US3616816A - Fluidic function generator - Google Patents

Abstract

A FLUIDIC BRIDGE CIRCUIT CONSISTING OF A PAIR OF FIXED RESTRICTORS AND A PAIR OF VARIABLE RESTRICTORS GENERATES A FLUID SIGNAL WHOSE PRESSURE VARIES IN A PREDETERMINED NONLINEAR MANNER. THE VARIABLE RESTRICTORS ARE FORMED BY AN AXIAL GROOVE IN A ROTARY SHAFT AND A VENTED GROOVE FORMED IN ACCORDANCE WITH A PREDETERMINED NONLINEAR MATHEMATICAL FUNCTION IN A SLEEVE MEMBER SURROUNDING THE SHAFT. THE VENTED POINT OF OVERLAP OF THE NONLINEAR GROOVE WITH RESPECT TO THE SHAFT AXIAL GROOVE DIVIDES THE AXIAL GROOVE INTO THE TWO VARIABLE RESTRICTORS. PRESSURIZED FLUID IS SUPPLIED TO THE JUNCTURE OF THE FIXED RESTRICTORS, AND THE FLUID PRESSURE AT THE JUNCTURE OF EACH FIXED AND VARIABLE RESTRICTOR VARIES NONLINEARLY WITH CHANGE IN SHAFT ANGULAR POSITION IN ACCORDANCE WITH THE PREDETERMINED NONLINEAR FUNCTION.

Description

Nov 2, 1971 HONDA 3,616,816

FLUIDIC FUNCTION GENERATOR Filed June 1, 1970 [77 Van g; Thomas 5. Hana/a,

by Q

3,616,816 FLUIDIC FUNCTION GENERATOR Thomas S. Honda, Scotia, N.Y., assignor to General Electric Company Filed June 1, 1970, Ser. No. 42,224 Int. Cl. F15c 3/02; F16k 11/14 US. Cl. 137-609 10 Claims ABSTRACT OF THE DISCLOSURE A fluidic bridge circuit consisting of a pair of fixed restrictors and a pair of variable restrictors generates a fluid signal whose pressure varies in a predetermined nonlinear manner. The variable restrictors are formed by an axial groove in a rotary shaft and a vented groove formed in accordance with a predetermined nonlinear mathematical function in a sleeve member surrounding the shaft. The vented point of overlap of the nonlinear groove with respect to the shaft axial groove divides the axial groove into the two variable restrictors. Pressurized fluid is supplied to the juncture of the fixed restrictors, and the fluid pressure at the juncture of each fixed and variable restrictor varies nonlinearly with change in shaft angular position in accordance with the predetermined nonlinear function.

My invention relates to a fluidic device for generating a pressure signal varying in a predetermined nonlinear manner, and in particular, to a device for generatnig such pressure signals as a nonlinear function of the angular position of a rotary shaft.

This application is related to a concurrently filed patent application S.N. 42,292, entitled Fluidic Angular Position Sensor having the same inventor and assigned to the same assi-gnee as the present invention.

In many control systems, specific nonlinear mathematical functions must be generated in order to accomplish a particular control action, examples of such functions being the sine or cosine of an angle parameter in the control system and the square or square root of a particular scaler quantity. Thus, in an attitude control, it is often necessary to transform signals according to the sine and cosine function of a relative gimbal angle. In the particular field of fluidic control systems, resolvers and other type fluidic function generators of high accuracy are not presently known and are a necessary component in order to obtain all fluidic control systems. The prior art function generators and resolvers are primarily electronic, mechanical or electromechanical, and thus their use in fluidic control systems necessitates the additional use of suitable transducers for converting the signals to the proper form.

Therefore, one of the principal objects of my invention is to provide a fluidic function generator and fluidic resolver.

Another object of my invention is to provide the device with an improved accuracy due to a relatively large range of motion of the elements of the device.

