Note: Descriptions are shown in the official language in which they were submitted.
SYSTEMS AND METHOD FOR USE OF SINGLE MASS FLYWHEEL
ALONGSIDE TORSIONAL VIBRATION DAMPER ASSEMBLY FOR
SINGLE ACTING RECIPROCATING PUMP
Background
Technical Field
[0001] The present disclosure relates to single acting reciprocating
pumps and,
more specifically, to single mass flywheels and torsional vibration dampers
for use with
single acting reciprocating pumps.
Discussion of Related Art
[0002] During fracturing operations, high and low frequency torsional
vibration is a
common occurrence through the driveline. Such torsional vibration is typically
generated
via the operation of a reciprocating pump. Reciprocating pumps are driven to
pump
"slugs" of fluid with as the pump reciprocates or cycles. The speed and
operating
pressure of the pump influences the amount of fluid pumped downstream of the
pump.
As the reciprocating pump is cycled, movement of the slugs create pressure
fluctuations
within fluid downstream of the pump. This pressure fluctuation may create
"hydraulic fluid
pulsation" within the pump that is added to the operating pressure of the
pump. The
hydraulic fluid pulsation may be transferred upstream to driving equipment
used to drive
the pump in the form of torque output variances. The driving equipment may
include one
or more components including, but not limited to, a driveshaft, an engine, a
transmission,
or a gearbox.
[0003] As noted, the nature of the suction and discharge strokes of the
reciprocating pump generate variable torque spikes that originate from the
discharge of
high pressure fluid and may migrate through the drive line and cause damage
and
premature wear on the driveline components including the prime mover.
Problematically,
each reciprocating pumps operating in the field generally have their own
torsional
vibration frequency and amplitude profile that is dependent upon the selected
operational
pressure and rate. Another problem arises when a group of reciprocating pumps
are
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Date Recue/Date Received 2020-09-11
connected to a common discharge line. In this operational scenario,
reciprocating pumps
may begin to synchronize such that the natural sinusoidal wave form of one
pump will
begin to mirror that of another pump from the group, which promotes pressure
spikes and
torsional distortion of even higher amplitude to pulsate through the drive
lines.
[0004] The torque output variances may create shock loading in the pump
and in
the driving equipment upstream from the pump. This shock loading may shorten
the life
of the driving equipment including causing failure of one or more components
of the
driving equipment. In addition, driving equipment such as combustion engines,
e.g., gas
turbine engines, have a movement of inertia, natural damping effects, and
stiffness
coefficients. Some driving equipment may have low natural damping effects that
may
allow for torsional resonance interaction within the driving equipment and/or
between the
driving equipment and the pump. This torsional resonance may shorten the life
of the
driving equipment including causing failure of one or more components of the
driving
equipment.
[0005] Thus there is a need to provide protection of hydraulic drive line
fracturing
equipment from imposed high frequency/low amplitude and low frequency/high
amplitude
torsional vibrations.
Summary
[0006] This disclosure relates generally to vibration dampening
assemblies for use
with pump systems including a reciprocating pump and driving equipment
configured to
cycle the pump. The vibration dampening assemblies may include single mass
flywheel(s) and/or torsional vibration dam pener(s) to reduce or eliminate
upstream shock
loading and/or dampen torsional resonance from reaching the driving equipment;
i.e., to
reduce or eliminate pump imposed high frequency/low amplitude and low
frequency/high
amplitude torsional vibrations.
[0007] According to some embodiments, a single mass flywheel or a series
of
single mass flywheels along the drive-train system components between the gear
box or
transmission and input shaft of a reciprocating pump may be used to reduce
output speed
fluctuations that may cause vibrational and torsional effects on the gearbox
and engine.
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Date Recue/Date Received 2020-09-11
Further, at least one torsional vibration dampener may be connected to the
drive-train
system to dampen the harmonic effects of the reciprocating pump. According to
some
embodiments, the at least one flywheel and the at least one torsional damper
may not
require electrical control to be able to function, but it is contemplated that
electrical
sensors and instrumentation may be present to monitor the condition of the
drive line.
