-
EXPERIMENTAL TEST FOR MEASURING THE NORMALAND TANGENTIAL LINE
CONTACT PRESSUREBETWEEN WIRE ROPE AND SHEAVES
Figure 1 depicts schematically how a traction elevatoroperates.
The system is basically composed of an ele-vator car (1), a
counterweight (2), a traction sheave ordrive (3), and some ropes
(4) that are disposed in par-
allel and that join the car with the counterweight
passingthrough the traction drive.
In this kind of elevator, it is crucial to ensure an
appropriateadherence between the traction sheave and the hoisting
ropesbecause if sufficient adherence is not guaranteed, the
ropecould start bodily slipping. This may cause the falling of
theelevator car or of the counterweight to the pit floor of
thehoistway, involving significant property damages as well asloss
of human life.
Traditionally, conventional elevators are dimensioned inorder to
ensure that between rope and sheave enough adher-ence region always
remains during duty service. This adher-ence region represents a
safeguard against bodily slippingbetween rope and sheave as was
introduced by Schulz.1 Evenso, the present tendencies in the
lifting sector lean toward thereduction of the traction sheave
diameter since it, in turn,reduces the required nominal torque of
the drive (note thatthe nominal torque can be written in a
simplified manner as2max T1 2T2
D ; see Fig. 1).
With a lower requirement of torque, a smaller hoisting ma-chine
is possible and thereby the drive fits in the hoistway,and there is
no need for additional room in the building inorder to house the
drive. These types of elevator solutionsare called machine roomless
elevators and they, at present,represent a competitive advantage in
the hoisting sector.
However, the reduction of the ratio between sheave and
ropediameter, D/d, beyond a determined value may entail, on
onehand, a drastic reduction of rope life and on the other, a
reduc-tion of the adherence capacity of the hoisting drive
(seeHeller2 and Nabijou3) and therefore of safeguard level in
theelevator. Under these circumstances, the sector is demandinga
more precise and accurate comprehension about the mecha-nical
interaction between rope and traction drive in order tocombine a
more reduced traction sheave diameter design withenough safeguard
level.
The authors have detected in this sense that little
experimen-tal work has addressed rope and traction drive
interaction. Thestudies made by Wiek4 and later by Haberle5 are
probably themost remarkable, and even in those articles, the study
isfocused on a particular operating situation. Therefore, in
order
to acquire a more profound comprehension, and in order toverify
the level of the agreement between testing and the cur-rent
theoretical models, a new testing procedure is discussed inthis
article. In the first part of it, a brief theoretical backgroundand
previous experimental work is introduced. Next, the test-ing
machine and procedures are presented and, finally, somepreliminary
results are discussed.
THEORY
RopeSheave Interaction Longitudinal ModelsThe longitudinal
models are bidimensional theoretical modelsthat in a simplified
manner characterize the interaction be-tween the rope and the
sheave along the plane that containsthe principal axis of the rope
when the latter is bent over thetraction sheave. The first
longitudinal model was developedby Eytelwein6 but should probably
be attributed to Euler (seeChaplin7) with whom Eytelwein worked for
some time inSwitzerland. The most popular formula derived from
thismodel is the one called Capstan formula, which is still
nowa-days the most widely used expression in order to
dimensiontraction drives. The Capstan formula:
qc 5T2T15 emu; 1
defines a limiting ratio, qc, between the rope tension,T1
andT2,at both sides, sides 1 and 2, of D diameter traction sheave.
m iscalled apparent friction coefficient of the sheave and u is
thetotal winding angle. Theoretically, if T2/T1 surpass the
ratiodefined by Eytelwein, the rope slips bodily through the
sheave.
Following the basis of the model, it also derived the normalline
pressure distribution, p(f) (note that this model
beingbidimensional, the normal and frictional contact pressure
arenot written in terms of [N/m2] but in terms of [N/m]), as wellas
the rope tension, T(f), for any angle f, which denotes aspecific
point of the winding arc.
