ANALOG COMPUTER FOR PROCESSING DELTA ROSETTE STRAIN GAGE DATA

• US 3,755,658 A
• Filed: 06/02/1972
• Issued: 08/28/1973
• Est. Priority Date: 06/02/1972
• Status: Expired due to Term

• Current Assignee: Robert M. Walters
• Original Assignee: Robert M. Walters
• Inventors: Walters, Robert M.
• Primary Examiner(s): Atkinson, Charles E.
• Assistant Examiner(s): Dildine, Jr., R. Stephen
• Application Number:
  US05/259,069
• Time in Patent Office: 452 Days
• Field of Search: 33/DIG.13 73/88R,88.5R,88.5SD,89 235/151.3,185,186 338/2,6
• US Class Current: 702/42
• CPC Class Codes: G06G 7/68 for civil engineering structures, e.g. beam, strut, girder, elasticity computation
• CPC Class Codes: Y10S 33/13 Wire and strain gauges

Abstract

An analog computer which determines the state of stress at a point on the surface of a body from data produced by a standard three-gage delta rosette. The computer solves this problem by use of an analog of Mohr circles rather than by direct solution of the rosette equations. Its circuit includes a circular potentiometer with two rotatable output contacts 90* apart which is interconnected at preselected points to a resistance triangle whose vertices correspond to those of the delta rosette. The normal and associated shear stress are available at these contacts when taken with respect to appropriate potential levels. Provision is included for changing one of these levels so that the computer may be utilized with materials having different Poisson'"'"''"'"'s ratios.

Claims

1. An analog computer for solving for the normal and the associated shear stress values from the three signal voltages developed by strain gages arranged in the delta rosette geometry comprising, in combination, a circular resistance potentiometer having two rotatable brushes which are spatially disposed at right angles to each other so as to contact points on said potentiometer which are 90* apart, said potentiometer being provided with equally spaced taps which subdivide said potentiometer into nine equal resistance sections;

a resistance triangle having three series connected resistors in each leg thereof;

means for interconnecting said circular resistance potentiometer and said resistance triangle such that each successive resistance section of said circle as measured from a first starting tap and proceeding around said circle in a given direction is in parllel with each corresponding successive resistor of said triangle as measured from a first starting vertex of said triangle and proceeding around the three legs thereof in the same direction;

means for applying a different one of said signal voltages to each vertex of said resistance triangle;

means for developing from said three signal voltages a hydrostatic strain potential level Epsilon H corresponding to the average magnitude of said three signal voltages and a potential level Epsilon f corresponding to (1 -v) . Epsilon H, where

2. In an arrangement as defined in claim 1, wherein said means for interconnecting said circular resistance potentiometer and said resistance triangle includes a corner resistor connected between each vertex of said trigangle and three taps on said circular potentiometer which are 120* apart.

3. In an arrangement as defined in claim 2 wherein each corner resistor has a value when normalized by being divided by the open-circuit magnitude of a resistance section of said circular resistance potentiometer of (2.15147(1-ko)/ko, where ko equals (1-vo/1+vo) and where vo equals a preselected Poisson'"'"''"'"'s design ratio.

4. In an arrangement as defined in claim 2 wherein said means for interconnecting said circular resistance potentiometer and said resistance triangle also includes direct connections between the other taps of said circular potentiometer and the junctions of the various resistors in the individual legs of said triangle.

5. In an arrangement as defined in claim 1 wherein all of the resistors of said resistance triangle which have one side thereof connected to a vertex of said triangle are of equal magnitude;

and all of the other middle resistors of each leg are also of equal magnitude.

6. In an arrangement as defined in claim 1 wherein all of said resistors that have one side connected to a vertex of said resistance triangle have a value when normalized by being divided by the open-circuit magnitude of a resistance section of said circular resistance potentiometer of (1.13725 -2.13725ko/ko). where ko equals (1-vo/1+vo) and where vo equals a preselected Poisson'"'"''"'"'s design ratio.

