Abstract:
A quartz tuning fork is provided which may be employed in several instruments for measuring the properties of fluids. The tuning fork may be employed, for example, in a gravitometer, a barometer, an altimeter or a temperature sensor.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates to devices employing vibrating members, and more particularly to a vibration instrument for producing an output signal proportional to fluid density and/or for use in the computation of a fluid property. 
     PRIOR ART STATEMENT 
     Vibration gravitometers are known in the art. For example, see U.S. Pat. No. 3,934,127 issued Jan. 20, 1976. 
     Vibration instruments used in the fluid measurement field such as in gravitometry demonstrate a low accuracy and a low degree of stability, repeatability, linearity and resolution. 
     SUMMARY OF THE INVENTION 
     In accordance with the vibration instrument of the present invention, the above-described and other disadvantages of the prior art are overcome by providing tuning fork means as a component in a closed loop electromechanical oscillator. 
     The invention demonstrates a high accuracy and a high degree of stability, repeatability, linearity and resolution. 
     The accuracy of the present invention will be found to be two or three times better than that of the prior art (e.g. better 0.2 percent reading--95 percent confidence level). 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings which illustrate exemplary embodiments of the present invention: 
     FIG. 1 is a top plan view of a gravitometer constructed in accordance with the present invention; 
     FIG. 2 is a side elevational view of the gravitometer shown in FIG. 1; 
     FIG. 3 is a transverse sectional view of the gravitometer taken on the line 3--3 shown in FIG. 2; 
     FIG. 4 is a vertical sectional view of a portion of the gravitometer taken on the line 4--4 shown in FIG. 2; 
     FIG. 5 is a schematic diagram of the gravitometer shown in FIGS. 1-4; 
     FIG. 6 is a schematic diagram of a portion of the gravitometer shown in FIGS. 1-5; 
     FIG. 7 is a block diagram of a gravity computer for use with the gravitometer of FIGS. 1-6; 
     FIG. 8 is a block diagram of an alternative embodiment of a gravity computer constructed in accordance with the present invention; 
     FIG. 9 is a block diagram of a second alternative embodiment of a gravity computer constructed in accordance with the present invention; 
     FIG. 10 is a side elevational view of a structure which may be employed in accordance with the present invention in a barometer or an altimeter; 
     FIG. 11 is a barometer computer constructed in accordance with the present invention; 
     FIG. 12 is a block diagram of an altimeter computer for use with that shown in FIG. 11; 
     FIG. 13 is a side elevation view of temperature sensitive apparatus constructed in accordance with the present invention; and 
     FIG. 14 is a block diagram of a temperature computer constructed in accordance with the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In FIG. 1, a gravitometer is illustrated at 10&#39; having hollow cylinders 11&#39;, 12&#39; and 13&#39;. Cylinder 12&#39; is divided in half by an elastomeric diaphragm 14&#39;. 
     A gas of interest is admitted through a needle valve 15&#39; and vented through an orifice 16 (see FIG. 2). 
     The chamber on the other side of diaphragm 14&#39; is charged with air. 
     The chambers have amorphous quartz tuning forks 17 and 18 with quartz stems and temperature sensors 19 and 20. See FIGS. 2 and 3. 
     In FIG. 4, tuning fork 17 is fixed to a magnetostrictive post 21 having a drive coil 22 therearound wound on a spool 23. Post 21 is fixed to a base 24. 
     Base 24 has cap screw holes 25 so that base 24 may be fixed to cylinder 11&#39;. Base 24 also has an O-ring groove 26 and an O-ring 27 therein. 
     Passageways 28 and 29 are provided through post 21 and base 24 for lead wires 30 from a piezoelectric crystal 31. 
     Fork 17 has legs 32 and a bight portion 33 to which crystal 31 is fixed. 
     Coil 22 has leads 34 which extend through a conventional sealed passageway 35. 
     The arrangement of fork 18 (FIG. 2) may be identical to that shown in FIG. 4, if desired. 
     FIG. 5 is a diagrammatic of FIG. 2 and includes sensors 19 and 20, forks 17 and 18, gas valve 15&#39;, an air charging needle valve 36, a check valve 37, orifice 16 and diaphragm 14&#39;. Chambers 38 and 39 are sealed except as described herein. Diaphragm 14&#39; keeps the pressure in chamber 38 equal to that in chamber 39, and vice versa. 
     Forks 17 and 18 are vibrated. They form parts of two electromechanical oscillators as shown in FIG. 6. The contents of chamber 38 shown in FIG. 6 has already been described. The contents of chamber 39 in FIG. 6 may, if desired, be identical to that shown in chamber 38 in FIG. 6. In chamber 39 an air driver or coil 22&#39; is provided to vibrate fork 18. Fork 18, in turn, has a crystal 31&#39; which may be identical to crystal 31. 
     Essentially identical conventional phase locked loops are provided at 40 and 41 in FIG. 6, if desired. Phase locked loop 40 has a preamplifier 42, a phase detector 43, a low pass filter 44, a voltage controlled oscillator (VCO) 45, and a power amplifier 46 connected from crystal 31&#39; to driver 22&#39;. Alternatively, phase locked loops 40 and 41 may be conventional divider operated frequency multipliers. 
     Similarly, phase locked loop 41 has a preamplifier 47, a phase detector 48, a low pass filter 49, a VCO 50 and a power amplifier 51. 
     Loops 40 and 41 have output leads 52 and 53, respectively, that have signals thereon of frequencies f a  and f g , respectively. 
     Sources 19 and 20 have signals T gl  and T al  on output leads 54 and 55, respectively, proportional to the temperatures (e.g. in Farenheit or Centigrade) in chambers 38 and 39, respectively. 
     The density of air in chamber 39 (FIG. 5) is D a  defined thus: ##EQU1## 
     Where A a  and B a  include values related to compressibility z a  and gas constant R a . A a  and B a  are, by calibration, derived from the known equation: 
     