Tf5 T1emf: 2
pf5 2T1emf
D: 3
On one hand, note that Eqs. 2 and 3 show that the two vari-ables
obey an exponential distribution. On the other, note thatEq. 1
suggests there is not any dependence of the D/d in thedrives
limiting T2/T1 ratio. However, as was mentionedbefore, the
influence of the ratio D/d in the critical imbalanceratio, qc, has
been reported (e.g., Nabijou
3).
TECHNIQUES by H. Usabiaga, M. Ezkurra, M.A. Madoz, and J.M.
Pagalday
H. Usabiaga is a PhD student in engineering and an assistant
researcher andJ.M. Pagalday is an engineer and head of the
Mechanical Department at Ikerlan.S. Coop., Arrasate-Mondragon
Gipuzkoa, Spain. M. Ezkurra is an engineer and as-sistant professor
at the Mondragon Unibertsitatea, Arrasate-Mondragon Gipuzkoa,Spain.
M.A. Madoz is a PhD and head of the Mechanical Department at Orona
S.Coop., Hernani Gipuzkoa, Spain.
34 EXPERIMENTAL TECHNIQUES September/October 2008 doi:
10.1111/j.1747-1567.2007.00294.x 2007, Society for Experimental
MechanicsDownloaded from http://www.elearnica.ir
-
Heller2 developed an equivalent expression to the
Eytelweinsformula which shows a diameter ratio dependence. The
mostsignificant difference between the Eytelwein and the
Hellermodels is that the former only considers the axial forces in
therope, whereas the latter, besides considering the axial
forces,also considers radial shear forces of the rope.
The expression for T(f) derived by Heller is represented inEq.
4.
Tf5 T2e2BfB
Csinh Cf 1 cosh Cf
; 4
where
B5Dd11
2m5
and
C5
B21
D
d
r: 6
Note that, as wasmentioned before, Hellers formula is depen-dent
on the ratio D/d since B and C depend on this ratio.Besides this,
note that Hellers approach for tension gives aswell a nearly
exponential distribution.
Figure 2 depicts the critical imbalance ratio, qc, estimated
bythe Heller and Eytelwein models against D/d for three differ-ent
apparent friction values. As illustrated in figure, the two
models lead to similar results if D/d is high. However, whenthis
ratio decreases, according to Heller, the shear internalforces
cannot be neglected and, as a result, Eytelweins modeldiverges
significantly from Hellers.
Rope and Sheave Slip StagesThe previous two expressions consider
only the situationwhere the sheave is about to slip bodily through
the sheave.Therefore, this situation implies theoretically the
maximumratio at which the traction drives could operate. However,
thetraction drive system must always operate under lower
T2/T1ratios. The literature describes three different
interactionstages as a function of the applied imbalance ratio,
that is,q 5 T2/T1. These three stages are schematically
representedin Fig. 3.
Following the same assumption than Eytelwein made in hismodel,
it can be derived that when an equal load, T15 T25 T0,is applied at
both ends of the rope, a constant contact pressureof value
p0 52T0D
7
as well as constant tension act respectively along the
contactarc and along the rope (see Fig. 3a). However, this
uniformsituation is not initially attained in practice during the
load-ing. Some sheave rotation is required in order to distribute
theuniform tension though the whole winding arc as was shownin
Usabiaga et al.8 Nabijou3 named the final uniform situationnonslip
stage (NSS) because, under this stage, no slip occursbetween the
rope and sheave.
D
Fig. 1: Main components of an elevator hoisting system
SHEAVEWIRE ROPE INTERACTION CONTACTPRESSURE MEASUREMENT
September/October 2008 EXPERIMENTAL TECHNIQUES 35
-
If we start reducing the load at one end of the rope, an
imbal-ance between both ends of the rope is prescribed. When
thishappens, part of the contact arc still remains under the
NSSsituation. However, on the remaining arc length, slipping aswell
as friction force start arising between the rope andsheave,
leading, in this manner and as it is depicted in Fig. 3,to
exponential rope tension and normal contact pressure pro-file. This
stage is called partial slip stage (PSS).
