**1. Ultra‐precision/micro machining of die steel by elliptical vibration cutting [1]**

A novel method to attain ultra‐precision sculpturing in micro/nano scale for difficult‐to‐cut materials is introduced. Elliptical vibration cutting technology is well‐known for its excellent performance in achieving ultra‐precision machining of steel materials with single crystal diamond tools. Elliptical vibration locus is generally controlled and held to a constant in practice. On the contrary, the proposed method utilizes the variations of the elliptical vibration locus in a positive manner. Depth of cut can be actively controlled in elliptical vibration cutting by controlling vibration amplitude in the thrust direction. By utilizing this as a fast tool servo function in elliptical vibration cutting, high performance micro/nano sculpturing can be attained without using conventional fast tool servo technology. Following sections describe the development of the high performance micro/nano sculpturing system and ultra‐precision/ micro machining applications.

## **1.1. Introduction**

The authors have developed "elliptical vibration cutting" technology [2], and have demon‐ strated that ultra‐precision machining of difficult‐to‐cut materials, such as hardened steel and hard/brittle materials, can be attained practically by applying ultrasonic elliptical vibration to single crystal diamond tools [3]. Several ultrasonic elliptical vibration tools and their control systems were also developed in the past studies [4]. Since variation of vibration amplitudes causes deterioration of machining accuracy and surface quality, most research efforts were dedicated to keeping the elliptical vibration locus ultra‐precisely constant. Otherwise, ultra‐ precision cutting cannot be achieved in practice.

© 2013 Shamoto et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Shamoto et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

On the other hand, the authors focus on utilizing the variation in vibration amplitude in a positive manner, in contrast with conventional studies. It is considered as a unique function, i.e., the depth of cut can be actively controlled by controlling the vibration amplitude in the depth of cut direction while machining. By utilizing this function to serve as a sort of fast tool servo (FTS), the ultra‐precision sculpturing of difficult‐to‐cut materials in micro/nano scale is achieved efficiently. Note that it is redundant and disadvantageous to combine the elliptical vibration tool with the conventional FTS, since both devices have actuators and the vibration tool is too heavy to be actuated at high frequency by the FTS.

study. The difference is insignificant in practice when the slope is not steep. The depth of cut can be controlled within half of the maximum amplitude in the depth of cut direction, and available frequency range of the amplitude control is limited to that which is relatively lower than the elliptical vibration frequency. Therefore, performance in the role as FTS strongly

Precision Micro Machining Methods and Mechanical Devices 51

Figure 2 shows thedevelopedsystem ofthe high‐speedamplitude control of elliptical vibration at a frequency of about 36 kHz. A two‐degree‐of‐freedom (2‐DOF) elliptical vibration tool [6], which was designed to generate arbitrary elliptical vibration, is utilized in the present study. The vibrator is actuated by using some PZT actuators, which are sandwiched with metal cylindrical parts, namely a bolt clamped Langevin type transducer (BLT). As the vibrator is designed to have same resonant frequencies in second resonant mode of longitudinal vibration and fifth resonant mode of bending vibration, it can generate large longitudinal and bending vibrations simultaneously at the same ultrasonic frequency by applying exciting voltages to the actuators. Thus, an arbitrary 2‐DOF elliptical vibration can be obtained at the diamond tool tip attached to the vibrator by combining both resonant vibration modes with some phase shift.

**1.3. Elliptical vibration tool and high‐speed amplitude control system**

**Figure 2.** Elliptical vibration control system and frequency response of amplitude control

Gain of the amplifier can be controlled by external input in the developed system, and thus the exciting voltage supplied to the actuator is changed. The amplitude is, consequently, controlled by the external input. As the maximum amplitude in the depth of cut direction is 4 μmp‐p, the vibration amplitude can be controlled to change the depth of cut within 2 μm by this system. Measured frequency response of amplitude control is shown in Figure 2. The developed system is able to control the vibration amplitude with a frequency bandwidth of more than 300 Hz. This frequency bandwidth is relatively narrow as compared with that of

depends on the specifications of the vibrator.