         PV=MZRT                                                    (2) 
    
     where 
     P is absolute pressure, 
     V is volume, 
     M is mass, 
     R is the gas constant, 
     T is absolute temperature and 
     Z is compressibility. 
     A a  and B a  are constants derived empirically in a known way described in U.S. Pat. No. 3,677,067 issued July 18, 1972. 
     Similarly, the density D g  of the gas in chamber 38 is: ##EQU2## where A g  and B g  are constants derived in the same way. 
     In the special case of chambers 38 and 39, and diaphragm 14&#39;, the pressures in chambers 38 and 39 are equal because diaphragm 14&#39; is flexible, elastic or rubber or the like. 
     
         If T.sub.g =T.sub.gl +T.sub.o                              (4) 
    
     
         and T.sub.a =T.sub.al +T.sub.o                             (5) 
    
     from (1) and (3), gravity G is: ##EQU3## where temperatures T gl  and T al  are sensed at 19 and 20 in FIG. 5, respectively. 
     Apparatus shown in FIG. 7 is an analog (but may be digital) computer that computes gravity according to equation (6). 
     In FIG. 7, inputs D a  (T al  +T o ) and D b  (T gl  +T o ) are supplied from a computer 54 to a divider 55 connected to a utilization device 56, which may be an indicator. 
     Computer 54 develops D a  (T al  +T o ) by squaring f a  at squarer 57, developing A a  /f a   2  by source 58 and divider 59, then developing (1) equal to D a  with the use of source 60 and adder 61 (all analog adders may be adders or substractors because subtraction merely requires a negative, positive, reverse voltage or otherwise). 
     The output of adder 61 is then D a . The term (T al  +T o ) is developed by source 62 and adder 63. The output of adder 63 is multiplied by D a  by multiplier 64. 
     The term D a  (T gl  +T o ) is computed in exactly the same way as D a  (T al  +T o ) by the use of squarer 65, sources 66, 67 and 68, divider 69, adders 70 and 71, and multiplier 72. 
     In FIG. 8, a correction is made for the temperature sensitivities of D a  and D g . Computer 54&#39; may be identical to computer 54. Sources 73, 74, and 75, adders 76 and 77, and multiplier 78 develop the term (1+K a  ΔT al ) where K a  is the thermal coefficient of air density and ΔT a1  is the change in temperature from a known reference temperature at which the density error is zero (e.g. zero degrees F. or zero degrees C.). 
     The term (1+K g  ΔT gl ) is developed exactly the same way through the use of sources 79, 80 and 81, adders 82 and 83, and multiplier 84. 
     A multiplier 85 produces a signal directly proportional to: 
     
         D.sub.a (1+K.sub.a ΔT.sub.al)(T.sub.al +T.sub.o)     (8) 
    
     A multiplier 86 produces a signal directly proportional to: 
     
         D.sub.g (1+K.sub.g ΔT.sub.gl)(T.sub.gl +T.sub.o)     (9) 
    
     Term (9) is divided by term (8) in a divider 87 to give G. 
     In any embodiment of the present invention, whether or not described herein, computations may all be or in part be performed by analog or digital computers. Signals f a  and f g  are in digital form to begin with and digital computers may be employed, if desired. 
     An indicator 56&#39; may be employed the same as or different from device 56 (FIG. 7). Further, device 56 may be any indicator or may be a process controller or otherwise. The same is true of any utilization or other device disclosed herein. 
     In FIG. 9, computer 54&#34; may be identical to computer 54&#39;, if desired. Indicator 56&#34; may also be identical to indicator 56&#39;. The embodiment of FIG. 9 can correct for errors in densities D g  and D a  due to changes in temperature. 
     If T ro  is a reference temperature: 
     
         ΔT.sub.al =T.sub.al -T.sub.ro                        (10) 
    
     
         ΔT.sub.gl =T.sub.gl -T.sub.ro                        (11) 
    
     from FIG. 8: ##EQU4## However, if, as they usually do: 
     
         K.sub.a ΔT.sub.al &lt;&lt;1                                (13) 
    
