CA1157008A - Roller belleville spring damper - Google Patents

Abstract

ROLLER BELLEVILLE SPRING DAMPER
Abstract of Disclosure:
A double acting damper for use in rotary drilling includes a splined tubular telescopic joint and employs plural paralleled stacks of double acting series stacked roller Belleville spring washers in an annular pocket be-tween the inner and outer tubular members of the joint. The springs, spline and telescopic bearings are in an oil filled volume sealed from the outside by a pressure seal at the lower end of the damper and a floating seal at the upper end. Electric and magnetic means are provided to check on the condition and quantity of the lubricant.

Description

-Table of Contents Background of the Invention 1. Field of the Invention

2. Description of the prior art Summary of the Invention Brief Description of the Drawings Description of Preferred Embodiments Damper Pressure Seal Test Probe Lower Bearing Means Spline Upper Bearing Means Resilient Means Neutral Position Travel Limits Pressure-Volume Compensation Means Lubricant Space Motion of Floating Seal Seal Position Indicator Springs Variable Moment Belleville Springs Roller Belleville Springs Spring Clearance and Guidance Variable Spring Modulus Double Action Balanced Load Drilling Stroke Comparison Constant Bit Load Drilling Roller Belleville Spring Damper Claims 'f'~

Background of the invention.
1. Field of the invention.
This invention relates to a damper, and more parti~ularly to a splined tubular telescopic, double acting resil:ient unit for incorporation in a drill string, next to the bit or higher up in the string, of a rotary drilling system for earth boring, e.g., petroleum well drilling.
2. Description of the prior art.
The prior art is discussed at length in the afore-mentioned Garrett application, including art relating todouble acting dampers, variable spring rate dampers, sealed lubricated spring-spline-bearing means, floating seals, parallel spring means, double acting springs, elastomer-metal sandwich springs and Belleville springs.

A form of variable lever arm Belleville spring per se, of the general type employed in the present invention, is disclosed in United States patent number 2675225-Migny However Migny does not appear to disclose the concept of roller Belleville springs, only variable moment, i.e. varia-ble lever arm, Belleville springs.

In one embodiment Migny shows only a single Belle-ville washer which is double convex in cross-section and is disposed between two flat plates. As load is imposed on the plates, the washer initially pivots about its upper inner edge and its lower outer edge as do ordinary Belleville springs, with a resultant linear force deflection curve, but as the washer flattens the washer's edges leave contact with the plates and force is transmitted to the washer through body areas inward of the edges, decreasing the lever arm and causing the force-deflection curve to become non-linear.

The initial pivoting of the Migny washer is of course not a rolling action but a pivot or hinge type action.
Even when the washer turns so that its edges are out of contact with the plates, the washer does not roll on the plates but instead slides relative thereto, because the curvature of the washer faces is different from that of the plates, because the plates do not expand under load the same as the washers, and because the curvature of the bottom of each washer apparently differs from that of the top of each washer.

In another embodiment Migny discloses a stack of groups of Belleville spring washers. The groups are in series and the washers in each group are in parallel. The conical abutting suraces of the paralleled washers in each group slide relative to each other as load is applied. Only the outer faces of the uppermost and lowermost washers in each group have convex sections. The latter washers may initially pivot relative to each other as does the washer of the first mentioned embodiment, and thereafter it is uncer-tain what the relative motion of the washers may be, for although such motion is described as being a "rocking"
motion, the convex cross-section surfaces of the springs are said to be curved like the washers of the first described embodiment and the drawing appears to show different curva-ture on different washers.

At least it can be said that Migny does not dis-cuss rolling or the conditions required to effect rolling of variable moment Belleville springs.

Early forms of drill string dampers are exempli-fied by patents such as German 631398 (1936) - Prussiche U. S. 2,991,935 - Warren wherein a splined tubular telescopic joint is provided with a helical spring means urging the joint to extended position.
These are single acting dampers, in that in the unstrained or neutral position of the damper, only contraction is L'~S~

possible, it being intended that in use the static load on the damper will compress the spring approximately half way, thereby to allow for resilient motion in both directions when the bit moves up and down.

For various reasons it has been disclosed that a variable modulus spring should be employed in a drill string damper. In this regard see United States Patents number

3,381,126 - Salvatori 3,409,537 - Falkner 3,871,193 - Young 3,949,150 - Mason The foregoing patents showing variable modulus dampers relate to single acting dampers. It may be assumed that these dampers, like other single acting dampers, are intended to operate about a static deflection point near the mid-range of the load-deflection curve. In this regard, note the Mason patent wherein operation with a static load of 25,000 lb/in is described (col. 10, 1. 63) with respect to a preferred variable spring rate curve as shown in the shaded area in Fig. 15 of thé patent (col. 10, 1. 6-10).

The dampers of the foregoing patents do not appear to gain much benefit from their variable modulus springs.
At the intended static deflection point the spring rate is well above the low spring rate which exists at low deflec-tion. If such a damper is operated at or near balanced load condition (drilling weight eguals pump apart force), where the static deflection is zero or low, the damper will bang against its travel limit stop on alternate half cycles of vi~ration. Even when operating at the middle of the load-deflection curve, such a damper may bang its expansion limit stop, since as in any single acting damper there is no spring opposition to extension of the damper from its par-tially contracted condition; in fact, the spring assists the extension.

Some account of the foregoing problem is taken in the damper disclosed in United States Patent number

4,139,994 - Alther wherein an additional spring element is provided for reverse `
loading. However the reverse load spring element is opera-tive only when the bit is off bottom or the bit is lightly loaded, and has a much shorter stroke than the direct load-ing spring element. As stated in the brochure of Drilco Industrial entitled "Shoc]- Sub" with reference to a commer-cial embodiment of the Alther damper:
"A second smaller elastmeric element is provided to cushion reverse loading during severe rebounds or when pulling from the hole."

In the aforementioned copending application of William R. Garrett there is disclosed a drill string damper which is especially constructed for balanced load drilling wherein the drilling weight and pump apart force are substan-~ 3'~

tially equal, the damper including resilient means that isstrained equally by like axlal displacements of the spring means from the neutral or unstrained position in the direc-tion of extension and the direction of contraction of the damper. The resilient means has a low spring modulus at positions near the neutral position and a higher modulus at positions farther from the neutral position. With this construction, the damper can operate at the very low modulus range of the spring means over an expected travel range, but will convert to a high modulus damper at each end of the stroke to prevent banging against the travel stops.

As set forth in the Garrett application, it was originally conceived that such a double acting variable modulus damper might employ as the spring means a stack of annular pads of felted steel wire, or a stack of elastomer-metal washer sandwiches, or a stack of Belleville springs.
All of such spring elements have various drawbacks. Wire pads have high internal friction and tend to crush and lose their resiliency when overstressed or fatigued; elastomer-metal sandwiches are subject to rapid deterioration in high temperature surroundings; ordinary Belleville springs, if designed to have a large variation in springs rate, will likely be stressed near or over the elastic limit, reducing their life expectancy.

None of the aforementioned all metal spring means has as wide a range of spring rates as is desirable. In this regard it is to be noted that an equation giving TR, the ratio between the magnitude of a transmitted vibratory force and an impressed vibratory force, is TR = [(1 + (2zr) ]/[(l-r ) + (2zr) ]
where r is the ratio of the impressed frequency to the natural frequency, and z is the damping factor. See eq. 2-87 on p. 72 and equation 2-41, on page 40 of the treatise entitled Mechanical Vibrations by Rolland T. Hinkle published 1963 by Allyn and Bacon, Inc. A curve plotting the relationship of TR and r, taken from Figure 2.32 on page 73 of the aforementioned treatise, appears as Figure 10 of the accompanying drawings.
From the curve it will be seen that the least transmission of force occurs for damping means which have a ratio r larger than (2) 1/2 and which have the smallest possible damping factor z.
Conversely, it will be seen that if the ratio r is less than (2) 1/2, there is a possibility of resonant vibration, unless the system is frictionally damped.
It may be assumed that in rotary drilling employing a three cone rock bit, the drill string rotating at 60 revolutions per minute, the impressed vibratory force as the bit moves past a rock or other high spot in the bottom of the hole is (3) x (60) = 180 cpm or 3 cps. It is therefore desirable that the natural frequency of the system comprising the damper and drill stem thereabove be less than 3(2)1/2=circa 2 cps.
The present invention is directed to provide a damper which will be soft enough to provide a natural frequency as low as possible over a wide range of deflection, with a gradually, then rapidly, increasing spring stiffness to provide a cushioned stop at the ends of the damper stroke as defined by the travel limit stops. The invention is further directed to provide such a damper which will have a long life even under high temperature conditions.

