maintenance scheduling and reliability estimation of

Copyright © 2014 IJISM, All right reserved4

International Journal of Innovation in Science and MathematicsVolume 2, Issue 1, ISSN (Online): 2347–9051

Maintenance Scheduling and Reliability Estimation ofStructural Lifting Cables Using the Theory of

Accelerated Tests: Approach Based on Reliability BlockDiagrams

CHOUAIRI AsmâaLaboratory of Control and Mechanical

Characterization of Materials andStructures, ENSEM, BP 8118 Oasis,

Hassan II University, Casablanca, Morocco

EL GHORBA MohamedLaboratory of Control and Mechanical



BENALI AbdelkaderLaboratory of Control and Mechanical



HACHIM AbdelilahFaculty of Science Ain Chock, BP 5366

Maarif, Hassan II University, Casablanca,Morocco

EL HAD KhalidHigher Institute of Maritime Studies

(ISEM), Department of Machinery, 7 kmRoad El Jadida, Casablanca, Morocco

BOUDLAL El mostaphaHigher Institute of Maritime Studies

(ISEM), Department of Machinery, 7 kmRoad El Jadida, Casablanca, Morocco

Abstract – In order to ensure the reliability of structuresand lifting equipment, mechanics need effective monitoringtools to determine the condition and life of these systems. Inthis context, the choice of reliability method using the theoryof accelerated tests was imposed by the ability of thistechnique to detect remotely the damage and predict theresponse time to maintain cables service and avoid evolvingfaults. Our goal is to study the reliability, dependability andavailability of lifting wire ropes using the theory ofaccelerated tests by analytical and numerical modeling, theresults will conduct to assess the relation reliability-damagein the case of strands arranged in series-parallel and in thecase of parallel-series configuration. The approach isconsidered as multi-scale with a total decoupling across wireand cable. The results will allow a comparison between thedifferent models of the literature to tie the better model ofmaintenance planning

Keywords – Structures, Duration of Life, Damage,Dependability, Availability, Multi-Scale.

I. INTRODUCTION

The use of cables as tight elements is widespread inrecent decades. They consist of high-strength wiresgathered into packets so as to obtain the desired tensilestrength (Fig.1).

Fig.1.Terminology of hoisting cables

The base material of metal wires is typically a low alloysteel containing a carbon content close to eutectoid, with

as main alloying elements manganese and silicon (Fig.2).These steels are formed by a drawing process [1]. Otherproduction processes also exist as the bainitic andmartensitic hardened, but they are less used for wires [2].

Fig.2. Component parts of a metal wire

To ensure the characterization of cables under optimalconditions, an analysis of its security must be combinedwith well-defined inspection procedures [3] [4] [5].

Unfortunately, many cables have never been subject toinspection or otherwise, only very partially, due to thelimitations of inspection techniques.

The safety analysis is to connect the estimation ofresidual strength of cable using inspection data, this link isdifficult to establish, even if we admit that the concept ofsafety factor of cable is a little insufficient to characterizeits present state [6]. The majority of works related todetermining the bearing of a suspension cable capacity arestatistical models that do not fit the complexity ofmechanical description (non-linear behavior, thedistribution of load, friction between the strands ....).

The behavior of cable is multi-level; therefore, we candistinguish two scales study: scale wires and wide strands.Systemic diagram of a suspended cable can be either aparallel series system: parallel (Number of wires) andseries (number of strands) or a series parallel system:series (Number of wires) and parallel (Number of strand)[7] [8].



The choice of these scales is given that a relevantportion of a wire behavior governs the behavior of entirecable. The physico - chemical processes such as the rate ofdegradation, due to the environment (corrosion) aredifferent for each layer, the outer layers is more exposed[9].

Indeed, when the wires are twisted and wound together,a broken wire has the ability to recover its strength in aspecific length; this length defines the size of effectivesegment, its value is 1 to 2.5 times cast length.

In this section, we will develop a new practical methodfor analyzing the reliability of metal hoisting cables.Among the existing predicting maintenance of complexsystems based on graph theory is particularly interestingbecause of its precise nature and with the least costmethods. For this we will bring several analyticalformulations to estimate the stress state in the internal andexternal cable and wires deduct of reliability that areessential for better maintenance.

