US3097433A

US3097433A - cubberly

Info

Publication number: US3097433A
Authority: US
Publication date: 1963-07-16
Anticipated expiration: 1980-07-16

Description

July 16, 1963 w. E. CUBBERLY, JR 3,097,433

BoREHoLE APPARATUS 5 Sheets-Sheet l Filed Sept. 30, 1960 240 INVENTOR.

BY M] July 16, 1963 w. E. CUBBERLY, JR 3,097,433

BOREHOLE APPARATUS Filed Sept. 50. 1960 /x v /V-m VVG/fer i Caer/y,

NVENTOR.

ATTORNEY July 16, 1963 w. E. CUBBERLY, JR 3,097,433

oREsHoLE4 APPARATUS Filed sept. so, 1960 s sheetssheet s United States Patent O ce 3,097,433 BDREHLE APPARATUS Walter E. Cubberly, Jr., Houston, Tex., assignor to Schlumberger Well Surveying Corporation, Houston, Tex., a corporation of Texas Filed Sept. 30, 1960, Ser. No. 59,758 Claims. (Cl. 33-178) This invention relates to apparatus for gauging the size of well bores as well as centralizing well logging tools .in -a well bore. More particularly, this invention relates toa device which performs a combined centralizercaliper function and is used with well logging apparatus.

Rigid arm calipering devices are well known and generally involve one or more rigid arms urged outwardly from a tool body by spring action into continuous contact with the well bore and include devices for measuring the radial extension of the rigid arms from the tool body to obtain indications of the diameter of the well bore.

Another type of caliper devices utilizes relatively long, arched springs attached to collars on a tool body wherein one of the collars is slidable along the tool body. The springs are normally preformed or curved to extend outwardly from the tool body to a larger diameter than the diameter of the borehole to be measured so that, when inserted into ya borehole, the arched portions of the springs contact the wall of the well bore and are forced inwardly. Hence, relative movement between the collars may be sensed to provide an indication of the borehole diameter. In practice, the length of such spring type calipers is at least six feet, so that the springs may operate over a wide range of borehole diameters. An example of this kind of caliper may be found in Patent No. 2,712,697.

Spring type centralizers, on the other hand, employ relatively strong, preformed, curved springs xed at their ends to a body member so as to extend outwardly normally to a given diameter which is slightly greater than the diameter of the borehole. With this construction, the resistance of the springs to compression provides the required centralizring force in boreholes of a particular diameter, yet permits sliding longitudinal movement of the centralizer through the well bore.

Hence, `spring type calipers and spring type ceutralizers are inapposite since a spring caliper requires a relatively long spring to respond to a wide range of borehole diameters and `a spring centralizer requires a relatively strong spring sized to a particular diameter to provide the necessary forces to centralize. Heretofore, it has been necessary to use both a centralizing device and ra caliper device when a caliper log is desired with la centralized tool and the caliper device is one of the rigid arm types. This type of caliper device has been favorably integrated into wall Contact devices which depend upon an electrode pad contacting the wall of the well bore. Hence, the length and complexity of the tool is not increased substantially since the caliper is operated conjunctively with the device to place the electrode pad in cont-act with the well bores. However, 4in certain types of well tools, for example, a sonic logging tool, wall-engaging pads .are not used. Hence, the complexity and length of the tool would be increased if a rigid arm caliper were added to the tool.

Accordingly, it is an object of the present invention to` provide a new and improved centralizing and well calipering device.

A further object of the present invention is to provide la new and improved combination centralizing-caliper device for use with a sonic logging tool.

A still further object of the present invention is to provide a new and improved centralizing-caliper device which is relatively short and compact in arrangement.

Apparatus, in accordance with the present invention, includes a tubular housing upon which relatively short,

y 3,097,433 Patented July 16, 1963 bowed, spring arms are mounted. The respective ends of each spring 'arm are supported for movement relative to one another. The central portions of the bow springs 'are arranged to extend outwardly of the tool body into contact with the well bore wit-h a substantially constant centralizing force and to deflect, in response to changes in the well bore diameter, thereby to produce relative movement between the ends of the spring, the relative movement being sen-sed by a measuring device. The measuring device develops an electrical signal representative of the well bore diameter. The bow springs are preformed to `a semi-elliptical shape or curvature so as to normally extend outwardly of the tool intermediate of a fully collapsed and 'a fully extended position for the central portions of the springs while a coil spring is .tensione-d between the ends of the bow springs tending to extend the bow springs from their normal position to ra fully extended position. The relationship between the bow springs and coil spring is such that the centering force of the bow springs is maintained substantially constant over a wide range of borehole diameters.