Accordingly, the present invention provides a well tool useful in earth boring by the rotary system comprising:
telescopically disposed inner mandrel and outer barrel members forming an annulus therebetween, connection means at one end of each member for making connection with a rotary drill string component, means for transmitting torque between said members while allowing relative axial motion therebetween, resilient means in said annulus for resiliently transmitting axial forces between said members, said resilient means having a non-linear force displacement characteristic requiring increasing added force increment per unit displacement upon increasing displacement of said members relative to each other in a direction effecting axial contraction of said resilient means, stop means imposing a limit on such relative displacement of ~aid members, said resilient means comprising a stack of variable moment arm Belleville spring washers, -the annular contacts between adjacent washers whose cone angles are oppositely directed moving radially away from the nearer of said barrel and mandrel members toward the middle part of said annulus as the length of the stack contracts to provide decreasing moment arms between said adjacent washers upon said increasing displacement of said members relative to each other, whereby said resilient means functions as a soft cushion bet~een said members when the tool is loaded lightly axially but upon increase of said relative displacement of said members becomes very stiff prior to said displacement reaching said limit imposed by said stop means.

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Thus a double acting damper is provided by a resilient, splined, sealed, lubricated telescopic joint wherein the spring means comprises one or more paralleled double acting stacks of series stacked variable lever arm Belleville spring washers shaped to provide pure rolling between washers. The washers, have upper and lower surfaces that are curved in such a manner that in combination with the other parameters (initial cone angle, height-thickness ratio and outer to inner diameter ratio) there results a damper having a very low spring rate over a large percentage of the damper stroke, with a gradually, then rapidly, increasing spring rate approaching the ends of the stroke, while at the same time the tensile stress in each disc remains below that corresponding to the desired endurance limit, e.g. 20,000 psi for steel for near infinite endurance without fatigue.
Preferably there results a damper which in combin-ation with e~pected drill string masses will result in a system having a natural frequency of around 2 cps or less.
In this regard it is to be noted that the natural frequency f is determined by the formula:

-lOa-; -fn = (kg/w) / /2 pi where k is the spring rate, g is the acceleration of gravityand w is the weight. In other words, the greater the weight, the lower the natural frequency. In deep holes, where the drill string is long and of great weight, the natural fré-guency is very low and resonant vibration is not a serious problem. On the other hand, in shallow holes, where the natural frequency is higher due to the low weight of drill stem, the formation being bored is usually softer, so there is a lower amplitude of impressed force on the bit. There-fore, it may be expected that problems of resonant ~ibration will be more likely to occur at depths of a few thousand feet.

Assume fox example, a drill stem length of one thousand feet above the damper; a substantial part of this, perhaps several hundred feet, will be represented by drill collars. The mass of such drill stem portion may therefore be of the order of thirty two thousand pounds. Using the foregoing equation for the natural freguency, assumed to be 2 cps, and solving for k, the spring rate, wé have 2 = (kg/32000)1/2/2 pi (4 pi)2= k(32/32000) = k/1000 k = (16)(pi)2(1000) lb/ft = about 13,000 lb./in.

which is a very low spring ra~e. Such a rate is achieved and surpassed according to the invention. At the same time, at the travel limit, a rate of the order of 280,000 lb. per in. is obtained.

A further advantage of the invention is the reduc-tion of friction in the damper. While friction tends to damp out resonant or near resonant vibrations, i.e., when the ratio r is less than (2)l/2, for ratios of impressed to natural frequency above (2)l/2 friction promotes transmis-sion of vibrations and therefore is detrimental. The damper of the present invention has a low friction due to the combination of the particular spring means, its mounting, its sealing means (Teflon), and its lubrication.

A further advantage of the invention is its adapt-ability to use under high ambient temperature conditions, all spring parts being metallic, e.g., spring steel or beryllium copper.

Brief Description of the Drawings:

For a description of a preferred embodiment of the invention, reference will now be made to the accompanying scale drawings, the elevational and cross-sectional views showing that the parts are made of metal, e.g. steel, except as otherwise indicated, e.g. the seals are preferably made of Teflon or a high temperture stable, oil and water resis-tant elastomeric material.

FIGURE 1 is an elevation, partly in section, showing a damper according to the invention assembled in the lower end o:E a drill string, with the spring means in the neutral or unloaded position.
FIGU~E lA is a detail, to a larger scale, showing the electrical test probe of the damper;
FIGURES 2A' and 2B', together hereinafter referred to as FIGURE 2', are fragmentary sectional views to a larger scale showing the pressure seal, bearing and spline at the lower end of the damper, with the damper in the open or extended position;
FI&URES 2A" and 2B" together hereinafter referred to as FIGURE 2", are fragmentary sectional views similar to FIGURE 2' showing the lower end of the damper in the closed or con-tracted position;
FIGURES 2' and 2" are drawn with a common center line for easy comparison and may be referred to together as FIGURE 2;
FIGURES 3A', 3B', and 3C', together hereinafter refer-red to as FIGURE 3', are fragmentary sectional views, also to a larger scale than FIGURE 1, showing the resilient unit at the medial portion of the damper in its open or extended position, FIGURES 3A", 3B", and 3C", together hereinafter refer-red to as FIGURE 3", are fragmentary sectional views, simi-lar to FIGURE 3', showing the medial portion of the damper in the closed or contracted position, FIGURES 3' and 3" are drawn with a common center line for easy comparison and these figures taken together may be hereinafter referred to as FIGURE 3;

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FIGURES 4A' and 4B', together hereinafter referred to as FIGURE 4', are fragmentary sectional views, also to a larger scale than FIGURE 1, showing the pressure volume compenating floating seal at the upper end of the damper in the open or extended position;
FIGURES 4A" and 4B", together hereinafter referred to as FIGURE 4", are views similar to FIGURES 4A' and 4B', showing the upper end of the damper in the closed or con-tracted position;

FIGURES 4' and 4" are drawn with a common center line for easy comparison and may be referred to together as FIGURE 4;

FIGURES 5, 5A and 6 are respectively sections taken at planes 5-5, 5~-5A, and 6-6 of FIGURES 3 and 2';

FIGURE 7 is a sectional view of one of the roller Belleville spring elements;

FIGURES 7A, 7B, 7C, 7D, 7E, and 7F are schemetic sectional views of stacks of various Belleville springs, and FIGURES 8, 9, 9A, 10 and 11 are graphs.

Description of Preferred Embodiments:

- Damper ~
i( Referring now to the drawings and in particular tG
` FIGURE 1, there is shown a damper 21 connected at its lower end to a three cone drill bit 23 and at its upper end to another lower drill string member 25 such as a stabilizer or drill collar. Although the drawing shows the damper dir-ectly above the bit, it may be employed at other places in the drill string, preferably however where most of the weight slacked off in the drill string is above the damper.
The apparatus is shown in a well bore 27 being drilled by bit 23 by the rotary system of drilling. The damper ln-cludes a tubular mandrel identified generally by reference number 29. The mandrel comprises a lower seal and bearing and spline portion 31, a medial spring portion 33, a cross over sub portion 35, and an upper compensator portion 37.
Mandrel portions 31, 33, and 35 are connected by rotary shouldered taper threaded connections, such connections being more fully described in United States patent number 3,754,609 - Garrett.

Mandrel portion 37 is shrink fitted to mandrel portion 35.

Mandrel 29 works telescopically within and about a tubular barrel indicated generally by reference character 39. The barrel includes a lower seal and bearing and spline portion 41, medial spring portions 42, 43, an upper cross over sub 45, and a depending compensator portion 47. Barrel portions 41, 42, 43, are connected by double tapered threaded buried pins 38, 40, screwed into correlative boxes in the barrel portions, similar to rotary shouldered connections, and barrel portions 43, 45 are connected together by rotary shouldered connections as above referenced. Barrel portions 45, 47 are connected together by a taper thread and are sealed by an 0 ring 49.

~ 3~

The connections between the damper and drill bit and between damper and the upper part of the drill string are also rotary shouldered connections. Such connections each comprise a pin and box connector and either type of connector may be provided at each end of the damper depend-ing on what type of use is to be made of the damper. As sho~m, a box connector 20 is provided a* the lower end of the damper for connection with a drill bit pin 22, and at the upper end of the damper there is a box connector 44 for connection with a pin 46 on lower drill string member 25.

Passage means through the damper for conveying drilling fluid from lower drill string member 25 to drill bit 23 include central passages 48, 50 through tubular mandrel portions 31, 33.

Referring now to FIGURE 2, there is shown most of the lower portion of the damper, forming the seal, bearing and spline part thereof. This includes portions 31, 41 of the mandrel and barrel.

