Page 418 - The Mechatronics Handbook

0066_frame_C19 Page 40 Wednesday, January 9, 2002 5:17 PM

The load P is linearly proportional to the output voltage E o . The sensitivity of the ring-type load cell
with an LVDT sensor depends on the geometry of the ring (R, t, and w), the material from which the
ring is fabricated (E), and the characteristics of the LVDT (S and E i ). The range of a ring-type load cell
is controlled by the strength of the material used in fabricating the ring.
Piezoelectric Methods
A piezoelectric material exhibits a phenomenon known as the piezoelectric effect. This effect states that
when asymmetrical, elastic crystals are deformed by a force, an electrical potential will be developed
within the distorted crystal lattice. This effect is reversible. That is, if a potential is applied between the
surfaces of the crystal, it will change its physical dimensions [4]. Elements exhibiting piezoelectric qualities
are sometimes known as electrorestrictive elements.
The magnitude and polarity of the induced surface charges are proportional to the magnitude and
direction of the applied force [4]:
Q = dF (19.52)

where d is the charge sensitivity (a constant for a given crystal) of the crystal in C/N. The force F causes
a thickness variation ∆t meters of the crystal:

F = aY (19.53)
------∆t
t
where a is area of crystal, t is thickness of crystal, and Y is Young’s modulus.

stress
Ft
Y = ------------- = --------- (19.54)
strain a∆t
The charge at the electrodes gives rise to a voltage E o = Q/C, where C is capacitance in farads between
the electrodes and C = εa/t where ε is the absolute permittivity.

------ =
E o = dF dtF (19.55)
-------
C ε a
The voltage sensitivity = g = d/ε in volt meter per newton can be obtained as:
t
E o = g--F = gtP (19.56)
a
The piezoelectric materials used are quartz, tourmaline, Rochelle salt, ammonium dihydrogen phosphate
(ADP), lithium sulfate, barium titanate, and lead zirconate titanate (PZT) [4]. Quartz and other earthly
piezoelectric crystals are naturally polarized. However, synthetic piezoelectric material, such as barium
titanate ceramic, are made by baking small crystallites under pressure and then placing the resultant
material in a strong dc electric field [4]. After that, the crystal is polarized, along the axis on which the
force will be applied, to exhibit piezoelectric properties. Artificial piezoelectric elements are free from
the limitations imposed by the crystal structure and can be molded into any size and shape. The direction
of polarization is designated during their production process.
The different modes of operation of a piezoelectric device for a simple plate are shown in Fig. 19.36
[4]. By adhering two crystals together so that their electrical axes are perpendicular, bending moments
or torque can be applied to the piezoelectric transducer and a voltage output can be produced (Fig. 19.37)
[4]. The range of forces that can be measured using piezoelectric transducers are from 1 to 200 kN and
5
at a ratio of 2 × 10 .
Piezoelectric crystals can also be used in measuring an instantaneous change in the force (dynamic
forces). A thin plate of quartz can be used as an electronic oscillator. The frequency of these oscillations
will be dominated by the natural frequency of the thin plate. Any distortion in the shape of the plate

©2002 CRC Press LLC