Abstract:
A high strength, high frequency acceleration transducer is used for measuring the acceleration of an impacted machine or structure. The acceleration transducer includes a diaphragm, the diaphragm including one or more strain gages for producing an output signal indicative of the transducer flexure. The diaphragm is securely clamped or held over part of its surface, and is free to deflect over other parts, for example, the remainder of its surface—the diaphragm can be clamped or held along its circumference with its middle free to flex, or alternatively the diaphragm can be clamped or held along its center with the outside portion of the diaphragm free to flex. The diaphragm preferably includes one or more holes positioned relative to the strain gages to concentrate the strains locally within the diaphragm towards the strain gages. Due to the small size, profile, shape, and configuration, the acceleration transducer is able to withstand high impact forces and reliably to measure acceleration without being damaged and while avoiding resonance or the like which would degrade the output signal from the strain gages.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of U.S. Provisional Application No. 60/065,948 filed Oct. 27, 1997. 
    
    
     TECHNICAL FIELD 
     The present invention relates to acceleration transducers and, more particularly, to acceleration transducers for measuring acceleration resulting from impact loading such as can occur in pile driving, impact forming or explosion. The invention is useful in a variety of applications, from slow vibratory applications to impact response applications. An exemplary embodiment of the invention is particularly useful for measuring steel-on-steel impact. 
     BACKGROUND OF THE INVENTION 
     Accelerometers for measuring impact behavior must exhibit a high capacity for measuring magnitude and a wide frequency range to capture the full range of signal. 
     It is desirable that the accelerometer have a first resonant frequency in excess of 20 kilohertz (KHz), thereby allowing it to capture the important components of the stress-wave signal. Consequently, the accelerometer needs to be very rigid and small in size to possess the desired resonant frequency. 
     There is a strong need in the art for a means for evaluating acceleration resulting from impact loading. In particular, there is a strong need in the art for an accelerometer which is better able to withstand the high impact forces involved in acceleration such as impact forming or blanking and which measures the acceleration and velocity of the tool while still providing a low noise output. This is in contrast to larger strain gage devices and accelerometers used in the prior art which have been found to encounter substantial resonance and other signal degrading conditions making it difficult to measure the acceleration characteristics of a machine under the high impact conditions to which it is exposed. 
     SUMMARY OF THE INVENTION 
     According to the present invention, a high strength, high frequency acceleration transducer is used for measuring the acceleration of an impacted machine or structure. The acceleration transducer includes a diaphragm, the diaphragm including one or more strain gages for producing an output signal indicative of the diaphragm flexure. The diaphragm is securely clamped or held over part of its surface, and is free to deflect over other parts, for example, the remainder of its surface—the diaphragm can be clamped or held along its circumference with its middle free to flex, or alternatively the diaphragm can be clamped or held along its center with the outside portion of the diaphragm free to flex. The diaphragm preferably includes a strain concentration mechanism to concentrate the strains locally within the diaphragm towards the strain gages. Due to the small size, profile, shape, and configuration, the acceleration transducer is able to withstand high impact forces and reliably to measure acceleration without being damaged and while avoiding resonance or the like which would degrade the output signal from the strain gages. 
     In accordance with one aspect of the invention, an acceleration transducer includes a diaphragm responsive to inertially-induced deformations so as to exhibit stress, strain, and deflection; a support attached to a part of the diaphragm; and at least one detector for producing an output in response to the deformations. 
     In accordance with another aspect, an acceleration transducer includes a diaphragm responsive to inertially-induced deformations so as to exhibit stress, strain, and deflection; a support for holding the diaphragm; and at least one detector for producing an output in response to the strain. 
     In accordance with yet another aspect, an acceleration transducer includes a housing, a diaphragm disposed within the housing such that the circumference of the diaphragm is rigidly secured or held within the housing and a central portion of the diaphragm is sufficiently free to deflect in response to acceleration of the housing, and at least one strain gage secured to the diaphragm for producing an output representative of the acceleration, the at least one strain gage being located towards an outer radial portion or circumferential portion of the diaphragm, or in any event in the region of measurable strain. 
     In accordance with still another aspect, an acceleration transducer includes a housing, a diaphragm disposed within the housing such that a central portion of the diaphragm is rigidly secured or held within the housing and the circumference of the diaphragm is sufficiently free to deflect in response to acceleration of the housing, and at least one strain gage secured to the diaphragm for producing an output representative of the acceleration, the at least one strain gage being located towards the central portion of the diaphragm, or in any event in the region of measurable strain. 
     In accordance with a further aspect, a method of evaluating the integrity of a bar or other object includes the steps of securing a mounting block to the bar to be impacted, securing an acceleration transducer to the mounting block, and monitoring an output of the acceleration transducer in response to impacting the bar. 
