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A sliding wear model and its application to heat exchanger tube wear Chen, JingPing 1994

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A SLIDING WEAR MODEL AND ITS APPLICATION TO HEATEXCHANGER TUBE WEARByJingPing ChenB.A.Sc., M.A.Sc. The National University of Defence Technology, Hunan, P.R. ChinaA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment ofMECHANICAL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAMarch 1994© JingPing Chen, 1994In presenting this thesis in partial fulfilment of the requirements for an advanced degree atthe University of British Columbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission for extensive copying of thisthesis for scholarly purposes may be granted by the head of my department or by hisor her representatives. It is understood that copying or publication of this thesis forfinancial gain shall not be allowed without my written permission.Mechanical EngineeringThe University of British Columbia2324 Main MallVancouver, CanadaV6T 1Z4Date:30, /td4 /‘1’14AbstnictThe objective of this study is to quantitatively determine wear and its main parameterrelationships for heat exchanger tube wear. A model has been proposed.The literature of the current state of heat exchanger tube wear study, wear mechanisms,and wear models were reviewed.Tube/disc sliding wear tests were conducted with an impact-fretting testing rigincorporated with an advanced control system and an accurate data acquisition system. Theseensured that the test results are reliable. The relationships between wear and normal load, wearand sliding distance, wear and frictional work were determined.Advanced surface analysis techniques were used to better understand the heat exchangertube wear problem. It was found that the roughness and its standard deviation of the tube and thedisc were much the same after wear, but surface roughness was neither directly related to thesliding distance nor to the normal load. Plastic deformation was observed. Oxidation became animportant mechanism for carbon steel disc/Incoloy tube combination even at room temperature.Based on the experimental results obtained, it was found that the dynamic model by Linand Cheng was quite suitable for the heat exchanger tube wear. The calculated resultssatisfactorily matched the test results. This model has been extented to calculate tube wear depth.11Table of ContentsAbstract iiTables of Contents iiiList of Tables vlist of Figures viAcknowledgement xiii1 Introduclion 12 Literature Survey 82.1 Heat Exchanger 82.2 Wear Mechanisms 152.3 Some Results of Wear Research 172.4 Sliding Wear Models 233 Expeiimental Tests 373.1 Test Procedure 373.2 Test Rig 393.3 Test Conditions and Material Properties 443.4 Test Results 451114 Surface Analysis 534.1 Material Transmission 534.2 Plastic Deformation 554.3 Surface Profile with Number of Sliding Cycles 644.4 Surface Profile with Normal Load 694.5 AECL High Temperature Worn Tube Analysis 725 A Model for the Heat Exchanger Tube Wear 795.1 Some Previous Model Analysis 795.2 Wear Phenomena and Test Results Analysis 845.3 Modelling 905.4 Calculations 955.5 Equation Extension 1076 Conclusions and Further Study 111Bibliography 114AppendicesA Test Results 120B Calculation of Jam and Bahadur Model 124C Equations of Gaussian Disttibution 128ivList of Tables2.1 Archard Wear Equation Extension 243.1 Chemical Composition of Materials 443.2 Mechanical Properties 444.1 Surface Parameters For The Group 1 Brass Samples 684.2 Surface Parameters For The Group 3 Brass Samples 685.1 Topographic Parameters 895.2 Initial Input Data 96VList of Figuns1.1 Classification of Wear 21.2 Typical Nuclear Power Station Schematic Diagram 41.3 Steam Generator Schematic Diagram 51.4 Worn Tube in Heat Exchanger 62.1 Multispan Test Rig 102.2 High Temperature Test Rig Li2.3 Effect of Temperature on the Wear Rate of Incoloy 800 Tubing 112.4a Effect of Support Land Length on Tube Wear 122.4b Tube Fretting in Interrupted Hole Supports 122.5 Single Span Tube Test Rig 132.6 Tube to Support Plate Region 142.7 Distribution of Contact Pressure for a Smooth Surface 192.8 Distribution of Contact Pressure for a Rough Surface 20vi2.9a Axial Pressure Profile With No Misalignment 212.9b Axial Pressure Profile With a Misalignment of 0.86E-3 rad 222.9c Axial Pressure Profile With a Misalignment of 1.25E-3 rad 222.10 Schematic Representation of Sliding Contact Between Two Rough Surfaces 262.11 Pressure Distribution on Indentation 343.1 Test Procedures 383.2 NRC Fretting-Impacting Test Rig 403.3 Dynamic Holder for Sphere Specimen 403.4 The Self-Aligning Tube Holder 413.5 Full Test System Schematic Diagram 423.6 Diagram of Friction Coefficient vs Cycles 433.7 Total Frictional Work vs Wear Loss (early test) 453.8 The Relationship of Lubricant and Wear Loss 463.9 The Shape of Brass Specimen For Tube Test 463.10 Sliding Distance vs Wear Loss 48vii3.11 Normal Load vs Wear Loss 483.12 Total Frictional Work vs Wear Loss (brass disc) 493.13 Total Frictional Work vs Wear Loss (stainless steel disc and tube) 503.14 Total Frictional Work vs Wear Loss (carbon steel disc, cutting fluid lubricant) 513.15 Total Frictional Work vs Wear Loss (tube, with carbon disc, cutting fluidlubricant 513.16 Total Frictional Work vs Wear Loss (carbon steel disc and tube, distilled water) 524.1 EDX Analysis of Material Transmission 544.2 SEM Analysis of Material Transmission 544.3 Brass Disc Wear Scar Map 564.4 Plastic Flow on Worn Brass Disc 574.5 Original Grain Boundaries of The Brass Disc 584.6 The Deformed Grain Boundaries 584.7 3-Zone Schematic Diagram 594.8 Zone 3 and Cracks 594.9 Contour Plot oft0/Pfor j.i=0.164 60viii4.10 The Coordinate Schematic Diagram 604.11 The Microstructure of Y-Z Plane 614.12 Grain Deformation Near The Contact Centre 624.13 Contour Plot of t/P0for .t=0.164 624.14 Contour Plot of a/P0for ii=0.164 (y-z plane) 634.15 Contour Plot of afP0for .t=O.164 (y-z plane) 634.16 Original Ground Surface 644.17 Brass Disc Surface After 9900 Cycles 654.18 Brass Disc Surface After 30,000 Cycles 654.19 Brass Disc Surface After 60,000 Cycles 664.20 Brass Disc Surface After 150,000 Cycles 664.21 Brass Disc Surface After 300,000 Cycles 674.22 Brass Disc Surface After 450,000 Cycles 674.23 Brass Disc Surface Under 50 N 694.24 Brass Disc Surface Under 100 N 70ix4.25 Brass Disc Surface Under 200 N 704.26 Brass Disc Surface Under 300 N 714.27 Brass Disc Surface Under 400 N 714.28 Tube Section (tested with carbon steel A36 ring) 734.29 Tube Section (tested with Inconel 600 ring) 744.30 Tube Cross Section Ni Composition Spectrum. 754.31 Tube Cross Section Cr Composition Spectrum 764.32 Tube Cross section Fe Composition Spectrum 774.33 Tube Cross Section Mn, Al, Ti composition Spectra 785.1 Schematic Diagram of Energy Distribution 835.2 Three Types of Wear 855.3 Three Regions of Wear 865.4 Brass Discs Against Incoloy 800 Tubes Test Results 865.5 The Relationship Between Tangential Load and Wear 875.6 Comparison of Test Results and Calculation Results (brass disc, diluted cuttingfluid lubricant) 97x5.7 Comparison of Test Results and Calculation Results (ss4lO disc,dilutedcutting fluid lubricant) 985.8 Comparison of Test Results and Calculation Results (tube, tested withss4lO disc, diluted cutting fluid lubricant) 985.9 Comparison of Test Results and Calculation Results (carbon steel 12L14disc, distilled water lubricant) 995.10 Comparison of Test Results and Calculation Results (tube, tested withcarbon steel 12L14 disc, distilled water lubricant) 995.11 Comparison of Test Results and Calculation Results ( carbon steel 12L14 disc,diluted cutting fluid lubricant) 1005.12 Comparison of Test Results and Calculation Results (tube, tested withcarbon steel 12L14 disc, diluted cutting fluid lubricant) 1005.13 Difference Between Test Results and Prediction (brass disc, dilutedcutting fluid lubricant) 1015.14 Difference Between Test Results and Prediction (ss4lO disc, distilled waterlubricant) 1015.15 Difference Between Test Results and Prediction (tube, against ss4lO disc,distilled water lubricant) 1025.16 Difference Between Test Results and Prediction (carbon steel disc 12L14 disc,distilled water lubricant) 102xi5.17 Difference Between Test Results and Prediction (tube, against carbonsteel 12L14 disc, distilled water lubricant) 1035.18 Difference Between Test Results and Prediction (carbon steel l2Ll4disc,diluted cutting fluid lubricant) 1035.19 Difference Between Test Results and Prediction (tube, against carbonsteel 12L14 disc, diluted cutting fluid lubricant) 1045.20 The Relationship Between Wear Rate and Sliding Distance 1055.21 The Relationship Between Antiwear Strength and Sliding Distance 1055.22 a Influence on Antiwear Strength U 1065.23 h Influence on Antiwear Strength U 1075.24 Tube/Ring Schematic Diagram 1105.25 Tube/Ring Misalignment Schematic Diagram 110xiiAcknowledgementI would like to thank those who helped in this research program. In particular, I would like toextend my appreciation to Atomic Energy of Canada Limited and the Natural Science andEngineering Research Council and to my supervisors Dr. P.L.Ko and Dr. H.Vaughan for theirvalued guidance and advice. As well, I am grateful for the help of Mr. M. Robertson at theNational Research Councile (NRC) for the experimental developments and for the support ofMr.E.E. Magel, Mr. R. Leung, Mr. S. Yick, Mr. T.Vanderhoek.I would like to express my special thanks to Dr. M. Raudsepp and P. Wong for their helpon surface analysis.Finally, I would like to thank my husband for his encouragement and patience.xiiiChapter 1IntmductionWear, as a phenomenon, has been recognized for a long time. However, it has been arelatively well defined discipline of science for only about thirty years. Wear is generally definedas “the progressive loss of substance from the operating surface of a body occurring as a resultof relative motion at the surface.”[l]. Wear is one of the major disciplines in tribology, the othertwo are friction and lubrication.Wear is an extremely complex process. The variables which affect wear life have beencompared to as many as those which affect human life [15]. Material properties, surfacetopography, component geometry, environmental factors such as lubricant, temperature, load,speed, sliding distance, and chemical reactions can affect the substance loss of the two contactingbodies. These parameters are related in a very complex way which is often hidden behind acurtain of mystery. Unlike most other subjects in mechanical engineering, the wear processusually happens on a microscopic level, i.e. the substance loss is not in tons or kilograms, butin milligrams or even less; the dimensions are not in meters or centimetres, but in millimetresor microns. Therefore, assumptions of” homogeneous”, “isotropic”, “continuity” which engineersare familiar with have to be reconsidered. For example, the material properties at the contactsurface are usually very different from the bulk properties, since the microstructure of thematerial has been changed due to machining, heat, lubrication, and even chemical reaction. It isobvious that special considerations are needed to deal with wear.In order to solve certain complex scientific problems, a knowledge of several branchesof science is needed. Tribology is one such example, it requires a knowledge of material science,surface physics, mathematics, mechanics and chemistry. Many papers have been published in the1Chapter 1. Introduction 2field of tribology over the past thirty years. Advancements made in different research fields havehelped to clarify our understanding of the problem. Further clarification is due to theadvancement in modern scientific instruments which play a very important role in wear study,since the micro-process of wear can not be observed directly.Wear depends on numerous conditions, which make the classification of wear verydifficult. As Ko pointed out [2], the simple definition of wear embraces a multitude of complexmechanisms involving a diversity of processes, such as adhesion, abrasion, fatigue and corrosionetc. One, or a combination of these process may be in operation in any particular instance ofwear. The interaction among these processes together with a variety of complex conditions at andbelow the contacting interface further adds to the complication. Among the various schemes toclassify wear are: (1) by relative motions, (2) by the mechanism of particle removal and (3) bythe type of wear. Figure 1.1 shows these various schemes. In his paper, Ko [2] also outlined thevarious wear modes and wear mechanisms.CHARACTERISTICMOTION MODE OR TYPE OF WEARBASICMECHAN I SMFigure 1.1 Classification of WearChapter 1. Introduction 3In engineering practice, there is a need for wear equations in order to develop wearmodels which can be used to design mechanical components for better performance and reliabilityleading to reduced running cost and maintenance. Studies have been made which show thepotential savings that tribology can have in modern industry. A report [3] issued in the U.K. in1966 estimated that there were savings of £515 million/year to be achieved through better useof available tribological knowledge in the design, production and maintenance operations ofindustry. In Canada, the result of a thorough investigation [4] in 1982 estimated the cost of thetribological losses to the Canadian economy was about $5 billion. It is thought that these lossescould be reduced by about 25% through cost-effective programmes of research, development andtechnology transfer.A concern in the nuclear power industry is the failure of the steam generator tubes bywear. This problem has become a high priority item in Canadian nuclear generating stations.Figure 1.2 is a schematic diagram of a typical nuclear power station: in the nuclear reactor, thedissociation of atoms generate large amounts of heat which is carried away by the closed circuitheavy water cooling system. At the next stage in the steam generator, the heavy water transfersthe heat to the feedwater which is turned into steam for the turbines to generate electricity. AsFigure 1.3 shows, a nuclear steam generator may contain over 4000 tubes each about 20 feet longand supported by several horizontal plates. Flow induced vibration causes the tubes to wear byimpacting and rubbing on the support plates and/or with adjacent tubes. The demand for highefficiency has resulted in higher flow rate with a consequential increase in the dynamic forcesbetween the tubes and their supports. Since the tubes separate the heavy water and the lightwater, the resulting wear may lead to heavy water leakage from the tubes (see Fig. 1.4). Thissimple mechanical failure may result in contamination of the environment and radioactiveexposure to station personnel. The current practice is to simply plug a worn tube so that it nolonger function. Downtime of the station is extremely costly and must be avoided. A statisticalinvestigation [5] carried out in a CANDU power station showed that the power output loss dueto the failure of major heat exchangers was 2300 GW.h in 1979 alone.COOLANT1HEAVYWATERIi1MODERATORJORDINARYWATE.R-($1STEAMLAKEWATERIHELIUMGAS(ONLYONEUNITOFFOURISSHOWN)PICKERINGNUCLEARPOWERSTATIONIITURBINE-GENERATORBUIlDINGREACTORBUILDINGSTEAMSTEAMGENERATORFUELRODSELECTRICITY.