Briefly stated, my fluidic function generator device includes a rotary shaft and a sleeve member supported in a housing. The rotary shaft is provided with an axial groove and is rotatable relative to the sleeve member. The sleeve member surrounds a portion of the shaft including the major portion of the axial groove in fluid-tight relationship and is provided with a vented groove formed in accordance with a predetermined nonlinear mathematical function in overlapping fluid communication with the axial groove. Pressure signals representing the nonlinear function are developed at the output of a fluidic bridge circuit consisting of a pair of fixed restrictors and a pair of variable restrictors. The vented point of overlap of the non- "United States Patent 3,616,816 Patented Nov. 2., 1971 "ice linear groove with the shaft axial groove divides the axial groove into the two variable restrictors. Pressurized fluid is supplied to a juncture of the fixed restrictors, and the differential pressure at the two junctures of the fixed and variable restrictors varies nonlinearly with change in shaft angular position in accordance with the predetermined nonlinear function.

The features of my invention which I desire to protect herein are pointed out with particularity in the appended claims. The invention itself, however, both as to its organization and method of operation, together with further objects and advantages thereof, may best be understood by reference to the following description taken in connection with the accompanying drawing wherein like parts in each of the several figures are identified by the same reference character, and wherein:

FIG. 1 is a diagrammatic view of a fluidic function generator constructed in accordance with my invention and capable of developing a signal which varies as the square of the shaft input angle;

FIG. 2 is a diagrammatic view of a fluidic resolver device capable of generating the sine or cosine function; and

FIG. 3 is a perspective sectional view taken along line 3-3 in FIG. 2 illustrating the vented groove formed only on the inside surface of the sleeve member.

Referring now in particular to FIG. 1, there is shown a cylindrical rotary shaft 4 and a circular sleeve member 5 both supported in a housing shown by the cross-hatching and identified as a whole by numeral 6. Shaft 4 is rotatable relative to sleeve member 5 but is in fluid-tight relationship therewith, the fluid-tightness being obtained by any conventional means such as capillary clearance. The drivenportion 4a of rotary shaft 4 extends outward of the housing, shown extending to the left of the housing, and the shaft is mounted in conventional thrust and journal bearings 7 and 8 for support within the housing. An axial groove 9 having constant narrow width and depth dimensions is formed into the outer surface of shaft 4 along the entire length of the central portion thereof. Shaft 4 has reduced diameter portions 4b intermediate bearings 8 and the shaft central portion to form two annular shaped chambers 10 in the volumes not occupied by the reduced diameter portions 412 of the shaft. A pair of first fluid flow passage 11 and 12 have first ends thereof in fluid communication with chambers 10 and second ends thereof comprise the outputs of my fluidic function generator device across which is developed a differential pressure P P A pair of second fluid flow passages 13 and 14 have first ends thereof in fluid communication with passages 11 and 12 and second ends thereof in fluid communication with a source of pressurized fluid P at the juncture of passages 13 and 14. The fluid utilized in my device may be a gas such as pressurized air, or a liquid such as pressurized oil, that is, my device can be pneumatic or hydraulic. Passages 13 and 14 are provided with fixed fluid flow restrictors 15 and 16', respectively. In general, restrictors 15 and 16 have equal flow restrictive values. Sleeve member 5 is concentric with shaft 4 and surrounds the central portion thereof. The ends of sleeve member 5 are in close proximity to the ends of the central portion of shaft 4, being spaced therefrom by the housing members 6a which support the ends of the sleeve member within the housing. Sleeve member 5 is provided with a vented groove of predetermined nonlinear shape which is adapted to be in overlapping fluid com munication with the axial groove 9 on rotary shaft 4. The particular shape of groove 17 determines the particular mathematical function to be generated by my device. Groove 17 may be vented to the atmosphere surrounding the housing by being formed completely through the side of sleeve member 5 as shown in FIG. 1, or alternatively, may be formed on the inner surface of the sleeve member in a manner similar to that depicted in a sectional view in FIG. 3 for a resolver device. The angular extension of groove 17 around sleeve member 5 is dependent upon the particular mathematical function to be generated. Thus, in the specific fluidic function generator device depicted in FIG. 1 for generating a mathematical square function, groove 17 extends less than 360 around sleeve member 5 in the predetermined nonlinear pattern necessary to generate an output differential pressure representing the square of the shaft angular displacement input P P =k() where 0 is the shaft angular displacement from a zero reference angle and k is the gain of the device. The shape of groove 17 for describing the mathematical square function is as follows. The starting point of the groove 17 is midway along the length of sleeve member 5 corresponding to the midpoint of axial groove 9. Groove 17 is then formed in sleeve member 5 in accordance with the square function, that is, the unidirectional axial displacement described by the groove for equal increments of angular displacement of the sleeve member varies nonlinearly from near zero for the smallest angular displacement to a relatively large and predetermined value for the larger angular displacement which is less than 360 from the starting point angular position. It should be obvious that the square root, cube, and other nonlinear function can be readily achieved by proper shaping of groove 17.