     To the accomplishment of the foregoing and related ends, the invention, then, comprises the features hereinafter fully described and particularly pointed out in the claims. The following description and the annexed drawings set forth in detail certain illustrative embodiments of the invention. These embodiments are indicative, however, of but a few of the various ways in which the principles of the invention may be employed. Other objects, advantages and novel features of the invention will become apparent from the following detailed description of the invention when considered in conjunction with the drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a perspective view of a center-mounted acceleration transducer in accordance with a preferred embodiment the present invention; 
     FIG. 2 is an exploded view of an edge-mounted acceleration transducer in accordance with the present invention; 
     FIG. 3 is a sectional view of the acceleration transducer of FIG. 2 in accordance with the present invention; 
     FIG. 4 is a plan view of an exemplary diaphragm with strain gages thereon in accordance with the present invention; 
     FIG. 5 is a top schematic view of the diaphragm of FIG. 4 illustrating the relative placement of the apertures in accordance with the present invention; 
     FIG. 6 is a side view of the diaphragm of FIG. 5; 
     FIG. 7 is a schematic diagram of the wiring connections between the respective strain gages in accordance with the present invention; 
     FIG. 8 is a plan view of a diaphragm in accordance with yet another embodiment of the present invention; 
     FIG. 9 is a side view of a diaphragm in accordance with still another embodiment of the present invention; 
     FIG. 10 is a sectional view of an acceleration transducer in accordance with another embodiment of the present invention; 
     FIG. 11 is a sectional view of an acceleration transducer according to yet another embodiment of the present invention; 
     FIG. 12 is a graph showing the calculated flexure and strain responses of an edge-mounted diaphragm modeled in accordance with the present invention; 
     FIG. 13 is an exploded view of the acceleration transducer of FIG. 1; 
     FIG. 14 is a sectional view of a transducer housing having mechanical stops which limit deformations of the diaphragm of the acceleration transducer of FIG. 1; 
     FIG. 15 is a plan view of the diaphragm of the acceleration transducer of FIG. 1; 
     FIG. 16 is a graph of the displacement and strain in a center-mounted transducer; 
     FIG. 17 is a plan view showing the details of the apertures in the diaphragm of FIG. 15 in the vicinity of a strain gage; 
     FIG. 18 is a plan view of the diaphragm in accordance with another embodiment of the invention; 
     FIG. 19 is a top schematic view of the diaphragm of FIG. 15 illustrating the relative placement of the apertures in accordance with an exemplary embodiment of the present invention; 
     FIG. 20 is a side view of the diaphragm of FIG. 19; 
     FIG. 21 is plan view of a diaphragm having added masses, in accordance with yet another embodiment of the invention; 
     FIG. 22 is a system view of a Hopkinson bar impact test application illustrating possible placements of acceleration transducers of the present invention; 
     FIG. 23 is a magnified view of the acceleration transducers and associated mounting blocks shown in FIG. 22; 
     FIG. 24 is a waveform diagram illustrating an exemplary output from a center-mounted acceleration transducer in accordance with the present invention; 
     FIG. 25 is a waveform diagram illustrating velocities and forces calculated from the output of FIG. 24; and 
     FIG. 26 is an exploded view of another alternative embodiment of the invention, a transducer which uses a strain concentration mechanism not involving apertures. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The acceleration transducer of the present invention will now be described with reference to the drawings, wherein like reference numerals are used to refer to like elements throughout. 
     Referring initially to FIG. 1, one embodiment in accordance with the present invention, a center-mounted acceleration transducer, is generally designated  10 . The transducer  10  includes a mounting support  12  which attaches to a diaphragm  14  at an attachment portion  15  thereof, leaving a flexure portion  16  thereof free to flex in response to inertial forces. Strain gages  18  and  19  are attached to the diaphragm  14  to function as a detector for measuring the flexure of the diaphragm  14 . 
     The attachment portion  15  will preferably be rigidly secured by the support  12 , since rigidly securing the attachment portion  15  will generally maximize the flexing response of the flexure portion  16 . However, it will be appreciated that the attachment of the attachment portion  15  by the support  12  may be other than rigidly securing the attachment portion  15 , leaving at least part of the attachment portion  15  free to flex. For example, the attachment may be an elastic coupling, a hinged connection, or involve some form of viscous damping. 
     In addition, it will be appreciated that attachment of a mounting support for a diaphragm need not be at the center of the diaphragm in order for a portion of the diaphragm to be left free to flex. The mounting support would preferably be attached at the center of the diaphragm, as shown in FIG. 1 for the transducer  10 , but may also be attached along the circumference of the diaphragm, or at some portion of the diaphragm between the center and the circumference. 
     For example, FIG. 2 shows an alternate embodiment of the present invention, an edge-mounted acceleration transducer which is generally designated  20 . The transducer  20 , shown in exploded view, includes a housing  22  having a head portion  24  and a threaded base portion  26 . The head portion  24  is integrally formed with the base portion  26  to form a generally hex bolt shape. The head portion  24  includes a central bore  28 , having a radius Rh, which is concentric with a central bore  30  through the base portion  26 . The central bore  30  has a radius Rb where Rh&gt;Rb. A step  32  is formed by the annular planar surface where the central bore  28  meets the central bore  30  as shown. 
     A circular diaphragm  34  having a radius Rd is seated flat on the step  32  so as to be supported around its entire circumference by the step  32 . Preferably, Rb&lt;Rd&lt;Rh and Rd is slightly smaller than Rh to allow insertion of the diaphragm  34  within the central bore  28 . A clamping ring  38  having an outer radius Ro and an inner radius Ri is insertable into the central bore  28  for rigidly securing the diaphragm  34  between the step  32  and the bottom of the clamping ring  38 . In the preferred embodiment, the outer radius Ro of the clamping ring  38  is approximately equal to the radius Rh of the central bore  28  such that the clamping ring  38  can be press fit into the central bore  28  and remain tightly secured. The inner radius Ri of the clamping ring  38  is preferably equal to the radius Rb of the central bore  30  such that the diaphragm  34  is securely held equally on both sides. 
     The transducer  20  further includes a cap  40  which covers the clamping ring  38  and diaphragm  34 . The cap  40  preferably forms a seal which prevents moisture, dirt and debris from entering the head portion  24  and protects the strain gages (not shown) on the diaphragm  34  from the environment. In the exemplary embodiment, the cap  40  has a lower portion  42  having a radius which is approximately equal to the inner radius Ri of the clamping ring so as to allow the lower portion  42  to be press fit into the clamping ring  38 . A flange portion  44  of the cap has a radius which is slightly smaller than the radius Rh of the head portion  24  such that the flange portion  44  can be recessed flush with the upper surface of the head portion  24  as seen in FIG.  2 . The radii of the lower portion  42  and/or flange portion  44  may be slightly tapered to facilitate press-in assembly of the cap  40  in the housing  22 . The outer circumference of the flange portion  44  is thus seated flat on the top surface of the clamping ring  38 . 
