CA1165830A - Isolating and temperature compensating system for resonators - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE
A mounting structure for resonators used as frequency standards and transducers which maximizes performance and reduces the sensitivity to environmental errors. In one embodiment, force sensitive resonators having inherent unmounted temperature sensitivities are used in conjunction with reactive spring-like mounting arrangements having predetermined temperature stress characteristics such that the thermally induced mechanical stress of the mounting arrangements changes, compensates, and optimizes the overall combined temperature characteristics. In another embodiment resonators are isolated from the external enviroment so that they are capable of sensing forces while operating in a vacuum or inert atmosphere. Enviromental isolation is provided by bellows and/or diaphragm arrangements used along or in conjunc-tion with air-tight enclosures which enable forces to be applied to stress-sensitive resonators while isolating the resonators from the external force producing enviroment.

Description

I 1 ~i5~J3() .GROUND OF THE INVENTION
_ Field of the Invention ~ This invention relates to o~,$~- resonators for oscillators and stress sensitive transducers, and more parti~
cularly, to improved resonator mounting structures having low sensitivities to environmental effects.
Descrlption of the Prior Art Crystal oscillators with low sensitivity to tempera-ture variations have been widely used as frequency standards.
10These oscillators, usually fabricated from quartz, may achieve their temperature insensitivity by careful selection of crys-tallographic axes, compensation through electronic oscillator components, compensation through addi~ional resonators and utilization of combinations of vibrational modes, such as flexural and torsional modes, to achieve specific temperature related performance. Tradeoffs exist in temperature effects versus crystal impedance and other performance aspects as well as manufacturability and cost considerations. It is desirable to have an additional temperature related degree of freedom affecting crystal frequency. This additional flexibility in design is derived from the concept of thermally induced mech-anical stress applied to a load sensitive crystal.
In contrast to crystal resonators used as transdu~
cers, crystal resonators used as frequency standards should be isolated from and unaffected by external forces. In general, crystal frequency standards have been designed with thin wire mountings attached to nodal points of vibration such that stress cannot be applied to the crystals.