—TURBINEGENERATORFUELING;p/jE1E______1CONDENSERPUMPL—-1—COOLINGWATERFROMLAKEFigure1.2TypicalNuclearPowerStationSchematicDiagramChapter 1. Introduction 5bUUMWItMM ItI’llzrcI-IurSTEAM OUTLET NOZZLESTEAM CYCLONESTUBE BUNDLEDIVIDER PLATE020 INLET NOZZLES020 OUTLET NOZZLEBASE SUPPORTPREHEATERFEEDWATERSUPPORTSFigure 1.3 Steam Generator Schematic DiagramChapter 1. Introduction 6,.1Figure 1.4 Worn Tube in Heat ExchangerSince the early ‘70s, there has been a major effort to develop analytical techniques topredict flow-induced vibration and wear phenomena. Ko [7] [8], Blevins [9] [10] Connors [14]and recently Magel [17] have performed research on this kind of problem. The objective of thisresearch project is basically to extend Ko and Magel’s work to reach two goals: the first, tounderstand the main factors that cause tube wear, by working on a further fundamentalinvestigation; the second, to find out the main quantitative relationships among wear parametersin order to build up a sliding wear model which can reasonably predict laboratory test results andwhich may then be used for real engineering design.IjChapter 1. Introduction 7This study is concerned with pure sliding wear only, chapter 2 will include a literaturesurvey of the tube wear problem and previous fundamental investigations, chapter 3 will describethe new testing rig, testing conditions, and material properties and some test results, chapter 4will include surface analysis such as surface parametric analysis, cross section microstructureanalysis and other techniques. Chapter 5 will include some previous model analysis, wearphenomena analysis, the new wear model for the heat exchanger tube wear, the discussion of thecalculation, and the model extension. The last part of the thesis, i.e. chapter 6, is the conclusionsand suggestions of further study.Chapter 2Iiteratun SurveySteam generator and heat exchanger tube wear is mainly a flow-induced fretting wearproblem. As the diagram in Figure 1.1 shows, fretting wear may involve several wearmechanisms: adhesion, abrasion, delamination, fatigue and corrosion. In the 1970’s, Ko, Blevinsand other researchers started to explore the tube wear problem. They conducted extensivecontrolled laboratory tests. Their research results have provided valuable information forsubsequent analyses of tube wear mechanism and tube wear modelling. In order to develop agood wear model, it is important to understand their previous studies. This chapter includes afour-part literature survey: 1) Heat Exchanger, 2) Wear Mechanisms, 3) Results of SomeFundain en to] Study 4) Sliding Wear Models.2.1 Heat Exchanger2.1.1 The Environment Parameters of Heat ExchangerBased on the information gathered by Mahail and Dueck [5] [6], physical data for theCanadian nuclear steam generators include the following:The temperature of the heavy water: 107—304°CTube materials: Incoloy 800, Monel 400, Inconel 600, 70/30 Cu/NiSupport materials: carbon steel (A245B or SA.516 grade7o), 70/30 Cu/Ni, brass 60/40Tube diameter: 12.7—19 mmTube wall thickness: 1.12—1.65 mmWater pressure: 5171—9650 KPa.8Chapter 2. Literature Survey 92.1.2 Heat Exchanger Tube Parametzic StudyResearch into heat exchanger tube wear has progressed at several stages, each stagecorresponding to the development of a new testing system. The first stage study relates to theflow induced vibration analysis. In 1980, Pettigrew [7] studied flow induced vibrationexcitation mechanisms. Combining the dynamic flow analysis and multi-span room temperaturedynamic testing (Fig.2.1 ), they found that the main tube vibration frequency is about 20-40 Hz[8]. In reference [7], Pettigrew considered the vibration response to random turbulence excitationof a hypothetical four span tube and found the maximum random vibration response was 33 .tmrms. He also estimated the impacting force between tube and support to be about 1.2 N rms.These figures indicate that tube wear is the result of low load, small amplitude vibrations - theconditions of fretting. Around the same period, Blevins [9] [10] [11] studied the fretting wearof heat exchanger tubes in a nitrogen/air mixture at room temperature. The effects of tube/tubesupport clearance, eccentricity, vibration frequency and mid-span displacement were investigated.Connors [14] also did valuable analysis of flow-induced vibration and wear of steam generatortubes.The second stage study was a high temperature wear study. A testing facility used by Ko[8] consisted of a series of high temperature autoclaves connected to a pressurized loopsimulating the high temperature/pressure operation environment (Fig. 2.2) This high temperatureenvironment is especially important considering the effect of oxidation to the wear process. Inthis facility, each autoclave contains a single span tube with an end mounted vibration excitationsystem which drives the tube impacting and sliding on the support. Ko performed tube wear testsin pressurized water at temperatures up to 265 °C [8]. Figure 2.3 shows the wear relationship ofIncoloy 800 tube to temperature. Two series of tests, one with carbon steel support specimensand the other with 304 stainless steel, were performed in two different excitation conditions. Theresults clearly show that the wear rate increases with temperature within the investigated range.Ko also studied the effect of support geometry on wear and concluded that the wear rateincreases with the tube/support clearance, but wear depth decreases with increased contact lengthand support circumferential length (Fig. 2.4a, 2.4b).Chapter 2. Literature Survey 10Figure 2.1 Multispan Test RigChapter 2. Literature Survey>.C)0ExIC.I—z>0’11Figure 2.2 High Temperature Test RigINCOLOY 800 TUBING I 30 STAINLESS STEELRADIAL CLEARANCE 0 9 mm0 INCOLOT 800 TUBING/CARBON STEELRADIAL CLEARANCE 0 38 mm2.0.50.500TEST TEMPERATURE. CFigure 2.3 Effect of Temperature on the Wear Rate of Incoloy 800 Tubing0.5-3C)VEz-3>0’S IC 15 20 25SUPPORT LAND LENOTH. wiFigure 2.4a Effect of Support Land Length on Tube Wear‘.5-30>-000C-302 04 0.8 0.8 IXFRACTION OF FULL CIRCOUFERENCEC12Chapter 2. Literature SurveyINCTLTT ADO OUTING 45 CAUBON STEEL SUPPORT SPECIRENS IN PRESSURIZED ICIER A 26SCEXCITATION FREQUENCY 28 HzTUBE/SUPPORT DIABETRICAL CLEARUNCE 0 3002—504.0 —3.0 —INCONEL. 600 TU8INO AS CaRBON STEEL SUPPORT SPECIWENS IN PRESSURIZEDlATER AT 265CEXCITATION FREDUENCY 28 NZTORE / SUPPORT DIARETRICAL CLEARANCE+—+ 0.16 n’—.-.-‘-.O—O 0.38a -.- I I 620—I0Figure 2.4b Tube Fretting in Interrupted Hole SupportsChapter 2. Literature Sziri.’ey 13The third stage study involved more fundamental studies. Ko [12][16][44J studied theeffect of impact force on wear at room temperature using a single-span tube test rig (Fig. 2.5)and later with a more advanced impact-fretting test rig (Fig. 3.2). He found that the wear rateincreased linearly with tangential impact energy for brass and 304 stainless steel (the tangentialimpact energy = friction force x the total sliding distance ). Ko emphasized that impact forcealone cannot be directly correlated to wear rate when other parameters such as tube and tubesupport clearance and the type of motion are varying.TUBE AND TUBESUPPORT SPECIMENSTRANSDUCERPLATFORMVIBRATIONRA:RFigure 2.5 Single Span Tube Test RigChapter 2. Literature Survey 142.1.3 Surface Analysis TechniquesIn 1985, Hogmark [13] had a rare opportunity to examine heat exchanger tubes takenfrom a nuclear power station. They applied surface analysis techniques (Energy Dispersive X-rayspectroscopy (EDX) and Auger Electron Spectroscopy (AES) ) to analyze the worn tube. Theyfound the tube was covered by a 0.1—2 tm oxide layer and the wear surface had a wavytopography. No plastic deformation was detected near the worn surface. Hogmark also found thatthe oxide layer is thinner (0.05—0.1 tim) in the worn area (Fig. 2.6 area 2) and thicker (0.5— in the unworn area of the tube to support plate region (Fig. 2.6, area 3) as compared to theoxide layer thickness of the reference surface (Fig. 2.6, area 1). Therefore, they concluded thatwear occurred by flow enhanced removal of material from the superficial layer of the oxide film.area 1. reference surfacearea 2. worn areaarea 3. unworn area of tube to support plate regionTubeSupport PlateFeedwatercurrentWorn areaFigure 2.6 Tube to Support Plate Region (dimensions in mm) [13]Chapter 2. Literature Survey 152.2 Wear MechanismsHeat exchanger tube wear is primarily the result of impact-fretting which is related toadhesive, abrasive, delamination, fatigue and oxidative wear mechanisms. The definition andbasic character for each of these mechanisms has been explained in many references [2][17][18].This section will briefly discuss the mechanisms often associated with the heat exchanger tubewear.2.2.1 Fntting WearFretting itself is not a mechanism. Rather, it is a type of wear which arises whencontacting surfaces undergo oscillatory tangential displacements of small amplitude (in microns).It represents the interaction of several wear mechanisms. Three names are often associated withfretting: fretting wear, fretting fatigue and fretting corrosion. Fretting wear is usually concernedwith larger amplitudes of motion than fretting fatigue. Fretting fatigue occurs in situations wherethe combined effect of small vibration amplitude and surface friction results in only microslip atthe contacting area. Fretting corrosion is due to combined mechanical and chemical actionsresulting in the continuous removal of oxidized surface layers. As Quinn discussed in his study[48], fretting corrosion is clearly a form of oxidational wear, occurring under conditions wheresmall oscillatory tangential motion occurs between two surfaces which are held together in sucha way that the oxide wear particles cannot escape, thereby causing severe stresses to be set upin the constraining mechanism (e.g. in the bolt holding together two plates subjected to vibrationswith extremely small amplitude (of the order of microns)).Johnson [19] studied the mechanics of microslip as the fundamental cause of fretting. Theoscillating force is a controlling parameter.2.2.2 AdhesionAdhesion is considered the most fundamental wear mechanism because it is a basicChapter 2. Literature Survey 16phenomenon that takes place whenever two solid surfaces are in dry sliding contact. Sincesurfaces are always microscopically rough, in dry sliding contact, the load is carried by surfaceasperities. As the local pressures are very high, the yield strength of the softer material may beexceeded. The high local pressures and traction force generated by relative sliding may causeminute welds or junctions to form at these local contacts.2.2.3 AbrasionAbrasive wear is produced by hard particles or asperities which cut or groove one of thesliding surfaces. Harder particles may be from one of the two rubbing surfaces or may be formedby chemical and thermal related processes such as oxidation or the precipitation of carbides. Theabrasive wear mechanism also includes third body wear. This type of wear occurs when hard,abrasive particles are trapped between two sliding surfaces. These hard particles may be productsof wear ( i.e. work hardened wear particles ) or may otherwise be introduced from outsidesources ( dust, sand, soil ). Moore [20] describes two mechanisms by which material may beremoved during the abrasive wear process: wear particles can be removed as prows which formin front of a moving asperity due to plastic deformation or as chips due to fracture with limitedplastic deformation.2.2.4 Delamination WearDelamination wear is defined as the loss of material in the form of flakes, caused by theformation and propagation of subsurface fatigue cracks running parallel to the surface. Thismechanism was first discussed by Suh and his co-workers at MIT [21]. In Suh’s theory [21] [22]he assumes that a metal under a slider wears layer by layer similar to the removal of an onionskin. Each layer consists of many sheets. The creation of these wear sheets is assumed to be acumulative process which results from the surface shearing a small amount with each passingasperity. A wear sheet maybe created after a large number of asperities have passed each pointon the surface.Chapter 2. Literature Survey 172.2.5 Fatigue WearFatigue is a broad term applied to the failure phenomenon where a solid is subjected tocyclic loading above a certain critical stress. The number of stress cycles necessary to causefailure increases with decreasing stress.Fatigue wear on a microscopic scale is associated with individual asperity contacts. Failureoccurs due to the repeated deformation and the relative displacement of the rubbing bodies.2.2.6 OxidationOxidation is the most common form of chemical attack on metallic wear surfaces.Corrosive or oxidative wear is the result of both corrosion and rubbing. It is usually considereda mild wear. Quinn and Sullivan [23] developed an oxidation wear model in which they assumedthat wear occurs when the sliding system is attacked by atmosphere oxygen, and the corrodedlayer on the contact surface is subsequently rubbed off. Under static conditions, the oxide filmacts as a barrier between the base metal and the absorbed oxygen inhibiting further oxidation,hence reducing the oxidation rate. In the dynamic case, i.e., with sliding, the oxide layer isrubbed away continuously. The oxidation rate therefore remains at the initial high value.2.3 Some Results of Wear Reseaith2.3.1 The Effect of Surface RoughnessThe effect of surface roughness on friction has been investigated by many researchers.Whitehouse [45] studied surface topography and quality and its relevance to wear. Stout etal [46]studied the micro-geometry of lubricated wear. Gupta [47] discussed several key points in thegeneral area of surface interaction and pointed out “a small change in sampling distance couldresult in significant changes in surface description”. Jeng [24] found that lower roughness heightyields lower friction, and that transverse roughness has lower friction than longitudinalChapter 2. Literature Survey 18roughness and surface roughness effects become increasingly significant as the film thicknessdecreases.Wang et al. [25] studied the relative surface conformation between two surfaces in slidingcontact. Their research shows that the relative surface conformation rises with increasing testduration, during running in.2.3.2 Reciprocating and Continuous Sliding WearIn 97O, Ward [26] compared the wear rate of continuous and reciprocating sliding undersimilar load, speed and nominal area of contact. Higher wear rates were observed duringreciprocating sliding for both mild and severe wear cases, the rate of increase of wear rate withload for severe wear was also greater under reciprocating conditions. The increased wear rate forreciprocating sliding was explained in terms of abrasion caused by the presence of loose weardebris i.e. the third body effects.2.3.3 Contact Stisses for Nonconforming SurfacesThe stress distribution associated with smooth surfaces in contact are rarely experiencedin practice. Factors such as surface roughness, lubricant films, and third body particulate areknown to influence the state of stress and the resulting rolling contact fatigue life. Bailey andSayles [27] developed a numerical technique for evaluating the complete subsurface field of stressbased on the measurements of surface profiles resulting from the elastic contact of nonconformingrough bodies. The result revealed that the presence of asperities within the contact range resultedin highly stressed regions on the surface ( Fig.2.7, 2.8 ), and that plastic deformation of theseasperities during running in reduced the peak contact pressures. During sliding and rolling, thecyclic nature of these stresses often initiates fatigue cracks which will eventually cause failureof the contact surfaces.T100 CD t)CD0 bChapter 2. Literature Sur’ey 20(a)/1 jFigure 2.8 (ref. [271) DistrIbution of contact pressure and subsurface orthogonal andprincipal shear stresses for the simulated elastic contact of the unrunground surfaceA(C) (C)Cd) (Q)2.3.4 MisalignmentFor a line contact case, misalignment is a common problem. It is mainly due to thedifficulties in machining and mounting components to the accuracy of micron levels. The seriouseffect on wear by misalignment was studied by Kannel eta! [28]. Figure 2.9a, 2.9b, 2.9c showthe relationship of misalignment and contact pressure. Kannel pointed out that at a misalignmentlevel on the order of 0.86 to 1.25x103 radians, edge stresses on the order of 2 GPa have beenmeasured and predicted. These stresses are more than twice those which would occur for idealline contact. The high stress region will certainly result in increased wear.20Ca( IS1.00.5Figure 2.9a (ref. [28]) Axial pressure profile for nearly cylindrical disk2224 N (500 Ib) with no a load ofChapter 2. Literature Survey 2125&0-01 0 01Distance From Disk Cecitertine, inchI I I—8 —6 —4 —2 0 2 4Distance From Disk Centerline, mm0.4L L J6 8 10ciae 1.5a-05-C —8 —6 —4 —2Distance From Disk Centerluie, mm4 6 8 10Figure 2.9b (ref.