carried out. Table 2 shows the experimental conditions.
Fig. 17

Surface topography of a 600-mesh-size diamond grinding wheel

Table 2

Experimental conditions

Diamond wheel

Shank materials

Cemented carbide

Diameter of grinding wheel (mm)

1, 3

Diamond grit mesh

#600, #1000, #3000

Workpiece

ZrO2 ceramics (13 × 14 × 17 mm3)

Grinding conditions

Rotation frequency (rpm)

500–2000

Feed speed along Y axis (mm/min)

0–5

Feed speed along Z axis (mm/min)

0–5

Grinding depth (μm)

About 3–20

Coolant

Solution type

Vibration conditions

Vibration frequency (LV) (kHz)

25

Vibration frequency (CV) (kHz)

19

Vibration amplitude (LV) (peak-to-peak) (μm)

3

Vibration amplitude (CV) (peak-to-peak) μm2

10 × 10

4.2 Experimental Results

The surface profiles were measured using a white light interferometer (Zygo, NewView 5000), and the surface textures were examined under scanning electron microscopy (Hitachi, SU1510). Surface textures fabricated using the CG and SG processes without the ultrasonic vibration motion were compared. Figure 18 shows the results when the 600-mesh-size diamond grinding wheel was used. The experimental results coincide well with the theoretical predictions shown in Fig. 13. The surface textures generated by the CG process were composed of continuous linear grooves along the horizontal feed direction. The depth of the linear grooves is determined by the maximum protrusion height of the diamond abrasives along each cross section of the diamond grinding wheel. In contrast, short linear grooves were fabricated one by one along the slant feed direction in the SG process. The same linear grooves along the slant feed direction were generated by the same cutting abrasive with a greater protrusion height, as described in section “Conventional Grinding and Slant-Feed Grinding.” If ultrasonic vibration motion was applied, the short linear grooves would be transformed into finer structures.
Fig. 18

Surfaces fabricated using the (a) CG process (#600, D = 3 mm, n t  = 500 rpm, and v fy = 3 mm/min) and (b) SG process (#600, D = 3 mm, n t  = 500 rpm, and v fy = v fz = 3 mm/min) (Xu et al. 2013)

Figure 19 shows the surface profiles and surface textures fabricated using the UASG method in the LV, CV, and HV modes. The surface profiles agree well with the surface generation model, as shown in Fig. 13d. The differences in the protrusion heights of the diamond abrasives on the grinding wheel also result in differences in the depth and width of the short linear grooves along the slant feed direction. The short linear grooves were changed to much finer structures, which coincide well with the cutting loci shown in Figs. 14, 15, and 16. The micro-sinusoidal grooves shown in Fig. 19a were fabricated using the LV mode. The micro-concave textures (e.g., micro-holes) shown in Fig. 19a were fabricated using the CV mode. When the HV mode was employed, a random-like rough surface was successfully fabricated.
Fig. 19

Surface profiles and textures fabricated using the UASG process (#600, D = 3 mm, n t  = 500 rpm, and v fy = v fz = 3 mm/min) in the (a) LV mode, (b) CV mode, and (c) HV mode

Figure 20 shows the experimental results when a 1000-mesh-size diamond grinding wheel was used. The CG and SG processes with and without ultrasonic vibration were compared. It can be observed that no obvious surface micro-/nano-textures were fabricated with the CG process even when ultrasonic vibration was used, as shown in Fig. 20ae. The reason for this is that the cutting loci overlap one by one along the horizontal feed direction, as shown in Figs. 14a and 15a. Different surface micro-/nano-textures were successfully fabricated along the slant feed direction when using the UASG processes. It can be observed that the surface micro-/nano-textures on the various surface areas along the slant feed direction differ owing to the different shapes of the diamond cutting abrasives. Figures 21 and 22 show different micro-/nano-textural patterns fabricated with the LV and CV modes. When the LV mode is used, the sinusoidal feature can be clearly observed on the textured surfaces; however, the textural patterns differ even when fabricated under the same experimental conditions. The reason for this is that the shapes of the diamond cutting abrasives also have a significant influence on the surface textural features. The diamond cutting abrasive intermittently contacts with the workpiece under the CV mode; therefore, the material is intermittently removed, and periodic micro-/nanostructures are generated. Owing to the different shapes of the diamond cutting abrasives, different textural patterns are also observed on the finished surfaces.
Fig. 20

Surface textures fabricated using the (a) CG process in the LV mode, (b) SG process in the LV mode, (c) CG process in the CV mode, (d) SG process in the CV mode, (e) CG process in the HV mode, and (f) SG process in the HV mode (#1000, D = 1 mm, n t  = 1000 rpm, v fy = 3 mm/min, and v fz = 3 mm/min (only for SG))

Fig. 21

Various surface micro-/nano-textures on the different areas along the slant feed direction as fabricated using UASG in the LV mode

Fig. 22

Various surface micro-/nano-textures on the different areas along the slant feed direction as fabricated using UASG in the CV mode

4.3 Limitations of the UASG Technique

The experimental results reveal that the UASG method can be used for fabricating different periodic micro-/nano-textures in the LV and CV modes or random-like surfaces in the HV mode. The irregular shapes of the diamond cutting abrasives also provided various machined structures in the UASG method. If the textural pattern must be controlled, the shapes and distribution of the diamond abrasives must be tailored. In addition, it is virtually impossible to determine the relationship between the shapes of the diamond cutting abrasives and the textural features. Therefore, it is preferable to use another tool to determine the mechanisms of material removal during the micro-/nano-texturing process. To fully control the texturing process, the cutting edges should be geometrically designed and regularly distributed on the surface of the tool. As such, the next section describes the design and manufacture of diamond tools with only one cutting tip. These are referred to as one-point diamond tools, and these were produced using electroplating in the RUT process.

