Angular rate sensor system
BACKGROUND OF THE INVENTION 
     The angular rate of motion of a craft is an essential input for all navigational and inertial guidance systems. Such systems are used conventionally for aircraft, spacecraft, ships, or missiles. The sensing of the angular rate of motion is presently accomplished by means of a gyroscope. 
     However, gyroscopes have various disadvantages. They must be built to extremely high accuracies and may have drift rates of fractions of a degree per hour. Due to the expense of building them, they are very costly; they are physically large and heavy. They must be frequently and precisely maintained, for the reason that critical movable elements such as bearings may change with time. They may also be damaged by even low levels of shock and vibration. This, in turn, may cause an increase in the drift rate of unknown size, occurring at unknown times. 
     Because gyroscopes are sensitive to the effects of shock and vibration, they frequently have heavy mounting configurations to protect them, which also are expensive. 
     SUMMARY OF THE INVENTION 
     It will accordingly be obvious that it is desirable to replace a gyroscope by some other device which is less expensive and which is capable of measuring angular rates, thereby measuring the attitude of a vehicle or craft. In accordance with the present invention, this is accomplished by a balanced resonant sensor. Such a sensor is represented, in accordance with the present invention, by a tuning fork. The tuning fork should be substantially mechanically temperature-stable, having low internal friction and following Hook&#39;s Law. According to Hook&#39;s Law, the strain of an elastic body is proportional to the stress to which the body is subjected by the applied load (within elastic limits); the elastic body is to return to its original state when the stress is removed. Preferably but not necessarily, the tuning fork consists of quartz. However, other piezoelectric materials may be used, such as synthetic crystals; for example ethylene diamine tartrate (EDT), dipotassium tartrate (DKT), or ammonium dihydrogen phosphate (ADP). Non-piezoelectric materials may be used with a piezoelectric drive. 
     Preferably the tuning fork consists of an insulating material such as quartz, but it is also possible to utilize conductive materials, in which case the tines of the tuning fork must be excited electromagnetically; that is, by stationary coils and a magnetic system on the tines. 
     The tuning fork consists of a pair of tines disposed parallel to each other and capable of vibrating. They are interconnected by an output shaft or handle, from which the output signal may be derived. The output signal is simply representative of the input angular rate of motion to which the system is subjected, which cases a deflection at right angles in the direction of vibration. An optical or frequency-modulated output signal may also be obtained. 
     The output signal may be obtained by coupling four capacitors to the tines or output shaft, or it may be obtained piezoelectrically, resistively, or optically. Measurable input rates of the order of ten degrees per hour of the sensor of the invention are sufficiently low for use as a magnetically corrected directional reference and as a gravitationally corrected vertical attitude reference. If input rates of 0.1 degree per hour are measurable, the system is usable for inertial quality references such as a self-contained inertial guidance system. 
     The novel features that are considered characteristic of this invention are set forth with particularity in the appended claims. The invention itself, however, both as to its organization and method of operation, as well as additional objects and advantages thereof, will best be understood from the following description, when read in connection with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a plan view of a tuning fork for explaining the principles of the present invention; 
     FIG. 2 is a side elevational view of the tuning fork of FIG. 1 and illustrating two pairs of electrodes for deriving an output signal; 
     FIG. 3 is a plan view of a preferred embodiment of the present invention and including two tuning forks, the casing being omitted; 
     FIG. 4 is a cross-section view of the embodiment of FIG. 3 and showing a casing surrounding the tuning fork; 
     FIG. 5 is a cross-sectional view on line 5--5 of FIG. 3, also showing the casing and illustrating a capacitive output which may be used in a bridge circuit; 
     FIG. 6 illustrates the capacitive bridge obtained with the electrode arrangement of FIG. 5; 
     FIG. 7 is a plan view on enlarged scale of a portion of the sensor of FIG. 3 and illustrating both the drive and the output electrodes, including the output leads for the sensor of FIG. 3; 
     FIG. 8 is a block diagram of the output circuit for the bridge circuit of FIG. 7; 
     FIG. 9 is a block diagram similar to that of FIG. 8 but illustrating a piezoelectric output such as obtainable with the electrode configuration of FIG. 13; 
     FIG. 10 is a plan view of another angular rate sensor consisting of two tuning forks disposed in line and normal to the output shaft; 
     FIG. 11 illustrates schematically the voltage developed at the output shaft due to the mechanical deformation; 
     FIG. 12 is another embodiment of the rate sensor of the invention providing four tuning forks, each pair of tuning fork being in line, the two pairs being disposed parallel to the output shaft; 
     FIG. 13 is a schematic view on enlarged scale of a portion of the sensor of FIG. 12 and illustrates the drive electrodes as well as one of the pick-up electrodes; and 
     FIG. 14 is a plan view of still another embodiment of the sensor of the invention, featuring eight tuning forks, four being disposed on the same axis and the axes of the two sets of tuning forks being disposed parallel to the axis of the output shaft. 
    
