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Optimization of a cutter wheel bearing

Optimering av lagring till cutterhjul

William Fagrell

Faculty of Health, Science and Technology

Degree Project for Master of Science in Engineering, Mechanical Engineering

Points: 30 hp

Supervisor: Anders Gaard

Examiner: Jens Bergstrom

Date: July 5, 2020

Abstract

This Master’s thesis project was provided by Epiroc Rock Drills AB and conducted at CamatecIndustriteknik AB in Karlstad, Sweden. The project is centered around the cutter wheel inthe mechanical rock excavator Mobile Miner 40V. This cutter wheel is equipped with cutterdiscs that grind rock into debris as the wheel rotates and thrusts forward. The internal systemconsisting of a bearing constellation and the components in its vicinity has experienced acertain degree of wear in the form of scuffing and this was detected on the surfaces of someof the components in the system. The reasons for this occurrence are unknown and per therequest of the thesis provider, this was to be determined. The thesis provider also requesteda new Finite Element Analysis (FEA) model of the system along with feasible load cases thatcan be applied to said model. The project was deemed extensive and was therefore decidedto be conducted by two students. This thesis covers the determination of the load cases aswell as the optimization of the current design of the system inside the cutter wheel.

During the pre-study, relevant background data was obtained for the cutter wheel and theinternal system. Methods and models considered to potentially be useful were also gathered.The system in question was divided into two separate models; one consisted of a tribo-systemwith two components in sliding contact and the other consisted of the bearing constellationalong with the outer-most section of the cutter wheel. The purpose of the first model wasto use it to determine the contact pressure between the tribo-surfaces and by doing so, beable to determine the expected lubrication regime for the oil in the tribo-system. A materialselection process was also conducted on the tribo-surface that had experienced the mostsevere surface damage. Additionally, minor reconstructions were made with the purpose ofoptimizing the system. The purpose of the second model was to apply the calculated loadcases to the cutter disc attachments located on the outer-most section of the cutter wheeland then determine the contact pressures that develop on the bearing roller elements.

The results of the thesis work consist of five potential material options, two reconstructionsand 60 different load cases for the FEA model. With the load cases, the largest contactpressures on the bearing roller elements was determined. In addition, the cause of the severesurface damage that had occurred in the system is believed to have been identified. Furtherwork on the project work is believed to be required. Future work of interest are determiningload cases that incorporate multiple cutter discs simultaneously in contact with the rock,reconstruction solutions for the oil inlet and outlet pipes, a more thorough materials selectionprocess and a criterion for the expected lubrication regime in the tribo-system based on testsperformed with materials that are more identical to the ones in this project.

Keywords: Mechanical rock excavation, cutter wheel, cutter disc, reaction force, contactpressure, scuffing, wear

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Sammanfattning

Detta examensarbete tillhandaholls av Epiroc Rock Drills AB och genomfordes hos CamatecIndustriteknik AB i Karlstad, Sverige. Projektet ar centrerat kring cutterhjulet i maskinenMobile Miner 40V som ar avsedd for mekanisk bergavverkning. Cutterhjulet ar utrustatmed cutter discar som maler berget till mindre flisor genom att hjulet roterar och trycksframat. Det inre systemet bestaende av en lagring med narliggande komponenter har utsattsfor en viss grad av notning i form av scuffing och detta upptacktes pa ytorna hos vissa avkomponenterna i systemet. De bakomliggande anledningarna for denna forekomst ar okandaoch utifran begaran fran projektgivaren skulle dessa anledningar faststallas. Projektgivareneftersokte aven en ny FEM-modell av systemet tillsammans med rimliga lastfall som ska kunnaappliceras pa modellen i fraga. Projektet ansags tamligen omfattande och det bedomdes darforatt tva studenter kravdes for att genomfora arbetet. Denna uppsats behandlar framtagningenav lastfallen saval som optimeringen av den nuvarande designen av systemet inuti cutterhjulet.

Under forstudien hamtades relevant bakgrundsdata for cutterhjulet och det interna systemet.Metoder och teorier som ansags vara potentiellt anvandbara samlades aven in. Systemeti fraga delades in i tva separata modeller; en bestod av ett tribo-system bestaende av tvatribo-ytor i glidande kontakt och den andra bestod av lagringen tillsammans med den ytterstasektionen hos cutterhjulet. Syftet med den forstnamnda modellen var att anvanda den foratt bestamma kontakttrycket mellan tribo-ytorna, och genom detta kunna faststalla denforvantade smorjningsregimen hos oljan i tribo-systemet. En materialvalsprocess utfordes avenfor tribo-ytan som hade utsatts for den mest allvarliga skadan. Aven smarre omkonstruktionerutfordes med syftet att optimera systemet. Syftet hos den andra modellen var att kunnaapplicera de beraknade lastfallen pa cutter discarnas infastningar som aterfinns i den ytterstasektionen hos cutterhjulet och sedan bestamma kontakttrycken som uppstar pa rullarna ilagren.

Resultaten fran arbetet bestar av fem potentiella materialval, tva konstruktionsandringaroch 60 olika lastfall for FEM-modellen. Genom att applicera lastfallen bestamdes de storstakontakttrycken pa lagrens rullar. Utover detta anses det att anledningen for den allvarligaytskadan som hade skett i systemet har identifierats. Det anses att fortsatt arbete kravsfor projektet. Kompletterande arbete som anses vara av intresse ar lastfall som inkluderarflera cutter discar i ingrepp samtidigt med berget, konstruktionslosningar for tillforsel ochbortforsel av oljan, en mer djupgaende materialvalsprocess och ett kriterium for forvantadsmorjningsregim hos tribo-systemet baserat pa tester utforda med material som ar meridentiska med dem som forekommer i projektet.

Nyckelord: Mekanisk bergavverkning, cutterhjul, cutter disc, reaktionskraft, kontakttryck,scuffing, notning

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Acknowledgements

Firstly, I would like to express my sincere gratitude to Epiroc Rock Drills AB for providingsuch a challenging, interesting and, above all, fun thesis project. I would also like to thankCamatec Industriteknik AB for the opportunity to conduct this project and for providing astimulating working environment with helpful people as well as software licenses. Thanks toJoakim Bengtsson, Jonas Andersson, Daniel Wannlund and Michael Olofsson for the helpthroughout the project work. A special thanks to Goran Karlsson for providing the necessarydata and information regarding the project and for taking the time to assist whenever it wasneeded. Lastly, a huge thank you to my supervisor from Camatec, Peter Wigarthsson, for thevaluable advice on how to approach the project and for the interesting conversations abouteverything from boundary conditions in Ansys to string theory.

I would also like to thank my supervisor from Karlstad University, Anders Gaard, for thelengthy conversation about tribology and for providing guidance in the writing of this report.

Finally, a huge thanks to Kebin Xie for your hard work and for conducting the thesis projectwith me.

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Contents

Abstract i

Sammanfattning ii

Acknowledgements iii

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Declaration of confidentiality . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.6 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Theory 52.1 Contact mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Equivalent static force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Centripetal force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.4 Sliding wear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4.1 Lubrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.5 Rolling wear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.6 Models for determining load cases in mechanical excavation machines . . . . 14

3 Method 183.1 Project plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 Background data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3 Establishing useful theories and models . . . . . . . . . . . . . . . . . . . . . 203.4 FEA model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.5 Determining the load cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.6 Construction alterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.7 Materials selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4 Results 374.1 Scuffing between Component 1 and Component 2 . . . . . . . . . . . . . . . 37

4.1.1 Determining the expected contact pressure . . . . . . . . . . . . . . . 374.1.2 Expected lubrication regime . . . . . . . . . . . . . . . . . . . . . . . 424.1.3 Dry sliding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2 Load cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3 Construction alterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

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4.4 Materials selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5 Discussion 595.1 Scuffing between Component 1 and Component 2 . . . . . . . . . . . . . . . 59

5.1.1 Density of Component 1 in Ansys . . . . . . . . . . . . . . . . . . . . 595.1.2 Centripetal force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.1.3 Oscillating impact motion and dynamic impact factor . . . . . . . . . 605.1.4 Sliding/impact model and equation . . . . . . . . . . . . . . . . . . . 605.1.5 Generalised Stribeck curve . . . . . . . . . . . . . . . . . . . . . . . . 615.1.6 Low contact pressure - dry sliding . . . . . . . . . . . . . . . . . . . . 615.1.7 Surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 Load cases for the C-model . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.2.1 CSM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.3 Materials selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.4 Construction alterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.5 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6 Conclusion 69

References 70

Appendix A 75

Appendix B 76

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1 Introduction

1.1 Background

Camatec Industriteknik AB is a consultancy engineering company with expertise in severaltechnical areas. One of their costumers is the company Epiroc Rock Drills AB, one of theleading productivity companies in the mining and infrastructure industries. Mining is aprocess where different types of rock are excavated through the use of various techniques.The four basic mechanisms include spalling, fusion and vaporization, mechanical stress andchemical reactions [1]. Mining is performed with two purposes. One is to create tunnelsor networks of tunnels in which people and vehicles can be and travel through. The otherpurpose is to extract elements, minerals or other objects from the rock being excavated.Before the industrialisation age, mountain rocks were excavated either by hand with primitivetools or with black powder. With new inventions, machine-driven devices were introducedand black powder was replaced with dynamite [2].The use of explosives cause vibrations and residual stresses in the rock, which in turn increasesthe need for rock reinforcement. Because of this, there is a high market demand of mechanicalrock excavation means that are at least as effective as the use of explosives. In order to fillthis need, Epiroc have developed the machines in the Mobile Miner series. The machinesin this series are reminiscent of Tunnel Boring Machines (TBM), but with some differences.Due to their design, the machines in the Mobile Miner series have higher steering flexibilityin comparison to TBMs because of their smaller turning radius. When using explosives toexcavate tunnels, a number of different machines have to be used in order to complete certaintasks. There needs to be loaders and trucks for the gathering and transportation of rockdebris, as well as machines for rock reinforcement. However, the machines in the MobileMiner series implement these separate functions into one unit, which makes continuousoperation possible and thereby vastly increasing efficiency. The machines excavate rock withthe use of a large rotating cutter wheel equipped with cutter discs that grind the rock intodebris. Depending on the model, the cutter wheel is oriented either horizontally or vertically.In the Mobile Miner 22H the cutter wheel is oriented horizontally, providing a tunnel heightas low as 2.2 meters. In the Mobile Miner 40V the wheel is instead oriented vertically, whichprovides a tunnel height of 4 meters. Illustrations of the two Mobile Miner machines areshown in Figure 1.1.

