US2019257653A1PendingUtilityA1
Method For The Measurement Of Angular And/Or Linear Displacements Utilizing One Or More Folded Pendula
Est. expiryAug 6, 2034(~8 yrs left)· nominal 20-yr term from priority
G01C 19/56G01P 2015/0805G01V 1/18G01B 5/24
49
PatentIndex Score
0
Cited by
0
References
0
Claims
Abstract
Systems are disclosed for the combined measurement of linear and angular displacements, with high sensitivity, wide measurement band at low frequency based on the configuration of the folded pendulum, and a linear and angular displacement sensor for applications of monitoring and control. Examples of possible applications of the combined sensor subject-matter of the present invention are sensor for the seismic monitoring, sensor for systems of monitoring and/or control of civil and industrial buildings, dykes, bridges, tunnels, etc., sensor for system of monitoring and/or control for the realization of systems of seismic attenuation and inertial platforms.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1 . A method for the measurement of the angular position of a folded pendulum with respect to a reference system xyz wherein the z-axis is along the direction of the gravity field or an equivalent conservative field, the folded pendulum comprising a support (F) with a base, a test mass (PM) with an oscillation direction, a simple pendulum arm (SP) and an inverted pendulum arm (IP) that connect the test mass (PM) to the support (F), the folded pendulum being positioned in such a way that said oscillation direction is along or parallel to the X-axis of a reference system XYZ obtained by rotation from the system xyz by the Tait-Bryan angles of roll α, pitch β and yaw γ, or another equivalent angular rotations description, the angles α,β, γ thus defining said angular position, the folded pendulum being subjected to a mechanical excitation or stress that makes it oscillate, and having a resonance frequency ƒ 0 , the method being characterized in that the following steps are executed when said folded pendulum is alternatively in a known angular position with known angle α=α known , or in a known angular position with known angle β=β known :
MB1. providing a function ƒ 0 =ƒ 0 (α,β) of said resonance frequency as a function of α and β, starting from a Lagrangian Λ describing the folded pendulum or a resonance frequency-angular position calibration curve of said folded pendulum;
MB2. measuring the resonance frequency ƒ 0 of the folded pendulum in said angular position starting from the oscillation motion of the test mass (PM) with respect to the support (F);
MB3. inverting the function ƒ 0 =ƒ 0 (α,β) with α=α known or β=β known and providing an angular position function β=β(ƒ 0 ) or |α|=α(ƒ 0 ) respectively as a function of the resonance frequency;
MB4. calculating the angles ρ or |α|, respectively starting from the function β=β(ƒ 0 ) or |α|=α(ƒ 0 );
wherein said mechanical stress or excitation is such to make the folded pendulum oscillate so as to comprise said resonance frequency ƒ 0 .
2 . The method according to claim 1 , wherein said folded pendulum is inclined with respect to said reference system XYZ by a known non-vanishing offset roll angle α 0 , and in steps MB1 and MB3 the function is ƒ 0 =ƒ 0 (α+α 0 , β), wherein in step MB3 the angular position function β=β(ƒ 0 ) or α=α(ƒ 0 ) is respectively provided as a function of the resonance frequency, assuming f=ƒ 0 (α+α 0 ,β) as invertible in the interval 2α 0 around α 0 .
3 . The method according to claim 1 , wherein:
steps MB1 to MB4 are first performed to obtain a first measurement of the roll angle module |α|; reference system XYZ is moved by changing the roll angle α; steps MB1 to MB4 are performed to obtain a second measurement of the roll angle module |α|; determining the sign of the roll angle α of said first measurement, by comparing said first and second measurements.
4 . The method according to claim 1 , wherein:
a first folded pendulum is fixed to the reference system XYZ on the plane XY in such a way that the direction of oscillation of its test mass lies on the XY-plane and coincides with the Xdirection, the first folded pendulum being positioned at a known offset roll angle α 0 ≠0 with respect to the reference system XYZ; a second folded pendulum is fixed to the reference system XYZ in such a way that the direction of its test mass oscillation lies on the XY plane at a non-null yaw angular distance, Δγ, from the first folded pendulum, the second folded pendulum being at known offset roll angle α 0 2 ≠0 with respect the reference system XYZ; the first and second folded pendulum have respectively a first ƒ 1 and a second ƒ 2 resonance frequency and are each subjected to a respective mechanical stress or excitation that makes it oscillate so as to comprise their respective resonance frequency,
wherein the following steps are executed in lieu of MB1-MB4:
MA1. providing a first function ƒ 0 1 =ƒ 0 1 (α+α 0 1 ,β) of said resonance frequency for the first folded pendulum and a second function ƒ 2 =ƒ 0 2 (α+α 0 2 ,β) values of said resonance frequency for the second folded pendulum, starting from a respective first and second Lagrangian Λ 1 and Λ 2 describing the first and the second folded pendulum or respective resonance frequency-angular position calibration curves of said first and second folded pendulum;
MA2. measuring the resonance frequency ƒ 0 2 of the first folded pendulum starting from the oscillation motion of the test mass (PM) with respect to the support (F);
MA3. measuring the resonance frequency ƒ 0 2 of the second folded pendulum starting from the oscillation motion of the test mass (PM) with respect to the support (F);
MA4. calculating angles α and 13 by solving the system of two equations ƒ 0 1 =ƒ 0 1 (α+α 0 1 ,β) and ƒ 0 2 =ƒ 0 2 (α+α 0 2 ,β) in two unknown quantities a, 3p.