III. DEGRADATION MECHANISMS OF CABLES

Cables suffer from continued aggression of environment(urban, industrial, marine…..). The effects of theaggression manifested through various events, includingthe direct effects are strong changes in geometrical andmechanical characteristics of the components, whichindicate a significant reduction in the strength capacity ofthe cable over time, which can sometimes lead to partialrupture.

In general, the defects of the hoisting ropes areclassified into four categories:1- Reduction of the section by wear, corrosion or abrasion;2 - Rupture of wires steel;3 - Strains such as bird cages, shell, crush....;4 - Fatigue.

This part presents a recall of main degradationmechanisms that affect the cables, their typical scenariosof accidents and losses they cause mechanical strength anddiscard criteria.A. Generalized corrosion

Non-alloy steel cables used for ordinary susceptibility tocorrosion by dissolution (Fig.3), that is to say a loss ofmore or less homogeneous section may allocate all or aportion of the wires and thereby cause loss of tensilestrength of cable [10].

External and internal corrosion of cables is caused byinfiltration of water and lack of lubrication [11]. Whenwater penetrates into inner layers of cables, it producesoxidation of steel. The corrosion is dependent on thepresence of aggressive media such as chlorides, sulphates,acids, etc. Breaks elementary wires are occur in severalways, and depend on the generator mechanism [12] [13].

The first mode of degradation is uniform corrosion ordissolution. This can cause a loss of more or lesshomogeneous section on wires and a reduction in thebreaking strength of cable [14]. This solution can also bemore localized and takes the form of craters that have thesame effect as the previous form of corrosion but they alsoreduce the strain at break of strands and promote fatigue

cracking. These two modes of corrosion can cause strandbreaks by exceeding the allowable stress.

Fig.3. Homogeneous dissolution wires with loss of section

B. Localized corrosionDissolving wires may also take the form of craters, in

addition to bearing capacity, reduce the strain at break ofstrands and also promote fatigue cracking (Fig.4).

Fig.4. Crater dissolution (locally reduced by 50% ofsection)

Elachachi [15] developed a model to predict the load-carrying capacity of a corroded cable, at various levels ofdamage to its components in order to estimate the residuallife and the risk assessment of broken wires for a givenlevel of stress.

The effect of corrosion on the behavior of a section ofstrand is presented with the average effort (1000simulations) as a function of displacement which is givenfor 8 deadlines (the time increment is 20 years). It is foundthat the corrosion influences the initial stiffness of sectionand on the maximum resistive force which decreases withtime (here 27% of 100 years).C. Corrosion cracking under stress

Steels wires cable is also susceptible to corrosioncracking under stress, sensitivity increases as theconstraint of service is high. The prestressing cables, inparticular, are used above the yield stress of occurrence ofcracking phenomena (Fig.5), while the average appliedstrain and the shrouds parabolas is below the threshold(Fig.6).

Fig.5. Primers breaking cracks on corrosion cracking



Fig.6. Breakage corrosion cracking under stress

Steels are also sensitive to stress corrosion cracking.This sensitivity is even more important that the constraintservice is high. The breaking load is reduced as well as theelongation at break. The latter can occur without anyplastic deformation (semi-fragile breaks) [16].D. Breakage of wire ropes

Wire break evolves disproportionately. This fact mustbe taken into consideration when determining the controlintervals (Fig.7).

Fig.7. Breakage of strand cables

The sudden termination of cables is often the result ofinteractions between two contacting wires, subjected torelative displacements of low or high amplitude. Severalphases can be distinguished in the behavior of cablebreakage. First, a more or less significant degradation andrapid wires with the formation of wear debris (third body)part of which may be ejected from the contact. During thesecond phase, there is the appearance of microcracksinitiated at the contacts which involved in the formation oflarger debris thereby increasing degradation strands. Thelast phase is the crack of contact when toughness cablereaches a critical value.