     
         K.sub.a ΔT.sub.gl &lt;&lt;1                                (14) 
    
     and it is possible 
     
         K.sub.a =K.sub.g =K                                        (15) 
    
     then, combining (11), (12) and (13) ##EQU5## 
     The arrangement of FIG. 9 calculates gravity according to (16). 
     Computer 54&#34; computes D g  (T gl  +T o ) and D a  (T al  +T o ). 
     The adder 88 produces (T gl  -T al ). Source 89 and multiplier 90 develop K(T gl  -T al ). 
     Source 91 and adder 92 develop [1+K(T gl  -T al )]. 
     Multiplier 93 develops: 
     
         [D.sub.g ]1+K(T.sub.gl -T.sub.al)][T.sub.gl +T.sub.o ]     (17) 
    
     Divider 94 develops G according to equation (16). 
     A device 95 is shown in FIG. 10 which may be employed in a barometer or altimeter. A bell jar 96 or the like is hermetically sealed except that it is vented through a desiccator 97 to the atmosphere. An amorphous or other quartz tuning fork is shown at 98 with a temperature sensor 99. Fork 98 is vibrated as before. 
     In FIG. 11, the barometric system is shown including chamber 96, a squarer 100, a divider 101, and an adder 102 connected in that order to a multiplier 103. Sources 104 and 105 are connected to divider 101 and adder 102, respectively. Phase locked loop 100&#39; may be of the type shown in FIG. 6 at 40 or 41. 
     Temperature signal T p  is impressed upon adder 106 and thence through multiplier 107 and adder 108 to multiplier 103. 
     Sources 106&#39;, 109 and 110 are connected to multiplier 107 and 108, respectively. 
     Temperature signal T p  proportional to the temperature inside bell jar 96 is also supplied to multiplier 103 through an adder 111. 
     Source 112 is connected to adder 111. 
     The pressure P p  in chamber 96 is then computed in FIG. 11 thus: ##EQU6## where D p  is equal to density, i.e. ##EQU7## 
     A p , B p  and K p  are constants, 
     T p  is a change in temperature, 
     (T p  +T o ) is absolute temperature, and 
     Z is the supercompressibility of air. 
     An indicator 113 is connected from multiplier 103. 
     An indicator 114 in FIG. 12 utilizes output signal P p  in FIG. 11 to produce altitude y in an altimeter. 
     Circuits 115 and 116 are natural or Napierian logarithmic function generators. 
     Source 117 produces a constant output P o  of a reference altitude pressure (e.g. sealevel). 
     Adder 118 adds as a subtractor to give: ##EQU8## from inputs: 1n P p                                    (20) 
     and: 
     
         1n P.sub.o                                                 (21) 
    
     Source 119 produces constants: ##EQU9## where 
     D o  is a constant reference density, and 
     g is acceleration due to gravity. 
     Thus from FIG. 12, ##EQU10## where P p  is defined in (18). 
     An air-tight bell jar having a vacuum therein is shown at 120 in FIG. 13. A member 121 provides a conductive path to a quartz tuning fork 122, whereby temperature may be detected and/or indicated. 
     One temperature indicator is shown at 123 in FIG. 14. Chamber 120 is connected thereto via phase locked loop 124, a squarer 125, a multiplier 126, an adder 127, and an adder 127&#39;. Sources 128, 129 and 123&#39; are connected to multiplier 126, adder 127 and adder 127&#39;. 
     The system of FIG. 14 computes temperature T x  as where: ##EQU11## 
     A and B are constants. 
     Phase locked loops 40 and 41 in FIG. 6 may be converted to frequency multipliers by the additions of dividers as is well known. 
     The phrase &#34;computer means&#34; is hereby defined for use herein and in the claims to include either analog or digital computer means, the same being equivalent for use herein. 
     In FIG. 13, ##EQU12## where 
     f is frequency, 
     (bt 3  /12) is the moment of inertia of a fork leg, 
     E is Young&#39;s modulus, 
     K e  is the temperature coefficient of the modulus, 
     K L  is the temperature coefficient of the fork leg length, 
     
         ΔT.sub.x =T.sub.x -T.sub.o                           (26) 
    
     W is leg width, 
     L is leg length. 
     
         If 3K.sub.L ΔT&lt;&lt;1                                    (27) 
    
     and: 
     
         K.sub.e ΔT&lt;&lt;1                                        (28) 
    
     then: 
     
         (1+K.sub.L ΔT.sub.x).sup.3 ≈(1+3K.sub.L ΔT.sub.x) (29) 
    
     Thus: 
     
         f.sup.2 =A(1+BΔT.sub.x)                              (30) 
    
     where ##EQU13## 
     Equation (29) from (26) and (27) may be written: 
     
         B=K.sub.e -3K.sub.n                                        (32) 
    
     and: ##EQU14## 
     All constants A, B and K with any one or more subscripts may be determined by an empirical calibration. 
     The general form of density D, with constants and variables of any subscripts is: ##EQU15## where: 
     f is directly proportional to the frequency of vibration of the tuning fork, and 
     A and B are empirically derived constants. 
     In prior equations, K o  may be defined as: 
     
         K.sub.o =K.sub.e -3K.sub.1                                 (37). 
    
     The words or equivalents of &#34;fork immersed in a fluid&#34; is hereby defined for use herein and in the claims to mean &#34;immersed in a gas or immersed in a liquid.&#34;