- Pressure Seal -At the lowermost part of the damper there is pressure seal means 51 disposed between the barrel and mandrel portions 31, 41. Seal means 51 comprises a plural-ity of double lip seal rings 53, 55, 57, 59. Seal rings 53, 55 face upwardly; seal rings 57, 59 face downwardly. The seal rings are preferably made of Teflon or other low fric-tion coefficient, high temperature resistant, flexible resil-ient, sealiny material. The lips of the seal rings are preloaded to move away from each other by corrosion resist-ant metal springs such as those indicated at 52, 54, 56, 58.

Metal wedge rings 61, 63, 65, 67 also hold apart the lips of the seal rings to assist them in moving into sealing engagement with low friction coefficient hard metal finished surface 68 at the cylindrical outer periphery of mandrel portion 31 and the finished surfaces 70, 72, 74 at the cylindrical inner periphery of barrel portion 41 and the cylindrical upper and lower inner peripheral portions of spacer ring 76. Weep holes 60, 62, 64, 66 equalize fluid pressure on opposite sides of the rings. The wedge rings have tongues extending to the bottoms of the annular spaces between the seal ring lips to transmit force through the bottoms of the seal rings when axial force is imposed on the wedge rings. Although as noted above, the wedge rings spread apart the lip5 of the seal rings, their function of transmitting force through the bottoms of the rings is their primary function, thus permitting stacking of the seal rings, as in the case of rings 53, 55. In addition, the flat surface of the uppermost wedge ring 61 facilitates retention of the seal rings in the barrel underneath steel retainer ring 69. Ring 69 is beveled and rests against bevel shoulder 71 in the barrel.

The force of the fluid pressure in the damper acting down on seal rings 53, 55 is transferred by end ring 73 through support ring 76 to end ring 77 and thence to snap ring 79, received in annular groove 81 in the lower end of the barrel.

Support ring 76 is sealed to the barrel by O rings 82, 83 received in annular grooves around the support ring.
The O rings are in slight compression between the bottoms of the grooves and barrel surface 85. Support ring 76 is held fi.xed in the barrel between end rings 73, 77, which are captured between snap ring 79 and a shoulder 87 at the juncture of upper seal surface 70 and larger diameter lower seal surface 85. Therefore O rings are suitable for the non sliding seal between the barrel and support ring 76. This is in contrast to the seals effected by seal rings 53, 55, 57, 59 with the mandrel, which are axially sliding seals.

Support ring 76 not only transfers load from the upper seal rings to snap ring 81 but also provides a car-tridge independently supporting seal rings 53, 55 so that load is not transferred from one through the other as in the case of the uppermost seal rings 53, 55, thereby insuring that the lip seal action of each ring remains unimpaired. A
similar cartridge construction could be used for the upper two seal rings if desired. Or if preferred, the lower seal rings 57, 59 could be stacked with only a wedge ring in between as in the case of the upper seal rings.

The lower seal rings 57, 59 seal primarily against upwardly directed fluid pressure from the fluid outside the damper. The force of the pressure is transferred to shoulder 87 through end ring 73 in the case of seal 57 and through support ring 76 and end ring 73 in the case of seal ring 59.
No force of pressure fluid is intended to be transferred from end ring 77 to wedge ring 66, nor from support ring 76 to wedge ring 65.

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- Test Probe -As will appear more clearly hereinafter, although seal means 51 seals against the pressure of fluid both in the well bore outside the damper and in the drill string connected to the damper, seal means 51 is exposed to drill-ing fluid only on its lower side. Above seal means 51 in the space between the barrel and mandrel there is a clean lubricating oil 91 extending all the way up to the compen-sator portions of the barrel and mandrel. Within this clean fluid work the spline and resilient means later to be de-scribed. It is important for the user to know if any of the damper seals has failed. If such failure causes an influx of drilling fluid, the lubricating fluid will become contami-nated by the drilling fluid, e.g. with water.
Referring now particularly to Figures 1, lA, and ~A', to detect such a change there is provided in the barrel just above lower seal means 51 a test probe comprising an electrically conductive (metal e.g. brass) electrode 93 extending through the barrel wall. The electrode is sur-rounded on its outer periphery by and bonded and sealed to electrically insulating sleeve 97 which in turn is mounted in and bonded and sealed to screw plug 99 which is the closure for a lubricant injection and drainage port provided by threaded hole 101 in the barrel wall. The plug is screwed into ~he port. To prevent the electrode from moving axially under the pressure differential between the interior and exterior of the barrel, the electrode is made of larger diameter at its mid portion than at its ends, leaving tapered shoulders 98, 100 adjacent each end. An annular recess in the screw plug is shaped correlative to the exterior of the --lg--electrode forming shoulders at each and of the recess facing toward the shoulders on the electrode. The insulation sleeve is captured at each end between the plug and elec-trode shoulders and resists relative motion of the electrode and plug. The outer diameter of the mid portion of the electrode is too big to pass through the recess in the plug at the outer end thereof. A material suitable for the insulation sleeve is one which can withstand pressure dif-ferential and well fluids such as a plastics material, e.g.
epoxy. At its outer end, the recess in plug 99 is formed as a wrench socket 102 to facilitate assembly and disassembly.

By connecting an ohmmeter 103 between the outer end of the electrode and a point such as 105 on the exterior of the barrel, the electrical resistance of the oil 91 can be measured to determine its character, i.e. whether or not it has become contaminated. If so, the damper seals and lubricant need to be checked for replacement and then re-placed to the extent required.

It may be noted that whereas the lubricating oil has a high resistivity, most drilling fluids have a low resistivity. Furthermore, the drilling fluid will usually be denser than the oil and will sink to the bottom of the space normally occupied by the oil. That is why the test probe is placed at the lowermost part of such space, just above lower seal means 51. At that point, the test probe will contact any such drilling fluid and the resistance test will show a low resistance path through such drilling fluid.

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- Lower Bearing Means -Still referring to FIGURE 2, above plug 99, the interior of barrel portion 41 is provided with a replaceable bushing or liner 121 made of a wear resisting, low friction coefficient, corrosion resistant bearing material compatible with hard facing material 68 on mandrel 31. For example, liner 121 may be made of beryllium copper or aluminum bronze or the equivalent. The bushing has a smooth cylindrical inner surface which cooperates with a continuation of surface 68 on the exteri-or of the mandrel to provide bearing means.
The bearing means transmits bending moment between mandrel and barrel while providing for relative axial motion there-between. To provide maximum area for taking bending moment, flutes 147 are made deeper than the~ are wide.

- Spline -Above the bearing means just described, the wall of barrel portion 41 thickens by a reduction in its inner diameter, and there is a correlative thinning of the wall of mandrel portion 31 by a reduction in its outer diameter.
Conical surfaces 123, 125 are formed where these transitions occur.

Referring now also to FIGURE 6, the interior of the thick walled part of barrel portion 41 is fluted paral-lel to the barrel axis, forming three vertical grooves 131, 133, 135. The mandrel at this level is provided with three splines 137, 139, 141 which fit into the grooves and cooper-ate therewith to provide spline means for transmitting torque between the barrel and mandrel while providing for relative axial motion. While a spline can be made to trans-mit bending moment, e.g. by having the spline bottom in the grooves, the spline means here disclosed is intended primar~
ily for transmission of torque through the side walls of the splines and grooves, the walls having large radial compon-ents. However some transmission of bending moment will also be provided by the spline means due to the circumferential components of the side walls of the splines and grooves.
Each spline side wall may, for example, make an angle of e.g. 15 to 45 with the radial plane therethrough, Figure 6 showing a representative desirable angle.

- Upper Bearing Means -Above the spline, just described, the inner peri-phery 143 of buried pin 38 is in sliding contact with the outer periphery 145 of mandrel portion 31, thus providing an upper guide bearing. The upper and lower guide bearings, being spaced apart axially, can take considerable bending moment without being overloaded. The outer periphery of mandrel 31 is fluted at 147, providing fluid passages for lubricating oil 91, as will be explained in more detail hereinafter.

- Resilient Means -Referring now to FIGURE 3, there is shown the medial portion of the damper including the resilient means thereof comprising mandrel portion 33 and barrel portions 42, 43 with spring means 151, 153 therebetween. Mandrel portion 33 has an outturned llange 155 (Figure 3B', 3C') therearound and buried pin 40 between barrel portions 43 forms in effect an inturned flange within the barrel. These flanges provide upwardly facing annular shoulders 158, 159 and downwardly facing annular shoulders 160, 161. These shoulders define the inner ends of annular pockets 162, 163 between mandrel portion 33 and barrel portions 42, 43. At the inner ends of these pockets are pressure rings 164, 165 engaged respectively with the ends of spring stacks 167, 169 and engageable with shoulders 158-161.