     FIG. 3 illustrates the fully assembled transducer  20 . As is shown, the diaphragm  34  is rigidly secured around its entire circumference between the clamping ring  38  and step  32  of the housing  22 . A central portion  46  of the diaphragm is free from obstruction and can flex in either direction in response to movement of the housing  22 . The threaded base portion  26  allows the transducer  20  to be secured to an object whose acceleration is to be measured. Wire leads  48  connected to strain gages (not shown) on the diaphragm  34  extend from the transducer  20  through the central bore  30 . The leads  48  are connected to appropriate circuitry (not shown) for processing the output of the strain gages in order to determine acceleration as is discussed more fully below in connection with FIG.  7 . 
     Turning now to FIG. 4, a top view of the diaphragm  34  is provided. The dotted line denotes an area  54  (sometimes referred to as a circumference or circumferential area) which is held by the clamping ring  38  and housing  22 . In accordance with the preferred embodiment, the diaphragm  34  includes strain gages T 1  and T 2  which are mounted on the same side of the diaphragm diametrically opposite each other and radially inward of the area  54 . The strain gages T 1  and T 2  are designed to measure the tensile strains which are present in the diaphragm  34  during downward flexure. The strain gages T 1  and T 2  are preferably located radially outward from the center C of the diaphragm  34 . 
     In order to increase the sensitivity of the transducer  20  via the strain gages T 1  and T 2 , the present invention includes a strain concentration mechanism such as a pair of apertures  58  positioned adjacent each strain gage on opposite sides. The apertures  58  tend to exaggerate the strain which is incurred by the flexing diaphragm  34  towards the middle regions  60  where the respective strain gages are located. Hence, the present invention is able to provide a transducer having a high first resonant frequency while still obtaining a suitable output response from the strain gages. Although FIG. 4 only shows strain gages T 1  and T 2 , the opposite side of the diaphragm includes strain gages C 1  and C 2  for measuring compression type strains in the diaphragm  34  during upward flexure. The strain gages C 1  and C 2  (not shown) are positioned in the same manner as gages T 1  and T 2  between the aperture pairs  58 , but simply on the other side of the diaphragm  34 . The strain gages T 1  and C 1 , and T 2  and C 2  can be connected in complementary fashion such that the tensile strain measured by T 1  is common to the compression strain measured by C 1 , for example. 
     The strain gages T 1  and T 2  measure tensile strains while the strain gages C 1  and C 2  measure compression strains when the deflection of the diaphragm is downward relative to the illustration in the drawings. On an upward excursion of the diaphragm the strain reverses, i.e., strain gages T 1  and T 2  become compressive while strain gages C 1  and C 2  become tensile. The placement of the strain gages and corresponding reversal of strain facilitates the connecting and operating of the strain gages in a Wheatstone Bridge circuit described further below. 
     Although FIG. 4 shows a particular arrangement of the apertures and strain gages in accordance with the present invention, it will be appreciated that other combinations and arrangements are possible. For example, the diaphragm may include more than four strain gages and apertures. Preferably, however, for a perimeter-clamped embodiment such as the one shown in FIGS. 2-4, the strain gages are located toward the outer radial portion of the diaphragm in order to capture the largest radial strain. In addition, one or more apertures are provided for concentrating the strains incurred by the diaphragm towards the strain gages. 
     FIG. 5 illustrates the relevant dimensions of the diaphragm  34  in accordance with an exemplary embodiment of the transducer. The diaphragm  34  has a diameter (2*Rd) of 0.5313 inch, which is approximately equal to the outer diameter of the clamping ring (2*Ro). The apertures  58  are circular holes having a diameter of 0.0760 inch and which are centered at a radius Ra equal to 0.1652 inch from the center C of the diaphragm  34 . Each aperture  58  is offset from a center line CL (on which the strain gages are located) by an angle θ, where θequals 17.9° . The apertures  58  preferably have sharp edges and no burrs. As is shown in FIG. 6, the diaphragm  34  has a thickness t of 0.0135 inch, and is flat to within 0.0001 inch TIR. The inner diameter of the clamping ring  38  is preferably about 0.4063 inch (2*Ri) as is the diameter of the central bore  30 . Thus, the central portion  46  (FIG. 3) of the diaphragm  34  has a diameter of approximately 0.4063 inch also. 
     The diaphragm  34  is preferably made of a hardened, corrosion resistant, fatigue resistant material. Exemplary materials are 316-type stainless steel, 304-type stainless steel, titanium, or other materials that have suitable properties. In addition, preferably the housing  22 , clamping ring  38  and cap  40  are made of the same material as the diaphragm  34  so as to avoid galvanic corrosion and thermal mismatch, which may result in temperature-induced strain, between the respective components. Also, in the illustrated and described embodiment the diaphragm  34  is made of stainless steel, which is electrically conductive; therefore, the strain gages T 1 -T 2  and C 1 -C 2 , and, if necessary, their associated leads, are mounted on the diaphragm in a manner to avoid shorting. 
     If the diaphragm  34  is made of an electrically non-conducting material, the adhesive used for mounting the strain gages and their associated leads need not be electrically non-conducting. Alternatively, if the diaphragm  34  is made of an electrically non-conducting material the strain gages could be formed directly on the diaphragm using a photolithography process. 
