*4.2.1. d*<sup>31</sup> *effect actuators*

12 Will-be-set-by-IN-TECH

Many actuation technologies are available to actuate every smart blade concepts. Among them, piezoelectric actuators have a tremendous potential to meet and exceed the various requirements of these specific applications. This section focuses on piezoelectric actuators

Piezoelectric materials are materials that have the property to convert mechanical energy into electrical energy. When such a material is subjected to a strain, an electrical charge is created inside the material. This property is called the direct piezoelectric effect. Additionally, when the material is subjected to an electrical field, it deforms according to the electrical field magnitude. This is called the converse piezoelectric effect. A piezoelectric material is characterized by the piezoelectric strain constant *dij* which relates the strain to the electrical field. The subscript *i* indicates the direction of the applied electrical field and the subscript *j* indicates the direction of the deformation. Prior to be used, the piezoelectric material is poled. Conventionally the poling direction is along the vertical axis (3-axis) as shown in Figure 9. When an electrical field is applied in the poling direction, the material is contracting in that direction and extending in other directions (1- and 2-axis). Changing the direction of the electrical field will result in a contraction along the 1- and 2-axis and extension along the vertical axis. To quantify these piezoelectric effects, the direct and shear strains are related to the electrical field by the following constants: *d*<sup>31</sup> = *d*32, *d*33, *d*<sup>25</sup> = *d*15. Equation 8 is the equilibrium equation that relates the electrical field *E* to the strain and shear components of

**4. Piezoelectric actuators for smart-rotor blade systems**

**4.1. Piezoelectricity**

1

**Figure 9.** Axis reference system for piezoceramic components.

⎛

*ε*1 *ε*2 *ε*3 *γ*23 *γ*<sup>31</sup> *γ*<sup>12</sup> ⎞

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ × ⎛ ⎝ *E*1 *E*2 *E*3

⎟⎟⎟⎟⎟⎟⎠ =

⎜⎜⎜⎜⎜⎜⎝

Electrodes

and their potential for the actuation of active systems for helicopter blades.

the material (*ε* and *γ*) when no mechanical constraint is applied on the material. 3

2

⎞

⎠ (8)

Poling direction

Piezoceramic actuators using the *d*<sup>13</sup> effect are based on the fact that a through-thickness electrical field will contract the material's width and length. The components manufactured

#### 14 Will-be-set-by-IN-TECH 670 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

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.

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