As stated hereinabove, axial groove 9 has a width and depth of narrow dimensions such that it presents a relatively high restriction to fluid flow therethrough. Groove 17 is of significantly larger depth, and, or width dimensions such that it prevents a negligible restriction to the fluid being vented therethrough. Thus, it can be appreciated that my fiuidic function generator device forms a fluidic bridge circuit including a pair of fixed restrictors and 16 and a pair of variable restrictors formed by the axial groove 9 divided into two variable length parts defined between the ends thereof and the vented point of overlap 19 with groove 17. Thus, in the particular angular position 0 of shaft 4 in FIG. 1, the first of the two variable restrictors 9a is defined by the length of the axial groove between the left end thereof and the point of overlap 19 with the vented groove 17, and the second variable restrictor 9b is the length of axial groove 9' defined between overlap point 19 and the right end of the axial groove. The fiuidic bridge circuit is thus completely described as including a pair of fixed restrictors 15, 16, a pair of variable restrictors 9a, 9b, a source of pressurized fluid supplied to the juncture of fixed restrictors 15- and 16, and a vent at the juncture 19 of the variable restrictors 9a and 917.

It is evident that the point of overlap 19 (i.e., the juncture of variable restrictors 9a and 9b) (shifts longitudinally) along the axial groove 9 with rotation of shaft 4, and in particular, varies nonlinearly with changes in angular position or angular displacement from a particular shaft 4 reference angular position, that is, the point of overlap 19 shifts axially in unequal increments for equal increments in angular displacement of shaft 4. The reference (or zero) position may be chosen at any particular angle orientation of shaft 4, but would commonly be at the orientation wherein axial groove 9 is overlapped by a point of the nonlinear groove 17 corresponding to zero angle of shaft 4, it being understood that in this first application, sleeve member 5 is maintained in a fixed position and only shaft 4 is movable relative thereto. It is apparent that the differential pressure P -P developed across the output ends of passages 11 and 12 is directly proportional to a predetermined nonlinear function of the angular displacement of the rotary shaft 4 from its reference position in accordance with the particular mathematical function described by groove 17 since the angular displacement determines the point of overlap 19 and thus the respective values of variable restrictors 9a and 9b. This differential output pressure varies nonlinearly with changes in the angular displacement of the shaft and it can be appreciated that the accuracy of my device can be improved by increasing the length of both the axial shaft groove 9 and nonlinear groove 17, or by increasing the diameters of shaft 4 and sleeve member 5 to obtain an even greater length of travel for a particular rotation of shaft 4. The accuracy of my device is also a function of the accuracy with which groove 17 can be formed on the sleeve member. In the case of the reference position corresponding to one end of groove 17 being located at the midpoint along groove 9, and the groove 17 being displaced from the center of axial groove 9 in only one direction as in the case of the square function depicted in FIG. 1, the output differential pressure F -P maintains the same polarity over the entire (less than 360) range of angular displacement of shaft 4. However, in the case of groove 17 being distributed on both sides of the midpoint of axial groove 9, as in the case of the geometric sine and cosine functions in FIG. 2, the output differential pressure changes in polarity as the vented overlapped point 19 passes from one side of the midpoint of axial groove 9 to the other.