Following sections introduce the proposed machining method and a vibration control system of a two‐degree‐of‐freedom (2‐DOF) elliptical vibration tool, which enables precise amplitude control of ultrasonic elliptical vibration at high speed. Subsequently, experimental verifica‐ tions in textured grooving and in nano sculpturing are described.

#### **1.2. Ultra‐precision micro machining method for difficult‐to‐cut materials**

Figure 1 shows the proposed machining with depth of cut control in elliptical vibration cutting. The tool is fed at a nominal cutting speed and vibrated elliptically at the same time. Because of this intermittent process at an ultrasonic frequency, tool wear and adhesion are restricted, and the ultra‐precision cutting of hardened steel can be attained with single crystal diamond tools. The vibration amplitude in the depth of cut direction is controlled simultaneously in the proposed machining process as shown in the figure. The trajectory of the cutting edge, then, changes dynamically, and its envelope is transferred to the finished surface.

**Figure 1.** Machining by controlling amplitude in elliptical vibration cutting

By controlling the amplitude ultra‐precisely at high speed, the ultra‐precision sculpturing of the difficult‐to‐cut materials can be achieved efficiently without using conventional FTS technology [5]. In other words, the elliptical vibration cutting technology is equipped with a FTS function by itself. Although amplitude control command is not identical with the envelope of the cutting edge trajectory, as shown in Figure 1, their difference is not crucial to the present study. The difference is insignificant in practice when the slope is not steep. The depth of cut can be controlled within half of the maximum amplitude in the depth of cut direction, and available frequency range of the amplitude control is limited to that which is relatively lower than the elliptical vibration frequency. Therefore, performance in the role as FTS strongly depends on the specifications of the vibrator.

### **1.3. Elliptical vibration tool and high‐speed amplitude control system**

On the other hand, the authors focus on utilizing the variation in vibration amplitude in a positive manner, in contrast with conventional studies. It is considered as a unique function, i.e., the depth of cut can be actively controlled by controlling the vibration amplitude in the depth of cut direction while machining. By utilizing this function to serve as a sort of fast tool servo (FTS), the ultra‐precision sculpturing of difficult‐to‐cut materials in micro/nano scale is achieved efficiently. Note that it is redundant and disadvantageous to combine the elliptical vibration tool with the conventional FTS, since both devices have actuators and the vibration

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

Following sections introduce the proposed machining method and a vibration control system of a two‐degree‐of‐freedom (2‐DOF) elliptical vibration tool, which enables precise amplitude control of ultrasonic elliptical vibration at high speed. Subsequently, experimental verifica‐

Figure 1 shows the proposed machining with depth of cut control in elliptical vibration cutting. The tool is fed at a nominal cutting speed and vibrated elliptically at the same time. Because of this intermittent process at an ultrasonic frequency, tool wear and adhesion are restricted, and the ultra‐precision cutting of hardened steel can be attained with single crystal diamond tools. The vibration amplitude in the depth of cut direction is controlled simultaneously in the proposed machining process as shown in the figure. The trajectory of the cutting edge, then,

By controlling the amplitude ultra‐precisely at high speed, the ultra‐precision sculpturing of the difficult‐to‐cut materials can be achieved efficiently without using conventional FTS technology [5]. In other words, the elliptical vibration cutting technology is equipped with a FTS function by itself. Although amplitude control command is not identical with the envelope of the cutting edge trajectory, as shown in Figure 1, their difference is not crucial to the present

tool is too heavy to be actuated at high frequency by the FTS.

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tions in textured grooving and in nano sculpturing are described.

**1.2. Ultra‐precision micro machining method for difficult‐to‐cut materials**

changes dynamically, and its envelope is transferred to the finished surface.

