Vibrator type densitometer

A densitometer of the vibrator type is disclosed wherein a spring mass system is immersed in a liquid whose density is to be determined. The system includes a pair of coaxial cylindrical masses in the form of fluid couplers having spaces which are open to the liquid. A torsion spring connects both cylindrical masses through mechanically stiff coupling means. The coupling means include a pair of high impedance transducers positioned at the shear interfaces normal to the common axis of the system, so as to take substantially the full torsional shear load between the spring and the cylindrical fluid couplers without contributing to the spring effect. The compliance of the torsion spring allows oscillatory motion of the spring mass system around its axis. An output signal having a high signal-to-noise ratio is provided at the natural resonant system frequency. The signal frequency is a measure of the density of the liquid contained in the spaces and it is substantially independent of the effect of temperature changes on the transducers. Thus, a highly sensitive and accurate densitometer is provided.

The present invention relates in general to new and improved densitometers 
and in particular to a densitometer of the vibrator type which measures 
the density of the substance in which it is immersed. 
BACKGROUND OF THE INVENTION 
Densitometers of the vibrator type which are immersed in a liquid or other 
substance whose density is to be measured are known in the art. Such 
instruments have been developed for various uses and are exemplified by 
the liquid densitometer disclosed in U.S. Pat. No. 4,129,031 to Stephen W. 
Tehon et al, which is assigned to the assignee of the present application. 
As shown in the patent, a pair of cylinders, positioned on a common axis, 
is attached to opposite ends of a compliant torsion spring supported at 
its nodal point intermediate the spring ends. Each cylinder has 
structurally defined spaces through which the ambient liquid may pass when 
the spring mass system is immersed therein. 
First and second pairs of transducers are positioned near the opposite ends 
of the spring. Each transducer is capable of converting between different 
forms of energy or energy domains, i.e. from stored potential energy 
produced by the physical distorsion of the transducer, to electrical 
energy and vice versa. The application of a first electrical signal to the 
first transducer pair produces distortion in each of these transducers, 
which is transmitted through the spring to the second transducer pair. The 
second transducer pair responds by generating a second signal whose 
amplitude and polarity depends on the magnitude and direction of the 
distortion of these transducers. The second signal is amplified and 
applied to the first transducer pair so as to set up a regenerative loop 
which oscillates at the natural resonant frequency of the spring mass 
system. Since the liquid contained in the cylinder spaces of the immersed 
apparatus is part of the overall spring mass system, the frequency of 
oscillation is a measure of the density of the liquid in the spaces. 
While the system disclosed in the referenced patent represents a 
substantial advance in the densitometer art over systems theretofore 
available for carrying out such measurements, it nevertheless includes 
areas susceptible of further improvement. Thus, the size of the 
transducers is determined by the dimensions of the torsion spring, which 
is seen to be a compliant bar. The size of the bar is determined by the 
desired parameters of the spring mass system and its cross-sectional 
dimensions must generally be kept small. The transducers are therefore 
likewise limited in size and hence their impedance is low. This results in 
a low signal-to-noise ratio which is improved somewhat by using a pair of 
transducers at each spring end. The manner in which the transducers are 
positioned on the bar spring subjects them to only a portion of the 
torsional load to which the bar spring itself is subjected. Thus, the 
position of the transducers in the instrument shown in the referenced 
patent is another factor which contributes to keeping the maximum 
obtainable output signal small. 
In a practical example of a densitometer of the type shown in the patent, 
the impedance of a single transducer was on the order of 50 pf. The 
obtainable output signal is correspondingly low, e.g. around 50 mv when 
the transducer is driven at 20 volts peak-to-peak. Thus, under high noise 
condition, for example when the densitometer measures the density of the 
fuel in the wing fuel tank of an aircraft, the low signal-to-noise ratio 
may affect closed loop performance. 
Another such area in prior art densitometers of the type under discussion 
here arises from the fact that the transducers contribute to the spring 
effect by being directly positioned on the spring. Since the transducer 
modulus of elasticity is sensitive to temperature changes, the spring 
modulus of elasticity will then also vary with temperature. If the 
temperature range to which the instrument is subjected varies widely, e.g. 
from -50.degree. C. to +60.degree. C. when the densitometer is used in 
aircraft in the manner discussed above, the accuracy of the instrument 
over the total temperature range may be affected. Experience with some 
prior art vibrator type densitometers has shown that the instrument error 
for the temperature range given above may be on the order of +4%. For 
critical measurements it is desirable to reduce this margin of error. 