[28]) —Axial pressure profile for nearly cylindrical disk at a load of2224 N (500 Ib) and a misalignment of 0.86 x iO rad.40C.25 —200 -C)-10 —8 -6 —4 - 0 2 4Distance From Disk Centerline, mm6 8 10Figure 2.9c (ref. 128]) Axial pressure profile for nearly cylindrical disk at a load of2224 N (500 Ib) and a misalignment of 1.25 x iO rad.Chapter 2. Literature Survey 2225 —2.0 —a-0-0.1 0 0.1Distonce From Disk Centerline, inchI I I I I300 —20 —(-) 15S—05 —0too -xxx.....“ x\Xx\xxI I-0.3 -0.2 —0.1 0 01Distance From Disk Centerline, inch—04 0.2 03 04Chapter 2. Literature Survey 232.4 Sliding Wear ModelsIn the large quantity of published literature, hundreds of wear models have beensuggested, each relating to a specific wear system. There is no generally accepted wear modelavailable. The following sections briefly describe some of these models to provide differentapproaches for wear modelling.2.4.1 Aithard Wear ModelArchar&s wear model which was published in 1953 [29], is the most widely quotedadhesive wear model. It is in a very simple form:V=k-L (2.1)Hwhere V is wear volume which is proportional to the normal load P and travelled sliding distanceL but inversely proportional to the softer material hardness H. In this equation, k is adimensionless constant known as the wear coefficient and can vary from 1O to 10b0.The Archard wear model dominated both the theoretical and experimental approaches inthe early period of wear study. In some cases, the Archard model can reveal the main factors thataffect wear volume loss without getting into too much detail. The Archard model, which wasoriginally for adhesive wear, was later extended to cover other wear mechanisms such as abrasivewear, fatigue wear, oxidation wear etc. (see table 2.1). In these equations, the wear coefficientk and its definition changes depending on the wear mechanism considered.24Chapter 2. Literature SurveyTABLE 2.1 ARCHARD WEAR EQUATION EXFENSIONTYPE OF WEAR EQUATION TYPE OF WEAR EQUATIONV P V KElmv2llAdhesive Wear — = KL acih— Erosive Wear —= — jwhere Kadh= m = mass of particleV = impact velocityV PAbrasive Wear —= Kb for v >> I.Lwhere K =K aCot’P K my2abr V -f-Ky5a1 to 26 H—[Q /RT]=parabohc oxidationconstant. Q = constants for givenmaterialrl/2—O.18afatfl [Ha = ratio of nominalarea of contact tofrictional area ofcontact.n = ratio of plasticstrain for fractureto the effectivestrain to the power=r]DelaminationWearV P—=KL delh1where KdlClFatigue WearK2h1-———C2V P—=K —L fat H(for plastic contact)whereh = thickness of layerC = critical plastic displacement1,2, denote the two contactingcomponetsOxidationWear ÷ = Koxidwherep e—[Q’12[f1lf,] vt = fatigue curveexponent powerh = depth of penetrationH = radius of curvatureof asperityH = universal gas constantT = temperature1’ = fraction of oxide which isoxygen.77 = critical oxide thickness= average density of oxidev = velocity of slidingChapter 2. Literature Survey 252.4.2 Jam and Bahadur Wear ModelThe wear model by Jam and Bahadur [30] was developed for the sliding wear ofpolymeric material. It was later verified experimentally [31]. They conjectured that theinteractions between asperities that occur during the sliding of surfaces lead to cyclic contact andreversals of principal tensile stress, and this tensile stress was responsible for the nucleation andpropagation of fatigue cracks.Their wear model included the following assumptions:1) The height of asperities on both surfaces in contact varied randomly. It was laterassumed to be a Gaussian distribution.2) The asperities have spherically shaped tips.3) The asperities on one surface are aligned with those on the other surface and have thesame pitch in the sliding direction.4) The deformation in the contact zone is of an elastic nature.5) The discrete contact zones were sufficiently separated to act independently of eachother.Four steps were used to derive the wear equation:First, the real contact area is determined by applying the Hertzian equation for eachindividual asperity.The Hertzian equation for elastic contact of a sphere with a smooth plane provided thefollowing expression for the contact radius a1, the area A1 and the load P1 [32]:(2.2)(2.3)Chapter 2. Literature Survey 26P=El213wherei 1-y 1-y (2,5)E’ E1 E2andy is the Poissons ratio, c is the compliance (distance by which the points outside the contactzone move closer owing to deformation), 13 the radius of the spherical asperity and E the modulusof elasticity. The subscripts 1 and 2 refer to the two surfaces in contact.ASPERITIES WITHHEIGHT DISTRIBUTION1z) AND AVERAGESTATIONARY SURFACE RADIUS1 2 3 4 56 7 8 g 10SURFACE pASPERITIES WITH______________HEIGHT DISTRIBUTIONSLIDING DIRECTION j2(z) AND AVERAGERADIUS 82REFERENCE PLANEIN ROUGH SURFACEROUGH SUREACEFigure 2.10 Schematic Representation of Sliding Contact Between Two Rough SurfacesChapter 2. Literature Survey 27Greenwood and Williamson [33] extended the above single contact equations to the caseof contact between a rough and a smooth surface ( Fig. 2.10 ) to develop expressions for thenumber of the discrete contact zones n0, the area of real contact A and load P. By normalizingwith respect to the standard deviation of the asperity height distribution, Jam and Bahadur arrivedat the following:n0=1Aof4z)dz=i1A0F(h) (2.6)Ar=AOi3f:(Z_d)(Z)dZ=7t11AO13 cF1(h)(2.7)P=-rjA0E’13112f(zd)3124(z)dz=iiA,E’13112ciF3(h)(2,8)where ‘q is the surface density of asperities, A0 is the nominal area of contact, 4(z) is thedistribution of asperity heights and d is the distance between the reference planes of the surfacesin contact. In this equation, h and s are standardized variables, which were obtained bynormalizing the heights d and z with respect to the standard deviation a of the asperity heightdistribution such that h=d/a and s=z/a. The generalized function F(h) is defined asF(h)=f(s-h)n (s)dsFor the case of two rough surfaces in contact, equivalent values for f3 and a are modifiedas:P12 213=n I)‘P1I2(The subscripts 1 and 2 refer to the two contact surfaces.)Chapter 2. Literature Survey 28The second step was to determine the principal stresses in a circular contact zone by usingthe Hamilton and Goodman analysis [34]. This analysis showed that two of the principal stressesin the contact zone were largely compressive in nature. As such, these would not be expected tocontribute to the initiation of a fatigue crack. The third principal stress was tensile in front of thecontact zone and compressive behind it. This stress was assumed to be responsible for the fatiguefailure. The expression derived by Hamilton and Goodman for the maximum tensile stress, S, is1 (r(4÷y)it÷’ 11) (2.10)2ta8 3where ji is the friction coefficient, y is the Poisson’s ratio. In order to determine the tensile stressS, the load P1 and the contact radius a1 for an individual asperity are needed. Greenwood [35] hasshown that the average size of discrete microcontacts was nearly constant for an elasticcontact situation. Therefore P1 and a1 could be determined from the following equations:(2.11)1 9A0F(h)a(Ar)112 (PGF1h))lfl (2.12)1 F0(h)Substituting equations 2.11 and 2.12 into equation 2.10, the tensile stress S is expressedas3kP1 (2.13)2icrA0faF1(h)Chapter 2. Literature Survey 29wherek =i.(4+y)t+i2118 3The third step involved the asperity fracture criterion, i.e. the fatigue failure criterion todetermine the failure in an asperity. The bulk fatigue property of a material was represented byWohler’s curve, the equation for which is [36](2.14)where Nf is the number of cycles to failure, S0 is the failure stress corresponding to theapplication of a single stress cycle, S is the applied cyclic stress and t is a material constant. Thefactors S and t for a material were determined from the plot of its fatigue data.Substituting equation 2.13 into equation 2.14:N(2ICSO11AOI3GFI(h))t (2.15)3k1PThe last step was the final wear equation. The starting point of the wear equation isVR=NWvP (2.16)where VR is the volume wear rate, v, is the average volume of a wear particle assuming theasperities were all in a spherical shape and N is the number of wear particles formed per unittime.It is assumed that one surface in the wear system is moving, while the other is stationary.If i is the line density of the asperities on the moving surface and L is the sliding distance,then iLL is the number of asperities considered on the moving surface. Remember n0 rA0F(h)is the number of asperities for the unmoving surface. The asperity interactions in a slidingChapter 2. Literature Survey 30distance L between these two surfaces is LLAoFo(h). The asperity encounter rate NR for asliding speed u will beNR= u’ri1’rjA0F(h) (2.17)The number of wear particles N formed is expressed in terms of the asperity encounterrate NR divided by the number of loading cycles Nf needed to cause fracture, i.e.N =. (2.18)Substituting equations 2.15, 2.17, 2.18 into equation 2.16, gives the volume wear rate VR— fl1v,,uF0(h)(kP)tAi)1-tR[(_--)sfaF1(h)]Substituting P from equation 2.8 into VR, the wear volume V for a sliding distance L isin a very complex form:12Y) (2.19)2S0 8 3whereK2k1E ! F3(h))t_1F0(h)I itS0 F1(h) F1(h)2.4.3 tin and Cheng Wear ModelThe wear model by Lin and Cheng [37] is a recent model which considers the dynamicprocess of wear.Chapter 2. Literature Survey 31In this model, it is postulated that the wear rate is proportional to a forcing term Finduced by the shear force at the asperity contacts, and inversely proportional to a wear resistanceterm U, which is related to the surface antiwear strength. Both F and U are time dependent orwear dependent because wear progress causes the material strength at various layers to change.The wear equation is of the formw =k_F (2.20)RUwhere WR is the wear volume per unit sliding distance and k is a dimensionless constant whichmay be determined either experimentally or theoretically.The shear force F was obtained by averaging the shear force over h which is the elasticilyand plasticlly deformed layer beneath the loaded asperity. The shear force was expressed by theshear stress t.(x,y,z) ( at point (x,y,z) and time t. ) integral in the area, i.e.F=kfh(ffdy)dz (2.21)For a rough surface contact, the shear force at z in equation (2.21) can be represented byan average shearing stress over all asperity areas at z, t1 avg(2), timesA0cI1(z) where A0 is thenominal area and 1(z) is the time dependent cumulative probability function of the asperityheight distribution at time t1. Thus, F becomesAhF=_f cL(z)r1(z)d 2.22where p p>JAJt.(x,y,z)dA‘EAJA is the area of asperity j at depth z.Chapter 2. Literature Survey 32The antiwear strength U is defined asu=!fhffoj(x,y,z)cu dy d (2.23)where h is the deformed layer beneath the loaded asperity, and is of the order of the averageradius of the asperity contacting area. The flow strength ö.(x,y,z) represents the ability of amaterial to resist plastic flow at point (x,y,z) and time t1. The flow strength is a microscopicproperty and can be related to the microhardness or the yield strength of the material.Since the geometrical area of contact is composed of many asperity contact areas, theintegration of ö is the summation of the integral for each asperity contact area. Thusu=f’( f fô(x,y,7idA) dzifh0(z)dz (2.24)where A is the area of asperity j at depth z, andD fA Jo (x,y)dA1is the average flow strength of the material at depth z. For a homogeneous material, the averageflow strength can be the yield strength. As shown in equation 2.24, the antiwear strengthcombines both geometrical and mechanical properties of the material. The flow strength ö1 (z)may increase due to work hardening or decrease due to the initiation and propagation of cracks.Chapter 2. Literature Survey 33For pure adhesive wear of a homogeneous material under constant friction and a steadywear condition, Lin and Cheng were able to reduce their model to the Archard equation. Fromthe preceding definitions, wear, antiwear strength and averaged shear force are time/weardependent. Therefore, this model is able to describe the nonlinear running-in wear behaviour.2.4.4 Magel Wear ModelMagel’s model 17] was originally derived for a single hard sphere sliding on a flatsurface. Later, the model was applied to multiasperity heat exchanger tube wear. The model isbased on the consideration of a certain amount of plastic deformation, i.e. shakedown, during thewear process.When a hard indenter is pressured against a softer flat surface, high pressures induced bythe spherical contact may exceed the elastic yield point and plastic deformation will commence.For the first few cycles the system will experience certain plastic deformation. With continuingdeformation, an indentation is formed as the material conforms to the geometry of the indenter.The maximum pressure beneath the indenter decreases as the pressure distribution changes toresemble that of a line contact. At the same time residual stresses are induced. The specimen willno longer deform if the pressure beneath the indenter does not exceed the shakedown pressurepSAfter several cycles, the deformed material reaches elastic shakedown and the indentationwill have a geometry such that the maximum stress at all points of contact between the indenterand the material is pS Also, steady state deformation will be entirely elastic (with a new,effective elastic yield point ofp0S)• The area of contact between the indenter and conformalindentation will appear as a long ellipse and for an ellipticity ratio greater than five, the contactcan be considered a line contact. The resulting pressure distribution will be as that shown inFigure 2.11.Chapter 2. Literature Survey 34Figure 2.11 Pressure Distribution on IndentationThe total load applied by the indenter is represented by the area under the pressuredistribution, i.e.P(x)=1.Pc(2a2b)=icPabK:(2.25)Chapter 2. Literature Suriey 35From Hertzian contact theory, the line contact formulae are/ 112a=2( ) (. )p (PE) (2.27)0tRLMagel assumed p pS by shakedown. Notice that P’ is the load/unit length, a is the semi-contact width, and combining equations 2.26 and 2.27 yields:(2.28)RL E”E”=(÷where E1 E2andRL=(! !)TL Pwhere rL is the radius of the indenter in the longitudinal direction, which is assumed constant,p is the longitudinal curvature of the wear scar.Substituting equations for the semi-contact width a and the semi-line contact length b,equation 2.25 can be expressed asChapter 2. Literature Survey 36P(x)=(P)2,4f 11) (2.29)p rLp N 12where rT is the transverse (perpendicular to the sliding direction) radii of the wear scar curvatureand 1 is the half sliding distance in one pass. Magel assumed that