5 . The method according to claim 1 , wherein each folded pendulum is modeled with two arms of equal length l inclined of an angle θ, that is positive for anti-clockwise rotations of the simple pendulum with respect to the direction of the Z-axis, said two arms being an arm of simple pendulum with mass m p 1 and an arm of inverted pendulum with mass m p 2 respectively concentrated in mass centers P 1 and P 2 , the two vertical arms being interconnected, between respective rotation points at a distance l P from the support, by a central mass m c modeled by two equivalent masses m c 1 and m c 2 placed on said rotation points and such that m c =m c 1 +m c 2 , k θ being the global flexional elastic constant of the rotation points, and g being the modulus of the force generated by said gravitational field, said Lagrangian Λ being:
Λ= T−U
wherein T is the approximated analytical expression of the kinetic energy:
T
=
1
2
(
J
1
+
J
2
)
θ
.
2
+
1
2
(
m
p
1
+
m
p
2
)
x
.
p
2
+
1
2
(
m
c
1
+
m
c
2
)
x
.
c
2
with J 1 and J 2 the moments of inertia of the two arms, {dot over (x)} p and {dot over (x)} c the speeds of the mass centers of the arms and central mass, respectively, and U the approximated analytical expression of the potential energy:
U
=
U
(
α
,
β
)
==
1
2
{
[
1
2
(
m
p
1
-
m
p
2
)
l
+
[
(
m
c
1
-
m
c
2
)
-
2
m
c
l
d
M
eq
g
K
e
eq
sin
β
]
l
p
]
g
cos
α
cos
β
+
k
θ
}
θ
2
wherein l d is the distance between the two joints,
M
eq
=
(
m
p
1
+
m
p
2
)
l
2
3
l
p
2
+
(
m
c
1
+
m
c
2
)
the equivalent mass,
K
e
eq
=
k
θ
l
p
2
the equivalent elastic constant, from the Lagrangian being derived the function ƒ 0 =ƒ 0 (α,β) given by the formula:
f
o
(
α
,
β
)
=
ω
o
(
α
,
β
)
2
π
=
1
2
π
K
eq
(
α
,
β
)
M
eq
=
1
2
π
K
g
eq
(
α
,
β
)
+
K
e
eq
M
eq
wherein the gravitational equivalent elastic constant, K g eq (α,β), is now function of the angles of roll, α, and pitch, β, and is expressed by
K
g
eq
(
α
,
β
)
=
{
(
m
p
1
-
m
p
2
)
l
l
p
2
+
[
(
m
c
1
-
m
c
2
)
-
2
m
c
l
d
M
eq
g
K
e
eq
sin
β
]
1
l
p
}
g
cos
α
cos
β
in such a way that said angular position depends from the resonance frequency by inverting said formula.
6 . The method according to claim 1 , wherein said mechanical stress or excitation is a noise with wide frequency spectrum.
7 . The method according to claim 6 , wherein said noise is a white noise.
8 . The method according to claim 1 , wherein steps MB2 and MB4 or MA2 and MA3 are repeated with varying time t, wherein ƒ 0 is the resonance frequency at time t, thus obtaining a function of the angular position along time, in the case the variation of the angular position is slower than the resonance frequency.
9 . The method according to claim 8 , wherein the variation of the angular position is at least of the order of 5 times slower than the resonance frequency.
10 . The method according to claim 8 , wherein the variation of the angular position is at least of the order of 10 times slower than the resonance frequency.
11 . The method according to claim 1 , wherein in each folded pendulum the simple pendulum arm and the inverted pendulum arm are connected at one of their ends to the test mass (PM) and at the other one of their ends to the support (F) by means of four corresponding joint systems (G), the test mass not being connected directly to the support (F) and being thus free to oscillate, wherein each joint system (G) relevant to the simple pendulum (SP) comprises one or more joint in tension, and wherein each joint system (G) relevant to the inverted pendulum (IP) comprises one or more joints in compression.
12 . The method according to claim 1 , wherein it is performed in the absence of gravity, said gravitational field being substituted by a local equivalent conservative field obtained for each folded pendulum by a constant force acting on the test mass.
13 . The method according to claim 12 wherein the constant force is a magnetic force.
14 . The method according to claim 1 , wherein each folded pendulum has a quality factor in air that is larger than 1.
15 . The method according to claim 1 , wherein each folded pendulum has a quality factor in air that is larger than 100.
16 . The method according to claim 1 , wherein each folded pendulum has a quality factor in air that is larger than 1000.
17 . The method according to claim 1 wherein said simple pendulum arm (SP) and said inverted pendulum arm (IP) are perpendicular, in a rest condition, to said base.
18 . The method according to claim 1 wherein known angle α=0 or known angle β=0.Join the waitlist — get patent alerts
Track US2019257653A1 — get alerts on status changes and closely related new filings.
We store only your email — no account needed. See our privacy policy.