**3. Development of the hybrid excitation methods**

#### **3.1 Smooth driving method using ultrasonic friction reduction**

#### *3.1.1 Operation principle of smooth driving method*

**Figure 6(a)** shows the working principle of the piezoelectric stick–slip actuator by traditional driving method (TDM), which includes the slow extension and rapid contraction stages of the traditional saw-tooth driving wave. As illustrated in **Figure 6(b)**, the smooth driving method (SDM) is realized by a composite wave, in which the composite wave includes a saw-tooth driving wave (SD-wave) and a sinusoidal friction regulation wave (SFR-wave), in which the SFR-wave can adjust the friction force between the frictional part and slider in resonant mode (RSFR-wave) or non-resonant mode (NSFR-wave) [15]. From the time A to B, the composite wave is equivalent to one part of the SD-wave. The piezoelectric element is excited to extend slowly, and the slider will move a distance together with the frictional part in the axial direction by a static friction force *f*s. From the time B to C, the composite wave is composed by an SFR-wave and another part of the SD-wave, which means that the ultrasonic friction reduction is introduced into the composite wave to decrease the kinetic friction force *f*d. Thus, the backward motion of the

#### **Figure 6.**

*Operation principle. (a) Principle of the traditional driving method. (b) Principle of the smooth driving method [15].*

stick–slip actuator can be restrained. The continuous output movement is gained by repeating the above motion process. The reverse motion can be realized by reflecting the symmetry of the SDM.

### *3.1.2 Research on non-resonant mode smooth driving method*

In this work, a non-resonant mode SDM is proposed to restrain the backward motion [15], which is realized by applying NSFR-wave to rapid deformation stage of the SD-wave. The specific work is as follows: the prototype includes a piezoelectric element, a frictional part, a slider and a preload mechanism, see **Figure 7(a)**. **Figure 7(b)** shows the experimental system of the prototype.

**Figure 7(c)** shows the amplitudes of the frictional part under the TDM and SDM. The frequency of the SD-wave is set as 800 Hz, and the voltage and frequency of the NSFR-wave are set as 4 Vp-p and 40 kHz. It can be seen that the amplitude of the frictional part is not affected obviously under the excitation of the SDM. **Figure 7(d)** illustrates the displacement curves of the prototype with a load of 4 g. Compared with the TDM, the better performance is achieved by the SDM. To quantify the restraint degree of backward motion, the backward rate (denoted by *ζ*) is defined by a ratio of backward distance *D*B and driving distance *D*S. The results indicate that the backward rate is decreased markedly by 83%. The relationship between the velocity and NSFR-wave voltage is plotted in **Figure 7(e)**. The velocity with the NSFR-wave voltage of 0 Vp-p represents the velocity under the excitation of the TDM; it is found that the velocity increases linearly with an increasing NSFRwave voltage, and the velocity is obviously improved using the SDM relative to the TDM. **Figure 7(f )** shows the relationship between the velocity and voltage. The results indicate that there is a linear increasing tendency between the velocity and voltage.

### *3.1.3 Research on resonant mode smooth driving method*

On the basis of our previous work, a resonant mode SDM is further developed to improve the performances of the actuators [16]. The resonant mode SDM is realized by applying a RSFR-wave to rapid deformation stage of the SD-wave. The relative

#### **Figure 7.**

*Non-resonant mode SDM. (a) Prototype of the stick–slip actuator. (b) Experimental system. (c) Amplitude of the friction part excited. (d) Displacement curves of the prototype. (e) Velocity versus the NSFR-wave voltage. (f) Velocity versus the voltage [15].*

#### *The Asymmetric Flexure Hinge Structures and the Hybrid Excitation Methods for Piezoelectric… DOI: http://dx.doi.org/10.5772/intechopen.95536*

research is as follows: the modal analysis of the stator is done by the FEM, aiming at obtaining the 1st longitudinal vibration mode, as illustrated in **Figure 8(a)**; and the theoretical result indicates that the resonant frequency of 38.55 kHz is obtained, which is considered the exciting frequency of the RSFR-wave.

**Figure 8(b)** shows the velocity versus the frequency of the RSFR-wave; the driving voltage of the SD-wave is set as 30 Vp-p, and the RSFR-wave voltage is selected as 6 Vp-p; the velocity of the actuator increases first and then decreases with an increasing frequency, and the maximum velocity is 0.41 mm/s under 39 kHz. Therefore, the RSFR-wave frequency of 39 kHz is chosen in subsequent experiments; there is a slight deviation between the test result and simulation result; the reasons may be caused by material errors between the model and the prototype, the omission of adhesive layers and the machining errors; besides, the comparative experiments of the SDM are also developed under the condition of 36 kHz and 42 kHz.