     A transducer  20  having the above-described construction has been found to have a first resonant frequency of over 20 KHz, due mainly to the small size and stiffness of the diaphragm and the small size and placement of the strain gages. The strain gages T 1 -T 2  and C 1 -C 2  are of commercially available design and are preferably of a semiconductor variety (e.g., silicon) which are bonded on the diaphragm  34  using established techniques in the regions  60  (FIG.  4 ). Such strain gages in combination with the diaphragm  34  have been found to produce an output response (normalized with respect to the voltage supplied to the below-described Wheatstone Bridge) on the order of 0.0063 millivolts/volt (mV/V) to 0.0019 mV/V per g acceleration, where “g” is equal to the acceleration of gravity. In addition, the transducer is capable of measuring on the order of 10,000 g&#39;s of acceleration. In another embodiment, other types of strain gages can be used such, as foil type gages, etc. In either case, an extremely clean signal can be received from the strain gages. 
     It will be appreciated that although the transducer  20  has been described above with respect to particular dimensions, materials, aperture arrangements, etc., the present invention is not necessarily limited to such dimensions, materials, etc. Such specific information is presented primarily for exemplary purposes. Other materials, dimensions, aperture arrangements, strain gage configurations, strain gage types, etc., can be used without departing from the scope of the invention. 
     Turning now to FIG. 7, the general wiring diagram for the strain gages T 1 -T 2  and C 1 -C 2  is shown. As can be seen, the strain gages are configured as part of a Wheatstone Bridge. Specifically, strain gages T 1 , C 1 , T 2  and C 2  are connected together end-to-end to form the four arms of the Wheatstone Bridge. The node between gages T 1  and C 1  serves as the P+ terminal. The node between gages C 1  and T 2  serves as the S−terminal. The node between gages T 2  and C 2  serves as the P−terminal, and the node between gages C 2  and T 1  serves as the S+ terminal. Wire leads  48  from the respective P+, P−, S+ and S− terminals are bonded to the strain gages and extend from the diaphragm through the central bore  30  as shown in FIG.  2 . The leads  48  allow the gages to be connected to the appropriate external circuitry (not shown) for analyzing the signal from the Wheatstone Bridge formed by the strain gages. Also, the wire leads  48  can extend through the apertures  58  as shown in FIG.  4  and can serve as a means for providing a connection between the strain gages T 1  and T 2  on the top surface of the diaphragm  34  and the strain gages C 1  and C 2  on the bottom surface of the diaphragm  34 . Thus, in addition to acting to concentrate the strain in the diaphragm  34  towards the strain gages, the apertures  58  serve as holes through which the wire leads  48  can be fed. 
     As mentioned above, the wire leads  48  are used for connecting the Wheatstone Bridge formed by the strain gages to external circuitry (not shown) for processing the output of the Wheatstone Bridge. Such external circuitry may include circuitry to balance the bridge and/or to provide power and calibration. Such circuitry is considered conventional and, consequently, further detail has been omitted. 
     Although connection of the strain gages in a Wheatstone Bridge is preferred, it will be appreciated that the resistance of the strain gages may be measured directly, for example by use of an ohmmeter. 
     FIG. 8 illustrates another embodiment of a diaphragm  34 ′ which can be used in place of the diaphragm  34  shown in FIG.  2 . Specifically, the diaphragm  34 ′ differs from the diaphragm  34  only in that it includes an added mass  120  located in the center of the diaphragm. Such a mass tends to increase the sensitivity of the strain gages (not shown); however, the increase in sensitivity can be at the expense of a loss in the high end frequency response of the transducer. The removal of mass, such as by providing a further hole in the diaphragm, e.g., at the center where the illustrated mass is located, would produce the opposite effect. A hole decreases sensitivity while increasing frequency response; a mass increases sensitivity but decreases frequency response. 
     FIG. 9 shows still another embodiment of the diaphragm designated  34 ″. In this embodiment, the diaphragm  34 ″ differs from those in the other embodiments in that the diaphragm is made of a laminated material. The laminations may be designed to provide the necessary damping to achieve a desired frequency response and strain signal, and may be used in the other embodiments hereof. Other variations in the design of the diaphragm will be apparent in view of the description herein. 
     FIG. 10 shows an embodiment of the invention in which a transducer  20 ′ is used as an inertia sensing device. The embodiment of FIG. 10 is similar to that shown in FIG. 3 with the exception that the diaphragm  34  serves as one plate of a capacitive element  130 . If desired, the diaphragm  34  in the transducer  20 ′ may be solid, e.g., without holes  58 , since it may not be necessary to connect leads or conductors through the diaphragm, as it is used as part of a capacitive element. The capacitive element  130  includes capacitance sensing probe  132  and a dielectric material located between the diaphragm  34  and the probe  132 . As the capacitive element  130  flexes due to changes in the inertia of the transducer  20 ′, the capacitance of the element  130  changes as measured across wires  48  which are connected to the respective plates. 
     FIG. 11 shows another embodiment of an inertia sensing device. The device  20 ″ includes a diaphragm  34  which is reflective on its lower face  136 . A light source  138  is mounted on one side of the central bore  30  and a light detector  140  is mounted on the other side as is shown. The output from the light source  138  is directed towards the diaphragm  34  so as to be reflected therefrom and received by the detector  140  as shown in dotted line. The light may be directed at the middle of the diaphragm which likely will undergo maximum deflection in use; but the light may be directed elsewhere, if desired. As the diaphragm  34  flexes, the location at which the light from the light source  138  is incident on the detector  140  will vary. By configuring the light detector  140  such that the output therefrom varies as a function of where the light strikes the detector, an indication of the inertia of the object to which the device  20 ″ is connected to can be obtained. An exemplary light detector  140  may be a photodiode array or a CCD array as will be appreciated, the output of the array varying as a function of the spatial location at which the light from the light source  138  is incident on the detector  140 . 