When we keep increasing the applied imbalance ratio, the arcwith
exponential profile contact pressure progressivelyenlarges and,
accordingly, the arc length that exhibits a con-stant profile arc
length reduces. The increase of imbalanceratio finally leads to a
fully sliding contact arc and, accord-ingly, to a fully exponential
normal contact line pressure andrope tension distribution. This
limiting ratio could be esti-mated, as mentioned before, by means
of Capstan formulaand the associated situation is called full slip
state (FSS)
(see Fig. 3c). Finally, a greater decrease in load at one
endproduces a bodily slipping of rope around the sheave, promot-ing
a very dangerous situation for the traction drive systems.
Besides these stages, another remarkable feature is thesheave
turning sense influence in the placement of the adher-ence contact
arc. This feature is evidenced for example inSchulz.1 After the
sheave has turned in one sense for sometime in a PSS situation, the
placement of the adherence con-tact arc seems to depend exclusively
on the sheave turningsense. According to Schulz, if the sheave has
been turning leftat constant speed, the constant pressure segment
is at theright side of the sheave (see Fig. 3) and, on the
contrary, ifit has been turning right, the constant pressure places
on theopposite side, namely on the left. Theoretically, it can be
dem-onstrated that the opposite statement can never happen usingthe
reduction ad absurdum as Johnson9 made for similarissues.
10 20 30 40 50 60 70 801
2
3
4
5
6
7
Diameters ratio (D/d)
Imba
lanc
e ra
tio (q
)Heller =0.2Eytelwein =0.2Heller =0.4Eytelwein =0.4Heller
=0.6Eytelwein =0.6
d=7.2mm
Fig. 2: Critical imbalance ratio, qc, versus diameters ratio,
D/d, according to Eytelwein6 and Heller2
(a) NSS (b) PSS (c) FSS
Fig. 3: Slip stages
SHEAVEWIRE ROPE INTERACTION CONTACTPRESSURE MEASUREMENT
36 EXPERIMENTAL TECHNIQUES September/October 2008
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Finally, the authors (see Usabiaga et al.8) have recently
devel-oped a numerical model that is mainly based on
Eytelweinsassumption but allows as well to analyze the mechanical
con-ditions along the traction drive under any slipping
stage.Moreover, the model considers the development in time ofthe
mechanical conditions when the sheave turning sensechanges or when
the load at one or both ends varies. Note thatthese two situations
are very common in elevator suspensionsystems.
In particular, the results presented in that paper
demonstratethat when the sheave is evenly loaded, a uniform
contactpressure and rope tension are not initially achieved.
Instead,two symmetrical exponential distributions are attained
forline tension and normal contact line pressure. However, themodel
also demonstrates that when the sheave starts turn-ing, this
situation gives way progressively to a completelyuniform line
tension and normal contact line pressure.According to the model,
this last uniform situation remainsuntil load changes at one or
both ends. Considering this, whenthe objective of the test is to
record the contact normal linepressure under a completely uniform
line tension and uniformnormal line contact situation, after
installing and loading therope and before recording pressure, the
sheave must turn atleast an angle equivalent to the total contact
arc angle. Notethat this fact has important consequences for the
design of thetesting procedure and machine because the testing
machinemust allow turning the sheave and running enough rope onthe
sheave in order to arrive to the uniform situation.
EXPERIMENTAL PROCEDURE
The key of the procedure introduced here lies in measuringnot
the normal and frictional contact pressures, p(f) and f(f),which
may be rather complicated, but the resultant contactforces along a
large contact arc angle. However, the pressurescan be derived from
the measured quantities by means ofsome mathematical manipulation
we will introduce later.
The testing machine developed throughout this article is
di-vided into
x the testing frame andx the sensing sheave.