**Figure 8(c)** shows the relationship between the displacement and time; the displacement using the TDM shows a fluctuated curve and the backward motion is seen in every step; conversely, the backward motion is restrained by the SDM; the displacement increases linearly with an increasing time; the linearity is better when the frequency of RSFR-wave is 39 kHz, because the smaller kinetic friction is realized relative to the 36 kHz and 42 kHz. **Figure 8(d)** shows the relationship between the velocity and voltage; the velocity approximately follows a linear increased tendency with the voltage; the velocity using the TDM is 0.163 mm/s under 30 Vp-p; meanwhile, the velocities through the SDM are 0.332 mm/s, 0.403 mm/s and 0.370 mm/s (i.e. 36 kHz, 39 kHz, and 42 kHz), and the corresponding velocities can be effectively improved by 103.68%, 147.23% and 126.99% compared with the TDM.

**Figure 8(e)** expresses the variation of the velocity with an increasing load; the standard weight is used to investigate the load characteristics, which are added to the slider. The measure results indicate that the velocity decreases with an increasing load, and the load can reach 125 g utilizing the TDM; meanwhile, the maximum load excited by the SDM are 290 g, 360 g, and 315 g under 36 kHz, 39 kHz and 42 kHz; besides, under the same load, a higher velocity by the SDM is achieved at the RSFR-wave frequency of 39 kHz. **Figure 8(f )** shows that the relationship between the driving capacity and load; the driving capacity of the actuator increases first and then decreases with an increasing load, and the maximum

#### **Figure 8.**

*Resonant mode SDM. (a) Modal analysis result of the stator. (b) Velocity versus the RSFR-wave frequency. (c) Displacement versus the time. (d) Velocity versus the voltage. (e) Velocity versus the mass of the load. (f) Driving capacity versus the mass of the load [16].*

driving capacity using the TDM is 0.62 [(mm/s)g/mW] at 70 g. In contrast, the maximum driving capacities using the TDM (i.e. 36 kHz, 39 kHz and 42 kHz) are 2.18 [(mm/s)g/mW], 3.51 [(mm/s)g/mW] and 2.75 [(mm/s)g/mW] under 120 g, 180 g and 150 g; the driving capacities based on the SDM can be increased by 251.61%, 466.13% and 343.55% under the SFR-wave frequencies of 36 kHz, 39 kHz and 42 kHz.

#### *3.1.4 Research on low voltage characteristics of smooth driving method*

In this work, the low voltage characteristics of the SDM is researched [17]. **Figure 9(a)** and **(b)** show the relationships between the velocity and voltage in forward and reverse directions; the experiments are carried out under the same load of 4 g, and the frequencies of the SD-wave and the SFR-wave are 800 Hz and 40 kHz; the voltages of the SDM and TDM are increased from 2 Vp-p to 10 Vp-p; the forward and reverse motions are changed by modifying the order of slow and rapid movements as 90% or 10%; the results indicate that the velocity of the actuator increase obviously as the voltage goes up. It also can be seen that the minimum input voltage is reduced from 3 Vp-p to 2 Vp-p under the SDM; there are the similar variation relations in the forward and reverse motions.

**Figure 9(c)** and **(d)** show the performances of the prototype with a load of 4 g by the SDM, in which the SDM is excited by the SD-wave voltage of 8 Vp-p and SFR-wave of 1.6 Vp-p, and the voltage of the TDM is also 8 Vp-p. The results indicate that the prototype can achieve a stable operation at low voltage, and the backward motion is observed in every step; and the forward average effective displacement *D*<sup>e</sup> is improved by 64%; the reverse average effective displacement *D*e is improved by 55%; thus, the output displacement characteristics of the prototype is improved at a lower input voltage.

**Figure 9(e)** and **(f )** show the load characteristics of the actuator excited by the SDM and TDM, respectively; the output velocities of the actuator decrease as the load go up; compared with the TDM, the velocities can be improved obviously under the same load condition; the maximum load capacity of the actuator is 24 g when the voltages are 8 Vp-p and 1.6 Vp-p, respectively, which is 2.4 times the load capacity of the actuator under the TDM. Therefore, the designed actuator excited by the SDM can achieve a larger load capacity.

#### **Figure 9.**

*Low voltage characteristics of the SDM. (a) Forward velocity versus the voltage. (b) Reverse velocity versus the voltage. (c) Forward displacement. (d) Reverse displacement. (e) Forward load characteristics. (f) Reverse load characteristics [17].*

*The Asymmetric Flexure Hinge Structures and the Hybrid Excitation Methods for Piezoelectric… DOI: http://dx.doi.org/10.5772/intechopen.95536*

### *3.1.5 Research on symmetry of smooth driving method*

In this work, the symmetry of the SDM is also studied in detail [18]. **Figure 10(a)** and **(b)** show the relationship between the symmetry and velocity under the TDM and the SDM with an initial slider mass of 30 g; the voltage and frequency are 10 Vp-p and 800 Hz. In terms of the TDM, the actuator under the symmetry of 50–80% and 20–50% cannot work properly, because the effective displacement cannot be generated; the maximum velocities are 0.21 mm/s and 0.20 mm/s under 95% and 5%; the symmetries between 80–95% and 5–20% are considered as the ideal working ranges. In terms of the SDM, the velocities under 95% and 5% can be improved obviously relative to the TDM, and the velocities can reach 0.24 mm/s and 0.23 mm/s. The maximum velocities in the forward and reverse directions can be achieved at 50%, and the corresponding velocities are 0.41 mm/s and 0.39 mm/s. It is found that the effective symmetry of the SDM is obviously widened relative to the TDM.

