Measuring and testing – Fluid pressure gauge – Diaphragm
Reexamination Certificate
2001-02-23
2002-12-24
Fuller, Benjamin R. (Department: 2855)
Measuring and testing
Fluid pressure gauge
Diaphragm
Reexamination Certificate
active
06497152
ABSTRACT:
TECHNICAL FIELD
This invention relates to pressure transducer designs and methods for selecting the dimensions and geometry of force-producing pressure elements such that spurious modes of oscillation do not coincide with the frequencies generated by force-sensitive resonators that are used to measure the applied pressures.
BACKGROUND OF THE INVENTION
A number of force-sensitive resonators are described in the prior art. Single vibrating beam force sensors are described in U.S. Pat. Nos. 3,470,400, 3,479,536, 4,445,065, 4,656,383, 4,658,174, 4,658,175, 4,743,790, 4,980,598, 5,109,175, and 5,596,145. Double vibrating beam force sensors, referred to as Double-Ended Tuning Forks (DETF), are described in U.S. Pat. Nos. 3,238,789, 4,215,570, 4,415,827, 4,469,979, 4,531,073, 4,757,228, and 4,912,990. Each of these patents describes a resonator to which a force, which may be induced by pressure, is applied. The force alters the resonant frequency of the resonator so that the frequency of oscillation is indicative of the magnitude of the applied force.
FIG. 1
is an isometric view of a force-sensitive transducer made with a conventional Double-Ended Tuning Fork (DETF), as described in U.S. Pat. No. 4,372,173. The DETF includes a pair of parallel beams
3
extending between a pair of mounting pads
1
,
2
. The mounting pads
1
,
2
are attached to respective mounting structures
9
,
7
by suitable means. Axial forces, applied along a longitudinal axis of the transducer extending between the mounting pads
1
,
2
stress the beams
3
, thereby changing the resonant frequency at which they vibrate in accordance with the magnitude of the applied force. The beams
3
are preferably fabricated using a piezoelectric material, such as quartz, and they are driven through piezoelectric excitation by an electrode pattern
15
placed on the beams
3
. The electrode pattern
15
is coupled to contacts
11
,
13
formed on the mounting pad
2
, which are, in turn, coupled to oscillator circuitry (not shown). The oscillator circuitry is designed to drive the beams
3
at their resonant frequency. Alternative means of excitation include passing an electrical current at the resonant frequency through the beams in a magnetic field or capacitive drive means. The transducer achieves low energy loss because most reactive moments and forces which might be transmitted to the mounting structures
7
,
9
are cancelled by the beams
3
being driven 180 degrees out of phase.
The resonant frequency f
o
of the unstressed double-ended tuning fork beam of length L, tine thickness in the direction of vibration t, tine width b, modulus of elasticity E, and density d, is given by the formula:
f
o
=(constant)(
t /L
2
)(
E/d
)
FIG. 2
is a graph that shows the change of the resonant frequency as a function of applied load. If the load is in compression, the resonant frequency decreases. Under tensile load, the resonant frequency increases. The resonator in the shown example changes frequency by approximately 10% under full-scale load.
Although the resonant frequency is generally a non-linear function of the applied load F, the change in frequency under load may be approximated by:
f=f
o
(1+
a*F
)
Where
a
=(constant)
L
2
/(
E*t
3
*b
)
The load on the resonator may be either compressive or tensile, causing a frequency decrease or increase, respectively. Thus the sign of the constant a can be positive or negative. The resonant frequency, f, will vary between a minimum, fmin, and a maximum, fmax, corresponding to the minimum and maximum applied loads.
The applied load also generates compressive or tensile stress &sgr; in the resonator beams (n=2 for double-ended tuning forks), the magnitude of which is given by the formula:
&sgr;=
F
/(
n*b*t
)
The resultant stresses must be within the elastic limits of the material and, when the transducer is used in compression, within the buckling limits of the material. The transducer is preferably highly sensitive and is stressed up to acceptable values, which defines the maximum load, Fmax, either in tension or compression. By the formulas given above, a corresponding frequency range of the resonator is found from the unstressed resonant frequency fo to the stressed frequencies fmax and fmin at the highest tensile and compressive loads on the resonator.
Various techniques have been employed to maximize the Q of these force-sensitive resonators by reducing the amount of energy lost through their mountings to the force-producing elements and structure. Flexurally vibrating beams, known as “fixed-fixed” beams, lose energy to the structure on which they are mounted when their reactive forces and moments are not perfectly balanced or filtered effectively. Vibration isolation systems act as low-pass mechanical filters to reduce the amount of lateral flexural energy lost by single beam resonators, as described in U.S. Pat. Nos. 3,470,400, 4,656,383, 4,658,174, 4,658,175, 4,743,790, 4,838,369, 4,980,598, 5,109,175, and 5,334,901. Double-Ended Tuning Forks (DETF) depend on the cancellation of lateral forces and moments between two symmetric beams vibrating in 180 degrees phase opposition.
Lateral flexing of vibrating beam resonators causes a longitudinal shortening for each half of a flexing cycle, therefore generating longitudinal pumping forces at twice the lateral flexing frequency. These pumping forces transfer energy to the structure on which the beams are mounted, thereby reducing the Q of such resonators. U.S. Pat. No. 4,321,500 discloses an isolation system that reduces the magnitude of such longitudinal pumping. U.S. Pat. No. 4,724,351 describes DETF sensors that are configured to minimize the longitudinal pumping by making the beams vibrate symmetrically.
U.S. Pat. No. 4,372,173 discloses a geometrical and dimensional selection process for force-sensitive resonators, which avoids spurious modes of oscillation within the resonator itself that would otherwise result in output discontinuities over the operational force range. However, even if these internal spurious modes of the resonator are avoided, residual lateral and longitudinal forces and moments remain due to imperfections in the manufacturing processes and the inability of mechanical isolation systems to totally eliminate these imbalanced forces and moments. Thus, force-sensitive resonators, including those designed according to the teachings of U.S. Pat. No. 4,372,173, apply lateral forces and moments at resonant frequency, f, and longitudinal forces and moments at double frequency, 2f, to the resonator mounting pads and thence to the force-producing structure. To a lesser degree, and dependent on mounting accuracies, the resonant frequency, f, can also be transmitted in the longitudinal direction, and the double frequency, 2f, can be transmitted in the lateral direction to the force-producing structure. As described in the U.S. Pat. No. 4,384,495, the DETF sensors must be symmetrically loaded to prevent spurious modes of oscillation that result from load-dependent differences in resonant frequencies of each beam overcoming the coupling between the two beams.
If the frequencies of the resonator's lateral and longitudinal forces and moments that are transmitted to the force-producing mechanism coincide with resonant frequencies of the force-producing mechanism, then enough energy can be lost from the resonator to produce discontinuities in output over the operating range. Indeed, enough energy could be lost to cease oscillation of the resonator. Even if insufficient energy is lost to stop the resonator from oscillating, the resonant force-producing mechanism has a tendency to “pull” the resonant frequency of the resonator toward the resonant frequency of the force-producing mechanism when the resonant frequency of the resonator is close to the resonant frequency of the mechanism. This phenomenon produces a discontinuity in the relationship between the resonant frequency of the resonator and the force that is being measured by the resonator. As a result, the resonator exhibits a
Paros Jerome M.
Schaad Theo P.
Dorsey & Whitney LLP
Ferguson Marissa
Fuller Benjamin R.
Paroscientific, Inc.
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