cracks initiate and propagateat the location of maximum octahedral shear stress, therefore the thickness of a wear particle canbe calculated.Magel assumed the basic wear parameter relationship is(2.30)where V is the total wear volume, W is the total frictional work input, v is the particle volume,and E is the tangential input energy to create the particle vp. Note that E is equal to tA 1(where A is the particle area, t,. is the yield shear strength, 1 is the sliding amplitude).Magel extended the model to non-smooth surfaces in sliding, following the method of Jamand Bahadur (see section 2.4.2, equation 2.3). According to Magelts experimental results, thesingle indentation geometry is well predicted, but the multi asperity wear model dramaticallyoverestimates the wear volumes primarily due to the simplified evaluation of E.Chapter 3Experimental TestsExperimental tests are very important in the study of wear. It enables researchers tounderstand the relative importance of various parameters. However, test results must beinterpreted carefully, since it is easy to jump to wrong conclusions. In order to isolate eachparameter during a test, a well controlled wear test system is very important. It is necessary todocument clearly test conditions and material properties so that the tests can be repeated and theresults compared with others. This chapter describes the test rig, test conditions, materialproperties, test procedure, and test results.3.1 Test ProcedutFigure 3.1 shows the overall path of specimen preparation and analysis. Specimenpreparation consists of machining of specimens, polishing the testing surfaces to the desiredfinish, cleaning and weighing prior to testing.Machining: Since wear is sensitive to material properties and heat treatment, it is important thatthe material for each group of specimens comes from the same batch. In this study, the materialused for the discs are cut from 1 inch diameter rods and the disc surfaces are machine ground.Polishing: For some wear studies, particularly those involving wear particle formationmechanisms, controlled precision polishing of each specimen surface is necessary. For the presentstudy, the majority of samples were polished by 1000 grit SiC paper, some of the samples werepolished to a 1 micron diamond finish. SEM analysis samples were all polished with 0.05 jimaluminum microfinish.37Chapter 3. Experimental Tests 38Figure 3.1 Test ProceduresCleaning: The specimens were cleaned to eliminate surface films and contaminants prior totesting. A second cleaning removed loose wear particles that remained at the surface after thetest. The cleaning procedure involves placing the specimens in an ultrasonic bath containingethenol three times.Weighing: Wear losses were obtained by weighing the specimen before and after testing, in bothcases after cleaning. An analytical balance with digital readout to 10 jig was used, the reliabilitybeing about 0.02 mg.For analysis, it is usually necessary to know the specimen microstructure changes, surfaceprofile or even performe Auger and EDX analyse and Micro -Prob Analysis. Detailed surfaceanalysis in this study will be discussed in the next chapter.Chapter 3. Experimental Tests 393.2 Test RigIn this thesis, most of the tests were carried out in the NRC Fretting-Impacting Test Rig,a detailed description of which may be found in references [12] [17]. Figure 3.2 shows thatexcitation is from the two shakers mounted at 9Q0 to each other. Figure 3.3 shows the holderdetail. The aluminum ring shaped dynamic specimen holder is connected to both shakers. Shaker1 provides the sliding displacement and shaker 2 provides the normal load between the dynamicand the static specimens. The normal load and frictional load can be measured by the triaxial loadcell located under the stationary specimen (e.g. Fz=normal load, Fx=friction load, Fy0, in thisspecial application). The stationary specimen assembly includes the load cell attached to a semicircular bar with its curved surface anchored at the lower half of the autoclave. A holder whichmounts a spherical specimen is fixed in the dynamic holder. By adjusting the DC level of shaker2, the preload between the two contact specimens can be set. In this study, most of the tests havea 5 N preload.The two shakers with phase-locked signals control the dynamic specimen loading andprovide impacting, sliding, oblique impacting or combined impact/sliding motion. For puresliding tests, the two signals are phase locked at 2700.The original NRC plug-in dynamic specimen holder was for a spherical shaped specimen.Since tube wear is the main concern in this work, a tube specimen holder (see Fig. 3.4) that canbe fixed in the dynamic specimen holder was designed. The tube holder has self-aligningcapability for providing near perfect line contact. An isometric diagram of the self-aligning tubeholder is shown in Figure 3.4. It contains a main body and a self-aligning component, the mainbody slide fits into the ring shaped dynamic holder, and the self-aligning part with the mountedtube specimen is connected to the main part by two pins so that it can rotate freely for selfaligningChapter 3. Experimental Tests 40Y xEigure 3.2 NRC Fretting-Impacting Test RigShaker 1(displacement)Triaxial Load CellShaker 2(normal Load)Plug—in DynamicBall SpecimenStationaryDisc SpecimenFigure 3.3 Dynamic Holder For Sphere SpecimenChapter 3. Experimental Tests 41///////Tube SpeciMense1c—ALlgrngPartFigure 3.4 The Self-Aligning Tube HolderFigure 3.5 is a schematic diagram of the test system, The system consists of three parts:1. Input Parameter Control System: This system provides the signal for actuating the shakers. Itproduces the normal load and displacement signals from computer 1. The shape of the waveform,signal frequency and test duration can be selected. The attenuator is for adjusting the normal loadand displacement in the open-looped system. More recently, the open-looped system has beenconverted to a close-looped system with much improved control accuracy. Thus, the input fornormal load and displacement can be prescribed initially and controlled throughout the test withthe closed-loop system. For the present series of tests, the normal load is always a half sine waveand the displacement a full sine wave.2. Test Section: This part includes the test rig and signal sensors for monitoring the normal force,friction force and displacement. The force signals are conditioned with charge amplifiers. Thedisplacement limitation has been increased from 3mm to 6mm.///COMPUTERI,SIGNALGENERATIONCOMPUTER2.DATAAQUISIS11ONSYSTEMFigure3.5FullTestSystemSchematicDiagramt’Chapter 3. Experimental Tests 433. Data Acquisition System: Computer 2 is used to store and analyze the full-term test resultswith the help of an external 100 Mbyte hard drive. An improved version of the acquisitionsoftware has auto-triggering, adjustable sampling rate, selective sample length and force gainfunctions. The data acquisition system includes an analysis package that calculates severalparameters including the maximum, minimum, and average displacement, normal and shear force;average friction coefficient, number of running cycles, and the total frictional work. Figure 3.6shows an example of friction coefficient vs running cycles.Calibration of the data acquisition system has been performed by comparing the analyticalvalues with those obtained by the data acquisition. The differences were found to be less than2% for the normal force, shear force, displacement, and less than 3% for the total work input(sine wave frequency is 20 Hz, sampling frequency is 300 Hz).1-zwC)L1Iiw0(.)z0I.0L1BRASS #8 FRICTION COEFF,vs CYC.CYCLES(Thousands)Figure 3.6 Diagram of Friction Coefficient vs CyclesChapter 3. Experimental Tests 443.3 Test Conditions and Material Pmper(iesExcept where indicated, all tests were lubricated with diluted cutting fluid or with distilledwater. The test parameters - normal load, sliding distance, numbers of cycles for each test aregiven in Appendix A. Tables 3.1 and 3.2 list respectively the chemical compositions and themechanical properties of several materials of interest.In all tests, the tube material is Incoloy 800, the counterface materials are brass C360000or carbon steel 12L14 or stainless steel 410. The other material listed in Table 3.1 and Table 3.2will be discussed in Chapter 4. In earlier tests, alloy steel ball AISI 52100 (hardened to 64-66Rc, ground and polished) were used in place of the Incoloy 800 tube.Table 3.1 Chemical Compositions of MaterialsFe Ni Cr C AL Cu Pb Ti S Mn Si PC36000 60-6:0.15 0.15— 0.26— 0.85— 0.04—12L14 rest max 0.35 0.35 1.15 0.09A36 rest 0.2A 1fC’ ci r t 11.5— 0.15 0.03 1.0 1.0 0.04‘±l.Ji. es 13.5 max max max max max304S.S rest —io. 18—20 0.08 0.03 2.0 1.0 0.045Incoloy 39.5 0.1 0.15- 0.75 0.15- 0.015 1.5 1.0800 miri. 3035 1923 max 0.6 max 0.6 max max maxTable 3.2 Mechanical Properties of MaterialsUT Entongation Poisson Reduction Hardness Fatigue ,O EMPa MPa % Ratio in area MPa strength GPoC36000 400 310 25 50 136 Hv 235 140 MPa 8.5 g’12L14 540 415 10 35 200 Hv — — —A36 400— 20250410S.S 25 1225 14.5 63.5 315 Hv — 7.8 —304S.S 690 415 60 70 212 HRB 8.0 193Incoloy 517- 207- — — —800 690 i4 5030 0.339 220 Hv ‘28 MPa 794Inconel 552— 172—600 o 345 55—35 0.29 83 HRB — 310 MPa 842 207Chapter 3. Experimental Tests 453.4 Test Results3.4.1 Preliminaiy Test ResultsThese tests were carried out with an alloy steel ball sliding on a flat brass disc withcutting fluid lubricant at room temperature. These tests were an extension of previous studies[17]. It also served to familiarize the author with the testing techniques.Some of the early tests did not have properly recorded data. These results are thereforesomewhat confusing, and some of them do not repeat well (see Appendix A, Table A. 1). Figure3.7 also shows a rather random relationship between the total frictional work input and wear massloss. Since material from the brass disc has been found to have transferred to the alloy sphere,the mass change of the sphere was not considered.The results in Figure 3,8 show that under similar load and sliding distance wear increasesas the dilution of the cutting fluid lubricant is increased. It is suggested that better lubricant willreduce the frictional force and reduce wear damage for the same travelled sliding distance andnormal force.1.61.41- -EO.8O.60.4 —_______ _______ _______ _______ _______0.2 — — —— —II02 6 10 12WORK INPUT (N-rn)(Thousands)Figure 3.7 Total Frictional Work vs Wear Loss (Early Tests)Chapter 3. Experimental TestsC)6(1)(I)00.60.6Figure 3.8 The Relationship of Lubricant and Wear Loss3.4.2 The Line Contact Tests Between Incoloy Tubing and Bmss Flat46The line contact tests between a tube and brass flat were originally designed to investigateplasticity deformation under pure sliding conditions. The brass specimen is a disc with a convexstrip (Fig. 3,9), The tests were arranged into five groups, each group related to a certain lubricantcondition. And the results are listed in Table A.2.1.6-1.4- 10 20 30 40 50 60SUDING CYCLES(Thousands)— 1:40 —1:80 -*-1:20[j64o +E- WATERFigure 3.10 The Shape of Brass Specimen For Tube TestChapter 3. Experimental Tests 47Group 1 involved 7 tests at 100 N normal force and 2 mm sliding amplitude. All the testswere lubricated with the same dilution of cutting fluid. The purpose is to investigate therelationship between sliding distance and the amount of wear.Group 2 involved 4 tests at 100 N normal load and 1 mm sliding amplitude. The samelubricated condition as group 1 was used. The purpose is to study the effect of sliding amplitudeon wear (compared with the group 1).Figure 3.10 shows that the two groups of results almost coincide and that the slidingdistance vs wear relationship is linear.Group 3 included 9 tests each subjected to 300,000 sliding cycles and 2mm slidingamplitude. This group of tests is mainly for investigating the normal load and wear lossrelationship. Since the friction coefficient has a strong effect, the results have been averaged.Figure 3.11 shows a linear relationship between wear loss and normal load.Group 4 and group 5 are additional results. In the tests of group 1 to 4, there ismisalignment between the contact surfaces. After modification group 5 tests achieved almostperfect line contact.The preceding results provide some fundamental relationship between wear and some wearparameters. But it is important to note that these tests are subjected to the same lubricationcondition.Figure 3.12 shows an important relationship between wear and the total frictional work.It includes all of the “Incoloy tube-brass disc” tests. The linear relationship is an important resultfor pure sliding wear. An interesting finding is that the misalignment problem did not affect thelinear relationship between total frictional work and wear. It appears that the higher load side haddeeper wear, and the lower load side had shallower wear, the effect of misalignment wasaveraged out.Chapter 3. Experimental Tests 484--iizz77-DIS(I)C,)0-JI—I(0Ui—— group 1 (2mm) —I— group 2 (1mm)• TESTING DATA— REGRESSIONFigure 3.11 Normal Load vs Wear Loss3....‘ 2.5COC,)0 ‘_J ‘-I—I1.510.5U 100 200 300 400 500 600 700 800 900SLIDING DISTANCE (mm)(Thousands)Figure 3.10 Travelled Sliding Distance vs Wear LossTUBE & BRASS LINE CONTACTgroup 3(DILUSION I :500,2mm300000cyc.):6__-_ /75. 74- 7_____- vzz. . j‘-I1) 100 200 300NORMAL LOAD (N)400 500Chapter 3. Experimental Tests 49EC,,C,,C-JC,,U)WORK vs MASS LOSS• GROUP1-4 + GROUP5 —REGRESSIONFigure 3. 2 Total Frictional Work vs Wear Loss(Brass Disc With Incoloy Tube, Cutting Fluid)3.4.3 Line Contact Between Incoloy Tube and Stainless Steel DiscIn order to investigate tube wear performance, a series of tests has been carried out withIncoloy 800 tube sliding on stainless steel 410 disc with distilled water as the lubricant. Theresults are listed in Appendix A Table A.3.Since the disc material is relatively hard and the lubrication poor, the tube wear rate andfriction coefficient are much higher. For better control, lower normal loads have been applied (20N, 50 N, 80 N).Figure 3.13 shows the relationship between frictional work input and wear mass loss forboth the stainless steel disc and tube. The tubes have higher wear than the stainless discs, andthe relationship is close to linear.0t_+ 7;7J,________0 5 10 15 20 25WORK INPUT (N-rn)(Thousands)30 35 40 45Chapter 3. Experimental Tests 501.2+I —_______0.8 ± ±A0.2—0.—0 1000 2000 3000 4000 5000 6000WORK (N-rn)A disc wear + tube wear re9ression regJFigure 3.13 Total Frictional Work vs Wear Loss(Stainless Steel Disc With Incoloy Tube, Distilled Water)3.4.4 Line Contact Test Between Incoloy Tube and Carbon Steel FlatIn many CANDU steam generators, Incoloy 800 tubing and carbon steel support structuresare implemented, A simplified configuration of an Incoloy tube sliding on a flat carbon steel discwas used in this investigation. Two different lubricant conditions have been applied, the resultsare listed in Appendix A, Table A.4 and A.5.The tests with cutting fluid lubricant involved carbon steel discs with two different surfacefinishes. One set was ground to 1000 grit SiC paper finish and the other set to a 6 microndiamond finish. The relationship between mass loss and the total frictional work input is fairlylinear (see Fig. 3.14). The unpolished condition appears to have lower mass loss as a groupbecause the preload is lower ( average 4.5 N compare to the polished group 5 N in preload). Inthese tests, the tube become noticeably worn after hours of testing and the wear amount is easilymeasured. Figure 3.15 shows the approximate linear relationship between tube wear loss andfrictional work input.Chapter 3. Experimental Tests 51Figure 3.15 Total Frictional Work vs(Tube, Cutting Fluid)Wear LossCARBON STEEL DISC AND TUBE TESTWORK INPUT vs MASS LOSSEC,)C,,0C,,C)C,:0EC,)C,,0C,)C,,2— —--———--— --z‘.5.