**Figure 10(c)** and **(d)** show the relationship between the load and velocity under the different symmetries, such as 90%, 70%, 50%, 30% and 10% in forward and reverse directions; the velocity of the actuator decreases with the increase of load; the velocities under 50%, 70% and 90% are almost equal at 110 g; when the load is less than 110 g, the maximum velocity can be achieved under 50%; when the load is greater than 110 g, the maximum velocity can be realized under 90%.

It is found that the asymmetrical SDM under 90% achieves the better load capacity when the SD-wave voltage is 10 Vp-p for 800 Hz and the SFR-wave is 2 Vp-p for 39 kHz; the actuator in the reverse direction can also achieve the similar load characteristics; the larger stiffness is obtained under 90% and 10%.

The relationship between the load and driving capacity is illustrated in **Figure 10(e)** and **(f )**; the driving capacities of the actuator can reach 7.92 [(mm/s) g/mW] and 6.77 [(mm/s)g/mW] under 70% and 90%; meanwhile, the driving capacities of the actuator can reach 8.42 [(mm/s)g/mW] and 7.11 [(mm/s)g/mW] under 30% and 10%. The results indicate that the symmetrical SDM such as 50% can achieve larger driving capacity relative to the asymmetrical SDM, such as 90%, 70%, 30% and 10%.

#### **Figure 10.**

*Symmetry of the SDM. (a) Forward velocity versus the symmetry. (b) Reverse velocity versus the symmetry. (c) Forward velocity versus to the load under 50%, 70% and 90%. (d) Reverse velocity versus to the load under 10%, 30% and 50%. (e) Forward driving capacity versus the load under 50%, 70% and 90%. (f) Reverse driving capacity versus the load under 10%, 30% and 50% [18].*

## **3.2 Direction-guidance hybrid method for high speed**

### *3.2.1 Operation principle of direction-guidance hybrid method*

To improve the speed of the stick–slip actuators, a direction-guidance hybrid method (DGHM) is proposed in this work [19]. The DGHM is a synthetic composite waveform, as shown in **Figure 11(a)**, which is mainly composed of a directionguidance (DG) waveform and a resonance drive (RD) waveform. The stator excited by the DG waveform to produce a pre-deformation with a lateral motion, which is of great significance to the output characteristics of the actuator. The direction of the slider can be guided by the lateral motion of the stator; besides, the locking force can be adjusted to achieve better output performance. After that, the high speed performance of the actuator can be achieved at a resonant frequency of the RD waveform.

The operation principle of the actuator under the DGHM is shown in **Figure 11(b)**. The specific operations are as follows:

Stage I: at time *t*0, the piezoelectric stack without input voltage, the length of the stack is *l*0, and the slider and the stator are at the initial position. Due to the existence of the initial locking force, there is a pair of equal and opposite interaction forces (*F*I0 and *F*R0) between the driving foot and the slider.

Stage II: the length of the stack extends to *l*1 quickly excited by the DG waveform at time *t*1 so that stator is produced an oblique deformation. The position of the driving foot is moved from position ① to position ②, which causes a pre-deformation of the stator. At the same time, the slider will produce a displacement of ∆*d*<sup>1</sup> along the o*x* axis with the help of the driving foot. In addition, the interaction force becomes *F*I1 and *F*R1 after incrementing ∆*F* (|*F*I1| = |*F*R1| = |*F*I0| + |∆*F*|), which can further increase the load capacity and horizontal thrust of the actuator within a proper range of regulation.

Stage III: the stack is excited by the DGHM at time *t*2. The excitation voltage of the DG waveform is kept constant. The RD waveform is composed of high frequency sine waveforms with the period of *T*R. The stack undergoes an elongation and contraction between the lengths of *l*1 and *l*2 in each cycle. Correspondingly, the driving foot vibrates rapidly between the positions of ② and ③. During the time of *T*R, a displacement ∆*d*2 of the slider is produced along the o*x* axis. The velocity of

#### **Figure 11.**

*Operation principle of the DGHM. (a) Schematic of the DGHM. (b) Specific operations of the DGHM [19].*

#### *The Asymmetric Flexure Hinge Structures and the Hybrid Excitation Methods for Piezoelectric… DOI: http://dx.doi.org/10.5772/intechopen.95536*

the actuator is *v* (*v* = *f*R × ∆*d*2), where *f*R is the frequency of the RD waveform. Even at a low voltage, the actuator can achieve a high speed by the DGHM.