Siegert [17] studied the fatigue mechanisms that arecausing ruptures wires in the steel cables, used for bracingof structures. For this, he relied on many experimentalresults. He also proposed a criterion to predict theinitiation and endurance of fatigue cracks in theinterfilaires contacts cables. This criterion is based on theconcept of critical facet amplitude maximum shear.Contact materials which reduce the wear of cable and theirstrands cracking are wear materials such as zinc oraluminum alloy and lubricant materials such as highdensity polyethylene. Studies by Urvoy [18] were used tocompare the change in wet or galvanized wires, strands ofcontact and mechanical stresses at interfilaires contactssubjected to friction between wires. These tests

demonstrate that the 100 MPa fatigue endurance limit ( Δσpeak/peak ) obtained by Siegert [17] on uncoated drywires is raised to 170 MPa for dry galvanized strands for200 MPa on uncoated lubricated .E. Fretting fatigue and tiredness

The constituent wires cable have, moreover, anendurance limit fatigue (Fig.8) which is a function ofaverage applied stress but that does not depend (formodern wires) on the diameter of wire or on presence ornot of a galvanized coating.

Fig.8. Fatigue multilayer strand breaks

The tiredness is a fretting mechanism of friction in smalldeflections that are also sources of disorders, and causewear or fatigue cracking. They may occur:- Either from interfiles contacts (interlayer) (Fig.9);- Or the contacts between neighboring strands (Fig.10);- Or contacts between strand and fixtures.

Fig.9. Case of fretting fatigue, friction strands / necklaces

Fig.10. Case of fretting fatigue, friction strands / strands

The main cause of breaking wires fatigue is associatedwith interfilaire friction between adjacent layers. Thesemovements are caused by fatigue stresses, and called“fretting fatigue” or small deflections induced by fatigue[6]. This is exacerbated at the output by the bending offatigue anchorages induced by external stress [17].



This is the result of interactions between two surfaces incontact which are subject to relative movements of smallamplitude. Several phases can be distinguished in fatiguebehavior of a cable. Firstly, a greater or lesser degradationand rapid formation of surfaces with wear debris (thirdbody) this part may be ejected from the contact. Duringthe second phase, we note the appearance of microcracksinitiated at the contacts involved in the formation of largerdebris thereby increasing the degradation of surfaces. Thelast phase is the propagation of some cracks under effectof causing volume forces out of one elements of a contactwhen the crack reaches a critical dimension related totoughness of concerned material [19].

The work of Zhan [20] treated wires of fatigue breaks inthe case of steel cables, subject to the phenomenon ofwear. He performed a series of experiments on steel wireusing a test bench swing. The results of research show thatthe wear depth wires of steel increases with contact loadsand number of cycles. For low contact forces, the peelmodes are dominant. When the contact loads increase, thethird body abrasion appears on the worn surfaces.

In other experiments in axial loading on seven strands,Giglio and Manes [21] were interested in the evolution ofstress state in the strand with applied stress. They alsoinvestigated the influence of interfilaire contact, the lengthand diameter of the wires and anchors of cables. Theyfound that the reduced friction interfilaire of tensilestrength is caused by the coil constituting of wire cable.

For the life of multilayer axially prestressed cables andsubjected to alternating bending free, Raoof and Hobbs [6]propose the use of a single criterion. This test uses thecalculated maximum tensile stress of the front surface ofthe point-like contact, the relative sliding between twolayers of strands and the spacing between two pointcontacts on the outer layer of the cable. Such a criterion isderived from Ruiz criterion that characterizes qualitativelythe risk of crack initiation. The results given by thismethod are in accordance with the measurements obtainedin five tests with four different compositions of multilayercables and a multitoron one.F. Friction interfilaire

The study of interfilaire contacts is essential formodeling the behavior of cables. In general, two types ofcontact exist in multilayer cables: the linear contactbetween the wires of a single layer and the point contactbetween two strands belonging to adjacent layers (Fig.11).The side contact is considered as a line contact when theinitial contact area is a curve. This contact also existsbetween core wire and strand of first wire [22].

The other type of interfilaire contact is present betweenwires of successive layers which are extended in oppositedirections. Therefore, wires in both layers cross at anangle, where a line contacts rather than point. The contactpressures are clearly higher in the case of a point contactas in the case of linear contact [23].

In general the behavior of the cable in axial load ischaracterized by a coupling between traction, torsion andbending. In the literature there are various models thatdescribe the behavior of the cable tension. Costello [24]and Hruska [25] have modeled the behavior of strands

subjected to different tensile forces. They confirmed thatthe Poisson effect, friction and geometric nonlinearitieshave a negligible influence on the overall behavior ofcables in tension. Moreover, the radial contact between thecore and outer wire are the only contacts that exist duringan axial loading.