—zJ0.5 -— ———0 5 10 15 20 25 30 35 40 45 50WORK INPUT (N-rn)(Thousands)L UNPOUSHED DISC C POUSI-IED DISC — REGRESSIONFigure 3.14 Total Friction Work vs Wear Loss(Carbon Steel, Cutting Fluid)CARBON STEEL AND TUBE FRETTING TESTWORK INPUT vs MASS LOSS:z0.100 5 ib 15 20 25 30• 35WORK INPUT (N-rn)(Thousands)1- TUBE MTH C IE TUBEmi P) — -REGRESSION40 45 50U-unpolishedP-polishedChapter 3. Experimental Tests 523)Cl)Cl)0-JCl)Cl)uJ— carbon steel disc ± incoloy tube regressionFigure 3.16 Total Frictional Work vs Wear Loss(Carbon Steel With Incoloy Tube, Distilled Water)The tests with distilled water lubricant are only for the polished carbon steel discs. In thiscase, the tube wear rate is lower compared to the stainless steel disc cases. The relationshipbetween the frictional work input and tubing and carbon steel disc mass loss is quite linear (seeFig. 3.16).From the above study, a conclusion can be drawn: for all the material combinations testedin this program, wear has a linear relationship with the frictional work.CARBON STEEL DISC WITH INCOLOY 800 TUBEDISTILLED WATER0.0.80.7 —06— -0.5040.30.20.1- -+-—--± ±I00 2 4 6 8 10 12FRICUONAL WORK INPUT (N-rn)(Thousands)14Chapter 4Suiface AnalysisSurface analysis is a very important component in tribology research. The wear process,because of its complexity and small scale, is very difficult to observe. Analyzing the specimensurface after testing is one way to better understand the actual wear mechanisms. There are manysurface analysis techniques that include topographical analysis, microstructure analysis, andchemical composition analysis. With advanced modern instruments, more and more evidence hasbeen found for explaining the wear mechanisms, and helping to guide new research initiations.This chapter describes some observed surface phenomena from the sphere/disc testsamples, tube/disc test samples, and some of the AECL high temperature (265°C) worn tubesamples. In this study, Stylus Profilometer analysis, Scanning Electron Microscopy (SEM)analysis, Energy Dispersion X-ray (EDX) analysis, Electron Micro-Probe analysis and X-rayPhotoelectron Spectroscopy (XPS) analysis have been applied.4.1 Material TransmissionIn the tests of a steel sphere against a brass disc or Incoloy 800 tubing against a brass flat,certain amounts of brass were transferred to the contact surfaces of the sphere and tube. By visualexamination, it was observed that the worn sphere or tube surface had turned to a brassy colour.EDX analysis confirmed that the worn sphere surface had elements of brass coating (Fig. 4.1).Examination by SEM also showed that brass material adhered to the worn sphere surface (Fig.4.2). One explanation is that the softer brass wear particles were trapped between the contactsurfaces, and eventually forming an adhered layer on the spherical specimen surface afterrepeated passes.53Chapter 4. Suiface Analysis 54FeCuZnCrZnDark: unworn ball #114 (Fe, Cr)Light : worn ball #114 (Fe, Cu, Zn, PbPbFigure 4.1 EDX Analysis of Material Transmission (ball #114 )Figure 4.2 SEM Analysis of Material Transmission (ball #114 )Chapter 4. Surface Analysis 554.2 Plastic DeformationFigure 4.3 is a typical brass disc wear scar map after rubbing against a sphere. Along thesliding direction, brass material has been pushed forward to the front tip. On the worn surface,plastic flow can be observed by SEM as shown in Figure 4.4.Figure 4.5 shows the cross-section of an unworn area of a brass disc sample. After test,the specimen was sectioned, polished (0.05 .tm aluminum finishing) and etched to show theundeformed grains. Figure 4.6 is from the worn area, where the sample is sectioned along thesliding direction. The microstructure of the material has been highly deformed and strained in thesliding direction, especially near the surface area. It resembles that displayed in Rice’smorphological analysis [41J. He suggests a zone structure for describing the deformed grainstructure under repetitive load as illustrated in the schematic diagram of Figure 4.7. Zone 1,furthest from the contact region, consists of undisturbed base material. Zone 2, the intermediateregion, is plastically deformed. Zone 3 is usually homogeneous and very finely structured.At the edge of the worn surface (zone 3), grain boundaries can not be observed any more,instead, a very fine layer has been formed (Fig. 4.8). In Figure 4.8, some cracks can be seen,these cracks have been blunted by the soft nature of the material. In wear processes, fractureproblems do appear, but the crack behaviour is complicated by the changing material propertiesand cyclic forces.Using Hertzian contact equations for a sphere contact, the octahedral shear stress can bedetermined. Figure 4.9 shows, when s0.I64, the maximum shear stress is about 0.34 P0 locatedat a depth about z = 0.5 a. The related coordinate is shown in Figure 4.10.Another interesting investigation involved sectioning the worn area in the transversedirection, i.e. perpendicular to the sliding direction . Figure 4.11 shows the deformed grainstructure. Figure 4.lla and are the two edges of the contact zone, 4.llb is the contactcentre. Near the centre of the surface, the grains have been highly compressed, from round orlong shape to flat shape (Fig. 4.12).The reason why the micro-structure has this kind of change may be explained by therelated stress analysis. Figure 4.13 shows the shear stress field t,, which is on the plane that isC)Q0CDD CDo-#0-4fr+)CDQD23-t—.CD In’ Ci)O CD 0CD-4 CDCD ‘-4-I_4—NCDCD-CDCDCDi—V)o 0z..C)Qo CDCD-4 -t-CDJ)-00LI I.-t CD C’,C’, 0 CD C,,0 -iID oJ U aIl)-, CCDm -a a,—.C—3—. a, -Jzra0Chapter 4. Surface A nalysis 57k I- A!L1-.A —___Figure 4.4 Plastic Flow on Worn Brass DiscChapter 4. Suijace A nalysisOriginal Grain Boundaries of The Brass Disc58Figure 4.5Figure 4.6 The Deformed Grain BoundariesT1 CD 00 N C CD 1 00 CD (110 CD 01 CDI.///——,/1J/___________//-•1Chapter 4. Suiface A nalysis 60X/a—2.00 —1.50 —1.00 —0.50 0.00 0.50 1.00 1.50 2.00_0.00z/a 0.00_____—0.50- 0—1.00—1.00—1.50—0.50—1.50&0—2.00—2.00 -O7—2.50 —2.50—3.00 —3.00—2.00 —1.50 —1.00 —0.50 0.00 0.50 1.00 1.50 2.00Figure 4.9 Contour Plot of t01/ P0 for ji=0.164 (brass disc #114 )Psliding directionzy0 XFigure 4.10 The Coordinate Schematic DiagramSphereFigure4.11TheMicrostructureofY-ZPlane(forbrassdisc#114,perpendiculartotheslidingdirection)4.11a4.11bChapter 4. Suiface A iialysis 62— ).,;;_:i -;-_-‘ -.- . - - --- -Figure 4.12 Grain Deformation Near The Contact Centrey/a—2.00 —1.50 —1.00 —0.50 0.00 0.53 1.00 1.50 2.000.00 0.00a/a—0.50 —050—1.00 —1.00—1.50 —1.50—2.00 —2.03—2.50 —2.50—3.00 —3.00—2.00 —1.50 —1.00 —0.50 0.00 0.50 1.00 1.50 2.00Figure 4.13 Contour Plot of tP0 for i=0.164 ( brass disc #114 )Chapter 4. Suiface A nalysis 63y/a—2.00 —1.50 —1.00 —0.50 0.00 0.50 1.00 1.50 ZOO0.00 ‘1z/a- /0—0.50-0.500.00—1.00- —1.000—1.50 —0.30 ) 1.50—2.00 —2.00—2.50—2.50I—3.00 —3.00—2.00 —1.50 —1.00 —0.50 0.00 0.50 1.00 1.50 2.00Figure 4.14 Contour Plot of JP0 for .iO.164 (brass disc #114 )yfa—ZOO —1.50 —1.00 —0.50 0.00 0.50 1.00 1.50 2.000.00-0.50 7 —0.50z/a0.00—1.00 —1.00—1.50I0.O8—1.50—2.00 —2.00—2.50 —2.500•—3.00 —3.00—2.00 —1.50 —1.00 —0.50 0.00 0.50 1.00 1.50 2.00Figure 4.15 Contour Plot of afP0 for ii=O.164 (brass disc #114 )Chapter 4. Suiface A nalysis 644.3 Surface Profile vs Number of Sliding CyclesFor the Incoloy 800 tube/brass bar tests mentioned in the Chapter 3, group 1 has revealedthe relationship between wear mass loss and sliding distance (see Appendix A, Table A.2). Arelated series of photomicrographs clearly illustrates the surface condition due to repeated slidingwith a 100 N normal load.Figure 4.1 6 shows the profile of the original ground surface. After 9900 cycles of sliding,the surface has become smooth (Fig. 4.17).Figures 4.17 to 4.22 show the surface conditions under different sliding cycles. A surfaceroughness measurement has been performed for the group 1 samples by stylus profilometry. Theresults are listed in Table 4.1. There is no obvious relationship between surface roughness andthe number of sliding cycles.ç;.___ _______r.4Figure 4.16 Original Ground SurfaceChapter 4. Swface A iialysis 65Figure 4.17 Surface After 9900 Cycles (brass bar #1, 100 N )Figure 4.18 Surface After 30,000 Cycles ( brass Bar #2, 100 N )Chapter 4. Surface A nalysis 66• .b I- S. •* %. -4...- e’%SS%. -:_ St %‘Z4tJ N—-- - - — . • -v-‘o ‘ _%%. ‘‘—‘Figure 4.19 Surface After 60,000 Cycles ( brass bar #3, 100 N )2.s S “4Figure 4.20 Surface After 150,000 Cycles ( brass bar #4, 100 N )Chapter 4. Surface Analysis 67______Lç-Figure 4.21 Surface After 300,000 Cycles ( brass bar #10, 100 N )‘Figure 4.22 Surface After 450,000 Cycles (brass bar #6, 100 N )Chapter 4. Suiface A nalysis 68Table 4.1 Surface Parameters For Group 1 Brass SamplesNUM Cycles Ra Skewness Kurtosis Sigma1 9900 0.3007 0.8353 3.8973 0.3952 30000 0.2255 0.7891 4.1766 0.31043 60000 0.3375 0.8528 3.5627 0.44214 150000 0.375 0.7609 3.4136 0.494810 300000 0.5057 0.7781 3.4278 0.64926 450000 0.2886 0.793 3.8474 0.3711Table 4.2 Surface Parameters For Group 3 Brass SamplesNUM load (N) Ra Skewness Kurtosis Sigma11 50 0.4327 0.9301 4.1064 0.56655 100 0.3214 0.7426 3.5001 0.4147 200 0.4694 1.3255 5.4849 0.6738 300 0.2008 0.5951 0.3692 0.25669 400 0.2802 0.5811 3.1835 0.3583Chapter 4. Sutface A nalysis 694.4 Surface Profile vs Normal LoadThe relationship between surface profile and normal load has been studied with the aidof SEM. The samples are from the Incoloy 800 tube and brass flat test group 3 (see Table A.2).Table 4.2 lists surface conditions measured by stulus profilometry for group 3 samples. Figures4.23-4.27 and the data from Table 4.2 show no obvious relationship between normal load andsurface condition.Figure 4.23 Surface Under 50 N ( brass bar #5, 300,000 cycles )Chapter 4. Sui’face A nalysis 70Figure 4.24 Surface Under 100 N (brass bar #11, 300,000 cycles)Figure 4.25 Surface Under 200 N ( brass bar #7, 300,000 cycles )Chapter 4. Surface A nalysis 71:%%;.NFigure 4.26 Surface Under 300 N ( brass bar #8, 300,000 cycles )________-—----Figure 4.27 Surface Under 400 N ( brass bar #9, 300,000 cycles )Chapter 4. Suiface A nalysis 724.5 AECL High Temperntuw Worn Tube AnalysisKo studied tube fretting wear in high temperature (265°C) water using a CRNL hightemperature autoclave rig (Fig. 2.2) and found that the wear rate of the two different tube/tubesupport material combinations can differ by a factor of ten, even though their vibration levels arethe same [8].With curiosity, this author studied two tube samples that were from Ko’s previous hightemperature tests. One was a piece of Incoloy 800 tube that was tested for 120 hours with acarbon steel A36 ring in water at 265°C and 900 psi.. The other one was a piece of Incoloy 800tube that was tested for 30 hours with an Inconel 600 ring under similar temperature andpressure. The former had little wear and the tube surface appeared to be very smooth (Ra0,3 786 m, longitudinal), the latter had severe wear and the surface was very rough(Ra=1.9139 m, longitudinal). The sectioned surfaces showed that the tube tested with the carbonsteel A36 ring had no apparent microstructural disturbance near the worn surface (Fig. 4.28), butthe tube tested with the Inconel 600 ring showed significant microstructure deformation near theworn surface (Fig. 4.29).With the help of Dr. Matti Raudsepp at Department of Geological Science UBC, thechemical composition of a tube (tested with carbon steel ring) cross section was investigated witha Cameca 5x50 Electron Microprobe. Figures 4.30, 4.31, 4.32 and 4.33 are Ni, Cr, Fe and Mn,Al, Ti spectra respectively. The results show that for the tube/carbon steel combination, there isno obvious chemical composition change across the section in this case, tube wear only happenedat the very top surface.Usually the colour of the tube surface alters during high temperature tests. It is interestingto note that different tube/ring material combinations resulted in different tube surface colours.A XPS analysis has been done at the Department of Chemistry of UBC with help from Dr. PhilipWong. It was found that the worn tube surfaces were fully covered by oxide and the materialelement composition (Fe, Cr, Ni mainly) has been significantly changed. This result coincideswith Sture Hogmark’s AES analysis [13] (mentioned in chapter 2). Since the tube samples arerelatively old and not very well preserved, further investigation would not be fruitful. But twoChapter 4. Suiface A nalysis 73things are worth noting. First, at high temperature, heat exchanger tube wear has a strongeroxidation than at room temperature; second, further investigation of the kind of oxide formed atthe tube surface for each tube/ring material combination may lead to the understanding of whythe wear rates are different. This information may reveal more about the nature of the heatexchanger tube wear problem.Figure 4.28 Tube Section (tested with carbon steel A36 ring )Chapter 4. Surface A nalysis 74Figure 4.29 Tube Section (tested with Inconel 600 ring )SX-SpectraAcquisitionandPlottinglc,keu40.nfl4.0sT’41e7DaLe:1G-PY-92I I.Figure4.30TubeCrossSectionNiCompositionSpectrumINC7.STGLinearEraversespecLrumILeri1h:First.point.caordjnales:G8S22La5tpointcoordinates:69856602-88JISX-SpectraAcquisitionandPlotting1.keU4.nIHRCg.STGLinearLraverespectrum4.e6T’4167Dale:1G-rPY-92ILenthFir5lpoint.caordinot.e5:Lostpointcoordinates:Figure4.31TubeCrossSectionCrCompositionSpectrumSX-SpectraAcquisitionandPlotting1S.keU40.nflIMCS.STGLineortraversespectrumFigure4.32TubeCrossSectionFeCompositionSpectrum4.66T’416?Date:1G-IPY-92Ct t1Length:96.60MicronsStep:1.62Microna90Firstpointcoordinates:698926692-8€Countingtine:38€msLostpointtoordinotes:698526682-84-a -aFigure4.33TubeCrossSectionMn,Al,TiCompositionspectra‘ISX-Spectraflcqui5ltlonandPlotting1.keU4.nflINC8.STGLineartraversespeclrum4.6T/ 5A Model For The Heat Exchanger Tube WearIn spite of several decades of efforts, wear modelling remains one of the most challengingareas in tribology. A complete fundamental principle is not yet available. However, there is agreat demand for wear equations in engineering practice.For wear modelling, it is important to determine which of the many parameters have thegreatest effects on the wear system. Compromise has to be made at this stage. As a result, somesimple empirical models can be available for some special wear problems.In this chapter, some early models are analyzed for heat exchanger tube wear applications.Based on the heat exchanger tube wear phenomena, test results and previous studies, a model hasbeen proposed and discussed. The calculated results are well matched to the experimental results.In order to make this model more suitable for the engineering application, an extension to themodel has been made so that the tube life can be estimated and the tube/ring misalignmentproblem can be considered.5.1 Some Eaily Analytical ModelsMany wear models have been published, usually, for specific conditions. With due respectto the previous studies, some of these models have been applied to the heat exchanger tube wear.5.1.1 Archard Model AnalysisAs we mentioned in chapter 2, the Archard model is the most widely accepted adhesivewear model. It is in a very simple form:79Chapter 5. A Model For The Heat Exchanger Tube Wear 80V=k!Lwhere wear volume V is proportional to the normal load P and the travelled sliding distance L,inversely proportional to the softer material hardness H, k is