A further factor which must be kept in mind with respect to such 
instruments is the inherent brittleness of the transducer material. The 
transducers typically consist of piezoelectric ceramic material, such as 
lead zirconate titanate or the like, and they are preferably manufactured 
in flat shapes for reasons of cost as well as structural stability. Where 
a more intricate shape is required, such as is the case in instruments of 
the type shown in the patent, the fabrication costs rise correspondingly. 
OBJECTS OF THE INVENTION 
It is a primary object of the present invention to provide a vibrator type 
densitometer which is free from the disadvantages of prior art 
instruments. 
It is another object of the present invention to provide a submersible 
vibrator type densitometer of improved accuracy. 
It is a further object of the present invention to provide a submersible 
densitometer of the vibrator type which is capable of providing a high 
signal-to-noise ratio. 
It is still another object of the present invention to provide a 
submersible densitometer of the vibrator type which is relatively immune 
to temperature variations. 
It is still another object of the present invention to provide a 
submersible instrument for measuring the density of an isotropic 
substance, wherein the geometry of the transducer shape is optimized to 
reduce the cost of manufacture. 
These and other objects of the invention, together with the features and 
advantages thereof, will become apparent from the following detailed 
specification when read in conjunction with the accompanying drawings of a 
preferred embodiment of the invention.

With reference now to the drawings, a preferred embodiment of the 
densitometer which forms the subject matter of the present invention is 
illustrated in FIGS. 1 through 3. In FIG. 1 the complete instrument, 
designated by the reference numeral 8, is shown and is seen to comprise a 
mass assemblage which consists of a pair of mass configurations. More 
specifically, the structure consists of a torsional spring, dual fluid 
couplers and dual piezoelectric ceramic elements. In the preferred 
embodiment of the invention, the fluid couplers take the form of 
cylindrical sleeves 10A and 10B, positioned on a common axis 12 and spaced 
from each other. As shown, sleeves 10, as well as other portions of the 
illustrated apparatus, form substantially identical, symmetrically 
positioned portions of a torsional spring mass system which are designated 
`A` and `B` respectively. For the sake of simplicity, the reference 
numerals bear A and B suffixes only when necessary to distinguish a 
component from its opposite counterpart. In order to illustrate the 
invention with greater clarity, different component parts of the identical 
A and B portions are shown in phantom outline in FIG. 1. 
As best shown in FIGS. 2 and 3, each sleeve has an outer and inner 
perimeter 14 and 16 respectively, the latter defining a hollow coaxial 
space within the sleeve. Each sleeve includes a plurality of structurally 
defined spaces 18, which take the form of identical numbers of cylindrical 
holes in the illustrated embodiment. All holes 18 extend completely 
through sleeves 10A and 10B respectively, in a direction parallel to axis 
12. For the sake of clarity of illustration, only some of the holes in 
sleeve 10A are so illustrated in FIG. 1. It is preferred to construct each 
sleeve of a pair of radially spaced cylindrical walls 15 and 17 and to 
position cylindrical tubes 19 therebetween to form holes 18. The tube 
structure thus defines further spaces 21 which likewise extend completely 
through each sleeve. The liquid or other isotropic substance in which the 
instrument is immersed is therefore able to enter and pass through spaces 
18 and 21 without obstruction to provide the desired coupling between the 
sleeve and the fluid. In an alternative embodiment, each sleeve 10 may be 
formed of a solid material between its outer and inner perimeters 14 and 
16 respectively. In the latter case, holes 18 are bored or otherwise 
formed in the solid material, parallel to the axis. In either form of 
construction, each sleeve has a precisely determined fixed moment of 
inertia, as determined by its mass and its radius, to which is further 
added the small moment of inertia of hub 38. Since the fluid coupling of 
the sleeve is determined by the configuration of the sleeve, there also 
exists a fixed relationship for any particular fluid between sleeve 
inertia and the inertia of the fluid coupled thereto. 