Yan Shen [26] studied the influence of applied loadingand lubrication strands on characteristics of cable (18 * 6)analyzed.

The variations of the friction coefficient according to themovement of steel in relatively stable wires stage atdifferent loads of contact are shown in the fig.12.

It can be seen that the coefficient of friction increasedby the applied loads and gradually decreased withincreasing amplitudes of displacement.

Fig.11.Line contact

Fig.12. Point contact

IV. MECHANICAL PROPERTIES AND CHEMICAL

COMPOSITION OF STUDIED CABLES

In our study, we will look at tests that will be performedon cables type 19 * 7 (19 strands and 7 wires ) rotatingstructures (1*7 + 6*7 + 12*7) 6 mm diameter composed oflight steel greased, metal core , cross right preformed usedincluding tower cranes and gantries (Fig.13).

They are made of two layers of strands wired inopposite directions, thereby preventing rotation of thesuspended load when the lift height is important and theload is not guided. Their use requires a certain amount ofcaution at rest and during operation. This construction,robust nature, is widely used for routine applications andespecially for lifting heights reduced [27].

The sample length of the cable is equal to 10 times thepitch of 20 mm reancrage more necessary to mooring.Therefore, the length of 700 mm was taken as the lengthof tests for these cables. The accuracy of measurement in a



length of ± one millimeter for all samples studied [28].The base material is steel from which wires are formed.

They are twisted to form the assembled strand. Then thestrands are wound in spirals around describing core (type 1+6). The cable is finally obtained from the strands with astructure of 19 x 7 (1 +6).

Fig.13. Cross section of a rotating rope "19 * 7"

V. MODELING AND ESTIMATION OF

DEPENDABILITY

Reliability is interested in estimating the life of a system(component, machine, production line, etc.) [29] [30]. Thesoftware tool is essential to treat this problem [31]. That iswhy we have modeled a digital library that allowsdetermining the reliability and the components ofdependability (maintainability, availability, failure rates....), in the form of block diagrams describing thefunctional role of components.

For the quantification of damage in the cable are used todetermine the damage variable for each fraction of life (forour study, the fraction of life shows the relationshipbetween the diameter of the wires and the critical value ofthe cable diameter), several models are presented in theliterature, we have chosen the law of damage given by theunified theory. The advantage of this act in relation toother approaches is to link the evolution of damage inmaterial directly to variation of residual ultimate limit: thedamage is thus directly connected to a characteristic of thecable.

In this section, we present the methodology forreliability analysis cables, implemented by the digitallibrary we have developed. We illustrate and compare theresults and deduce the proper maintenance in case ofhoisting ropes.G. Relation reliability – fraction of life Compound system: Series-parallel

A composite system is a redundant system in which thedifferent components work together to complete the task,one of the components being able to provide only resultsin failure of others.

The series-parallel system has both of reliabilitystandpoint, sub-sets in series and in parallel subsets.Considering that the cable (19 * 7) analyzed system is aseries - parallel, his wires (S = 133 wires) are connected inseries, and strands (P = 19 strands) are connected inparallel.

Fig.13 explains the results of reliability based onfraction of life, in the case of system series - parallel.

The function of reliability shown in Fig.13 providesgradual decrease in proportion to the fraction of life. Weclearly see the influence of the series trend wires on thereliability of the cable.

We also note that the cable maintains some internaltensile strength (B = 1), this resistance becomes when thecable is completely broken.

Fig.13. Curve representing the reliability Rs-p dependingon the fraction of life B

Compound system: Parallel –seriesConsidering that the cable (19 * 7) analysis is a parallel

system - series, his wires (S = 133 wires) are connected inparallel, and strands (P = 19 strands) are connected inseries.

Fig.14 explains the results of the reliability based on thefraction of life, in case of parallel – series system.

It shows the reliability Rp-s depending on the fraction oflife B, we find that the curve is influenced by the tendencyof parallel components. The reverse is observed: thesystem is less reliable than if we increase the number ofblocks in series, and we keep the same number of parallelcomponents.

