Note: Descriptions are shown in the official language in which they were submitted.
1:~735Z8
BACRGROUND OF THE INVENTION
This application is directed to an improved vibration
absorber for individual suspended cables including but not
limited to electrical transmission lines; and more specifically
to a device for absorbing energy to suppress aeolian vibration
of such cables.
The vibration absorber herein described operates on the
principles disclosed in U.S. Patent 4,346,255. This prior patent
discloses and claims an essentially dissipative (as opposed to
spring-type) vibration absorber having a damping meohanical
impedance which essentially matches the mechanical impedance
of the transmission line to which the damper is attached. The
acceptable range of damper impedance of the absorber is indicated
as being anywhere between half and three times the transmission
line mechanical impedance.
By essentially matching the transmission line mechanical
impedance and providing a dissipative (i.e., frequency independent)
damping effect, the vibration absorber of the aforesaid
U.S. Patent 4,346,255 provides optimum energy coupling between the
transmission line and absorber, thus effectively absorbing
travelling waves on the line before they build up to large ampli-
tude standing waves which can cause damage to the line and
associated supporting elements.
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Until the aforesaid invention was made, prior art spring-
type dampers had to be designed so that they operated effectively
over the resonant frequency range of the transmission line to be
damped. These dampers also had to be situated at points on
the transmission line where standing waves would be of relatively
large amplitude, i.e., at distances of a quarter wavelength
from adjacent nodes.
The invention of U.S. patent 4,3~6,255 relates to the
use of vibration absorbers which can be connected to transmission
lines to provide essentially dissipative damping. That is,
these dampers utilize viscous-type effects, so that damping is
essentially frequency independent. In contradistinction,
those prior art dampers which utilized springs or other resilient
elements had undesirable resonance characteristics. A typical
15 prior art vibration damper of this type is shown in U.S. Patent
No. 3,885,086. The vibration damper shown in this patent,
however, is unsuitable for use in the arrangement contemplated
by the aforementioned U.S. Patent 4,346,255, because it is
incapable of providing the critical dissipative damping required.
20 In U.S. patent 3,885,086, the annular washers 12 are situated
between clamp arms 16 and adjacent frame portions 10, and
secured thereto so that said washers do not rotate. The washers
are of a resilient material, so that rotation of the clamp arm
16 results in deformation of the washers, the resilient charac-
25 teristics of which then return the clamp arms to their initial
; orientations. In this arrangement, the only dissipative damping
effects are provided by hysteresis losses within the resilient
washers.
.
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Any attempt to increase the hysteresis losses byincreasing the size of the washers results in the spring
force of the washers rising substantially faster than their
hysteresis losses, making such a design impractical. Further,
limitations of the resilient material itself make it
impracticable to obtain sufficiently great hysteresis losses
to provide critical dissipative damping. In addition, the
hysteresis losses in the washers 12 are dependent upon
both frequency and amplitude of vibration.
Vibration absorbers intended for use with single
cables or conductors utilize a mass which a~ts as a platform
to induce oscillation within the vibration absorber. Where
the cable or conductor is stranded and therefore exhibits a high
level of torsional damping (due to interstrand friction),
torsional vibration absorbers may be employed to reflect
the vertical aeolian vibrations into torsional conductor
oscillations. Such torsional vibration absorbers are des-
cribed in Canadian Patent Nos. 377,602; 546,134; 559,081;
567,131; and 570,780; and in the following articles:
1. Measurement and Control of Conductor Vibration
by Gordon B. Tebo
AIEE Transactions
Volume 60 - 1941
pp 1188 - 1193
2. Conductor Vibration - Theory of Torsional Dampers
by James W. Speight
AIEE Transactions
Volume 60 - 1941
pp 907 - 911
Canadian Patent No. 570,780 utilizes rubber washers
to internally damp the vibration absorber. In common with
the o~her prior art single cable vibration absorbers, however,
this structure provides poor damping action since it has
a high spring constant and has no means for positive damping,
relying solely on hysteresis losses in the rubber.
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The aforementioned prior art vibration absorbers
have a limited ability to dissipate energy, pronounced
resonances, and a limited effective frequency range.
They also suffer from incompatability between the spring
constant required to restore the vibration absorber to
its neutral position and the rubber (or other resilient
material) characteristics required to provide the optimum
mechanical impedance. That is, a compliance low enough
to provide proper restoration to the neutral position
results in an undesirably high mechanical impedance which
reflects (rather than absorbing) a considerable amount of
aeolian vibration energy back to the cable supports at
the suspension points thereof.