    
     DETAILED DESCRIPTION 
     Referring now to the drawings, and particularly to FIGS. 1 and 2, there is illustrated a simple tuning fork to explain the basis of the operation of the present invention. As set forth above, the tuning fork 10 is of a piezoelectric material such a certain synthetic crystals, and preferably of quartz. Thus, FIGS. 1 and 2 illustrate a tuning fork 10 having two tines 11 and 12 and an output shaft or handle 13. The tines may be caused to vibrate by applying an electric field thereto, such as will be explained in connection with FIGS. 4 to 6. A pair of electrodes 14, which are spaced from the free ends of each of the tines such as 11, are shown in FIG. 2 to provide a capacitive output. The tines are now vibrated toward each other, as shown by arrows 15, and away from each other on the next-half-cycle, as shown by arrows 16. Therefore, the tuning fork represents a balanced resonant circuit, because the tines 11, 12 are balanced. 
     The electrical output may be obtained by another pair of electrodes 17, 18, which may be directly applied to the area between the tines 11, 12 and the output shaft 13. The two electrodes 17, 18 assume different polarities due to the deflection of the tuning fork 10 caused by angular motion of the system. Once the angular motion is applied, the time derivative; that is, the angular rate of motion, may readily be obtained. 
     Assuming, now, a tuning fork having a distance of 0.5 cm from the center of motion to the end of the tine 11, or a distance of 0.2 cm for the portion of the tine covered by the electrode 14, a distance of 0.4 cm from the center of motion to the center of the electrode 14, a width of each tine of 0.05 cm, a thickness of each tine of 0.005 cm, while half the amplitude of vibration is 0.00025 cm and the drive frequency is 10 KHz, while the specific density of the quartz is 2.6 gm/cm 3 . With these assumptions, the angular momentum H may be calculated as follows: 
     
         H=6.53×10.sup.-4 gm cm.sup.2 /sec                    (1) 
    
     Similarly, the torque T may be calculated as follows: 
     
         T=1.89×10.sup.-7 gm cm                               (2) 
    
     Finally, the deflection of the tines is: 
     
         Y=1.62×10.sup.-7 cm                                  (3) 
    
     It can now be shown that the effect of increasing the size of the tuning fork, but not its width, is N, which goes with the fifth power of an increase of the dimensions. Hence, the following table can be calculated: 
     
                       TABLE 1                                                     
______________________________________                                    
N     1         2       3       4     5                                   
______________________________________                                    
N.sup.5                                                                   
      1         32      243     1024  3125                                
Y.sub.N                                                                   
      1.62 ×                                                        
                5.18 ×                                              
                        3.94 ×                                      
                                1.66 ×                              
                                      3.13 ×                        
(in cm)                                                                   
      10.sup.-7 10.sup.-6                                                 
                        10.sup.-5                                         
                                10.sup.-4                                 
                                      10.sup.-4                           
______________________________________                                    
 