5 Rotary Ultrasonic Texturing Using One-Point Diamond Tools

5.1 Theories of Texturing Mechanisms

A cutting tip usually comprises three parts: the cutting corner, the cutting edge, and the cutting face (Boothroyd and Knight 2006). In this section, only the effects of the cutting corner and the cutting edge in the RUT process are discussed. Two types of cutting tip, one with a conical shape (cutting tip 1) and the other with a triangular prism shape (cutting tip 2), as shown in Fig. 23, were used to analyze the texturing mechanisms of the RUT process in the LV and CV modes. The conical cutting tip is assumed to have a cutting corner that is sharp enough to fabricate grooves of any width. The triangular prism cutting tip is assumed to have a cutting edge of a length that is much larger than the vibration amplitude of the tool in the RUT process. A simple texturing procedure, as shown in Fig. 24, was used to study the technical requirements of the RUT methods. With rotational motion of an ultrasonic vibration spindle, a one-point diamond tool is fed along the negative Z-axis direction on the flat surface of a workpiece. Thus, (1) the diamond cutting tip moves along a helical path, (2) the cutting tip removes the work material to a certain cutting depth (only in the labeled machined area), and (3) the diamond tool vibrates in the LV mode or CV mode simultaneously. To analyze the texturing mechanisms, several assumptions are made: (1) the radial motion of the cutting tip on the tool is ignored when removing the material, and the cutting depth in the machined area is assumed to be constant, (2) the cutting direction in each rotation period is assumed to be along the Y axis, (3) the cutting speed along the Y axis is assumed to be equal to the peripheral velocity of the tool, and (4) the work material is assumed to be completely removed during the material removal process.
Fig. 23

Two types of cutting tip: (a) a conical shape and (b) triangular prism shape

Fig. 24

Texturing procedure used for the RUT process (Xu et al. 2017)

5.1.1 Surface Generation Mechanisms in the LV Mode

On the basis of the assumptions described above, if diamond cutting tip 1 is used, linear grooves will be generated on the machined area (as shown in Fig. 25a) in the absence of ultrasonic vibration. When the LV mode is employed, the linear grooves become sinusoidal grooves, as shown in Fig. 25b. The width of the sinusoidal grooves (w s ), the axial height of the sinusoidal grooves (A s ), the wavelength of the sinusoidal grooves (l s ), and the distance between two adjacent sinusoidal grooves along the Z axis (l z ) can be calculated by Eqs. (7), (8), (9), and (10), respectively, where α c is the cone angle of the conical cutting tip. Figure 25c shows the changes in the textural patterns with changes in the texturing parameters, from which it can be seen that different textural patterns can potentially be fabricated by modulating the cutting locus in the texturing process. When the triangular prism cutting tip is used, as shown in Fig. 26a, at an angle oblique to the surface of the workpiece, the cutting edge will remove the material, and the cutting corner will produce textures on the surface generated by the cutting edge, as depicted in Fig. 26b.
Fig. 25

Schematics of surface textures fabricated by the conical cutting tip under the LV mode: (a) linear grooves, (b) sinusoidal grooves, and (c) textured surfaces fabricated under different texturing parameters

Fig. 26

Schematics of (a) a triangular prism cutting tip and (b) surface textures fabricated by the triangular prism cutting tip in the LV mode

$$ {w}_s=2{a}_p\, \tan \frac{\alpha_c}{2} $$
(7)
$$ {A}_s={A}_l+{w}_s+\frac{v_{\mathrm{fz}}}{120{f}_l} $$
(8)
$$ {l}_s=\frac{\pi {\mathrm{Dn}}_t}{60}\times \frac{1}{f_l} $$
(9)
$$ {l}_z=\frac{v_{\mathrm{fz}}}{n_t} $$
(10)

5.1.2 Surface Generation Mechanisms in the CV Mode

The same assumptions were used to analyze the texturing process in the CV mode. The CV mode provides the cutting tip with the vibration of the circular locus on the XY plane, as shown in Fig. 27a. The instantaneous speed of the cutting tip (v c ) generated only by the circular vibration can be calculated by Eq. (11), where A c is the diameter of the circular vibration. The peripheral velocity of the tool (v p ) can be calculated by Eq. (12) when the tool rotates along the spindle axis. The combination of v c with v p finally determines the shape of the whole cutting locus. For a certain vibration condition, Fig. 27b shows two typical cutting loci. Two parameters, h c * and w c *, as shown in Fig. 27b, must be considered for the RUT process in the CV mode. The term w c * can be calculated using Eq. (13), and h c * is given by Eq. (14); τ is the solution of Eq. (15).
Fig. 27

Schematics of (a) circular vibration locus, (b) two types of cutting loci, and (c) textural patterns fabricated using cutting tips 1 and 2 (Xu et al. 2017)

If 0 < a p < h c *, the depth of the textured patterns (h c ) is equal to a p , and the width of the textured patterns (w c ) is smaller than w c *; thus, discontinuous textured patterns will be generated. If a p h c *, the depth of the textured patterns (h c ) is equal to h c *, and the width of the textured patterns (w c ) is equal to w c *; thus, continuous textured patterns will be fabricated.