A torsion spring is coupled to sleeves 10A and 10B and takes the form of a 
coaxially positioned hollow tube in the preferred embodiment, having a 
predetermined torsional spring constant. A single compliant tube is shown 
in the drawings, having symmetrical halves on opposite sides of a nodal 
mount 22 which is integral with the tube. Alternatively, a pair of 
separate compliant tubes may be fastened to opposite sides of the nodal 
mount. The mount itself is seen to be disc-shaped in form. The plane of 
the disc lies in a plane normal to axis 12 and is centrally positioned 
between opposite ends of spring 20. The rim of disc-shaped nodal mount 22 
is concave, as shown at 24, adapted to accept an O-ring 26. The nodal 
mount itself is adapted to be held in position between the clamping 
portions of a mounting fixture which forms no part of the present 
invention. Thus, the entire spring mass system is adapted to be supported 
solely by its nodal mount so as to be free to oscillate around axis 12. 
The densitometer is preferably held in an upright position so that bubbles 
in the liquid in which the instrument is immersed are purged. 
The opposite ends of the tube which constitutes torsion spring 20 each 
comprise an integral flange 28. Each flange includes a flange surface 30 
substantially normal to axis 12 and concentric therewith, which faces 
outward from the centrally located nodal mount 22. Each spring end further 
includes a shaft 32 integral with flange 28 and extending axially outward 
from flange surface 30. Shaft 32 terminates in a externally threaded shaft 
portion 34 adapted to accept a threaded nut 36. 
Each cylindrical sleeve 10 is supported on a coaxial hub 38 which is either 
integral with the sleeve, i.e. integral with cylindrical wall 17 thereof, 
or fast therewith. Each hub is located within the hollow space defined by 
inner perimeter 16 and it includes a bonding surface 40. The latter 
surface is substantially normal to axis 12 and concentric therewith and it 
faces inward toward the nodal mount. Thus, at each end of torsion spring 
20 a pair of mutually facing surfaces 30, 40 is located. Hub 38 further 
includes an axial bore 46 of a diameter adapted to make a sliding fit with 
shaft 32. Bore 46 extends completely through hub 38, including the 
aforementioned bonding surface 40. 
Each cylindrical sleeve 10, together with its associated hub 38, forms a 
discrete mass configuration within the overall torsional spring mass 
system, which has its center of gravity positioned on axis 12. Each of 
these mass configurations is connected to torsion spring 20 by means of a 
mechanically stiff coupling that includes a thin, flat, disc-shaped, 
ceramic transducer 42. Each transducer 42 has a thickness of the order of 
0.050" and an axial bore adapted to accept shaft 32. Further, each 
transducer is metalized on each face and is fastened to its corresponding 
bonding surface 40 on hub 38 by means of a bonding agent such as solder, 
epoxy or the like, which establishes a substantially rigid bond between 
the transducer and the bonding surface. A thin, flat washer 48, which is 
substantially coextensive with its corresponding transducer, is interposed 
between the latter and each flange surface 30. Each washer preferably 
consists of a ceramic insulating material, metalized on each face and 
having an overall thickness of the order of 0.050". The washers are bonded 
in a manner similar to transducers 42. In the preferred embodiment of the 
invention each washer is undercut as shown in FIG. 2, to allow room for an 
electrical interconnection to the high voltage side 45 of each 
piezoelectric transducer 42. The interconnection path leads via hole 43 
and slot 44 to remote electronic circuitry illustrated in FIG. 4. 
Internally threaded nut 36, which engages the threaded shaft end 34, urges 
the contacting hub 38 in the direction of flange surface 30 to place 
transducer 42 and washer 48 under compression therebetween. Nut 36 is 
tightened sufficiently to maintain a compressive load on transducer 42 and 
on washer 48 under all load conditions. Thus, a mechanically sound and 
torsionally stiff coupling is established between flange 28 and hub 38 and 
hence between torsion spring 20 and each cylindrical sleeve 10. Stated 
differently, the natural resonant frequency of the coupling is very high 
with respect to the natural torsion resonant frequency of the spring mass 
system. Such mechanical stiffness requires that the component parts of 
each coupling, i.e. transducer 42 and washer 48, be selected to be 
individually mechanically stiff, i.e. to have a high natural resonant 
frequency with respect to the torsion frequency of the spring mass system. 