[0008] According to some embodiments, a pump system may include a pump, a
driveshaft, driving equipment, and a vibration dampening assembly. The pump
may have
an input shaft that is connected to the driveshaft. The driving equipment may
include an
output shaft that has an output flange connected to the driveshaft. The
driving equipment
may be configured to rotate the driveshaft to rotate the input shaft of the
pump therewith.
The vibration dampening assembly may include at least one flywheel that is
operably
connected to the input shaft and is configured to rotate therewith. The input
shaft may
include an input flange that is connected to the driveshaft. According to some
embodiments, the at least one flywheel may comprise a first flywheel.
[0009] According to some embodiments, the pump may be a single acting
reciprocating pump. The first flywheel may be a single mass flywheel. The
first flywheel
may be connected to the output flange of the driving equipment or the first
flywheel may
be connected to the input flange of the single acting reciprocating pump.
[0010] In some embodiments, the vibration dampening assembly may include
at
least one torsional vibration damper that is operably connected to the input
shaft.
According to some embodiments, the at least one torsional vibration damper may
comprise a first torsional vibration damper that may be connected to the input
flange of
the pump, may be connected to the output flange of the driving equipment,
and/or may
be connected to the first flywheel.
[0011] According to some em bodiments, the first flywheel may be
connected to the
output flange of the driving equipment and the first torsional vibration
damper may be
connected to the first flywheel. The vibration dampening assembly may include
a second
torsional vibration damper that may be connected to the input flange.
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Date Recue/Date Received 2020-09-11
[0012] According to some embodiments, the vibration damping system may
include a second flywheel that may be connected to the input flange. The
second
torsional vibration damper may be connected to the second flywheel.
[0013] According to some embodiments, the first and/or the second
flywheel may
be configured to absorb a torque shock in the form of torque variance
resulting from
hydraulic fluid pulsation within the pump. The first and/or second torsional
vibration
damper may be configured to reduce torsional resonance within the driving
equipment or
the pump.
[0014] According to some embodiments, a method of sizing a flywheel for a
pump
system that has a single acting reciprocating pump and driving equipment
configured to
cycle the pump may include calculating a desired moment of inertia of the
flywheel and
sizing the flywheel to have the desired moment of inertia. The desired moment
of inertia
may be calculated using a kinetic energy "KE" of a torque variance within the
pump
system above a nominal torque of the pump system that results from hydraulic
fluid
pulsation within the pump.
[0015] In some embodiments, calculating the desired moment of inertia of
the
flywheel may include calculating a first desired moment of inertia of a first
flywheel from
a first portion of the kinetic energy "KE" of the torque variance within the
pump system as
a result of hydraulic fluid pulsation within the pump, and calculating a
second desired
moment of inertia of a second flywheel from a second portion of the kinetic
energy "KE"
of the torque variance within the pump system as a result of hydraulic fluid
pulsation within
the pump. The first portion may be greater than, lesser than, or equal to the
second
portion. Sizing the flywheel may include sizing the first flywheel to have the
first desired
moment of inertia and sizing the second flywheel to have the second desired
moment of
inertia.
[0016] Still other aspects, embodiments, and advantages of these
exemplary
aspects and embodiments, are discussed in detail below. Moreover, it is to be
understood
that both the foregoing information and the following detailed description are
merely
illustrative examples of various aspects and embodiments, and are intended to
provide
4
Date Recue/Date Received 2020-09-11
an overview or framework for understanding the nature and character of the
claimed
aspects and embodiments. Accordingly, these and other objects, along with
advantages
and features of the present disclosure herein disclosed, will become apparent
through
reference to the following description and the accompanying drawings.
Furthermore, it is
to be understood that the features of the various embodiments described herein
are not
mutually exclusive and may exist in various combinations and permutations.
Brief Description of the Drawings
[0017] The accompanying drawings, which are included to provide a further
understanding of the embodiments of the present disclosure, are incorporated
in and
constitute a part of this specification, illustrate embodiments of the present
disclosure,
and together with the detailed description, serve to explain the principles of
the
embodiments discussed herein. No attempt is made to show structural details of
this
disclosure in more detail than may be necessary for a fundamental
understanding of the
exemplary embodiments discussed herein and the various ways in which they may
be
practiced. According to common practice, the various features of the drawings
discussed
below are not necessarily drawn to scale. Dimensions of various features and
elements
in the drawings may be expanded or reduced to more clearly illustrate the
embodiments
of the disclosure.