A number of load sensitive crystals and transducers are known. In an unstressed condition, under constant envir-onmental conditions, a crystal has a unique resonant frequency ~, , '3 0 ~ `rmined by its dimensions and material composition. The resonant frequency increases under tensile loadlng and de-creases under compressive loading. The resonant frequency should thus be a true and accurate measure of the applied load.
Force sensitive crystals are described in U.S. Pat-ent No. 2,984,111 issued to Kritz and U.S. Patent No.
3,093,760 issued to Tarasevich in which loads are applied to the crystals near the nodal points. Imprecise location of these nodal points results in energy tranmsission through the mounts, degrading the "Q", or quality actor, of the resonator with a consequential loss of accuracy. Also, forces and mo-ments produced by the mounting structure can be transmitted to the resonator due to the imprecise nodal point loca~ion.
U.S. Patent No. 3,470,400 issued to Weisbord des-cribes a single beam force transducer with an integral mount-ing system which effectively decouples the beam vibrations from the mounting point through a spring and mass arrangement.
This resonator is complex, relatively large, and difficult to manufacture.
A potentially small, simple and easy to manufacture device using photolithography is the closed end tuning fork described in U.S. Patent No. 3,238,789 issued to Erdley. The Erdley device consists of two tines or bars vibrating 180 de-grees out of phase such that the reactive forces and moments cancel.
Techniques for developing resonators with a low tem-perature cvefficient u~ing combinations of flexural and tor-sional modes of vibration were described by Momosaki et al in a paper presented in 1979 at the 33rd Annual Symposium on Fre-quency Control. This approach is both complex and restric-, i :~ 6$~30 -t~ . A new variable relating frequency to ternperature can offer flexibility in design as well as improved performance.
One technique for temperature compensatlng crystal resonators is described in a paper presented in 1961 by Gerber et al at the Fifteenth Annual Symposium on Frequency Control.
Gerber et al disclose mounting a relatively high frequency, shear mode crystal resonator on a base, and biasing the reson-ator against the base by a pair of temperature sensitive bi-metalic bars. One of the bars is used for relatively low tem-peratures while the other bar is used for higher temperatures.
While the Gerber et al approach may be satisfactory for temper-ature compensating shear mode crystals which are highly insen-sitive to external forces, it is not applicable to flexurally vibrating crystal resonators which are orders of magnitude more sensitive to external forces. In fact, if the teachings of Gerber et al were applied to flexurally vibrating resona-tors excessive forces would certainly be imposed on the re-sonators by the bi-metallic bars.
SUMMARY OF THE INVENTION
It is an object of this invention to provide rela-tively low frequency, flexurally vibrating resonators with low sensitivity to temperature variations.
It is still another ob]ect of this invention to max-imize performance by isolating load sensitive resona-tors from the external environment.
The sensitivity of resonators to temperature varia-tions is minimized by connecting one end of the resonator to a flexible bellows or spring having a coefficient of ther-mal expansion different from that of the resonator. The co-efficient of thermal expansion of the bellows or spring is selected so that the termally induced stress applied to the ~ ~ 3 65(~3(7 ~ nator combines with the inherent unrnounted temperature sensitivity of the resonator, such that ~he overall tempera-ture sensitivity is relatively low at the operating tempera-ture of the resonator. When the resonator is to be thermally compensated, it is positioned within an elongated resilient spring or bellows having its ends closed by respective covers to which the mounting pads are secured. Alternatively the resonator may be positioned within an air-tight enclosure to which one of the mounting pads is secured. An opening in the enclosure is covered by one end of a thermally compensating flexible bellows with the other end of the bellows being closed by an end cap to which the other mounting pad is secured to allow forces to be applied to the resonator through the bel-lows. An alternative mounting structure for resonators may also be employed as part of the temperature compensating system. This alternative mounting system includes a rigid force transmitting member adapted to receive a force adjacent one end with one mount of the resonator secured to the force transmitting member adjacent the opposite end. The force transmitting member is mounted on a rigid base by a flexure hinge pivot. The flexure hinge is relatively compliant a-bout a pivot axis perpendicular to the force to allow the force transmitting member to pivot about the axis as a force is applied to the force transmitting member in order to uni-formly couple the force to the resonator. The force transmi-t-ting member, base and flexure hinge may be positioned within an air-tight enclosure. An opening in the enclosure is cov-ered by one end of a flexible bellows with the other end of the bellows being closed by an end cap to which the force re-ceiving end of the force transmitting member is secured. The coefficient of thermal expansion of the bellows and suspension 5 ~ 3 .r) tem may be selected to minimize the overall thermal sensi~
tivity of the resonator at its operating temperat~re~ Pres-sure compensation may be achieved by placing a second bellows between a surface of the force transmitting member opposite the first bellows with the bellows extending to a second open-ing in the enclosure. The cross-sectional areas and positions of the two bellows are selected to cause the moment imparted to the force transmitting member by the pressure in the first bellows to counteract the moment imparted to the force trans-mitting member by the pressure in the second bellows.

BRIEF DESCRIPTION OF T~E DRAWINGS

. ~
Fig. 1 is an isometric view illustrating a conven-tional single beam force transducer with integral mounting isolation~
Fig. 2 is a plan view illustrating a conventional closed end tuning fork force sensor.
Fig. 3 is a cross-sectional view of a load sensitive crystal encapsulated by a bellows or sprin~ assembly for tem-perature compensating and environmentally isolating the crystal.
Fig. 4 is a plan view of an inventive suspension system, bellows or spring, and crystal arrangement offering improved temperature performance and environmental isolation.
Fiy. 5 is a plan view illustrating one embodiment of the inventive bellows and crystal arrangement isolating the environment of the device from the force producing structure.
Fig. 6 is a plan view illustrating an inventive em-bodiment of a force sensitive crystal which is isolated from the environment through a double bellows arrangement which is insensitive to pressure variations.