     Although the inertia sensing device  20 ″ is described above in terms of detecting reflected light, it will be appreciated that the same principle may employed in an inertia sensing device reflecting sound waves, radio waves, microwaves, or other sorts of radiation, by substituting suitable sources and detectors for the light source  138  and the light detector  140 . 
     Referring briefly to FIG. 12, the results of modeling the response of the transducer  20  shown in FIG. 3 are shown. The horizontal axis represents the position (in inches) along the diameter of the unsupported central portion  46  of the diaphragm  34 . The left vertical axis represents the displacement of the diaphragm  34  under an exemplary condition. The right vertical axis represents the radial and tangential strain (in inches per inch). Curve E shows the displacement of the diaphragm  34  under the given condition. Curve F illustrates the radial strain of the diaphragm  34  along its diameter in the central portion  46 , and curve G shows the tangential strain. Marks  150  and  152  represent the respective locations of the pairs of strain gages T 1 , C 1  and T 2 , C 2  on the diaphragm  34 . As is shown, the average radial strain seen by the strain gages is 120μin/in and the average tangential strain is −11 μin/in. 
     It is noted that the average radial strain at the strain gage locations  150  and  152  represents approximately 75% of the maximum radial strain. The average tangential strain represents approximately 25% of the maximum tangential strain. For a rim-supported diaphragm without apertures, the maximum displacement occurs at the center and the maximum strains are at the supports. See FIG.  12 . When apertures are added near the rim support, the strains are increased without substantial change in the displacements. At the same time, the first resonant frequency of the transducer  20  is substantially higher than in conventional devices. 
     Returning to the preferred embodiment shown in FIG. 1, the support  12  of the acceleration transducer  10  comprises a retaining screw  162  and a base  164 . As best illustrated in the exploded view shown in FIG. 13, the screw  162  has an externally-threaded shaft  166  integrally formed with a head  168 . The base  164  has an internally threaded hole  169  therein which mates with the shaft  166 , thereby allowing the screw  162  to be connected to the base  164 . One end  170  of the base  164  has an integrally-formed generally hex bolt shape. 
     The transducer  10  preferably is enclosed in a sealed housing  171 , which functions to protect the transducer  10  from moisture, dirt, and debris, as well as from larger foreign objects. The configuration of the housing  171  is not generally determined by design of the transducer  10 , and the details of the housing  171  and the mounting and placement of the transducer  10  therein will depend on the requirements of the transducer application. 
     However, the housing  171  and/or the support  12  may include mechanical stops to limit movement of the diaphragm  14 . An example is housing  171 ′ shown in FIG. 14, which has surfaces  172  and  173  to limit the travel of the diaphragm  14 . By limiting the movement of the diaphragm  14 , damage to the diaphragm  14  may thereby be prevented. 
     Referring to FIGS. 13 and 15, the diaphragm  14  has a central hole  174  therein which allows the shaft  166  to pass therethrough. A dashed boundary line  176  indicates the boundary between the attachment portion  15 , which is held by the support  12  (clamped or otherwise held between the head  168  of the screw  162  and the base  164 ), and the flexure portion  16 . The strain gages  18  and  19  are mounted on the same side of the diaphragm  14 , diametrically opposite each other. 
     The strain gages  18  and  19  are preferably located in the flexure portion  16  close to the boundary line  176 . FIG. 16 shows radial strain RS and displacement DS as a function of radius for a flexing center-mounted transducer disk which does not include the below-described apertures and weakening holes. The radial strain RS is seen from FIG. 16 to be have a maximum absolute value at the boundary line  176 , at radial location  177  in FIG. 16, where the displacement DS is zero. Therefore strain gage radial locations  178  and  179  of the strain gages  18  and  19  are chosen close to the boundary line  176 , where the strain is high. Although the displacement of the diaphragm  14  is greater near its circumference  180 , it is seen in FIG. 16 that the radial strain RS is at its lowest absolute value near radial location  182  of the circumference  180 . Thus it is believed that the transducer  10  of the present invention is able to achieve a higher first resonant frequency as well as a stronger response by locating the strain gages  18  and  19  toward the boundary line  176  rather than towards the circumference  180 . 
     In order to increase the sensitivity of transducer  10  via the strain gages  18  and  19 , the present invention includes four apertures  184 , two of the apertures  184  positioned adjacent each of the strain gages  18  and  19  on opposite sides thereof. The apertures  184  tend to exaggerate the strain which is incurred by the flexing diaphragm  14  towards the middle regions  186 , which are between the pairs of apertures  184  and are where the respective strain gages  18  and  19  are located. It is believed that the apertures  184  amplify the strains in the middle regions  184  by a factor of two or three compared with the strains in the corresponding regions of a transducer without apertures, such as the one modeled in FIG.  16 . 
     FIG. 17 is an enlarged view of the diaphragm  14  in the vicinity of the strain gage  18 , showing the details of the apertures  184  and the middle region  186 . Each of the apertures  184  has a straight inner edge  190 . The straight inner edges  190  and the boundary  176  define a root  192  which connects the attachment portion  15  and the middle region  186 . The root  192  is tapered, being relatively wide near the boundary  176 , and narrowing to a width slightly greater than the width of the strain gage  18  where the root  192  meets the middle region  186 . This tapered shape of the root  192  provides increased stiffness, thereby reducing the relative flexure of the root  192  and increasing the relative flexure in the middle region  186 . The middle region  186  is bounded by edges  194  of the apertures  184 . The edges  194  are preferably substantially parallel to the outer boundaries  196  of the strain gage  18 . Each of the edges  194  defines at its ends corners  200  and  202 . The corners  200  and  202  act as stress concentrators, with flexure of the diaphragm  14  occurring most prominently in the middle region  186  in the vicinity of the corners  200  and  202 . The apertures  184  are designed such that the strain gage  18  is longer than and spans the middle region  186  between the respective pairs of the corners  200  and  202 , thereby increasing the output response of the strain gage  18 . 