Therefore, by controlling the cutting depth and shape of the cutting loci, different surface textures can be fabricated. For example, continuous micro-dimples and microgrooves (as shown in Fig. 27c) can be fabricated when a p is bigger than h c * using diamond cutting tips 1 and 2, respectively. In the case of the continuous microgrooves, the aspect ratio (the width and depth of the textured grooves) can be plotted against the ratio of v p to v c , as shown in Fig. 28. Under a certain vibration condition, v c is constant according to Eq. (11). Therefore, v p /v c increases when n t is increased. It can be found that the maximum depth of the machinable textured groove is determined by the vibration amplitude of the circular vibration; the largest aspect ratio (approximately 0.32) of the textured groove can be obtained when v p is equal to v c . Continuous grooves of several micrometers in depth and from several micrometers to several tens of micrometers in width can be fabricated if the work material is efficiently removed during the RUT process.
Fig. 28

Aspect ratio h c /w c (black line) of the continuous textured grooves as a function of v p /v c non-conditionally. Width and depth (red and green lines) of the continuous textured grooves as a function of v p /v c when D = 3 mm, A c  = 10 μm, and f c  = 19 kHz (Xu et al. 2017)

$$ {v}_c=\pi {A}_c{f}_c $$
(11)
$$ {v}_p=\pi {\mathrm{Dn}}_t $$
(12)
$$ {w_c}^{\ast }=\frac{v_p}{f_c} $$
(13)
$$ {h}_c^{\ast }=\left\{\begin{array}{c}\frac{A_c}{2}\left[1-\cos \left(2\pi {f}_c\tau \right)\right]\, {v}_c>{v}_p\\ {}{A}_c\, {v}_c\le {v}_p\end{array}\right. $$
(14)
$$ {v}_p\tau +\frac{A_c}{2}\sin \left(2\pi {f}_c\tau \right)=\frac{v_p}{2{f}_c}\, {v}_c>{v}_p $$
(15)

5.2 Texturing Procedures and Corresponding Cutting Loci

To control the texturing process for specific textural patterns in the machined surface, the cutting loci should first be calculated and intentionally controlled (based on the analysis in the above section). Figure 29 shows the two texturing procedures used in this chapter for the RUT process. In Fig. 29a, the diamond tool is firstly fed along the axial (negative Z) direction, and then, the cutting process is repeated with an intermittent feed distance (d y ) along the horizontal (Y) direction. In Fig. 29b, the tool is firstly fed along the Y axis, and then, the cutting process is repeated with an intermittent feed distance (d z ) along the axial (Z) direction. The center point of the tool shank’s cross section, where the diamond cutting tip is located, is assumed to be the original point in the tool-in-hand coordinate system, as shown in Fig. 29. Therefore, the cutting loci in the LV and CV modes can be calculated in a similar manner to that described in section “The Calculation of the Cutting Loci.”
Fig. 29

Schematics of two RUT procedures

It is necessary to analyze the kinematics of the cutting tip during the RUT process. Figures 30 and 31 describe the feed paths and the cutting loci of the texturing procedures under certain experimental conditions, as shown in Figs. 29a, b, respectively.
Fig. 30

Feed path and cutting loci of the texturing procedure in Fig. 29a (n t  = 1000 rpm, v fz = 3 mm/min, d y  = 1000 μm, and a p  = 3 μm): (a) the feed path, (b) the cutting loci along the Z axis in the LV mode, and (c) the cutting loci along the Z axis in the CV mode

Fig. 31

Feed path and cutting loci of the texturing procedure in Fig. 29b (n t  = 500 rpm, v fy = 600 mm/min, d z  = 10 μm, and a p  = 5 μm): (a) the feed path, (b) the cutting loci along the Z axis in the LV mode, and (c) the cutting loci along the Z axis in the CV mode

In Fig. 30a, the parameter (w g ), the width of a machined area at a certain cutting depth (a p ) in one rotation period, has to be considered; this can be calculated using Eq. (16). If w g is smaller than d y , each machined surface along the Y axis will be disconnected. In contrast, if w g is bigger than d y , the machined surface areas along the Y axis will be connected. In the LV mode, sinusoidal cutting loci (as shown in Fig. 30b) can be generated, whereas in the CV mode, 2D cutting loci (as shown in Fig. 30c) can be generated.