[0018] FIG. 1 is a schematic view of a pump system having a first
exemplary
embodiment of a vibration dampening assembly provided according to an
embodiment of
the disclosure.
[0019] FIG. 2 is a graph illustrating a pressure, acceleration, and
suction pressure
of an exemplary pump of the pump system of FIG. 1 through a cycle of the pump
according to an embodiment of the disclosure.
[0020] FIG. 3 is a schematic front view of a flywheel of the pump system
of FIG. 1
according to an embodiment of the disclosure.
[0021] FIG. 4 is a schematic side view of the flywheel of the pump system
of FIG.
3 according to an embodiment of the disclosure.
Date Recue/Date Received 2020-09-11
[0022] FIG. 5 is a table providing exemplary properties of flywheels that
each have
the same moment of inertia.
[0023] FIG. 6 is another schematic front view of a flywheel of the pump
system of
FIG. 1 illustrating bolt holes and rotational stresses of the flywheel
according to an
embodiment of the disclosure.
[0024] FIG. 7 is a graph illustrating tangential and radial stresses of
the flywheel of
FIG. 1 according to an embodiment of the disclosure.
[0025] FIG. 8 is a schematic side view of a portion of the pump system of
FIG. 1
illustrating a bolt and nut securing the flywheel to an output flange
according to an
embodiment of the disclosure.
[0026] FIG. 9 is a schematic view of the pump system of FIG. 1 with
another
exemplary embodiment of a vibration dampening assembly according to an
embodiment
of the disclosure.
[0027] FIG. 10 is a schematic view of the pump system of FIG. 1 with
another
exemplary embodiment of a vibration dampening assembly according to an
embodiment
of the disclosure.
[0028] FIG. 11 is a schematic view of the pump system of FIG. 1 with
another
exemplary embodiment of a vibration dampening assembly according to an
embodiment
of the disclosure.
[0029] FIG. 12 is a graph showing torsional vibration analysis data
results
demonstrating the reduction in synthesis and torque spikes with the use of a
torsional
vibration dampener (TVD) and a single mass produced by a pump system such as
shown
in Figure 1 according to an embodiment of the disclosure.
Detailed Description
[0030] The present disclosure will now be described more fully
hereinafter with
reference to example embodiments thereof with reference to the drawings in
which like
reference numerals designate identical or corresponding elements in each of
the several
views. These example embodiments are described so that this disclosure will be
6
Date Recue/Date Received 2020-09-11
thorough and complete, and will fully convey the scope of the disclosure to
those skilled
in the art. Features from one embodiment or aspect may be combined with
features from
any other embodiment or aspect in any appropriate combination. For example,
any
individual or collective features of method aspects or embodiments may be
applied to
apparatus, product, or component aspects or embodiments and vice versa. The
disclosure may be embodied in many different forms and should not be construed
as
limited to the embodiments set forth herein; rather, these embodiments are
provided so
that this disclosure will satisfy applicable legal requirements.
[0031] As used in the specification and the appended claims, the singular
forms
"a," "an," "the," and the like include plural referents unless the context
clearly dictates
otherwise. In addition, while reference may be made herein to quantitative
measures,
values, geometric relationships or the like, unless otherwise stated, any one
or more if
not all of these may be absolute or approximate to account for acceptable
variations that
may occur, such as those due to manufacturing or engineering tolerances or the
like.
[0032] Referring now to Figure 1, an exemplary pump system 1 having a
vibration
dampening assembly 10 described in accordance with the present disclosure. The
pump
system 1 includes driving equipment 100 and driven components including a
driveshaft
200 and a pump 300. The vibration dampening assembly 10 is secured to portions
of a
pump system 1 between the driving equipment 100 and the pump 300 to dampen
upstream high frequency/low amplitude and low frequency/high amplitude
torsional
vibrations generated by the operating pump 300 from reaching the driving
equipment 100.
[0033] The driving equipment 100 is illustrated as a power transfer case.