In contradistinction, dampers of U. S. Patent Serial
No. 4,346,255 being dissipative and therefore frequency-
independent, need not be concerned with the resonant
frequencies of the transmission line to which they are
to be attached. Further, such dampers, being essentially
impedance matched (i.e., within a range of one-half to
three times the characteristic impedence of the trans-
mission line to which they are to be attached), absorb
travelling waves, so that they can be placed at any
desired place on the transmission line to be damped.
Thus, there remains a need for an improved vibration
absorber capable of being utilized with individual sus-
pended cables or conductors according to the aforementioned
principles.
Accordingly, an object of the present invention is
to provide an improved vibration absorber for individual
- 4 -
11'~3528
suspended cables or conductors in which the damping
effect produced is essentially dissipative and therefore
frequency-independent, and wherein the damping impedence
is adjustable to a value capable of essentially matching
the mechanical characteristic impedance of the cable to
which the vibration absorber is connected.
- 4a -
SUM~ARY
11~73S28
A vibration absorber for a suspended cable,
comprising a housing; a first annular member secured to
said housing and having an exposed frictional surface;
a clamp body having a first portion for engaging a cable
in a predetermined position and a second portion rota-
tably mounted to said housing for rotation of said clamp
body about an axis spaced apart from said predetermined
position of said cable; weight means secured to sa.id
housing at a position remote from said axis; a second
annular member secured to said second portion of said
clamp body, and having an exposed frictional surface in
rotating frictional engagement with said exposed frictional
surface of said first annular member; a third annular
member secured to said second major surface and to said
housing, said third annular member comprising a resilient
material; and means for adjusting the frictional force
between said exposed frictional surfaces, said frictional
force generating frictional losses upon vibration of
said cable which substantially exceed any hysteresis
losses within said annular members, so that the frictional
force between said first and second annular members
provides dissipative damping for both said cable and
said third annular member.
IN THE DRA~ING:
FIG~RE lA is a front elevation vi.ew of a vibration
absorber according to a first embodiment of the invention,
for damping vertical aeolian vibrations in a single suspended
cable or conductor;
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FIGURE lB is a pa~ side cross sectional
view thereof;
FIGURE lC is an exploded perspective view thereof;
FIGURE lD is a schematic front elevation view thereof;
FIGURE 2A is a front elevation view of a vi~ration ab-
sorber according to a second embodiment of the invention, for
damping vertical aeolian vibrations in a suspended cable or con-
ductor by reflecting said vibrations into a torsional mode;
FIGURE 2B is a front elevation view thereof, showing
the installation position of said vibration absorber;
FIGURE 2C is a partial right side elevation cross-
sectional view thereof;
FIGURE 2D is an exploded perspective view thereof;
and
lS FIGURE 2E is a perspective view thereof, showing the
installation position of said vibration absorber.
DETAILED DESCRIPTION
Aeolian vibration derives its excitation from the
minute forces associated with the release of vortices on the
leeward side of conductors and cables when they are subjected
to a steady air flow across their surfaces. It is believed
that the excitation of aeolian vibration is derived.from the
detachment of the vortices.
This release of vortices produces travelling waves
which proceed along the span in opposite directions from their
origin towards the suspension points. These waves in turn
release other vortices to reinforce and amplify the wave
motion. When the travelling wave arrives at the sus~ension
point of the conductor, that is the attachment point of the
conductor to the supporting structure, it is reflected with a
180 phase reversal due to the rigidity of the support point.
--6--
,
11735~28
The damping characteristics of the conductor and the suspension
hardware in this mode of vibration are very small, so that
attenuation of the travelling wave is also very small. This
allows the travelling wave to make a large number of passes
in a given span to thereby generate a standing wave having an
amplitude of constant value, the amplltude being determined by
the total damping of the system.
The aforementioned vibration phenomena may be avoid-
ed by preventing the formation of a standing wave rather than
attempting to control the amplitude of the standing wave.
Since it is not feasible to Prevent vortex detachment, the
present invention provides an absoxber which will absorb the
travelling wave and prevent its reflection back along the con-
ductor. This is achieved by matching the dissipative impedance
of the absorber with the characteristic mechanical impedance of
the conductor.
The characteristic mechanical impedance of a conduct-
or is defined as the ratio of force and velocity amplitudes
of the travelling wave. Since the mechanical impedance of
the conductor is a function of the tension in the conductor and
the mass of the conductor per unit length, an absorber can be
designed to match the mechanical impedance of the conductor
for any given installation. Further, because the use of a
dissipative damper for absorbing the wave does not require a
frequency dependent resilient system, the absorber may be placed
at any convenient location along the span of the conductor and
not, as previously described, just at ~/4 wave points of the
center aeolian frequency of the conductor; although performance
of the absorber will still vary somewhat with its location.
