Note: Descriptions are shown in the official language in which they were submitted.
CA 02851725 2014-04-10
Method for determination of the stability of a mast that has
been properly set up at an installation site
The invention relates to a method for determination of the
stability of a mast that has been properly set up at an
installation site and attached to a substratum.
Furthermore, the invention relates to an apparatus for
implementation of this method.
A corresponding method is known, for example, from WO
2010/128056 Al. The disclosure content of this international
patent application is supposed to belong to the disclosure
content of the present application, by inclusion.
Within the scope of the invention, a mast can be an essentially
= vertically oriented support, for example for lighting fixtures,
traffic signs, traffic lights, cables, antennas, sign gantries,
or the like.
Such masts can be damaged, for example by environmental
influences, accidents or vandalism, so that the stability of a
mast can be in danger for example due to corrosion, material
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fatigue, or crack formation. The term stability particularly
covers, in the sense of the invention, the possibility that
persons who must undertake repair, maintenance, or installation
work on the mast, for example, can climb the mast. Methods for
determination of the stability of masts, therefore fulfill the
purpose, in the sense of the invention, among other things, of
checking the mast just before someone climbs it, in order to
determine whether or not climbing the mast is safe. Independent
of this, it is necessary to check the stability of a mast at
regular intervals, in order to be able to determine in timely
manner whether the stability is impaired to such an extent that
a mast must be replaced.
It is the task of the invention to make available a novel method
for determination of the stability of a mast properly set up at
an installation site, which reliably and very accurately allows
a determination of the stability of the mast.
This task is accomplished, in a method of the type stated
initially, in that the vibrations, for example in the form of
the vibration spectrum of the mast, excited to vibrate
artificially or by means of environmental influences, are
detected, and at least one natural frequency of the mast is
determined from this.
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An essential aspect of the invention is that a non-linearity of
the vibration behavior of the excited mast is analyzed. On the
basis of the result of this analysis, it can be directly
determined whether damage to the mast and/or to its attachment
in the foundation region is present.
A non-linearity of the vibration behavior can express itself,
for example, in a dependence of the vibration frequency on the
vibration amplitude. This dependence can be analyzed directly
and very easily. This dependence in turn can be used as an
indicator for a "healthy," i.e. intact, or an "unhealthy," i.e.
damaged mast foundation.
Preferably, the dependence of the vibration frequency on the
vibration amplitude is determined for the analysis of possible
non-linearities of the vibration behavior. On the basis of this
dependence, a calibration frequency can then be derived, with
which a mechanical (static and/or dynamic) model of the mast,
determined in advance (for example as described in the document
WO 2010/128056 Al cited above) is calibrated, whereby the
rigidity of the mast is then determined on the basis of the
calibrated model.
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This method can be used for masts made of the most varied
materials and the most varied shapes. It can be used, for
example, in the case of a mast configured conically or in
stepped shape, with a cross-sectional jump. Furthermore, the
method can be used not only for posts, posts in water or
overhead line masts, but also for other mast types such as, for
example, whip masts, outrigger masts, traffic light masts,
double masts, A masts, lattice masts, traffic sign gantries, and
simple frames.
An artificial excitation of the mast can take place using .a
hammer, using a cable, if necessary an imbalance exciter, or the
like. Also, an artificial excitation of the mast can take place
manually. The determination of the stability according to the
method according to the invention is based not solely on a
comparison of theoretical rigidities with a rigidity derived
from a measurement. Instead, deformations as the result of
external influences such as, for example, wind loads or man
loads of the mast are calculated using a calibrated preferably
numerical model of the mast established in advance, and then
compared with limit values. In this way, a very individual
determination of the stability of a mast is possible. This
evaluation is not only mast-specific, but also dependent on the
type of stress. Thus, for example, not only the stability with
õ
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regard to rated loads (generally wind loads) but also the
stability with regard to a person climbing it (man loads) can be
evaluated.