Sleeve member 5 has been described hereinabove as being supported in a fixed (nonrotary) position within housing 6 of my device. There are applications, however, wherein relative motion between two rotatable members occurs, and it is desired to sense the relative motion inputs. In such case sleeve member 5 is not retained in a fixed nonrotary position but is adapted for rotary motion by any suitable means such as the depicted gear 18 mounted around a central portion of sleeve member 5 in FIG. 1. The gear teeth are not illustrated in order to more clearly depict the shape of groove 17, but they would be parallel to the coincident axis of shaft 4 and sleeve member 5. In the case wherein the means for rotating sleeve member 5 is a gear, a second gear (not shown) is positioned in meshing engagement with gear 18 and such second gear is suitably driven by an actuator device such as a motor. In this case wherein both shaft 4 and sleeve member 5 are rotated by independent means, the differential pressure P P 'developed across the output ends of passages 11 and 12 is related to the relative motion inputs to shaft 4 and sleeve member 5 in accordance with the particular nonlinear mathematical function described by groove 17.

Groove 17 as depicted in FIG. 1 is formed completely through the side of. sleeve member 5. Alternatively, as depicted in FIG. 2 and the sectional view thereof in FIG. 3, groove 17 is formed in the inner surface of sleeve member 5 and does not pass completely through the side thereof as in the case of FIG. 1. Suitable venting to the atmosphere is provided by one or preferably more than one vent holes 30 passing radially outward of groove 17 to the outer surface of sleeve member 5. Groove 17 in the FIG. 1 embodiment may also be formed only in the inner surface of sleeve member 5, and suitably vented, rather than being formed completely through the sleeve member.

The operation of the FIG. l embodiment of my fluidic function generator (with sleeve member 5 fixed) may be described as follows. At initial steady state conditions, the vented point of overlap 91 of groove 17 relative to axial groove 9 is midway along the axial groove such as variable restrictors 9a and 9b are equal, that is, the vented point of overlap coincides with a zero value 6 of the angular position of shaft 4. At this initial or reference condition of shaft 4 relative to sleeve member 5, output pressures P =P A change in angular displace ment of shaft 4, such as by rotation through an angle 0 from the reference or zero angle results in the vented point of overlap 19 being shifted axially to the left of the midpoint as shown in FIG. 1 whereby variable restrictors 9a or 9b are unequal and result in a particular differential pressure Pol-"P02 not equal to zero developed across the output ends of passages 11* and 12. A further in.-

crease in the angular displacement of shaft 4 results in a greater differential pressure developed across the output in passages 11 and 12 in accordance with the mathematical square function. Likewise, a subsequent decrease in the angular displacement of shaft 4 would result in a smaller differential pressure.

In the case wherein there is relative motion between two rotary members, the output differential represents the square of the relative displacement or motion inputs of the two rotary members P P =k( 0 where 0 is the angular displacement of the other rotary member, assuming a unity gear ratio, and k is a gain factor for the device.

FIG. 2 illustrates my fluidic function generator operable as a resolver in that it generates the geometric sine or cosine functions. The elements of the FIG. 2 embodiment may be identical to that in FIG. 1 except for the groove 17' formed in sleeve member 5. The shape of groove 17' necessary to describe the geometric sine and cosine functions is circular when viewed from the side as illustrated in FIG. 2 and when viewed from the end of sleeve member 5. When taken along a plane 45 relative to the (longitudinal) axis of sleeve member 5, groove 17 has a shape of an ellipse. Groove 17' thus describes a 360 path around sleeve member and in view of such groove orientation, it is desirable to form such groove into the inner surface of sleeve member 5 and not completely through the sleeve member as in the case of the square function illustrated in FIG. 1 which would result in the sleeve member being split into two parts. The perspective sectional view in FIG. 3 illustrates one half of groove 17' as would be seen in the plane taken along line 3-3 in FIG. 2. Suitable means for venting groove 17' to the atmosphere surrounding sleeve member '5 must be provided and for such purposes a plurality of vent holes 30 oriented at 90 intervals around sleeve member 5 are formed radially from the groove to the outer surface of the sleeve member. The outer edges of groove 17' at the inner surface of sleeve member 5 are indicated by numerals 31 and the inner edges of the groove at the surface parallel to the inner and outer surfaces of sleeve member 5 and intermediate thereof are designated by numerals 32.