a dimensionless constant whichcould be in a very wide range (from 10.1 to 10’°).In the heat exchanger tube/brass disc experimental tests, the wear amount is not alwaysproportional to the normal load. However, if the friction coefficient is a constant, wear volumedoes have the linear relationship with normal load. During the rubbing process, the frictioncoefficient varies (see Fig. 3.6), which may be caused by the change of wear surface topography,wear particles trapped between the contact surfaces, and the change in the lubricant filmthickness.5.1.2 Jam and Bahadur Model AnalysisThe Jam and Bahadur wear model [30] was proposed in 1980 for polymer wear. The keypoint is to assume that the fatigue failure of asperity interactions cause wear. They found that thecomputed steady state wear rates are in excellent agreement with the experimental results for thethree polymers tested [31]. It is worthwhile to test this model for its suitability for the heatexchanger tube wear problem.In chapter 2, the basic concepts of the model have been explained. In order to calculatethe wear amount for brass/tube tests, more detailed assumptions are added to the original model:1). Asperity heights have a Guassian distribution2). Both surfaces have a similar asperity distribution i.e.111=112, 11L1=2’ P1=P2 a1—02(where r is asperity density per area, 11L is linear asperity density, f3 is asperity radius, a isChapter 5. A Model For The Heat Exchanger Tube Wear 81asperity standard deviation, the subscripts 1 and 2 refer to the two surfaces in contact). Thisassumption can be explained by the conformity of the two contact surfaces.3). The distance between the reference plane of the surfaces in contact (Fig. 2.10) isassumed to be the mean asperity height, i.e. d=Ra.4). The failure stress corresponding to the application of a single cycle is assumed to bethe true fracture strength for necking [40], i.e.s- Go° (1- Area Reduction %)Detailed wear calculation for brass/tube specimen #1 is listed in the Appendix B. Theresults show a significant difference between the theoretical prediction and the experimentalmeasurement.Many factors might be responsible for this difference. The main reason could be thatmetal behaves very differently from a polymer. For example, metal wear profiles are verydifferent from that of the polymers (compare and TIL of the two cases). In the model, the bulkmaterial fatigue property has been used to judge the failure of asperities. But for metal, thecontact surface material property is very different from the bulk property. On the other hand, themeasurement of the surface parameters has become a significant problem, for instance, the samespecimen can have an asperity radius 174.8 im at 5 jim per sampling step, and a radius of 627jim at 10 jim per sampling step. This kind of problem has been pointed out by P.Gupta [47] inhis discussion of surface topography in 1978.5.1.3 Magel Model AnalysisIn this model, Magel applied Herzian line contact theory, shakedown theory and fracturemechanics to predict wear for a sphere sliding against a flat surface.Herzian line contact theory provides a good opportunity to describe the pressuredistribution and stress fields within elastic range. Shakedown theory allows the application ofelastic theory under small amount of plastic deformation. By combining the shakedown andChapterS. A Model For The Heat Exchanger Tube Wear 82Herzian theory, Magel can successfully predict the wear geometry of the indentation created bya sphere on a flat. But the prediction of the heat exchanger tube wear is claimed to besignificantly larger than the experimental results.The expression for predicting the amount of wear is given by equation 2.30, i.e.v=-vThis is a straight forward equation, the relationship among the parameters being quiteobvious.The difficult part is to get an accurate particle size v, and the energy to generate theparticle EIn order to remove the obstacle, Magel made the following assumptions1). cracks initiate and propagate at the depth Z of the maximum octahedral shear stress2) the energy input E required to form a wear particle of size A and thickness Z is equalto t>, A L1Magel calculated A as the scar area and Z by the location of the maximum octahedralshear stress. He assumed that applying energy E= t, A L can generate a wear amount v,A Z The evaluation of the wear amount is significantly higher than the experimental results.By looking into each step of the equations, the E/V ratio has been found to be very farfrom the testing evaluation.In reality, to generate observable wear, usually thousands of cycles are needed under mildnormal load with lubricant. Before fracture happens, a large amount of energy goes intogenerating heat and plastic deformation.Therefore, a relatively small amount of shear energy E= t AL1 can not generate wear volume v AZ. H.Vetz and J.Fähl discussed this phenomenain their early paper [43]. They described the energy absorbing process on a pair of metallicmaterials (Figure 5.1). They point out “The main energy term, at least for metallic materials,comes from deformation. The fracture energy is estimated to amount to only a few percent of thetotal absorbed energy”. This may explain why the calculated tube wear is much higher than thereal measurement.Chapter 5. A Model For The Heat Exchanger Tube Wear 83deformation energyformation of dislocation(stored deformation)thermal energyfracture energyproduction of newsurface (wear partictes(energy for secondary processesexot her micendofhermic Iribochemicial reactionsstructural transformationsresidual stressestribo sublimationtribe — luminescencetribo — emissionsmechanical oscillations,soundFigure 5.1 Schematic Diagram of Energy Distribution (ref.[43])5.1.4 Tin and Cheng Model AnalysisThe Lin and Cheng model is a dynamic wear model which permits the wear rate to varywith time. Therefore, it is able to explain the commonly observed running-in, steady-state, oraccelerated wear phenomena.The model can be expressed asw= c:UIChapter 5. A Model For The Heat Exchanger Tube Wear 84where W is the wear amount, L is the sliding distance, F is the forcing term which represents thewear causing agent, U is an antiwear strength term that represents the wear resisting agent, c isa nondimensional constant.The antiwear strength U is defined as the average material strength within a layer ofthickness h near the surface. For some simple cases, Lin and Cheng suggested that U can berelated to the measurable material property such as the hardness or the yield strength (seeequation 2.23). The average shear force is defined as the shear force averaged over a thin layerof thickness. Both F and U are time and wear dependent.Since this model includes time dependent parameters such as the shear stress t(x,y,z) andflow strength ö(x,y,z), for asperity involved conditions, the calculation could be rathercomplicated, especially when plastic deformation is also considered.This model has not been directly test proved. But by comparing the model calculation tosome experimental results obtained by others, the authors claimed that the model could give arather good wear prediction.5.2 Wear Phenomena and Test Results AnalysisIn spite of the complexity of the wear problem, some wear phenomena have beengenerally recognized and classified. The experimental results of this study have revealed severalrelationships among the wear parameters which provided the fundamental criteria of heatexchanger tube wear.5.2.1 Wear Volume and Sliding Distance“The longer the component used, the larger the wear.” is a common wear phenomenon.This phenomenon has been classified by Hirst and Lancaster [49]. Figure 5.2 shows severalpossible relationships between wear and time. Figure 5.3 is a typical wear-time curve which isgenerally recognized. There are three wear stages shown in Figure 5.3. Stage one is the running-in regime, in which wear and time relationship is nonlinear, usually it is the wear of type I, ofChapter 5. A Model For The Heat Exchanger Tube Wear 85which the wear rate is initially high but later decreases to a lower value. Stage two is the steadystate wear process. In stage two, the wear-time function is linear, i.e. type II of which the wearrate is a constant. Wear stage three is the accelerated wear regime, a catastrophic surface damagemay occur in a short time because wear increases beyond a critical wear value, usually it is thewear of type III, in which wear rate linearly increases.A curve that has a similar pattern to Figure 5.3 can be drawn from data presented inFigure 5.4 under the condition of constant load. Otherwise, the results can be in a randompattern as shown in Figure The Load and Wear RelationshipIn wear studies, load has been considered an important wear causing agent. For manywear cases, wear is proportional to the applied normal load. This has been described by theArchard model. For the heat exchanger tube wear tests, it is true only under a constant frictionalcoefficient conditions. Further data analysis shows, that under the same sliding distance andenvironmental conditions, the tangential load and wear relationship is linear (see Figure 5.5).TIME OR SLIDING DISTANCE0::TYPE IIITYPE IITYPE IFigure 5.2 Three Types of WearChapter 5. A Model For The Heat Exchanger Tube WearUFigure 5.486I — RUNNING—INII— STEADY STATEIII— ACCELERATINGI42’TIME OR SLIDING DISTANCEFigure 5.3 Three Regions of WearD5 ...: .3I2Li0 100 200 300 400 500.ThC (m)600 700 800 900Brass Discs Against Incoloy 800 Tubes Test ResultsChapter 5. A Model For The Heat Exchanger Tube Wear0,U,87Figure Wear StateThe Relationship Between Tangential Load and WearAs Figure 5.3 shows, the wear process experiences three stages. Running-in is an initialbreak-in period in which wear behaves differently from that during the steady state. At this break-in period, the wear system is in an adjusting stage, many variables such as surface topography,lubricant characteristics, near surface temperature, micro structure, and hardness change withtime. It has been reported [50] that running-in will depend strongly on the initial materialstructure and properties and on the surface conditions such as the surface finish and the natureof any film present. During this transition period, films may be destroyed or modified, thematerial may work-harden, phase transformations may occur, temperature will rise as a result offrictional heating, energy will be stored and the micro structure and surface topography willevolve toward a steady-state condition. All these changes affect the frictional coefficient.86—.———2010 20 30 40 50Frictional Load (N)60 70 80Chapter 5. A Model For The Heat Exchanger Tube Wear 88At steady state, wear variables will be relatively constant with time. Compared to therunning-in state, steady state last much longer. If one waits long enough, and if the design allowsthe achievement of steady-state conditions, any initial surface finish should evolve to the surfacefinish appropriate to steady state for the given system. The choice of initial surface finish mayaffect the time needed to achieve steady-state, but the same steady state should be reachedeventually.The third wear state is the accelerating stage. At this stage, wear failure is indicated.From the heat exchanger tube experimental observation, the steady state is the dominantstate. Running-in is not obvious (Figure 3.15-3.18). The third stage, i.e. the accelerate state, isnot considered here, because the application must be stopped at this stage to avoid severe damageto the heat exchanger tubes.5.2.4 HanlnessIn wear study, hardness is an important material property. For many cases, it is claimedthat wear is inversely proportional to the softer material hardness, such as in the Archardequation. In other literature, it has been found that wear hardness does not inversely propotionalto the material hardness [51].For the heat exchanger tube experimental tests, under similar testing conditions, higherhardness materials experienced less wear. However, tests with carbon steel 12L14 disc are theexceptions, since oxidation problems become another significant factor on wear.5.2.5 RoughnessThe effect of surface roughness on wear has been recognized for decades. However,mathematically describing the way it affects wear is still difficult, because different filmthickness, material, and speed have different interactions and effects.The majority part of the wear state for heat exchanger tube wear is steady state, in steadystate, the original surface condition does not affect wear (Fig. 3.17). But during the running-inChapter 5. A Model For The Heat Exchanger Tube Wear 89stage, the original surface finishing has a strong influence on wear. This is also observed inKnowles work [52].Table 5.1 shows some topography results from the heat exchanger tube test. It has beenfound that under similar grinding processes, harder material exhibit finer surface finishing, andno matter what kind of material the disc is, no matter what the original surface roughness the dischas, the Ra and a values of the disc and tube after wear are much the same. It indicates that thecontact surfaces finally reached conformity, i.e. the test reached the steady state.The surface roughness Ra and standard deviation a are relatively stable parameterscompared to other surface topographic parameters such as asperity radii.Table 5.1 Topographic ParametersOriginal IRa(umj4 Rg(umj Ra(um) [ Rg(um)Tube 03082424 0.425425— 4 —SS41 0 (S3) 0.074889 0.096151 1 .71 177 2.2893Tube — — 2.26346 2.8256512L14 (P8*) 0.136182 0.173356 0.567285 0.669829UnpolishedTube — — 0.44677 0.56463612L14 (P3) 0.037122 0.04482 1.37814 1.74464Polished &cutting fluidTube — — 1.29396 1.588681 2L1 4 (P8) 0.041937 0.050276 0.808337 0.996448Polished &WaterTube — — 0.74338 0.926871Brass Disc (B4) 0.195494 0.248733 0.291 606 0.377036Chapter 5. A Model For The Heat Exchanger Tube Wear 905.3 Modelling5.3.1 CiiteiaFrom the previous discussion, it is clear that the following parameters need to beconsidered for heat exchanger tube wear:A wear is proportional to the sliding distance LA wear is proportional to the frictional force FA wear may be inversely proportional to the material hardness HA the running-in stage is related to the topographyA at the steady stage, wear variables will be relatively constant with timeTherefore the wear equation can be written as(5.1)U Uwhere EF L.This is the Lin and Cheng wear model.5.32 DiscussionIn equation 5.1, each term has a certain physical meaning.The paremeter F is the frictional force, L the accumulated unit direction sliding distance(the backward movement is load free). Reciprocating sliding wear is not considered here. Inequation 5.1, both F and L are the external wear causing agents and both are measurableparameters. E may be viewed as the external energy input to generate wear.The parameter c is a non-dimensional wear coefficient which contains plenty ofundetermined information such as lubricant film thickness (external factor), material microstructures (internal factors) and the surface temperature, oxidation (both external and internalfactors). As previously discussed, at the running-in stage, these parameters are time dependent.Chapter 5. A Model For The Heal Exchanger Tube Wear 91Therefore, strictly, at the initial stage, c should be a time dependent function instead of aconstant. At the steady wear stage, these parameters are independent of time, thus c will be aconstant. Latter, the parameter c may be separated into many parameters or functions such asc=f1•f2f3••• f.The antiwear strength U is a wear resisting term. It represents the energy required togenerate a unit wear volume, similar to the term E/V in Magel’s model (i.e. equation 2.30). Ucan also be called a specific wear energy. Jahanmir [53] pointed out “the specific wear energyis composed of surface energy, cutting energy and plowing energy. The contribution of eachcomponent to the specific wear depends on the wear mechanism, but in most cases the plasticstrain energy for subsurface deformation predominates”. For the whole wear process, U is timeand wear dependent. At the running-in state, the wear system is in an adjusting stage, wearparameters vary with time, so that U changes until the two surfaces reach conformity. At theaccelerating state, the component is close to failure, the antiwear strength U decreases drastically.Some papers have considered that U is a function of material properties [53].5.3.3 EquationsEquation 5.1 simply describe the relationship of the wear causing agent and the wearresisting agent. More detailed calculation is based on further assumptions. Assumptions1. The material is simplified to be homogeneous and time independent2. At the running-in stage, the surface topography is the main factor to causenonlinear wear behaviour. In other words, the wear coefficient c is considered a constant.3. The asperity distribution is exponential i.e. the asperity height probability functionis4(z)=Aexp(—)z)Chapters. A Model For The Heat Exchanger Tube Wear 924. The asperity distribution at time t1 and t1+ is assumed to be the same, i.e.41(z) =4+1(z)5. The antiwear strength is defined asU=H/hf1 (z) dzIn these assumptions, z1 is the wear depth at time t, h is the thickness of the surface layerthat has been deformed elastically and plastically, H is the material hardness, 4(z) is the asperityheight distribution, c1(z) is the cumulative probability distribution. DenvationCombining equation 5.1 and the assumptions, at t1 the following equations can beestablished:E.V.