In the present context where stiffness is considered with respect to 
resistance to torsion, such stiffness is a function of the torsion modulus 
of elasticity of the materials of the transducers and washers 
respectivley, as well as their diameters. In a preferred embodiment of the 
invention, transducers 42 consist of a piezoelectric ceramic material and 
washers 48 consist of an alumina ceramic material. Both have a large 
enough diameter to be substantially stiff relative to the torsional 
stiffness of torsion spring 20. 
Each transducer is capable of converting between the respective domains of 
electrical signal energy and potential energy, the latter being created by 
the deformation of the transducer. As will become clear from the 
discussion below, one of the transducers, i.e. sensing transducer 42A, is 
used in a manner whereby it provides an electrical signal whose amplitude 
and polarity depend on the magnitude and direction of the torsional 
distortion of the transducer. Driving transducer 42B provides torsional 
distortion corresponding in magnitude and direction to the amplitude and 
polarity of a signal applied to this transducer. 
FIG. 4 illustrates a preferred measuring circuit which utilizes the 
instrument shown in FIGS. 1 through 3. Densitometer 8 is shown with 
sensing transducer 42A and driver transducer 42B positioned at opposite 
ends of torsion spring 20. These transducers form the electrical output 
and input respectively of the instrument. The output of sensing transducer 
42A is connected to the input of an amplifier 50 and is adapted to apply a 
voltage thereto referenced to ground. Amplifier 50, which further receives 
a B+ voltage, has its output connected to the input of driver transducer 
42B in a manner adapted to form a regenerative loop. The amplifier output 
is further connected to a frequency meter 52. 
In operation, when a voltage is applied to the terminals of driver 
transducer 42B, the latter undergoes torsional distortion around axis 12. 
The magnitude and direction of this distortion correspond to the amplitude 
and polarity respectively, of the signal applied to transducer 42B. In a 
practical embodiment of the invention, the distortion was less than one 
milliradian for an applied voltage of 10 volts peak to peak. Since 
transducer 42B is fastened to one of hubs 38 by way of bonding surface 40, 
the distortion of the transducer results in an angular displacement of 
mass configuration B, i.e. sleeve 10B and its corresponding hub. Such 
displacement imparts angular acceleration to mass configuration B and 
causes torsion spring 20 to twist with respect to nodal mount 22. This 
dynamic action serves to apply a torsional shear torque to sensing 
transducer 42A, which provides a responsive signal corresponding in 
amplitude and polarity to the magnitude and direction respectively, of the 
applied torque. As stated above, the signal provided by transducer 42A is 
amplified and is regeneratively applied to transducer 42B to produce 
oscillation of the overall spring mass system. The gain of amplifier 50 is 
selected to sustain this oscillation of the system at its natural resonant 
torsion frequency. 
As stated above, the mass of each sleeve 10 (which includes the mass of hub 
38), together with the sleeve radius, determines the moment of inertia of 
the sleeve and is precisely determined. When the sleeve is immersed in a 
fluid or other isotropic substance, the resultant moment of inertia 
includes whatever portion of the fluid is coupled to the sleeve, i.e. the 
fluid contained in the structurally defined spaces 18 and 21 of each 
cylinder, or in spaces 18 only where the alternative configuration is 
used. The portion of the fluid contained in these spaces thus forms part 
of mass configurations A and B respectively, which jointly constitute the 
overall spring mass system together with torsion spring 20. The ratio of 
fluid mass to sleeve mass is selected as large as possible, but it is 
limited by practical considerations. In an actual embodiment of the 
invention this ratio was approximately 1:4. Since the mass of the fluid 
contained in spaces 18 and 21 is a function of fluid density, the latter 
directly affects the natural resonant frequency of oscillation of the 
system. Thus, the frequency measured by frequency meter 52 is a direct 
function of the density of the liquid in which the instrument is immersed. 