    
     Hence, it will be evident from Table 1 that an increase of the size of the tuning fork will cause a considerable increase in the deflection of the tine. 
     Referring now generally to FIGS. 3 through 9 and particularly to FIGS. 3 through 6, there is illustrated a preferred embodiment of the present invention. This embodiment includes two tuning forks, the two axes of which are disposed spaced from and parallel to the central axis. Thus, the first tines 20, 20&#39; of the pair of tuning forks is made up of a single section 22. The section 22 is divided into two portions which make up the two tuning forks 20 and 21 by a gap 23, which, however, leaves a small bridge 24 to interconnect the two portions 20, 21. The other section 22&#39; is exactly symmetrical with the section 22 and provides the other tines 20&#39;, 21&#39; of the two tuning forks. 
     The two ends of each of the two sections 22 and 22&#39; are interconnected by an interconnecting member 25, 25&#39;. The member 25 is separated from the two sections 22 and 22&#39; by two gaps 26 and 26&#39;. The other interconnected member 25&#39; is similarly separated from the two sections 22 and 22&#39;. 
     The two interconnecting members 25 and 25&#39; form the output shaft. They are each connected by a small bridge portion 27 and 27&#39; with a surrounding frame 30, separated from the two sections 22 and 22&#39;. As shown in FIG. 4, the tuning fork may be surrounded by a casing 31. Thus, the portion 20, 20&#39; form one pair of tines and the portion 21, 21&#39; form the other tuning fork. 
     FIG. 5 illustrates the electrodes which may be provided at the ends of a pair of tines 20, 20&#39; of a tuning fork. The tine 20 is provided on opposite sides with a single electrode 32, 33. Similarly, the tine 20&#39; is provided with one electrode 34, 35. One of the inner surfaces of the casing 31 is provided with a similar electrode 36, while the other, or opposite, inner surface bears an electrode 37. 
     A sense oscillator 38 is connected to the two inner electrodes 36, 37 on the casing 31. Hence, a capacitance 40 is formed between electrodes 37 and 32. Another capacitance 41 is formed between the electrodes 33 and 36. A third capacitance 42 is formed between the electrodes 34, 37, and the fourth capacitance 43 is formed between the electrodes 35 and 36. 
     The output of the bridge circuit of FIG. 6 may be obtained by the meter 44. 
     The output circuit of the capacitance bridge of FIG. 6 is shown in FIG. 8. The drive oscillator 46 may be multiplied to some higher frequency by a multiplier 47. The drive oscillator is applied to the sensor of FIG. 3. A bridge amplifier 48 may be used to amplify the signal obtained from meter 44. This is followed by a phase detector 50 which uses a reference phase from the multiplier 47, coupled to the drive oscillator 46. The phase detector is followed by a filter 51 and an A/D converter 52 which feeds a microprocessor, linearizer, display driver and D/A converter 53. Hence, the output signal may either be obtained from the digital output lead 54 or the analog output lead 55 and may be applied to a suitable display device. 
     Reference is now made to FIG. 7, which shows, on enlarged scale, a portion of the sensor of FIG. 3 and the electrodes therefor. A pair of drive electrodes 60 and 61 is disposed on the tine 20. The two drive electrodes are connected respectively to leads 62 and 63, which in turn are connected to the drive oscillator. The two electrides are slightly spaced from each other to set up an electrical field to cause the tine to vibrate. The other tine 20&#39; is also provided with similar electrodes 60&#39; and 61&#39;, which are also connected to output leads 62&#39; and 63&#39;, leads 62 and 62&#39; being tied together. 
     A pick-up electrode 64 is connected to another pick-up electrode 65, also disposed on the tine 20. The output electrodes 64 and 65 are connected to lead 66 and to the frame 30. The other tine 20&#39; is provided with similar output electrodes. 
     It will be noted that the output electrodes 64 and 64&#39; are directly disposed on the tine, to provide a capacitive output, as shown in FIG. 6. It will be understood that one of the output leads such as 62, 63, may be grounded. 