=c— (5.2)IV1=Af’ (z) dz (5.3)(5.4)uj=-fz1+I (z) dz (5,5)Chapter 5. A Model For The Heat Exchanger Tube Wear 93v=y2v1 (5.6)where A is the nominal contacting area.If the asperity height probability distribution is exponential, then the cumulativeprobability function is(z) =fP(z)dz=1_ex(_Az) (5.7)From the definition of the exponential distribution, is related to the root mean squarea, i.e. ?1/a.Substituting the equations 5.3, 5.4, 5.5 into equation 5.2, it arrives at(z) dz=cF1iL1fZi+h(z) dz5.8wherecF.iL.K=HASubstitute equation 5.7 into equation 5.8 and integrate, the following equations can beobtained:Chapter 5. A Model For The Heat Exchaiiger Tube Wear 94(z1—z) + (exp(—).z1)—exp(—)z)=Kh/ ( (h+exp(-z)) (exp(-Ah) -1)/A)) (59)letthenexp(-A(z÷z))exp(—Az) —Aexp(-Az1z (5.10)Substituting equation 5.10 into equation 5.9, thenKb(511)(1-exp(-Az)) (h+exp(-Az1(exp(-Ah)-1))The antiwear strength can be written asUj=4fZ2(l_exp(_Az) )dz(exp(—Ah) —1)) (5.12)Chapter 5. A Model For The Heat Exchanger Tube Wear 955.4 Calculations5.4.1 Data InputTable 5.2 listed the original data input of the calculation for all the testing conditions.In this table, is the inverse of a. For two rough surface in contact, a=(a12+a)”then.i= 1/(a2+a2)112. Since the running-in stage is related to the initial surface topography, here, theunworn surface parameters a, (i=1,2) is used. H is the material hardness, A is the nominal weararea, c is an empirical wear coefficient, and h is the deformed depth of the material which canbe obtained by the observation of the cross section using SEM. In equation 5.11, z0 =0 is asingularity point, this problem comes from the original assumption of the exponential distributionof asperity height. For Gaussian distribution, this problem can be avoided, but the calculation forAz. is more complicated, detailed derivation is explained in Appendix C.Table5.2lntialInputDataHAhZoFTdL_i(1/rn)(N/m”2)(m”2)(m)(m)(N)(m)BrassQ.4928027x10”—61.3328x109i12.7x1O”—6305x1O”—5x10”—41x10—820Ox1O’—3SS41O14361552x10”—65087x10”91.75x10’’—6.376x10’—51x10—4ixlO”—82OOx10”—3Tube*).4361552x10”_—6.156x1O”9‘31.75x10”—6S.170x10’—5x1O—41x1O—8200x10”—312L14(W)**).4283855x1Q”—61.96Ox1O’931.75x1O”—61.592x10’—5?xlO”—4lxlO”—82O0x10”—3Tube*).4283855x10”—6.156x1O’91.75x10—61.078x10”—6x1O”—41x10”—8200x10—312L14(L)**p.4593895x10”—61.96Ox1O’91.75x10’—61.12x10”—5x1O—4lxlO”—8200x1O”—3Tube*J4593895xiq—6.156x1O”91.75x10”—64.68x10”—6x10”—4lxlO”—82002x10’—3ItubematerialisIncoloy800**W—waterlubricant,L—dilutedcuttingfluidlubricant.Chapter 5. A Model For The Heat Exchanger Tube Wear 975.4.2 Compatison and Diffeince AnalysisSeven groups of data have been calculated: brass disc wear, 410 stainless steel disc wear,Incoloy 800 tube wear (against SS41O discs), carbon steel 12L14 disc wear (with distilled waterlubricant), Incoloy 800 tube wear (against the 12L14 discs, with distilled water lubricant), carbonsteel 12L14 disc wear (with diluted cutting fluid lubricant), Incoloy 800 tube wear (against 12L14discs, with diluted cutting fluid lubricant).Figures 5.6 to 5.12 show the comparison of the calculated results to the testing results.The differences are described in Figures 5.13 to 5.19 respectively. Generally, the more significanterrors happen at regions of low frictional work. These errors are mainly due to the wear lossbeing too small to accurately measure. Even under accurately controled conditions, if the wearamount is too small, it is very easy to get significant error. Figure 5.17 is an exception, the wearunderestimation is caused mainly by oxidation which is not considered for running-in in thismodel. But for carbon steel case, oxidation is an very important wear mechanism, modificationis needed in future study. Fortunately, what we are really interested in the heat exchanger tubewear problem is long-term wear. From this point of view, the calculated results appears to beacceptable.Wear Volume Corn panson (theory vs test)brass disc vs Incofy 800 tube (brass disc) ::0.20.100-___H—------—.--_____ZE__20 30 40 50Thousandsfrictional work (N—M)theory • testFigure 5.6 Comparison of Brass Disc/Tube Test Results and Calculation Results(Brass Disc, Diluted Cutting Fluid Lubricant)Chapter 5. A Model For The Heat Exchanger Tube Weartheory * test98Figure 5.7 Comparison of SS41O Disc/Tube Test Results and(SS41O Disc, Distilled Water Lubricant)Calculated Resultsall0. Volume Comparison (theory vs test)ss4lO disc & Incoloy 800 tube (ss4IO disc).*0 1 2 3 4 5 6theory • testFigure 5.8 Comparison of SS41O Disc/Tube Test Results and Calculation ResultsWear Volume Comparison (theory vs test)ss4lO disc & Incoloy 800 tube (Incoloy 800 tube)0.150.10>0.0500 1 2 3Thousandsfrictional work (N—M)4 5 6Thousandsfrictional work (N—M)(Tube, Distilled Water Lubricant)Chapter 5. A Model For The Heat Exchanger Tube Wear 990.140.12.— 0.1$ 0.08V- Volume Comparison (theory vs test)12L14 disc vs Incoloy 800 tube (W) (12L14 disc).>0 5 10Thousandsfrictional work (N—M)theory • testFigure 5.9EEa)Figure 5.10Comparison of Carbon Steel 12L14 Disc/Tube Test Results andCalculation Results ( Disc, Distilled Water Lubricant)Comparison of Carbon Steel 12L14 Disc/Tube Test Results andCalculation Results ( Tube, Distilled Water Lubricant)15Wear Volume ComparIson (theory vs test)12L14 disc vs Incoloy 800 tube (W) (Incoloy 800 tube)0.0 150.010.00500 5 10 15Thousandsfrictional work (N —M)Chapter 5. A Model For The Heat Exchanger Tube Wearz0>CSC)_____________ ______________100Figure 5.11 Comparison of Carbon Steel 12L14 Disc/Tube Test Results andCalculation Results (Disc, Diluted Cutting Fluid Lubricant)Figure 5.12 Comparison of Carbon Steel 12L14 Disc! Tube Test Results andCalculation Results (Tube, Diluted Cutting Fluid Lubricant)Wear Volume Comparison (theory vs test)12L14 disc vs Incoloy 800 tube (L) (12L14 disc) 10 20 30 40 50Thousandsfrictional work (N—M)Wear Volume Comparison (theory vs test)12L14 disc vs Incoloy 800 tube (L) (Incoloy 800 tube)——p •. .410 20 30Thousandsfrictional work (N—M).theoiy • test40 50Chapter 5. A Model For The Heat Exchanger Tube Wear76CVCCVCCaI02VVE.C>aVC0.50Wear Volume Comparison (theory vs test)brass disc & Incoly 800 tube(brass disc)50101Figure 5.14 Difference Between Test Results and Prediction(SS41O Disc, Distilled Water Lubricant)0 10 20 30 40Thousandsfrictional work (N—M)Figure 5.13 Difference Between Test Results and Prediction(Brass Disc, Diluted Cutting Fluid Lubricant)Wear Volume Comparison (theory vs test)ss4lO disc0 1 2 3 4 5 6Thousandsfrictional work (N—M)Chapter 5. A Model For The Heat Exchanger Tube Wear2fl.5VV:: 10>V00.50Wear Volume Comparison (theory vs test)ss4lO disc vs Incoloy 800 tube (Incoloy 800 tube)102a)Ca)CCFigure 5.15Figure 5.16Difference Between Test Results and Prediction(Tube, against SS41O, Distilled Water Lubricant)Difference Between Test Results and Prediction(Carbon Steel 12L14 Disc, Distilled Water Lubricant)0 1 2 3 4 5 6Thousandsfrictional work (N—M)Wear Volume Comparison (theory vs test)12L14 disc vs Incoloy 800 tube (W) (12L14 disc)21.510.500 5 10 15Thousandsfrictional work (N—M)thoeryChapter 5. A Model For The Heat Exchanger Tube Wear 10312,l00I)0340020Wear Volume Comparison (theory vs test)12L14 disc vs incoioy 800 tube (W) (Incoloy $00 tube)Thousandsfrictional work (N—M)Figure 5.17Figure 5.18Difference Between Test Results and Prediction(Tube, against carbon steel disc, Distilled Water Lubricant)Difference Between Test Results and Prediction(Carbon Steel 12L14 Disc, Diluted Cutting Fluid Lubricant)0 5 10 15Wear Volume Comparison (theory vs test)12L14 disc vs Incoloy 800 tube (L) (12L14 disc)2i.sVVo 10>V4-00.500 10 20 30 40Thousandsfrictional work (N—M)50Chapter 5. A Model For The Heat Exchanger Tube Wear 1045.4.3.1 Running-InFrom Figures 5.6 to 5.12, a non-linear process is not observable This is because runnig-inhappens only at the very begining.Figure 5.20 shows wear rate (i.e. wear volume/sliding distance) decreases when slidingdistance increases (with constant frictional force). After a certain time, the wear rate becomes aconstant.Figure 5.21 shows antiwear strength U against sliding distance L. It describes how theantiwear strength changes before conformity.Wear Volume Comparison (theory vs test)12L14 disc vs Incoloy 800 tube (L) (Incoloy 800 tube)25)5)z 1C5,30.500 50Figure 5.19 Difference Between Test Results and Prediction(Tube, against carbon steel 12L14, Diluted Cutting Fluid Lubricant)5.4.3 Discussion10 20 30 40Thousandsfrictional work (N—M)KI(-‘44-z—‘ v—a.) 0IV(‘aChapter 5. A Model For The Heat Exchanger Tube Wear 105ss4lO(W) disc1546.215461545.81545.61545.41545.215451544.81544.60.3Figure 5.20 The Relationship Between Wear Rate and Sliding Distancess4lO(W) disc30775003077000307650030760003075500307500030745003074000307350030730000 0.05 0.1 0.15 0.2 0.25sliding distance L (m)0 0.05 0.1 0.15sliding distance L (m)0.2 0.25Figure 5.21 The Relationship Between Antiwear Strength and Sliding DistanceChapter 5. A Model For The Heat Exchanger Tube Wear 1065.4.3.2 a andFigure 5.22 shows the effect of a on antiwear strength U. As the surface gets rougher (aincreases), the antiwear strength U is smaller.Figure 5.23 shows the effect of h on antiwear strength U. When elastic and plasticdeformation goes deeper, which means more material is used to resist wear. For the samematerial, h increases, antiwear strength increases.comparisondifferent sigma’s (h= 10 urn)z_________ _________ _________ _________Q2—Ci2‘-4__ _ __ __ __ _ __ __ __ _ _ __ __a= 0.05 .tm/140013501300125012001150110010501000z_-\ a=2m0 0.1 0.2 0.3 0.4sliding distance (m)— sigma=0.OSum — sigma=0.3um — sigma=2umFigure 5.22 a Influence on Antiwear Strength UChapter 5. A Model For The Heat Exchaiiger Tube Wear 107cornparisondifferent h’s (sigma2 urn)14001350 ,,,.-h=300 .tm1300h=100 .tmz1250. c,1200j :10501000 I0 0.1 0.2 0.3 0.4sliding distance (rn)_h=lOum h=lOOurn _1i=300umFigure 5.23 h Influence on Antiwear Strength U5.5 Equation ExtensionThe previous model is for a tube sliding on a flat disc with a perfect alignment. It can beextended to a more realistic form for application to heat exchanger tube wear.As Figure 5.24a shows, D1 is the tube inside diameter, D0 is the tube outside diameter,B is the ring thickness. According to the observation of the worn tubes from the previous studyChapter 5. A Model For The Heat Exchanger Tube Wear 108(Fig. 1.4), the tube wear scar is almost uniform around the contacting area. If the worn depth ofthe tube is d, thenV=itDBd (5.13)whereD=D0-dSubstitute equation 5.13 into equation 5.1, i.e7tDBd=c—E’ (5.14)UIt is postulated that the tube has a critical worn depth d*, after this depth, further wearcauses unacceptable damage. In practice, the frictional force F, sliding amplitude are random. Inorder to simplify this problem, the averaged frictional force F8, calculated sliding distance L andthe averaged sliding speed u8 are used. Therefore, the external energy input for causing wear isE=Fa•L=Fa•Ua•t (5.15)where t is the contacting time.Substitute equation 5.15 into equation 5.14(5,16)itUDBChapter 5. A Model For The Heat Exchanger Tube Wear 109For the critical worn depth d*, the heat exchanger tube life T isT— (5.17)CFaUaFor the tube/ring misalignment case as shown in Figure 5.25, if B is contact width,the wear volume can become:v=itD4- (tanc÷ ‘ ) (5.18)2 tancwhere ct is the tilted angle, d is the wear depth.Let d=d*, and substitute the equation 5.18 into 5.17, the tube wear life istUDd (tan+ 1 (5.19)2CFaUa tangChapter 5. A Model For The Heat Exchanger Tube Wear hOFigure 5.24(a)RINGBTube/Ring Schematic Diagram(b)TUBEABCBWORN AREAWORN SCAR ON TUBE_________ ______CLCLFigure 5.25 Tube/Ring Misalignment Schematic DiagramChapter 6Conclusions and Further StudyIn this study, room-temperature tube/disc sliding wear has been investigated with the aid of atesting rig incorporated with improved systems of testing control and data acquisition.Quantitative relationships among wear and its parameters have been determined and a heatexchanger tube wear model has been proposed.The following is a summary of the main conclusions of this research work:1. Under constant load and similar frictional conditions, cumulative sliding distance and wearare related linearly. This is true for both the 2mm and 1mm sliding amplitude cases. As well,under constant sliding distance and similar frictional conditions, the relationship between wearand normal load is linear. Further more, under constant sliding distance, the tangential load andwear relationship is also linear.2. Frictional work, which equals frictional force times sliding distance, is proportional to wear.This has been confirmed for the tube/brass disc, tube/ss4lO disc, tube/carbon steel disccombinations under both diluted cutting fluid lubricant and distilled water lubricant conditions.3. Tube/ring misalignment does not appear to affect the above relationships. With same wearvolume, the higher load side will have deeper wear, the lower load side will have shallower wear.The effect of misalignment is averaged out.4. For alloy tube against brass disc, material transmission has been observed on the tube surface.For the sphere/disc tests, plastic deformation and cracks have been observed on the brass discsurface and its cross section. Stress analysis show a is the dominant stress to compress the111Chapter 6. Conclusions and Further Study 112material at the contact centre. Away from the centre, the shear stresses ;, play an importantrole.5. After wear, the roughness Ra and its standard deviation a of the tube and the disc are muchthe same. But surface topography analysis show that surface roughness neither directly relatesto the sliding distance nor to the normal load.6. At high temperature, with carbon steel A36 ring, the worn tube surface was very smooth, andthe sectioned surface showed no observable disturbance