In some
embodiments, the driving equipment 100 includes a driveshaft, a transmission,
a gearbox,
or an engine, e.g., an internal combustion engine or a gas turbine engine. The
driving
equipment 100 includes an output shaft 110 that has an output flange 112. The
driving
equipment 100 is configured to rotate the output shaft 110 about a
longitudinal axis
thereof. The driving equipment 100 may include an engine and a transmission,
gearbox,
and/or power transfer case that may be configured to increase a torque and
decrease a
rotational speed of the output shaft 110 relative to a driveshaft of the
engine or that may
be configured to decrease a torque and increase a rotational speed of the
output shaft
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Date Recue/Date Received 2020-09-11
110 relative to a driveshaft of the engine. The pump 300 includes in input
shaft 310
having an input flange that is configure to receive input from the driving
equipment 100 in
the form of rotation of the input flange about a longitudinal axis of the
input shaft 310.
[0034] The driveshaft 200 has a driving or upstream portion 210, a driven
or
downstream portion 240, and a central portion 230 between the upstream and
downstream portions 210, 240. The upstream portion 210 includes an upstream
flange
(not shown) that is connected to the output flange 112 of the driving
equipment 100 such
that the upstream portion 210 rotates in response or in concert with rotation
of the output
shaft 110. The central portion 230 is secured to the upstream portion 210 and
rotates in
concert therewith. The downstream portion 240 is secured to the central
portion 230 and
rotates in concert therewith. The downstream portion 240 includes a downstream
flange
242 that is connected to an input flange of the pump 300 such that the input
flange rotates
in response or in concert with rotation of the drives haft 200. The downstream
portion 240
may also include a spindle 244 adjacent the downstream flange 242. The
upstream
flange (not shown) may be similar to downstream flange 242 and the upstream
portion
210 may include a spindle (not shown) that is similar to the spindle 244 of
the downstream
portion 240.
[0035] In some embodiments, the output shaft 110 of the driving equipment
100 is
offset from the input shaft 310 of the pump 300 such that the longitudinal
axis of the output
shaft 110 is out of alignment, Le., not coaxial with, the longitudinal axis of
the input shaft
310. In such embodiments, the upstream portion 210 or the downstream portion
240 may
include a constant velocity (CV) joint 220, 250 between the spindle 244 and
the central
portion 230. The CV joints 220, 250 allow for the output shaft 110 to be
operably
connected to the input shaft 310 when the output and input shafts 110, 310 are
offset
from one another.
[0036] During operation, the output shaft 110 is rotated by the driving
equipment
100 to rotate the input shaft 310 of the pump 300 such that the pump 300 is
driven to
pump slugs of fluid. Specifically, the driving equipment 100 is configured to
rotate the
input shaft 310 at a constant velocity such that the pump 300 provides a
constant flow of
8
Date Recue/Date Received 2020-09-11
fluid. As the pump 300 pumps slugs of fluid, the pulses of the slugs of fluid
create a
pulsation pressure that adds to the nominal operating pressure of the pump
300.
[0037] With additional reference to Figure 2, the pressure P of the pump
300 is
illustrated through an exemplary cycle of the pump 300. The pump 300 has a
nominal
pressure PN of 8250 psi with a normal operating pressure in a range of 7500
psi to 9000
psi. The pulsations of the operating pressure illustrate the pulsation
pressure described
above which is known as "hydraulic fluid pulsation." This hydraulic fluid
pulsation may
lead to pressure spikes Ps as illustrated between points 60 and 150 of the
cycle of the
pump 300 in Figure 2. The pressure spikes Ps are measured as peak to peak
pressure
variations, which as shown in Figure 2 is 2,500 psi.
[0038] The hydraulic fluid pulsation describe above may be transferred
upstream
from the pump 300 to the driving equipment 100 through the driveshaft 200.
Specifically,
the hydraulic fluid pulsation results in torque variations in a crank/pinion
mechanism of
the pump 300 that are transferred upstream as torque output variations at the
input shaft
310 of the pump 300. These torque output variations may create a torsional
shock Ts at
the output flange 112 of the output shaft 110. A single large torsional shock
Ts may
damage components of the driving equipment 100. In addition, an accumulation
of minor
or small torsional shocks Ts may decrease a service life of one or more of the
com ponents
of the driving equipment 100.
