Abstract:
A sensor of force or viscosity or other attributes of a fluid comprises a mechanical resonator ( 10 ) including an element ( 11; 18; 123 ) of which the stiffness at least partially determines a modal shape of the resonance of the resonator and means ( 21-23 ) for measuring a variation of a measure of the resonance as the stiffness of said element changes. The resonator ( 10 ) may comprise two beams ( 10   a,    10   b;    120, 121 ) connected at or near one end by a yoke ( 12; 122 ) which provides a clamped condition of the resonator at said one end and connected at or near another end by said element.

Description:
This invention is concerned with the use of a vibrating resonant structure for the measurement of physical and chemical properties of fluids and solids. 
   It is known to measure an attribute such as the density or viscosity of a medium, whether solid or fluid, by measuring some characteristic or parameter of vibration of a vibratile structure. Some examples which illustrate the general state of the art are shown in U.S. Pat. Nos. 5,023,560, 5,363,691 and 5,670,709. 
   The present invention is based on measuring vibration of amplitude, phase or frequency of a mechanical resonator as a result of a change in modal shape of a resonant system, caused for example by a change in stiffness of a beam element which form part of or is coupled to the resonator. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIGS. 1 and 2  illustrate beam resonators various resonant systems. 
       FIGS. 3 and 4  illustrate various resonant characteristics. 
       FIGS. 5  to  8  illustrate various beam resonators. 
       FIG. 9  illustrates a particular embodiment of the invention ( FIG. 9A ) and characteristics of its resonant modes (FIG.  9 B). 
       FIG. 10  illustrates a resonant characteristic. 
       FIG. 11  illustrates another embodiment of the invention. 
       FIG. 12  illustrates another embodiment of the invention. 
       FIG. 13  illustrates the embodiment shown in  FIG. 12  but vibrating in a different mode. 
       FIGS. 14   a  and  14   b  illustrate the change of a resonator from a ‘clamped-pinned’ state to a ‘clamped-free’ state. 
   

   DETAILED DESCRIPTION 
   Various embodiments are described by way of example to illustrate the principles employed in the invention. 
     FIG. 1  illustrates a beam resonator  10  comprising two substantially parallel beams  10   a  and  10   b  which are rigidly connected at their extremities. The connections of the beams at their extremities are substantial and yokes  11  and  12  thus formed at the extremities have a high stiffness. The beams are therefore referred to, in the terminology of modal beam analysis, as ‘clamped’. The vibration of the beams is denoted by the arrows Y. 
   Such a resonator, referred to herein as ‘clamp-clamp’, will resonate at a first mode natural frequency given by the equation:
 
 f =22.3733√{square root over ( )}( EI/ML   4 )  (1)
         f=Frequency   E=Young Modulus   I=Mass Moment of Inertia   M=Mass/Unit Length   L=Beam Length       

   If the connecting yoke  11  at one end of the resonator  10  is substantially weakened the beams can no longer be considered clamped, as they are allowed a degree of rotation about their connection point, in the terminology of modal beam analysis the yoke is then approaching the ‘pinned’ condition. This condition is shown in  FIG. 2 , and the ‘clamp-pinned’ system will now resonate at a natural frequency given by the equation: 
     f= 15.4182√{square root over ( )}( EI/ML   4 )  (2) 
   From equations (1) and (2) it can be seen that the transition from fully clamped to fully pinned results in an approximately 30% change in frequency. If the yoke connection is lost the beams are referred to as ‘free’, and the clamped-free system now resonates at a natural frequency given by the equation:
 
 f= 3.516√{square root over ( )}( EI/ML   4 )  (3)
 
