Electrical generator or motor structure – Non-dynamoelectric – Piezoelectric elements and devices
Reexamination Certificate
2001-07-30
2003-07-22
Budd, Mark O. (Department: 2834)
Electrical generator or motor structure
Non-dynamoelectric
Piezoelectric elements and devices
C310S365000, C310S359000
Reexamination Certificate
active
06597085
ABSTRACT:
FIELD OF THE INVENTION
This invention relates in general to a piezoelectric energy conversion apparatus and, in particular, to one with high energy conversion efficiency. More particularly, this invention relates to a piezoelectric transformer having modal-shaped electrode for efficiently converting electric power.
BACKGROUND OF THE INVENTION
Piezoelectricity is widely utilized in various applications. As a transducer for converting energy in one form into another, a piezoelectric material block is useful as a workpiece for converting mechanical energy to electrical or vice versa. A piezoelectric workpiece can be used to convert an electrical power at one AC frequency and voltage into another at different frequency and voltage. This specific application of AC electrical power conversion involving converted (frequently raised) voltage makes a piezoelectric transducer device a useful piezoelectric transformer suitable for various industrial and consumer applications.
Charles A. Rosen proposed his piezoelectric transformer in the 1950's. It is not until the 1990's when piezoelectric transformer has become more and more popular in electronic devices. Piezoelectric transformers have been used such as in the power supply section of various electronic devices, portable ones in particular. Due to benefits such as their size and weight, it is obvious that piezoelectric transformers will become even more popular. Improved safety is another desirable feature of a piezoelectric transformer. A failed piezoelectric transformer normally breaks itself and ceases to function. Fire hazards are virtually of no concern at the part of the piezoelectric workpiece itself.
Electrodes plated to the surface of a piezoelectric material block are necessary for conveying electric power into and/or out of the workpiece in order for the piezoelectric system to function. Traditionally, dimensioning factors including both shape and size of the electrodes have not been carefully considered parameters when designing a piezoelectric system. Typically, rectangular-shaped electrodes are used for rectangular-shaped workpieces. In disk- or ring-shaped workpieces, electrodes are typically also disk-shaped or having the shape of a section of the disk or ring. These electrode shape configurations are considered uniform electrodes in the description of the present invention.
Traditionally, piezoelectric systems have been analyzed based on circuit theories. Mechanical considerations of a piezoelectric system are “translated” into parameters that are fit into circuit models. Piezoelectric workpieces thus developed are not optimized in issues such as energy conversion efficiency and parasitic noises—signals at undesirable frequencies with sufficiently significant amplitudes mixed in the output of a piezoelectric workpiece.
FIG. 1
is a perspective view of a piezoelectric workpiece outlining the definition of the piezoelectric parameters, both electrical and mechanical, and material orientation and dimensions for the analysis of a piezoelectric system. As is illustrated, the piezoelectric workpiece
100
is, in general, an elongated thin rectangular-shaped plate having a length L, a width W and a thickness, or height, H. Note that in the following theoretical development for the description of the piezoelectric transducer apparatus of the present invention, the IEEE Compact Matrix Notation system is employed.
By convention, the two largest surfaces of the elongated thin-plate workpiece are the side surfaces, and the two smallest are the end surfaces. The direction along the longitudinal axis of the workpiece is the first orientation, that perpendicular to the first orientation and parallel to the side surfaces is the second, and that perpendicular both to the side surfaces and to the longitudinal axis is the third, as is shown in the drawing by an orientation axis system
110
labeled with orientations 1, 2 and 3 respectively.
Also, in the theoretical development of the invention in the following detailed description, a variable x is set up along the direction of the first orientation. This coordinate axis, one measuring the longitudinal dimension, or length, of the elongated workpiece
100
, serves as a variable in the analysis of the piezoelectric system according to the teaching of the present invention. One end of the workpiece
100
is set conveniently as the origin of the x coordinate axis, as is seen in FIG.
1
.
The workpiece
100
has a side-plated electrode
102
and another not shown in the perspective view. That electrode which opposes electrode
102
and provides for a complete electrical circuit path is plated on the other side of the workpiece opposite to the side for the electrode
102
.
Each of the electrodes is connected to a corresponding terminal of an electric circuit
120
, represented in the drawing by a voltage sign V that signifies a voltage across the electrodes of the piezoelectric workpiece. The current corresponding to the voltage V in the circuit
120
is identified by I. P represents the electrical power arising from voltage V and current I.
External mechanical forces applied to the workpiece
100
is identified in the drawing by the symbol F, the corresponding mechanical velocity induced as a result of an applied force F is identified by U.
The piezoelectric system of
FIG. 1
, which has a workpiece
100
with side-plated electrodes including
102
, is in the 31 mode, i.e., the polarization is in orientation 3, and the mechanical vibration is in orientation 1. By contrast, a system such as that illustrated in
FIG. 3
which has a workpiece
300
with end-plated electrodes
302
and
304
is in 33 mode. Both its electrical polarization and mechanical vibration are along orientation 3 of its orientation axis system
310
.
Based on the traditional method of analysis that relies on circuit theories, a piezoelectric system such as that depicted in
FIG. 1
which has side-plated electrodes and operates in the 31 mode has the following constitutive equations:
S
1
=s
11
E
T
1
+d
31
E
3
(1)
D
3
=d
31
T
1
+&egr;
33
T
E
3
. (2)
In Equations (1), (2) and those to be discussed below, the parameters and constants are in accordance with their respective definitions in the IEEE notation system mentioned above.
Based on the relationship between the piezoelectric constants and between the longitudinal strain u and the longitudinal stress S
1
, considering the longitudinal motion equation for the system, the following governing equation may be derived for the 31 mode piezoelectric workpiece:
-
ρ
∂
2
u
∂
t
2
+
c
11
E
∂
2
u
∂
x
2
=
E
3
∂
e
31
∂
x
.
(
3
)
Since a conventional piezoelectric workpiece employs uniform electrodes characterized by its rectangular-shaped electrode patterns, Equation (3) may thus be reduced to:
-
ρ
∂
2
u
∂
t
2
+
c
11
E
∂
2
u
∂
x
2
=
0.
(
4
)
Equation (4) is a homogeneous one-dimensional wave equation, which has a general solution for the longitudinal strain u that can be expressed as
u
=(
B
1
sin &bgr;
x+B
2
cos &bgr;
x
)
e
j&ohgr;t
(5)
wherein
&bgr;=&ohgr;/
c
(6)
and
c={square root over (c
11
E
/&rgr;)},
(7)
in which j={square root over (−1)}, &ohgr; is the angular frequency, &bgr; is the wave number, c is the velocity of wave propagation, and B
1
and B
2
are, respectively, coefficients to be determined by the boundary condition of the examined system.
In addition to the mechanical piezoelectric parameters as incorporated into the analysis above, electrical ones also need to be considered in the analysis as well. In a 31 mode piezoelectric system of
FIG. 1
, the electromechanical coupling coefficient can be defined to be
k
31
2
=
d
31
2
c
11
E
ϵ
33
T
.
(
8
)
Assuming that the 31 mode piezoelectric workpiece in the system is clamped at its both ends, the mechanical characteristic impedanc
Hsiao Wen-Hsin
Hsieh Chih-Wen
Hsu Yu-Hsiang
Lee Chih-Kung
Budd Mark O.
J.C. Patents
Lee Chih-Kung
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