The upper end of pocket 163 is defined by annular shoulder 171 on barrel portion 43 and annular shoulder 173 provided by the lower end of mandrel portion 35. Pressure ring 174 is engaged with the upper end of spring stack 169 and is engageable with shoulders 171, 173.
The lower end of pocket 162 is defined by annular shoulder 175 provided by the upper end of buried pin 38 connecting barrel portions 41, 43, and annular shoulder 177 formed by the upper end of mandrel portion 31. Pressure ring 183 is engaged with the lower end of spring stack 167 and is engageable with shoulders 175 and 177.

It will be apparent that for each spring means 151, 153 the mandrel is provided with upper and lower shoul-ders and the barrel is provided with upper and lower shoul-ders, and that since the mandrel and barrel shoulders do not overlap, they can pass each other whichever way the barrel and mandrel are moved axially relative to each other.
Regardless of whether the damper is contracted or extended, .

pairs of mandrel and barrel shoulders will engage the pres-sure rings to cause the spring means to be compressed axial-ly. Such action is indicated in the left and right hand halves of Figure 3.

- Neutral Position -! Referring now to Figure 1, the damper is shown in the unextended, uncontracted, or neutral position in which the spring means are of maximum length. In the neutral position, the shoulders 158, 160 on the mandrel flange 155 (Fig. 3B', 3C') are co-level or in alignment with shoulders 159, 161 on barrel pin 46. At the upper end of spring means 153 (referring to Fig. 3C' and 3C" for reference numbers but not for position), in the neutral position pressure ring 174 is engaged both with mandrel shoulder 173 and barrel shoulder 171. Similarly (referring to Figures 3A' and 3A" for refer-ence numbers but not for position), in the neutral position pressure ring 18~ is engaged both with mandrel shoulder 177 and barrel shoulder 175.

- Travel Limits -A nut 189 is screwed onto a straight thread on the exterior of the upper end of mandrel portion 31. Nut 189 provides shoulder 191 at its lower end to engage barrel shoulder 175, forming therewith stop means limiting exten-sion of the damper. Nut 189 is provided with a collar 193 which makes an interference (shrink) fit with the uppermost part of mandrel portion 31. A thin section 195 between collar 193 and the body of nut 189 facilitates sawing off the collar if the nut needs to be removed.
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Pressure ring 183 is provided with an engageable surface 207 to engage shoulder 177 and an annular tongue 209 whose lower end 210 is adapted to engage shoulder 175.
Tongue 209 spans nut 189 and the threaded connection between mandrel portions 31 and 33. Although the latter connection is a rotary shouldered connection as previously mentioned, it is also provided with an O ring seal 211 in case there is difficulty in applying adeguate make up torgue to the con-nection to effect a seal at shoulders 213, 215. Screw threads 217, 219 are straight (untapered) threads to facili-tate make up.

The L-shaped cross-section of pressure ring 183, which provides tongue 209, permits shoulders 175 and 177 to be in different planes, i.e. non-coplanar, as occurs, e.g.
because of the presence of nut 189.

. Means limiting contraction of the damper is pro-vided by stop shoulder 208 (Figure 2A') on the lower end of the barrel and stop shoulder 210 on the lower part of the mandrel. It will be seen that the possible contraction of the damper from the neutral position eguals the possible extension from the neutral position. However they could be made unequal if desired.

-Pressure-Volume Compensation Means-Referring now in part to FIGURE 3C' and more particularly to FIGURE 4, there is shown the upper part of the damper including mandrel portions 35 and 37 and barrel portions 43, 45, and 47. An annular volume 231 is formed 7(~0~

between mandrel portion 37 and barrel portion 47. Due to the presence of cross over mandrel portion 35, mandrel portion 37 is of larger inner diameter than the outer dia-meter of the wash pipe formed by barrel portion 47; in other words, mandrel portion 37 is outside of barrel portion 47.
Barrel portion 47 forms a part of and a continuation of the drilling fluid conduit means through the damper, which means, as previously mentioned, includes the passages 48, 50 through the interiors of tubular mandrel portions 31, 33.

Annular volume 231 between barrel portion 47 and mandrel portion 37 is closed by floating seal means 233 comprising tubular metal cartridge 235 carrying a plurality of sliding seal elements. Because barrel portion 37 is outside mandrel portion 47, an inversion of the usual barrel and mandrel relationship, any drilling fluid tending to flow through volume 231 must flow upwardly. Therefore detritus, sand and other particulates carried by the drilling fluid, when stopped by seal means 233, will fall down out of volume 231, away from seal means 233.

Summarizing, there is no problem of drilling fluid particulates accumulating above the seal means at either the lower or upper end of the damper, since the spaces above these seal means are filled with lubricating oil and since at the lower faces of these seal means any drilling fluid particulates will fall out of the seal means due to the force of gravity.

Floating seal means 233 includes double lip, spring loaded seal rings 237-240 on the interior of cart-ridge 235 to seal between the cartridge and the outside of wash pipe barrel portion 47. Similar seal rings 2~1-244 seal between the outside of the cartridge and the interior of mandrel portion 37. Seal rings 237-244, similar to the seal rings in seal means 51 at the lower end of the damper, are provided with preload springs 245-252 to press their lips apart into sealing engagement with the cartridge and barrel and mandrel portions. Also, wedge rings 253-260 are provided to allow for stacking the seal rings in series, to transmit forces from one seal ring to another, and to facil-itate retention. The wedge rings are provided with weep holes, e.g. as shown at 261, for pressure balancing as in the case of the wedge rings forming parts of the sealing means at the lower end of the damper. The seal rings and wedge rings are retained on the cartridge against back up flanges 265, 267 by end rings 269-272 and snap rings 274-277, the latter being received in annular grooves in the ends of cartridge 235.

The whole seal means 233 is free to move as a unit axially up and down within volume 231, travel being limited by the upper end of the cartridge engaging annular shoulder 278 on washpipe barrel portion 47 and by the lower end of the cartridge engaging shoulder 279 on the upper end of mandrel portion 35. In normal operation the cartridge will never engage the stops. As long as the seal means is free to move, there is no pressure differential across it. It moves up or down so as always to be in contact with and sup-ported by lubricating fluid 91 that fills the lubricant space between the barrel and mandrel in between pressure seal means 51 and floating seal means 233. Floating seal ~ ~7~ ~ ~

means 233 thus provides a pressure-volume compensator accomo-dating to changes in the volume of the lubricant space, allowing lubricating oil 91 to flow into the space 283 between washpipe barrel portion 47 and mandrel portion 37 when the lower part of the lubricant space between the barrel and mandrel reduces, and causing lubricating oil 91 to flow back into the space 283 when it enlarges, while keeping the lubricating oil separate from the drilling fluid at all time~.

- Lubricant Space -The space occupied by lubricating oil 91, extend-ing from the lower part of the damper to the upper part thereof, may be traced from just above pressure seal means 51, past test probe electrode 93, between liner 121 and bearing surface 68, into space 281 between conical portions 123, 125, in betweenthe splines 131, 133, 135 and groovés 137, 139, 141, through flutes 147, between channels 282, 284 cut across the lower ends of nut 189 and tongue 20g (e.g.
when the nut and tongue engage shoulder 175 as in Figure 3A'), past the outer and inner peripheries of ring 183 (and its tongue 209) inside barrel portion 42 and outside mandrel portion 33, through spring pocket 162 inside and outside spring stack 167, between pressure ring 165 and shoulder 160 or 161 (one or the other is out of contact with the ring except in neutral position), or in neutral position through radial channels 286 (or 288) across the uppermost face of ring 165 as it happens to be assembled, through annular space 156 between barrel and mandrel, between pressure ring 164 and shoulders lS9, 158 (one or the other is out of contact with the ring except in neutral position), or in neutral position through radial channels 287 (or 289) across the lowermost face of ring 164 as it happens to be assem-bled, through spring pocket 163 inside and outside spring st:ack 169, between ring 174 and shoulder 173 when out of contact or between ring 174 and shoulder 171 when out of contact (one or the other shoulders is out of contact except in the neutral position), or in neutral position through radial channels 283 (or 285) across the uppermost face of ring 174 as it happens to be assembled, through annular spaces 204, 206, 208, and into uppermost space 283.

- Motion of Floating Seal -It is to be noted that when the damper is in use, the desired end result is zero axial motion of the barrel, which is connected to the upper part of the drill string, despite up and down motion of the mandrel, which is con-nected to the drill bit. As the mandrel moves up and down the volume of the space between the parts of the mandrel and barrel delimited by the lower seal means and the volume compensator changes and the compensator moves up and down to accomodate for the volume change. Large volume changes occur at space 281 between conical surfaces 123, 125 (FIG.
2) and at space 283 above the upper end of mandrel portion 37. Floating seal means 233 (Figure 4) therefore moves up and down rapidly relative to both barrel portion 47 and mandrel portion 37 during operation of the damper. In the embodiment shown, the axial travel of the floating seal is about 3/5 of the axial travel of the mandrel relative to the barrel. For this reason the outer periphery of washpipe barrel portion 47 and the inner periphery of mandrel portion 37 are each provided with a hard metal coating, e.g. nickel plated, as shown at 275 and 276, such coating having a low friction coefficient and a smooth finish. Both wash pipe b~rrel portion 47 and mandrel partion 37 are readily replace-able should they become unservicable for any reason.