   From equations (2) and (3) it can be seen that the transition from fully pinned to fully free results in an approximately 77% change in frequency. 
   In addition to a change in frequency, the modal shape of the clamp-clamp system differs significantly to that of the clamp-pinned arrangement. A generalised view of the displacement of the beam in clamped and pinned mode is shown in FIG.  3 . The curve  30  illustrates the variation in maximum displacement of the beam over its length when the yokes  11  and  12  are ‘clamped’. The curve  31  illustrates the corresponding displacement when the yoke  11  is ‘pinned’.  FIG. 4  shows the variation of local beam bending with respect to position along the beam for the clamp-clamp state (curve  40 ) and the clamp-pinned state (curve  41 ). There are further modal changes as the clamp-pinned condition progresses to clamped-free. 
   A sensor, such as a piezoelectric device, responding to localised beam flexure would exhibit a signal response with position along the length of the beam in a manner similar to the profiles shown in FIG.  4 . As well as a voltage amplitude variation with length there can also be observed a polarity change, or phase change, of the vibration signal along the length. 
   In summary, the transition from a clamp-clamp state to a clamp-pinned state, or from a clamp-pinned state to a clamp-free state results in changes in frequency, amplitude and phase of vibration relative to position on beam. It also follows that a change from clamp-clamp to clamp-free will obviously have a similar result. The measurement of change of these parameters in response to an event influencing the modal classification of the resonator (e.g. clamp-clamp to clamp-pinned, clamp-pinned to clamp-free) forms the basis of this invention. 
   In applications where there is depletion of a substance or build-up of material, such as corrosion or scaling, the actual substrate may form a stiffening member on the beam yoke and thus contribute to the status of the yoke as clamped or pinned. 
     FIG. 5  shows a simple embodiment of a dual beam system, similar to that shown in FIG.  1 . Depletion of material at the connection of the beams forming yoke  11  produces a thinner, less substantial connection as shown at  13  in FIG.  5  and can produce a change to a pinned state at this end of the resonator. However in general such a system would require significant depletion of material to manifest a modal change. 
   Improvements on this basic system are shown in FIG.  6  and  FIG. 7 ; in both these cases the simple connection yoke  11  is replaced by a box section  15 . The section achieves its stiffness from the spatially separated members  14  and  14   a,  and a small reduction of thickness of a part of either member  14 ,  14   a  will manifest a substantial change in rigidity—thus altering the stiffness of the section. 
     FIG. 6  particularly shows a system where in the rigidity of the box section is modulated by the longitudinal stiffness of the member  14 .  FIG. 7  shows the segments  16  and  17  between the members  14  and  14   a;  they will significantly influence the rigidity of section  15  if their flexural or longitudinal stiffness is altered. 
     FIG. 8  shows a refinement of the system in FIG.  6  and allows for a ‘bolt-on’ section stiffener  18  to be used to join the beams at the end in place of member  14 . The stiffener  18  is secured by bolts  19  to each of the beams  10   a  and  10   b,  This forms a convenient means of selecting the material, shape and size of a section member to suit a particular application. 
     FIG. 9A  illustrates a specific embodiment based on the system shown in  FIG. 8 , although in principle any of the systems previously described could be used. Piezoelectric transducers are strategically placed to indicate the amplitude and phase of the flexure of the beam at a specific location. The signal from each transducer relates directly to the modal pattern formed by the clamp or pinned condition of the yoke. Lateral vibration of the beam structure is shown by the arrows Y. 
   In the system shown in  FIG. 9A , piezoelectric transducers  21 ,  22  and  23  are disposed at different locations along the inner surface of the lower beam  10   b  in order to obtain a measure, represented by the relevant piezo output voltage, of the displacement of the beam at those locations when the system is in a resonant vibratory mode induced by a drive piezoelectric transducer  24  disposed (in this example) at the clamped end of the resonant beam system. In this system the transducer  23  acts as a reference, because it is located close to a node and the displacement of the adjacent part of the resonator is minimal. The drive transducer  24  may have a regenerative feedback connection (known per se in the art) from one or more of the sensing transducers  21 ,  22  or  23 . Electromagnetic drive and sensing transducers may be used in place of piezoelectric transducers. Other forms of transducer, such as capacitative, optical or acoustic transducers may be used as appropriate. 
     FIG. 9B  is a graph of piezo voltage against distance measured along the beam, the curves  90  and  91  being for the clamped and pinned condition respective at the end  11 . The particular piezo voltages are given by the intersections of the projection lines  21 ,  22   a  and  23   a  (through respective transducers  21 ,  22  and  23 ) with the curves  90  and  91 . 
   The embodiment shown in  FIG. 9  includes an enclosure  93  for the sensor, the enclosure comprising a tube which has a gland  94  for wires to pass to the transducers through a closed end of the tube. O-ring seals  95  and  96  are disposed between the beam structure  10  and the tube near the ends of the tube, from the open end of which the box section  15  protrudes. 
     FIG. 10  illustrates the variation of the piezoelectric voltages V a  and V b , from the sensors  21  and  22  (curves  101  and  102 ) and the frequency of resonance (curve  103 ), as a function of the decreasing stiffness of the section stiffener  18 . Curve  101  exhibits a phase change (shown at  104 ). The curve  100  shows the substantially constant piezo voltage V ref  obtained from the transducer  23 . It follows that the progress of any physical, chemical, or biological effect leading to the depletion or build-up of the sacrificial section stiffener material can be monitored by measuring the modulation or variation of these piezoelectric sensor signals over time. As an example, a section stiffener made from iron will have its thickness, and hence its stiffness depleted, in a corrosive environment over time and measurement of Va, Vb or frequency will indicate the rate of corrosion. It further follows that selection of other materials in the electrochemical series can exhibit the same corrosion/deposition effects in the appropriate electrolyte or reactive medium. 
   Signal processing techniques, such as the following, can be employed to enhance the result:
         (a) Division of Va by Vb will result in a ratio dependent on section stiffness but independent of amplitude of signals or system damping.   (b) Division of Va or Vb by Vref will result in a ratio dependent on section stiffness but independent of amplitude of signals or system damping.   (c) Measurement of phase of Vb will form a simple method of indicating the point at which a specific section stiffness is reached.   (d) A plurality of piezoelectric sensor mounted alone the beam can be monitored for change of phase to indicate progress of change of section stiffness.   (e) If the resonator is at fill temperature equilibrium with its environment the modal shape will indicate section stiffness independently of temperature.   (f) Frequency signal has some temperature dependency so comparison of modal shape with frequency signal will yield both temperature and section stiffness from a single resonator.       