1 1 6~330 Fig. 7 is an isometric view of one embodiment of a mounting system which isolates the crystal from external pressure variations through a bellows and suspension system arrangement.

DETAILED DESCRIPTION OF THE INVENTION

_ The present invention is equally applicable to load sensitive crystal resonators of various shapes and configura-tions; however, for simplicity and clarity, only the applica-tion to flexurally vibrating force sensitive beam and closed end tuning fork devices will be described in detail, it being understood that the same or similar principles apply in the general case.
Fig. 1 illustrates a conventional single beam force transducer 2 with integral mounting isolation as disclosed in the aforementioned patent to Weisbord. The transducer 2 consists of a flexurally vibrating center beam 4, two sets of isolator masses 6, and isolator springs 8 extending from each end of the beam 4 to mounting surfaces 10. Axial forces, applied along the longitudinal axis of the transducer 2 stress the vibrating beam 4, thereby changing its resonant fre~uency in accordance with ~he magnitude of the applied loads. The isolator masses 6 and isolator springs 8 are designed to decouple the reactive forces and moments generated by the beam 4 from the mounts 10, thus reducing the energy losses. As a result, the transducer 2 has a high "Q" so that its resonant frequency is an accurate representation of the applied forces. The beam 4 may be driven at its resonant frequency using electrodes 12 and oscillator circuitry in any conventional manner such as is described in U.S. Patent No.
3,479,536 issued to Norris. Although effective in many ways as a force sensitive crystal, the transducer 2 is complex, 1 1 6~33~) relatively large and difficult to manufacture. It also suffers from a relatively high sensitivity to temperat~re and is not environmentally decoupled from the force producing structure.
Fig. 2 is a plan view of a conventional closed end tuning fork 20 as described in the aforementioned patent to Erdley. This device 20 achieves low energy loss, high "Q"
operation by driving a pair of closely matched tines 22, 180 degrees out of phase, thus cancelling the reactive moments and forces which might be transmitted to a mount 24 from which the tines 22 projectO
Under constant environmental conditions, the resona-nt frequency in Hertz, fo~ of an unstressed fixed-ended flexurally vibrating beam of length L, thickness t, width b, modulus of elasticity E and density d is given by the formula:

fo = lconstant) t V r - (Equation 1) L d Although the resonant frequency is generally a non-linear function of the applied load, the first order load sensitiv-ity, SF, may be calculated as:

SF = (Constant)-~b~3 (applied load) (Equation 2) The quantitative relationships between resonant frequency, applied load, and resonator dimensions and composition can be determined from the above formulae. In particular, thermally induced mechanical stress may be applied to load sensitive crystals to optimize the overall temperature performance as described hereinafter.

~ ~ ~5~30 Although a number of load sensitive crystals rnay be mechanically stressed through thermal means to optirnize over-all temperature performance, the following discussions will illustrate the inventive thermal compensation using flexing bar crystals such as the single beam force transducer with integral mounting isolation and the closed end tuning fork force sensor.
The resonant frequency in Hz, f, of an oscillating crystal can be expressed as a power series expansion function of the temperature, T, taken about the reference temperature, To, as follows:

f = fo[l + A~T-To) + B(T-To)2 + C(T-To)3 + ]
(Equation 3) The coefficients A, B, C are the first, second and third order temperature coefficients, respectively. In substances such as quartz, these coefficients are strongly related to the orientation of the crystallographic axes.
Interrelationships also exist between the coeffi-cients and the temperature turnover point, Tp, which is the temperature at which the frequency function given by Equation 3 peaks and the slope of the freguency-temperature curve equals zero. The frequency sensitivity to temperature, ST, may be obtained by differentiating Equation 3 with respect to temperature as follows:

ST = ~)= A + 2B(T To) + 3C(T - To)2 (Equation 4) Equation 4 indicates that the temperature sensitivity can be minimized through the use of compensating first, second and third order terms and by operating at temperatures other than the reference temperature To. In general, however, the coef-, 3 ~
~ ients A, B, C and the temperature turnover point are f~nc-tions of the crystallographic orientation. Also, each succes-sive order of temperature coefficient decreases by several orders of magnitude. This means that coefficients B and C
are so small that they can only be used to compensate for the effects of A at temperatures far from the reference tempera-ture. Thus, to minimize the temperature sensitivity at reason-able turnover temperatures, an additional thermal degree of freedom can be employed which affects crystal frequency. It has been shown by Equation 2 that crystals change frequency due to applied loads. As will be shown~ frequency changes due to thermally induced mechanical stress, SF, can combine with the unmounted temperature sensitivity, ST, to provide optimized total temperature performance.
As illustrated in Fig. 3, a load sensitive crystal tuning fork 60 is encapsulated by a bellows 62 which is attach-ed to tuning fork mounts 64. The bellows 62 has a coefficient of thermal expansion, c~, which is different from that of the crystal, G~c. If the temperature is changed~ the thermal mismatch causes differential thermal growth over the length, ~, which reacts against the bellows spring rate, XB~ to load the tuning fork 60 and change its resonant frequency. The thermally induced change in load with temperature is given by:

d F/~T = KB ~ C~ ) (Equation 5) Using Equation 2, the fractional change in frequency with tem-perature STF due to the mechanical stress is defined by:

STF = S~ [KB~it (~
(Equation 6) ~ ~ ~5~,30 ~-ne thermally induced stress sensitivity, STF, of Equation 6 combines with the unmounted crystal temperature sensitivity, ST, of Equation 4 to minimi~e the overall temperature sen-sitivity at desired reference temperatures. That is, the spring rates, coefficients of expansion, dimensions, crystal force sensitivity and crystallographic orientations are chosen such that the overall combined temperature frequency curve peaks and is thus constant at the desired turnover temperature in the sensor's operating range. The bellows 62 may be re-placed with an equivalent spring. However, the sealed bellows 62 isolates the tuning fork 60 from the external environment and thus allows the tuning fork 60 to operate in a vacuum or inert atmosphere 66. The vacuum reduces the energy loss of the tuning fork 60, improving its Q and eliminating contamin-ants which can cause frequency drift. Also, the bellows 62 allows crystal operation in the vacuum or inert atmosphere 6Ç
and the measurement of external forces while isolating the crystal from the force producing environment.
Fig. 4 illustrates another embodiment of the inven-tive temperature compensation arrangement. A load sensitive crystal resonator 70 is loaded by force transmitting member 72 which is mounted on a base 74 by a flexure hinge 76, which allows rotation only about an axis perpendicular to the plane of the figure. A bellows or reactive spring 78 reacts against the thermally induced growth to generate mechanical stress on the resonator to compensate for its inherent, unmounted tem-perature sensitivity. With the wse of a bellows 78 the reson-ator 70 may operate in a vacuum or inert atmosphere 80 within an encloswre 82, so that the device may be used as a force sensor which is isolated from the force producing environment.
The overall reactive spring rate includes the effects of the bellows or spring 78 plus the effects of the flexure hinge 76.