In Fig. 31a, the parameters l y and h g must be considered. The term l y can be calculated using Eq. (17), and h g is given by Eq. (18); δ is the solution of Eq. (19). It can be found that the rotational speed and the feed speed along the Y axis determine l y and h g . If a p is smaller than h g , each machined surface area along the Y axis will be disconnected. In contrast, if a p is no smaller than h g , the machined surface areas along the Y axis will be connected. The specific shapes of the cutting loci depend on the tool parameters and experimental conditions. The radial motion of the tool changes the cutting depth from 0 to the maximum value (a p ) and then back to 0 during each rotation period; this must be considered in the RUT process.

$$ {w}_g=2\sqrt{{\left(\frac{D}{2}\right)}^2-{\left(\frac{D}{2}-{a}_p\right)}^2} $$
(16)
$$ {l}_y=\frac{v_{\mathrm{fy}}}{n_t} $$
(17)
$$ {h}_g=\frac{D}{2}\left[1-\cos \left(2\pi \frac{n_t}{60}\delta \right)\right] $$
(18)
$$ {v}_{\mathrm{fy}}\delta +\frac{D}{2}\sin \left(2\pi \frac{n_t}{60}\delta \right)=\frac{60{v}_{\mathrm{fy}}}{2{n}_t} $$
(19)

5.3 Design of Geometrically Defined One-Point Diamond Tools

When fabricating textures on flat surfaces using the RUT method, the radial motion of the diamond cutting tip makes the instantaneous cutting depth change periodically from 0 to the maximum and then back to 0 during each tool rotation period. Therefore, a design for an advance cutting edge is required to maintain the instantaneous cutting depth at a fixed value. The sinusoidal cutting locus under the LV mode makes the two-rake-face design essential for efficiently removing the work material. When designing tools for the RUT method under the CV mode, the relationship between the tool clearance angle and the curvature of the cutting locus also needs to be considered. Figures 32, 33, and 34 show three types of geometrically defined one-point diamond tool designed for the RUT process. A diamond cutting tip of a certain geometrical shape is cemented to the tool shank. The specifications and SEM images of these diamond cutting tips are given.
Fig. 32

The geometrically defined one-point diamond tool with a square pyramid cutting tip (Xu et al. 2016)

Fig. 33

The geometrically defined one-point diamond tool with a triangular pyramid cutting tip for the RUT process in the LV mode (Xu et al. 2016)

Fig. 34

The geometrically defined one-point diamond tool for the RUT process in the CV mode (Xu et al. 2017)

The diamond cutting tip shown in Fig. 32 was used for preliminary testing of the RUT process in the LV and CV modes. A square pyramid cutting tip is fixed at the bottom of the tool shank. The included angle of two opposite faces (e.g., face ABE and face CDE) is about 70.5°, and the nose radius is approximately 200 nm.

Figure 33 shows the diamond tool with a triangular pyramid cutting tip, which was used for micro-/nano-texturing in the LV mode. The cutting edge AD (or BD) acts as the advance cutting edge when the tool feeds along the negative (or positive) Z axis. The faces ACD and BCD are the two rake faces when the tool vibrates downward and upward, respectively. The cutting corner D has a radius of approximately 200 nm.

Figure 34 shows the one-point diamond tool designed for the RUT process in the CV mode. The turning diameter is 3.6 mm. A two-level flank face was designed with clearance angles of 15° and 30° to ensure the strength of the cutting edge and reduce the interference between the rake face and workpiece. The major cutting edge has an included angle of 5° to the Z axis, and the minor cutting edge has an included angle of 10° to the Y axis. The nose radius is approximately 20 μm.

5.4 Modeling of the Surface Generation Process

The final research objective of the work described in this chapter was to fabricate different surface micro-/nano-textures using the RUT method. Therefore, before conducting practical experiments, it was necessary to predict the machinable structures based on the cutting locus and the diamond cutting tip’s geometry, which can also be used to guide the design of cutting tip geometries and texturing parameters. There have been many approaches reported (Ehmann and Hong 1994; Lin and Chang 1998; Lee and Cheung 2001; Kim et al. 2002) for predicting surface topography in the diamond machining processes. However, most of these studies only report the resultant surface profiles, and they focus on changes in surface roughness. In this chapter, the textural features of the finished surface at the micrometer/nanometer scale are of greater interest. The material removal process during each vibration period must also be visualized in order to determine the material removal mechanisms. Therefore, a new modeling method applicable to surface generation in the RUT process is proposed. This method can be used to simulate the 3D surface profiles of finished surfaces and visualize the cutting process in each vibration period.

5.4.1 Assumptions in the Modeling Process

In the RUT process, each tool rotation fabricates a cut track on the surface of the workpiece at a certain cutting depth. The feed rate along the Z axis is usually set at 0 or a value much lower than the peripheral velocity of the rotating tool. Thus, the included angle between each cutting path on the machined area and the Y axis is maintained at 0 or a very small value, which can be ignored. Therefore, in the modeling process, the direction of each cutting path along the workpiece should be horizontal along the Y axis. The instantaneous cutting depth is also assumed to be constant along each cutting path and equal to the cutting depth. Mechanical deformation of the workpiece is not considered, and the workpiece material is assumed to be fully removed when the rake face contacts the workpiece. The interference between the flank face and workpiece is taken into account.