**Figure 1.** Machining by controlling amplitude in elliptical vibration cutting

Figure 2 shows thedevelopedsystem ofthe high‐speedamplitude control of elliptical vibration at a frequency of about 36 kHz. A two‐degree‐of‐freedom (2‐DOF) elliptical vibration tool [6], which was designed to generate arbitrary elliptical vibration, is utilized in the present study. The vibrator is actuated by using some PZT actuators, which are sandwiched with metal cylindrical parts, namely a bolt clamped Langevin type transducer (BLT). As the vibrator is designed to have same resonant frequencies in second resonant mode of longitudinal vibration and fifth resonant mode of bending vibration, it can generate large longitudinal and bending vibrations simultaneously at the same ultrasonic frequency by applying exciting voltages to the actuators. Thus, an arbitrary 2‐DOF elliptical vibration can be obtained at the diamond tool tip attached to the vibrator by combining both resonant vibration modes with some phase shift.

**Figure 2.** Elliptical vibration control system and frequency response of amplitude control

Gain of the amplifier can be controlled by external input in the developed system, and thus the exciting voltage supplied to the actuator is changed. The amplitude is, consequently, controlled by the external input. As the maximum amplitude in the depth of cut direction is 4 μmp‐p, the vibration amplitude can be controlled to change the depth of cut within 2 μm by this system. Measured frequency response of amplitude control is shown in Figure 2. The developed system is able to control the vibration amplitude with a frequency bandwidth of more than 300 Hz. This frequency bandwidth is relatively narrow as compared with that of

conventional FTS. It might not, however, be a big problem because the elliptical vibration cutting technology is available only at relatively low cutting speed.

motion in the X‐axis, and then, arbitrary micro/nano sculpturing can be attained on a flat top surface of a steel workpiece by merely combining simple planing operations at constant cutting speed with high‐speed depth of cut control. An industrial computer is utilized to detect the coordinate positions and generate the voltage signal for controlling vibration amplitude. The coordinate values are constantly monitored in the developed system by directly communicat‐ ing with NC control system or by using an external optical sensor. The dynamic command signal for vibration amplitude control is generated to change the depth of cut in accordance

Precision Micro Machining Methods and Mechanical Devices 53

The developed machining system was applied to nano sculpturing experiments of picture images. CAD data for sculpturing were produced from gray scale images, where the gray values of 8 bits (256 gradations) in pixels were converted into the amplitude commands. As the vibration amplitude in the experiments was changed within a range from 2 μmp‐<sup>p</sup> to 4 μmp‐p, the depth of cut was changed within 1 μm. The resolution of the depth of cut control is, therefore, about 4 nm. Hardened steel workpieces (64x48 mm, JIS: SUS420J2, HRC53) were machined with single crystal diamond tools with a nose radius of 1 mm. The size of original

images is set to 3200x2400 pixels, and thus, 1 pixel corresponds to 20x20 μm.

**Figure 4.** Developed micro/nano sculpturing system using elliptical vibration cutting

Figure 5 shows an example of the nano sculpturing of picture images. The depth of cut was controlled in nano scale in accordance with the image data. As shown in Figure 5, the gray scale picture image, the microphotograph of the machined surface and its profile, which was measured by optical surface profiler (ZYGO NewView 6200), correspond well to each other.

with the CAD data.

#### **1.4. Ultra‐precision micro/nano sculpturing of textured grooves**

The developed control system was applied to grooving experiments. The ultrasonic elliptical vibration tool was mounted on an ultra‐precision planing machine, NIC‐300 (Nagase Integrex Co., Ltd.), and was fed straight for grooving. The vibration amplitude was controlled with sinusoidal and zigzag wave commands at the same time, and then, micro textured grooves were formed on the surface of a hardened steel workpiece. The vibration amplitude was controlled to change from 2 μmp‐<sup>p</sup> to 4 μmp‐p. This corresponds to the depth of cut variation of 1 μm. On the other hand, the amplitude in the cutting direction is set to be constant, 4 μmp‐p.

Figure 3 shows photographs of grooves machined at the cutting speed of 0.2 m/min by the single crystal diamond tool with a nose radius of 1 mm and their surface profiles measured by a laser microscope, VK‐9500 (Keyence Corp.). It was confirmed that the grooves with various ultra‐precision micro textures can be machined successfully on the hardened steel, and mirror surface quality can be obtained on all grooves. Measured surface profiles of sinusoidal grooves agreed precisely with the command waves. On the other hand, measured corners of zigzag grooves are rounded, and their step heights were relatively smaller than the variation width of command waves of 1 μm. This is considered to be caused by cutting off high‐frequency components in the amplitude control commands by the LPF, which the zigzag waves include at their sharp corners.