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(a) The Mobile Miner 22H [3]. (b) The Mobile Miner 40V [4].

Figure 1.1: Illustrations of the two mentioned machines in the Mobile Miner series.

The thesis work presented in this report has been conducted on the cutter wheel of the MobileMiner 40V, see Figure 1.2.

Figure 1.2: Mobile Miner 40V cutter wheel.

1.2 Problem description

Inside the cutter wheel is a hydraulic motor that drives the wheel, as well as a bearingconstellation consisting of a radial bearing with a thrust bearing on both sides. Currently, thedesign of the cutter wheel assembly is not optimal as there is a presence of wear within theconstruction that occurs at a rate that exceeds what is considered acceptable. The bearings inthe bearing constellation and a number of components in contact with them contain surfaceswhich, to different degrees, have been exposed to tribological phenomena such as scuffing.The phenomena scuffing is characterized by macroscopically observable changes in the surfacetexture, with features related to the direction of relative motion [5]. In this particular case,

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the presence of scuffing has led to severe chip formation, which in turn has affected adjacentsurfaces and caused them to wear unexpectedly fast. The hydraulic system that provides thefeed of the lubricant oil is also affected by the chip formation. In Figure 1.3, two surfacesthat have undergone different degrees of scuffing are shown.

(a) Surface showing severe scuffing damage. (b) Surface showing less severe scuffing.

Figure 1.3: Severe surface wear indicating that scuffing has occurred.

The current design of the cutter wheel was developed with the use of a Finite ElementAnalysis (FEA) model using different load cases. However, test running of the machine in theKvarntorp Mine in Orebro yielded unexpected results in the form of high wear, as mentionedearlier. The thesis project providers therefore believe this indicates that the numerical modelused as validation when developing the current version of the machine contains an unknownamount of discrepancies. As of today, it remains unknown if it is the FEA model that isinadequate, or if it is the assumed load cases or a combination of both. Hence, because ofthis, it is desired that the work presented in this report leads to an altered construction ofthe cutter wheel with a longer expected life-time compared to the current design. The newconstruction is to be based on a new FEA model along with applied load cases that bettercorrespond with expected realistic load cases.

1.3 Purpose

The purpose of this project is to obtain a better understanding of why the system in the cutterwheel has been worn the way it has and using this new knowledge, try to work out solutionsto improve the system’s performance. The FEA model with assumed load cases developedduring the project work is expected to provide a theoretical basis for the mechanical influencesthat affect the system as the machine is operating. Given that the working principle withmachines in the Mobile Miner series diverges considerably from traditional mining operationssuch as the use of explosives, and to a lesser extent TBMs, they could potentially offercostumers more value compared to the other alternatives.

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1.4 Goal

The project consists of two sub-goals that need to be achieved in order to reach the maingoal. One of the sub-goals consists of developing an FEA model containing the relevant partsin the cutter wheel in the software Ansys. It should be possible to make changes to theconstruction of the individual parts so that the user may test how these changes affect theresults of the simulations. Another sub-goal consists of establishing a feasible estimation ofthe directions and magnitudes of the forces working on the cutter wheel in a realistic setting.Given that the thesis providers are interested in learning about how the worst-case scenariosshould affect the cutter wheel, it is relevant to include a combination of the most extremeloads in the estimation of the load cases. By accomplishing these sub-goals, the main goalcan then be achieved. The main goal of this project is to establish the reason or reasonswhy components in the system have suffered such serious surface damage and then, with thisknowledge, optimize the current design of the cutter wheel so that the expected life-time ofthe machine increases as much as possible. This includes conducting construction alterationsto one or several components in the vicinity of the bearing constellation, making appropriatematerial selections where it is deemed necessary and designing to ensure that contact surfacesare sufficiently lubricated during operation.

1.5 Declaration of confidentiality

Epiroc have expressed the need for the author of this Master’s thesis and K. Xie [6] to notdisclose specific details about components that have failed in the machine. For this reason,classified components will not be referred to with their actual names and will be illustratedin the form of simplified models in this report.

1.6 Delimitations

• The rock wall was approximated as an ideally smooth half-space.

• The ground upon which the Mobile Miner 40V is standing was assumed to be ideallysmooth and horizontal.

• The load cases were determined by assuming that only one cutter disc at a time madecontact with the rock wall.

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2 Theory

2.1 Contact mechanics

Contact mechanics is the name of the study of the deformation of solids that come intocontact with each other [7]. The Hertzian contact stress signifies the localized stresses thatdevelop in the relatively small contact area that forms as two solids come in contact throughthe application of imposed loads. The dimensions of the two bodies that are coming intocontact vary from one case to another, but the parameters that influence the magnitude ofthe Hertzian contact stress is the normal contact force, the radii of curvature of the twobodies and their respective elastic modulus. The theory is usually only valid when the twosurfaces that come into contact cannot conform, e.g. one of the surfaces is convex while theother is a half-plane or both of the surfaces are convex. However, the theory can be used inthe case of one of the surfaces being concave [8], under the condition that the inner radius ofthe container (the concave surface) is far greater than the radius of curvature of the convexsurface. From this, an effective diameter of curvature, d∗ [m], can be determined accordingto Eq. 2.1,

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d∗=

1

d1+

1

d2(2.1)

Where d1 [m] is the diameter of the concave part (set as a negative value) and d2 [m] isthe diameter of the convex part. In addition, an effective elastic modulus, E∗ [Pa], is alsodetermined according to Eq. 2.2,

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E∗ =1− ν21E1

+1− ν22E2

(2.2)

Where ν1 and E1 [Pa] are the Poisson’s ratio and elastic modulus of material 1, respectively,and ν2 and E2 [Pa] are the Poisson’s ratio and elastic modulus of material 2, respectively. Forcylinder-to-cylinder contact, the width of the contact surface that forms is defined accordingto Eq. 2.3,

b =

√2Fd∗

πLE∗ (2.3)

Where F [N ] is the applied load and L [m] is the contact length. The maximum pressure islocated in the middle of the contact width and can be determined according to Eq. 2.4,

pmax =2F

πbL=

√2FE∗

πLd∗(2.4)

2.2 Equivalent static force

Many systems contain features that can be approximated as a body with a certain massimpacting another body with a certain velocity. What this means is that the impacted body

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is exposed to a suddenly applied impact load. To study the effects of such an impact, adynamic analysis would prove useful. However, the necessary resources to conduct such ananalysis are sometimes not accessible and in those cases, an amplified static analysis canbe used instead, at the very least for preliminary design purposes. This is performed bydropping a body with known mass, m [kg], from a certain height, h [m], above the memberbeing exposed to the impact. For generally increased simplicity, the member being exposedto the impact should be approximated as a beam, if possible. The dynamic impact factor isthen determined according to Eq. 2.5,

n = 1 +

√1 +

2h

δstatic(2.5)

Where δstatic [m] is the static deflection of the member. This approximation with the use ofthe dynamic impact factor is valid if the resulting response of the member is purely elastic[9]. The dynamic impact factor is then multiplied by the static load, i.e. the mass m timesthe gravitational constant g, in order to obtain the approximated maximum dynamic loadPmax [N ] that the member is exposed to, according to Eq. 2.6,

Pmax = nmg (2.6)

2.3 Centripetal force

In the existing system in the cutter wheel assembly, there are a total of two constellationsconsisting of two rotation symmetric parts that are mounted together with a certain clearancefit. The parts with the smaller diameter are fixed and as such, do not move or rotate whenthe cutter wheel is rotating. The parts with the larger diameter, however, rotate in relationto the rotational speed of the outer-most section of the cutter wheel. The outer-most sectionwith its attached cutter discs is driven by a hydraulic motor and is seen in Figure 1.2. Giventhat the rotation symmetric parts are fed with a certain clearance and that the parts withlarger diameter rotate, the parts with larger diameter will be exposed to certain centripetalforces. Centripetal force is defined according to Eq. 2.7 as

Fc = mac = mv2

r(2.7)

Where m [kg] is the mass of the object that is moving with a tangential speed v [ms

] alonga circular path with radius of curvature r [m]. The centripetal acceleration, ac [m

s2], is

proportional to the square of the tangential speed and inversely proportional to the radius ofcurvature.

2.4 Sliding wear

A tribo-system is defined as a system consisting of interacting surfaces in relative motion.These surfaces are known as tribo-surfaces [10]. The basic principle of sliding wear is that

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two bodies are in contact with each other under the influence of a certain normal force andthe bodies are moving in relation to the other. Given that the bodies are always in contact,this movement will be a sliding motion and the speed with which the bodies slide in relationto each other is known as the sliding speed.

When studying tribological fields such as wear, the presence of asperities is an importantcontributing factor [5]. A tribo-surface in contact with another tribo-surface in relativemotion has on a microscopic level an uneven surface with higher and lower areas. Theseareas form peaks and valleys, respectively, on the surface that are known as asperities. Whentribo-surfaces come into contact on a macroscopic level, what really happens is the highestasperity peaks of the respective surfaces come into contact and start to deform plasticallyas the normal load forcing the two tribo-surfaces together increases. As the asperities aredeformed, the surfaces move closer to each other and more asperities subsequently comeinto contact. The more the asperities deform plastically, the larger the real area of contactbetween the tribo-surfaces will be.When the subject of sliding wear of tribo-surfaces is studied, one of the most central theoriesregarding the wear of the surfaces is known as the Archard wear equation [5], as shown in Eq.2.8,

Q = KW

H(2.8)

Where Q [mm3

mm] is the volume of material worn per sliding distance, W [N ] is the normal load

and H [MPa] is the hardness of the softer surface. The coefficient K is often times knownas the wear coefficient and is of great importance as it provides an indication of how severewear processes will be in different systems.From Eq. 2.8 it can be understood that the wear rate is proportional to K, meaning thatif lower wear rates in a system are desired, as is often the case, there should be effort putinto making sure that the value of K is reduced for said system. One phenomena thathas a significant impact on the wear coefficient is the so called tribological compatibilityof the system [5]. The tribological compatibility of a system refers to a reluctance of thetwo tribo-surfaces to form a strong interfacial bond. The stronger the interfacial bond, themore material would be removed upon relative dry (unlubricated) sliding of the surfaces andas such, the system would have a higher wear rate. The term metallurgical compatibilitycan be seen as being inversely proportional to the tribological compatibility between twomaterials. For example two identical materials would have the highest possible metallurgicalcompatibility, but the lowest tribological compatibility. In Figure 2.1 it is illustrated how thecompatibility influences the value of the wear coefficient.