   In general terms the invention can provide a force transducer. With the section stiffener removed as shown in  FIG. 11  (which otherwise resembles  FIG. 9 ) the stiffness of the pinned yoke will be altered towards the clamped state by the presence of external forces  111 ,  112  on the yoke, either in compression or tension. These forces can be mechanical, electrical or magnetic. 
   The movement of the beams  10   a  and  10   b  will create a velocity and therefore a shear action within a fluid. By measuring energy loss, or the quality factor Q, of the signal the viscous shear loss can be determined, and thus the fluid viscosity. Similarly, the damping capacity of any solid connected to the yoke can be determined from the Q of the resonant signal. 
   The elastic properties of a viscoelastic fluid can be derived from the change in resonant frequency due to the stiffening of the yokes a result of the elastic modulus of the fluid. 
     FIG. 12  illustrates sectionally a different embodiment in which the beam structure  10  comprises an internal cyclindrical beam  120  and an external cylindrical beam  121 . The beams are connected by a relatively thick yoke member  122  at a ‘clamped’ end and by a yoke member  123  at the other end. Reduction of the stiffness of this yoke  123  changes the connection at this end from ‘clamped’ to ‘pinned’. 
     FIG. 12  includes sensing transducers  21 ,  22  and  23  disposed on the external beam and a drive transducer  24  disposed on the yoke member  122 . The beam structure is enclosed by a tube  93  which has a gland  94  and intermediate O-ring seals  95  and  96 . 
     FIG. 13  is similar to  FIG. 12  but illustrates vibration of the structure in a longitudinal mode (arrow X). 
   As a further example,  FIGS. 14   a  and  14   b  shows the degeneration of a clamp-pinned structure  10  shown in  FIG. 14   a  to the clamp-free condition as the member  11  at one end vanishes The structure is clamped at its other end  140 . 
   All the resonators can be operated in harmonic modes above the natural frequency. There are proportional movements in modal/frequency behaviour at higher modes than a fundamental mode.