**3. A new fluid bearing utilizing traveling waves [11]**

A new non‐contact fluid bearing utilizing traveling waves is proposed in this research. Conventional hydrostatic bearings utilize externally compressed fluid, which requires plumbing and compressors. In contrast, on proposed bearing system the moving part is supported with a thin fluid film compressed by the waves traveling radially on the bearing surface. The proposed bearing realizes non‐contact smooth motion without such a large apparatus, and furthermore it has a capability to electrically control the bearing force or clearance.

## **3.1. Introduction**

under the figure. For example, severe chatter was detected at *d*>2 mm and *ix*=10 deg, where the measured displacement has a large chatter frequency component of *s*0>1.3 μm. On the other hand, only the spindle speed harmonics were observed at *d*=2.5 mm and *ix*=45 deg. The analytical and experimental results are all in a good agreement as shown in the figure. There were no chatter vibrations at *gm*>1.2, while severe chatter vibrations were detected at *gm*<0.6.

Spindle

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

Displacement sensor

 *x* 

 *z* 

 *y* 

<sup>10</sup> Predicted


Tool inclination angle *ix* deg

**Figure 10.** Predicted gain margins and chatter stability limits, and experimental results at varied tool inclination angle ix. Workpiece: aluminum alloy (JIS:A5052); Cutter: HSS ball end mill (EBD80820, OSG Corp.), Cutter: number of flutes nf = 2, radius r = 10 mm; Cutting conditions: iy = 0 deg, pick feed p = 1 mm, n = 6240 min-1, feed rate of 0.01 mm/tooth; Cutting fluid: soluble. Chatter vibrations were classified as follows; ○: no chatter (s0 ≤ 0.12 μm), ∆: slight chatter (0.12

The analytical model of the ball end milling process with the self‐excited chatter vibration was developed with consideration of the tool inclination, and it was applied to predict the chatter

Predicted gain margin

1

0.1

*gm*

100

1 2

3

stability limit  *gm*=1

Machining center

**Figure 9.** Ball end milling experiment with tool inclination.

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Workpiece

Ball end mill

μm < s0 ≤ 0.24 μm), ×: chatter (0.24 μm < s0 ≤ 1.2 μm), \*: severe chatter (1.2 μm < s0).

Depth of cut *d* mm

**2.5. Conclusion**

4 5 Bearings are one of the most fundamental and necessary elements for machines to generate motion between to surfaces smoothly with low friction. There have been constant demands for low friction or non‐contact bearings for many years [12‐14].

As for non‐contact bearings, L. ‐D. Girard invented a hydrostatic bearing in 1865 [15]. An active magnetic bearing was invented around the same time, and its actual system was developed as early as 1950 [16]. The feasibility of a squeeze bearing was first demonstrated and reported in 1964 [17]. These non‐contact bearings have been improved and utilized in practice according to their different characteristics. However, it seems that no fundamental principles of non‐ contact bearings have been proposed after those inventions.

A new principle of non‐contact fluid bearings, which utilizes traveling waves, is proposed in this research, and a prototype device is developed on the basis of the proposed principle.

## **3.2. Working principle of the new fluid bearing system**

According to this new principle the non‐contact fluid bearing is realized by generating the traveling waves radially on the bearing surface as shown in Figure 11.

The working principle of the first prototype is illustrated in Figure 11a. Three sets of piezo actuators are placed radially around the bearing surface, and sinusoidal voltage is applied to the actuators with a phase shift to generate traveling waves on the flexible surface (Figure 11b). As the waves are generated radially, the fluid is transported from outside to the center, which in return generates pressure and a floating force to support an object. When the amplitude and frequency of the voltage are increased, more fluid is pumped underthe bearing surface allowing higher loads to be supported.

The following key properties show that this new bearing design is promising for high precision applications:

i) It is very compact, does not require any pump or bulky tubes to supply air, ii) the bearing gap can be controlled by adjusting driving voltages, iii) it has a natural resistance to moment of force with a single pad, and iv) can be used during high speed motion.

by considering phase shifts from the applied voltages, and one cycle of their transient change is shown in Figure 13. It shows that the traveling wave is generated with amplitude of about 6 μm and it is absorbed near the center. As shown, a nearly perfect wave to transport the fluid

> Displacement Pm

> > Displacement Pm

Displacement Pm

Displacement Pm

Distance from center mm

Distance from center mm

Distance from center mm

Distance from center mm

Distance from center mm

Distance from center mm

d) 135<sup>0</sup>

Distance from center mm

f) 225<sup>0</sup>

Distance from center mm

h) 315<sup>0</sup>

**Figure 13.** One cycle of traveling wave (Conditions: Freq.: 100Hz, Voltage: 80Vp-p)

b) 45<sup>0</sup>

Distance from center mm

Precision Micro Machining Methods and Mechanical Devices 61

Distance from center mm

Distance from center mm

Distance from center mm

could be generated on the bearing surface.