The following points are important within the scope of the
present invention:
As has been mentioned, a calculation of the amplitude dependence
of the at least one natural frequency and, based on that, a
calculation of the decisive natural frequency for the stability
evaluation can take place.
Furthermore, the foreseeable useful lifetime can be calculated
in non-linear manner for masts, based on a velocity of damaging
effects that is obtained from the measurement results. In this
connection, an increase in precision (i.e. an improvement in the
accuracy) of the results can take place, starting with the
= second measurement.
By providing a link, a read-in possibility for characteristic
mast data from Excel files or a database, for example, can be
provided.
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Automatic localization of masts using available GPS data and an
assignment of mast data from databases can take place. The wood
moisture can be predetermined as a function of the date, in each
instance, and automatically be converted to the measurement time
point.
A routine for identification of cable frequencies in the case of
masts carrying cables and for automatic determination of mast
frequencies can be used.
The cable hang can automatically be determined or calculated
from tables. The dependence of the hang of the cable on the
temperature in the environment of the cables can be taken into
consideration. In a calculation program, a selection
possibility can be provided as to whether the cable hang and/or
the dependence of the hang on the temperature should be
automatically predetermined or input.
A relationship between or the ratio of rotational spring
rigidity and overall rigidity (see WO 2010/128056 Al) for an
evaluation of the damage source (shaft or foundation) can be
used, taking into consideration the amplitude dependence of the
natural frequencies. ,
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The distance between the first natural frequencies and the
values of other natural frequencies can be analyzed. From this,
it is possible to draw conclusions concerning further system
parameters.
The method can also be used for glass fiber reinforced plastic
masts, taking into consideration the special characteristic
material data for glass fiber reinforced plastics.
The method can also be used for the evaluation of attached parts
(for example traverses). For this purpose, the natural
frequency and vibration forms of the attached parts are
determined either taken out of the remaining system (if there is
sufficient uncoupling) or within the overall system (in the case
of coupled vibration forms.
= The method can also be used for masts in bends of conductor
routes.
One or more sensors that can be connected with the mast can be
used for implementation of the method.
Multiple measured, dynamic characteristic values can be taken
into consideration in the determination of stability, such as,
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for example, taking into consideration multiple natural
frequencies and/or taking into consideration measured ordinates
of vibration forms when using multiple sensors. Multiple
dynamic characteristic values can be used when the search is
related not only to foundation rigidity, for example, but also
to information concerning the mast shaft, concerning regions
with damaged locations, concerning the bearing capacity of
individual rods in frameworks, etc.
The method can allow localization of system regions with
identified weak points or damaged areas.
The method can fundamentally be used for masts having a very
complex construction. Examples of this are projection arms with
outriggers (traffic light mast or outrigger sign masts on
highways), frames (sign gantry on highways or toll bridges),
masts for overhead lines (railways, public transit), masts of
cable cars, etc.
The method can fundamentally be used for masts of any kind, such
as, for example, also framework masts (such as for overhead line
masts of railways), or mobile radio masts, centrifugally cast
concrete masts or floodlight masts (also with an angular cross-
section at the foot).
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Next, an exemplary embodiment for the analysis of non-linear
vibration behavior by means of a determination of the dependence
of the natural frequency of the mast determined from the
vibration spectrum of the mast, on the vibration amplitude, will
be explained:
First, a calculation of the natural frequency in the time range
is undertaken. By means of this evaluation, any dependence of
the natural frequency on the vibration amplitude that might be
present can be determined. This dependence, in turn, can be
used as an indicator for a "healthy" or an "unhealthy"
foundation. Furthermore, this evaluation possibility allows
taking the difference between the dynamic and static modulus of
elasticity into consideration, for example for the ground or
also for wood as a material, which is important for the
determination of the static rigidity values. This evaluation is
particularly recommended for masts having markedly non-linear
behavior.