[0039] With continued reference to Figure 1, the vibration dampening
assem bly 10
is provided to reduce the transfer of the torsional shock Ts upstream to the
driving
equipment 100. The vibration dampening assembly 10 may include at least one
flywheel.
In one aspect, the at least one flywheel may comprise a flywheel 22 that is
connected to
the output flange 112 and disposed about the upstream portion 210 of the
driveshaft 200.
In some embodiments, the flywheel 22 may be connected to the output flange 112
and
be disposed about the output shaft 110.
[0040] As the output shaft 110 rotates the driveshaft 200, the flywheel
22 rotates
in concert with the output shaft 110. As shown in Figure 3, torque provided by
the driving
equipment 100 to the input shaft 310 of the pump 300 is illustrated as an
input torque Ti
9
Date Recue/Date Received 2020-09-11
and the torque output variations at the input shaft 310 of the pump 300 result
in a reaction
torque illustrated as torque spikes Ts. As the flywheel 22 rotates, angular
momentum of
the flywheel 22 counteracts a portion of or the entire torque output variances
and reduces
or eliminates torsional shock Ts from being transmitted upstream to the
driving equipment
100. Incorporation of the flywheel 22 into the vibration dampening assembly 10
allows
for the vibration dampening assembly 10 to dampen the low frequency, high
amplitude
torsional vibrations imposed on the drivetrain system that is caused by the
hydraulic fluid
pulsation.
[0041] The angular momentum of the flywheel 22 may be calculated as a
rotational
kinetic energy "KE" of the flywheel 22. The "KE" of the flywheel 22 may be
used to absorb
or eliminate a percentage of the torsional shock Ts. The "KE" of the flywheel
22 is a
function of the moment of inertia "F' of the flywheel 22 and the angular
velocity "w" of the
flywheel 22 which may be expressed as:
KE = 1 - (I co) 2 (1)
2
As noted above, the driving equipment 100 is configured to rotate at a
constant angular
velocity "w" such that with a known "KE" or a known moment of inertia "F' the
other of the
"KE" or the moment of inertia "F' may be calculated. In addition, the moment
of inertia "F'
of the flywheel 22 is dependent on the mass "m" and the radial dimensions of
the flywheel
22 and may be expressed as:
m(ri2-Fr22)
i = (2)
2
where ri is a radius of rotation and r2 is a flywheel radius as shown in
Figure 3. This
equation assumes that the flywheel 22 is formed of a material having a uniform
distribution
of mass. In some embodiments, the flywheel 22 may have a non-uniform
distribution of
mass where the mass is concentrated away from the center of rotation to
increase a
moment of inertia "F' of the flywheel 22 for a given mass. It will be
appreciated that the
mass may be varied for a given a radius of rotation ri and a given a flywheel
radius r2 by
varying a thickness "h" of the flywheel 22 in a direction parallel an axis of
rotation of the
flywheel 22 as shown in Figure 4.
Date Recue/Date Received 2020-09-11
[0042] The dimensions and mass of the flywheel 22 may be sized such that
the
flywheel 22 has a "KE" similar to a "KE" of an anticipated torque variance
above a nominal
operating torque of the pump 300. In some embodiments, the flywheel 22 maybe
sized
such that the "KE" of the flywheel 22 is greater than an anticipated torque
variance such
that the flywheel has a "KE" greater than any anticipated torque variance and
in other
embodiments, the flywheel 22 may be sized such that the "KE" of the flywheel
22 is less
than the anticipated torque variance such that the flywheel 22 is provided to
absorb or
negate only a portion of the anticipated torque variances. In particular
embodiments, the
flywheel 22 is sized such that the "KE" of the flywheel 22 is equal to the
anticipated torque
variance such that the flywheel 22 is provided to absorb or negate the
anticipated torque
variance while minimizing a moment of inertia "I" of the flywheel 22.