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Figure 2.1: Typical values of the wear coefficient K for different degrees of tribologicalcompatibilities sliding under different states of lubrication. Reprinted with permission fromThe American Society of Mechanical Engineers © [11].

As can be deducted from Figure 2.1, the more identical the two materials in the tribo-systemare, the higher the value of the wear coefficient K will be, which in turn leads to higher wear.

2.4.1 Lubrication

Lubricants serve several purposes in systems that contain elements in contact and in relativemotion. One purpose is to reduce the friction of the tribo-system by reducing the frictionalforces between the surfaces. The lubricant serves as a thin film with low shear strength thatseparates the tribo-surfaces. Another purpose is to reduce the wear in the system. This ispossible due to the fact that the lubricant reduces surface contact. The lubricant also sealsagainst contamination and if the lubricant is a fluid, it can also wash away wear particles.The third purpose of lubricants is to protect the surfaces against corrosion by reducing thesurface temperature and oxygen levels in the system [12].Many different materials can be used as a lubricant in a system, including gases, liquids orsolids. There are four types of lubrication [5]:

• Hydrodynamic - Complete separation of the surfaces by a fluid film that transmits theload. The friction is determined by the viscosity of the lubricant.

• Elastohydrodynamic - A combination of high local pressures and thin lubricant filmcauses elastic deformation of the surfaces that can not be neglected.

• Boundary - Oil or grease molecules are adsorbed at asperity tips. The moleculesgenerally separate the surfaces, although a certain degree of asperity contact may still

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occur. The load is transmitted by the asperity contacts and friction is determined bythe strength of the boundary layer.

• Solid - No external oil, grease or other material is added. Instead, one of thetribo-surfaces (or both) provides the tribo-system with a solid interfacial film thateither has low shear strength or results in an interface with a low shear strength.

The minimum lubricant film thickness, hmin [m], is dependent on the viscosity of the oil andoperating conditions such as applied load and sliding velocity [13]. The relationship betweenthe minimum lubricant film thickness and the surface roughness, σ∗ [m] can tell when thefull fluid film lubrication will begin to break down [5]. The so-called lambda ratio in Eq. 2.9,

λ =hminσ∗ (2.9)

gives an indication of how likely and how severe asperity interactions will be in lubricatedsliding. For λ > 3, the tribo-surfaces will be completely separated by the lubricant film,asperity contact can be neglected and the wear is expected to be low. When λ < 1, the filmthickness is too small to prevent increasingly severe surface damage. The middle-ground forthe value of lambda, i.e. when 1 < λ < 3, represents a lubrication condition where someasperity contact occurs. This regime is known as mixed lubrication.

The most commonly used measure of the surface roughness is the average roughness, Ra,which is defined as the arithmetic mean deviation of the absolute values of the asperity peaksand valleys from the mean line through the profile. The mean line is the line of best fit withequal areas of the asperity peaks and valleys profile lying above and below it [5].

There is a proven correlation between a material’s (average) roughness and its wear resistance.Experimental studies on the sliding wear of carburized steel alloy samples [14] have shownthat when the roughness value increases, the critical normal load required for the lubricationto transition into boundary lubrication and scuffing decreases.

As stated previously, having a satisfactory amount of lubrication in a system is in many casesdesirable and if the amount of lubrication is not adequate or if there is no lubricant presentat all, gross surface damage can occur. An example of such surface damage is the phenomenaof scuffing that has occurred in some of the components in the cutter wheel assembly in theMobile Miner 40V. Scuffing is characterized by macroscopically observable changes in thesurface texture, with features related to the direction of relative motion [5], as can clearly beseen in Figure 1.3. An inadequate amount of lubrication is not necessarily the only reasonwhy scuffing occurs in a system where surfaces slide against each other. It can also occureven if there is a lubricant separating the surfaces. If the normal force acting on the surfacesis high enough and if the sliding speed is high enough, the lubricant will no longer be able to

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separate the two surfaces and they will come into contact, which means that scuffing at thatpoint is no longer impossible.

Given that lubrication plays such an important role in how long mechanical systems areexpected to function without suffering serious damage, it can be valuable to establish criteriato be able to determine which lubrication types are expected to exist in said systems. In slidingwear for lubricated AISI-52100 steel contacts, it has been shown [15] that scuffing frequently, ifnot exclusively, occurs when there is a mixed lubrication between the tribo-surfaces. Whetheror not the system in question will operate under mixed lubrication, or any other type oflubrication, depends on the so-called lubrication number. The lubrication number, L, isdefined in Eq. 2.10 as

L =ηiV+pRat

(2.10)

where ηi [Pa ∗ s] is the inlet viscosity of the lubricant and p [Pa] is the mean contact pressure.The sum velocity, V+ [m

s] is defined in Eq. 2.11 as

V+ = V1 + V2 (2.11)

where V1 and V2 are the respective velocities of the tribo-surfaces. The Combined CenterLine Average (CLA) surface roughness, Rat [m] is defined in Eq. 2.12 as

Rat =

√Ra21 +Ra22 (2.12)

where Ra1 and Ra2 are the respective surface roughness values of the tribo-surfaces. In Figure2.2, a generalised Stribeck curve is shown with three lubrication regimes. Depending on thevalue of the lubrication number, the system will operate under either boundary lubrication,mixed lubrication or elastohydrodynamic lubrication.

10


Figure 2.2: Generalised Stribeck curve with lubrication regimes. Reprinted with permissionfrom John Wiley and Sons © [15].

Several other diagrams found during the project’s pre-study were similar in that they provideda relationship between normal force and sliding speed, such as the IRG Transition Diagram[15] and showed if wear in the system would be expected to be mild, severe or catastrophic.However, it was thought that using normal force as a determining variable for expected wearwould not be reliable since the test specimen used for the IRG Transition Diagram had anunknown contact area. Therefore, a wear diagram using contact pressure was instead preferred.

The Generalised Stribeck curve depicts the lubricated sliding of steel-contact pairs. For dry(unlubricated) sliding, another type of diagram could be used [16]. The wear-mechanismmap presented in Figure 2.3 depicts the measured wear mechanisms depending on thenormalized pressure, F , and the sliding velocity, v. The test was performed with a pin-on-discconfiguration and the material used for both contact surfaces were a medium-carbon steel.Medium-carbon steels are similar to low-carbon steels, with the difference that their carboncontent ranges from 0.3% to 0.6% and their manganese content ranges between 0.6−1.65% [17].

11


Figure 2.3: The wear-mechanism map of a medium-carbon steel contact pair underunlubricated sliding. Reprinted with permission from Elsevier © [16].

The map depicts the different wear mechanisms that dominate depending on the pressure inthe contact surface and the sliding velocity. If these variables are known and if unlubricatedsliding steels are used as material in the tribo-system, this map could provide useful insightinto which wear mechanism(s) should be present.

Sliding wear is a field that has garnered a relatively large amount of research over the yearssince it was first studied. However, one type of wear mechanism related to sliding wearhas not been studied as extensively and the mechanism is known as impact wear. Impactwear is reminiscent of erosive wear, but the difference lies in how the particles strike theworn surface. In erosive wear, several hard particles strike a surface either carried by a gasstream or entrained in a flowing liquid, while in impact wear a single body wears down asurface through percussion, i.e. repetitive contact [18]. Depending on from which angle theabrasive particle strikes the worn surface, this percussive motion can either include only aforce component normal to the worn surface or it can also include a shear component. As aresult of the small amount of research invested in the wear mechanism, wear data is scarceand no extensively applied modeling techniques are available. One of the models that hasbeen developed [19] is able to predict wear rates with good correlation to experimental data.The test rig used in the work consisted of a steel hammer striking a rotating sintered bronzeplate in a percussive manner. The model defines the worn volume, W [m3], according to Eq.

12


2.13 as

W = (kPNx

H+ kN exp (n))(

AiA

)j (2.13)

where

• k is a sliding wear coefficient

• P [N ] is the mean load

• N is the number of impact cycles

• x [m] is the sliding distance

• H [ kgm2 ] is the hardness

• n is an impact wear coefficient

• Ai [m2] is the initial contact area

• A [m2] is the contact area after N cycles

• j is a constant

Another study [20] conducted on the wear behaviour for different complex impact-slidingmotions in impact wear has shown that the amount of surface damage sustained dependson which type of impact-sliding motion is used. It was shown that a unidirectional motionleads to the most severe surface damage, compared to a reciprocating motion and a combinedmotion. There is a presence of both sliding force and impact force affecting the worn surface,however, the correlation between the two forces remains unclear.