Fig.14. Curve representing the reliability Rp-s depending onfraction of life B

H. Relation reliability – failure Compound system: Series-parallel

The superposition of reliability and failure curvesindicates intersection which coincides with a reversalposition.



Indeed, the reliability was initially greater than thefailure and becomes smaller beyond this point, which infact corresponds to the acceleration of damage, andtherefore a critical part of life, where the intervention ofpreventive maintenance.

Fig.15. Overlay curves reliability and failure for a cable(19 * 7) mounted in series-parallel system

Studied for the cable, which is considered as a series-parallel system, coordinated the critical point are Bc (0.85,0.5), indicating that maintenance should be 85% of thetotal life imposed by the manufacturer. Compound system: Parallel -series

This part will link reliability to damage through thefraction of life, these results associating with each point ofdamage corresponding reliability.

Parallel-series systems are of particular interest inindustry, this is because the system can continue to operateand fulfill its task even if some of its components arecompletely ruined. We will follow the same approach asfor the series-parallel system.

Fig.16. Overlay curves reliability and failure for a cable(19*7) mounted in parallel-series system

In the case of a cable connected in parallel - series,coordinated the fraction of life are critical in Bc (0.72, 0.5).This value is smaller than the cable connected in series -parallel, which requires preventative maintenance in thecase of cable connected in parallel - series before the eventof a cable connected in series - parallel (Fig.16).

Thus, the parallel-series system is most compatible forcable study and for any other complex system.

V. CONCLUSION

Metal cables are primordial elements and should bechecked regularly by qualified personnel. The frequencyof tests shall be chosen so as to detect the damage in time.

The failure criteria for the cable are more complex thanthose applied to continuous structures, where themeasurement of crack length or the simple observation ofthe loss of integrity may suffice. Generally, these criteriaare based on a mixture of past experience, personalpreference and prejudice for each particular type ofapplication. The occurrence of unacceptable number ofwire breaks is by the most common adopted for theassessment of damage to the cable action, which justifiesour choice.

In our study, we proposed a practical method forreliability analysis applied to the hoisting ropes. Amongexisting for reliability analysis system, graph theoryreliability is particularly interesting because of its intuitivenature, which is an extension curve reliabilityconventional methods.

Analysis to assess the impact of factors affecting thereliability of hoisting ropes which constituted the essenceof this work. It developed a model for predicting thereliability and dependability of a cable at various stages ofhis period in service. In this study , our contribution isessentially reliability engineer through a system based on amathematical approach that determines the reliability ofthe cable , taking into account all its parameters and itsphysical and chemical characteristics model .

REFERENCES

[1] G. Simonnet, Steel Wire Drawing, Technical Engineer. Metallicmaterials, 1996 Vol.MC2, N.M645, p. M645.1-M645.12.

[2] Canadian Centre for Occupational Health and Safety "wire ropelifting" in February 2010.

[3] D.Siegert, P.Brevet, Fatigue of stay cables inside end fitting highfrequencies of wind induced vibrations, OIPEEC Bulletin,2005,No.89, pp.43-51.

[4] D.K. Zhang, S.R. Ge, Y.H. Qiang, Research on fatigue behaviordue to the fretting wear of steel wire in hoisting rope, Wear,2003, Vol.255, pp.1233-1237.

[5] JR Urvoy, D.Siegert, L.Dieng, P.Brevet, Influence of metalliccoatings and lubricants on the fatigue interfilances contactscables, August 29-September 2 2005, the 17th French Congressof Mechanics, Troyes, France.

[6] R. E.Hobbs et M. Raoof , «Mechanism of fretting Fatigue insteel cables», Vol. 16, pp. 273-280, 1994.

[7] A. CHOUAIRI, M. EL GHORBA, A. BENALI « Reliability andmaintenance analysis of complex industrial systems», LAPLambert Academic Publishing AG & Co. KG, Mechanicalengineering and manufacturing technology, paperback: 52 pages,ISBN-13: 978-3-659-24578-7, ISBN-10: 365924578X, EAN:9783659245787, Germany (2013-06-02).