[0043] The rotational kinetic energy "KE" of the torque variance is
calculated from
the specifications of a particular pump, e.g., pump 300, and from empirical
data taken
from previous pump operations as shown in Figure 2. For example, as shown in
Figure
2, the pressure spike Ps is analyzed to determine a magnitude of the pressure
spike Ps
and a duration of the pressure spike Ps. As shown, the duration of the
pressure spike Ps
occurred over 0.628 radians of the cycle and using the specification of the
pump resulted
in a torque above the nominal operating torque of 1420 lb-ft. From these
values and
given the constant velocity of the particular pump of 152.4 radians/second,
the "KE" of a
torque variance resulting from the pressure spike Ps may be calculated as 8922
lb-ft or
12,097 N-m of work.
[0044] The "KE" of the torque variance may be used to size a flywheel 22
such that
the flywheel 22 has a "KE" greater than or equal to the "KE" of the torque
variance.
Initially, equation (1) is used to calculate a desired moment of inertia "I"
of the flywheel 22
solving for the "KE" of the torque variance created by the pressure spike Ps
for a given
angular velocity "w" of the flywheel 22. For example, the angular velocity "w"
of the output
shaft 110 may be 152.4 radians/second with the "KE" of the torque variance
created by
the pressure spike Ps being 12,097 N-m. Solving equation (1) provides a
desired moment
of inertia "I" of the flywheel 22 as 1.047 kg m2.
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Date Recue/Date Received 2020-09-11
[0045] Once the desired moment of inertia "I" of the flywheel 22 is
determined,
equation (2) is used to determine dimensions of the flywheel 22 using desired
moment of
inertia "r. As shown in Figure 4, with the desired moment of inertia "r, a set
radius of
rotation "ri", and a set thickness of the flywheel 22, the flywheel radius
"r2" and mass "m"
may be manipulated such that the flywheel 22 has dimensions and a mass that
are
optimized for a particular application. Referring to Figure 4, for example and
not meant
to be limiting, a 10 kg flywheel with an outer radius "r2" of 0.45 m has the
same moment
of inertia as a 100 kg flywheel with an outer radius "r2" of 0.13 m such that
either the 10
kg flywheel or the 100 kg flywheel would have the same "KE" to absorb the "KE"
of the
torque variance created by the pressure spike Ps.
[0046] It will be appreciated that for a given system, the radius of
rotation "ri" of the
flywheel is set by a diameter of the spindle or flange on which the flywheel
is secured,
e.g., upstream flange of the upstream portion 210 or the flange 242 or the
spindle 244 of
the downstream portion 240 (Figure 1). In addition, the thickness "h" of the
flywheel 22
may also be manipulated to vary a mass of the flywheel for a given outer
radius "r2".
[0047] With additional reference to Figure 6, the flywheel 22 is
subjected to
rotational stresses that differ within the flywheel 22 dependent on the radial
distance "rd"
away from axis of rotation "AR" of the flywheel 22. It is important to choose
a material for
the flywheel 22 that is capable of withstanding the rotational stresses of the
flywheel 22.
To determine the rotational stresses of the flywheel 22, the flywheel may be
treated as a
thick-walled cylinder to calculate the tangential and radial stresses thereof.
The
calculations detailed below assume that the flywheel 22 has a uniform
thickness "h", the
flywheel radius "r2" is substantially larger than the thickness "h" (e.g.,
r2>5h), and the
stresses are constant over the thickness "h". The tangential stress " ot" and
radial stress
" r" of the flywheel 22 may be expressed as follows:
r 2fr 2 \
Gt 19602 ( -v8 tr 12 r2 2 _ (r A2 ))
rd 3+v "
(3)
= 1,602 (3-v8 tr 2 r22 _ 2(r2\ _ (rd2))
rd (4)
12
Date Recue/Date Received 2020-09-11
where p is a mass density (Iblin3) of the material of the flywheel 22, w is
the angular
velocity (rad/s) of the flywheel 22, and v is the Poisson's ratio of the
flywheel 22. As
shown in FIGURE 7, when the inner radius ri is 2.5 inches and the outer radius
r2 is 8.52
inches the maximum tangential stress " ot" is 1027 psi at 2.5 inches from the
axis of
rotation and the maximum radial stress " or" is 255 psi at 4.5 inches from the
axis of
rotation.
[0048] The installation or securement of the flywheel 22 to the pump
system, e.g.,
to output flange 112 of the output shaft 110 (Figure 1), must also be analyzed
to confirm
that the means for attachment is suitable for the calculated stresses. For
example, the
planar stresses occurring at the point of installment may be calculated.