     Referring briefly back to FIG. 15, a pair of weakening holes  204  is provided in the diaphragm  14 . The holes  204  reduce the overall stiffness of the diaphragm  14 . In addition, the holes  204  are preferably sized so as to balance the stiffness of the diaphragm  14 , with the holes  204  giving substantially the same reduction of stiffness as the apertures  184 . The holes  204  will preferably be diametrically opposed and adjacent the boundary line  176 , with each of the holes  204  located substantially the same distance from each pair of the apertures  184 , although the holes  204  may also be placed in other locations. The holes  204  will preferably be round for ease of manufacture, but may have other shapes. 
     It will be appreciated that the functions of the weakening holes  204  could alternatively be performed by use of an elliptical diaphragm  14 ′, shown in FIG.  18 . The elliptical diaphragm  14 ′ has a length L 1  along the axis containing the strain gages  18  and  19  that is greater than the width L 2  in the direction perpendicular thereto. It will be appreciated that the elliptical diaphragm  14 ′ may also be designed to contain weakening holes. While a round diaphragm such as the diaphragm  14  is preferred, the diaphragm may have other shapes. 
     Although FIG. 15 only shows strain gages  18  and  19 , the transducer  10  includes on the opposite side of the diaphragm  14  strain gages  18 ′ and  19 ′ (not shown) for measuring compression type strains in the diaphragm  14  during downward flexure. The strain gages  18 ′ and  19 ′ are positioned in the same manner as gages  18  and  19  between the aperture pairs  184 , but simply on the other side of the diaphragm  14 . The strain gages  18  and  18 ′, and  19  and  19 ′ may be connected in complementary fashion such that the tensile strain measured by  18  is common to the compression strain measured by  18 ′, for example. This arrangement of strain gages on the transducer  10  is analogous to the placement of the strain gages T 1 , T 2 , C 1 , and C 2  on the diaphragm  34  of the transducer  20  described above and shown in FIG.  4 . The strain gages  18 ,  18 ′,  19 , and  19 ′ have wire leads (not shown) connected thereto which are also connected to appropriate circuitry (not shown) for processing the output of the strain gages. If necessary, the wire leads can be passed through openings in the diaphragm  14 , either through the apertures  184  or the weakening holes  204 . It will be appreciated that the strain gages  18 ,  18 ′,  19 , and  19 ′ may be connected and operated in a Wheatstone bridge in a manner similar to the connection of the strain gages T 1 , T 2 , C 1 , and C 2  described above and shown in FIG.  7 . 
     Although it will be appreciated that stress would most effectively be concentrated in the middle region  186  if the corners  200  and  202  were sharp, in actuality the sharpness of the corners  200  and  202  is limited to prevent premature cracking and subsequent fatigue failure. As shown in FIG. 19, each of the apertures  184  has its rounded corners defined by first, second, and third circles  206 ,  208 , and  210 , respectively. The first circle  206  is located adjacent the boundary line  176 . The second circle  208  is located further from the center of the diaphragm  14  and such that a line tangent to both of the circles  206  and  208  forms the inner edge  190  of the aperture  184 , which gives the root  192  the desired tapered shape discussed above (see FIG.  17 ). The third circle  210  is located relative to the second circle  208  such that a line tangentially connecting the two circles  208  and  210 , the edge  194 , is substantially parallel to the outer boundaries  196  of the strain gages  18  and  19  as discussed above (see FIG.  17 ). A line tangentially connecting the second circle  208  and the third circle  210  completes the boundary of the aperture  184 . 
     Although FIG. 15 shows a particular arrangement of the apertures and strain gages in accordance with the present invention, it will be appreciated that other combinations and arrangements are possible. For example, the diaphragm  14  may include more than four strain gages and apertures. Preferably, however, the strain gages are located in the flexure portion of the diaphragm toward the boundary between the flexure portion  16  and the attachment portion  15  in order to obtain a higher signal. In addition, one or more apertures are preferably provided for concentrating the strains incurred by the diaphragm towards the strain gages. 
     Further, although the apertures  184  pass completely through the diaphragm  14 , it will be appreciated that strain concentration may by achieved in the vicinity of the strain gages without having holes in the diaphragm, for example by use of grooves in the diaphragm or areas of the diaphragm with reduced thickness. And while the strain gages  18  and  19  are shown as not overlapping the apertures  184 , it will be appreciated that strain gages could be positioned to partially or fully overlap the apertures or other stress concentrators. 
     FIGS. 19 and 20 illustrate the relevant dimensions of the diaphragm  14  in accordance with an exemplary embodiment of the transducer  10 . The diaphragm  14  has a diameter Dd of 0.4200 inch. The central hole  174  has a diameter Dh of 0.090 inch. Each of the apertures  184  is defined by the three circles  206 ,  208 , and  210  in the manner described above, with each of the circles  206 ,  208 , and  210  having a diameter Dc of 0.012 inch. Each first circle  206  is located a distance R 1  of 0.0726 inch from the center C of the diaphragm  14 . Each circle  206  is offset from a center line CL (on which the strain gages 18 and 19 are located) by an angle φ1, where φ1, equals 30.4602°. Each second circle  208  is located a distance R 2  of 0.0861 inch from the center C, and is offset an angle φ2 of 11.0489° from the center line CL. Each third circle  210  is located a distance R 3  of 0.0959 inch from the center C, and is offset an angle φ3 of 9.9042° from the center line CL. Each weakening hole  204  has a diameter Dw of 0.033 inch and is located a distance Rw of 0.0845 inch from the center C. The diaphragm  14  has a thickness Td of 0.025 inch. 