5.4.2 Surface Generation Model Under the LV Mode

On the basis of the above assumptions, the modeling process of surface generation using the triangular pyramid cutting tip is described in Fig. 35. The cutting edge AD acts as an advance cutting edge when the feed direction is along the negative Z axis. The faces ACD and BCD alternately act as the rake face during the texturing process. When the cutting tip vibrates upward from a lower peak point to an upper peak point along the sinusoidal locus, the rake face BCD acts as the rake face and removes the material from the workpiece, as shown in Fig. 35c, e; when the cutting tip vibrates downward, the rake face ACD acts as the rake face and removes the material from the workpiece, as shown in Fig. 35d. The material removal process is carried out along the sinusoidal cutting locus, as shown in Fig. 35b; thus, a surface texture, such as that shown in Fig. 35f, will be generated. The sinusoidal groove is generated by cutting corner D, and the oblique parallel grooves above and under the sinusoidal groove are generated by cutting edges BD and AD, respectively.
Fig. 35

Illustration of the surface generation model of the RUT process in the LV mode: (a) the triangular pyramid cutting tip, (b) the sinusoidal cutting locus along the workpiece, (ce) the material removal processes, and (f) a textured surface

The relationship between the geometries of the cutting tips and the shapes of the cutting loci also requires attention, as shown in Fig. 36. The reason for this is that, when one rake face (e.g., face BCD) removes the material from the workpiece, the interface volume between the other rake face (ACD) and the workpiece must also be considered. The included angle (β *) of the line segment (between the two adjacent lowest and highest points at the cutting locus) in the horizontal direction (as shown in Fig. 36a) is a critical value and must be considered as follows: if β * is equal or greater than β/2 (as shown as shown in Fig. 36b), the rake face BCD removes the material along the sinusoidal cutting locus when the tool vibrates upward. The interference volume between the face ACD and the workpiece is relatively small under these conditions, which are assumed to be only just capable of generating elastic deformation and so are ignored in the present modeling process. The same assumption is used when the tool vibrates downward. However, if β * is smaller than β/2 (as shown in Fig. 36c) when the tool vibrates upward (or downward), the interference volume between face ACD (or face BCD) and the workpiece can be large enough to generate plastic deformation or material removal, which cannot be ignored. Therefore, in the modeling process, the two rake faces are assumed to simultaneously remove the material when β * is smaller than β */2.
Fig. 36

(a) Relationship between the geometries of the cutting tips and the shapes of the cutting loci, (b) the material removal process (β *β/2), and (c) the material removal process (β * < β */2)

The overall surface textures depend not only on the geometry of the diamond cutting tip but also on the shapes and combinations of the sinusoidal cutting loci along the Z axis. The shape of the sinusoidal cutting locus is determined by (1) the resultant motion of the ultrasonic vibration, (2) the rotation, and (3) the feed motion, which can be fully controlled during the texturing process. Figure 37 shows two types of textured surface when the phase difference of every two adjacent sinusoidal loci along the Z axis is 90°. Figure 38 shows another combination of sinusoidal cutting loci (0-degree phase difference) and the corresponding textured surfaces. It can be seen that different 3D textural patterns can be generated by combining various parameters in the RUT process. All of the textural features of these 3D shapes can be mathematically calculated in the present modeling process. For instance, as shown in Fig. 37b, if the surface height of the sinusoidal groove is assumed to be 0, then the surface heights (h 1 and h 2) of the two representative points H 1 (with the maximum surface height) and H 2 can be described by Eqs. (20) and (21), respectively. The length of the oblique parallel grooves (l o ) can be calculated by Eq. (22). Therefore, it can be concluded that the present modeling process can be used to predict and control the textural patterns of the finished surfaces in the LV mode.
Fig. 37

(a) Two adjacent sinusoidal cutting loci with 90-degree phase difference, (b) generated surface topography when l z  = 3A l , and (c) generated surface topography when l z = A l

Fig. 38.

(a) Sinusoidal cutting loci with 0-degree phase difference, (b) generated surface topography when l z  = 3A l , and (c) generated surface topography when l z  = 2A l

$$ {h}_1=\frac{l_z+{A}_l}{2}\times \tan \angle \mathrm{BAC}\times \tan \alpha =\frac{l_z+{A}_l}{4} $$
(20)
$$ {h}_2=\frac{l_z-{A}_l}{2}\times \tan \angle \mathrm{BAC}\times \tan \alpha =\frac{l_z-{A}_l}{4} $$
(21)
$$ {l}_o=\frac{l_z-{A}_l}{2}\times \frac{1}{\cos \angle \mathrm{BAC}}\times \frac{1}{\cos \angle \mathrm{DAC}}=\frac{l_z-{A}_l}{\sqrt{2}} $$
(22)

5.4.3 Surface Generation Model for the CV Mode

Figure 39 describes a surface generation process of the RUT method in the CV mode (v c > v p , a p > h c *). The diamond tip has one rake face and one flank face, as shown in Fig. 39a. The clearance angle is 15°, and the major cutting edge has an included angle of 5° to the Z axis. The interference volume between the flank face and workpiece is very small and not considered in this modeling process. Figure 39c, d depicts the material removal process when using the rake face and the textured pattern after one tool rotation period, respectively. Along the cutting locus (as shown in Fig. 39b), the rake face will intermittently remove the work material to generate surface textures, as shown in Fig. 39e.
Fig. 39

Illustration of the surface generation model of the RUT process in the CV mode: (a) the diamond cutting tip, (b) the cutting locus along the workpiece, (c) the material removal process, and (d, e) surface textures generated along the cutting locus