of the microstructure, there was noobvious chemical change across the section. This indicates that the tube wear happened at thevery top surface. With Inconel 600 ring, the worn tube surface was very rough, and the sectionedsurface showed microstructure disturbance. It is believed that for high temperature tests, oxidationbecomes an important mechanism for heat exchanger tube wear. An interesting low wear rate forcarbon steel 12L14 disc and Incoloy 800 tube combination has been found even at roomtemperature.7. A model for heat exchanger tube wear has been developed based on the wear model by Linand Cheng. The calculated results satisfactorily match the test results. This model has beenextented to predict tube life.8. At the running-in stage, the new model can dynamically describe the non-linear process. Atthis stage, wear rate decreases with time because the antiwear strength increases with time untilthe two contact surfaces reach conformity. The standard deviation a and the deformed materialthickness h are the two factors affect the antiwear strength. It has been found by analyzing thatfor the same material rougher surface weakens the antiwear strength, but as the deformedthickness h increases, the antiwear strength increases.Chapter 6. Conclusions and Further Study 113For engineering application, further studies may need to be carried out for the betterapproaches of the heat exchanger tube wear:1. High temperature and high pressure study. It has been found from the AECL hightemperature and high pressure tube/ring tests (Chapter 4), the worn tube surfaces are obviouslyoxidized, which is concordant to the Hogmark’s study. The investigation of this thesis is only forthe room temperature study, because of the limited facility. For the high temperature and highpressure application, modification is needed.2. Surface analysis. Under high temperature and high pressure condition, the worntube surfaces have different colour by the different ring material combination (Chapter 4). By thelimitation of the provided worn tube specimen, a complete surface analysis can not be carried out.However, a further detailed observation and surface analysis may lead to fruitful understanding,and the results may provide a fundation to consider oxidation and improve this model.3. Random process. In a real steam generator, the contacts of the heat exchangertubes and the support plates are random. From the investigation of this thesis, it has shown thatthe product of frictional force times sliding distance is proportional to the wear amount. In reality,the frictional force and the sliding distance are both random. Therefore, the further investigationof the behaviour of the frictional force and sliding distance as functions of time may benecessary.4. The improvement of the antiwear strength U. In this investigation, the antiwearstrength U only include the original surface parameter a and material hardness H. Other factorswhich affect the antiwear strength may need to be quantitatively analyzed.5. Slip amplitude. In this study, all the tests are under 2mm or 1mm sliding amplitudewhich are closer to sliding wear than fretting. This is mainly due to the limitation of the testfacility. In real heat exchanger tube wear, the sliding distance is much smaller. 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InternationalConference on Wear of Materials, ASME, 1977, pp 110-115.[24] Jeng, Y.R.,”Experimental Study of the Effects of Surface Roughness on Friction”, TribologyTransitions, Vol. 33-3, 1990, pp 402-410.[25] Wang, F.X., Lasey, P., Gates, R.S. and Hsu, S.M.,”A Study of The Rejative SurfaceConformity Between Two Surfaces in Sliding Contact”, J. of Tribology, Vol. 113,oct. 1991,pp 755-761.[26] Ward, R.,”A Comparision of Reciprocating and Continuous Sliding Wear”, Wear,Vol. 15,1970, pp 423-434.Bibliography 117[27] Bailey, D.M. and Sayles, R.S.,”Effect of Roughness and Sliding Friction on Contact Stress’,Journal of Tribology, Vol. 133, 1991, pp 729-738.[28] Kannel, J.W. and Hartnett M.J.,”Theoretical and Experimental Evaluation of Edge StressUnder Severe Edge Loads”, ASLE Transaction, Vol. 26, 1, 1983, pp 25-30.[29] Archard, J.F.,”Contact and Rubbing of Flat Surfaces”, J of Applied Physics, Vol. 24, 1953,pp 24.[30] Jam, V.K. and Bahadur, S.,”Development of A Wear Equation for Polymer-Metal Slidingin Term of the Fatigue and Topography of the Sliding Surfaces”, Wear, Vol. 60, 1980, pp237-248.[31] Jam, V.K. and Bahadur, S.,”Experimental Verification of a Fatigue Wear Equation”,Wear,Vol. 79, 1982, pp 241-253.[32] Timoshenko, S.P. and Goodier, J.N.,”Theory of Elasticity”, 3rd Edn., McGraw-Hill, NewYork, 1969, pp. 409-420.[33] Greenwood, J.A., and Williamson, J.B.P.,” Contact of Nominally Flat surfaces”, Proc. R.Soc. London, Ser. A, 295 (1442), 1966, pp.300-319.[34] Hamilton, G.M. and Goodman, L.E.,”The Stress Field Created by a Circular SlidingContact”, J. AppI. Mech., Vol.33(2), 1966, pp. 371-376.[35] Greenwood, J.A.,”The Area of Contact Between Rough Surfaces and Flats”, J.Lubr.Technol.,Vol. 89, 1967, pp. 81-91.Bibliography 118[36] Reznikovskii, M.M.,”Relation Between The Abrasion Resistance and Other MechanicalProperties of Rubber”, In DI. James (ed.), “Abrasion of Rubber”,Maclaren,London,1967,pp. 119-126.[37] Lin J.Y. and Cheng, H.S.,”An Analytical Model for Dynamic Wear”, Transactions of theASME, Vol. 111, July 1989, pp 468-474.[38] HaIling J.,”Principles of Tribology”, The Macmillan Press LTD. 1983[39] Johnson K.L.,” Contact Mechanics” Cambrige University Press, 1985[40) Garaham J.A, et al.” Fatigue Design Handbook”Society of Automotive Engineers Inc.,TwoPennsylvania plaza, New York, N.Y.10001, 1968[41] Mesterton-Gibbons Michael, “A Concrete Approach to Mathematical Modelling”, Addison-Wesley Publishing Company, 1989[42] Stephen L. Rice, Hans Nowotny and Steven F. Wayne,”Formation of subsurface Zones InImpact Wear”, Presented at the 35th Annual Meeting in Anaheim, California, May,1980[43] H. Uetz and J. Fôhl, “Wear As An Energy Transformation Process “, Wear, Vol. 49, 1978,pp 253-264[44] Ko, P.L., and Magel, E.E.,”Impacting and Sliding Wear in Steam Generators and HeatExchangers: New Experimental Test Rig and Wear Model”, ASME PVP vol. 154, pp63-70Bibliography 119[45] Whitehouse, D.J., “Surface Topography and Quality and Its Relevance to Wear”Fundamental of Tribology, Edited by Suh, N.P., and Saka,N., MIT 1978, pp 17-5[46] Stout, K.J., Watson,W., and King, T.G., “The Micro-Geometry of Lubricated WearClassification and Modelling” Fundamental of Tribology, Edited by Suh, N.P., and Saka,N., MIT, l978,pp83-99[47] Gupta,P., “On Surface Topography and Quality and Its Relevance to Wear”, Fundamentalof Tribplogy, Edited by Shu, N.P., and Saka, N., MIT, 1978, pp67-72[48] Quuin, T.F.J., “The Classifications, Laws, Mechanisms and Theories ofWear”, Fundamentalof Tribology, Edited by Suh, N.P., and Saka, N., MIT., 1978, pp477-492[49] Hirst, W., and Lancaster, J.K., “Surface Film Formation and Metallic Wear”, Journal ofallied Physics, Vol. 27, 1956, pplOS7-lO65[50] Rigney, D.A., “Introduction” of The Fundamentals of Friction and Wear of Materials, ASMMterial Science Seminar,oct. 1980,Pittsburgh, Pennsylvania[51] Richard, R.C.D., “The Maximum Hardness of Stained Surface and the Abrasive Wear ofMetals and Alloys”, Wear, Vol.. 10, 1967, pp-351-82[52] Knowles, G.D., “ Mechanisms of Wear Particle Formation and Detachment “,Master’sThesis, University of British Columbia, 1994[53] Jahanmir, S. “ On the Wear Mechanisms and the Wear Equations”, Fundamental ofTribology, Edited by Suh, N.P., and Saka, N., MIT. 1978, pp455-67.Appendix ATest ResultsTable A.3 410 Stainless Steel Disc and Incoloy Tube Test Results(Lubricated With Distill Water>num. N—load F—Load Dspl. T—Work D—Wear T—Wear(N) (N) (mm) (N—rn) (mg) (mg)s2 59.6 44.4 2.056 3427 0.37 0.79s3 29.3 22 2.056 1796 0.11 0.37s4 84 65.4 2.082 5437 0.31 1.05s5 52.7 41 2.042 2378 0.18 0.67s6 53.7 44.9 2.075 4793 0.24 0.76Table A.5 410 Carbon Steel Disc and Incoloy Tube Test Results(Lubricated With Distill Water)num. N—load F—Load Dsp!. CF T—Work D—Wear T—Wear(N) (N) (mm) (N—rn) (mg) (mg)p16 18.7 20.3 1,985 1093 1913 0.13 0.08p15 44 26.02 2.014 0.598 3238 0.29 0.08p17 82.5 41.5 2.015 0.504 4149 0.33 0,07p9 173.6 78.7 2.032 0.454 4742 0.48 0.06p19 170.9 82.8 2.04 0.485 8389 0.51 0.1p8 172.9 83,7 2.035 0.484 13509 0.92 0.0720Appendix A. Testing Data 121Table A.1 Sphere and Disc Test Results(Lubricated With Diluted Cutting Fluid)num. lub. cyc. N—load F—Load Dspl. wear(N) (N) (mm) (mg)89 1:40 2100 400 49.3 1.57 00990 1:40 9900 389 58.4 1.88 0.1491 1:40 30000 372 56.9 1.84 0.392 1:40 60000 394 62.2 1.97 0.5393 1:80 2100 325 44 1.51 0.194 1:80 9900 369 55.3 1.8 0.1497 1:80 9900 386 61.6 1.91 0.1395 1:80 30000 393 63 1.95 0.3496 1:80 60000 428 65.8 1.97 0.6398 1:80 60000 394 64.4 1.97 0.64102 1:320 2100 396 70.6 1.97 0.06101 1:320 9900 396 71.1 1.98 0.16100 1:320 30000 397 71.5 1.98 0.4299 1:320 60000 398 74.4 2 1107 1:640 2100 391 65 1.9 0.06105 1:640 9900 396 66.3 1.98 0.16106 1:640 9900 395 68.3 1.96 0,2104 1:640 30000 397 67.1 1.99 0.48123 1:640 30000 399 65.4 2.02 0.43103 1:640 60000 400 71.6 2 1.22124 1:640 60000 399 69.3 2 0.81115 1:1000 9900 396 61.1 1.95 0.16116 1:1000 30000 397 64 1.98 0.34132 1:1000 30000 394 65.6 1.92 0.2133 1:1000 30000 0.23134 1:1000 30000 384 53.7 1.9 0.22114 1:1000 60000 399 70.7 2 1.44117 1:1000 60000 398 69.5 2 0.62135 1:1000 60000 400 78.7 1.99 1.13136 1:1000 60000 399 66.7 2 0.42137 1:1000 60000 398 64.5 2 0.54119 1:1280 30000 0.36120 1:1280 30000 401 72.1 2.02 0.18118 1:1280 60000 400 67.5 2.01 1.23109 water 379 51.3 1.73 0.08110 water 393 60.1 1.9 0.19113 water 392 65.9 1.92 0.24111 water 397 65.2 1.99 0.66112 water 398 66.1 1.99 1.48108 dry 2100 16.42N.B.: specimen #121 ,#122,#133,#108,#1 19 are not recorded well.Appendix A. Testing Data 122Table A.2 Flat Brass and Incoloy Tube Test Results(Lubricated With Diluted Cutting Fluid)— num. N—load F—Coeff. Cyc Dspl. wear(N) (N) (mm) (mg)GROUP 1bl 100 018 9900 2 0.18b2 100 0.18 30000 2 0.33b3 100 0.2 60000 2 0.45b4 100 0.22 150000 2 1.06b5 100 0.24 300000 2 3.56blO 100 0.19 300000 2 1.74b6 100 0.2 450000 2 3.65GROUP 2b27 100 0.16 30000 1 0.17b26 100 0.17 60000 1 0.25b28 100 0.15 105000 1 0.48b29 100 0.16 150000 1 0.64b30 100 0.17 246000 1 0,95GROUP 3bli 50 0.25 300000 2 1.09blO 100 0.19 300000 2 1.74b12 100 0.19 300000 2 1.58b7 200 0.2 300000 2 5.03b13 200 0.17 300000 2 2.81b8 300 0.22 300000 2 6.16b14 300 0.24 300000 2 5.99b9 400 0.18 300000 2 7.76b15 400 0.19 300000 2 6,7GROUP 4b17 100 0.17 30000 2 0.35b19 100 0.17 30000 2 0.36b20 100 0.18 30000 2 0.34b21 100 0.19 30000 2 0.45b22 100 0.16 30000 2 0.22b23 200 0.14 30000 1 0.13b24 200 0.16 30000 2 0.6b25 100 0.18 80000 2 0.62N.B.: specimen #16, #18, #31 are not well controled.Appendix A. Testing Data 123Table A.2 continuedGROUP 5nurn. N—load F—Load F—Coeff. Cyc. OspI. T—Work wear(N) (N) (N) (mm) (N—rn) (mg)#4 92.35 16.61 0.18 3624 1.858 102 0.09#5 82.83 15.2 0.18 10008 1.881 258 0.29#2 96.58 18.77 0.19 60000 1.949 1945 0.8#8 192.5 29.97 0.16 60000 1.963 3178 0.9#7 98.6 19.38 0.2 150000 1.81 4137 0,98#9 285.9 40.59 0.14 60000 1,977 4406 1.25#6 153,6 23.14 0.15 149906 1.936 5897 1.31#10 388.5 54.73 0.14 60000 1,973 5774 1.53#3 97.71 17,57 0.18 450000 1.968 12983 1.88N.B.: specimen 1 is not recorded.Table A.4 410 Carbon Steel Disc and Incoloy Tube Test Results(Lubricated With Diluted Cutting Fluid)num. N—toad F—Load Dspt. CF T—Work 0—Wear T—Wear(N) (N) (mm) (N—rn) (mg) (mg)p*1 186.5 27.04 2.165 0.145 3228 0.04 0.06p*2 359.8 43.84 2.305 0.121 5476 0.05 0.04p*3 430.4 44.42 1.319 0.103 3019 0.02 0.04p*4 100.3 15.8 1.915 0.158 1653 0.01 0.03p*5 191.6 30.91 1.915 0.161 8306 0.03 0.05p*6 287.8 40.96 1.869 0.142 10693 0.19 0.05p*7 99.05 16.88 1.926 0.17 4551 0.01 0.01p*8 388.4 46.43 1.887 0.119 11797 0.2 0.13p*9 238.1 33.52 1.935 0.141 9007 0.14 0,1p11 190.7 27.64 1.861 0.145 7209 0.27 0.12p*10 193.3 32 1.862 0.166 24470 0.77 0.39p*12 394.7 55.79 1.782 0.136 33897 1.34 0.49p10 190.8 32.24 1.868 0.169 24523 0.99 0.44p5 92.94 18.62 1,837 0.201 13855 0.94 0.35p1 299.2 48.12 1.954 0.161 33236 1.64 0.65p2 395.7 57.59 1.865 0.148 42976 1.91 0.74p3 390.6 57.42 1.727 0.147 47016 2.07 0.86p7 190.2 31.03 1.892 0.16 13281 0.72 0.28p10 190.8 32.24 1.868 0.169 24523 0.99 0.44p11 390.2 56.65 1.775 0.145 30280 1.39 0.49p12 288.5 44.27 1.923 0.151 19259 1.05 0.32p13 298.1 43.7 2.02 0.147 14977 0.56 0.24pi4 306.4 53.69 2.104 0.135 9583 0.67 0.08*for unpalihed carbon teeI disc.Appendix BCalculation of Jam and Bahadur ModelIn order to examine the availability of Jam and Bahadur wear model for heat exchangertube wear, a specimen of brass C36000 disc/Incoloy 800 tube test is analyzed. The specimen isfrom the brass disc #1.1. Matezial PnpertiesLi Tn.ze Tensile Strength For FractureFor brass C36000 disc, aT=380 N/mm2,Area Reduction=52%, thens=__ p =__________0Atrue A0 (1 -AreaReduc ti on%) (1 -AreaReducti on%)S0=791. 67N/n2m21.2 Fatigue Strength PrepertyFor the material C36000, fatigue strength=140 MPa at io cycles.From equation 2.14, parameter t can be obtained asigNlgS0—lgS124Appendix B. Calculation Of Jam and Bahadur Model 1251.3 Equivalent Young’s Modulus E’brass, E1= 97 GPa, y1= 0,3tube, E2= 196.5 GPa, 0.339From the equation 2.52 2____+ )=72.017E3 N/mm2E22. Test ParametersFrictional Coefficient ji=0.18Travelled Sliding Distance L19800 mmNominal Contact Area A=7.36 mm2Normal Load P100 NSliding Speed u=80 mm/sSurface Roughness Ra=d=0.3007 urnStandard Deviationa1=0.3950 jim, a=0.5586 p.mAsperity Radius 13=0.175 mm (0.5 jim for sampling step), f3=0.0875 mmh=d/cy=0. 54Line Density of Asperities (longitudinal) rlL2.4 (1/mm)Line Density of Asperities (transverse) rjT=28 (1/mm)Area Density of Asperities 11 rjl= 67.2 (1/mm)From the Table Al of the reference [31]F1(0.54) = 0.186132, F312(0.54) /F1(0.54)= 0.98084Appendix B. Calculation Of Join and BahadurModel 126F0(0.54) = 0.294794, F0(0.54) /F1(0.54)= 1.58379F312(0.54) = 0.1825663. Calculation of Wear Particle Volume VpIn the reference [31], Vp is defined as a flattened sphere (special case of ellipsoid)where the radius of the spherical portions of the particle was taken equal to the radius of adiscrete contact zone. Thus, the volume of a particle is given by2where a is the radius of a discrete contact zone and c is the thickness of a wear particle.Assume the half maximum particle height above Ra is c which can be obtained fromthe bearing ratio curve c = 0.7 jim.From the equation 2.12, the radius a can be determined.p 1/2a=(F0(h)/F1)) =5.555E—3mm17=45 . 24E-9rnm34. Final Calculationk1=j.L( 4±y) l-2y..0437Appendix B. Calculation Of Jam and Bahadur Model 127From the equation 2.8P=33.854 NFrom the equation 2.19K1=23.4 E6 (1/mm2)The calculated wear volume is=K1PLVPk =470 .038 (m&)2S0Since the material density is p 8.5 (mg/mm3), the measured wear volume isv= 0.18mg =0.021(mm3)8. 5mg/mm3The difference is significantAppendix CEquations for Gaussian DistributionFor zero mean Gaussian distribution,the distribution function is1 exp(-———)2awhere a is the sdandard deviation.The cumalative probability function of the asperity height is(z) =f Zci (z) dz=fZ 1 exp dz- -/7Ja 2aSince about 99.9 per cent of all events lie within ± 3a, therefore, in practice, thedistribution curve is truncated to finite limits. ThenE,z 1 z2exp(-———)dz2aSubstitute I(z) and z÷1= z1+ into the equation 5.8pz.+z. j’ zJ U ti?(z)dzdz=ZI fzi÷hf: (z) dzdz128Appendix C. Equations for Gaussian Distribution 129When zz1 is small, thenzjfZcz)dz=30 (z) dzdzTherefore,Khj.zJ 4(z)dzj j 4(z)dzdz—30 z1 —3awhere1 z2exp(—----—-)2aandH1’Z÷h.Z 1U1 =— I I exp C-——) dzdzh1 J-3a1/0 202


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