*3.2.1 A flexure-based EVC vibrator actuated by three perpendicular piezoelectric actuators*

For 3D type EVC vibrator, three perpendicular piezoelectric actuators configuration are the most commonly used method. A piezoelectric actuated monolithic compliant spatial vibrator with decoupled translational vibration was developed to construct the rotary spatial vibration-assisted diamond cutting system [13]. The 3D model of the rotary spatial vibration-assisted diamond cutting system and the mechanical structure of compliant spatial vibrator are respectively shown in **Figures 9(a)** and **9(b)**. The rotary spatial vibration-assisted diamond cutting system consists of a tool holder, compliant spatial vibrator, piezoelectric actuator, compliant spatial vibrator holder, connection shaft, and fixture. The fixture is used for attaching the whole mechanism onto the spindle of the machine tool through a vacuum chuck. The compliant spatial vibrator and its holder are made of aluminum alloy to reduce the mass of the whole mechanism. The steel was adopted for connecting shaft manufacturing to increase connection stiffness. In this work, a complete compliance modeling was established based on the matrix-based compliance modeling method for compliant spatial vibrator. The dynamic model was established based on Lagrangian principle. FEA simulation was also used to study the static and dynamic characteristics. To evaluate the stroke and parasitic motions, a maximum sinusoid driving voltage (u = [50 + 50sin(2πt)] V) was separately applied to each piezoelectric actuator. The displacement results of compliant spatial vibrator in driving direction and the parasitic motion in other motion directions are shown in **Figure 9(c)**. It can be seen that the practical stroke can reach 11.067 μm, 10.100 μm, and 12.254 μm along the *x*, *y*, and *z* axes directions, respectively. The parasitic motions along *y* and *z* axes directions are about ±1.39% and 1.34% with respect to the motion along *x*-axis direction, respectively. Similarly, the parasitic motions along the *x* and *z* axes directions are about ±1.11% and 0.46% with respect to the motion along *y-*axis direction, respectively. The parasitic motions along the *x* and *y* axes directions are about ±1.21% and 0.31% with respect to the motion along *z*-axis direction, respectively. In addition, the dynamic performance tests were carried out by swept excitation method. Signals with an amplitude of 1.5 V with varying frequency were applied to each piezoelectric actuator, separately. The results of

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

#### **Figure 9.**

*Illustration of 3D model, mechanical structure and testing results. (a) 3D model of the rotary spatial vibrationassisted diamond cutting system. (b) Mechanical structure of the compliant spatial vibrator. (c) Displacement results of compliant spatial vibrator in driving direction and the parasitic motion in other motion directions. (d) Experimental results of dynamic performance [13].*

dynamic performance are shown in **Figure 9(d)**. The first natural frequency along *x* and *y* axes directions are approximately the same, which are about *f*x = *f*y = 2.8 kHz. While the natural frequency along the *z-*axis direction is about 4.3 kHz. This vibrator provides a new method for rotary vibration machining.

Different from the above 3D type EVC vibrator, a piezo-actuated tri-axial compliant mechanism was developed to modulate the workpiece for nano cutting [14]. The 3D model of the compliant mechanism is shown in **Figure 10(a)**. Three identical compliant chains were adopted to construct the vibrator. For one compliant chain, the double parallelogram mechanism with eight right circular flexure hinges and a spatial transition mechanism with four sets of parallelogram limbs were adopted. Each limb has two bi-axial right circular flexure hinges. In this work, multi-objective optimal design of the tri-axial compliant mechanism was carried out based on the stiffness modeling, kinematic modeling and dynamic modeling. A Pareto-based multi-objective differential evolution algorithm was utilized to find the global optimal solution.

Then a prototype was manufactured and the performance tests were conducted through the experimental setup which is shown in **Figure 10(b)**. A harmonic signal with frequency of 1 Hz and amplitude voltage of 5 V was applied to each actuator

#### **Figure 10.**

*Illustration of 3D model, experimental setup and testing results. (a) 3D model of the compliant mechanism. (b) Testing experimental setup. (c) Results of harmonic response and the corresponding parasitic motions. (d) Harmonic tracking performance for x-axis. (e) Results of the frequency responses. (f) Harmonic tracking performance for y and z axes during cutting [14].*

to assess the motion stroke and the parasitic motion. The results are shown in **Figure 10(c)**, the strokes along *x*, *y* and *z* axial directions are respectively 12.37 μm, 13.14 μm and 11.72 μm. The maximum parasitic motion (about 3.8%) was generated along *z* axial direction when driving the piezoelectric actuator along *x* axial direction. When actuated the piezoelectric actuators along with *y* and *z* axial directions, the parasitic motion along the other two directions are almost the same, which are about 1.37% and 2.51% of the corresponding actuation motions. In addition, a typical proportion-integration-differentiation controller is employed for the feedback control. The influences of system noises were eliminated by a low pass filter, and a velocity feedforward compensator was utilized to enhance the response speed. In order to assess the tracking performance, a harmonic signal with frequency of 90 Hz and amplitude of 2 *μ*m was adopted as the desired motion. Only the tracking performance along *x* axial direction was performed to avoid repetition. The tracking results in **Figure 10(d)** shows a tracking error of around ±70 nm, which is about ±1.75% of the motion span. **Figure 10(e)** shows the dynamic performances. The

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

natural frequency for each direction is around 3.7 kHz due to the identical chain. What's more, the tracking performance along *y* and *z* axial directions were also tested during cutting, results of which are shown in **Figure 10(f )**. It should be noted that the noise during cutting is slightly larger than that in offline testing.