7. In an arrangement as defined in claim 1 wherein all of said middle resistors of each leg have a value when normalized by being divided by the open-circuit magnitude of a resistance section of said circular resistance potentiometer of 1.13725 - 2.13725ko, where ko equals (1-vo/1+vo) and where vo equals a preselected Poisson'"'"''"'"'s design ratio. In an arrangement as defined in claim 1, an X-Y recorder;

and means for coupling to the '"'"''"'"''"'"''"'"'Y'"'"''"'"''"'"''"'"' terminals of said recorder the voltage appearing across one of the brushes of said circular potentiometer and epsilon f and the '"'"''"'"''"'"''"'"'X'"'"''"'"''"'"''"'"' terminals the voltage appearing across the other brush of said circular potentiometer and epsilon H, whereby as said brushes are rotated a Mohr stress circle is reproduced on said recorder. 9 An analog computer for processing the three signal voltages produced by a delta rosette configuration of strain gages so as to obtain an indication of the principal stresses in the material under test, comprising a circular resistance potentiometer having equally spaced taps which subdivide said potentiometer into nine equal resistance sections;

a resistance triangle having three series connected resistors forming each leg thereof;

means for interconnecting said circular resistance potentiometer and said resistance triangle such that each successive resistance section of said circle as measured from a first starting tap and proceeding around said circle in a given direction is in parallel with each corresponding successive resistor of said triangle as measured from a first starting vertex of said triangle and proceeding around the three legs thereof in the same direction;

means for energizing said resistance triangle by applying one of said signal voltages to each veRtex of said triangle;

means for developing from said three signal voltages a potential level epsilon f corresponding to (1 -m) . epsilon H, where epsilon H equals the average magnitude of said three signal voltages; and

where m equals

10. In an arrangement as defined in claim 9, wherein said means for developing said potential level epsilon f includes means for producing the potential level epsilon H;

and wherein said circular resistance potentiometer has a second rotatable brush spatially disposed at right angles to said first brush so that both brushes contact points on said potentiometer which are 90* apart.

11. In an arrangement as defined in claim 10, an X-Y display device;

and means for coupling the voltage appearing between one of said brushes and the potential level epsilon f to the Y deflecting terminals and the voltage appearing between the other brush and the potential level epsilon H to the X deflecting terminals of said display device, whereby as said brushes are rotated a Mohr circle of stress is produced by said display device.

12. In an arrangement as defined in claim 9 wherein said means for interconnecting said circular resistor potentiometer and said resistance triangle includes equal magnitude resistors joining the three vertices of said triangle to three taps of said circular potentiometer which are 120* apart.

13. In an arrangement as defined in claim 12 wherein all of the six resistors of said resistance triangle which have one side thereof connected to a vertex of said triangle have equal magnitudes;

and the three other resistors of said triangle also have equal magnitudes.

14. In an arrangement as defined in claim 9 wherein said means for developing said potential level epsilon f includes an output potentiometer connected between a potential corresponding to epsilon H which is equal to the average magnitude of said three signal voltages;

and a reference potential, with the movable tap of this output potentiometer being the location whereat said potential epsilon f with respect to said reference potential occurs.

15. An analog computer for solving the delta rosette strain gage equations comprising, in combination, a circular resistance potentiometer having two rotatable brushes which are arranged to contact points on said potentiometer which are 90* apart;

a resistance triangle;

means for interconnecting said circular potentiometer and said resistance triangle such that they form an electrical analog of a Mohr circle of stress inscribed within an equilateral triangle that is inscribed within a concentric Mohr circle of strain;

means for energizing said resistance triangle with the three signal voltages obtained from a delta rosette configuration of strain gages;

means for developing a potential level epsilon H equal to the average value of said three signal voltages; and

an output potentiometer connected between said potential level H and a reference potential level, the voltage between one of said brushes and potential level epsilon H being indicative of the magnitude of the shear stress and the voltage between the other of said brushes and the movable tap of said output potentiometer being indicative of the magnitude of the normal stress.