I 1 ~;5~30 .
Fig. 5 is another embodim~nt of the inventive bel-lows and crystal arrangement which isolates a crysta1 tuniny fork 90 from the environment. An enclosure 92 surrounds the tuning fork 90 and a bellows 94 which are connected in series between the end walls of the enclosure 92 such that the tuning fork 90 can operate in a vacuum or inert atrnosphere 95 while still sensing forces applied to the tuning fork 90 through the bellows 94. In this embodiment the bellows 94 does not encap-sulate the tuning fork 90 as with the embodiment of Fig. 3.
The arrangement may also be used to perform the inventive tem-perature compensation scheme through reactive thermally in-duced mechanical stress produced by the enclosure 92 and/or bellows 94. The embodi~ent of Fig. 5, as well as ~he embodi-ments of Figs. 3 and 4, are particularly adapted for use -as a pressure sensor, although they may be modified for use as a force sensor. As with the previously described devices, the bellows 94 can be merely a spring having specified thermal characteristics, but tuning fork 90 will then not sense input forces while operating in a vacuum or inert atmosphere. When a spring is used instead of bellows, the basic difference between the embodiments of Figs. 3 and 5, is that the spring 62 and tuning fork 60 of Fig. 3 are connected in parallel while the spring 94 and tuning fork 90 of Fig. 5 are arranged in series.
Fig. 6 illustrates a crystal force transducer 100 which is insensitive to pressure variations. A housing 102 captures two bellows 104, 106 of equal effective area.
Bellows 106 encapsulates a load sensitive crystal resonator 108 which is attached to the housing 102 and a force loading arm 110. Bellows 104, 106 may be evacuated or contain an rt atmosphere 112 in which the resonator lO~ operates.
Since bellows 104, 106 have the same effective area, forces caused by pressure variations cancel and only forces applied to the loading arm 110 are measured. The bellows spring rates, coefficients of thermal expansion of the bellows 104, 106 and housing 102, dimensions, resonator force sensitivity and crystallographic orientation are such as to minimize over-all temperature effects.
Fig. 7 is an isometric view of a temperature and pressure compensated force transducer 120. The transducer 120 employs a suspension system and closed end tuning fork sensor with an isolating bellows arrangement. The transducer in-cludes a force transmitting member 122 positioned between a pair of bellows 124 r 126 with the force transmitting member 122 being loaded through one of the bellows 124. External pressure variations are coupled equally to opposite sides of member 122 through the bellows 124, 126 so that they cancel each other. The force transmitting member 122 is mounted on a base 128 through a flexure hinge 130 J and the end of the mem-ber is secured to a tuning fork force sensor 132. The entire structure is housed within an enclosure 134 so that the tuning fork 132 can resonate in a vacuum or inert environment 136. A
force, F, applied to force transmitting member 122 through bellows 124 causes a torque about axis A-A of flexure hinge 130 which applies stress to the closed end tuning fork 132 to change its resonant frequency in accordance with the magnitude of the applied force. Even though bellows 124, 126 have ap-proximately equal areas, area tolerance and mismatches can be compensated for by varying the lever arm distance for one bel-lows 124, 126 relative to the other. For example, if bellows 126 has a smaller effective area than bellows 124, the trans-]2 l~5~3~

er 120 can still be made insen6itive to pres5~re variations by moving bellows 126 away from flexure hinge 130, or moving bellows 124 towards flexure hinge 130, thus making the ratio of the lever arms between each bellows 124, 126 and the flex-ure hinge 130 inversely proportional to the effective areas of the bellows 124, 126. The spring rates of the bellows 124, 126 and the flexure hinge 130 produce the thermal growth re-action forces on the tuning fork 132 for temperature compensa-tion.

Claims (6)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. A system for temperature compensating a relatively low frequency, flexurally vibrating resonator having a pair of mounts, comprising an elongated spring having its ends connected to respective mounting pads of said resonator to resiliently bias said resonator, wherein the coefficients of thermal expansion, dimensions, and reactive spring rates are chosen so that the thermally induced stress sensitivity combines with the unmounted temperature sensitivity of said resonator such that the overall temperature sensitivity is relatively low at the operating tempera-ture of said resonator.

2. The isolating system of claim 1, wherein said resonator is a tuning fork having a pair of tines extending between said mounts.

3. The isolating system of claim 1, wherein said resonator is a resonant beam extending between said mounts.

4. The system of claim 1, wherein said spring and resonator are arranged in substantially parallel relationship with the ends of said spring connected directly to the ends of said resonator.

5. The system of claim 1, wherein said spring and resonator are arranged in a substantially series relationship with one end of said spring connected directly to one end of said resonator and the other end of said spring indirectly connected to the other end of said resonator through an enclosure surrounding said spring and resonator.

6. The system of claim 5, wherein said spring is in the form of a bellows islating said resonator from an external environment.