Testing Frame DescriptionThe bed frame of the testing machine is
depicted in Fig. 4. Itbasically consists of what in the elevator
sector is described as2:1 hoisting suspension. Two variable mass
counterweights(1,2) are used, in order to prescribe an average rope
tensionas well as an imbalance ratio between both ends of the
rope.Note that the selected suspension scheme provides a gain oftwo
in the ratio between the stroke length of the rope and thestroke
length of the counterweights, so that a ls length ofcounterweight
stroke involves 2ls length of rope running thesheave. This type of
hoisting suspension is found particularlyuseful when the stroke of
the counterweight is limited. Notethat when the counterweights
start and end a stroke, thesheave must change the turning sense and
therefore, for sometime in each stroke, the sheave must
respectively accelerateand decelerate. If the interest of the test
lies in recording theinteraction conditions under constant sheave
turning speed,and if the counterweight stroke is short, the length
of rope
stroke that runs the sheave under constant speed could be
tooshort if a 1:1 suspension system is considered. A 2:1
suspen-sion system could represent an alternative solution in
thosecases.
The two counterweights are guided by two vertical rails (7),as
is illustrated in Fig. 4. Special care has been taken inorder to
minimize the friction between the rails and the shoeguides (8)
installed at the counterweights. Note that thisfriction generates
additional imbalance force in the hoistingsystem; therefore, it
must be minimized as far as possible. Tothis end, very low friction
glide shoes which are commonly
Fig. 4: Bed frame scheme
SHEAVEWIRE ROPE INTERACTION CONTACTPRESSURE MEASUREMENT
September/October 2008 EXPERIMENTAL TECHNIQUES 37
-
used at the elevator sector have been selected for guiding
thecounterweight along the rails. The stroke of the counter-weights
is 12.5 m, which implies that the stroke of the rope(4) along the
driving sheave (1) is 25 m. In order to turn thesheave, a permanent
magnet synchronous motor wasselected. This machine together with an
appropriate control-ler can govern the turning speed of the
traction sheave asrequired.
Instrumented SheaveThe main goal of the experiment consists in
measuring theresultant normal and tangential force acting onto an
arc por-tion of the sheave. Properly postprocessed, this value can
beconverted to its respective local value, namely p(f) and
f(f).
Based upon this principle, a classical elevator cast iron
driv-ing sheave (1) with a nominal diameter of 0.250m and
7.5-mmdiameter U-type groove was selected for the experiment
(seeFig. 5). A 158 and 40-mm deep sheave portion was machinedwith
an electrical discharge machining device taking specialprecaution
in order to preserve the cut part.
After this, a triaxial piezoelectric load cell (reference:
PCB260A01, PCB Piezotronics, Inc., Depew, NY) was selectedfor
measuring the applied load on the removed part. Thesetransducers
are ceramic made and therefore very stiff. Thedecision to select a
very stiff transducer was made after run-ning several
finite-element methodbased calculations of theassembly and
afterward concluding that any displacement ofthe transducer or the
detached part could generate undesiredinfluence on the measured
magnitudes. The selection ofa ceramic transducer should avoid
this.
Figure 6 depicts the final assembly of the sensing sheave.
Thetransducer (2) was placed in the cavity left for this purpose
inthe sheave. Above it, the grooved side of the removed part,which
from here on we will call detachable part (3), wasmounted again.
Note that this part had to be carefullymachined in order to take
out from it the same volume isnow occupied by the transducer.
The transducer together with the detachable part were fixedto
the sheave with a CopperBeryllium screw rod (4) which isalso very
stiff and therefore should prevent any disturbance ofthe normal and
tangential contact pressure distribution. Thefixing nut (5)
prestresses the screw rod, avoiding in this man-ner any nonlinear
behavior between forces and relative dis-placements of the sensing
sheave parts.
It should be remarked that a very strong effort was madeto place
the demountable part of the sheave on the samelevel as the rest of
the sheave surface. High-definition geo-metric measuring machines
were used and corrective meas-ures were taken until the groove was
placed according tojD12D3j
-
the experimental conditions along the contact arc. Therefore,in
the following, a procedure is introduced in order to com-pute
pressure values from the transducer-measured resul-tant forces.
In this sense, note that the operation that performs the
trans-ducer when it collects the resultant forces along the
wholecontact arc can be reinterpreted as a mathematical opera-tion
called convolution between the local pressure function,namely, p(f)
and f(f), and a particular transfer function.