2.5 Rolling wear

Another field in the study of tribology is Rolling wear. In the case of a tribo-system with atleast one of the tribo-surfaces moving in relation to the other by a rolling motion, rolling wearwill be present. For machine components such as bearings, the roller elements, be it balls,rollers, needles or any other element, roll in relation to the counter-surface and dependingon a number of factors the bearing will have a certain life expectancy. The rating life, L10

of a bearing is defined as ”the fatigue life of 90% of a sufficiently large group of identicalbearings operating under identical conditions can be expected to attain or exceed” [21]. Itis measured in millions of revolutions, is determined in accordance to ISO 281 [22] and iscalculated according to Eq. 2.14 as

L10 = (C

P)p (2.14)

13


where C [kN ] is the basic dynamic load rating and p = 3 for ball bearings and p = 103

forroller bearings. P [kN ] is the equivalent dynamic bearing load determined from Eq. 2.15,

P = XFr + Y Fa (2.15)

where

• Fr [kN ] is the actual radial bearing load

• Fa [kN ] is the actual axial bearing load

• X is the radial load factor for the bearing

• Y is the axial load factor for the bearing

Eq. 2.14 can be very useful if life expectancy of the bearing is of interest, but it does not givea clear indication of how large the maximum allowable stresses affecting the bearing can be.The basic static load rating of a bearing is determined in accordance to ISO 76 [23] and isdefined as the load that results in a certain value of contact stress at the center of contact inthe most heavily loaded rolling element. For roller bearings this contact stress is σH = 4000MPa. The total residual strain arising from these contact stresses are approximately equal to0, 0001 of the diameter of the rolling element. It should be noted that the static load ratingshould be of importance only if the bearing is subjected to static loading, i.e. either when itis not rotating and is subjected to continuous high load or intermittent peak loads or if itsrotational speed is less than 10 RPM and it is required to only have a limited life time [24].For radial and radial-thrust bearings, the static load rating corresponds to the force Fr, whichonly causes radial displacement of the roller elements in relation to each other. For thrustand thrust-radial bearings, the static load rating instead corresponds to the force Fa, whichonly causes axial displacement of the roller elements in relation to each other. Under staticloading conditions, the damage of the roller bearings is present in the form of the workingsurface plastic strain. The strain of 0, 0001 that the contact stress σH causes should not behigher than the allowable contact stress, [σ]H [25].

2.6 Models for determining load cases in mechanical excavationmachines

The cutter wheel in the present study is designed to excavate rock through continuousgrinding that leads to spalling of rock debris. The cutter wheel is driven by a hydraulic motorand the cutter discs that are mounted around the circumference of the outer-most sectionof the cutter wheel (see Figure 1.2) rotate along with the cutter wheel. The Mobile Miner40V excavates rock by a certain procedure. An assembly of hydraulic cylinders provide thecutter wheel with several degrees of freedom. With the use of these cylinders, the wheel

14


can thrust forward and backwards, tilt upwards and downwards and also perform sweepingmotions within certain degree limitations. During operation, the rotating cutter wheel isthrust forward with a certain thrust force, which serves as the force with which the cutterdiscs grind the rock with. When the cutter discs make contact with the rock, a certainreaction force will develop that is picked up by the cutter discs and then transferred to theouter-most section of the cutter wheel and subsequently the bearing constellation. The cutterdiscs are fixed in place, but each are equipped with double conical roller bearings fittedon a shaft that is mounted between attachment plates that allow them to rotate aroundtheir own axis. Because of this, the cutter discs will rotate around their own axis as theyare thrust against the rock. This means that the prominent frictional force affecting eachcutter disc will be that of a rolling friction force. It could be argued that a certain degreeof sliding friction will be present, however that contribution should be so low that it canbe considered negligible. Depending on the angle of the cutter discs relative to the rockwall when they make contact with the rock wall, they will be exposed to a certain sideforce. This means that the reaction force will be a resultant force of the thrust force andthe side force. Its magnitude and direction will depend on the respective thrust force andside force vector components. In addition to the thrust force and the side force, the cutterwheel is also permanently exposed to a gravitational force, Fmg, caused by its own static weight.

Several models for predicting resulting cutter disc forces in tunneling machines exist, althoughmost of these studies have been conducted on TBMs. The front face of TBMs is a flat planeequipped with cutter discs. They excavate rock by rotating the front, allowing the cutter discsto grind the rock into debris. The process is rather similar to that of the Mobile Miner 40V,but the difference is that all of the cutter discs in a TBM are always oriented perpendicularto the rock wall and all of the discs are always in contact with the wall. One of the modelsdeveloped for TBMs [26], named the CSM model, is based on a large data base of full-scalelinear cutting tests performed on rock samples. This model takes into account properties suchas tensile and compressive strength of the rock being excavated, cutter disc geometry andpenetration depth. Recently, this model was altered [27] by using different cutting conditionsand linear cutting machines. It has been argued that the previous model needed modificationfactors in order to predict more accurate results. A schematic view of the forces acting onthe cutter disc can be seen in Figure 2.4. The contributions of the normal force, FN , andthe rolling force, FR, both lead to a resultant force, FT .

15


Figure 2.4: Schematic view of the forces acting on the cutter disc. Reprinted by permissionfrom Springer Nature © [27].

The modified equation for the resultant force affecting the cutter disc is defined in Eq. 2.16 as

FTRost,M = KT ∗ FTRost (2.16)

where FTRost,M [N ] is the modified resultant force, KT is a modification factor and FTRost[N ] is the resultant force obtained with the use of the CSM model. FTRost is determinedaccording to Eq. 2.17,

FTRost =

∫ φ

0

TP θRdθ =

∫ φ

0

TP 0(θ

φ)ψRdθ =

P 0RTφ

ψ + 1(2.17)

where R [m] is the radius of the cutter disc and T [m] is the cutter disc tip width. ψ is acontact pressure distribution constant determined according to Eq. 2.18 as

ψ = 0.3714− (0.0229T ) (2.18)

The contact angle between the rock surface and the disc cutter, φ [rad], is determined by Eq.2.19,

φ = arccos (R− pR

) (2.19)

where p [m] is the disc cutter penetration depth. The variable P 0 [Pa] is the base contactpressure immediately underneath the cutter disc and is determined according to Eq. 2.20 as

P 0 = C 3

√sσ2

cσt

φ√RT

(2.20)

16


where C is a constant in the semi-theoretical CSM prediction model that is usually taken as2.12. The variable s [m] is the disc cutter spacing and σc [Pa] and σt [Pa] are the uniaxialcompressive strength and Brazilian tensile strength of the rock, respectively.

17


3 Method

3.1 Project plan

This particular phase was the first of the entire project work and it was conducted incollaboration with K. Xie [6] as well as the project’s supervisor from Camatec. The purposeof this phase was to establish a project plan with an associated project timeline that bothparticipants was expected to follow in order to be able to accomplish the individual tasks.Both individuals first required an FEA model of the system with associated load cases inorder to be able to proceed with their respective goals. Therefore it was decided that fourdifferent major activities needed to be completed in order to obtain the FEA model. Theactivities were defined as:

• Gather all the relevant information regarding the Mobile Miner 40V. In addition tothis, also determine theories and methods that could be applied to the various systemsin the project.

• Develop an FEA model in Ansys that consists of the relevant components in the cutterwheel.

• Determine which forces act on the cutter wheel during excavation. With these forcesdetermined, calculate the force components that should affect each cutter disc. Acquirea list of load cases by gathering all of these sets of force components.

• Define how the simulations from the FEA model should be interpreted. By establishingwhich criteria to use, the simulation results can be compared to this and it can then bedetermined what the results indicate for the system.

Given the limited time scope of the thesis projects, it was determined that the activities had todistributed to some extent between the two participants. The author of this report was to beresponsible for the third activity listed above, i.e. determining the different load cases of thesystem. K.Xie [6] was to be responsible for the second activity; the development of the FEAmodel in Ansys. The two remaining activities were considered to be linked to the respectivepre-studies of the projects and therefore it was decided that both participants would conductthese activities. The information regarding the Mobile Miner 40V was essential for bothprojects and a lot of the theories and methods would also be used in both projects.Once these four activities had been accomplished, the author of this report would then be ableto pursue the individual goal of the thesis work. In order to be able to optimize the currentdesign of the cutter wheel, the areas in need of rework would have to be identified. Afterpersonal communication with G. Karlsson, Camatec (February 2020), the author decided onsome key areas to focus the work on. These were listed as:

18


• Construction alterations - make either minor or major changes to the constructions ofone or several of the components in the vicinity of the bearing constellation.

• Lubrication - An important factor in making sure that mechanical systems involvingmoving parts can have as long lifetime as possible. By making sure that the systemin question has an adequate amount of lubrication present at all times, this could beaccomplished.

• Materials selection - Another important factor from a tribological point of view.Choosing appropriate materials for surfaces that are in contact can potentially increasethe lifetime of the system drastically.

The methods with which these key areas were investigated will be presented later on in thereport.

3.2 Background data

The Mobile Miner 40V in its entirety is shown to the right in Figure 1.1. A CAD model ofthe cutter wheel, which this thesis project is based on, is shown in Figure 1.2. The interior ofthe cutter wheel contains several components and systems. The system relevant for this thesiswork is the bearing constellation with the components that are in its vicinity. It is in thissystem that excessive wear has occurred and it is considered to be in need of optimization.Due to the fact that the thesis provider has expressed that the names and exact models of theworn components are classified information, these components have therefore been assignedother names in this report and their models have been simplified (except in Section 3.6 and3.7). The two rotation symmetric steel components, named Component 1 and Component2, are shown as an assembly in a section view in Figure 3.1. Component 1 has an internaldiameter of 1930+2.2

+1.6 mm, while Component 2 has an external diameter of 19300−0.23 mm.

Figure 3.1: A section view of the simplified assembly of Component 1 and Component 2.The yellow part on top is Component 1 and the green part at the bottom is Component 2.

19


The bearing constellation consists of a radial bearing in combination with a thrust bearingon each side. With the cutter wheel being oriented vertically, the bearing constellation isnot located in line with the cutter wheel’s center of gravity (COG). The assembly of bearingcomponents are positioned with a certain distance to the left of the COG and as such, havean inherent moment arm. The outer ring of the radial bearing is attached to the outer-mostsection of the cutter wheel by interference fit. So when the hydraulic motor drives theouter-most section and causes it to rotate, the outer ring of the radial bearing rotates alongwith it. Since it is a radial bearing, its main purpose is to absorb the radial reaction forcesthat originate from the cutter discs. The thrust bearings on either side of the radial bearingserve the purpose of keeping the radial bearing in place as it experiences bending momentscaused by the reaction forces originating from the cutter discs that would otherwise causethe radial bearing to bend.