The novel features of the present invention are set forth with particularity in the appended claims. The present invention, both as to its organization and manner of operation, together with :further objects and advantages thereof, may best be understood by way of illustration and example of certain embodiments when taken in conjunction with the Iaccompanying ldrawings in which:

FIG. l is an illustration of Iapparatus embodying the present invention disposed in a well bore;

PIG. 2 is a view in cross section of the centralizercaliper as embodied in the present invention;

FIG. 3 is a view in cross section taken along line 3-3 of FIG. 2;

FIG. 4 is a graphical depiction of the relationship of yforces in the centralizer-caliper;

FIGS. 5 and 6 lare schematic illustrations of various operating positions of the centralizer-caliper;

FIG. 7 is an electrical equalizing circuit for use with the centralizer-caliper;

FIG. 8 is =a partial view in cross section of another ernbodiment of the caliper-centralizer; and

FIG. 9 is `a View in cross section taken along line 9-9 of FIG. 8.

Referring now to FIG. l, lnumeral 10 identities a typical sonic apparatus arranged to be suspended by a cable 11 and winch (not shown) in a ll-uid iilled borehole 12. The sonic apparatus 10 includes an upper electronic cartridge '10a and a lower transducer section 10b which contains the sonic transducers. A centralizing and caliper device 13, embodying the present invention, is illustrated as coupled to the lower end of the transducer section 10b. The sonic apparatus 10 may be, for example, of the type illustrated in the co-pending application of Frank Kokesh, application Serial No. 745,548, tiled .Tune 30, 1958, and assigned to the assignee ofthe present invention.

The electronic cartridge 10a is generally a metal housing and contains the necessary yelectrical circuitry for the transducer section 10b, while the transducer section 10 includes a stilibut somewhat liexible, toil-filled, tubular mem- -ber 14 in which a transmitter T and lixed, `spaced receivers R1 and R2 are mounted on a low velocity supporting member 15 such as a stilf coiled spring or Teflon rod. In operation, the electronic circuitry periodically energizes the transmitter T to periodically emit pulses of acoustic er1- er-gy which pass through the well fluid 16 in the well bore 12 to the earth formations. The acoustic energy later successively arrives at the receivers R1 and R2 which respectively develop electrical signals in response to the arrival of acoustic energy and the time interval between the `developed electrical signals is measured by the electrical 3 circuitry which provides, for example, a measurement of the velocity of the earth formations. The velocity of the formations is, of course,y related to the porosity of the earth formations.

Referring now to lFIGS. l-3 in particular, the centralizing and caliper device 13 generally includes a rigid tubular member or housing 2i) upon which bow springs 24a-c are mounted for relative movement betweenV their ends by means of a pair of

tubular spring collars

21 and 22 slidably mounted on the housing. The

collars

21, 22 in the preferred embodiment of the invention are arranged to be non-rotatable on the tubular member and have limited longitudinal movement relative to one another lon the tubular member 20.

The calipering of the well bore 12 is accomplished by the spring arms 24a-c which are preformed to a semielliptical curvature and have an essentially rectangular cross section. Preferably three springs are employed which are secured by their `ends to the

spring collars

21 and 22 by suitable pin connections and the springs are equidistantly spaced about the central axis of the tool. The central portions `of the spring arms 24a-c engage the bore wall and their spacing is a function of the diameter of the Well bore which is related to the relative spacing betweenI the ends of the spring arms attached to the

collars

21, 22. The relative spacing `between

collars

21 and 22 is sensed |by measuring means such as a potentiometer 40 (FIG. 2). The centralizing effect of the device 13 in the well bore 12 to develop a substantially constant centralizing force over a range of borehole diameters is accomplished iby the combined action of spring arms '24a-c and a coil spring 25 suitably coupled under tension between the ends of the bow springs 24a-c coupled to the

spring collars

21, 22.

