*4.2.3. d*<sup>15</sup> *effect actuators*

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using this principle are consequently laminates of fine piezoceramic sheets. Electrodes are bonded on the upper and lower faces of the piezoceramic patch. Applying a voltage through the patch's thickness causes a contraction in the plane of the patch as shown in Figure 11. These can be easily bonded or embedded inside a structure, thanks to their low weight and volume. Thus, they are mainly used to manufacture unimorph and bimorph structures.

Piezoceramic actuators using the *d*<sup>33</sup> effect are based on the fact that a through-thickness electrical field will modify the material's thickness. Within piezoceramics, the *d*<sup>33</sup> coefficient is always more important than the *d*<sup>31</sup> coefficient, therefore using the *d*<sup>33</sup> effect is preferable. Consequently, there are many types of actuators that try to take advantage of the larger *d*<sup>33</sup>

Stack actuators use the *d*<sup>33</sup> effect to achieve deflection. They consist of multiple layers of piezoceramic plates separated by electrodes as shown in Figure 12. This configuration allows long elements to be made for higher displacement capabilities while high voltage is not needed to obtain high electrical fields if the piezoceramic layers are small enough between two electrodes. Stack actuators are capable of delivering higher forces than

Long piezoceramic components have better displacement capabilities. Active Fibre Composite (AFC) consists of piezo ceramic fibres embedded into a protective polymer substrate and poled into the fibre direction to use the highest strain coefficient. Interdigitated electrodes bonded onto the fibres ensure high electrical fields. The voltage required by these components depends on the fibre diameter and the distance between electrodes. Compared with laminar actuators, these components require less voltage to achieve the same force and displacement. Macro Fibre Composite exploit the same principles as AFC, except that they are made of fibres having an improved contact with electrodes, which plays an important role in the electrical field magnitude inside the material. Furthermore, those actuators are much more flexible than a strip made of the

laminar actuators as they are fully using the highest strain coefficient available.

• Macro Fibre Composites (MFC) & Active Fibre Composite (AFC)

Electrical field

Displacement

Poling direction

+ -

*4.2.2. d*<sup>33</sup> *effect actuators*

• Stack actuator

same material.

coefficient using various geometries.

**Figure 11.** Principle of a piezoelectric laminar actuator

Electrode

The *d*<sup>15</sup> effect is a shearing effect. The material shears in the 3-1 or 3-2 plane when an electrical field is applied in the 1-axis or 2-axis respectively, perpendicular to the poling direction as shown in Figure 14.

The *d*<sup>15</sup> shearing effect can be used to manufacture a tube actuator that twists when actuated as shown in Figure 15. Centolanza has discussed the manufacturing of an induced shear actuator and its testing [12]. Kim has tested the same component with feedforward control and pointed out fatigue and heating issues [27]. Their conclusions are that such an actuator is a promising option and more studies of the piezoceramic material would improve their models accuracy.

16 Will-be-set-by-IN-TECH 672 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

**Figure 14.** *d*<sup>15</sup> effect in piezoceramics.

**Figure 15.** Twisting motion for the *d*<sup>15</sup> effect in a shear tube actuator.

#### **4.3. Performances**

#### *4.3.1. Block force and free displacement*

The performance of piezoelectric actuators is evaluated in block force and free displacement. The block force is the maximum force the piezoelectric actuator can deliver when clamped. The free displacement is the displacement achieved by the actuator when no force is applied on it. These two parameters depend on the values of the piezoelectric strain coefficient, the electrical field inside the material and the geometry of the actuator. For a *d*<sup>31</sup> patch actuator the free displacement Δ and the block force *Fblock* can be directly derived from the Equation 8.

$$
\Delta = d\_{31} L \frac{V}{t} \tag{9}
$$

where *d*<sup>31</sup> is the piezoelectric strain coefficient, *L* the length of the actuator, *V* the applied voltage and *t* the distance between the two electrodes.

$$F\_{block} = \frac{d\_{31}AV}{S\_{11}t} \tag{10}$$

where *A* is the cross-section area of the actuator, *t* the distance between two electrodes and *S*<sup>11</sup> the compliance in the plane of the actuator.

Piezoelectric actuators provide large blocking forces but only very low displacements. Therefore, typical mechanisms that involve piezoelectric components contain systems to amplify the displacement of the actuator. The amplification can be achieved by the use of level arms or by the integration of the piezoelectric component in a structure providing that amplification. Cedrat Technologies develops these systems based on stack actuators [11, 44].

### **4.4. Bandwidth**

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Electrical field

3

Shear strain γ23

2

Electrical field

Poling direction

+


+


Poling direction

*<sup>t</sup>* (9)

1

+

Electrode θ


3

**Figure 15.** Twisting motion for the *d*<sup>15</sup> effect in a shear tube actuator.

2

The performance of piezoelectric actuators is evaluated in block force and free displacement. The block force is the maximum force the piezoelectric actuator can deliver when clamped. The free displacement is the displacement achieved by the actuator when no force is applied on it. These two parameters depend on the values of the piezoelectric strain coefficient, the electrical field inside the material and the geometry of the actuator. For a *d*<sup>31</sup> patch actuator the free displacement Δ and the block force *Fblock* can be directly derived from the Equation 8.

<sup>Δ</sup> <sup>=</sup> *<sup>d</sup>*31*<sup>L</sup> <sup>V</sup>*

1

**4.3. Performances**

*4.3.1. Block force and free displacement*

**Figure 14.** *d*<sup>15</sup> effect in piezoceramics.

The first widespread use of piezoelectric actuators was for manufacturing acoustic sources for sonar because of their large actuation frequency bandwidth. Overall, piezoelectric actuators have a very small actuation time and can achieve large motion speed and acceleration. Cedrat Technologies manufactures actuators with a response time below 1ms [11]. Moreover, the typical resonance frequency for piezoelectric actuators is in the kHz range, leaving a very comforting margin for structural applications [11, 45].

#### **4.5. Power consumption and voltage**

The power consumption of piezoelectric actuators depends on the type of actuation. Integrated inside an electrical circuit, a piezoelectric actuator behaves like a capacitor. Under harmonic actuation, the energy required to charge the piezoelectric actuator can be recuperated in the system for the next charge. When fast positioning is required, the electrical components which drive the piezoelectric actuator must be able to provide large currents. For the discharge, the circuit and its components must be able to dissipate quickly the energy stored in the piezoelectric. Therefore, active systems using harmonic actuation only need around 100W in operation, while a fast actuation system requires close to 1000W of power depending on the actuation profile. However, the main problem is not the amount of electrical power required but the time during which the power is required.

### **4.6. Reliability and operational environment**

Piezoelectric actuators are very reliable and can perform a large number of cycles under good operating conditions. For instance piezoelectric stack actuators manufactured by Physik Instrumente feature 109 cycles [45]. Cedrat technologies is developing high end actuators with 1010 cycles before failure [11]. Furthermore, piezoelectric actuators can operate in very harsh environments. Physik Instrumente provides piezoelectric stack actuators capable of operating in cryogenic environments [45]. Moreover, piezoelectric actuators can operate at high temperatures as long as the Curie temperature is not reached. The Curie temperature is the temperature at which the piezoelectric material looses its electro-mechanical coupling and this temperature is usually higher than 200◦C as shown in Table 2.