Component 1 is mounted on the outer surface of Component 2 with a certain clearancefit. Lubricant oil flows into the system through an inlet hole located slightly to the left ofComponent 2 in Figure 3.1 and at the top. The oil then flows down along the componentsin the cutter wheel and flows out through an outlet hole located at the bottom. Duringexcavation, Component 1 rotates in relation to the outer ring of the radial bearing, whileComponent 2 is fixed in place. Due to gravity, a certain surface area of Component 1 willalways be in contact with Component 2. The size of this surface area is determined by thesize of the clearance fit and the gravitational force of Component 1. Both Component 1 andComponent 2 are located on the left side of the radial bearing. On the right side of thebearing, two identical (although mirrored) components are located. The same contact slidingconditions apply for these two components, but the wear damage they had suffered was notas severe as for Component 1 and Component 2. That is why the majority of this thesis workis focused on the components on the left side of the radial bearing and not the componentson the right side of the radial bearing.

3.3 Establishing useful theories and models

As described in Section 3.2, the inner-diameter surface of Component 1 and the outer-diametersurface of Component 2 will always be in contact. It is also known that Component 1 willrotate in relation to the outer ring of the radial bearing. It will therefore slide on Component 2whenever the cutter wheel is rotating. From this, it is obvious that this particular tribo-systemwill be demonstrate sliding wear. Component 1 has a certain mass and its gravitational forcecan be interpreted as the normal force. It rotates with a certain rotational speed, ω [ rad

s],

which can be converted into its equivalent tangential speed, v [ms

], according to Eq. 3.1,

v = rComponent1ω (3.1)

20


where rComponent1 [m] is the inner radius of Component 1. These two tribo-surfaces will havea certain surface area - the contact surface. Contact pressure, p [Pa], is defined according toEq. 3.2 as

p =F

A(3.2)

where F [N ] is the applied force and A [m2] is the true contact area. The value of the appliedforce is usually rather simple to determine, including in this particular tribo-system. However,the true contact area is in this particular tribo-system much harder to determine. Whensolids come into contact, it can be linked to Contact mechanics, as described in Section 2.1.In this tribo-system, one of the surfaces is convex while the other is concave, which shouldmean that Hertz contact theory could potentially be used to determine the contact pressurebetween the surfaces. The condition that needed to be fulfilled to be able to use the theorywas that the radius of the concave surface (in this tribo-system the inner radius surface ofComponent 1) must be far greater than the radius of the convex surface (in this tribo-systemthe outer radius of Component 2). Since the components each have large diameters and areassembled with a clearance fit, this condition was ultimately not met. As such, Hertz contacttheory could not be used. Instead, the contact pressure had to be determined numericallywith the use of a simplified model in Ansys depicting the tribo-system. This model wasnamed Two-ring case and is illustrated in Figure 3.2.

Figure 3.2: The simplified FEA model of the tribo-system of Component 1 and Component2. The red circle indicates that the largest clearance will be at the bottom due to gravity andtheir differences in diameter.

Component 1 was assigned a density of ρComponent1 = 9656 kgm3 - significantly larger than

common densities of steel grades [17] - and a gravitational field was added. With this, the

21


contact pressure between the surfaces could be determined. However, other forces werealso thought to be involved in the system. Component 1, having a certain mass, rotatingaround its axis with a certain velocity would mean that it should be exposed to a centripetalforce. If such a force was determined to be large enough to be significant, it would havean impact on the contact pressure and would therefore be necessary to be accounted for.Furthermore, another factor was considered. The clearance fit between Component 1 andComponent 2 means that Component 1 could potentially be displaced in the radial direction.The maximum allowed displacement would then be the maximum radial clearance. If thereexisted forces in the opposite direction large enough to overcome Component 1’s gravitationalforce in the system, it would thereby cause it to lift off from Component 2’s surface. If thoseforces then were to be removed, Component 1 would fall downwards and impact Component2. It was thought to be a possibility that this oscillating impact motion where Component 1lifts from Component 2’s surface and falls back down and impacts it could be present in thetribo-system. The force from this impact would then have an effect on the contact pressurethat arises between the surfaces. Since such a force would be a dynamic force, a certaincorrelation between it and its corresponding static force would be needed in order to makethe determination of the contact pressure more simple. The dynamic impact factor from Eq.2.5 could then prove useful under those circumstances. To determine the static deflectionof Component 2, it was approximated as a beam with length L [m] and a constant flexuralrigidity, EI [Pa ∗m4], where E [Pa] is its Young’s modulus and I [m4] is its second momentof area. The equation to use in order to determine the deflection would be the Euler-Bernoulliequation defined in Eq. 3.3 as

EId4w

dx4= q(x) (3.3)

where w(x) [m] is the static deflection (same as δstatic), q(x) [Nm

] is a distributed load and x[m] is the position on the beam.

With the current design of the cutter wheel, an unacceptable amount of wear had occurredon the surfaces of Component 1 and Component 2, as shown in Figure 1.3. As such, acriteria was needed to be able to obtain an estimation as to how much wear is expectedin the tribo-system upon altering of certain variables. The generalised Stribeck curve inFigure 2.2 was chosen as a useful tool for this. As explained in Section 2.4.1, the boundarylubrication regime indicates that asperity tips adsorb oil or grease molecules and partiallyseparates the surfaces. In mixed lubrication, some asperity contact occurs but it had beenshown that this particular regime was the one that almost exclusively featured scuffing. Inelastohydrodynamic lubrication, the film is very thin and local pressures are high, whichcauses elastic deformation of the surfaces, but from the same study it was shown [15] that thisregime featured virtually negligible wear. Because of this, the priority became to try to ensurethat the lubrication type of the tribo-system in question would be in the elastohydrodynamicregime in order to reduce the wear generated. The lubrication number, L, in Eq. 2.10 then

22


became the determining factor in which regime the tribo-system was expected to be. Thevariables involved were the inlet viscosity of the lubricant, sum velocity and combined surfaceroughness of the surfaces as well as the mean contact pressure between the surfaces.

3.4 FEA model

The development work of the FEA model in the software Ansys was conducted by K. Xie [6]and details about the method with which the model was created will not be presented inthis thesis work. For further details about the development of the FEA model, the reader isreferred to that thesis report.

Two separate models were created; the aforementioned Two-ring case (see Figure 3.2) and theC-model. The Two-ring case model was used for the tribo-system consisting of Component1 and Component 2 in order to determine the contact pressure between the surfaces. TheC-model was used to determine the contact pressures on the rollers in the radial bearing andthe thrust bearings. The model is presented in Figure 3.3.

(a) Full view of the C-model in Ansys. (b) Sectional view of the C-model.

Figure 3.3: The C-model used for determining contact pressures on the roller elements.

The load cases described in Section 3.5 and later on calculated in Section 4.2 were applied tothis model.

23


3.5 Determining the load cases

One of the major activities of the thesis work included determining the load cases that thecutter wheel is expected to be exposed to. In order to obtain feasible load cases, the possibleexternal factors for the cutter wheel had to be taken into consideration. In reality, the rocksurface being excavated is not particularly smooth, but rather coarse and dented. If the loadcases were to be more precise, the uneven surface of the rock wall would need to be factoredinto the calculations. However, due to the uncertainty about just how coarse the surfacesbeing excavated are and how to implement this into the calculations in a reasonable way, itwas decided early on that this would not be taken into consideration when determining theload cases. Instead, the rock wall was henceforth treated as an ideally smooth surface.

As mentioned previously, the cutter wheel is equipped with cutter discs. These cutter discs aremounted in pairs along the circumference of the outer-most section of the wheel, amountingto a total of 16 pairs of cutter discs. The discs are identical in terms of dimensions, but theyare oriented in different configurations in relation to the cutter wheel. The angle of the cutterdiscs on the left side of the cutter wheel is termed γleft and the angle of the cutter discs onthe right side of the cutter wheel is termed γright. These angles are measured in reference tothe normal plane of the cutter wheel. The five configurations are shown in Figure 3.4.

Figure 3.4: The five cutter disc configurations. The configuration (a) is configuration 1in Table 3.1, (b) is configuration 2, (c) is configuration 3, (d) is configuration 4 and (e) isconfiguration 5.

24


The five different cutter disc configurations are listed in Table 3.1.

Table 3.1: The configurations of the cutter discs

Configuration γleft[°] γright[°]

1 90 90

2 105.82 74.18

3 121.78 58.22

4 137.38 42.62

5 153.02 26.98

Because of their different configurations, the cutter discs will make contact with the rock fromdifferent angles. As a result of this, the reaction force components that they are exposed towill differ from one disc to another. But before those force components could be determined,an additional variable had to be put into consideration. As previously mentioned, the cutterwheel has a number of degrees of freedom due to a number of hydraulic cylinders. It canthrust forward with a thrust force which leads to a reaction thrust force, Fr, but dependingon the rotation of the cutter wheel and the configurations of the cutter discs, it will alsoexperience a reaction side force, Fa. It can also tilt upwards and downwards with certainangles, according to Figure 3.5.

25


Figure 3.5: The maximum cutter wheel tilt angles. Viewed from the side.

Additionally, the cutter wheel can be rotated in certain angular configurations, like the cutterdiscs. It rotates around an axis normal to its rotational axis, pointed upwards. From thestarting configuration where it is placed parallel to the machine, it can then be rotatedbetween −25° to 25° relative to the machine, as shown in Figure 3.6.

Figure 3.6: The maximum cutter wheel angles. Viewed from above.

26


This angle was termed β and is the angle of the cutter wheel relative to the rest of themachine as the cutter wheel is rotated. During operation, five different configurations of thecutter wheel are used and these are listed in Table 3.2.

Table 3.2: The configurations of the cutter wheel

Configuration β[°]

1 25

2 14

3 0

4 -14

5 -25

When excavating rock, the Mobile Miner 40V operates under certain procedures. The cutterwheel is oriented according to one of the configurations listed in Table 3.2 and it then thrustsforward with a certain thrust force from a hydraulic cylinder. The cutter wheel’s orientationis fixed when thrusting forward and the wheel always thrusts in a direction parallel to therest of the machine. This is illustrated in Figure 3.7.