As shown in detail in FIGS. 2 and 3, the tubular body member 26 is provided with an upper pair of longitudinally extending, Adiametrically opposed, slots 26 and a lower pair `of longitudinally extending, diametrically opposed, slots 27. Over the upper slots '26, the upper spring collar 21 is slidably received on the tubular mem-ber 20, While a tubular support member 30 (FIG. 2) is slidably received within the tubular member 20. The upper spring collar 21 has diametrically opposed

openings

31, 31a sized to receive guide pins 32, 32a, the guide pins Vbeing sized to the width of the slots 26 and secured to the inner tubular support member 30 by an'exemplary threaded connection. 'I'he length `of the guide pins 32, 32a is such that they extend from support member 30 into the

openings

31, 31a of the spring collar 21, and thus the [guide pins 32, 32a and slots 26 prevent rotation of the collar 21 and support member 30 relative to `body 20 while the ends of the pair of slots 26 limit longitudinal movement of the spring collar 21 and inner support member 30 relative to the tubular member 20.

Similarly, over the lower slots 27, the lower spring collar 22 is slidably received on the tubular member 20, While an inner cylindrical support member 35 is slidably received within the tubular member 20. Also, lower spring collar 22 has diametrically opposed

openings

36, 36a, which receive guide pins 37, 37a which are threadedly secured to the cylindrical support member 35. Thus, the lower spring collar 22 and cylindrical support member 35 are arranged on the tubular member 20 for limited longitudinal movement yet will not rotate relative to the tubular member 2G.

The spacing between the pairs of

slots

26 and 27 is such that, when springs 24a-c are completely flat and parallel to the longitudinal axis of the body 20, guide pins 32, 32a are adjacent `one extremity of slots 26, Iwhile guide pins 37, 37a are adjacent a corresponding extremity of slots 27. Hence, with the springs dat, the

collars

21, 22 may ybe simultaneously moved over the length of

slots

26, 27.

A linear resistance potentiometer 40 (FIG. 2) is received within the tubular member 20 intermediate of the

slots

26 and 27 and includes a potentiometer housing 46a coupled to the tubular support member 30 and a sliding potentiometer plunger 4o!) adjustably coupled to the cylindrical support member 35. Within the tubular support member 30, a cylindrical closure member 41 is provided to form one end of a fluid tight chamber for the potentiometer housing 40a, while a tubular, flexible, boot member 42 has i-ts ends respectively secured =to the open end of the tubular support member 30 and sliding potentiometer plunger fitlb to complete the fluid enclosure chamber for the potentiometer, the fluid chamber being filled with toil. Hence, the potentiometer `40 is protected from such fluids as may be in the Well bore and is pressure balanced with respect to the hydrostatic pressure of the uid in the well bore. The electrical conductors 4-3 of the potentiometer 40 are passed through the closure member 41 and Y extend upwardly to be coupled to the circuitry for sending a signal representative of the diameter of 'the well bore via the cable conductors (not shown) to conventional indicator means 44 (FIG. l) at the surface of the earth.

Each of the

spring collars

21, 22 has an onter, annular recess 45, 46 (FlG. 2) respectively formed by

flanges

47, 48 on the collars and snap rings 49, 50` suitably received in grooves in the collars. Annular

spring support members

52, 53 are respectively received in each

recess

45 and 46 and the three flat, semi-elliptical spring members 24a-c are equidistantly spaced about fthe circumference of the

annular support members

52 and 53 and pivotally secured thereto. It will, therefore, be appreciated that inward and outward radial displacement of the central portions of the springs 24a-c will bring about a corresponding relative displacement of the spring ends which are attached to the

spring collars

21, 22 by means of

annular support members

52, 53. Also, equally apparent is the fact that body member 20 may rotate relative fto the springs 24a-c; hence, build-up of cable torque is prevented.

Coil spring 25 is coupled to

lthe spring collars

21, 22 under tension so as to normally urge the collars towards one another, the spring 25 being secured to the respective collars by suitable clamping means. Each of the spring members 24a-c is covered with a coating 56 of resilient material such as rubber to reduce the generation of sound noises in the Well bore.

In the operating position of the foregoing described assembly, before insertion into the well bore, the leaf springs 24a-c are fully extended to their maximum calipering and centralizing diameter by virtue of the tension of coil spring 25. When fthe caliper-centnalizer 13 and apparatus 10 are inserted into the well bore, the leaf springs 24a-c are deflected inwardly. The relative spacing between the

collars

21, 22 is measured by the potentiometer 4i) as a function of the well bore diameter which, of course, determines the outward extension of the central portions of the leaf springs 24a-c. The leaf springs 24a-c and coil spring 25 in combination develop a substantially constant centralizing force to support the apparatus .10 centrally in the well bore. Obviously, in relatively vertical well bores, the centralizing or `supporting force required for the apparatus is negligible. However, all well bores deviate relative to a true vertical so that a component of the weight of apparatus is developed and it is this component force that the centralizer force supports.

