Note: Descriptions are shown in the official language in which they were submitted.
-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-
-6-
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-
--7--
~ 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
-8-
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.
--1 1\
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.
-12-
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;
. ~
':`
-13-
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
-14-
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.
-15-
~ 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
-16-
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.
-17-
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.
.
-18-
~:~s~
- 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.
.
-20-
- 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-
-21-
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,
.
-23-
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.
';
-24-
r~
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
-25-
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-
-26-
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
-27-
~ ~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
-28-
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
-29-
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-
-30-
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.
:``
-32-
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
-36-
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-
-37-
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.
-38-
- 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.,
-39-
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
-40-
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
-41-
"~
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
-43-
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
-44-
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.
-45-
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 .
-47-
~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
-48-
~ 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
-49-
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.
-50-
~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.
-52-
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.
-53- ,