First, the measured time recording of the acceleration values
recorded at the mast after excitation, by means of an
acceleration sensor, is bandpass-filtered. The frequency band
is established from the standard evaluation, from the selected
-- -
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natural frequency ( 20% of the selected natural frequency from
the standard evaluation). In this way, disruptive components
(noise or frequency components having higher natural
frequencies) are eliminated from the time recording.
Using an identification routine, the envelope curves for the
local maxima (upper envelope curve) and minima (lower envelope
curve) are first calculated. These envelope curves are than
also smoothed by means of approximating splines that have the
same support points as the envelope curves (see Figure 1). In a
further step, this routine then looks for the range in which no
manual excitation takes place any longer and the .mast is
vibrating freely until the vibration dies away. This range
generally lies at the end of the time progression. This range
is extracted (see Figure 2).
In the extracted decay range, the distances between the local
maxima and the distances between the local minima as well as the
related vibration amplitudes ypp,i (accelerations) are then
calculated. The distances are the periods Ti of the time
progression, from which frequency values fi = 1/Ti can then be
calculated, section by section (per period i). The frequency
can thereby be represented as a function of the acceleration
vibration amplitude ypp. An example is shown in Figure 3.
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The dependence of the frequency on the vibration amplitude
determined in this way is then approximated using a potency
function. This function is defined as follows:
f(2) = a = yb
First, the quality of the adaptation is checked by way of an
error value. If this error value is close to zero, practically
no adaptation is present. For an error value close to 1,
practically perfect adaptation is present. Preferably,
approximations having error values less than 0.3 are not
evaluated. In these cases, it is assumed that no dependence of
the frequency on the amplitude exists.
If dependence is present (error > 0.3), the exponent b is
analyzed:
If b < 0, a degressive dependence is present. This means that
the frequency becomes smaller with an increasing amplitude.
This case indicates problems in the foundation, since a
progressive dependence normally occurs there.
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If b 0, a progressive dependence is present. In this case,
the frequency increases with an increasing amplitude. This is
the normal case, which is based, just like the modulus of
elasticity, on the effect that during rapid movements in the
ground, the water in the capillaries cannot be displaced just as
quickly, and an apparent increase in rigidity of the ground
occurs.
In both cases, a calibration frequency fa, which is used for
calibration of the mathematical model of the mast and thereby
for calculation of the deflections and deformations of the mast,
is recalculated using the dependence of the natural frequency
that was found. For these calculations, the following
amplitudes are used;
,
13
Value range Amplitude y for frequency Amplitude Consequence
for co- calculation in the case dependence
efficient b of amplitude dependence
and frequency fa for
evaluation
0Sb<0.01 f a=f a none
none
b>0.01 Ygrenz= 0.2-0. 2-2-(0.05.H) progressive Foundation OK
but frequency is
fa=a = ygrenz b
being reduced as compared with the
value from the spectrum
n
-0.01b<0 Ygrenz=0 . 02-2- (0.05=H)
weakly Foundation still OK but frequency i
fa=a ' Ygren zb ' 0 . 952 degressive is being
somewhat reduced as 0
I.)
co
compared with the value from the in
H
spectrum
--3
I.)
-0.02b<- Ygranz=0.02=2=(0.05-H) moderately
Foundation should be watched, in
0.01 fa=a = Sigreazb = 0.92 degressive frequency is
being reduced as I.)
0
H
compared with the value from the a,
1
0
spectrum
a,
, 1
b<-0.02 Ygrenz=0 . 02 -6)2- (0.05-H) strongly Foundation is
probably damaged, H
0
f a=a- ' Sigrenzb ' 0 . 852 degressive
frequency is being clearly reduced
as compared with the value from the
spectrum
_
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The limit amplitudes result from the spectrum, as a function of
the mast height H above ground level and the natural circular
frequency w from the spectrum.