The geometric sine function is obtained by establishing the reference orientation (i.e., zero angle) of axial groove 9 and groove 17' such that the vented point of overlap 19 thereof occurs at the midpoint of axial groove 9 such that restrictors 9a and 9b are equal. This would correspond to overlap point 19 being the top or bottom of groove 17' as viewed in FIG. 2. The particular point of overlap 19 illustrated in FIG. 2 is representative of the sine of 90 and 270. Thus, it is evident that at the zero reference angular position of shaft 4 with respect to sleeve member 5, output pressures P and P are equal and represent the sine of 0 or 180. Assuming the zero reference angle to be at the top of groove 17' as viewed in FIG. 2, it is noted that angular displacement of shaft 4 through an angle of 90 in the direction wherein overlap point 19 shifts to the right of the midpoint of axial groove *9 results in the output differential pressure P -P increasing from zero to its maximum value at the 90 point. Further angular displacement of shaft 4 of an additional 90 results in the output differential pressure being reduced to zero corresponding to the 180 point. An additional angular displacement of 90 in the same direction causes a reversal in sign of the output differential pressure which again increases to its maximum value at the 270 point and then reduces to zero for an additional 90 displacement, ending up at the starting point and satisfying the identity sine O=sine 360=0.

The function generator in FIG. 2 operates as a geometric cosine generator by establishing the Zero reference angle at an orientation of the axial groove 9 and groove 17' such that the point of overlap is at the extreme left or right of groove 17 as viewed in FIG. 2.

Thus, as depicted in FIG. 2, the point of overlap 19 at the extreme left of groove 17 represents the cosine of 0 or 180. Assuming such reference position establishes the cosine of 0, the output differential pressure P -P is a maximum due to the maximum unbalance of variable restrictors 9a and 9b. Angular displacement of shaft 4 through obtains a zero output differential pressure due to restrictors 9a and 9b being equal at such point of overlap. A further angular displacement of shaft 4 in the same direction results in the point of overlap shifting to the extreme right of groove 17 as viewed in FIG. 2 thereby establishing a maximum output differential pressure of opposite polarity from that occurring with the point of overlap at the extreme left of groove 17'. Further, angular displacement of shaft 4 results in the output differential pressure assuming values which represent the cosine of angles between and 360 and it is noted that the zero degree point is in correspondence to the 360 point as in the case of the sine function.

From the foregoing description, it is apparent that my invention attains the objectives set forth and makes available a new fluidic function generator having a high degree of accuracy over its entire range of operation. The range of motion of the function generator may be increased, as desired, by lengthening the axial groove 9 and the groove 17 in the sleeve member for certain mathematical functions (i.e., the square or square root functions), and by increasing the diameter of shaft 4 and correspondingly increasing the diameter of sleeve member 5 for all mathematical functions including the geometric functions. Thus, the accuracy of my fluidic function generator can be controlled to any desired degree.

What I claim as new and desire to secure by Letters Patent of the United States is:

1. A fluidic function generator comprising:

a rotary shaft having an axial groove in the outer surface thereof,

means surrounding a portion of said shaft including the axial groove in fluid-tight relationship and having a vented groove of predetermined nonlinear shape corresponding to a particular nonlinear mathematical function in overlapping fluid communication with the axial groove, said shaft being rotatable relative to said nonlinear groove means,

first passage means including a pair of fixed fluid flow restrictors therein for forming one-half of a fluidic bridge circuit, first ends of said fixed restrictors connected at a juncture supplied from a source of pressurized fluid, and

second passage means interconnecting nonjuncture second ends of said fixed restrictors with the two ends of the axial groove on said rotary shaft for performing the second half of the fluidic bridge circuit consisting of a pair of variable fluid flow restrictors formed by the axial groove divided into two variable length parts defined between the ends thereof and the vented point of overlap thereof with the nonlinear groove wherein the point of overlap varies nonlinearly with change in angular position of the rotary shaft in accordance with the particular nonlinear mathematical function.