Although floating seal ~eans 233 moves rapidly up and down to accomodate changes in volume of the space occu-pied by the lubricating oil, it may also move up and down more slowly in response to changes in the volume of the oil itself as temperature and pressure change.

- Seal Position Indicator -Still referring to FIGURE 4, on the upper end of cartridge 235 is disposed a cap 291 having a skirt 293. A
plurality of screws 296 circumferentially spaced apart around the skirt extend through holes in the skirt into threaded holes in the cartridge. The upper end 297 of cap 291 has a conical top face pointing upwardly. Surmounting the cap is permanent magnet ring 299, which has a lower conical face correlative to the top face of cap 291, being suitably secured thereto, e.g. by epoxy cement or by sinter-ing or soldering. Magnet ring 299 is magnetized radially, whereby its inner periphery is of one polarity and its outer periphery is of an opposite polarity. Cartridge 235 and wash pipe 47 are made of non-ferro-magnetic material, such as stainless steel. A magnetic probe, such as a steel building stud locator, lowered into wash pipe 47, will indi-V~

cate the level of the magnet ring and hence of the floating seal. If the damper is fully contracted, as shown in FIGURE
4A", the floating seal should be near its lowermost normal position due to the lubricant flowing into the space 283 at i1;s top side. If the damper is fully extended, as shown in Figure 4A', the floating seal should be near its uppermost normal position, due to the lubricant flowing away from space 283 at its top side. If the damper is in its neutral position, the seal should be in a normal median position, as shown schematically in Figure 1.

If the seals leak so that there is a loss of lubricant from the chamber, the floating seal will be near its uppermost position, or at least above its normal posi-tion. If the seals leak in a manner that intrusion of well bore fluid increases the fluid in the chamber, the floating seal will be at its lowermost position or at least below its normal position.

Of course in both conditions, insufficient and excess liguid in the chamber, the problem may not be with the seals but rather be one of initial insufficient or excessive filling of the chamber with lubricant. Whatever the problem is, it can be corrected.

- Springs -Referring again to FIGURE 1, and more particularly to FIGURE 3, each of spring stacks 167, 169 comprises a plurality of Belleville spring washers 321 positioned with their cones pointing up, interleaved with a plurality of $~

Belleville spring washers 323 disposed with their cones pointing down. This mode of stacking places the spring washers in series. The more spring washers in series, the greater the damper deflection for any given axial load. The use of two spring stacks in parallel reduces the stress in each Belleville spring washers for any given deflection of the damper. If required, additional stacks of spring washers beyond two stacks e.g. three, four or more stacks may be paralleled to keep the stress in each Belleville spring washer below the elastic limit or below the endurance limit or any other desired limit.
It may be noted that merely making the spring washers thicker or placing some of the washers in each stack in parallel, that is with their cones pointing in the same direction, though reducing some of the stresses in the washers, will not entirely solve the problem. Making the washers thicker will actually make the tensile stresses on the inner faces of the washers greater. If washers are paralleled within the stack, there will be sliding friction between the washers thus paralleled. This sliding friction causes the outer washers of the spring stack to suffer damaging fatigue because the force of the vibration is not uniformly distributed to all the washers. Said another way, the inner washers of the stack are isolated from the vibra-tion by the outer washers so that, while having the same average load, they are subject to a smaller amplitude of alternating load. This consequence arises from ingrtial and frictional causes. Therefore paralleling several separate stacks may be necessary in order to achieve the desired result.

:``

Due to manufacturing tolerances, the length of a spring stack of a preselected number of spring washers may not exactly fit the cavity between mandrel and barrel. In swch case, as shown only in Figure 1, one or more flat washers or shims 280, 282, 284 may be employed to achieve the desired fit. Alternatively, pressure rings 164, 165, 174, 183 (Figure 3) of varying thickness may be employed.

- Variable Moment Belleville Springs -Due to the small seal, Figure 1 shows spring stacks 167, 169 to be composed of ordinary Belleville spring washers, i.e. with cross sections having straight sides.
Although such springs may be employed while obtaining some of the advantages of the invention, and may even be con-structed to provide a variable modulus as set forth, e.g. at pp. 155-157 of Mechanical Springs, by A. M. Wahl, Second Edition, published by McGraw Hill Book Company, 1963, it is preferred to use variable moment arm Belleville springs of the general type disclosed in the aforementioned Migny patent. Furthermore it is preferred to use a particular form of variable moment arm Belleville spring, herein termed a roller Belleville spring, in which there is pure rolling between adjacent washers as they are loaded and unloaded, as next described.

- Roller Belleville Springs -The Belleville spring washers 321, 323 are identi-cal, merely being positioned oppositely during assembly.
Such a spring washers is shown to a larger and more precise scale in FIGURE 7. As there shown, the radius R' = R" of to'~

the outwardly and inwardly tilted faces of the spring washer is 10-11/64 inches. The outer diameter of the spring washer is typically 5.827 inches. The spring washer thickness is 0.250 inch and the cone angle is 3.75 degrees measured at the part of the spring washer midway between its inner and outer peripheries. It will be noted that the center O" of the radius R" for the outwardly facing face (the left hand face in Figure 7) of the washer lies substantially on a line through the inner peripheral edge of such face parallel to the cone axis C of the washer. When the washer is stacked with others and assembled in the damper, the slight preload in the neutral position will cause the center of such radius R' to be exactly on said line.
Similarly it will be noted that the center O' of radius R' for the inwardly facing face (the right hand face of Figure 7) of the washer lies substantially on a line through the outer peripheral edge of such face parallel to the cone axis of the washer.- When the washer is stacked with others and assembled in the damper, the slight preload in the neutral position will cause the center of such radius R' to be exactly on said line.
With O' and o" so located for the neutral position of the damper, and R' being equal to R", the contacting areas of the washers of the inner and outer peripheries of the stack will, as shown in Figure 7A, be tangent, the common tangents being shown at T' and T". As shown in Figure 7B when the damper is deflected the contacting areas of the washer move closer together and remain tangent, the washers rolling upon each other without sliding. It will be noted that when the contacting areas of the washer move together so as to be in vertical alignment, that is, so that they are equidistant from the axis of the washers, the :
;
;' .