For the case b < 0, it was assumed, in this connection, that
proceeding from a maximal amplitude of 5% of the mast height,
the quasi-static range of the decay curve is reached when the
vibration amplitudes have decayed to 2% of the maximal
amplitude. In this amplitude range, it is assumed that the
dynamic rigidities correspond to the rigidities that occur in
the case of quasi-stationary stress. The calibration frequency
fa is then reduced once again as a function of the order of
magnitude of the parameter b. These reduction factors are quasi
safety factors that are supposed to absorb the uncertainties of
this evaluation routine, among other things, in the case of
degressive dependence. As a function of the order of magnitude
of b, these factors correspond to reductions in rigidity by 5%
(f: -0.01 S b < 0), 10% (f: -0.02 S b < 0.01) or 15% (f: b < -
0.02).
For the case b > 0.01, a smaller amplitude is used for
calculation of the calibration frequency. This amounts to 20%
of the amplitude for the case b < 0.
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The further calculation (for example according to WO 2010/128056
Al) then takes place using the calibration frequency fa. This
frequency is generally less than or at most equal to the natural
frequency fa determined from the spectrum.
According to another important aspect of the invention, the
stability of a mast set up at an installation site, attached to
a foundation, can be determined, whereby the vibration spectrum
of the mast, excited to vibrate artificially or by means of
environmental influences, is detected, and at least one natural
frequency of the mast is determined from this, and whereby the
useful lifetime of the mast is then determined on this basis.
For example, the residual useful lifetime can be estimated based
on the results of the frequency measurements, as described
below.
A useful lifetime is estimated for the mast, depending on the
year of construction of the mast and/or depending on the
calculated displacement or deflection or deformation and, if
applicable, the class limits (as described, for example, in WO
2010/128056 Al).
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In general, the measurements lead to the conclusion that the
masts have greater displacements at the measurement time point
than a perfect, "undamaged" mast. The causes for the greater
displacements are, among others, due to the rigidity of the
foundation (softer than in the case of a perfect mast) and by
time-related factors that lead to a decrease in system rigidity.
Because no information concerning the mast properties at an
earlier point in time are available during a first measurement
on a mast, it is assumed that the mast was perfect, i.e. intact
at the time of installation. From the assumption of system
rigidity during the time period between installation and first
measurement, a speed of rigidity decrease can thereby be
derived. For this purpose, it is assumed that the mast is
always clamped in place, and that changes in rigidity are caused
only by a (time-dependent) reduction in cross-section. In this
connection, it is assumed that the mast cross-section, i.e. the
outside diameter, decreases from the outside to the inside at
this speed. This assumption results from the consideration that
according to various standards (for example DIN 4133), corrosion
supplements have to be taken into consideration in the
dimensioning of specific components. In principle, these
corrosion supplements also describe a decrease in the statically
relevant cross-section as a function of time. In the case of
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wooden masts, the reduction in cross-section results, for
example, from shrinkage, rot or fungal infestation.
The diameter of the masts is thereby a function of time t:
d5(t) = de) - v. = t
with da0 outside diameter at the time of installation
d.(t)outside diameter at the time point t
di inside diameter in the case of a circular ring cross-
section
v8 speed of decrease in the outside diameter in mm/year
From the underlying mechanical model, the head point
displacements of the mast El(t) can be calculated as a function
of time, at an acting force (for example wind load typical for
the location). A determination equation for v2 can thereby be
obtained, because the variable v5 is the only unknown. The
solution of this equation and the determination of v5 takes place
by means of an iteration algorithm, for example. With this
speed võ it can then be calculated at what point in time the
permissible deformation Etna is exceeded. For this purpose, the
time t is increased until the following equation has been met:
5(t = tim) = 6zul. The time tw is the estimated useful lifetime.
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The difference between tix and the time that has elapsed from the
installation time point until the measurement time point tmes is
the estimated residual duration of use being searched for.
In this connection, the speed is still multiplied by a safety
factor of 1.5, in order to take an increase in the speed of
damage into consideration by approximation. The time dependence
of the rigidity taken into consideration by the method described
is non-linear, because the assumed speed of damage relates to
the diameter.