Mathematically the convolution is written as follows:
hgt5ht2tgtdt; 10
where hg represents, for this particular case, the
resultantforce measured by the transducer, h; the local pressure;
andg, the test function.
The test function can be computed bearing in mindx the measuring
rate of the signal acquisition device,x the arc length that
occupies the detachable part, andx the prescribed turning speed of
the sheave.
The inverse of this mathematical operation is called
deconvo-lution and can be used together with the previously
intro-duced transfer function in order to invert the process,
sothat the pressures can be computed from the resultant
forcesrecorded by the transducer.
Tested Ropes and Testing ConditionsRegarding the tested ropes,
two elevator rope constructionswere considered:
x a 7.2 2 8 3 19S-FC (the designation of wire rope
followsISO17893:2003) rope
x a polyurethane (PU)-jacketed 6.5-mm diameter 4.8 2 63 19S wire
strand core (WSC) rope.
The comparison between jacketed and conventional ropeshould
contribute to determining if the literature hypothesesare also
acceptable in order to model jacketed ropes.
Regarding the imbalance of the prescribed load, during thetest,
the imbalance ratio was varied. For the conventionalrope, one
counterweight was load with 2000 N, whereas thesecond counterweight
was load with 2000 N, 1800 N, 1660 N,and 1560 N, applying in this
manner respectively an imbal-ance ratio of q 5 1, q 5 1.1, q 5 1.2,
and q 5 1.3.
Due to the higher adherence friction coefficients between
thejacket and the sheave, higher imbalance ratios were used
withthis second rope construction. In that case, one
counterweightwas loaded with 2000 N, whereas the second was loaded
with2000 N, 1660 N, 1430 N, and 1250 N, applying this time
animbalance ratio of q 5 1, q 5 1.2, q 5 1.4, and q 5 1.6.
Finally, regarding the sheave-turning speed, all the testswere
carried out under constant 0.8rad/s sheave turningspeed. The
relatively low speed was selected keeping in mindthat quasistatic
hypothesis are considered by Eytelwein. Theselected speed together
with keeping sheave speed constantshould prevent any significant
influence of inertial forces onthe traction drive interactions and
should help make a muchclearer comparison between theory and
tests.
RESULTS
Test Carried Out with Conventional RopeFigure 8 shows some
normal contact pressure distributionresults for q 5 1, q 5 1.1, q 5
1.2, and q 5 1.3 imbalanceratios. Not including the first peaks
that arise during therunning off and winding region (this phenomena
will be dis-cussed later in Normal Pressure Peaks Near Winding
andRunning Off Points section), the test we carried out showsthat
for q 5 1 (see Fig. 8), a uniform constant pressure dis-tribution
is attained along the sheave contact arc. However,
Fig. 6: Final sensing sheave assembly
SHEAVEWIRE ROPE INTERACTION CONTACTPRESSURE MEASUREMENT
September/October 2008 EXPERIMENTAL TECHNIQUES 39
-
when the applied imbalance ratio increases progressively,
anearly exponential-like distribution starts arising on the
rightside of the sheave according to what Schulz pointed out in
hisarticle about sheave-turning sense influence on the
adherenceregion placement. Finally, q 5 1.1 and q 5 1.2 show that
theconstant pressure gives way progressively to an
exponentialpressure distribution until the highest imbalance ratio,
q 51.3, shows a nearly FSS situation.
Tests Carried Out with PU-Jacketed RopeSome disagreements
between the theoretical model and theexperimental test arose with
the jacketed rope test. In thiscase, even in a balanced situation,
the experimental measuresshow not a constant distribution but an
increase of pressuretoward the middle arc of the sheave (see Fig.
9a).
For the conventional rope case, the friction force between
ropeand sheave should be the responsible of any rope tensionchange.
For the jacketed rope case, the friction distributionsshows that
friction force is distributed, in the case of q 5 1,evenly
symmetrical and oriented from the outer limits of the
winding arc toward the center. Therefore, the recorded fric-tion
force supports the idea that tension is not constant andthat it
increases toward the center of the contact arc in thecarried out
tests.