Distance from center mm

a) 0<sup>0</sup>

Distance from center mm

c) 90<sup>0</sup>

Distance from center mm

Distance from center mm

g) 270<sup>0</sup>

e) 180<sup>0</sup>

Displacement Pm

Displacement Pm

Displacement Pm

Displacement Pm

**Figure 11.** Principle of proposed fluid bearing – a) Working Principle b) Traveling Wave

### **3.3. Evaluation of the developed bearing system**

In order to study the properties of the proposed bearing system a prototype bearing is developed with respect to the bearing structure illustrated in Figure 11. Figure 12 shows the prototype bearing structure floating on the guide surface. Atmospheric air is utilized as the bearing fluid in this prototype.

**Figure 12.** Prototype fluid bearing system

The developed fluid bearing is controlled with a piezo driving apparatus, and it is confirmed that the device can be floated successfully and can move smoothly with almost no friction like a hydrostatic air bearing. The performance of the developed bearing is evaluated experimen‐ tally in the following.

### *3.3.1. Traveling wave on the bearing surface*

Displacement distribution on the bearing surface, and its transient change are measured with an optical fiber sensor in the circular direction. The measured displacements are synchronized by considering phase shifts from the applied voltages, and one cycle of their transient change is shown in Figure 13. It shows that the traveling wave is generated with amplitude of about 6 μm and it is absorbed near the center. As shown, a nearly perfect wave to transport the fluid could be generated on the bearing surface.

i) It is very compact, does not require any pump or bulky tubes to supply air, ii) the bearing gap can be controlled by adjusting driving voltages, iii) it has a natural resistance to moment

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

In order to study the properties of the proposed bearing system a prototype bearing is developed with respect to the bearing structure illustrated in Figure 11. Figure 12 shows the prototype bearing structure floating on the guide surface. Atmospheric air is utilized as the

The developed fluid bearing is controlled with a piezo driving apparatus, and it is confirmed that the device can be floated successfully and can move smoothly with almost no friction like a hydrostatic air bearing. The performance of the developed bearing is evaluated experimen‐

Displacement distribution on the bearing surface, and its transient change are measured with an optical fiber sensor in the circular direction. The measured displacements are synchronized

Guide surface

of force with a single pad, and iv) can be used during high speed motion.

**Figure 11.** Principle of proposed fluid bearing – a) Working Principle b) Traveling Wave

Developed device

**3.3. Evaluation of the developed bearing system**

bearing fluid in this prototype.

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**Figure 12.** Prototype fluid bearing system

*3.3.1. Traveling wave on the bearing surface*

tally in the following.

**Figure 13.** One cycle of traveling wave (Conditions: Freq.: 100Hz, Voltage: 80Vp-p)

#### *3.3.2. Maximum load capacity*

Utilizing the above traveling wave method, maximum load capacity ofthe bearing is measured on the prototype bearing. Weights are stacked on the center of the device. Critical weight load between the contact and the non‐contact is recorded as the maximum load capacity. Figure 14 shows the maximum load capacity measured at various amplitudes and frequencies of the driving voltage. The maximum load capacity is increased as the amplitude and the frequency are increased. This tendency is the same as that of the floating displacement, but the effect of the frequency is relatively small in this case. The maximum load capacity of about 100 N can be obtained at 80 Vp‐p.

Vibration of the supported object is evaluated by using the optical sensor. For example, the supported object is vibrated vertically with an amplitude of 0.66 μm at the center, when the device is driven at 80 Vp‐p and 100 Hz. It is considered that this vibration is mainly caused by the incompleteness of the traveling wave, whose value is roughly the same as this vibration

Precision Micro Machining Methods and Mechanical Devices 63

A new fluid bearing is developed which utilizes traveling waves. Evaluating the prototype

Floating displacement orload capacity is increased with an increase in the driving voltage and frequency, i.e. the device is electrically controllable. Maximum load capacity is recorded as

The proposed device can also produce attractive force instead of the floating force by reversing

