Accelerometer with floating beam temperature compensation

An accelerometer with a pivoting beam to accommodate differential thermal effects. The accelerometer measures acceleration along a sensitive axis, and comprises a housing, a proof mass, support means and a coupling assembly. The support means mounts the proof mass with respect to the housing. The coupling assembly is connected to the proof mass and housing, and comprises a beam and first and second force sensing elements. The beam is mounted for pivotal movement about a compensation axis normal to the sensitive axis. The first and second force sensing elements are connected to the pivot member at spaced-apart connection points on opposite sides of the compensation axis from one another, such that an acceleration along the sensitive axis results in respective compression and tension forces on the force sensing elements, and such that differential thermal expansion results in rotation of the beam about the compensation axis.

TECHNICAL FIELD 
The present invention relates to accelerometers and, in particular, to an 
accelerometer in which movement of a proof mass is constrained by a force 
transducer. 
BACKGROUND OF THE INVENTION 
In one type of prior accelerometer, a proof mass is mounted to a housing by 
a flexure hinge, and a force transducer is connected along the 
accelerometer's sensitive axis between the proof mass and the housing. An 
acceleration along the sensitive axis results in a compression or tension 
force on the force transducer. This force is converted into an electrical 
signal that indicates both the direction and magnitude of the 
acceleration. 
In an accelerometer of the type described above, the coefficient of thermal 
expansion of the force transducer in general cannot be precisely matched 
by the coefficient of thermal expansion of the proof mass and housing. As 
a result, the proof mass moves relative to the housing as the temperature 
changes. This thermally induced movement has a number of adverse effects 
on the operation of the accelerometer. The flexure hinge resists the 
thermally induced movement and thereby causes a change in the bias of the 
instrument. A change in the axis alignment of the accelerometer also 
occurs as the thermally induced movement causes the position of the center 
of gravity of the proof mass to change relative to the housing. In 
addition, the thermally induced movement results in changes in the damping 
gap and the shock gap clearances between the proof mass and housing, 
thereby modifying the damping and limiting functions respectively of these 
components. 
One method of providing temperature compensation for such an accelerometer 
is described in the U.S. patent application entitled Temperature 
Compensation of an Accelerometer, Ser. No. 879,262, Brian E. Norling, 
Inventor, filed concurrently herewith. This technique involves connecting 
two force transducers between the housing and the proof mass in such a way 
that differential thermal expansion or contraction results in rotation of 
the proof mass about a compensation axis normal to the sensitive axis. 
Such rotation is resisted by the flexure hinge, resulting in equal forces 
applied to both force transducers. The equal forces produce a common mode 
signal that can be eliminated by appropriate signal processing. 
The twisting of a flexure hinge caused by thermally induced proof mass 
rotation produces certain side effects that may limit the usefulness of 
the described technique for certain applications. These side effects 
include a change in the compliance of the flexure to sensitive axis 
acceleration, and a resulting change in the accelerometer scale factor. 
Flexure twisting may also lead to a bias/temperature component in the 
accelerometer output. Axis alignment may also be influenced by flexure 
twisting. The reaction forces on the force transducers due to the flexure 
twisting may produce accelerometer output errors due to nonlinearities and 
inequalities in the force transducers. Finally, the torsional compliance 
of the flexure hinge may result in the flexure hinge being less rigid in 
one or both orthogonal axes, thereby reducing the mechanical natural 
frequencies of the accelerometer and limiting the accelerometer's g-range. 
SUMMARY OF THE INVENTION 
The present invention provides an accelerometer in which the movement of a 
proof mass in constrained by two force transducers. The proof mass is 
coupled to a housing through the force transducers and through a pivot 
member such that differential thermal expansion is accommodated by pivot 
member rotation. As a result, errors due to temperature changes are 
significantly reduced in comparison to prior accelerometers. 
In one embodiment, the accelerometer is adapted to measure acceleration 
along a sensitive axis, and comprises a housing, a proof mass, support 
means and a coupling assembly. The support means mounts the proof mass 
with respect to the housing. The coupling assembly is connected to the 
proof mass and to the housing, and comprises a pivot member or beam and 
first and second force transducers. The pivot member is mounted for 
pivotal movement about a compensation axis normal to the sensitive axis. 
The first and second force transducers are connected to the pivot member 
at spaced-apart connection points on opposite sides of the compensation 
axis from one another, such that an acceleration along the sensitive axis 
results in a compression force on one force transducer and a tension force 
on the other force transducer, and such that differential thermal 
expansion or contraction between the force transducers and the other 
accelerometer components results in rotation of the pivot member about the 
compensation axis. In one preferred embodiment, the pivot member is 
pivotally connected to the proof mass, and each force transducer is 
connected between the housing and the pivot member. In a second preferred 
embodiment, the pivot member is pivotally connected to the housing, and 
each force transducer is connected between the pivot member and the proof 
mass.