In the case of applying an imbalance between wire rope
andsheave, a similar behavior is attained. However, this time
thedistribution is not symmetric. Note that this lack of symmetryis
required, since the resultant friction between sheave andrope must
balance the prescribed imbalance.
Normal Pressure Peaks Near Winding andRunning Off PointsIn all
the tests that we carried out, near the winding on andrunning off
points, the pressure peaks always rise divergingfrom what was
expected from the theoretical point of view.Wiek4 and later
Haberle5 describe the same peaks in the teststhat they carried
out.
As it is depicted in Fig. 10a, due to its bending stiffness,
theropes need certain transition length before taking the same
Fig. 7: Conversion to local quantities
60 80 100 120 140 160 180 200 220 240 260
0
5
5
10
15
20
25
Nor
mal
line
pre
ssur
e (p)
[N/m
m]
Winding angle ( ) [degrees]
q= 1.0q= 1.1q=1.2q= 1.3
D=200mmU groove (dg=7.5mm)
p0 p0
Fig. 8: Normal line contact pressure, p(f), versus sheave
winding angle, f, for q 5 1, q 5 1.1, q 5 1.2, and q 5 1.3
withconventional rope
SHEAVEWIRE ROPE INTERACTION CONTACTPRESSURE MEASUREMENT
40 EXPERIMENTAL TECHNIQUES September/October 2008
-
radius of curvature as the sheave. This transition curvaturewas
theoretically estimated by Feyrer.10 As it is depicted inFig. 10a,
the transition length makes the rope meet thesheave curvature
beyond the point it would, if such transitionlength would not exist
when winding on and previously whenrunning off, which creates, in
turn, additional moments andincreasing peaks at the external
regions of the sheave contactarc (see Fig. 10b).
Haberle5 has made thorough considerations with respect tothis
phenomena. By means of a regression analysis, the
experimental test that he carried out provides expressionsfor
estimating the peak level as well as the delay and leadangle, nA
and nB, of, respectively, the winding on and run-ning off contact
points. Feyrer11 gives some theoreticalexpressions as well in order
to estimate n and the reactionforce Q.
The test that we carried out shows also a slight windingangle
difference with respect to the theoretical 1808, so thereason
argued by the former authors is consistent in ourtests.
50 0 50 100 150 200 2505
0
5
10
15
20
25
Nor
mal
line
pre
ssur
e (p)
[N/m
m]
Nor
mal
line
pre
ssur
e (p)
[N/m
m]
5
0
5
10
15
20
25
Tang
entia
l line
pre
ssur
e (f)
[N/m
m]
Tang
entia
l line
pre
ssur
e (f)
[N/m
m]
Tangential line pressureNormal line pressure
p0p0
4.8619 SWSC (jacketed dj=6.5mm) D=200mmU groove(dg=7.5mm)
50 0 50 100 150 200 250
5
0
5
10
15
20
25
30
5
0
5
10
15
20
25
30
Tangential line pressureNormal line pressure
4.8619 SWSC (jacketed dj=6.5mm) D=200mmU groove(dg=7.5mm)
(a)
(b)Winding angle ( ) [degrees]
Winding angle ( ) [degrees]
Fig. 9: Normal and tangential normal line contact pressure, p(f)
and f(f), versus winding angle, f, for (a) q 5 1 and (b) q 5
1.6with jacketed rope
SHEAVEWIRE ROPE INTERACTION CONTACTPRESSURE MEASUREMENT
September/October 2008 EXPERIMENTAL TECHNIQUES 41
-
DISCUSSION
According to the test performed during this study, the
hypoth-esis assumed by the theory characterize correctly the
phe-nomena, at least under constant sheave-turning speed andfor
conventional (not jacketed) ropes.
Inparticular, for theq51case, theresultsattained in those
testsare very similar from the ones obtained by Haberle.5 In
bothcases, the agreement between the experimental value and
thetheoretical value estimated from Chaplin7 is very
remarkable.
