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TMM60-50-10LA Datasheet(PDF) 7 Page - NEC

Part # TMM60-50-10LA
Description  Piezoelectric Ceramics
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Manufacturer  NEC [NEC]
Direct Link  http://www.nec.com/
Logo NEC - NEC

TMM60-50-10LA Datasheet(HTML) 7 Page - NEC

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2010.03.19 9307PIEVOL04E
●All specifications in this catalog and production status of products are subject to change without notice. Prior to the purchase, please contact NEC TOKIN for updated product data.
●Please request for a specification sheet for detailed product data prior to the purchase.
●Before using the product in this catalog, please read "Precautions" and other safety precautions listed in the printed version catalog.
Piezoelectric Ceramics Vol.04 7
3) Relative dielectric constant
When the electric flux density caused by applying an
electric field E between electrodes of a transducer
under a constant stress is regarded as D, the relative
dielectric constant is obtained by dividing the constant,
defined by D/E=
εT, by the vacuum dielectric constant
ε0. This relative dielectric constant is expressed by
εT33/ε0when the direction of polarization and applied
electric field are the same; it is expressed by
εT11/ε0 when these directions are perpendicular.
Calculation of relative dielectric constant is shown in
Eq. 11. Static capacitance is usually measured at 1kHz
using an all-purpose bridge or a C meter.
(
εT110 is also calculated using the same equation.)
Where
ε0 : Relative dielectric constant in vacuum
(8.854x10
-12 F/m)
t
: Distance between electrodes (m)
S : Electrode area (m
2)
C : Static capacitance (F)
E
P
E
P
Fig.1-8
Where
Kr : Electromechanical coupling coefficient for radial
vibration
K31: Electromechanical coupling coefficient for
lengthwise vibration
K33: Electromechanical coupling coefficient for
longitudinal vibration
Kt : Electromechanical coupling coefficient for thick-
ness vibration
K15: Electromechanical coupling coefficient for shear
vibration
fr : Resonant frequency [Hz]
fa : Antiresonant frequency [Hz]
εε
ε
33
0
0
T
tC
S
/
=
εε
11
0
T /
εε
33
0
T /
· · · · · · · · · · · · · · · · · · · · · · · · · · · (11)
· · · · · · · · · · · · · · · · (8)
· · · · · · · · · · · · · · · · (9)
· · · · · · · · · · · · · · · (10)
K
fr
fa
fr
fa
Kt
fr
fa
fr
fa
K
fr
fa
fr
fa
=⋅
=⋅
=⋅
22
22
22
33
15
cot
cot
cot
ππ
ππ
ππ
4) Young's modulus
For different modes of vibration, Young's modulus is
calculated by Eq. 12, based on the sonic velocity and
density of the material.
Where
ρ: Density (kg/m3)
ν(=2fr ): Sonic velocity (m/sec.)
N: Newton
5) Mechanical Q
The mechanical Q is the "sharpness' of mechanical
vibration at resonant frequency, and is calculated with
Eq 13.
Where fr : Resonant frequency (Hz)
fa : Antiresonant frequency (Hz)
Zr : Resonant resistance (
Ω)
C : Static capacitance (F)
Where a simpler method is called for, mechanical Q
may be calculated with Eq. 14, using frequencies f1
and f2 which are each 3 dB from the resonant frequency.
The values shown for material characteristics in this
catalog are calculated using Eq. 13.
6) Piezoelectric constant
There are two types of piezoelectric constants, the
piezoelectric strain constant and the coefficient of
voltage output.
a)
PiezoeIectric strain constant
This is a measure of the strain that occurs when a
specified electric field is applied to a material that is in
the condition of zero stress. This constant is calculated
with Eq. 15.
Where k : Coefficient of electromechanical coupling
εT : Dielectric constant
Y
E : Young's modulus (Newton/m2)
Qm
fr
ff
=
12
dk
Y
mV
T
E
=
(
)
ε
/
YN m
E
=
[]
ρν22
/
Qm
fa
fr
=
2
2
2 fr Zr C(fa
2
π
)
· · · · · · · · · · · · · · · · · · · · · · (12)
· · · · · · · · · · · · (13)
· · · · · · · · · · · · · · · · · · · · · · · · · · (14)
· · · · · · · · · · · · · · · · · · · · · · · (15)
e
rive field
ctrode is
olarization.
t is
on (Hz-m)
ibration
vibration
ibration
n (Hz-m)
er (m)
Hz-m)
cylinder (m)
coupling
ing repre-
n a ceramic
input. This
dividual
r fm) and
applicable
· · · · · · (6)
· · · · · · (7)


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