DETAILED DESCRIPTION OF THE INVENTION 
FIG. 1 illustrates a prior art accelerometer related to the accelerometer 
of the present invention. The accelerometer of FIG. 1 comprises proof mass 
12 suspended from housing 14 by flexure hinge 16, and a force transducer 
comprising force sensing element 24 connected between the proof mass and 
housing. The proof mass, housing and flexure hinge are all preferably 
fabricated from a metal such as beryllium copper. Proof mass 12 is 
generally rectangular in shape, and occupies a similarly shaped but 
slightly larger cavity 18 within housing 14. Flexure hinge 16 is adapted 
to permit movement of proof mass 12 upward and downward along sensitive 
axis SA, but to prevent significant movement of the proof mass in 
directions normal to the sensitive axis. Damping gaps 20 and 22 between 
housing 14 and the upper and lower surfaces respectively of proof mass 12 
serve to damp unwanted vibrations of the proof mass by providing a limited 
path for the movement of air as the proof mass moves. The width of damping 
gaps 20 and 22, and the widths of the corresponding damping gaps of the 
other Figures, are exaggerated for the purpose of illustration. 
Force sensing element 24 preferably comprises a quartz crystal having the 
double-ended tuning fork construction illustrated in U.S. Pat. No. 
4,215,570. Such a crystal, in combination with a suitable drive circuit, 
comprises a vibrating beam force transducer having a resonant frequency 
that is a function of the axial force along the quartz crystal, i.e., 
along force sensing element 24. In particular, a compression force along 
the force sensing element produces a decrease in the resonant frequency of 
the force transducer, and a tension force exerted along the force sensing 
element results in an increase in the resonant frequency of the force 
transducer. Therefore, by connecting the force transducer output signal to 
a suitable frequency measurement circuit, the force exerted on force 
sensing element 24 by accelerations of proof mass 12 can be determined. 
The accelerometer of FIG. 1 also includes shock stops 26 and 28 extending 
from housing 14 above and below proof mass 12 respectively. The shock 
stops limit the motion of the proof mass along sensitive axis SA, and 
thereby prevent damage to force sensing element 24 that might otherwise be 
produced by large (out-of-range) accelerations. 
It is generally very difficult to match the coefficient of thermal 
expansion of force sensing element 24 to the coefficient of thermal 
expansion of the proof mass, housing and flexure hinge, particularly in 
the case where the force sensing element comprises a quartz crystal. A 
change in temperature of the accelerometer therefore generally results in 
movement of proof mass 12 along sensitive axis S, which movement is 
resisted by flexure hinge 16. As a result, a force is exerted on force 
sensing element 24 in the absence of, or in addition to, any forces that 
may occur due to accelerations, resulting in a temperature dependent bias 
error in the output of the accelerometer. Temperature induced movement of 
the proof mass also causes a change in the alignment of the sensitive axis 
and a change in the shock stop clearances. 
FIG. 2 presents a conceptual view of one embodiment of the accelerometer of 
the present invention. The accelerometer comprises proof mass 30 mounted 
to housing 32 by flexure hinge 34. As with the accelerometer of FIG. 1, 
flexure hinge 34 permits motion of proof mass 30 along sensitive axis SA. 
The accelerometer of FIG. 2 includes a coupling assembly comprising beam 
36 and force sensing elements 38 and 40. Beam 36 is mounted to proof mass 
30 at pivot 42. Each force sensing element has one end connected to beam 
36 and its other end connected to housing 32. Force sensing elements 38 
and 40 are connected to beam 36 at connection points 44 and 46 
respectively, connection points 44 and 46 lying on opposite sides of pivot 
42 from one another. Force sensing element 38 extends upward from beam 36 
parallel to sensitive axis SA, and force sensing element 40 extends 
downward from the beam along the sensitive axis. Pivot 42 permits beam 36 
to rotate with respect to the proof mass about compensation axis CA. 
Compensation axis CA is normal to sensitive axis SA and is also normal to 
a line that extends perpendicular to axis SA between connection points 44 
and 46. 