Figure 40 shows the textured surfaces when v c  = 5v p . It can be found from Fig. 40c that discontinuous textured patterns can be fabricated when the cutting depth is smaller than the critical value (h c *). With an increase in the cutting depth, continuous linear grooves can be generated. The width and depth of the linear grooves (as shown in Fig. 40e) are equal to w c * and h c *, respectively.
Fig. 40

(a, b) Texturing parameters (v c  = 5v p ), (c) textured surface when a p  = 0.5 μm, (d) textured surface when a p  = 1 μm, and (e) textured surface when a p  = 3 μm

Figure 41 shows the textured surfaces when v c  = v p . It can be found from Fig. 41a that only when the cutting depth is greater than the vibration amplitude (10 μm) of the CV mode can the continuous linear grooves be fabricated. However, the volume of the material removed during each period of vibration is very large, and the interference volume between the flank face and the workpiece is also very large; therefore, severe wear of the diamond tools may result. Figure 41b, c shows discontinuous textured patterns when the cutting depth is smaller than the critical value (h c *, without considering the interference between the flank face and workpiece). All of the textural features can be directly obtained for the results of the modeling processes.
Fig. 41

(a) Texturing parameters (v c = v p ), (b) textured surface when a p  = 1 μm, and (c) textured surface when a p  = 5 μm

5.5 Fabrication of Micro-/Nano-textures

5.5.1 Micro-/Nano-texturing in the LV Mode

The diamond cutting tools shown in Figs. 32 and 33 were used successively for texturing experiments in the LV mode. The experimental conditions are listed in Table 3. The 3D textured surfaces were measured using SEM and a white light interferometer (Taylor Hobson, Talysurf CCI – lite noncontact 3D profiler).
Table 3

Experimental conditions

Workpiece (Ni-P plating)

Phosphorous content

10 wt.%

Machining conditions

Rotational frequency (rpm)

250–1000

Feed speed along Z axis (mm/min)

1–6

Cutting depth (μm)

0–10

Ultrasonic vibration spindle (SD-100)

Vibration frequency (kHz)

62

Vibration amplitude (peak to peak) (μm)

2

Ultrasonic vibration spindle (SC-450SP-H24)

Vibration frequency (kHz)

25

Vibration amplitude (peak to peak) (μm)

3

Figure 42 shows the SEM images of surfaces fabricated using the tool with the square pyramid cutting tip. To evaluate the texturing performance in the RUT process, the cutting depth was increased gradually along the negative Z axis with an inclined workpiece surface. Owing to the radial motion of the cutting tip, from left to right on the workpiece, the instantaneous cutting depth of the cutting corner E increases from 0 to the maximum and then back to 0, as shown in Fig. 42a. The volume of the work material removed by the cutting tip between every two neighboring peak points at the sinusoidal locus increased when the cutting depth was increased. It can be observed that this kind of tool cannot efficiently remove the cutting chips. Only at a very small cutting depth were the cutting chips removed from the workpiece and the sinusoidal grooves successfully fabricated, as shown in Fig. 42a. However, it is very difficult to control the cutting depth at such a small value in the actual texturing process. The machining efficiency also has to be considered. With an increase in cutting depth, the cutting chips occupy the machined area, and no obvious surface textures are observed, as shown in Fig. 42b. The experimental results reveal that micro-/nano-fabrication cannot be achieved if the volume of the work material removed by the cutting tip between every two neighboring peak points cannot be controlled. The generation of cutting chips along the sinusoidal locus in an ultrasonic periodical manner also has to be considered in relation to the design of a new tool. Therefore, the triangular pyramid cutting tip, with an advance cutting edge and two rake faces, was proposed for controlling the generation and removal of cutting chips in the RUT process.
Fig. 42

Textured surfaces fabricated by the tool with the square pyramid cutting tip (SC-450SP-H24; n t  = 500 rpm and v f  = 2 mm/min): (a) top area and (b) bottom left area (Xu et al. 2016)

Figure 43 shows the textured surfaces fabricated using the tool with the triangular pyramid cutting tip. It can be observed that all of the cutting chips have been removed from the workpiece and that the textured surfaces are successfully fabricated in all of the machined areas, as shown in Fig. 43a, b. The textural features are clearly depicted in Fig. 43c, d, which show a larger magnification image and the 3D profile, respectively. It can be seen that the experimental results coincide well with the results of the modeling processes, as illustrated in section “Surface Generation Model Under the LV Mode.” As such, the sinusoidal grooves with maximum depth are fabricated by cutting corner D; the oblique parallel grooves above and under the sinusoidal grooves are fabricated by cutting edges BD and AD, respectively; the periodic 3D shapes with features similar to those shown in Fig. 37b are successfully fabricated; and the textural features can be calculated using equations in section “Surface Generation Model Under the LV Mode,” i.e., h 1 = 2 μm, h 2 = 1 μm, and l o  ≈ 2.83 μm. Note that no device for synchronizing the rotation, vibration, and feed motion was employed in the present study. The phase differences between every two adjacent sinusoidal grooves along the Z axis are not constant. Therefore, the surface heights of the representative points H 1 and H 2 (as shown in Fig. 43b) are not strictly the same as those shown in Fig. 43d.
Fig. 43