Specifically, the
flywheel 22 may be installed to the output flange 112 as described above or to
the input
flange of the pump as described below. For the purposes of this analysis, it
will be
assumed that the flywheel 22 is installed with a number of bolts 72 and nuts
76 as shown
in Figure 8. To secure the flywheel 22 to the output flange 112 (Figure 1),
each bolt 72
is passed through a bolt hole 70 defined through the flywheel 22 at a bolt
radius "rB"
(Figure 6) from the axis of rotation "AR" of the flywheel 22. The planar
stresses may be
calculated as follows:
FB = (5)
rB
Vs = ¨ (6)
AB
FB
Vb = ¨ (7)
hd
where FB is a force (lbf) applied to the bolt 72, T is a torque (lb-ft)
applied to the flywheel
22, AB is a bolt bearing stress area (in2) of the bolt 72, d is a diameter
(ft) of the bolt hole
70, vs is a shear stress (psi) of each bolt 72, and Vb is a bearing stress on
the flywheel
22/bolt hole 70 (psi).
[0049] Continuing the example above, given a maximum torque "T" applied
to the
output flange 112 of 35,750 lb-ft with a bolt radius "rs" of 7.6 inches, the
force applied to
the bolts FB is 56,447 lbf. With the bolt bearing area of each bolt 72 being
0.785 in2 the
shear stress vs of each of the 10 bolts is 7,187 psi. With the thickness of
the flywheel "h"
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Date Recue/Date Received 2020-09-11
being 1.54 inches and a diameter of each bolt hole being 1.06 inches, the
bearing stress
VB is 3,885 psi.
[0050] From the calculated stresses of the example above and applying a
factor of
safety, a material for the flywheel 22 should have should have a tensile yield
strength
greater than or equal to 75 ksi. Examples of some suitable materials for the
flywheel 22
are 1040 carbon steel, 1050 carbon steel, or Inconel() 718; however, other
suitable
metals or other materials may also be used. In addition, the materials sued
for the bolts
72 and the nuts 76 should have a tensile strength greater than the calculated
stresses.
Examples of some suitable materials for the bolts 72 and the nuts 76 are Grade
8 carbon
steel, Grade 5 carbon steel, or Grade G (8) steel; however, other suitable
metals or other
materials may also be used.
[0051] Referring briefly back to Figure 1, the vibration dampening
assembly 10
may also include at least one torsional vibration damper. The at least one
torsional
vibration dam per may comprise a torsional vibration dam per 24 disposed
upstream of the
pump 300. As shown, the torsional vibration damper 24 is disposed about the
upstream
portion 210 of the driveshaft 210 and is connected to a downstream side of the
flywheel
22. The vibration damper 24 may be connected directly to the flywheel 22 or
directly to
the output flange 112 of the driving equipment 100 and may be disposed about
the
upstream portion 210 of the driveshaft 210 or the output shaft 110. The
torsional vibration
damper 24 is configured to prevent torsional resonance within the driving
equipment 100
that may lead to damage or fatigue of components of the driving equipment 100,
the
driveshaft 200, or the pump 300. Incorporation of the torsional vibration
damper 24 along
the drivetrain in between the gearbox and/or transmission and the single
acting
reciprocating pump 300 allows for the vibration dampening assembly 10 to
dampen the
high frequency, low amplitude torsional vibrations imposed on the drivetrain
system that
is caused by forced excitations from the synchronous machinery. The torsional
vibration
damper 24 may be a viscous, a spring-viscous, or a spring torsional vibration
damper.
Examples of suitable torsional vibration dampers include, but are not limited
to, a
Geislinger Damper, a Geislinger Vdam p0, a Metaldyne Viscous Damper, a
Kendrion
Torsional Vibration Dampener, a Riverhawk Torsional Vibration Dampener, and
the like.
14
Date Recue/Date Received 2020-09-11
[0052] As shown Figure 1, the vibration dampening assembly 10 is secured
to the
output flange 112. Specifically, the flywheel 22 is connected to the output
flange 112 and
the torsional vibration damper 24 is connected to the flywheel 22. However, as
illustrated
below with reference to Figures 5-7, the flywheel 22 and/or the torsional
vibration damper
24 may be disposed at other positions within the pump system 1 and the
vibration
dampening assembly 10 may include multiple flywheels and/or multiple vibration
dampers.