moment arm becomes zero and the spring has gone solid.
During the motion from unloaded condition to the solid condition, only the inner portions of the washer faces that moment arm becomes zero and the spring has gone solid.
During the motion from unloaded condition to the solid condition, only the inner portions of the washer faces that are in contact nearest the washer axis are engaged and only the outer portions of the washer faces that are in contact farthest from the washer axis are engaged, such portions being the functional portions of the surfaces. The non-func-tioning portions of the washer surfaces never engage any other surface.
With the foregoing background, the conditions for pure rolling of the washer may be summarized as follows:
(1) The contacting areas of the faces of the washers are tangent, to avoid pivoting.
(2) The washers are identical, i.e. of like size, thickness, dish (cone angle~, and facial curva-ture, so that they will have equal angles of deflection and the same position of their respec-tive neutral axes, as reguired to avoid slippage.
(3) To avoid sliding, the curves of the functional portions of the two opposite faces of each washer should be the same, i.e. one curve would be the double reflection of the other about a medial cone and a cone perpendicular thereto (complementary therewith).
(4) The curves of the functional portions of the cross sections of the surfaces of the washers must be continuously convex, to avoid bridging.
These requirements are met by the construction shown in ~lS7~08 Figures 7A and 7B, but are not satisfied by the ordinary Be~leville spring washers of Figure 7C nor the variable moment Belleville spring washers of Figure 7D. In the case o~ the ordinary Belleville spring washers of Figure 7C, the engaged surfaces are not tangent and the washers pivot about their outer peripheries as they are loaded and unloaded. In the case of the variable moment Belleville spring washers of Figure 7D, the initially engaged surfaces of the washers are not tangent so that there is an initial pivoting of the washers about their peripheral edges when the springs are loaded, and even after the engaged areas have moved toward each other there is sliding because the curvatures of the engaged surfaces are unequal.
Relative to the requirement that to effect pure rolling the cross sectional curvature of the faces of the washers must be continuously convex, it may be noted that if there were any concavity in such cross-section there would occur during the compression of a stack of washers a posi-tion in which there would be two separate areas of contact between adjacent washers, the areas being on opposite sides of the concavity. This is the situation illustrated in Figure 7E.
With the foregoing limitations, any shape of con-tinuously convex cross-sectional curvature maybe used for the washer surfaces, and such curvature will define the force-deflection curve for the washer.
The particular cross-sectional curves for the roller Belleville spring washers shown in the preferred embodiment of Figures 7, 7A and 7B are arcs of circles.
Actually, this curvature was selected as an approximation to an ellipse. As shown in Figure 7F, if the washers are of elliptical cross-section there is no possibility of any pivoting therebetween. However the outer ends of the elip-pses never come into contact, so they can be chopped off;
and that was done in the evolution of the preferred embodi-ment. Finall~, it was decided to thicken the washers and this resulted in the Figure 7 construction.
The faces of the Figure 7 washer, viewed in cross-section, are therefore parts of two separate curves, rather than of a single curve, as in the case of the Figuxe 7F
elliptical cross-section washers.
The family of single curve washers of which the elliptical washer is but one example, include also, for example, parabolically and hyperbolically curved washers.
With elliptical cross-section washers, it will be observed that at the limits of eccentricity there are the cases of zero eccentricity, corresponding to circular cross-section washers, which would have no spring action, and infinite eccentricity corresponding to parallel line cross-sections, the same as ordinary Belleville springs, which have a constant moment arm. Neither such extreme of eccentricity would therefore be suitable.
In considering the curvature of the faces of a roller Belleville spring washer, it must be borne in mind that only the functional portions of the faces of the washers are to be considered. Surfaces which never engage may be of any shape. For example, referring to an upwardly pointing washer, the inner portion of the upper face and the outer portion of the lower face are the functional surfaces which need to have particular cross-sectional curvature. The outer portion of the upper face and the inner portion of the inner face could, for example, be straight lines in cross-sections; such a configuration may be used to make the spring thicker and hence stiffer.
- Spring Clearance and Guidance -Referring once more to Figure 7 the minimum diame-ter of the inner periphery of the washer is 03.543 + 0.005 inches, which is enough larger than the diameter d of the outer periphery of mandrel 33 (FIG. 5) that the spring washers can freely move up and down axially relative to the mandrel even when the damper is extended or contracted causing the washers to be compressed (flattened). If any part of the spring stack moves laterally, the mandrel will limit the movement, one or more of the spring washers making line contact with the side of the mandrel. The inner corners of the cross-section of the spring washer are more fully rounded to avoid cocking on the mandrel during as-sembly and to reduce stress concentration.

The outer periphery of the spring ~ashers is considerably smaller than the inner diameter D (FIG. 5) of the barrel, so that the washers can expand circumferentially when they are compressed (flattened), as the damper extends or contracts, and still remain out of contact with the barrel. Also, there is left plenty of room for lubricating oil 91 to move past the washers.

If desired, the washers could more nearly make a close fit with the barrel and, at the same time, if so desired, less nearly make a close fit with the mandrel, relying on the barrel to limit lateral travel of the springs.

The minimum radial clearance betweenthe inner and outer peripheries of the washers, and the adjacent outer periphery of the mandrel and inner periphery of the barrel required to accommodate for change in the spring washer diameters when flattened is only a few thousandths of an inch, which is less than that required by manufacturing tolerances.

- Variable Spring Modulus -The spring stacks, when assembled in their respec-tive pockets, are slightly compressed even when the damper is neither contracted nor extended, but only just enough to keep them from being loose in the pockets. In this condi-tion, as shown in FIGURES 1 and 7A, the spring washers are in contact over circular areas near their inner and outer peripheries, each spring washer contacting either the inner or outer periphery of the spring washer above and the oppo-site (outer or inner) periphery of the spring washer below.
This is the unloaded condition of the damper.

When the spring stacks are compressed, upon either contraction or extension of the damper, the circular areas of contact between the spring washers move away from the peripheries toward each other, i.e. towards the mid widths of the washers, as shown in Figure 3. This results in a reduction of the leverage of the axial forces on the spring in their action to flatten the washers, causing the spring rate (force/deflection ratio) to increase. Roller Belleville springs thus have a pronounced variable spring modulus.

Referring now to FIGURE 8, there are shown a curve A plotting spring force versus deflection, and also a curve X plotting spring rate versus deflection. Curve X shows a very low spring rate of the order of 4,000 to 10,000 lb./in.
at moderate values of spring deflection, reflecting the low slope of the nearly straight line portion of the spring force deflection curve A below 10,000 lb. At a deflection of 1.0 inch, corresponding to a spring force of 12,500 lb., the spring rate is still less than 30,000 lb./in. Even at a deflection of 1.3 inches, corresponding to a spring force of 30,000 lb., the spring rate is but 85,000 lb./in. Only as the deflection approaches the travel limit of 1.5 inches does the spring rate exceed 100,000 lb./in. to bring the damper travel to a cushioned stop.

- Double Action -FIGURE 8, curve A, also shows that for negative loads, i.e. loads tending to extend the damper, the load deflection curve is reflected about the ordinate. In other words, the same load deflection curve, except with negative deflections, applies. That is because the resilient means is being stressed regardless of whether the damper is being contracted or extended. In fact, in the preferred embodi-ment the same spring means is strained in the same way (flattened) regardless of whether the damper is contracted or extended. Curve B shows that the spring rate remains low over a wide range of deflection, both positive and negative from the neutral or zero deflection position.

Balanced Load Drilling Referring now to Figure 9, there is shown curve A, which is the same as curve A of Figure 8, plotting spring force as a function of spring deflection Figure 9 also shows a curve B plotting spring force as a function of decreasing spring flexibility, that is, the abscissae scale of curve B has its origin at a flexibility of 25 inches per 100,000 pounds, with decreasing flexibility proceeding away from the origin. Also, flexibility is plotted as positive both to the left and to the right of the origin; this ac-counts for the fact that the flexibility curve includes a portion in the lower left hand ~uadrant rather than in the upper left hand quadrant. Flexibility is the reciprocal of spring rate; therefore curve B is closely related to curve X
of Figure 8. However spring rate curve X is plotted against deflection whereas curve B plots spring force against flexi-bility. Note further that in curve X, spring rate is plotted as ordinates, whereas in curve B flexibility is plotted as abscissae. In fact in Figure 8, one should consider the abscissae, the deflection, as the independent variable, reflecting the fact that the bit moves up and down as the contour of the bottom changes, to some extent regardless of what force is imposed on the ~it, whereas Figure 9 is best appreciated viewing the ordinates, the spring force, as the independent variable, reflecting the information known to the driller, i.e. the static load on the damper.

It may be noted here that although the static load on the damper is the difference between the drilling weight and the pump apart force, the load on the bit is the drill-ing weight, unaffected by the pump apart force. Although the pump apart force acts down on the bit, it also acts upwardly on the swivel to relieve the drawworks of some of the drill string weight. Since drilling weight is calcu-lated on the basis of weight of drill string less line tension, the upward pump apart force, which actually further reduces the unsuspended weight of the drill string, equals the downward pump apart force acting to increase the force on the bit o~rer tha~ which is due to the unsuspended weight "~

of the drill string. In other words, the pump apart force is neglected twice with opposite effect.

Figure 9, in the upper left hand guadrant, includes a table showing typical drilling conditions. The items in the table, and elsewhere in Figure 9, that are marked with a check mark, correspond to a near balanced load condition, CONDITION I, including an average drilling weight of 45,000 pounds and an average pump pressure of 1,500 psi correspond-ing to a pump apart force of 44,000 pounds. The items marked with an asterisk correspond to an extreme condition, CONDITION II, wherein the pump apart force dominates, the pump pressure of 2,000 psi producing a pump apart force of 59,000 pounds compared to a drilling weight of only 30,0~0 pounds, a difference of 29,000 pounds acting to expand or extend the damper. The items marked with a double dagger correspond to an extreme condition, CONDITION III, wherein the drilling weight dominate~, the pump pressure of only 1,000 psi producing a pump apart force of only 29,000 pounds compared to a drilling weight of 60,000 pounds, a difference of 31,000 pounds acting to compress or contract the damper.

Having noted the parameters in the upper left hand guadrant of Figure 9, one may refer to the scale of pump pressures at the lower left hand side of Figure 9. There, selecting a pump pressure of 1,500 psi, marked with a check mark, and following the heavy line in the direction of the arrows, one finds that this pressure corresponds to 44,000 pounds of pump apart force, a negative force, i.e. one expanding the damper, to which one adds a positive force of 45,000 pounds of drilling weight to provide a net force o~

1,000 pounds contracting the damper, at which load the flexibility of the damper is a maximum, i.e. 25 inches per 100j000 pounds. This is CONDITION I.