Figure 3.7: The thrust motion of the Mobil miner 40V. The cutter wheel’s orientation isfixed when thrusting and the direction of the thrust motion is always parallel to the MobilMiner. Viewed from above.

27


Due to the cutter wheels orientation, it will therefore experience both a reaction thrust force,Fr, and a reaction side force, Fa. Depending on these force vectors, the resulting force thatthe cutter discs are exposed to will vary. There are six excavation procedures and they arelisted in Table 3.3.

Table 3.3: The six excavation procedures. Due to the confidentiality of the thesis work, thevalues of the thrust forces and side forces are classified information

Procedure β[°] Fr[kN ] Fa[kN ]

1 -25 Fr1 Fa1

2 -14 Fr2 Fa2

3 0 Fr3 Fa3

4 0 Fr4 Fa4

5 14 Fr5 Fa5

6 25 Fr6 Fa6

So far, there are three angle variables of importance in determining the load cases - the angleconfiguration of the cutter wheel, β, and the angle configuration of the left and right cutterdiscs, γleft and γright, respectively. There is also another factor influencing the reaction forcesthat the cutter discs are exposed to. Initially, during the beginning of the excavation, onlyone or two cutter discs will be in contact with the rock at a time since the wheel at thatpoint just started to make contact with the rock. As the cutter wheel excavates the rockby thrusting forward, the wheel will progressively penetrate deeper into the rock. Becauseof this, the wheel’s contact area with the rock will increase and more cutter discs will be incontact with the rock at all times. The thrust force will be the same in all the cases, butthe difference will be in how many cutter discs are in contact with the wall. In other words,the more cutter discs that are in contact with the wall, the more the reaction force from thethrust force will be divided among the cutter discs. In the case of only one cutter disc beingin contact with the wall, that single cutter disc will take up the entirety of the reaction forces.Due to this, the case where only one cutter disc is in contact with the rock should be thecase where the reaction forces affecting a cutter disc are at a maximum. Therefore, it wasdetermined that the most relevant excavation case would be the case where only one cutterdisc is in contact with the rock wall, since that case would arguably result in the highest

28


reaction forces in a single cutter disc. As such, the load cases determined for the FEA modelin this thesis work was determined under the basis that only one cutter disc is in contactwith the rock wall at a time.

As mentioned, the cutter discs experience reaction thrust forces and reaction side forces. Thereaction force from the thrust force will be directed parallel to the cutter wheel, while thereaction force from the side force will instead be directed perpendicular to the cutter wheel.Figure 3.8 illustrates a load case with the cutter disc having an arbitrary value of the variableγright. The forces F represent the resultant forces.

Figure 3.8: The thrust force results in two reaction forces. The reaction force Fr is alwaysdirected parallel to the cutter wheel (not included in the figure) while the reaction force Fa isalways directed perpendicular to the cutter wheel. The aforementioned angle β signifies this.

In order to simplify the process of applying the loads in the FEA model in Ansys, the reactionforces affecting the cutter disc had to be explored further. As mentioned previously, onereaction force is parallel to the cutter wheel, Fr, and one reaction force is perpendicular to thecutter wheel, Fa. From these forces, two equivalent forces, Qz and Qx, could be determined,as illustrated in Figure 3.9.

29


Figure 3.9: The forces Qz and Qx.

The force Qz represents the equivalent reaction force parallel to the cutter disc and the forceQx represents the equivalent reaction force perpendicular to the cutter disc. The force Qz iscompressive while the force Qx leads to a bending moment at the cutter disc’s attachmentplates. Through trigonometric means, the forces Qz and Qx could then be determined. Usingthe cutter discs as reference, the forces Fr and Fa both contribute to the magnitudes of theforces Qz and Qx. In Figure 3.10, these respective forces are shown for an arbitrary cutter disc.

Figure 3.10: Combination of the reactions forces contribution to the forces Qz and Qx.

30


From this, four general equations could be established as shown in Eqs. 3.4-3.7:

Qxa = Fa cos (γ − (π

2)) (3.4)

Qza = Fa sin (γ − (π

2)) (3.5)

Qxr = Fr sin ((π

2)− γ) (3.6)

Qzr = Fr cos ((π

2)− γ) (3.7)

In order to obtain the values of Qz and Qx, Eqs. 3.8 and 3.9 were used:

Qz = Qza +Qzr (3.8)

Qx = Qxa +Qxr (3.9)

Every individual load case would have certain values of the forces Qz and Qx and all of thesecases were to be applied in the C-model in Ansys. With the C-model, the contact pressureson the rollers in the radial bearing and the thrust bearings could be determined. Dependingon the different load cases, these contact pressures would vary.

3.6 Construction alterations

Another approach to optimizing the cutter wheel was to conduct construction alterations.There were certain limitations to this, however. The system of interest in this thesis workwas the bearing constellation and the components in its vicinity. The bearing constellationconsists of one radial bearing and two thrust bearings manufactured specifically for thisparticular application. As such, these components could not be altered in any way. This leftthe author with limited options in how the system would have to be redesigned in order toreduce the stress distributions experienced by the components. Despite this, other solutionswere possible, including reconstructions with the purpose of simplifying assembling of thecutter wheel.One construction alteration was considered with regards to fitting purposes. In Section 3.2,only simplified models of Component 1 and Component 2 were shown. However, in orderto properly demonstrate the reasoning behind this construction alteration, a more detailedillustration would be needed. Component 2 is not only in contact with Component 1, butalso a solid ring. The contact between Component 1’s and Component 2’s surfaces is a slidingcontact, but as illustrated in Figure 3.11, the solid ring is mounted onto Component 2 withan interference fit and no sliding occurs.

31


Figure 3.11: Solid ring mounted with an interference fit onto Component 2.

As can be seen from the figure, the contact length is approximately 14.25 mm. To the left ofthe contact length, Component 2 has a rounded corner, while the solid ring has a chamferededge. This construction solution had been implemented with the intention of removing thesharp corner that otherwise would have been present and would have lead to high stressconcentrations. To the right of the contact length, the surface had been chamfered in orderto facilitate the mounting process. The width of the solid ring’s contact surface is 26.5 mm,which means that with the current solution, 14.25

26.5≈ 54% of the ring’s contact area is in

contact with Component 2. It was assessed that this fraction would need to be increased. Itwas mentioned in Section 3.2 that two identical components of Component 1 and Component2 are located on the right side of the radial bearing in the cutter wheel assembly. The sameconstruction alteration made for Component 2 would also need to be made for the similarpart on the right-hand side of the bearing constellation, given that the two parts are identical.The construction alteration is presented in Section 4.3.

In terms of calculations regarding wear and contact pressure, the components on the left side- Component 1 and Component 2 - were of much larger interest in this work compared to thetwo similar components on the right side. That being said, the right-hand side componentswas deemed to be in need of a slight revision with regards to the mounting process ofthe cutter wheel. Given the large size of the involved parts, the mounting process is timeconsuming and requires precision. The respective parts in the bearing constellation and theparts in its vicinity are assembled lying down horizontally. The parts are lowered in placewith the use of an overhead crane. The left-hand side is assembled first, followed by thebearing constellation and then the right-hand side versions of Component 1 and Component2. Similar to Component 1 and Component 2, the two identical parts on the right-handside are also mounted with a certain clearance fit. Given the clearance between the two

32


parts’ diameters, assembling is a possibility, but difficult. The two parts in question arenamed Component 1RHS and Component 2RHS from this point in the report. After the theleft-hand side and the bearings have been assembled, Component 1RHS is placed so that itrests on the outer ring of the radial bearing. After that, Component 2RHS has to be fit insidethe inner diameter of Component 1RHS. Figure 3.12 illustrates the fit with the current designof the system.

Figure 3.12: Component 2RHS is fit inside the inner diameter of Component 1RHS.

As can be seen from the figure, the mounting process requires precision in order for Component2RHS to fit. The solution for this is presented in Section 4.3.

3.7 Materials selection

One additional approach that can be pursued with the intention of reducing the wear inthe system in question is to make a proper material selection. As explained in Section 2.4,material compatibility plays a vital role in how much wear is expected when surfaces slideagainst each other. As such, this was one of the most important limiting factors when itcame to weighing in the different material options. Both Component 1 and Component 2have experienced significant wear in the current design of the system, but Component 1 is acomponent that can not be replaced as easily as Component 2 and because of this, it willnot be altered in any way. Component 2, on the other hand, is more flexible in terms ofconstruction alterations and material selection and it was therefore decided that it would bethe subject of the necessary design changes. Currently, Component 1 is made out of S275JR- a structural steel alloy. Its hardness is usually in the range 121− 163 HB but in this case,its contact surface has been coated with manganese phosphate - a certain coating methodthat provides hardness and excellent wear resistance [28]. The hardness of the steel aftercoating was unknown, but it was estimated by the author of this report to be in the range

33


of 140− 180 HB, which converts to 141− 177 HV [29]. With this in mind, new materialoptions for Component 2 had to be considered. Naturally, the ideal case would be if neitherof the two surfaces experience wear, but this is not possible since every system experienceswear to a certain amount. However, given that Component 1 is much more difficult to replacecompared to Component 2, measures needed to be taken so that Component 2 would bethe wear surface. As such, one of the decisions made was that the new material chosen forComponent 2 would have to be softer than the steel alloy that Component 1 is made out of.Although not always the case, a general rule of thumb is that the softer the material surfacein a tribo-system, the more the wear it suffers. Therefore, a satisfactory starting point forthe material selection process was thought to be to limit the list of materials to those thatare softer than Component 1.

Another important consideration was the size of the two components. Given their relativelylarge diameters, manufacturing is difficult. In order to simplify the manufacturing process itwas determined that the whole component did not need to be remade in a different material,it would be enough to only replace the surface in contact with Component 1. By lathingComponent 2 according to Figure 3.13a, the surface in contact with Component 1 would beremoved. The volume of lost material can then be replaced by a thin ring consisting of thematerial later selected as the replacement, according to Figure 3.13b.

(a) Section view of Component 2 aftersuggested lathing operation.

(b) Section view of Component 2 fit with thering made out of the new material.

Figure 3.13: Manufacturing solution for Component 2.