[8] A.CHOUAIRI Mr. EL Ghorba, A.BENALI, A. Maziri"Reliability and maintainability of complex preventive systemsdedicated to lifting: applications to metallic cables offshore"International Workshop on Information and Communication(WOTIC'11), National School of Electricity and Mechanics(ENSEM), 13-15 October 2011.

[9] H.Zejli, Detection and localization of acoustic emission inbroken anchors of work of art cables strands.



[10] P. BREVET "Pathology of stays and cables: Fatigue-corrosion"cables Day 2005.

[11] HRUSKA F. H., « Calculation of stresses in wire ropes», Wireand Wire Products, Vol. 26, No. 9, pp. 766-767, 799-801, 1951.

[12] HRUSKA F. H., Radial forces in wire ropes, Wire and WireProducts, Vol. 27, No. 5, pp. 459-463, 1952.

[13] HRUSKA F. H., Tangential forces in wire ropes, Wire and WireProducts, Vol. 28, No. 5, pp. 455-460, 1953.

[14] LUTCHANSKY M., « Axial stresses in armor wires of bentsubmarine cables», Journal of Engineering for Industry, Vol. 91,pp. 687-693, 1969.

[15] S. M. Elachachi, D. Breysse, S. Yotte, C. Cremona, Probabilisticmodeling of the load-carrying capacity and the residual life ofcorroded structures, XXII nth Dating University of CivilEngineering cables - CITY & ENGINEERING, France, 2004.

[16] LANTEIGNE J., « Theoretical estimation of the response ofhelically armored cables to tension, torsion and bending»,Journal of Applied Mechanics, Vol. 52, pp. 423-432, 1985.

[17] D.Siegert, Mechanisms of fretting fatigue in the guy wires ofCivil Engineering, June 1997, Thesis of Sciences GraduateSchool of Engineering Nantes.

[18] JR Urvoy, Fatigue interfilaire Contacts: Effect of coatings andlubricants, September 21, 2005, Technical Workshops Cables2005 LCPC Nantes, France. [24] R. E.Hobbs and M. Raoof,«Mechanism of fretting Fatigue in steel cables», Vol. 16, pp.273-280, 1994.

[19] D. Siergert, Mechanisms guy wires, 2000 Franco-Japaneseseminar Kampont 2000 Edition of the Ministry of Equipment.

[20] D.K. Zhang, S.R. Ge, Y.H. Qiang, Research on fatigue behaviordue to the fretting wear of steel wire in hoisting rope, Wear,2003, Vol.255, pp.1233-1237.

[21] M. Giglio, A. Manes, Life prediction of a wire rope subjected toaxial and bending loads, Journal of Engineering FailureAnalysis, pp. 549–568, Elsevier, 2005.

[22] CASTILLO E. and RUIZ-COBO, R. » Functional equation andModelling in Science and Engineering», Marcel Dekker, 1992.

[23] R. E. Hobbs, M. Raoof, Behviour of cables under dynamic orrepeated loading, Journal of constructional research, 1996, Vol.68, pp. 31-50.

[24] G.A. Costello, Theory of wire rope, 1990, Theory of wire rope,Springer.

[25] F. Hruska, calculation of stresses in wire ropes, Wire and wireproducts, 1957, Vol.26, pp.761-768.

[26] Yan Shen , Dekun Zhang, Junjie Duan, Dagang Wang, Frettingwear behaviors of steel wires under friction-increasing greaseconditions, Journal of International Tribology, pp. 16-21, 2010.

[27] J.M. Walton, Developments in steel cables, Journal ofconstructional steel research, 1996, Vol.39, No.1, pp.3-29.

[28] M. Arend, The load transfer mechanisms anchoring high-strength tension elements, OIPEEC round table conference 1993,Delft university of technology, Delft, Holland, 8-11 September1993.

[29] F. GUERIN, B. DUMON AND R. HAMBLI. Determining theshape parameter of a Weibull distribution from mechanicaldamage models, In IEEE International Conference on Reliabilityand Maintenability, Philadelphia, Pennsylvania, USA.2001.

[30] M. Raoof, I. Kraincanic, « Characteristics of fiber – core wirerope», Journal of Strain Analysis Vol. 30, No. 3, pp.217-226,1995.

[31] F. Hruska, calculation of stresses in wire ropes, Wire and wireproducts, 1951, Vol.26, pp.766-767.

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