We developed a novel methodology to fabricate three‐dimensional passive‐type mixer based on the baker's transformation (BT). BT is the best transformation for mixing fluids of laminar flow. We newly designed the BT structure with isovolumetric change without any separation/ joining process of two channels. It is a suitable solution for mass‐producing BT mold structures by utilizing precision cutting techniques. Two scales of BT mixers with similar structures are introduced herein. The one is for microfluidic analytical systems to accomplish well‐mixed solutions in a short channel length, and the other one in miniature scale aims at high perform‐ ance mixing of high viscosity fluids in food processing or resin blending. An ultraprecision five‐axis planing machine and diamond cutting tools were used for a microfluidic BT mixer mold on a oxygen‐free copper block, in which the flow passage area was 3.2E‐9 m2

miniature BT mixer mold on an aluminium block, a precision machining center and an end

mixing performances by numerical analyses and obtained the BT mixing results showing good similarities with that of numerical analyses. Moreover, the mixing performance of the micro‐ BT mixer was quantitatively examined to accomplish complete mixing over a wide range of

In the past decades microfluidic systems have been widely used in chemistry, biology, and nanobiotechnology, including DNA [18] or protein analysis [19], cell sorting [20], and chemical

mill with a 1 mm radius were used. The flow passage area was 3.2E‐5 m2

**4.1. Background of micromixers for bio‐informatics**

. For a

. We studied their

It is possible to realize a non‐contact air bearing by the proposed method.

The bearing also has resistance to moment of force even with a single pad.

**4. Mass‐producible rapid mixer based on Baker's transformation**

amplitude.

100N.

flow rates.

**3.4. Conclusion**

the traveling wave.

device the following remarks can be concluded:

**Figure 14.** Maximum load capacity under various driving conditions.

#### *3.3.3. Evaluation of various properties*

Other properties of the bearing system are also studied experimentally. An experiment to produce the attractive force is also carried out by reversing the traveling waves. It is confirmed that the device can be attracted to the guide surface. For example, the negative gauge pressure measured with the pressure sensor is about –3.6 kPa at the center under conditions of 80 Vp‐ p and 50 Hz.

Moment of force is applied to the device, and it is confirmed that the present device has resistance to the moment of force without using plural bearing pads. For example, the developed device is floated even when a weight load of 30 N is applied on it at an eccentric position, which is 40 mm away from the center. This is considered to caused by viscosity of the air, i.e. the air pressure distribution can be asymmetric to produce the resistance force to the moment.

Vibration of the supported object is evaluated by using the optical sensor. For example, the supported object is vibrated vertically with an amplitude of 0.66 μm at the center, when the device is driven at 80 Vp‐p and 100 Hz. It is considered that this vibration is mainly caused by the incompleteness of the traveling wave, whose value is roughly the same as this vibration amplitude.

#### **3.4. Conclusion**

*3.3.2. Maximum load capacity*

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be obtained at 80 Vp‐p.

**Figure 14.** Maximum load capacity under various driving conditions.

*3.3.3. Evaluation of various properties*

p and 50 Hz.

the moment.

Utilizing the above traveling wave method, maximum load capacity ofthe bearing is measured on the prototype bearing. Weights are stacked on the center of the device. Critical weight load between the contact and the non‐contact is recorded as the maximum load capacity. Figure 14 shows the maximum load capacity measured at various amplitudes and frequencies of the driving voltage. The maximum load capacity is increased as the amplitude and the frequency are increased. This tendency is the same as that of the floating displacement, but the effect of the frequency is relatively small in this case. The maximum load capacity of about 100 N can

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

Other properties of the bearing system are also studied experimentally. An experiment to produce the attractive force is also carried out by reversing the traveling waves. It is confirmed that the device can be attracted to the guide surface. For example, the negative gauge pressure measured with the pressure sensor is about –3.6 kPa at the center under conditions of 80 Vp‐

Moment of force is applied to the device, and it is confirmed that the present device has resistance to the moment of force without using plural bearing pads. For example, the developed device is floated even when a weight load of 30 N is applied on it at an eccentric position, which is 40 mm away from the center. This is considered to caused by viscosity of the air, i.e. the air pressure distribution can be asymmetric to produce the resistance force to A new fluid bearing is developed which utilizes traveling waves. Evaluating the prototype device the following remarks can be concluded:

It is possible to realize a non‐contact air bearing by the proposed method.

Floating displacement orload capacity is increased with an increase in the driving voltage and frequency, i.e. the device is electrically controllable. Maximum load capacity is recorded as 100N.

The proposed device can also produce attractive force instead of the floating force by reversing the traveling wave.

The bearing also has resistance to moment of force even with a single pad.