Further exploring Figure 9, one may start at the lower left at a pump pressure of 2,000 pounds marked with an asterisk, and following the dotted line one first notes that this pump pressure produces a pump apart force of minus 59,000 pounds. To this is then added a drilling weight of 30,000 pounds leaving a net negative force of 29,000 pounds expanding the damper, at which point the flexibility of the damper is 0.85 inch per 100,000 pounds. This is CONDI-TION II.

Condition III may also be traced on Figure 9, starting at the lower left with a pump pressure of 1,000 psi, marked with double dagger. Following the broken line one finds that 1,000 psi pressure corresponds to a pump apart force of minus 29,000 pounds. Adding a drilling ; weight of 60,000 pounds creates a net contractive force on the damper of 31,000 pounds, which corresponds to a flexi-bility of 0.B0 inch per 100,000 pounds, substantially the ~ same as for CONDITION I I .
:
; Assuming a case wherein the pump apart effect balances the unsuspended weight of the drill string (drill-ing weight), identified as CONDITION I in Figure 9, there is no static load on the damper spring and the damper will operate about the zero load, zero deflection point, the origin of the FIGURE 9 load-deflection curve, which is the neutral position as previously defined. The damper will then be very soft and very little motion will be transferred to the drill string. This is in contrast with single acting variable modulus dampers in which under balanced load condi-ti.on alternate half cycles of vibration would cause engage-ment of the travel stops, thereby losing the benefit of the low spring rate on alternate half cycles of damper vibration.

Consider next the case of drilling with unbalanced load. As the unbalance increases, the flexibility at the static deflection point decreases. However, at a load unbalance of plus or minus 10,000 lb., the flexibility is still over 4 inches per 100,000 lb., which is very high, and the deflection is about 0.95 in. which leaves 0.55 inch of travel to the nearest travel stop.

It may be noted here that the drop in flexibility from 25 inches per 100,000 pounds under balanced load condi-tions to 4 in./100,000 lb. at 10,000 pounds unbalance appears to be major. However the amplitude of transmitted vibration to impressed vibration is actually more nearly a function of the reciprocal of flexibility, i.e. of spring rate, and as appears from Figure 8, at a deflection of O.95 in. the spring rate is only about 23,000 pound/in., which is still quite low.

If the drilling weight exceeds the pump apart effect, or vice versa, by thirty thousand pounds, the condi-tions are those identified on Figure 9 as CONDITION II and CONDITION III. Conditions II and III represent extreme conditions of load unbalance which are met in practice per-haps only about 5 per cent of the time. ~owever even under these conditions although the action of the damper is not as good as under balanced load, the damper, having a flexibil-ity of 0.8 or more and a travel of 0.2 in to the nearest stop, is still soft enough to dampen substantially transmis-sion of vibration to the drill string. The damper therefore may be used with varying degrees of effectiveness over a typical range of drilling weights in the range from 30,000 pounds to 60,000 pounds and pump apart forces in the range from 30,000 pounds to 60,000 pounds corresponding to a 5-1/8 inch diameter seal area (e.g. 8 inch diameter damper) with pump pressure in the range of 1,000 psi to 2,000 psi.

-Stroke-Assuming the drill string above the damper to be at rest vertically, the damper needs to have sufficient contractive and extensive stroke to allow for the maximum anticipated rise and fall of the drill bit without having the damper become inoperative by the travel limit stops becoming engaged or the springs reaching their limit of deformation (going solid i.e. flat in the case of Belleville springs). It will be seen from FIGURE 8 that the damper has a working range of plus or minus one inch deflection with a very low spring rate when the pump apart effect balances the drilling weight. Even at the extreme condition of a thirty thousand pound difference (plus or minus) between drilling weight and pump apart effect, there is still available a travel of about .2 inch in the direction toward the nearest travel limit stop before the spring rate of the spring stacks becomes exceedingly high.

If one is willing to accept a higher spring rate at balanced load, the available travel to the nearest stop for any given unbalanced load and the spring rate at that load can both be enhanced by employing additional stacks of springs in parallel. Referring to Figure 9A, curve A shows the load deflection curve for the previously described apparatus. Curve Al shows the result of employing four stacks of springs in parallel (twice as many as for Curve A).
It is seen that although the spring rate for balanced load is doubled (twice the slope), it is still very low, and at 30,000 lb. static load the deflection is only l.l inch, leaving 0.4 inch travel to the nearest stop (compared with 0.2 in. for curve A) and the spring rate is lower (lower slope) than for curve A.

Curve Al also shows that at 60,000 lb. static load (twice the limit of the working range for the damper of Curve A) the deflection is only 1.3 inches, the same as for a 30,000 lb. load in the case of the curve A damper (although the spring rate is greater for curve Al at 60,000 lb. than for curve A at 30,000 lb.

Summarizing, by putting more variable modulus springs in parallel, one can not only reduce the deflection, but also reduce the spring rate at the same 30,000 lb.
static load, or increase the static load for the same 1.3 inch deflection.

If an overall longer stroke is reguired, the lengths of the spring stacks can be increased. For example, referring now to cur~e A2 of Figure 9, by doubling the ., .

-~6-length of the spring stacks, the low spring rate working range would become plus or minus two inches, and there would be a travel of about .4 inch to the nearest travel stop when static load is unbalanced by 30,000 pounds.

Lengthening the sPring will also lower the spring rate in the middle of the range,.e.g. at the neutral posi-tion. Therefore.if it is desired to increase the working range of unbalanced load5as well as increase the stroke, without sacrificing flexibility at any load, additional stacks of springs in parallel may be employed. For example, by both doubling the lengths of the springs and employing twice as many in parallel as shown in curve A3, the same low spring rate at midrange as for curve A will be achieved, and the unbalanced load working range for the same maximum spring rate within the range will be increased to plus or minus 60,000 lb. with a travel limit of 0.4 inches to the nearest stop.

It is to be particularly noted from curve A2 that by doubling the spring length and the number of stacks in parallel, the travel to the nearest stop at plus or minus 30,000 pounds would be increased to 1.08 inches and the spring rate would be only about 25,000 lb/in. This improved effect achieved with the seriating and paralleling of vari-able modulus springs is in contrast with that achieved with constant modulus springs where only the travel to nearest stop would be increased without any change in spring modu-lus .

~i7~

-COMPARISON-The subject construction with a stroke of plus or minus 1.5 inches and a spring rate of 30,000 lb./in. or less over a range of plus or minus one inch when operating under balanced load conditions, is to be compared with the result that would be obtained with a constant spring rate and with single acting spring means.

First of all consider the situation with a con-stant spring rate single acting spring means having a spring rate of 4,000 lb. per inch, corresponding to the spring rate of the present construction at 2ero deflection. Upon imposi-tion of a static load of thirty thousand pounds, the deflec-tion would be 7.5 inches, which is way beyond the range of travel of the assumed situation. To accomodate such a stroke, the seals, spline, and guide bearings would all have to be lengthened, as well as providing a spring of such a stroke. The question arises if this problem could be over-come merely by changing the position of the travel limit stops. The answer is simply, no. If the stops were set to limit deflection to plus or minus 1.5 inch, upon imposition of an unbalanced static load of only 6,000 pounds the damper would be in engagement with one stop and therefore inopera-tive on alternate half cycles.

At this point one may introduce the concept of the load carrying capability of a spring. This is the maximum load which a spring can carry without going solid, or other-wise expressed, the maximum load which a spring can carry and still function as a spring, i.e. as a device in which ~ 7~ ~

the ratio of load to deflection per unit length of spring is less than the modulus of elasticity of the material of which the spring is made. In this case, unless the spring of the spring means has a load carrying capacity of thirty thousand pounds, it will not be effective as a spring upon imposition of a 30,000 pound load, no matter where the travel limit stops are placed. If a spring is soft, it likely will have a low load carrying capacity.

Consider next a damper with a constant spring rate of 30,000 lb./in., near the maximum rate for the damper of the present invention, when operating under balanced load conditions. Under a static load of 30,000 lb., the spring deflection would be one inch, leaving only a half inch of travel to reach the nearest travel limit stop. Since a one inch deflection is to be expected according to the original assumptions, such a damper would strike its travel limit stop once during each cycle of vibration, there being no increasing modulus as the stop is approached to cushion the end of the travel.

To provide a one inch travel to the nearest stop when operating with a 30,000 lb. static load, the spring rate would have to be such that the static deflection would be only one-half inch (1.5-1.0 = 0.5). In other words, a constant spring rate of 30,000/0.5 = 60,000 lb./in. would be reguired. This is fifteen times as stiff as the zero deflec-tion spring rate of the previously described construction embodying the invention. In addition, should there be any abnormal deflection of a damper with the assumed 60,000 lb./in. constant spring rate, the damper would strike its r~

travel limit stop. In contrast, the spring means of the present construction, being of increasing spring rate as the deflection approaches the limits, will still effect a cush-ioned stop upon abnormal deflection, even though the cushion-ing will be less than under normal conditions.