An acceleration along sensitive axis SA will result in a compression force 
on one force sensing element and a tension force on the other force 
sensing element. In a preferred embodiment in which each force sensing 
element comprises a portion of a vibrating beam force transducer, the 
result will be that the output signal frequency of one force transducer 
will decrease, and the output signal frequency of the other force 
transducer will increase. The acceleration may then be determined by means 
of a relationship such as: 
EQU a=A.sub.1 f.sub.1 -A.sub.2 f.sub.2 +A.sub.0 (1) 
where f.sub.1 and f.sub.2 are the output signal frequencies of the two 
force transducers, and where A.sub.1, A.sub.2 and A.sub.0 are constants 
determined through calibration procedures. More complex relationships 
between output signal frequencies and acceleration may also be used. In 
Equation (1), constants A.sub.1 and A.sub.2 represent the sensitivities of 
the respective force tranducers, and constant A.sub.0 represents the bias 
or offset of the accelerometer. Since the force transducers are preferably 
as similar as possible to one another, constants A.sub.1 and A.sub.2 are 
typically nearly equal to one another. Suitable systems for determining 
acceleration according to Equation (1) are set forth in U.S. Pat. No. 
4,467,651. 
When the accelerometer of FIG. 2 is subjected to temperature changes, 
differential thermal expansion or contraction between the force sensing 
elements and the proof mass, beam, flexure hinge and housing will result 
in forces that will tend to rotate beam 36 about pivot 42. For example, if 
the thermal expansion of the force sensing elements if proportionally 
greater than the thermal expansion of the other components of the 
accelerometer, then force sensing element 38 will exert a downward force 
on beam 36 and force sensing element 40 will exert an upward force on the 
beam. These forces will combine to rotate the beam in a counterclockwise 
direction, as viewed in FIG. 2, around pivot 42. If pivot 42 does not 
resist such rotation, then the temperature change will not result in any 
force being exerted by the force sensing elements and beam on proof mass 
30, and will therefore not result in a reaction force on the force sensing 
elements. The absence of a reaction force means that there will be no 
change in the output signals of the force sensing elements caused by the 
thermally induced movement. Furthermore, any net reaction force that does 
occur due to, for example, friction in pivot 42, will result in identical 
tension or compression forces on the force sensing elements that will 
cause the output signal frequencies of the transducers associated with the 
force sensing elements to be increased or reduced by approximately equal 
amounts. Referring to Equation (1) above, the frequency changes caused by 
the thermal expansion will tend to cancel, and as a result the 
differential thermal expansion will not cause significant errors in the 
measured acceleration. 
Connection points 44 and 46 are preferably selected such that for a given 
temperature change, the quotient of the length change of the force sensing 
element divided by the distance between pivot 42 and the connection point 
for that force sensing element is the same as the corresponding quotient 
for the other force sensing element. By making such quotients equal, a 
given differential thermal expansion between the force sensing elements 
and the other accelerometer components will not tend to cause 
translational movement of proof mass 30. Equality of the quotients can 
readily be achieved by making the force sensing elements identical to one 
another and by making the distances to the connection points equal. 
However, in many applications, it may be desirable to make such distances 
unequal and to use different force sensing elements, while preserving the 
quotients constant, in order to minimize cross talk between the force 
sensing elements. The above analysis may be generalized by defining a 
thermal expansion coefficient equal to the change in position of the force 
transducer or force sensing element at the beam connection point divided 
by the temperature change that caused the position change. In this 
formulation, the quotient that is preferably kept constant between the 
force transducers or force sensing elements is the thermal expansion 
coefficient divided by the distance between the force transducer 
connection point and pivot 42. 
A further consideration relating to the relative positions of the force 
sensing elements has to be with the stiffness of such elements. The 
stiffness of a force sensing element is equal to the force applied to the 
force sensing element along the sensitive axis divided by the resulting 
change of length of the force sensing element. Preferably, the product of 
the stiffness of each force sensing element multiplied by the distance 
between the center of mass of the proof mass plus beam and the connection 
point of the force sensing element is the same for both sensing elements. 
If such products are not the same, then the beam will tend to rotate in 
response to an acceleration along the sensitive axis. For most 
applications, it will be desirable to locate the center of gravity of the 
proof mass plus beam along compensation axis CA. 
A second embodiment of the present invention is illustrated in FIG. 3. The 
accelerometer of FIG. 3 includes proof mass 50 that is mounted to housing 
52 by flexure hinge 54. The proof mass is also connected to the housing by 
a coupling assembly that comprises beam 56 and force sensing elements 58 
and 60. Beam 56 is mounted to U-shaped bracket 62 at pivot 64 for 
rotational movement around compensation axis CA. Bracket 62 is in turn 
rigidly secured to housing 52. Arms 66 and 67 extend from proof mass 50 
parallel to compensation axis CA. Force sensing element 58 is connected 
between arm 66 and one end of beam 56 at connection point 68, and force 
sensing element 60 is connected between arm 67 and the other end of beam 
56 at connection point 69. Connection points 68 and 69 are spaced on 
opposite sides of pivot 64 from one another. Force sensing element 58 
extends upward from connection point 68 to arm 66 along sensitive axis SA, 
while force sensing element 60 extends downward from connection point 69 
to arm 67 along the sensitive axis. 