     The diaphragm 14 is preferably made of a hardened, corrosion resistant, fatigue resistant material. Exemplary materials are 316-type stainless steel, 304-type stainless steel, titanium, or other materials that have suitable properties. Also, in the illustrated and described embodiment the diaphragm  14  is made of stainless steel, which is electrically conductive; therefore, the strain gages  18 ,  18 ′,  19 , and  19 ′, and, if necessary, their associated leads, are mounted on the diaphragm using electrically non-conducting adhesive to avoid shorting. The central hole  174 , the apertures  184 , and the weakening holes  204  may be formed or cut in the diaphragm  14  by processes such as machining, photoetching, stamping, or laser cutting. 
     If the diaphragm  14  is made of an electrically non-conducting material, such as a composite or a non-conducting laminated material, the adhesive used for mounting the strain gages and their associated leads need not be electrically non-conducting. Alternatively, if the diaphragm  14  is made of an electrically non-conducting material the strain gages could be formed directly on the diaphragm using a photolithography process. 
     A transducer  10  having the above-described construction has been found to have a first resonant frequency of over 20 KHz, due mainly to the small size and stiffness of the diaphragm and the small size and placement of the strain gages. The strain gages  18 ,  18 ′,  19 , and  19 ′ are of commercially available design and are preferably of a semiconductor variety (e.g., silicon) which are bonded on the diaphragm  14  using established techniques. Such strain gages in combination with the diaphragm  14  have been found to produce an output response (normalized with respect to the voltage supplied to the Wheatstone Bridge) on the order of 0.004 millivolts/volt (mV/V) to 0.006 mV/V per g acceleration, where “g” is equal to the acceleration of gravity. In addition, the transducer is capable of measuring on the order of 10,000 g&#39;s of acceleration. In another embodiment, other types of strain gages can be used such, as foil type gages, etc. In either case, an extremely clean signal can be received from the strain gages. 
     As compared with the edge-clamped transducer  20  shown in FIG. 2, the center-clamped transducer  10  has the advantage of higher strain levels and thus increased sensitivity. These higher strain levels are produced because clamping the diaphragm at the center leaves a maximum amount of diaphragm mass free to flex. It will be appreciated that the diaphragm  14  may be modified by adding masses at its circumference or elsewhere to further increase sensitivity of the strain gage. 
     FIG. 21 shows such a diaphragm, a diaphragm  14 ″ with added masses  220  attached to the diaphragm  14 ″ at evenly spaced locations near circumferential edge  230 . It will be appreciated that a greater or lesser number of masses may be used, that the masses need not be identical, and that they need not be placed symmetrically about the diaphragm  14 ″. 
     FIGS. 22 and 23 illustrates how the transducer  10  can be used to measure the acceleration and/or velocity of an impact bar  300 , also known as a Hopkinson bar. In FIG. 22, the impact bar  300  is secured by hinged connections  302  and  304 . The bar  300  is struck at end  306  with great force by end  308  of an impacting bar or hammer  310 , which is secured by hinged connections  312  and  314 . The hinged connections  302 ,  304 ,  312 , and  314  are also hinged at their mounting points  316  on supporting structure (not shown). As shown in FIG. 23, transducer  10  may be mounted to the bar  300  axially, on non-impacted end  318  of the bar  300 , by use of a mounting block or housing  320 . Alternatively the transducer  10  may be mounted offset from the axis of the bar  300 , on the side of the bar  300 , by use of a mounting block or housing  322 . It will be appreciated that the aforementioned external circuitry for processing the signal from the transducer  20  may be located either in the mounting blocks or housings  320  and  322  or elsewhere remote from the blocks or housings  320  and  322  and the bar  300 . 
     An advantage of the present invention is that because of the small size and hence small profile of the transducer  10 , the mounting blocks or housings  320  and  322  also can have a small size and small profile relative to the bar  300 . This enables the mounting blocks or housings  320  and  322  and transducer  10  to be securely mounted to the bar  300  with relatively little movement or vibration relative to the bar  300 . Hence, the output from the transducer  10  has been found to produce a very clean signal. 
     FIGS. 24 and 25 shows exemplary waveforms which are produced by the transducer  10  when mounted to an axially impacted bar in a Hopkinson bar test. The results shown in FIGS. 24 and 25 are from tests with the transducer  10  mounted close to the impacted end  306  of impacted bar  300 , corresponding approximately to location  340  shown in FIG.  22 . In both FIGS. 24 and 25 the horizontal axis represents time and the vertical axis represents the amplitude of the respective signals. Waveform A represents the acceleration of the bar  300  via the output signal provided by the strain gages in the transducer  10 . Waveform B represents the velocity of the bar  300  computed by integrating the waveform A using a computer. Waveform C represents the force in a cross-section of the impacted bar  300 , with compression forces being positive. The force is measured by strain gages (not shown) mounted directly on the impacted bar  300 . It will be appreciated the force could also be calculated using known relationships between the force and the velocity of the bar, the modulus of elasticity of the bar material, the cross-sectional area of the bar, and the speed of sound in the bar material. 