(a)textured groove with sinusoidal command (b)textured groove with zigzag command

**Figure 3.** Microphotographs and surface profiles (cutting speed: 0.2 m/min, freq.: 100 Hz)

#### **1.5. Ultra‐precision micro/nano sculpturing on plane surfaces**

In order to attain arbitrary sculpturing, an ultra‐precision micro/nano sculpturing system was developed by using the developed vibration control system and the ultra‐precision planing machine. Figure 4 shows the developed sculpturing system, where the planing machine is simply controlled to machine a plane surface at constant cutting speed. The ultrasonic elliptical vibration tool is attached on a Z‐axis table of the machine tool. The vibration amplitude in the depth of cut direction along the Z‐axis is controlled in synchronization with cutting feed motion in the X‐axis, and then, arbitrary micro/nano sculpturing can be attained on a flat top surface of a steel workpiece by merely combining simple planing operations at constant cutting speed with high‐speed depth of cut control. An industrial computer is utilized to detect the coordinate positions and generate the voltage signal for controlling vibration amplitude. The coordinate values are constantly monitored in the developed system by directly communicat‐ ing with NC control system or by using an external optical sensor. The dynamic command signal for vibration amplitude control is generated to change the depth of cut in accordance with the CAD data.

conventional FTS. It might not, however, be a big problem because the elliptical vibration

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

The developed control system was applied to grooving experiments. The ultrasonic elliptical vibration tool was mounted on an ultra‐precision planing machine, NIC‐300 (Nagase Integrex Co., Ltd.), and was fed straight for grooving. The vibration amplitude was controlled with sinusoidal and zigzag wave commands at the same time, and then, micro textured grooves were formed on the surface of a hardened steel workpiece. The vibration amplitude was controlled to change from 2 μmp‐<sup>p</sup> to 4 μmp‐p. This corresponds to the depth of cut variation of 1 μm. On the other hand, the amplitude in the cutting direction is set to be constant, 4 μmp‐p.

Figure 3 shows photographs of grooves machined at the cutting speed of 0.2 m/min by the single crystal diamond tool with a nose radius of 1 mm and their surface profiles measured by a laser microscope, VK‐9500 (Keyence Corp.). It was confirmed that the grooves with various ultra‐precision micro textures can be machined successfully on the hardened steel, and mirror surface quality can be obtained on all grooves. Measured surface profiles of sinusoidal grooves agreed precisely with the command waves. On the other hand, measured corners of zigzag grooves are rounded, and their step heights were relatively smaller than the variation width of command waves of 1 μm. This is considered to be caused by cutting off high‐frequency components in the amplitude control commands by the LPF, which the zigzag waves include

(a)textured groove with sinusoidal command (b)textured groove with zigzag command

In order to attain arbitrary sculpturing, an ultra‐precision micro/nano sculpturing system was developed by using the developed vibration control system and the ultra‐precision planing machine. Figure 4 shows the developed sculpturing system, where the planing machine is simply controlled to machine a plane surface at constant cutting speed. The ultrasonic elliptical vibration tool is attached on a Z‐axis table of the machine tool. The vibration amplitude in the depth of cut direction along the Z‐axis is controlled in synchronization with cutting feed

**Figure 3.** Microphotographs and surface profiles (cutting speed: 0.2 m/min, freq.: 100 Hz)

**1.5. Ultra‐precision micro/nano sculpturing on plane surfaces**

cutting technology is available only at relatively low cutting speed.

**1.4. Ultra‐precision micro/nano sculpturing of textured grooves**

at their sharp corners.