An acceleration along sensitive axis SA results in proof mass 50 exerting a 
tension force on one force sensing element and a compression force on the 
other force sensing element. The resulting compression and tension forces 
result in a net force on beam 56 that is preferably balanced with respect 
to pivot 64, such that beam 56 does not rotate in response to an 
acceleration. However, differential thermal expansion of the force sensing 
elements with respect to the other accelerometer components results in 
similar foces (tension or compression) exerted on beam 56 by the force 
sensing elements, which forces tend to rotate the beam about pivot 64. As 
with the accelerometer of FIG. 2, if such rotation does not result in a 
reaction force, the output of the accelerometer will not be affected. To 
the extent that friction in pivot 64 does resist rotation of beam 56, the 
result will be identical forces acting on the force sensing elements, 
which forces will tend to cancel as per Equation (1) above. 
As with the embodiment of FIG. 2, the quotient of the thermal expansion 
coefficient divided by the distance between pivot 64 and the connection 
point should be constant for the two force sensing elements. However, such 
coefficients and lengths may differ from one another, to reduce cross talk 
between the force sensing elements. The product of the stiffness times the 
distance between the pivot and the connection point is also preferably the 
same for the two force sensing elements. 
FIGS. 4 and 5 illustrate a particular and preferred embodiment of the 
invention illustrated in FIG. 2. In the embodiment of FIGS. 4 and 5, proof 
mass 70 is supported from housing 72 by flexure hinge 74. Two closely 
spaced cylindrical openings 76 and 78 are cut into the side of proof mass 
70 opposite flexure hinge 74, the openings beign parallel to compensation 
axis CA. Slots 80 and 82 are cut completely through proof mass 70 in a 
direction parallel to sensitive axis SA, the sensitive axis being normal 
to the plane of the drawing in FIG. 4. Slots 84-87 are cut partially into 
proof mass 70 parallel to the sensitive axis, each of slots 84-87 
extending between slots 80 and 82 from the upper or lower face of the 
proof mass to one of the underlying cylindrical openings. In particular, 
slot 84 extends from the upper surface 88 of the proof mass to opening 78, 
slot 86 extends from upper surface 88 to opening 76, slot 85 extends from 
lower surface 90 of the proof mass to opening 78, and slot 87 extends from 
lower surface 90 to opening 76. As a result of this configuration, beam 92 
is formed, beam 92 being connected to proof mass 70 at two aligned pivots 
or flexures, one pivot 94 being the material between openings 76 and 78 in 
the cross section shown in FIG. 5, and the other pivot being the material 
between openings 76 and 78 in a cross section (not shown) that intersects 
slots 85 and 86. Force sensing element 100 extends downward (as viewed in 
FIG. 4) from one end of beam 92 to housing 72, and a second force sensing 
element 102 extends upward from the opposite end of beam 92 to housing 72. 
The operation of the accelerometer illustrated in FIGS. 4 and 5 is 
identical to that described for the accelerometer of FIG. 2 above. 
FIGS. 6 and 7 illustrate a second particular embodiment of the invention 
illustrated in FIG. 2. In the embodiment of FIGS. 6 and 7, proof mass 110 
is supported from housing 112 by a pair of flexures 114 and 116. Proof 
mass 110 is in turn pivotally connected to pivot member 120, and the pivot 
member is connected to housing 112 through the force sensing elements 122 
and 124. In the fabrication of the illustrated accelerometer, proof mass 
110 and pivot member 120 are preferably fabricated from a single block of 
material. Two closely spaced cylindrical openings are first cut into the 
side of such block adjacent flexures 114 and 116, and then slot 130 is cut 
to form the proof mass and pivot member. Slot 130 includes outer sections 
132 and 134 that are cut completely through the block, and inner sections 
136, 138 and 140 that extend down to cylindrical openings 126 and 128. By 
reason of such slots and openings, pivot member 120 can rotate with 
respect to proof mass 110 about compensation axis CA. Force sensing 
elements 122 and 124 are connected to pivot element 120 at recesses 142 
and 144 respectively. The operation of the embodiment of FIGS. 6 and 7 is 
identical to the operation of the embodiment of FIG. 2 and of FIGS. 4-5. 
The accelerometer shown in FIGS. 6 and 7 illustrates that the pivot member 
can include the major fraction of the seismic mass of the accelerometer. 
While the preferred embodiments of the invention have been illustrated and 
described, it should be understood that variations will be apparent to 
those skilled in the art. Accordingly, the invention is not to be limited 
to the specific embodiments illustrated and described, and the true scope 
and spirit of the invention are to be determined by reference to the 
following claims.