However, the tests performed for the jacketed rope case
showremarkable differences between test and theory. This
mayindicate that, for the jacketed rope, Eytelweins or
Hellershypothesis is not appropriate for measuring the
phenomenon.
In this sense, note that, although frictional
distributionmatches the normal pressure distribution, suggesting
thatrope is not constant, as it is depicted in Figs. 9a and b,
thefrictional pressure distribution is not proportional to the
nor-mal pressure distribution as would be expected if Amontonslaw
was fulfilled and sliding between the polymer jacket andthe sheave
would occur.
These disagreements may be attributed to the local compres-sion
of the polyurethane jacket. Due to the winding and run-ning off
peaks, the jacket may be unevenly compressedbetween the outer
regions and the mid-length region of thewinding arc. Note that this
difference of compression existsalso for the conventional rope
case; however, the compressiondeformation level is not as
significant for the jacketed ropecase because the jacket stiffness
is remarkably lower thanthe stiffness of rope cross-section.
The higher compression of the polyurethane jacket along theouter
region of the winding arc might locally reduce the effec-tive
sheave diameter and this in turn might stretch the ropein the mid
length of the winding arc.
The relation between the recorded frictional and the
normalpressure distribution could also be consistent with the
exist-
ing theories. The stretch of the rope in the mid-length
arcshould not obligatorily mean that the polymer surface in
con-tact with sheave should be as well stretched in the same
way.Therefore, it does not necessary imply slipping between
jacketand sheave.
Thanks to the polyurethane flexibility, the polymer jacketcould
be subjected to shear deformation in such a way thatthe inner
surface of the sheave is deformed according tothe rope deformation
(which in turn might be producedby the effective sheave diameter
variation), and on the con-trary, the outer part remains in
adherence with regardsto the sheave. Note that if the sheave is in
adherence withthe jacket, the recorded values are still compatible
withAmontons law and that in this case, the tangential forcewe are
measuring is strictly the applied shear force inthe jacket.
However, note that the thickness of the jacket is very thin,0.85
mm. Therefore, there might be reasonable doubtsfor this particular
case whether the effective diameterchange promoted by the jacket
uneven compression alongthe winding arc could produce such
significant effects inthe interaction.
CONCLUSIONS
The experimental procedure described in this article is
dem-onstrated to be particularly robust and useful in order
todetermine experimentally the interaction conditionsbetween the
rope and the sheave. This is particularly truefor the ease of
analysis for certain rope and sheave configu-rations to determine
the effect of the
x prescribed mean load,x prescribed imbalance load, andx sheave
turning speed
in the mechanical conditions of the hoisting drive.
The carried out preliminary tests show that conventional
ropecould exhibit a very close behavior from what was
theoreti-cally expected. However, further studies should be carried
outin order to certify the explanation that is given for
under-standing the disagreements between the theoretical
hypoth-esis and the result we attained.
References1. Schulz, S., Braking Equipment for Friction Hoists,
The
South African Mechanical Engineer 28:426433 (1978).
2. Heller, S.R., The Contact Pressure Between Rope andSheave,
Naval Engineering Journal 4957 (1970).
3. Nabijou, S., Frictional Behaviour and Fatigue Perfor-mance of
Wire Ropes Bent Over Small Diameter Sheaves, PhDThesis, Imperial
College of Science, Technology and Medicine,London, UK (1990).
4. Wiek, L., The Distribution of the Contact Forces on SteelWire
Ropes, OIPEEC Bulletin 44:1025 (1982).
5. Haberle, B., Pressung zwischen Seil und Seilrille, PhDThesis,
Universitat Stuttgart, Stuttgart, Germany (1995).
6. Eytelwein, J.A., Ausgaben grobtentheils aus der angen-wandten
mathematik, Freidrich Manrer, Berlin, Germany (1793).
(a) (b)Fig. 10: Source of the apparition of the peaks at the
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SHEAVEWIRE ROPE INTERACTION CONTACTPRESSURE MEASUREMENT
42 EXPERIMENTAL TECHNIQUES September/October 2008
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