Manufacturing a thin ring instead of an entire new version of Component 2 would certainlyreduce the resources spent, but additional solutions can be implemented. The size of the rodor tube of raw material needed in order to manufacture a ring of such size would also proveto be difficult. Fitting the ring in place would also be more complicated than necessary in

34


such a scenario as there would be relatively fine tolerance limits. Instead of manufacturing asolid ring, it could instead be manufactured in the form of smaller segments. The individualsegments would then need to be joined through means appropriate for the different materials.This was a factor that also needed to be considered when the possible materials were chosen.

The software used for identifying possible materials to use was CES Edupack. The softwarehas a database with thousands of different materials from different groups so in order tonarrow the selection down, certain restrictions needed to be set. The procedure used foridentifying relevant materials can be divided into three stages. In the first stage, the materialgroups of interest was specified. Materials that did not belong to the specified groups weresubsequently eliminated. In the second stage, limits were set for different properties andparameters and the materials that did not fulfill these requirements were eliminated. In thethird stage, the remaining materials were added in a chart that plotted certain variableson the y-axis against certain variables on the x-axis. Depending on their properties, theirpositions in the chart would differ.

The thesis providers wished for material price to be a variable when plotting the differentmaterials in the graph. They also expressed that manufacturability and mounting werefactors that needed to be kept in mind when choosing which materials to pursue. CESEdupack allows for the user to define which type of system the material in question will beused in. One of the systems to choose from was that of a tribo-system fairly similar to theone made up by Component 1 and Component 2 presented in this thesis work. It involvedabrasion by blunt contact with a sliding load. The goal in this particular system was tooptimize the resistance to yielding, since the wear would be promoted by the onset of yielding.No free variables were set, the contact radius was set as a fixed variable and the limitingconstraint was yielding. From this, a so-called Performance Index was given for the system.This Performance Index was set as H3

E2 and its inverse value needed to be minimized in orderto find the best materials suited for the system. In other words, the most optimal materialwould have a small value of the ratio between its Young’s modulus E and its hardness H,while at the same time having a small value of the price per kilogram.

As mentioned, the hardness of the surface that the material in question would be in contactwith was estimated to be in the range of 141−177 HV . The material chosen would preferablyhave to be softer than that to make it more likely that Component 1’s surface would notexperience more wear than Component 2’s surface. The three stages in the material selectionprocess were determined to be arranged accordingly:

Material groups

• Metals and alloys (excluding ferrous alloys)

35


• Technical ceramics

• Polymers: plastics and elastomers

Limits

• Minimum Young’s modulus: 0.5 GPa

• Hardness: 10− 150 HV

• Weldability: Good or Excellent (metals only)

• Galling resistance: Excellent (metals only)

Materials chart

• y-axis: Inverse Resistance to yielding 1H3

E2

• x-axis: Price per kilogram SEKkg

The fraction H3

E2 could potentially provide misleading results. If a particular material has anextremely low Young’s modulus, it would result in a high value of the resistance to yielding,even if that is not the case in sliding contact. Materials with high values of the fraction H3

E2

therefore needed to be researched for if they can be used in sliding wear applications such asthe one in this thesis work. Ceramics such as silicon carbide and silicon nitride both have veryhigh hardness. They exhibit great wear resistance, but has been shown to be an exception tothe general understanding that the softer surface suffers more wear than harder surface in atribo-system. In a study of wear rates for a tribo-system containing silicon nitride and steel[30], it was shown that the wear rate of silicon nitride was as low as 1 ∗ 10−11 mm3/Nm, butthe wear rate of the steel after a running-in period was slightly lower at 5 ∗ 10−12 mm3/Nm.In another study conducted in unlubricated sliding between silicon nitride and steel [31],formation of ferrous deposits on the ceramic in combination with a protective layer on thesteel resulted in a larger degree of wear on the silicon nitride surface compared to the steelsurface. Despite the conclusions from these studies, the hardness limit presented was kept.The reason will be discussed further in Section 5.3.

36


4 Results

4.1 Scuffing between Component 1 and Component 2

The rotational speed of Component 1 is half that of the rotational speed of the outer ringof the radial bearing. This means that its equivalent tangential speed is also half of thetangential speed of the outer ring. During testing of the Mobile Miner 40V, the cutterwheel was rotating at 7 RPM . Using Eq. 3.1, this would mean that the tangential speed ofComponent 1 would be

v = (1

2) ∗ rComponent1 ∗ 7 ∗ (

2π

60) ≈ 0.354

m

s(4.1)

By implementing Eq. 2.11, the sum velocity of Component 1 and Component 2 would thenbe

V+ = 0.354 + 0 = 0.354m

s(4.2)

Component 1 is made out of the steel alloy S275JR with an average roughness value ofRa1 = 0.8 µm. Component 2 is made out of the steel alloy S355JRG2 with an averageroughness value of Ra2 = 1.6 µm. By using Eq. 2.12, the Combined CLA surface roughnesswould be

Rat =√Ra21 +Ra22 ≈ 1.789µm (4.3)

The oil used as lubricant for the system has a density of ρlubricant = 870 kgm3 and a kinematic

viscosity at 40 °C of νlubricant = 220 ∗ 10−6 m2

s. The actual temperature in the tribo-system

in question has been described through private communication with G. Karlsson, Camatec(Mars 2020) to be in the range of 40− 50 °C, which makes the kinematic oil viscosity at 40°C a feasible value to use. This gives an inlet (dynamic) viscosity, defined in Eq. 4.4, of

ηi = ρlubricant ∗ νlubricant = 0.1914Pa ∗ s (4.4)

In order to determine the lubrication number, L, from Eq. 2.10, the only remaining unknownvariable was the mean contact pressure, p.

4.1.1 Determining the expected contact pressure

The oscillating impact motion was a factor that could affect the contact pressure in thesystem. Given the forces that the cutter wheel is exposed to during excavation, it wasthought as a possibility that Component 1 would be exposed to large shock forces that wouldoccasionally cause it to lift off from Component 2’s surface and then fall down and impact itwith a dynamic impact force. In order to determine the dynamic impact factor from Eq. 2.5,the static deflection first had to be determined with the use of Eq. 3.3 by approximatingComponent 2 as a beam. The CAD-model of Component 2 is shown in Figure 4.1. Its length

37


was set as L = 0.04 m, the width of the simplified model of Component 2 in Ansys, and itswidth was set as w = 0.0337 m.

Figure 4.1: CAD-model of Component 2 approximated as a beam.

The second moment of area was determined by using the mass properties function on theCAD-model in Creo Parametric, as shown in Figure 4.2.

Figure 4.2: Determination of the second moment of area for the beam.

It was determined to be I ≈ 2.416 ∗ 10−8 m4. The Young’s modulus was set as E = 210GPa. The load used was the gravitational force of Component 1, Q = mg = 1600 N . The

38


distributed load case used in the calculations is presented in Figure 4.3.

Figure 4.3: The distributed load case. The beam is fixed in its left end.

The calculations were performed in Wolfram Mathematica and the code with the full solutioncan be found in Appendix A. The deflection of interest was the deflection at the positionwhere the mass impacts the beam. Given that in this case, the mass was approximated as adistributed load, the position chosen was the midpoint of the length where the distributedload was applied, at the length 0.0247 m measured from the free end of the beam. The

length fraction of the total length was then0.0015+ 0.0276

2

0.04= 0.3825. The static deflection was

determined to be δstatic ≈ 4 ∗ 10−5 m.

During the thesis project, data from more recent test runs of the Mobile Miner 40V wasprovided through private communication with G.Karlsson, Camatec (April 2020). Sensorshad been placed at the bottom of the bearing constellation assembly inside the cutter wheelwith the purpose of measuring the clearance between Component 1 and Component 2 andbetween Component 1RHS and Component 2RHS during the time when the wheel rotates.This data revealed information about the radial motion of Component 1 and Component1RHS during excavation. The data is shown in Figure 4.4.

39


Figure 4.4: The radial displacements of Component 1 (left graph) and Component 1RHS(right graph). Obtained following private communication with G.Karlsson, Camatec (April2020).

The data plots the components’ radial displacement over a full revolution. The differentcolored curves are the data for different time periods, or rather every new revolution thatthe components rotate. From the right graph it can be concluded that Component 1RHSdisplaces radially with a similar pattern with every new revolution. This indicates thatit rotates with a close-to constant velocity. Component 1, on the other hand, displays amore irregular pattern of radial movement and prominent phase shifts can be distinguished.Some degree of slip seems to be present, causing it to not rotate at half of the velocityof the cutter wheel, as was originally expected. The data of the radial displacements ofthe two components also reveal that the sensors on both sides register changes in radialposition, which could mean that the parts are in fact moving up and down as the cutterwheel rotates. Per Eq. 2.5, the dynamic impact factor is dependent on the height from whichthe mass is falling and the static deflection of the member that the mass hits. Assumingthat Component 1 and Component 1RHS would suddenly get displaced by a shock force andthen fall down and impact the counter-surface, their maximum fall height would only beas large as the maximum radial clearance between the surfaces. The theoretical maximumclearance would be 1932.2

2− 1929.77

2= 1.215 mm. Inserting the values h = 1.215 ∗ 10−3 m and

δstatic = 4 ∗ 10−5 m into Eq. 2.5, the dynamic impact factor would then be n ≈ 8.86. UsingEq. 2.6, the approximated maximum dynamic load impacting Component 2 would then be

40


Pmax = 8.86 ∗ 1600 = 14.176 kN .However, given the time it takes for the parts to displace radially (approximately 200 s), incombination with the very small distance they move (approximately 0.8 mm at most), it wasdetermined that the influence of the oscillating impact motion would be neglected.

The contact pressure was determined with the use of the Two-ring case model in Ansys. Astandard Earth gravitational field was added, according to Figure 4.5 , exposing Component2 to Component 1’s gravitational force.

Figure 4.5: The boundary conditions in the Two-ring case FEA model. Component 2 wasfixed while the sliding and rotation of Component 1 was prevented.

The result from the simulation is presented in Figure 4.6.

Figure 4.6: The contact pressure on Component 2’s surface obtained from the Two-ringcase model.