Starting from the second measurement, a more precise calculation
of the speed of damage can take place by taking the first
measurement values into consideration. In this way, a possible
increase in the speed of damage can be detected more precisely,
but on the other hand, overestimated speeds of damage from the
first estimate can also be corrected, and thereby a more
advantageous estimate of useful lifetime can be achieved.
Next, an exemplary embodiment will be given for taking the
influence of wood moisture on properties of structural mechanics
into consideration in the evaluation of frequency measurements
on overhead line masts made of wood:
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The wood moisture influences properties of structural mechanics
of wood as a material. In the case of wooden masts freely
exposed to the weather, the wood moisture approximately follows
the changes in temperature, on average. Over the course of the
year, variations in wood moisture of approximately 12% to 20%
can occur as a result. A range of approximately 12% to 18% is
relevant for wooden masts, because there, temperatures of >0 C
can be assumed. In the case of temperatures below 0 C, the
= possibility exists that the ground is frozen, so that in this
case, the system rigidity is not representative for the case
with maximum wind (winter storm or spring storm with air
= temperature approximately 4-5 C). Short-term increases as the
result of precipitation are possible. As a result, wood
moisture values on the outside of up to 30% can be reached, but
these generally dry off again quickly due to the influence of
wind.
A decisive parameter of structural mechanics is the modulus of
= elasticity (which also influences the bending rigidity). This
parameter is dependent on the current wood moisture. It turns
out that the modulus of elasticity varies, in the relevant
moisture range u = (12%-18%), from about 9200 MPa to 10,000 MPa,
in other words by approximately 8%. This range can be viewed as
being realistic for impregnated wooden masts. In the short
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term, wood moisture values of 30% on the outside are possible.
There, the modulus of elasticity drops to about 8600 MPa.
However, the modulus of elasticity relevant for bending rigidity
appears as an average value, depending on the tension
distribution over the cross-section. Because the inner regions
of the mast are not influenced or influenced only slightly by
short-term increases in moisture on the outside (depending on
the duration of exposure), the variation range can be assumed to
be as indicated above.
If the moisture i$ not explicitly entered, a modulus of
elasticity is used that applies for a moisture of 15%. This
means that the maximal deviations for the calculated bending
rigidity and thereby the calculated deformations from the
bending component lie at about 3.5%. These deviations can
already be viewed as tolerable, taking implemented safety values
into account. In this connection, it must also be considered
that the overall rigidity is composed of a rotational spring
component (foundation) and a bending component (mast). Because
the rotational spring component can certainly amount to as much
as 30-40% in the case of realistic masts, the variation range of
the overall rigidity dependent on the moisture is less than the
variation range of the bending rigidity alone. Variation ranges
of approximately 2.5% are realistic.
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Nevertheless, a correction function that makes use of the
dependence of the wood moisture on the time of year is
preferably used.
The system rigidity is thereby calculated based on a modulus of
elasticity that applies for u = 15% or for the moisture u mess read
in during the measurement. This rigidity represents the status
at the measurement. For the perfect system (clamped in place),
a comparison frequency of fvoll,mes is thereby obtained. For the
evaluation of the system behavior, the modulus of elasticity is
converted to a moisture of u = 18% (matches 5 C in the case of a
storm). In this way, the calculated displacements that are used
for the evaluation are maximally approximately 5% greater (for
the case: measurement at u = 12% in the summer). The frequency
of the perfect system fvou, bewertung at u = 18% thereby becomes
less, specifically by maximally approximately 2.5%.
The invention relates not only to a method but also to an
= apparatus for implementation of the method according to one of
the preceding claims, using a calculation unit that supports the
determination of the rigidity of the mast. For this purpose,
the calculation unit has suitable programming with corresponding
program steps. The apparatus can have at least one acceleration
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sensor and means for transmission of vibration measurement
values detected by the sensor to the calculation unit.
Furthermore, the apparatus can have a moisture sensor and means
for transmission of moisture values detected by the sensor to
the calculation unit. Finally, it is practical if the apparatus
has output means for output of the stability data of the mast
that are determined.
