Page 585 - The Mechatronics Handbook

0066_Frame_C20 Page 55 Wednesday, January 9, 2002 5:49 PM

TABLE 20.6 Piezoelement Sensing/Actuators Possibilities
Action Mode (L, length; W, width;
T, thickness; D, diameter) Generated Voltage, V Displacement, ∆L (∆T) Capacitance, C
T
--------------
----------V
Transverse length mode: L > 3W > 3T V = g 31 ∆l = d 31 L C = ε 3 LW
------F
W T T
3
S
2
1
T
Thickness extension mode: D > 5T V = 4Tg 33 ∆T = d 33 V C = πε 3 D 2
---------------
-------------F
πD 2 4T
3
S
2
1
Radial mode: D > 5T Not applied ∆D = d 31 D C = π T D 2
-----------V
---K 3 ε 0 ------
T 4 T
3
S
2
1
2
πD
4L
T
Longitudinal mode: L > 3D V = ---------g ∆L = d 33 V C = ---------K 3 ε 0
2 33 F
pD 4L
3
S
2
1

------F
Thickness shear mode: W > 5T, L > 5T V = g 15 ∆x = d 15 V C = LW T
---------K 1 ε 0
W T
3
2
S
1
T T
Note: F is the force and is dielectric permittivity of the material at constant stress in direction 3, K i is
ε 3
T T
relative dielectric constant (K i = ε i /ε 0 ), and ε 0 is dielectric permittivity in vacuum.
This way of connection allows greater travel at lower voltage. Usually these wafers are 0.3–1 mm thick.
The stack is often referred to operating mode d 33 . Total travel up to 200 µm can be achieved, and in this
case it is in proportion to the number of wafers, if no external load is applied:

∆l = Vnd 33 (20.37)

where n is the number of elements.

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