As best shown in FIG. 3, each transducer 42 comprises a disc-shaped, flat 
wafer with an axial opening adapted to receive shaft 32. The area of the 
disc is seen to be relatively large. Since electrical impedance varies 
directly with area, transducer 42 presents a relatively high impedance 
which minimizes circuit loading attenuation effects. As a consequence, the 
output signal provided is high compared to that obtainable in prior art 
apparatus. In an actual embodiment of the invention, transducer impedance 
was on the order of 500 pf. When the transducer was driven 10 volts 
peak-to-peak and a 1 megohm load was used, a 7 volt peak-to-peak output 
signal was obtained. By comparison, prior art instruments of the type 
shown in the aforesaid patent have a transducer impedance of the order of 
50 pf. Using the same load resistance, a maximum output signal no greater 
than 50 millivolt is obtainable for a 20 volt peak-to-peak excitation. If 
the noise coupled through to the signal remains substantially constant as 
the signal increases in amplitude, the larger output signal obtainable 
with the present invention provides a higher signal-to-noise ratio. Thus, 
the closed loop stability of the instrument is high. A still higher output 
signal level is possible by scaling up the dimensions of the respective 
component portions of the instrument shown in FIGS. 1 through 3. 
Alternatively, the geometry of the instrument with respect to the location 
of the hub may be rearranged so that bonding surfaces 40 are positioned 
clear of sleeves 10 in an axial direction. In such an arrangement the area 
of the transducer disc may be increased without changing the dimensions of 
the other parts of the configurations. 
Since transducer impedance varies inversely with transducer thickness, it 
is desirable to keep the latter dimension small. In prior art 
densitometers of the kind shown in the above-referenced patent, this is 
possible only to a point due to the nature of the transducer 
configuration, the exposed position of the transducer and the inherent 
brittleness of the transducer material. It is a feature of the present 
invention to provide an instrument in which the transducers take the form 
of thin flat wafers. With such a transducer shape a much smaller thickness 
dimension is possible, notwithstanding the brittleness of the material. 
Moreover, since the transducer is axially loaded as threaded nut 36 is 
tightened against hub 38, the vulnerability of the densitometer through 
damage to the transducers is greatly reduced. It must also be kept in mind 
that the axial compression of the transducer reduces the chance of cracks 
developing in the transducer material. Thus, for a given thickness, 
restrictions on the size of the transducer area are either eliminated or 
minimized in the present invention. Of equal importance is the 
considerable reduction in the cost of manufacture of the transducers, 
owing to their greatly simplified configuration. 
In the present invention, the position of each transducer is such that it 
takes substantially the full torsional shear load between the 
corresponding sleeve 10 and torsion spring 20. Therefore, as compared to 
prior art instruments, transducer distortion is maximized upon oscillation 
of the spring mass system. Hence, the obtainable output signal is further 
increased as a consequence of transducer position alone. 
As previously explained, the stiffness of the transducer, i.e. its natural 
resonant frequency, is high compared to that of the torsion spring. This 
property, coupled with the position of the transducer between the spring 
and each mass configuration, assures that the transducer acts only as a 
stiff intervening layer without contributing materially to the torsional 
spring effect. Thus, whatever the sensitivity to temperature changes of 
the piezoelectric ceramic transducer material may be, it has no 
significant effect on the spring. In a practical embodiment of the 
invention, using typical aircraft fuels, the error due to temperature 
sensitivity of the instrument was reduced to less than 1% of full scale 
over a temperature range from -50.degree. C. to +60.degree. C. 
Various modifications of the disclosed apparatus are feasible within the 
scope of the present invention. For example, the torsion spring need not 
be a compliant tube and may take a number of other forms. Further, as 
discussed above, various changes of the geometry of the disclosed 
apparatus may be made for the purpose of increasing the transducer area 
and hence transducer impedance. Such modifications may be carried out 
without detriment to the other features and advantages of the present 
invention, such as transducer positioning to carry substantially the full 
torsional shear load while remaining substantially stiff relative to the 
spring effect of the system; axial compression loading of the transducers 
which permits the use of a thin wafer of the brittle transducer material 
having a large surface area; the use of a simple transducer configuration 
in order to reduce manufacturing costs; etc. 
From the foregoing discussion of a new and improved densitometer of the 
torsional vibrator type, it will be apparent that numerous variations, 
modifications, changes and equivalents will now occur to those skilled in 
the art, all of which fall within the spirit and scope of the present 
invention. Accordingly, it is intended that the invention be limited only 
by the scope of the appended claims.