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The developed machining system was applied to nano sculpturing experiments of picture images. CAD data for sculpturing were produced from gray scale images, where the gray values of 8 bits (256 gradations) in pixels were converted into the amplitude commands. As the vibration amplitude in the experiments was changed within a range from 2 μmp‐<sup>p</sup> to 4 μmp‐p, the depth of cut was changed within 1 μm. The resolution of the depth of cut control is, therefore, about 4 nm. Hardened steel workpieces (64x48 mm, JIS: SUS420J2, HRC53) were machined with single crystal diamond tools with a nose radius of 1 mm. The size of original images is set to 3200x2400 pixels, and thus, 1 pixel corresponds to 20x20 μm.

**Figure 4.** Developed micro/nano sculpturing system using elliptical vibration cutting

Figure 5 shows an example of the nano sculpturing of picture images. The depth of cut was controlled in nano scale in accordance with the image data. As shown in Figure 5, the gray scale picture image, the microphotograph of the machined surface and its profile, which was measured by optical surface profiler (ZYGO NewView 6200), correspond well to each other.

The result shows that picture images can be printed successfully on hardened steel as nano‐ scale sculptures.

**2. Analytical prediction of chatter stability in ball end milling with tool**

Precision Micro Machining Methods and Mechanical Devices 55

A new analytical model to predict chatter vibration in ball end milling with consideration of

The ball end milling is an important precision machining process, which is used in production of dies, molds, impellers, screw propellers and parts with free‐form surfaces. As the slender ball end mills or the thin workpiece structures are flexible, the self‐excited chatter vibration often occurs and causes severe problems such as short tool life and deterioration of surface quality. Many researchers investigated prediction of the self‐excited chatter vibration in the milling process. Altintas and Budak [8] developed an analytical model to solve the chatter stability forthe cylindrical end mills. Altintas, Shamoto, Lee and Budak extended the analytical model for the cylindrical end mills to predict the stability limits in ball end milling [9], but the tool inclination has not been considered due to geometric complexity of the ball end milling

On the other hand, 5‐axis machining technology has been widely spread recently, and it enables arbitrary tool inclination for better machining efficiency, accuracy and stability.

Therefore, an analytical model of the ball end milling process with the self‐excited chatter

**2.2. Outline of analytical model to predict chatter stability in ball end milling with tool**

The ball end milling process with the tool inclination is illustrated in Figure 7. The Cartesian coordinates *xyz* are fixed to the ball end mill and aligned with the workpiece coordinates *uvw* before the inclination. The origins of both the coordinate systems are placed at the present ball

vibration is developed and verified with consideration of the tool inclination.

**inclination [7]**

**2.1. Introduction**

process.

**inclination**

tool inclination is introduced in this section.

**Figure 6.** Microphotographs of sculptured dimples

**Figure 5.** Gray scale image for amplitude command, machined surface and measured surface profile

Nano sculpturing experiments involving dimple patterns were also carried out with the developed sculpturing system. Sinusoidal commands to control the vibration amplitude were input to the elliptical vibration control system during machining, and the phase of the sinusoidal commands was changed by 180 degrees in every cutting feed, so that precisely aligned patterns were sculptured.

Figure 6 shows microphotographs. The hexagonal dimple patterns, whose borders are sharp, can be observed on the left. On the other hand, isolated circular dimple patterns were also sculptured successfully on the right, as the maximum depth of cut was considerably smaller than the amplitude variation.The results show that a variety ofdimple patterns can be obtained ultra‐precisely on the steel materials by using the developed sculpturing system.

## **1.6. Conclusion**

Novel ultra‐precision sculpturing technology for difficult‐to‐cut materials at micro/nano scale was proposed by utilizing elliptical vibration cutting technology. In the proposed method, the depth of cut is controlled without the conventional FTS technology by actively manipulating the vibration amplitude in the depth of cut direction. In order to verify the proposed method, the vibration amplitude control system and a high performance micro/nano sculpturing system were developed and applied to sculpturing experiments on hardened steel. Conse‐ quently, micro textured grooves, an image of a picture and various dimple patterns were manufactured on the hardened steel workpiece successfully as nano‐scale sculptures. These were done by merely combining a simple feed motion at a constant speed with high‐speed depth of cut control.

**Figure 6.** Microphotographs of sculptured dimples