Consider next the case of a known damper employing a variable modulus spring but with single action. Such a damper operating under balanced load would strike its travel limit stop once during each vibration.

CONSTANT BIT LOAD DRILLING

The type of drilling contemplated by the present invention may be further understood by referring once more to FIGURE 8. It will be seen from curve X that for deflec-tions between plus and minus 0.5 inches the spring rate is nearly constant and quite low. Therefore, if drilling is conducted in such a manner that the pump force balances the drilling weight so that the static deflection of the damper is zero, the damper will allow the drill bit to move up and down following the contour of the bottom of the hole under the constant downward force of the pump apart force with very little force variation transmitted to the drill string through the damper. Since the bit will remain in contact with the bottom of the hole with the desired force on bottom, drilling should proceed in a most efficient manner and at the same time there will be minimum wear and tear on the drill string.

~r~

ROLLER BELLEVILLE SPRING DAMP~R

Some consideration has already been given to roller Belleville springs in the section hereof entitled Springs. At this point it is desired to point out a charac-teristic of the preferred form of spring which is distinc-tive. Referring to Figure 11 there is plotted a curve showing spring rate versus deflection which is similar to curve X of Figure 8, the only difference being that Figure 8 has reference to spring means in which there are 38 cones per stack whereas Figure 11 has reference to spring means in which there are 40 cones per stack; resulting in a stroke which is nearly six percent longer, as may be desirable in some cases. As in the case of the spring means whose curve is plotted in Figure 8, the spring means whose curve is plotted in Figure 11 exhibits a very low spring rate at zero deflection and over a considerable range of deflection in both directions, the spring rate being below 13,000 lb./in.
up to plus or minus 1.2 inches of deflection and being only

5,000 lb./in over a range extending from neutral position to plus or minus one inch.

Figure 11 also plots spring flexibility versus deflection. It will be seen that the flexibility curve consists of two, like, nearly straight line (linear) sections at the left and right of the point of zero deflection extend-ing to and beyond plus or minus one inch deflection. A
roller Belleville spring of preferred form according to the invention may therefore be characterized as one having a flexibility function of LAMBDA or inverted V shape centered at zero deflection.

Properties of a variable moment Belleville spring, and especially of a roller Belleville spring, that are particularly advantageous in a drill string damper, may be enumerated as follows:

(1) The deflection is delimited while load bear-ing capacity is enhanced.

(2) The positive tensile stresses (those due to tension) are held under control, thus allowing greater fatigue life.

(3) The spring rate is non-linear.

(4) With particular reference to roller Belleville springs, friction is reduced, lowering transmission of vibration, and more uniformly distributing the vibration among spring washers thereby increasin~ spring life.

The desirability of using low friction spring means, especially in conjunction with low friction seals and lubricated splines, was treated mathematically earlier in discussing the prior art.

Roller Belleville cones (washers) stacked in series have a low friction. When used in a double acting device, it is possible to exploit their non-linearity to the best advantage. The small friction provides for a low damping factor while the small spring rate insures that f/fn is greater than (2)1/2.

v~

A double acting roller belleville vibration damper at the bottom of a shallow hole drill string of mass 20,000 with an initial spring rate of 5000 lb/in would have a natural frequency of 1.6 cyles per second, already well below the applied freguency (2.5 to lOhz).

While a preferred embodiment of the invention has been shown and described, many modifications thereof can be made by one skilled in the art without departing from the spirit of the invention.

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Claims (18)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE PROPERTY OR
PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. Well tool useful in earth boring by the rotary system comprising:
telescopically disposed inner mandrel and outer barrel members forming an annulus therebetween, connection means at one end of each member for making connection with a rotary drill string component, means for transmitting torque between said members while allowing relative axial motion therebetween, resilient means in said annulus for resiliently transmitting axial forces between said members, said resilient means having a non-linear force displacement characteristic requiring increasing added force increment per unit displacement upon increasing displacement of said members relative to each other in a direction effecting axial contraction of said resilient means, stop means imposing a limit on such relative displacement of said members, said resilient means comprising a stack of variable moment arm Belleville spring washers, the annular contacts between adjacent washers whose cone angles are oppositely directed moving radially away from the nearer of said barrel and mandrel members toward the middle part of said annulus as the length of the stack contracts to provide decreasing moment arms between said adjacent washers upon said increasing displacement of said members relative to each other, whereby said resilient means functions as a soft cushion between said members when the tool is loaded lightly axially but upon increase of said relative displacement of said members becomes very stiff prior to said displacement reaching said limit imposed by said stop means.

2. Well tool according to claim 1, said resilient means further comprising a second like stack of variable moment arm spring washers disposed between said mandrel and barrel member transmitting axial force between the mandrel and barrel in parallel with said first stack, whereby the load-deflection modulus of said tool at certain deflections of the resilient means is less than that which would exist if there were but one stack acting alone at the same load.

3. Well tool according to claim 1, said washers being stacked solely in series within the stack, whereby there is no sliding friction between the washers in the stack as the length of the stack changes under load.

4. Well tool according to claim 1, said stack of variable moment arm Belleville spring washers being characterized as follows:
(a) the contact areas of adjacent faces of the washers are always tangent, (b) the washers are identical, (c) the engageable portion of the upper face of each washer is a double reflection of the engageable portion of the lower face of the washer about conjugal medial conical surfaces coaxial with the washer, one medial conical surface being midway between the inner and outer peripheral edges of the washer, (d) the engage portions of the faces of each washer are continuously convex in cross-sections through planes in which lies the washer axis.

5. Well tool according to claim 4 wherein the entire upper face of each washer is a reflection of the entire lower face about a medial conical surface coaxial with the washer.

6. Well tool according to claim 1, the engageable portions of the faces of each washer being convex, the meridians of the upper faces of the washers having their centers of curvature offset from the cone axis of the washers, lying on lines parallel to the cone axis through the inner periphery of the washers, and the meridians of the lower faces of the washers having their centers of curvature on lines parallel to the cone axis passing through the outer peripheries of the washers.

7. Well tool according to claim 1, said washers being roller Belleville spring washers.

8. Well tool according to claim 1, said resilient means resiliently transmitting axial forces between said members upon relative axial motion of said members in both directions from a neutral position of minimum stress of said resilient means, said non-linear force displacement characteristic of said resilient means requiring equally increasing added force increment for unit displacement the farther said members are displaced in either direction from said neutral position.

9. Well tool according to claim 8, said mandrel and barrel members being tubular providing a flow passage therethrough, sliding pressure seal means between said members sealing said flow passage against fluid flow from said passage outwardly through said tool between said member and vice versa, floating seal means between said members forming with said pressure seal means an annular chamber between said members, said chamber including said annulus, lubricant in said chamber, said resilient means being at all times, as said members move axially relative to each other, radially spaced from said barrel member and freely movable axially relative to said mandrel member, said stack of variable moment arm Belleville spring washers included in said resilient means being spindled on said mandrel member.

10. Well tool according to claim 8 said Belleville spring washers having surface contour, thickness, cone angle, and inner and outer diameter such as to result in the resilient means having a substantially linear flexibility-deflection function, with highest flexibility at zero deflection.

11. Well tool according to claim 8, said washers being roller Belleville spring washers.

12. Well tool according to claim 8, said resilient means having a spring rate of about 5000 lb/in or less over a range of deflection of plus or minus one inch.

13. Well tool according to claim 8, the spring washers in the stack being entirely in series.

14. Well tool according to claim 8, for use in a drill string to reduce transmission of vibration from the drill bit to the upper drill string, i.e., that part of the drill string above the drill bit, said tool including:
means to contract the length of and thereby equally increase the strain of the resilient means upon equal departures from neutral position upon both extension and contraction of the joint, said stop means imposing limits on relative dispalcement of said members in both directions, said resilient means providing a low spring rate over a working range of travel constituted by positive and negative deflections from said neutral position and a gradually increasing and then sharply increasing spring rate as the limits of both extension and contraction of the joint are approached upon farther positive and negative deflection respectively, said unit, when employed between a three cone rock bit and an upper drill string having a mass of 32,000 pounds rotating at one revolution per second, providing at said zero deflection neutral position a frequency ratio in excess of the square root of two.

15. Well tool according to claim 4, said tool having a flexibility function of substantially inverted V
shape centered at zero deflection.

16. Well tool according to claim 4, said tool having a spring rate of less than 13000 lb/in over a range of deflection of plus or minus 0.8 inch and over 100,000 lb/in at a deflection of plus or minus 1.4 inch.

17. Well tool according to claim 4, said unit having a spring rate of less than 5000 lb/in at zero deflection.

18. Well tool according to claim 4, said Belleville spring washers being roller Belleville spring washers.