Textured surfaces fabricated by the tool with the triangular pyramid cutting tip (SD-100; n t  = 1000 rpm and v f  = 6 mm/min): (a) the middle part, (b) the bottom left area, (c) greater magnification, and (d) the 3D surface profile (Xu et al. 2016)

Figure 44 shows the 3D surface profiles of a hybrid linear groove with micro-/nanostructures on its inner surface. This was fabricated with the triangular pyramid cutting tip after one feed path along the Z axis. The following are observed: (1) the linear groove is approximately 10 μm in depth and 340 μm in width; (2) the change in the cutting depth of the cutting corner with radial motion of the cutting tip can be observed in Fig. 44b; (3) the advance cutting edge AD removes most of the work material and fabricates oblique parallel grooves in advance, as shown in Fig. 44c; and (4) various 3D shapes are seen in Fig. 44d owing to the change in phase differences between every two adjacent sinusoidal grooves along the Z axis, which also suggests that different structures could be fabricated if the rotation, vibration, and feed motion can be synchronized in the RUT process. SEM images and 3D surface profiles of three other types of textured surfaces with a bigger magnification are presented in Fig. 45. The results clearly show that various periodic sinusoidal grooves and 3D shapes with dimensions of several micrometers and even several hundred nanometers are successfully fabricated. The value of l z remains the same in all of the three images, whereas l s doubles as n t doubles. The highest points of the 3D shapes, which can be clearly observed in Fig. 45c, agree well with the results of the modeling processes described in section “Surface Generation Model Under the LV Mode.”
Fig. 44

3D surface topographies of a hybrid groove along the Z axis, as fabricated by the tool with a triangular pyramid cutting tip (SD-100; n t  = 1000 rpm and v f  = 2 mm/min): (a) linear groove along the Z axis, (b) bottom left of the textured area, (c) middle bottom of the textured area, and (d) textures on the groove’s inner surface (Xu et al. 2016, 2017)

Fig. 45

Three other textured surfaces fabricated using the tool with a triangular pyramid cutting tip (SC-450SP-H24): (a) n t  = 250 rpm and v f  = 1 mm/min, (b) n t  = 500 rpm and v f  = 2 mm/min, and (c) n t  = 1000 rpm and v f  = 4 mm/min (Xu et al. 2016, 2017)

5.5.2 Micro-/Nano-texturing in the CV Mode

The diamond cutting tools shown in Figs. 32 and 34 were successively used for surface texturing experiments in the CV mode. The experimental conditions are listed in Table 4. A 3D ultrasonic vibration spindle (SC-450SP-H24) was utilized to generate circular vibration in the experiments. All workpiece samples were pre-machined using a single-point diamond tool for generating flat surfaces with roughness of less than 0.01 μm.
Table 4

Experimental conditions in the CV mode

Workpiece

Pure aluminum

99.9 wt.%

Ni-P plating

Phosphorous content: 10 wt.%

Machining conditions

Rotational frequency (rpm)

500, 1000, 3000

Feed speed along Z axis (mm/min)

2, 4, 40, 120

Cutting depth (μm)

0–10

Ultrasonic vibration spindle (SC-450SP-H24)

Vibration frequency (kHz)

19

Vibration amplitude (peak to peak) (μm2)

10 × 10

Figure 46 shows SEM images of the textured surfaces fabricated on an aluminum sample using the tool with a square pyramid cutting tip (as shown in Fig. 32). It can be seen that the cutting tip was sufficiently sharp to scratch cut tracks on the finished surface. However, the material was not efficiently removed from the workpiece; rather, it gathered on both sides of the cut tracks. The reason for this is that the instantaneous rake angle in the texturing process was around −35° (the negative value of half of the included angle); therefore, the ductile material, pure aluminum, was extruded and flowed to both sides of the cut tracks with plastic deformation. The experimental results indicate that the negative rake angle may result in the gathering of cutting debris on the textured surface; this requires further attention.
Fig. 46

Textured surfaces fabricated using the tool with a square pyramid cutting tip (n t  = 500 rpm and v fz = 2 mm/min)

Figures 47, 48, and 49 show SEM images and surface profiles of the textured surfaces fabricated on the Ni-P plating samples using the tool shown in Fig. 34. In Fig. 47, l z can be calculated as 4 μm, which is too small to generate obvious linear grooves along the Z axis. With an increase in feed speed along the Z axis while keeping the rotation speed constant at 1000 rpm, the continuous linear grooves shown in Fig. 48 were successfully fabricated. The experimental results coincide well with the results of the modeling processes, as depicted in Fig. 40e. The cutting debris was efficiently removed from the workpiece, and textured surfaces with few burrs were fabricated. Again, since no device for synchronizing rotation, vibration, and feed motion was employed (as explained in section “Micro-/Nano-texturing in the LV Mode”), the phase differences of every two adjacent cutting loci along the Z axis were not controlled during the texturing process. Therefore, phase shifts of the linear grooves along the Z axis were observed. The 2D surface profile along the axial direction (as shown in Fig. 48) is caused by the included angle (5°) between the major cutting edge and the Z axis. Therefore, the continuous linear grooves were fabricated on inclined surfaces. The surface profile along the horizontal direction (as shown in Fig. 48) shows that the width of the linear grooves is approximately 9 μm, which agrees with the result (8.2 μm) calculated using Eq. (13). When the rotation speed increased further, linear grooves with larger depth and width can be generated, as described in the modeling process. Figure 49 shows the structures and profile of a textured surface fabricated at the maximum rotation speed of the 3D ultrasonic vibration spindle. Continuous linear grooves with a depth of approximately 4 μm and a width of approximately 25 μm were successfully fabricated. However, cutting burrs were observed on the conjunct areas of every two adjacent linear grooves. The interference between the flank face and the workpiece may partly result in the cutting burrs. Another reason is that the instantaneous rake face may maintain a very large negative value when (1) the cutting depth is larger than the vibration amplitude and (2) the rotation speed is greater than the critical value, as described in the modeling process.
Fig. 47

