2. Components for ultrasonic vibration-assisted hot glass embossing process

In general, an ultrasonic vibration-assisted hot glass embossing process has three main components: heating furnace, compression tester, and ultrasonic vibration

device. The role of heating furnace is to heat the glass and the mold to the embossing temperature. Vacuum environment is usually remained within the heating furnace to prevent the heat loss. The ultrasonic vibration device is usually compiled with one of the molds, which transfers ultrasonic vibration to the mold directly. Both the heating furnace and the ultrasonic vibration are attached to the compression tester, as shown in Figure 5. The role of compression tester is to control the embossing load after receiving feedback signals from the load cell.

#### 2.1 The heating furnace

A cross-sectional diagram of a heating furnace is shown in Figure 6. The heating furnace is integrated by a quartz tube. Because the heating furnace is fixed to the wall, the lower die is controlled by the compression tester to move up and down, so that it can emboss the glass inside the chamber and de-mold the product. Some infrared heaters are distributed around the quartz tube. Energy from the infrared light penetrates through the quartz to heat the molds and the specimen inside.

During the embossing stage, temperature is very high. To protect the load cell, which is located inside the lower die, from damage under high temperature, a cooling system is set up. Besides that, the load cell is also working in the vacuum environment. This condition helps the load cell detect external forces precisely. Although vacuum environment is useful for the load cell, it is useless for the infrared heaters. Therefore, the infrared heaters are placed outside the vacuum chamber to increase their lifetimes.

2.2 Ultrasonic vibration device

An ultrasonic vibration device.

Cross-sectional diagram of a heating furnace [3].

Ultrasonic Vibration-Assisted Hot Glass Embossing Process

DOI: http://dx.doi.org/10.5772/intechopen.86546

Figure 6.

Figure 7.

19

As shown in Figure 7, an ultrasonic vibration device consists of a piezoelectric transducer, a booster, and a horn. The vibration is generated from the transducer by inputting an electrical signal through a frequency generator. Resonance phenomenon is usually adopted in ultrasonic vibration devices and then harmonized with the frequency of electrical signals. The ultrasonic vibrating device is designed to work

Figure 5. Schematic of apparatus design [2].

Ultrasonic Vibration-Assisted Hot Glass Embossing Process DOI: http://dx.doi.org/10.5772/intechopen.86546

Figure 6.

device. The role of heating furnace is to heat the glass and the mold to the embossing temperature. Vacuum environment is usually remained within the heating furnace to prevent the heat loss. The ultrasonic vibration device is usually compiled with one of the molds, which transfers ultrasonic vibration to the mold directly. Both the heating furnace and the ultrasonic vibration are attached to the compression tester, as shown in Figure 5. The role of compression tester is to control the embossing load after receiving feedback

Noise and Vibration Control - From Theory to Practice

A cross-sectional diagram of a heating furnace is shown in Figure 6. The heating furnace is integrated by a quartz tube. Because the heating furnace is fixed to the wall, the lower die is controlled by the compression tester to move up and down, so that it can emboss the glass inside the chamber and de-mold the product. Some infrared heaters are distributed around the quartz tube. Energy from the infrared light penetrates through the quartz to heat the molds and the specimen inside. During the embossing stage, temperature is very high. To protect the load cell, which is located inside the lower die, from damage under high temperature, a cooling system is set up. Besides that, the load cell is also working in the vacuum environment. This condition helps the load cell detect external forces precisely. Although vacuum environment is useful for the load cell, it is useless for the infrared heaters. Therefore, the infrared heaters are placed outside the vacuum

signals from the load cell.

2.1 The heating furnace

chamber to increase their lifetimes.

Figure 5.

18

Schematic of apparatus design [2].

Cross-sectional diagram of a heating furnace [3].

Figure 7. An ultrasonic vibration device.

## 2.2 Ultrasonic vibration device

As shown in Figure 7, an ultrasonic vibration device consists of a piezoelectric transducer, a booster, and a horn. The vibration is generated from the transducer by inputting an electrical signal through a frequency generator. Resonance phenomenon is usually adopted in ultrasonic vibration devices and then harmonized with the frequency of electrical signals. The ultrasonic vibrating device is designed to work

properly at a constant frequency. For thermal protection, a horn cooler is mounted outside the ultrasonic horn. O-rings placed between the ultrasonic horn and the horn cooler to form a water seal do not significantly affect the ability of the ultrasonic device to vibrate.