As shown in FIG. l, when the assembly is inserted in a Well bore,the friction of the leaf springs 24a-c resists downward movement of lthe assembly; however, this friction force is overcome by the greater Weight of the apparatus y10. Since

collars

21 and 22 are slidable on member 20, collar `22 is urged upwardly until guide pins 37, 37a abut the upper ends of slots 27, while collar 21 assumes a position relative to slots 26 `depending upon the deflection of the leaf springs 24a-c. Hence, if the Well bore diameter decreases, the collarY 21 moves upwardly and, conversely, if the well bore diameter increases, the collar 21 moves downwardly. As noted heretofore, springs 24a-c may be completely depressed without the ends of the leaf lsprings 24a-c becoming fixed relative to member 20. Thus, the centralizer-caliper is not subject to the leaf springs binding in small diameter well bores.

In a like manner, when the apparatus 10 is raised upwardly, collar 21 shifts to a lowermost position until guide pins 32, 32a :abut .the lower ends of slots 26, while collar 22 assumes a position relative to slots 27 dependent upon the deflection of leaf springs 24a-c. Hence, the centralizer-caliper is not subject to the leaf `springs binding in small diameter well bores While moving upwardly. As the apparatus is passed through the well bore, it is free to rotate relative to leaf springs 24a-c by virtue of the mounting of

annular support members

52, 53 on

collars

21 and 22 so that objectionable cable torque is not developed.

'Ihe central pontions of leaf springs 24a-c which contact the well bore determine the relative spacing between

collars

21 and 22. which is measured by potentiometer 40 and recorded by recorder 44 as a function of depth.

Further, to illustrate the present invention, the particular relationship between the flat spring larms 24a-c and coil spring 25 will now be more fully explained with reference to FIGS, 4-6. The leaf springs 24a-c, as shown in FIGS. 5 and 6 and explained heretofore, have an initial, preformed, `semi-elliptical, curvature. In FIG. 5, numeral 24 indicates the position rthat springs 24a-c -Would normally assume in the absence of coil spring 25. The three preformed leaf springs in position 24 thus extend outwardly so that their central wall contacting portions lie on an imaginary circle 57 (FIG. 6) having a diameter il. 'Ilhe curvature of leaf springs 24a-c in position 24 is such that a sufficient force in the center of the springs 24a-c will completely depress the springs to be flat or straight or, more precisely, the full length of the springs would lie parallel to the longitudinal axis of body 20. When the springs 24a-c are so depressed to a flat position along the body 20, as shown by numeral 24", the central contacting portions of springs 24a-c lie on an imaginary circle 58 (FIG. 6) having a vdiameter d which is the minimum diameter of the centralizer-caliper. When springs 24a-c are forced outwardly to ya greater curvature than position 24 to a position as indicated by numberal 24', the central contacting portions of springs 24a-c lie in an imaginary circle S9 (FIG. 6) having a diameter D which is the maximum diameter to be measured. Thus, it will be appreciated that diameter d is intermediate of diameters d and D and the central portion of a spring has an initial deflection or spacing Y0 from the central portion of a spring at a flat position 24". It will also be appreciated that fthe overall change in deflection AY of the central portion of the springs 24a-c between positions 24 and 24' is accompanied by an overall change in spacing AL between the ends of the springs. As will hereinafter be set forth, the change in spacing AL is a function of the change in deflection AY. Also, as will become apparent from the `discussion to follow, the preformed curvature of the leaf springs 24a-c in position 24 in combination with the coil spring 25 cooperate to obtain a substantially constant -centralizing force.

The mathematical analysis of the relationship between the leaf springs 24a-c and coil spring 25 will now be Set forth and following this, an exemplary design will be developed on the basis of the mathematical relationships between the springs 24a-c and coil spring 2S.

The mathematical equation for preformed shape or curvature of springs 24a-c to permit depression from position `24 to the flat position 24 may be simply derived by considering only one-half of a single bow or leaf spring since a bow or leaf spring is symmetrical about its center. Therefore, the equation for the shape of one-half of a leaf spring may be derived by cantilever beam formulas.