[0053] Referring now to Figure 9, the vibration dampening assembly 10
includes a
first flywheel 22, the torsional vibration damper 24, and a second flywheel
32. The second
flywheel 32 is connected to the input flange of the pump 300. When the
vibration
dampening assembly 10 includes the first flywheel 22 and the second flywheel
32, the
sum of the "KE" of the flywheels 22, 32 may be configured in a manner similar
to the "KE"
of a single flywheel as detailed above with respect to the flywheel 22. In
some
embodiments, each of the first and second flywheel 22, 32 is sized to have a
similar
moment of inertia "r. In such embodiments, the first and second flywheel 22,
32 may
have similar dimensions and mass or may have different dimensions and mass
while
having a similar moment of inertia "r. In other embodiments, the first
flywheel 22 is
configured to have a moment of inertia "F' different, e.g., greater than or
lesser than, a
moment of inertia "F' of the second flywheel 32.
[0054] With reference to Figure 10, the vibration dampening assembly 10
includes
the flywheel 22, a first torsional vibration damper 24, and a second vibration
damper 34.
The flywheel 22 is connected to the output flange 112 of the driving equipment
100 and
the first torsional vibration damper 24 is connected to the flywheel 22. The
second
vibration damper 34 is connected to the input flange of the pump 300. Using
first and
second vibration dampers 24, 34 instead of a single vibration damper may allow
for
greater resistance to torsional resonance within the driving equipment 100
and/or for each
of the first and second vibration dampers 24, 34 to have a reduced size
compared to a
single vibration damper.
[0055] Referring now to Figure 11, the vibration dampening assembly 10
includes
the first flywheel 22, the first torsional vibration damper 24, the second
flywheel 32, and
Date Recue/Date Received 2020-09-11
the second vibration damper 34. The first flywheel 22 is connected to the
output flange
122 of the driving equipment 100 with the first torsional vibration damper 24
connected to
the first flywheel 22. The second flywheel 32 is connected to the input flange
of the pump
300 with the second torsional vibration damper 34 connected to the second
flywheel 32.
As noted above, the first and second flywheels 22, 32 may be sized such that
the sum of
the "KE" of the flywheels 22, 32 is configured in a manner similar to the "KE"
of a single
flywheel detailed above with respect to the flywheel 22. In addition, using
first and second
vibration dampers 24, 34 instead of a single vibration damper which may allow
for greater
resistance to torsional resonance within the driving equipment 100.
[0056] The configurations of the vibration dampening assembly 10 detailed
above
should be seen as exemplary and not exhaustive of all the configurations of
the vibration
dampening assembly 10. For example, the vibration dampening assembly 10 may
consist of a flywheel 32 and a torsional vibration damper 34 as shown in
Figure. 6. In
addition, it is contemplated that the vibration dampening assembly 10 may
include more
than two flywheels or more than two torsional vibration dampers. Further, the
vibration
dampers may each be connected directly to a respective flange, e.g., output
flange 112
or input flange, and not be directly connected to a flywheel, e.g., flywheels
22, 32.
[0057] FIG. 12 is a graph showing torsional vibration analysis data
results
demonstrating the reduction in synthesis and torque spikes with the use of a
torsional
vibration dampener (TVD) and a single mass produced by a pump system such as
shown
in Figure 1 according to an embodiment of the disclosure. A significant
reduction in
amplitude and frequency of the system torque spikes is noticeable over entire
speed
range of the reciprocating pump.
[0058] While several embodiments of the disclosure have been shown in the
drawings, it is not intended that the disclosure be limited thereto, as it is
intended that the
disclosure be as broad in scope as the art will allow and that the
specification be read
likewise. Any combination of the above embodiments is also envisioned and is
within the
scope of the appended claims. Therefore, the above description should not be
construed
as limiting, but merely as exemplifications of particular embodiments. Those
skilled in the
art will envision other modifications within the scope of the claims appended
hereto.
16
Date Recue/Date Received 2020-09-11