     A piezoelectric output circuit for the electrodes of FIGS. 3 and 13 are shown in FIG. 9. Again, the drive oscillator 46 energizes the balanced sensor of FIGS. 3 and 13 via the leads 90 and 91. In this case a piezoelectric voltage appears at electrodes 96 and the corresponding hidden electrode, due to the strain in the crystal due to the tine deflection. A buffer amplifier 67 follows the sensor of FIG. 3 or 13, which in turn is followed by a phase detector 50, filter 51, A/D converter 52 and D/A converter 53. This will, again, provide either a digital or an analog signal on output leads 54, 55. It should be noted that the gaps such as 23, 26 (see FIG. 3) make it possible to increase the mass of the tines and hence to provide a lower resonant frequency. The resonant frequency of the tine in the direction of the output deflection may be made to equal the frequency of the drive signal. Thus, the resonant frequencies depend on the mass of the tines such as 20, 21, and the dimensions of the gaps 23, 26. Hence, these values can be adjusted at will. 
     Referring now to FIGS. 10 and 11, there is illustrated another configuration of the sensor in accordance with the present invention. As clearly shown in FIG. 10, the sensor comprises two tuning forks 70 and 71, disposed on a common axis at right angles to the output shaft 72. 
     The output shaft 72 is preferably fixed between two walls 73, 74. Preferably the output shaft 72 is provided with two symmetrical substantially rectangular openings 75&#39; primarily to reduce the weight of the output shaft and to reduce its stiffness. As a result, the resonant frequency of the output shaft 72 is reduced. Hence, the output shaft 72 may also serve as a pair of tuning forks. 
     FIG. 11 illustrates the polarity of the output voltage shown on curves 76, 77; that is, on opposite sides of the output shaft 72. 
     FIGS. 12 and 13 show another configuration of a sensor of the invention, providing two pairs of tuning forks. As clearly shown in FIG. 12, there is provided a first pair of tuning forks 83, 84 having a common axis, and a second pair of tuning forks 85, 86 also having a common axis, the two axes being spaced from the output shaft 87. The two pairs of tuning forks are connected to the output shaft 87 by connecting member 88. 
     FIG. 13 shows, by way of example, how the tuning forks can be driven. The input leads 90, 91 from the drive oscillator are connected so that input lead 91 goes to tuning forks 83 and 84. At the same time the upper casing 94 is energized from the input lead 90, as is the lower casing 95, thus generating an electric field between the casings 94, 95 and tuning forks 83, 84. 
     One of the output or pick-up electrodes 96 may be disposed on the interconnecting portion 88. The other output electrode is behind the electrode 96 and is not visible in FIG. 13. 
     The sensor of FIG. 14 is characterized by two pairs of four tuning forks each. Thus, a first set of tuning forks 100, 101, 102, and 103 has a common axis. The second set of four tuning forks 100&#39; through 103&#39; also has a common axis, but is spaced from that of the output shaft 105. The output shaft 105 may again be provided at each end with a rectangular relief or cutout 106 to reduce its weight and its stiffness and, hence, its resonant frequency. The tuning forks, such as 100 to 103, are separated from the output shaft by large gaps 107, 108, and 110. The output shaft 105 may again be disposed between two walls 111 and 112. 
     The output shaft 105 may be pretwisted to provide a phase shift; that is, prestressed, thereby to detect the direction of the angular motion in addition to its rate. Hence the output shaft 105 may be used to provide an output frequency that may be higher than the driving frequency. The same is true of the output shaft 72 of FIG. 10. 
     It should be noted that the electrodes preferably consist of a gold plating. By means of laser trimming, the two tines of each tuning fork may be balanced; that is, the laser may remove an appropriate portion of the electrode of one tine. This will increase the Q of the circuit. 
     There has been disclosed an angular rate sensor comprising basically a tuning fork energized by a drive oscillator. Angular motion of the system will cause a deflection of the output shaft at right angles to the direction of vibration. This deflection can be measured either by a capacitance effect, by a resistive effect, or by an electric voltage generated by the piezoelectric effect. Also, a frequency-modulated output signal may be obtained, or an optical pick-up may be used. Various configurations have been shown providing a multiplicity of tuning forks. The preferred arrangement permits control of the frequency of the output signal with respect to the vibration of the sensor. Such an angular rate sensor can be manufactured by semiconductor techniques much more inexpensively than a conventional gyroscope. In addition to being less expensive to manufacture, its accuracy should be sufficient for most practical applications, as directional and attitude references with magnetically or gravitationally corrected applications and even for inertial quality references used as a self-contained inertial guidance system.