For example, considering the center of a spring as fixed and the end of the spring as free, the equation derived for the initial curvaure of one-half of a leaf spring is:

eater-eea where the free end of the spring in an initial unloaded condition is considered as the origin; Y equals the deflection of a point on the spring due to force P applied to the end of the spring normal to the length of the spring; X equals the distance from the origin along the spring to the aforesaid point at a deflection Y; Y0 equals the maximum deflection of the spring due to the applied force; and l equals one-half of the overall length L of the spring.

Equation l above is derived from the tions for one-half of the spring, i.e.,

d2Y M Px-Elz (2) where M equals the bending moment; P equals the force applied to the end of the spring normal to the length of the spring and X is the distance from the origin to any point on the spring; E is Youngs modulus of elasticity; I is the moment of inertia about the axis of bending; and

is the second derivative of the relationship between Y and X. A simplified way of achieving the proper curvature of the preformed spring is to support a normally flat spring at its ends and provide a concentrated load at its center sufficient to deflect the spring to the selected maximum deflection Y0.

It will be appreciated that the centralizing force exerted by the leaf springs is analogous to the force P applied normal to the length of the springs. However, in addition to the force P, the coil spring also exerts a total axial force on the three springs, which is normal to the force P. Thus, the force Q of the coil spring applied to one leaf spring is equal to moment equa- 3 Therefore, assuming the half-spring, as defined by Equation l above, to be at the initial preformed curvature, the relationship between the force P and the force Q axially applied to the end of the spring normal to force P at the normal rest position of the spring is derived by the strain energy method for a statically indeterminate member. The expression for deflection Sp in the direction of the force P is determined by taking the partial derivative of the strain energy (taking into consideration both of the forces P and Q) with respect to the force P which gives the following equation Evaluating the Equation 3 on the basis that the spring is constrained from deflecting in the direction of the force P, Sp is set equal to Zero. Simplifying the equation and solving for P yields 4 which is the expression for the relationship between P and Q at the initial position.

general form by replacing Y with'CYo so that where C is a proportionality factor relating the new position of the end of the spring due to the additional force P0 to the initial position of the end of the spring due to force P. Hence, for C=1, the end position is at Y0, the initial position.

Equation 3 can also be rewritten to the general form by the same substitution of 1CY0 for Y0 so that l2 6 lsVTE-I[Pz-gono] (s) The deflection SI, to the new position is also equatable as By substituting Equation 7 in Equation 6 and rearranging terms, the expression for the force P vs. the force Q at any position of the spring may be expressed as To expand the above mathematical analysis to apply to the full length, three arm centraliZer-caliper, Equation 8 is multiplied by two for the full length of the spring and further multiplied by three for the gross centralizing effort of the device and nally multiplied by one-half to determine the minimum centralizing effort, Fmm of the centralizer. `It should be noted that in determining the minimum centralizing effort Fmm, the factor of one-half is based upon a three arm centralizer in its normal logging position in a well bore wherein two of the arms are positioned at an angle of 60 to the lowermost portion or generatrix of the well bore. Therefore,

Since, in Equation 9, the force Q of the coil spring is equal to Fmin=3 and the half length l of a leaf spring equals the overall length L divided by two, substituting these values in Equation 9 determines the expression for the minimum force (Fmm) for the three arm centralizer, which is 72EIY0(1 C +12Y0C L3 5L Equation 10 may be simplified by considering the force Fs required to flatten one spring which is min Equation 12 is shown plotted in FIG. 4 for values of Fs and C where o It will be appreciated from Equation 12 and FIG. 4 that (a) the centralizing effort is equal to centralizing force would be a straight line function Where Fs is constant regardless of the well bore diameter. The

value of the coil spring force to give this constant response is computed by setting the bracketed terms in Equation 12, i.e.

12 3 gEYOQ 5ml equal to zero and solving for which yields In actual practice, the centralizer is designed so that an ideal 'Q is obtained at the maximum diameter of the centralizer. Since the coil spring force will increase according to its spring rate as the diameter of the well bore decreases, the actual centralizing force is not ideally constant but is substantially constant as indicated by the dashed curve 69 in FIG. 4. It will be noted that curve 60 ultimately arrives at a value of 3/2 :Fs when the leaf springs atten.

It will be appreciated from the foregoing and particularly Equation 12 that both the leaf springs 24a-c and coil springs 25 contribute to the total centralizing force. Rewriting Equation 12 as follows:

It will be seen that the term 3/2 FS (l-C) is the component of force FL of the centralizing force Fmm due to the leaf springs and the term 5 L is the component of force FC due to the coil spring. The proportionality constant C is a function of the diameter of the circle enclosing the central portions of springs 24a-c and, hence, the scale of well bore diameters is shown in FIG. 4 as Well as the values of C. 'In FIG. 4, the minimum diameter d is equal to 4', the diameter E equal to 10% and the diameter D equal to 14".