SZ8
Under ideal conditions where the absorber is
insta~led at any point on the conductor, the absorber
impedance should be k ~ , where T is the tension of the
conductor, m is the mass of the conductor per unit length,
and k is the damping factor wh-ch, under the aforementioned
ideal conditions, equals 2.0 to reflect the fact that
the conductor extends in both directions from the absorber.
It has been found that significant improvements in vibration
control may be achieved by selecting an absorber impedance
or damping factor in the range of 0.5 ~ to 3 ~ . Thus,
increases in T and m due to icing of the conductors will
not unduly affect the operation of the absorber.
Figs. lA through lD show a "vertical" type vibration
absorber/for directly damping vertical aeolian vibrations
in the suspended cable or conductor 15, i.e., without
reflecting said vibration into a torsional mode. The
vibration absorber 16 has three major components, viz.,
a housing 17 having a central axis 18, a dumbbell 1
secured to the housing 17 and having the major portion
la thereof remote from the axis 18, and a clamp body 9
which cooperates with a clamp keeper 10 to attach the
vibration absorber 16 to the cable 15.
The clamp keeper and clamp body are urged toward
each other by the bolt 11, which threadably engages the
clamp body 9. The vibration absorber 16 is installed
vertically, so that the housing 17 lies vertically above
or below (preferably below) the cable 15, and the dumb~
bell 1 is vertically aligned with and extends in the
same general direction as the cable 15. The axis 18 of
the vibration absorber 16 is spaced apart from and extends
in a direction generally orthogonal to that of the cable
15.
The clamp body 9 is rotationally mounted on the
bolt 6 for rotation about the axis 18, the bolt 6 being
secured by a washer 8 and nut 7.
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Disposed within the housing 17 (the enclosure of
which is completed by the keeper 2), are a resilient
annular washer 5, annular bearing ball 4, and resilient
annular bearing socket 3, all of said annular members 3,
4 and 5 being secured within the housing 17. The resilient
washer 5 and bearing socket 3 are secured within the
housing 17 (which includes the keeper 2) so that they do
not rotate with respect thereto; while the bearing ball
4 is secured to one major surface of the clamp body 9 so
that it does not rotate with respect thereto.
Rotation of the annular members 3, 4 and 5 with
respect to the elements to which they are secured is
prevented by engagement of peripheral protuberances on
said members with corresponding recesses in the surfaces
to which they are secured.
The resi]ient washer 5 comprises a suitable
durable resilient material such as polyisoprene, an
elastomeric polymer. Other suitable elastomeric polymers
may of course be employed for this purpose. The ball 4
and socket 3 are preferably of rigid low friction'coefficient
material, with low friction coefficient surfaces.
The socket 3 has a recess therein comprising an
exposed frictional surface; and the bearing ball 4 has a
mating exposed frictional surface. The frictional surfaces
' 25 of the ball 4 and socket 3 rotatably engage each other
when the clamp body 9 rotates with respect to the housing
17, so ~hat coulomb friction forces are generated therebetween
to provide dissipative damping of corresponding vibrations.
Rotation of the clamp body 9 with respect to the
housing 17 is resisted by the spring action of the resilient
washer 5, which acts to restore the housing 17 to its
initial or "neutral" position with respect to the clamp
body 9 after the housing has been angularly deflected by
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aeolian vibration forces.
Dissipative energy losses occur primarily as a
result of coulomb friction between the exposed frictional
surfaces of the ball 4 and socket 3, losses due to hysteresis
and in the resilient washer 5 being relatively small in
comparison with said dissipative energy losses.
The amount of frictional force, i.e., the dissipative
damping factor of the vibration absorber, may be adjusted
by varying the normal force between the exposed frictional
surfaces of the ball 4 and socket 3, by tightening or
loosening the bolt 6 and nut 7; such adjustment having
relatively little effect upon the torsional spring action
of the resilient washer 5.
By appropriately selecting the contact area
between the ball 4 and socket 3 and adjusting the normal
force therebetween, dissipative damping factors in the
aforementioned desired range of 0.5 ~ to 3 ~ can be
obtained.
Preferably, the material and surface texture of
the exposed frictional surfaces of the ball 4 and socket
3 should be such that the coefficient of static friction
therebetween is on the order of (i.e., within 25% of)
the coefficient of moving or kinetic friction therebetween~
For best results, said coefficient5should be essentially
equal.
With the aforementioned arrangement, the engagement
of the frictional surfaces of the ball 4 and socket 3
provides damping not only for the vibrations of the
cable 15, but also for the resilient washer 5.
