*3.1.2 A flexure-based EVC vibrator actuated by vertical piezoelectric actuator configuration*

## *3.1.2.1 Piezoelectric actuators serial drive*

In this work, a flexure-based EVC vibrator with vertical piezoelectric actuator configuration was proposed. In order to avoid the installation error, the base part and the hinge part were designed to be an integral flexure hinge structure [10]. Additionally, the integral flexure part was made from 65 Mn steel. As shown in **Figure 6(a)**, the compliant mechanism was driven by two vertical piezoelectric actuators in serial drive mode. The advantage of this serial design is that the crosstalk between two motion axes can be ignored theoretically. However, the working bandwidth decreases with the increased moving inertia.

The testing experiments were carried out to evaluate the performance. As shown in **Figure 6(b)**, the first natural frequencies along Z direction and Y direction are

#### **Figure 5.**

*Offline testing results. (a) Step responses. (b) Amplitude-frequency responses. (c) Motion stroke. (d) Resolution tests. (e) Motion tracking for z1 axis and parasitic motion for z2 axis. (f) Motion tracking for z2 axis and parasitic motion for z1 axis. (g) Input signals and tool vibration locus [9].*

1257.74 Hz and 1896.19 Hz, respectively. It can be found from **Figure 6(c)** that the resolution in Z direction and Y direction are all within 8 nm. **Figure 6(d)** and **(e)** show the tracking accuracy and coupling motion in Z direction and Y direction. The maximum following error in Z direction is 0.6 μm, which is about 1.5% of the full testing stroke. The coupling motion in Y direction is 0.06 μm, which is 0.6% of the Y-direction testing stroke. The maximum following error in Y direction is less than 0.2 μm, which is 2% of the testing stroke. The coupling motion in Z-direction can be considered as noise and ignored. **Figure 6(f )** shows the resultant ellipses with different phase shifts and frequencies. It should be noted that the errors in the two directions ascend with the frequency rising. The error in Z-direction is smaller than that in Y-direction. **Figure 6(g)** shows the resultant tool paths with different phase shifts under-cutting speed of 150 μm/s. **Figure 6(h)** shows the resultant tool paths

*Design, Analysis and Testing of Piezoelectric Tool Actuator for Elliptical Vibration Cutting DOI: http://dx.doi.org/10.5772/intechopen.103837*

#### **Figure 6.**

*Illustration of mechanical structure, experimental setup and testing results. (a) Mechanical structure and experimental setup. (b) Amplitude-frequency responses. (c) Resolution tests. (d) Motion tracking for Z-axis and parasitic motion for Y-axis. (e) Motion tracking for Y-axis and parasitic motion for Z-axis. (f) Resultant ellipses with different phase shifts and frequencies. (g) Resultant tool paths with different phase shifts. (h) Resultant tool paths at different frequencies [10].*

with different frequencies under cutting speed of 150 μm/s and 90° phase shift. These two figures demonstrate the double-frequency EVC tracking ability.

#### *3.1.2.2 Piezoelectric actuators parallel drive*

Compared with the piezoelectric actuators' serial drive configuration, the parallel drive configuration of piezoelectric actuators is more easy to obtain a higher working bandwidth. However, the cross-axis coupling is a problem that need to be solved.

In general, the mechanical structure decoupling design is usually adopted. In this work, a modified bridge-type amplification mechanism was utilized to meet the requirements among the stroke, output stiffness, resonant frequency, and the drive current [11]. Spring steel was adopted as the material. As shown in **Figure 7(a)**, two perpendicular leaf-spring flexure hinges were applied to decouple the 2D motion. **Figure 7(b)** shows the FEA results of modal analysis. The natural frequency is 6452 Hz and the corresponding mode of vibration is in cutting direction. The mode of vibration in thrust direction corresponds to the natural frequency of 7432 Hz.

In order to evaluate the performance of the prototype. The experimental test was conducted and the experimental setup is shown in **Figure 7(c)**. The sweep experiments were conducted by setting the input voltage amplitudes to 5 V and

#### **Figure 7.**

*Illustration of mechanical structure, experimental setup, and testing results. (a) Mechanical structure. (b) Modal analysis results. (c) Experimental setup. (d) Frequency response. (e) axis coupling results. (f) Comparison between designed and measured cutting tool locus [11].*

the frequency from 0 to 10 kHz linearly. The amplitude-frequency responses and phase-frequency responses are shown in **Figure 7(d)**. The natural frequencies in X and Y directions (i.e. cutting direction and thrust direction) are 6100 Hz and 7100 Hz, respectively, which have good agreement with the results of FEA simulation. Coupling tests of the two motion axes were performed by using sinusoidal signals with frequency of 200 Hz and amplitude of 120 V. The results are shown in **Figure 7(e)** that the coupling ratios between two motion axes are within 5%. The comparison between designed and measured cutting tool locus are shown in **Figure 7(f )** for both low-frequency (200 Hz) and high-frequency (5.5 kHz). The measured results indicate that the agreement between designed and measured ones are good for low frequency.

*Design, Analysis and Testing of Piezoelectric Tool Actuator for Elliptical Vibration Cutting DOI: http://dx.doi.org/10.5772/intechopen.103837*

However, there is a discrepancy between designed and measured ones under higher frequency caused by linearly increasing phase shift which can be eliminated by frequency compensation.

In fact, the angle between two decoupling flexure hinges can influence the decouple performance. A new type of 2 degrees of freedom piezo-actuated pseudodecouple compliant mechanism was developed which considering the influence of the decoupling angle [12]. As shown in **Figures 8(a)** and **8(c)**, the two perpendicular piezoelectric actuators are configured in parallel. In this work, the influence of decoupling angle Θ on tracking accuracy of elliptical locus was studied by static FEA method. First, a dimensionless aspect ratio λ of the major semi-axis *a* to the minor semi-axis *b* of the ellipse locus was introduced. The influence of decoupling angle on the elliptical parameters and relative ratio is shown in **Figure 8(b)**. It can be seen that the developed 2D pseudo-decouple compliant mechanism generated an approximately perfect ellipse locus when the decoupling angle was set to be 102.5°. Then a 3D model of EVC vibrator was established as shown in **Figure 8(c)**. The prototype was manufactured and the experimental tests were carried out to evaluate the performance. Experimental setup is shown in **Figure 8(d)**. **Figure 8(e)** shows the experimental results of kinematic performance. From the resultant tool locus, it can

#### **Figure 8.**

*Illustration of mechanical structure, experimental setup, and testing results. (a) Mechanical structure of compliant mechanism. (b) Influence of decoupling angle on the elliptical parameters and relative ratio. (c) 3D model of the EVC vibrator. (d) Experimental setup. (e) Experimental results of kinematic performance. (f) Experimental results of dynamic performance [12].*

be seen that the experimental results have a good agreement with the fitted curve and FEA results. **Figure 8(f )** shows the results of dynamic performance by using hammering method. The first two natural frequencies of the pseudo-decouple compliant mechanism are 863 Hz and 1893 Hz, respectively.