From the foregoing, it will also be appreciated that the contributions of the coil spring and leaf springs to the total centralizing form Fm, are complementary and combine to provide a substantially constant centralizing force over a wide range of well bore diameters. This complementary relationship is more clearly shown in FIG. 4, wherein a straight line or linear function 61 illustrates the component force Fc of centralizing force Fmm that the coil spring contributes. The straight line or linear function `62 in FIG. 4 illustrates the component force FL of the total centralizing force the leaf springs contribute. It should be noted, however, in actual practice, that the curve 6@ is the result of a slight curvature of function 61 due to the spring rate of the coil spring and the ratio of travel of the collars to the bow spring deflection and a slight curvature of function 62 because the value of L does not remain constant.

A practical example of a caliper centralizer design is as follows:

Selected known factors are:

The value for l is based upon a 1/16 x 1 spring stock steel SAE 615 0 or equivalent. Next, a range of diameters for the centraliZer-caliper is selected, for example:

d=4 diameter of springs flat on tool body D=14 maximum diameter of borehole to be calipered.

The next consideration is the potentiometer 40 and how much travel the potentiometer plunger 40a should have. A suitable value is, for example, 2.31 of movement of the potentiometer plunger 40b relative to the potentiometer housing 40a. From the range of 4" and 14" diameters selected, it is known that the deflection (Y) of a leaf spring will be 5 and this deflection should produce a travel of 2.31 between the ends of the springs 24a-c and

slidable collars

21, 22. The length L of a leaf spring to give a -5 deection with its ends moving from 0-2.31, is determined from the formula:

where AL equals the relative travel between the sliding collars and movement of the spring ends (2.3l); y equals the deection of the spring and L equals the length of the spring. Hence, solving Equation l5, the length L of a spring is equal to 26".

The next consideration is the minimum centralizing force Fmm necessarily required to centralize the weight of the apparatus and this, of course, is dependent upon the weight of the apparatus and the maximum deviation in the Well bore in which the apparatus should be centered. For example, a value of 8.5# centralizing force may be adequate for apparatus weighing 56# in 8# mud in deviated well bores up to 10. From the known value of 8.5# for Fmm, the force FS to depress one spring can be determined from Equation l2 where n(5::0 and C=0 so that Substituting the values thus far obtained into Equation ll, the dellection Y0 of the curved spring in the position 24 is calculated to be 3.375. Hence, a bow spring with a lAG" x 1 cross section and length of 26l is preformed to have a center deflection of 3.375. The springs are thus preformed to this curvature and, when attached to

collars

21 and 22, their ends are spaced 2 radially from the axis of body while the central portions extend outwardly to the circle 57 with a diameter of 10%".

The coil spring -force necessary to complement the leaf spring force is then calculated by Equation 13 and is found to be 27.25# Of course, to maintain the substantially constant centralizing force, the spring rate should be low, for example lit/1. Using the above figures, the centralizing force Fmm varies generally from 8.5# at a 4 diameter to a maximum value of 10.2# at an intermediate diameter to the value of 8.5# at a 14 diameter, thereby providing a substantially constant centralizing force.

In the foregoing description, the potentiometer 40 was noted as linear. Thus, its electrical response is a linear function of the position of plunger 40h in potentiometer housing 40a. On the other hand, the travel of the potentiometer plunger 40b is related to an exponential function of the deflection of the springs 24a-c (see Equation 15). Hence, .function forming electrical circuit 65, as shown in FIG. 7, may be employed to convert the electrical signal into a signal which is a linear lfunction of the deflection of springs 24ac. Circuit 65 includes a resistance R and a resistance r coupled across the input which is the electrical signal from the potentiometer 40 while the output is taken across resistance r. The values of resistances R and r are selected in a known manner so that the quadratic electrical input across R and r is converted to a linear by varying potential across or directly proportional to the deflection of springs 24a-c.