     At time T, the bar  300  having the transducer  10  mounted thereto is struck by the impacting bar  310 . This impact causes a compressive wave to propagate through both the impacting and impacted bars. The initial upward acceleration peak  400  represents the acceleration of the bar  300  in the vicinity of the transducer  10  as it accelerates from a stationary position towards a relatively constant velocity. Besides moving at a relatively constant velocity, the bar  300  in the vicinity of the transducer  10  is in compression. 
     The compressive wave in the impacting bar  310  is reflected at its free end  342  as a tensile wave. When this tensile wave reaches the point of contact between the impacting and impacted bars  310  and  300 , the two bars separate, and a corresponding tensile wave begins to propagate through the impacted bar  300 . The downward peak  402  in waveform A represents the deceleration of the bar  300  from the relatively constant velocity back to a stationary position due to this tensile wave. At this point the portion of the bar  300  in the vicinity of the transducer  10  is neither in tension nor compression. 
     The initial compressive wave which produced acceleration peak  400  is reflected by the free end  318  of the impacted bar  300  as a tensile wave. This tensile wave produces acceleration peak  404  when its effect is felt at the transducer  10 . Upon reaching the originally-impacted end  306  of the impacted bar  300  the tensile wave is reflected as a compressive wave, which produces acceleration peak  406 . 
     The tensile wave which produced downward peak  402  is reflected by the end  318  of the bar  300  as a compressive wave which propagates along the bar  300  to produce downward peak  408  and (after reflection at end  306  as a compressive wave) downward peak  410 . 
     It will be appreciated that the appearance of the outputs shown in FIGS. 24 and 25 will vary greatly depending upon the type of acceleration being measured and the location of the transducer  10 . However, the waveforms in FIGS. 24 and 25 illustrate the clean signal obtainable using an acceleration transducer of the present invention, avoiding the relatively large oscillations and noise which are found in outputs from existing devices placed near the impact end of a bar. 
     It is noted that the output of the transducer  10 ,  20  depends somewhat upon the damping effect of the air or other fluid in the chamber where the diaphragm  14 ,  34  is located. As the diaphragm  14 ,  34  flexes the volumes of the portions of the chamber above and below the diaphragm change. This causes the fluid filling the chamber to rush from one portion of the chamber to the other through the holes in the diaphragm  14 ,  34 , such as the apertures  58  in the diaphragm  34  and the apertures  184  and the weakening holes  204  in the diaphragm  14 . For the diaphragm  14 , the fluid may also move through a gap between the circumference  180 , which is not clamped, and the housing  171 . This movement of fluid creates a viscous drag on the diaphragm  14 ,  34  which damps its motion. It will be appreciated that the damping effect described is affected by the configuration of holes in the diaphragm  14 ,  34  and, for the diaphragm  14 , by the configuration of the gap as well. The damping is also affected by the type of fluid in the chamber. For example, damping could be increased by replacing the air in the chamber with oil. It will also be appreciated that the rushing of the fluid through the holes in the diaphragm  14 ,  34  may tend to change the temperature of the diaphragm  14 ,  34 . 
     FIG. 26 shows another alternative embodiment of the invention, a transducer  420  which uses a strain concentration mechanism not involving apertures. Except as indicated below, the transducer  420  is similar to the transducer  20  shown in FIGS. 2-4 and described above. 
     The transducer  420  has a circular diaphragm  434  which is clamped along its perimeter by a clamping ring  438 . Wire leads  448  are connected to strain gages (not shown) which are located on the bottom of the diaphragm  434 . The leads  448  are connected to appropriate circuitry (not shown) for processing the output of the strain gages. 
     Strain concentration in the vicinity of the strain gages is accomplished by a sharp edge  450  along the bottom inside diameter of the clamping ring  438 . The sharp edge  450  causes stresses to be concentrated in the portion of the diaphragm  434  near the clamping ring  438  as the diaphragm  434  flexes. This concentration of stress causes an increase in strain where the strain gages are located, which results in an increase output from the strain gages. 
     It will be appreciated that the sharp edge may be provided only along the portion of the bottom inside diameter of the clamping ring nearest the strain gages, as opposed to fully around the bottom inside diameter, as is shown. 
     It will further be appreciated that a strain concentration mechanism involving a sharp edge may also be employed with transducer having a center-clamped diaphragm. 
     It will be appreciated that although the transducers  10 ,  20 , and  420  have been described above with respect to particular dimensions, materials, aperture arrangements, etc., the present invention is not necessarily limited to such dimensions, materials, etc. Such specific information is presented primarily for exemplary purposes. Other materials, dimensions, aperture arrangements, strain gage configurations, strain gage types, etc., can be used without departing from the scope of the invention. And while the diaphragms  14 ,  34 , and  434  are preferably flat, other shapes such as a dish-like shape may be used. 
     As previously mentioned, different aperture arrangements and/or number of strain gages can also be utilized. Though the strain gages are preferably of a semiconductor type which can be formed directly on the diaphragm, other strain gages which can be applied to the diaphragm are also within the scope of the invention. The preferred embodiment configures the strain gages in a Wheatstone Bridge configuration, but other configurations are similarly possible. 
     It will be appreciated that piezoelectric devices may be substituted for one or more of the strain gages. Piezoelectric devices have the characteristic that a mechanical stress on the device produces a voltage across the device. The voltages in the piezoelectric devices can be measured using conventional means. 
     What has been described above are preferred embodiments of the present invention. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the present invention, but one of ordinary skill in the art will recognize that many further combinations and permutations of the present invention are possible. Accordingly, the present invention is intended to embrace all such alterations, modifications and variations that fall within the spirit and scope of the appended claims. In addition, while a particular feature of the invention may have been described above with respect to only one of several illustrated embodiments, such feature may be combined with one or more other features of the other embodiments, as may be desired and advantageous for any given or particular application.