The manner in which the parameters of the vibration
absorber shown in Figs. lA to lD may be calculated is
described below:
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1~73528
The absorber is to develop a mechanical impedance
that lies within the limits of
0.5 ~ _ D' 3.0 ~ , (1)
where T = the conductor tension
m = the conductor mass per unit length
The mechanical impedance D associated with the
torsional mode of operation in the vertical plane through the
Conductor, can be derived from the actual mechanical impedance DT
of the device by the following equation:
DT
D = k ~ = 2
R cOs2e (2)
where R = distance between centroid of mass and
pivot axis
e = angular deflection of the mass
from the horizontal
Rearranging Equation 2:
; DT = k ~ . (R Cos e) (3)
The torsion damper polar moment of inertia J is
; related to the required mechanical impedance thereof by the
equation:
Dm J~O (4)
where ~ = 2 br ~ (5)
and~o is the lowest expected response frequency (Hz.).
From Equations (3) and (4):
2 2
k ~ (R Cos e)
J = (6)
~o
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In most transmission lines the lowest frequency
of aeolian vibration is in the order of 5 Hz., corresponding
to an angular frequency ~O= 101~radians/sec.
The vibration absorber mass M is given by:
M = J
R2 (7)
Combinin~ Equations 5 and 7 and using W = 10~
(other values of ~may of course be used for transmission lines
having lower aeolian vibration frequencies):
M = k ~ . Cos2 e
10~ (8)
The vibration absorber spring constant S is given
by
S = k J~ )o (R2 Cos2 e)
In thellverticalllvibration absorber of Figs. lA
through lD, the dumbbell 1 is asymmetrically positioned with
respect to the axis 18.
The vibration absorbers described herein provide a
substantial improvement in suppression of aeolian vibration,
operate over a wide range of frequencies, exhibit improved
durability, and need not be positioned at particular points of
the suspended cable.
Preferably, for optimum performance the vibration
absorbers should be positioned at a distance ~from the insulator
support for the corresponding span given by:
4~1 ~ (10)
where ~ 1 is the predominant anticipated frequency
of aeolian vibration ~typioally lS ~z.).
-12-
~, I
11'73S28
In the vibration absorber ~0 shown ln Figs. ~A
through 2D, the rotational axis 18a thereof lS arranged
parallel to the cable 15, and in a different vertical plane,
so that the dumbbells la and lb (whlch are symmetrically
positioned with respect to the axis 18a and housing 17a)
reflect vertical aeolian vibrations into torsional oscilla-
tions of the conductor 15. Parts of the vibration absorber
20 which corresponds to similar parts o~ the vibration
absorber 16 are identified with the same numerals. The
numeral 12 identifies a lockwasher for the bolt 11.
As shown in Fig. 2B, the vibratlon absorber 20 is
preferably installed so that a 1ine extending from the
conductor 15 to the vibration absorber axis 18a is essenti-
ally horizontal. Good results may be obtained provided that
said angle is maintained in the range o~ -60 to +60~ from
the horizontal.
In the embodiment designed to operate ln a torsional
mode in a vertical plane perpendicular to the longitudinal
conductor axis, as shown in Figs. 2A and 2B, one must deter-
mine the dissipative mechanical impedance of the coulomb
element DT, the spring constant S1 of the spring element
required to return the mass to the neutral axis, the mass M,
the dlstance R, the half masses M/2 are displaced from their
axis of rotation 18a, the length of the clamp arm r and the
installation distance ~ at which the device should be spaced
from the support point. These parameters are given by:
DT = k ~ . r2 ~ Cos2 ~ (11)
M = ~ ~rr2 cos~ fo2
S~ r20 Cos2~ fO (13)
~ 2 ~ S f3 (14)
X 4f3 ~ (15
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li73SZ8
where:
k = Damping constant, 0.5~ k <3.0 and k = 2.0
is ideal
T - Conductor tension, lbs.
m = Conductor mass per unit length, lb ft 2
sec2
S = Torsional stiffness of the conductor per
unit length, lb ft2 rad 1
f3= Mid frequency of expected aeolian vibration
range, Hz
fO= Desired lower threshold frequency, Hz
M = ~bell mass, lb ft 1 sec2
r = Offset distance - Conductor centre to
rotational axis of mass M
Sl= Torsional stiffness of dumbbell, ft lb rad 1
R = Distance from centroid of effective mass M/2
~nd rotational axis of mass M, ft.
~(= Distance from absorber to conductor support
point, ft.
D = Required dissipative mechanical impedance,
lb ft 1 secs.
DT= Required dissipative mechanical impedance of
coulomb element, lb ft secs.
The amplitude of angular deflection ~of the dumbbell
mass is given by
~ 9L~ (12)
where g = acceleration of gravity
and should preferably be such that the dumbbell does not deflect
into contact with the housing.
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