Measuring and testing – Speed – velocity – or acceleration – Temperature compensator
Reexamination Certificate
2001-05-24
2003-02-18
Moller, Richard A. (Department: 2856)
Measuring and testing
Speed, velocity, or acceleration
Temperature compensator
Reexamination Certificate
active
06520015
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to machined micro-mechanisms comprising return elements in the form of beams subjected to simultaneous bending and torsion deformations. More precisely, the invention relates to diapason type gyrometers using a micro-mechanical structure of vibrating beams.
2. Description of the Related Art
In some machined micro-mechanisms, it is sometimes necessary to have resonance modes in translation and other resonance modes in rotation simultaneously. The sensitive element of a diapason gyrometer is one of these micro-mechanisms.
FIG. 1
shows a simplified drawing of a sensitive micro-machined element
10
of a diapason type gyrometer with a symmetrical double beam structure. The sensitive element has two degrees of freedom about the Ox and Oz axes perpendicular to a reference coordinate system Oxyz. The purpose of the gyrometer is to measure the angular velocity &OHgr; of the reference Oxz rotating about the Oy axis perpendicular to this reference.
The sensitive element of the gyrometer comprises a first pair of two excitation beams
12
and
14
, and a second pair of two other excitation beams
16
and
18
. The excitation beams in the first pair and the second pair are located in the same Oxy plane of the reference coordinate system and are parallel to a sensitive axis YY′ coincident with the Oy axis. The first and the second pairs are located on opposite sides of the YY′ axis and at approximately equal distances from it.
Each pair of excitation beams comprises a central mass connecting the two beams in the pair at their center, a mass ml at the middle of the first pair and a mass m
2
at the middle of the second pair.
The ends of the beams
12
,
14
,
16
,
18
located on one side are connected to a first transverse element
20
and to a second transverse element
22
located in the same Oxy plane as the excitation beams and approximately perpendicular to these beams.
The first
20
and second
22
transverse elements comprise a first return beam
24
and a second return beam
26
(or return element) respectively, that have torsion axes collinear with the sensitive axis YY′ of the gyrometer. The ends of the first and the second return beams are connected to a first frame
28
and a second frame
30
respectively, rigidly fixed to the gyrometer.
In order to measure the angular velocity during one rotation of the gyrometer, an electrostatic device
32
creates deliberate excitations E
1
and E
2
respectively on masses m
1
and m
2
respectively at the resonant natural frequency of the excitation beams and the return beams. These excitation forces E
1
and E
2
have the same amplitude but opposite directions, and are applied to masses m
1
and m
2
parallel to an XX′ axis coincident with the Ox axis of the reference coordinate system. The excitations E
1
and E
2
produce displacements of masses m
1
and m
2
in two opposite directions at instantaneous velocities v
1
and v
2
respectively. One rotation of the gyrometer with a sensitive element
10
subject to excitations E
1
and E
2
produces a pair of Coriolis forces F
1
and F
2
about the sensitive axis YY′ on masses m
1
and m
2
respectively, causing a rotation of the transverse elements
20
,
22
and torsion of the return beams
24
and
26
about this axis.
The angular rotation velocity &OHgr; of the sensitive element
10
is determined by a measurement of the position of masses m
1
and m
2
. The Coriolis moment at masses m
1
and m
2
is calculated as follows:
Mcor
/
y
=
ⅆ
ⅆ
t
(
J
·
Ω
)
where J≈J
0
+J
1
sin &ohgr;t
Mcor/
y
: Coriolis moment applied on masses m
1
and m
2
;
&OHgr;: angular velocity of the sensitive element
10
about the sensitive axis YY′;
&ohgr;: natural angular frequency of masses m
1
and m
2
;
J: moment of inertia of masses m
1
and m
2
about the YY′ axis;
Jo: constant part of the moment of inertia J;
J
1
: oscillating part of the moment of inertia generated by movement of the masses about the XX′ axis at the natural angular frequency &ohgr;.
The positions of the masses m
1
and m
2
are calculated by capacitive effect, and the angular velocity &OHgr; of the gyrometer is calculated using known methods making use of the masses m
1
and m
2
and the torsion and the bending constants of the beams of the sensitive element.
Coriolis forces exerted on the element during one rotation of the gyrometer create a torsion in the return elements at the oscillation frequency of the excitation, while the deliberate excitation of masses m
1
and m
2
causes bending of the excitation beams.
The resulting bending force and amplitude of bending on a beam are related to each other by Young's modulus for the material used, while the torsion forces and the resulting torsion angle for the same material are related by Poisson's ratio for the mechanical behavior that varies depending on the geometry of the beam subjected to torsion.
In gyrometers according to known practice, an attempt is made to make two systems of beams (excitation beams and detection beams) that have the closest possible resonant natural frequencies to amplify the two movements (the excitation vibration movement and the detection vibration movement) produced by the Coriolis force on the sensitive element
10
. On gyrometers according to known practice, the excitation vibration takes place on a bending mode, whereas the detection vibration takes place on a torsion mode.
These two resonance modes have different behaviors in terms of frequency variation
as a function of beam machining uncertainties: the stiffness of a beam with a rectangular cross-section in bending depends mainly on its thickness and length, whereas the stiffness in torsion depends mainly on the thickness and the width. The two types of stiffness are expressed by:
Stiffness in bending: Kbending proportional to E.W.(H
3
/L
3
)
Stiffness in torsion: Ktorsion proportional to [E./2(1−&ngr;)].W
3
.H
3
/[L.(W
2
+H
2
)]
where L, W, and H are the length, width and depth of the beams,
E and &ngr; are the Young's modulus and the Poisson's ratio for the material.
as a function of the temperature: the bending mode being related only to the Young's modulus for the material, while the torsion is dependent on Young's modulus and Poisson's ratio; these two parameters do not have the same thermal behavior and therefore do not vary in the same way to temperature fluctuations applied to the gyrometer.
These disadvantages cause a change in the resonant frequencies between beams operating in different modes (bending and torsion), that limit the performance and stability of the gyrometers.
SUMMARY OF THE INVENTION
In order to overcome the disadvantages of angular velocity measurement systems according to prior art, the invention proposes m gyrometer comprising a micro-machined sensitive element with at least two symmetrically positioned excitation beams on each side of and parallel to a sensitive Oy axis of the gyrometer, excited in bending about an Ox axis perpendicular to the sensitive Oy axis, and connected through their ends to at least one transverse element fixed in its central part to the sensitive Oy axis, to a frame through an elastic torsion return element acting in opposition to the rotation of the transverse element about the Oy axis, characterized in that elastic return element(s) are sized such that the variation of their resonant natural frequency in torsion with temperature is similar to the variation of the resonant natural frequency in bending of the beams with temperature.
According to a first embodiment of the gyrometer according to the invention, the elastic return element of a transverse element comprises at least one beam elongated in a direction perpendicular to the Oy axis such that the torsion return force due to this elastic return element is essentially due to the resistance of this elongated beam to bending.
In a second embodiment of the gyrometer accordin
Alause Hélène Wehbe
Formosa Fabien
Moller Richard A.
Oblon & Spivak, McClelland, Maier & Neustadt P.C.
Thales Avionics S.A.
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