2. The fluidic function generators set forth in claim 1 and further comprising:

a housing for supporting said rotary shaft and nonlinear groove means, said nonlinear groove means provided with means for rotary motion relative to said rotary shaft,

said second passage means having first ends in fluid communication with the two ends of the axial groove and second ends comprising the output of said bridge circuit across which is developed a differential pressure that varies nonlinearly with change in relative angular displacement between said rotary shaft and said nonlinear groove means.

3. The fluidic function generator set forth in claim ll wherein:

said nonlinear groove means comprises a sleeve member concentric with said rotary shaft and surrounding a. portion of said rotary shaft including the major part of the axial groove,

the vented nonlinear groove consisting of a groove formed completely through the side of said sleeve member.

4. The fluidic function generator set forth in claim 1 wherein:

said first and second passage means comprise first and second pairs of fluid flow passages, respectively,

5. The fluidic function generator set forth in claim 1 and further comprising:

a housing for supporting said rotary shaft and nonlinear groove means, said nonlinear groove means being retained within said housing in a fixed position,

said second passage means having first ends in fluid communication with the two ends of the axial groove and second ends comprising the output of said bridge circuit across which is developed a differential pressure that varies nonlinearly with change in angular displacement of the rotary shaft from a reference angular position in accordance with the particular nonlinear mathematical function.

6. The fluidic function generator set forth in claim 5 wherein:

said first passage means having first ends in fluid communication with the juncture supplied from the source of pressurized fluid,

the source of pressurized fluid being maintained at a relatively constant pressure,

said first passage means having second ends in fluid communication with said second passage means intermediate the ends thereof, and

said rotary shaft provided with reduced diameter portions adjacent both sides of the shaft portion including the axial groove, the reduced diameter shaft portions forming annular shaped chambers for providing fluid communication between the ends of the axial groove and the first ends of said second passage means.

7. The fluidic function generator set forth in claim 5 wherein:

said nonlinear groove is formed in accordance with a mathematical square function whereby the differential pressure varies nonlinearly with change in shaft angular displacement as the square thereof.

8. The fluidic function generator set forth in claim 5 wherein:

said nonlinear groove means comprises a sleeve member concentric with said rotary shaft and surrounding a portion of said rotary shaft including the major part of the axial groove, the nonlinear groove being of circular shape when viewed from the side or end of said sleeve member, and being of elliptical shape when viewed in a plane 45 relative to the axis of said rotary shaft and sleeve member whereby the differential pressure varies nonlinearly with change in angular displacement of the rotary shaft from a reference angular position in accordance with the geometric sine or cosine function. 9. The fluidic function generator set forth in claim 1 wherein:

said nonlinear groove means comprises a sleeve mem ber concentric with said rotary shaft and surrounding a portion of said rotary shaft including the major part of the axial groove, the vented nonlinear groove consisting of a groove formed into the inner surface of said sleeve member but not passing completely through the side thereof, and vent means provided from the nonlinear groove to the outer surface of said sleeve member. 10. The fluidic function generator set forth in claim 9 wherein:

said axial groove having constant narrow width and depth dimensions to provide a relatively high restriction to fluid flow therethrough, said nonlinear groove having larger width and or depth dimensions than the axial groove to provide a neg ligible restriction to fluid being vented therethrough.

References Cited UNITED STATES PATENTS 2,833,311 5/1958 Baldelli 138-43 2,840,096 6/1958 DuBois 13843 X 3,103,231 9/1963 Moen 137-625.4 X 3,148,703 9/1964 Kachline 138-43 X 3,410,291 11/1968 Boothe et al 1378l.5 3,461,833 8/1969 Boyadjiefi 137608 X 3,532,127 10/1970 Vobelsang et al. 137--608 X 3,554,229 1/1971 Coyle 137608 SAMUEL SCOTT, Primary Examiner U.S. Cl. X.-R. 13781.5

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