Piezoelectric Ceramics ("PIEZOTITE") Sensors

!Note • This !Note PDF catalog • Please is downloaded read rating and from !CAUTION the website (for of Murata storage, Manufacturing operating, rating, co., ltd. soldering, Therefore, mounting it’s specifications and handling) are in subject this catalog to change to prevent or our smoking products and/or in it may burning, be discontinued etc. without advance notice. Please check with our
sales representatives • This catalog or product has only engineers typical specifications before ordering. because there is no space for detailed specifications. Therefore, please approve our product specifications or transact the approval sheet for product specifications before ordering.
• This PDF catalog has only typical specifications because there is no space for detailed specifications. Therefore, please approve our product specifications or transact the approval sheet for product specifications before ordering.
P19E.pdf
08.6.4
2
Characteristics of Piezoelectric Ceramics
2
1 Frequency Constant N
The velocity of sound that propagates through a piezoelectric
ceramics has a specific value in each vibration
mode when the resonance of other vibration modes is not
in the vicinity. For a piezoelectric ceramics with a certain
shape, the relationship of wavelength λ of a vibration with
propagation lengthrat the resonant point is given by
equation (4). Because the sound velocity is constant, we
obtain the following equations (5) and (6):
v
fr • r = = N ( HZ • m)
(6)
2
where N is the frequency constant. The frequency constant
depends on the vibration mode. The resonant frequency
may also be determined by the equation, fr = N/r
as shown in Fig. 2.
2 Piezoelectric Constants d and g
q Piezoelectric Strain Coefficient d
Piezoelectric distortion constant is the distortion resulting
from the application of an electric field of uniform strength
with no stress. It is given by equation (7):
where ε T : Dielectric constant
where Y E : Young's modulus (N/m 2 )
where k : Electromechanical coupling coefficient
w Voltage Output Coefficient g
Voltage output coefficient refers to the field strength
which results from a uniform stress applied under no electrical
displacement. It is given by equation (9):
6
2. Piezoelectric Material Constant Symbols
λ
= r
2
v = fr • λ
d = k
ε
Y
T
E
(m/V)
(4)
(5)
(7)
T
T
T
ε 33
ε 33
ε 11
d31= k 31 E , d33 = k 33 E , d 15 = k 15 E
(8)
Y 11 Y 33 Y 44
g =
Constants d and g depend on the vibration mode, and the
constants in each vibration mode are given by the subscripted
symbols shown in Fig. 2.
Displacements generated under an electric voltage or a
voltage generated under force can be determined by constants
d and g. For example, the displacement ∆rcaused
by voltage V applied across the electrodes in the lengthwise
vibration mode is given by:
∆r
r
d
T
ε
= d •
31
( V•m/N )
d 31 d 33 d
g =
31 T
g
33 T
g
ε
, =
15
ε
, =
ε
V
t
33
(11)
Conversely, the voltage V caused by force F applied along
the direction of vibration is given by:
33
15
T
11
(9)
(10)
1
V = g •
(12)
31
F
a
3 Electro Mechanical Coupling Coefficient k
The electromechanical coupling coefficient is a constant
representing the piezoelectric efficiency of a piezoelectric
ceramic. More specifically, it represents the efficiency of
converting electrical energy (applied across the electrodes
of a piezoelectric ceramic) into mechanical energy,
and it is defined as the root mean square of the energy
accumulated within the crystal in a mechanical form. This
accumulated energy reflects the total electrical input.
Electromechanical Accumulated Mechanical Energy
=
Coupling Coefficient Supplied Electrical Energy
The electromechanical coupling coefficient depends on the
vibration mode, as shown in Fig. 2. It is determined by
the following equations using the resonant frequency fr,
anti-resonant frequency fa, and their difference ∆ f = fa–fr.
q Radial Vibration of Disk
2
E
kp ( 1 - σ ) J 1{ ψ1 ( 1 + ∆ f / fr) } - ψ1( 1+ ∆ f / fr) J 0{
ψ1(
1+
∆ f / fr)
}
=
2 E
1-kp
( 1 + σ ) J { ψ1
( 1 + ∆ f / fr)
}
(13)
where J 0, J 1 : Type 1 vessel functions of the 0th and 1st
where J 0, J 1 : dimensions
where Jσ E : Poisson's ratio
where Jψ 1 : Lowest dimension of positive root of
where Jψ1 : (1– σ E ) J 1 (ψ) = ψJ 0 (ψ)
If kp is relatively small, equation (13) may be approximated
as follows:
∆f
2
kp ~ 2.529 • (14)
fr
w Lengthwise Vibration of Rectangular Plate
k
1–k
2
31
2
31
π fa π fa
= – • cot •
2 fr 2 fr
e Longitudinal Vibration of Cylinder
2
π fr π fr
k = •
33 cot •
2 fa 2 fa
r Vibration Along Thickness of Disk
2 π fr
k t
= •
2 fa
cot
π fr
•
2 fa
t Shear Vibration of Rectangular Plate
2
π fr π fr
k 15
= •
2 fa
cot •
2 fa
(16)
(17)
(18)
(15)
4 Mechanical Qm
Mechanical Qm gives the "steepness" of resonance of a
mechanical vibration at and around the resonant frequency.
It is given by the following equation:
1
1
Qm = =
2
(19)
π fr R 1C
1
2 πfr
1 fr 2
R 1Cf
{ –
fa
}
where R 1 : Resonant resistance
where Cf : Free capacitance across electrodes