Turning now to FIGS. `8 and 9, a modification of the rotatable connection between tubular member 20' and the ends of bow springs 24a-c is illustrated. Since the connections at the ends of the bow springs are similar, the description of only one arrangement |will suice. Tubular member 20 in this modiiication has, as described heretofore, longitudinally extending slots 27. Cylindrical support member 35 is received Within body 20X while a tubular collar 22 is slidably mounted on the body 20. Annular support member 53 is, however, rigidly secured to collar 22. Collar Z2 is provided With

access openings

36, 36a and the inner surface of the collar adjacent these openings has an annular recess 67. Pins 37,` 37a inserted through

openings

36, 36a and slots 27 are threadedly received by support member 25. The pins` 37, 37a are dimensioned to slidably lit in the slot to prevent rotation of support member 35 relative to body 20 and terminate short of the bottom surface of the annular recess `67 so that the collar 22 is free to rotate relative to the body member 20. At the same time, the

pins

37, 37a in ar1- nular recess 67 are movable longitudinally relative to body 20 vwhen the collar 22' slides along the body.

The operation of this modified apparatus is, of course, similar to the previously described operation.

While particular embodiments of the present invention have been shown and described, it is apparent that changes and modifications may be made without departing from this invention in its broader aspects and, thenefore, the aim in the appended claims is to cover all such changes and modifications as 4fall the true spirit and scope of this invention.

I claim:

1. A well tool for use in a \Well bore including a housing, a pair of tubular collars on said housing wherein at least one of said collars is slidable on said housing permitting relative movement between said collars, bow springs pivotally connected to said collars, respectively, having a preformed curvature so that the central portions of said springs normally extend outwardly of said housing intermediate of a fully collapsed and a fully extended position for said central portions of said springs, said preformed curvature being symmetrical about a midpoint of each spring, the shape of one-half of each spring having a curvature defined by the formula when considered from an origin at the midpoint of a spring wherein Y0 equals the maximum deflection of the spring due to a given applied force, Y equals the deection of a point on the spring due to the given applied lforce, X equals the distance from the origin along the spring to the aforesaid point at a deflection Y, and l equals one-half the overall length of the spring, and a coiled spring coupled in tension between said collars for extending said bow springs to a fully extended position when unconstrained by a bore wall.

2. A well tool for use in a Well bore including a housing, a pair of tubular collars on said housing wherein at least one of said collars is slidable on said housing permitting relative movement between said collars, bow springs pivotally connected to said collars and having a prefonmed, semi-elliptical curvature so that the ce-ntral portions of said springs normally extend outwardly of said housing intermediate of a fully collapsed and a fully `extended position for said central portions of said springs yet -will assume a at position when fully collapsed, and a coiled spring coupled in tension between :said collars for extending said springs to a fully extended position when unconstrained by a bore wall.

3. A well tool Ifor use in a Well bore including a housing, a pair of tubular collars on said housing fwherein at least one of said collars is slidable on said housing, bow springs pivotally connected to said collars and having a preformed curvature so that the central portions of said springs normally extend outwardly of said housing intermediate of a fully collapsed and a fully extended position for said central portions of said springs yet will assume a flat position when fully collapsed, and a coiled spring coupled in tension between said collars for extending said springs to a fully extended position fwhen unconstrained by a bore Wall, said coil spring having a force equal to 1 l where L equals the length of a bow spring, Yo equals the initial preformed deflection of a bow spring and Fs equals the force required to flatten one bow spring. V

4. A well tool for use in a well bore including a housing; a pair of tubular collars on said housing wherein at least one collar is slidable on said housing permitting relative movement between said collars; at least three bow springs coupled to said collars and respectively having a preformed curvature so that the central portions of said bow springs normally extend outwardly of said housing intermediate of a fully collapsed and a fully extended position for said central portions of said bow springs; and a coil spring coupled in tension between said collars for extending said bow springs to a fully exten-ded position when unconstrained by a bore wall, said bow springs and coil spring providing aminimum centralizing force Fmg, for the centralizer wherein:

and where FS is the force required to flatten one spring, C is a proportionality factor calculated from movement of the end of spring from its initial preformed position to another position due to an additional force, Yo is the initial preformed deflection of the bow spring, L is the length of a bow spring and Q is the force of the coiled spring.

5. A well tool for use in a well bore including a tubular housing, bow springs having a preformed curvature so that the central portions of the springs normally extend outwardly of the housing intermediate of a fully collapsed and fully extended position for the central portions of the springs, means attaching the ends of said springs to said housing for relative longitudinal movement therebetween an-d along said housingmeans to limit longitudinal movement of said attaching means along said housing, spring means coupled in tension between said attaching means for extending said bow springs to a fully extended position when unconstrained by a bore wall, and measuring means in said tubular housing coupled to said attaching means to facilitate measurement of relative movement between the ends of said bow springs.