Surface structures and profiles of the textured surfaces fabricated using the tool shown in Fig. 34 (n t  = 1000 rpm and v fz = 4 mm/min) (Xu et al. 2017)

Fig. 48

Surface structures and profiles of the textured surfaces fabricated using the tool shown in Fig. 34 (n t  = 1000 rpm and v fz = 40 mm/min) (Xu et al. 2017)

Fig. 49

Surface structures and profiles of the textured surfaces fabricated using the tool shown in Fig. 34 (n t  = 3000 rpm and v fz = 120 mm/min) (Xu et al. 2017)

5.6 Discussion

5.6.1 Effect of Cutting Loci Shape

The surface condition that occurs in most machining operations is a result of the cutting edge exiting the workpiece (Boothroyd and Knight 2006). The ultrasonic vibration makes the tool periodically vibrate at a very high frequency; thus, the cutting edge contacts and exits the workpiece at the same frequency along the cutting locus. Specifically, the sinusoidal cutting locus in the LV mode in the RUT process makes the cutting edge remove the material and exit the workpiece at each peak point of the sinusoidal locus, which results in the formation of cutting debris and the generation of burrs around the peak points on the textured surfaces. The cutting loci in the CV mode, as described in the modeling process, make the cutting edge intermittently or continuously remove the material. The relationship between the shape of the cutting edge and the shape of the cutting loci determines the interference between the flank face and the workpiece. It also determines the instantaneous rake angle, which results in different material removal mechanisms. The large interference volume and large negative rake angle could be prevented by an improved design of the shape of the cutting loci. The work material is sheared and removed in an ultrasonic periodical manner, which is fundamentally different from that of the conventional cutting process. Therefore, the geometry of the tool cutting tip should be carefully designed to control the generation and removal of cutting chips along the cutting loci, thus allowing for efficient chip removal and the fabrication of surfaces with fewer cutting burrs.

5.6.2 Effect of Cutting Edge Geometry

The geometry of the cutting edges should be designed to more efficiently remove cutting chips and decrease cutting burrs on the edges of textural patterns. This would increase the stability and capability of the micro-/nano-texturing technique.

The radial motion of the diamond cutting tip makes the instantaneous cutting depth change periodically when fabricating textures on flat surfaces. The advance cutting edge could be designed to control the instantaneous cutting depth along the feed direction, i.e., by modulating the amount of the work material removed by the cutting tip in each vibration period, thus making the texturing process more stable.

When the LV mode is employed, the design of the triangular pyramid cutting tip can be used to efficiently remove the cutting chips. As shown in Fig. 36b, the cutting chips and cutting burrs generated in one vibration period can be removed by the cutting process in the next vibration period along the sinusoidal cutting locus. In the case shown in Fig. 36c, the cutting chips and cutting burrs generated by the upper rake face or lower rake face in a half vibration period can be immediately removed by the same rake face in the next half vibration period. Therefore, the adverse effect of the high-frequency tool-exit-workpiece motion can be largely eliminated. Ultimately, the micro-/nano-textures were successfully fabricated.

When the CV mode is employed, the large interference volume between the flank face and workpiece should be avoided. Continuous textural patterns are required to eliminate the adverse effect of the high-frequency tool-exit-workpiece motion. Therefore, the tool flank angle should be designed based on a consideration of the shapes of the applied cutting loci.

6 Summary and Outlook

The newly proposed ultrasonic-assisted texturing method provides designers with additional freedom to fabricate precisely controlled micro-/nano-textured surfaces at relatively high speed. The geometrically defined one-point diamond tools enrich tool design principles in the diamond machining field, and they also enlarge the range of machinable structures possible using diamond machining techniques. Theoretically, various surface textures other than those discussed in the present dissertation can be fabricated using the RUT method if the diamond tools are designed with cutting edges of appropriate geometry. To further develop the RUT technique, diamond tools should be designed and optimized so as to be capable of fabricating the textural patterns required in practical application fields.

In a future work, a more robust and flexible ultrasonic-assisted texturing method should be developed based on the rotary ultrasonic spindle. Moreover, the scientific principles applicable to the design of textural patterns for functional performance should be given greater attention.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Masayoshi Mizutani
    • 1
    • 3
  • Shaolin Xu
    • 2
  • Keita Shimada
    • 1
  • Tsunemoto Kuriyagawa
    • 1
  1. 1.Tohoku UniversitySendaiJapan
  2. 2.Southern University of Science and TechnologyShenzhenChina
  3. 3.Department of Mechanical Systems Engineering, Graduate School of EngineeringTohoku UniversitySendai-cityJapan

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