Since the material properties of the horn would change in elevated temperature, its resonant frequency is shifted, and a mismatch with the frequency generator occurs. Hence, the ultrasonic device must be modified to ensure that it can operate correctly at high temperature. By simplifying theoretical equations, the speed of a wave traveling along a one-dimensional medium is described by

$$\mathbf{c}\_{L} = \sqrt{\frac{\mathbf{E}}{\rho}}\tag{1}$$

3. Effects of ultrasonic vibration on hot glass embossing process

In a dynamic experiment, if a sinusoidal strain with angular frequency ω and

the resulting stress would be also sinusoidal with the same frequency which is

ε ¼ ε<sup>0</sup> sin ð Þ ωt (3)

σ ¼ σ<sup>0</sup> sin ð Þ ωt þ δ (4)

½ cos δ þ i � sin δ� ¼ G<sup>0</sup> ð Þ þ i � G} (6)

cos δ (7)

sin δ (8)

<sup>ε</sup> <sup>∗</sup> <sup>¼</sup> <sup>ε</sup><sup>0</sup> exp i½ � ð Þ <sup>ω</sup><sup>t</sup> ; <sup>σ</sup> <sup>∗</sup> <sup>¼</sup> <sup>σ</sup><sup>0</sup> exp i½ � ð Þ <sup>ω</sup><sup>t</sup> <sup>þ</sup> <sup>δ</sup> (5)

3.1 Glass behavior under the application of ultrasonic vibration

the complex modulus G<sup>∗</sup> is then defined by the relation

exp ið Þ¼ � <sup>δ</sup> <sup>σ</sup><sup>0</sup>

ε0

the real part of the complex modulus, often called the storage modulus:

<sup>G</sup><sup>0</sup> <sup>¼</sup> <sup>σ</sup><sup>0</sup> ε0

<sup>G</sup>} <sup>¼</sup> <sup>σ</sup><sup>0</sup> ε0

The first term on the right-hand side of Eq. (6) is in phase with the strain and is

The second term of Eq. (6) represents the imaginary part of the complex mod-

The ratio G}=G<sup>0</sup> ¼ tanδ, so-called loss factor, is widely used as a measure of the

amplitude ε<sup>0</sup> is applied into a viscoelastic solid

Ultrasonic Vibration-Assisted Hot Glass Embossing Process

DOI: http://dx.doi.org/10.5772/intechopen.86546

lagging with a phase angle δ (Figure 9):

Using complex notation

<sup>G</sup><sup>∗</sup> <sup>¼</sup> <sup>σ</sup> <sup>∗</sup>

<sup>ε</sup> <sup>∗</sup> <sup>¼</sup> <sup>σ</sup><sup>0</sup> ε0

ulus, often called loss modulus:

Figure 9.

21

Oscillating strain ε, stress σ, and phase lag δ.

damping capacity of viscoelastic materials.

where E and ρ are Young's modulus and density, respectively. The wavelength is

$$
\lambda = \frac{\mathbf{c}\_L}{f} = \frac{\sqrt{\mathbf{E}/\rho}}{f} \tag{2}
$$

where f is the resonance frequency of the ultrasonic vibration device. In longitudinal vibration mode, multiples of (λ=2) can be used as reference for the design of the device length.

As the temperature of a device whose geometry is fixed rises, its resonant frequency falls due to the decrease in Young's modulus [4], so such frequency will shift beyond the tracking range of the frequency generator. To increase the resonant frequency of the device at high temperature, its length must be reduced. With theoretical perspective, reducing the device length could increase the resonant frequency in longitudinal vibration mode. It means that the length reduction could compensate the frequency decrease caused by the increase in temperature. This trend has been verified by both finite element analysis and experiments as shown in Figure 8.

#### Figure 8.

Resonant frequency of the ultrasonic vibration device with different horns and heating temperatures at 25°C [5].