6. An elongated apparatus for surveying a well bore and adapted to be passed through a well bore including a well tool having a tubular housing, a pair of tubular collars on said housing said collars being slidable on said tubular housing permitting relative movement between said collars, means on said housing limiting sliding movement of said collars thereon, bow springs coupled to said collars and having a preformed curvature so that the central portions of said springs normally extend outwardly of said housing intermediate of a fully collapsed and a fully extended position for said central portions of said springs, a coiled spring coupled in tension between said collars for extending said bow springs to a fully extended position when unconstrained by a bore wall, measuring means in said tubular housing, and means coupling said measuring means to said collars to facilitate measurement of relative movement between said collars.

. 7. An elongated apparatus -for surveying a well bore and adapted to be passed through a well bore including a well tool having a tubular housing, a pair of tubular collars on said housing, at least one of said collars being slidable on said housing, bow springs, means coupling said ybow springs to said collars so that said bow springs are free to rotate relative to said housing, said springs having a preformed curvature so that the central portions of said springs normally extend outwardly of said housing intermediate of a fully collapsed and a fully extended position for said central portions of said springs, spring means coupled in tension between said collars for extending said bow springs to a fully extended position when unconstrained by a bore wall, measuring means in said tubular housing, and means coupling said collars to said measuring Vmeans including guide pins extending through slots in said housing, said guide pins being connected between at least one of said collars and said measuring means whereby measurement of the relative longitudinal movement of said collars is achieved.

8. An elongated apparatus for surveying a well bore and adapted to be passed through a well bore including a well tool having a tubular housing, a pair of tubular collars on said housing, at least one of said `collars being slidable on said housing, at least three bow springs equidistantly spaced about said housing, means coupling said bow springs to said collars at such equidistant locations so that said bow springs are free to rotate relative to said housing, said springs having a preformed curvature so that the central portions of said springs normally extend outwardly of said housing intermediate of a fully collapsed and a fully extended position for said central portions of said springs, spring means coupled in tension between said collars for extending said bow springs to a `fully extended position, measuring means in said housing, and means coupling said collars to said measuring means including guide pins extending through slots in said housing, said guide pins being -connected between at least one of said collars and said measuring means whereby measurement of the relative longitudinal movement of said collars is achieved.

9. An elongated apparatus for surveying a well bore and adapted to be passed therethrough including: a well tool having a tubular housing, a pair of tubular collars slidably mounted on said housing, bow springs, pivotal connecting means -for the respective en-ds of said bow springs, said pivotal means being mounted onsaid collars, said springs having a preformed curvature so that the central portions thereof normally extend outwardly of said housing intermediate of a fully collapsed and fully extended position for the said central portions of said spring, spring means coupled in tension between said collars for extending said bow springs to a fully extended position when unconstrained by a bore wall, measuring means in said tubular housing, and means coupling said collars to said measuring means including guide pins extending through slots in said housing, said guide pins being connected to said collars and said measuring means whereby measurement of the relative longitudinal movement between said collars is achieved.

10. The'apparatus of claim 4, and further including means pivotally connecting said bow springs to said collars.

Culbertson Aug. 22, 1939 Legrand May 26, 1953

Claims

1. A WELL TOOL FOR USE IN A WELL BORE INCLUDING A HOUSING, A PAIR OF TUBULAR COLLARS ON SAID HOUSING WHEREIN AT LEAST ONE OF SAID COLLARS IS SLIDABLE ON SAID HOUSING PERMITTING RELATIVE MOVEMENT BETWEEN SAID COLLARS, BOWS SPRINGS PIVOTALLY CONNECTED TO SAID COLLARS, RESPECTIVELY HAVING A PEREFORMED CURVATURE SO THAT THE CENTRAL PORTIONS OF SAID SPRINGS NORMALLY EXTEND OUTWARDLY OF SAID HOUSING INTERMEDIATE OF A FULLY COLLAPSED AND A FULLY EXTENDED POSITION FOR SAID CENTRAL PORTIONS OF SAID SPRINGS SAID PREFORMED CURVATURE BEING SYMMETRICAL ABOUT A MIDPOINT OF EACH SPRING, THE SHAPE OF ONE-HALF OF EACH SPRING HAVING A CURVATURE DEFINED BY THE FORMULA