41


As can be seen, the maximum contact pressure was determined as pmax = 4.8291 MPa. Fromthis, the mean contact pressure [32], p, is given by Eq. 4.5,

p = (π

4)pmax (4.5)

This gave the mean contact pressure a value of p ≈ 3.79 MPa.

4.1.2 Expected lubrication regime

With the mean contact pressure numerically determined, the value of the lubrication numbercould then be determined. By inserting the corresponding values of the four variables in Eq.2.10, the lubrication number became L ≈ 0.01. The Generalised Stribeck curve in Figure 2.2was revisited in order to determine in which regime the tribo-system consisting of Component1 and Component 2 would be expected to be under the current conditions, as seen in Figure 4.7.

Figure 4.7: The expected lubrication regime based on the Generalised Stribeck curve.

A lubrication number as large as 0.01 is not included in the diagram. The elastohydrodynamicregime is the regime for the largest values of the lubrication number and it was estimatedthat the tribo-system in question would be expected to be in this regime under lubricatedconditions.

4.1.3 Dry sliding

The result from Section 4.1.2 indicates that the tribo-system should not demonstrate seizurewear in the form of scuffing, but instead should show milder wear rates. But the system in

42


question did demonstrate such a wear mechanism during extended test-running with themachine and the wear rate was unexpectedly large. The wear-mechanism map in Figure 2.3was then used in an attempt to determine if the system might be insufficiently lubricated.The normalized pressure, F , is defined according to Eq. 4.6 as

F =p

H(4.6)

where p is the contact pressure and H is the indentation hardness of the softer surface [16].The contact pressure used was the maximum contact pressure, so that p = 4.8291 MPa.Component 2 has the softer surface with a hardness range of 140 − 190 HB. The exactvalue was unknown to the author, so the mean value 165 HB was used. The convertedhardness value [29] would then be H ≈ 560 MPa. This would give a normalized pressure of

F ≈ 0.0086. The sliding velocity had previously been determined to be v = 0.354 ms

. Theexpected wear mechanism for the tribo-system, assuming dry sliding conditions, is presentedin Figure 4.8.

Figure 4.8: The expected wear mechanism for the tribo-system, marked by the red dot,assuming dry sliding.

The expected wear mechanism of the system would then be severe wear.

43


4.2 Load cases

The method with which the load cases were determined was presented in Section 3.5. Atotal of 60 load cases were determined to be used in the FEA model. These load cases arepresented in Table 4.1 and 4.2. Due to the confidentiality of this thesis work and the thesiswork conducted by K.Xie [6], the exact values of the forces Qz and Qx could not be revealed.

44


Table 4.1: Load cases for left cutter discs for excavation procedures (a) 1-3 and (b) 4-6

(a)

β[°] γleft[°] Qz[N ] Qx[N ]

-25 90 - -

105.82 - -

121.78 - -

137.38 - -

153.02 - -

-14 90 - -

105.82 - -

121.78 - -

137.38 - -

153.02 - -

0 90 - -

105.82 - -

121.78 - -

137.38 - -

153.02 - -

(b)

β[°] γleft[°] Qz[N ] Qx[N ]

0 90 - -

105.82 - -

121.78 - -

137.38 - -

153.02 - -

14 90 - -

105.82 - -

121.78 - -

137.38 - -

153.02 - -

25 90 - -

105.82 - -

121.78 - -

137.38 - -

153.02 - -

45


Table 4.2: Load cases for right cutter discs for excavation procedures (a) 1-3 and (b) 4-6

(a)

β[°] γright[°] Qz[N ] Qx[N ]

-25 90 - -

74.18 - -

58.22 - -

42.62 - -

26.98 - -

-14 90 - -

74.18 - -

58.22 - -

42.62 - -

26.98 - -

0 90 - -

74.18 - -

58.22 - -

42.62 - -

26.98 - -

(b)

β[°] γright[°] Qz[N ] Qx[N ]

0 90 - -

74.18 - -

58.22 - -

42.62 - -

26.98 - -

14 90 - -

74.18 - -

58.22 - -

42.62 - -

26.98 - -

25 90 - -

74.18 - -

58.22 - -

42.62 - -

26.98 - -

The results from the simulations will be described by presenting the cutter disc configurationsfrom the load cases (without the exact values) from each of the six excavation proceduresthat yielded the highest contact pressures on the radial bearing rollers and thrust bearing

46


rollers, respectively. Additionally, the ratios between the forces Qz and Qx for the respectivecutter disc configurations were calculated. The results are presented in Table 4.3. The largestmeasured contact pressure on one of the radial bearing rollers is defined as pr and the largestmeasured contact pressure on one of the thrust bearing rollers is defined as pa.

Table 4.3: The respective cutter disc configurations that resulted in the largest contactpressures for the six excavation procedures and their ratios between the forces Qz and Qx

Excavation procedure β [°] Largest pr [°] QzQx

Largest pa [°] QzQx

1 -25 137.38 -0.353 137.38 -0.353

2 -14 137.38 -0.545 137.38 -0.545

3 0 137.38 -0.811 42.62 1.043

4 0 137.38 -1.043 42.62 0.811

5 14 137.38 -1.52 26.98 0.23

6 25 90 2.333 58.22 0.701

Generally, the largest contact pressures on the bearing roller elements were found for the loadcases where the loads Qz and Qx were applied to the cutter discs on the left-hand side of thecutter wheel. The mean values of the contact pressures between the five disc configurationsof the left-side discs, pr,left and pa,left, and the five disc configurations of the right-side discs,pr,right and pa,right, were calculated. The difference between these mean pressures, named∆pr and ∆pa, were calculated according to Eqs. 4.7 and 4.8,

∆pr = pr,left − pr,right (4.7)

∆pa = pa,left − pa,right (4.8)

The results are shown in Table 4.4.

47


Table 4.4: The differences between the mean contact pressure values for the radial rollersand thrust rollers

Excavation procedure β [°] ∆pr [MPa] ∆pa [MPa]

1 -25 434.46 201.1

2 -14 362.46 163.82

3 0 221.64 -2.12

4 0 131.42 -129.26

5 14 7.34 -224.62

6 25 -45.44 -208.3

The load cases that resulted in the largest contact pressure on one of the thrust bearingrollers and the largest contact pressure on one of the radial bearing rollers, respectively, arepresented in Table 4.5.

Table 4.5: The two load cases that resulted in the largest total contact pressures on a radialbearing roller and a thrust bearing roller, respectively

Excavation procedure β [°] γ [°] p [MPa]

2 -14 137.38 pr,max

6 25 58.22 pa,max


The contact surface between Component 2 and the solid ring was mentioned in Section 3.6.In the current cutter wheel assembly, approximately 54% of the solid ring’s inner surface isin contact with Component 2. The construction alteration made can be seen in Figure 4.9.

48


Figure 4.9: The contact width between Component 2 and the solid ring after adjustingComponent 2.

The length of the surface upon which the solid ring is mounted was increased from 14.25 mmto approximately 18.25 mm. By doing this, the contact area increased to 18.25

26.5≈ 69%. The

outer chamfered edge was left unchanged. As mentioned in Section 3.6, the same constructionalteration was performed on Component 2RHS, although this is not illustrated in the reportsince the parts are identical.

As described in Section 3.6, the mounting process needed revising and in order to make theprocess of fitting Component 2RHS in Component 1RHS less tedious, a construction alterationwas made and is presented in Figure 4.10.

Figure 4.10: Component 2RHS was reconstructed slightly in order to simplify the mountingprocess.

49


The length of the revolved bulk material of Component 2RHS was increased by 3 mm andthe edge was then chamfered.


As described in Section 3.7, price, manufacturability and mounting were important factorsfor choosing the appropriate material for the system. In CES Edupack,the Performance IndexH3

E2 was determined to be another criteria. Three material groups were chosen to be amongthe candidates. In order to obtain more easily distinguishable figures of the material charts,the material groups were examined separately. Some properties of the relevant materialsfound are presented in Appendix B. For metals and alloys (excluding ferrous alloys), thechart is presented in Figure 4.11.

Figure 4.11: Metals and alloys chart plotted for inverse resistance to yielding against price.

The chart shows metals that are able to be welded. However, a certain brass alloy was foundprior to applying the condition of weldability. This particular alloy exhibited a higher valueof the resistance to yielding, while at the same time not being more expensive. As such anadditional chart for metals and alloys is presented in Figure 4.12, including the brass alloy(as well as other additional alloys).

50


Figure 4.12: Metals and alloys chart plotted for inverse resistance to yielding against price,without the condition of good or excellent weldability.

From Figures 4.11 and 4.12, four alloys were chosen to inspect further. These alloys are theones highlighted in the two Figures.

• The two bronze alloys both have good weldability, although their typical uses differ.Bronze, CuAl10Fe5Ni5, C95820, cast (aluminum bronze) is used in applications suchas high strength applications, heavy gears and paper making. Bronze, CuNi12Zn24,C75700, hard (12% nickel silver) on the other hand is typically used as in decorativeitems, fasteners, clips and electrical contacts. It was therefore decided that this alloywould be discarded.

• The Copper-beryllium alloy is typically used in high-conductivity/high-strength electricalcomponents, forgings, springs etc.

• The brass alloy is typically used in highly-stressed components such as rolling millcastings, slow spur and gear wheels. As mentioned, it can not be welded, however itcan be joined by soldering or brazing.

The three metal alloys chosen to proceed with after researching them were therefore the brassalloy, the copper-beryllium alloy and the aluminum bronze alloy.

51


The next material group to be examined were the technical ceramics. The materials chart ispresented in Figure 4.13.

Figure 4.13: Technical ceramics chart plotted for inverse resistance to yielding against price.

As can be seen, the chart did not yield many options. Almost all of the materials with highresistance to yielding were different types of graphite. Graphite has been shown to be avaluable material in terms of reducing wear in systems. An example of this is by using it as afiller material in different groups, like metals [33, 34] and polymers [35]. The material to thefar left, Halite, was excluded since it is only typically used in optical windows [36].

The third and final material group was polymers. The materials chart is shown in Figure4.14.

52


Figure 4.14: Polymers chart plotted for inverse resistance to yielding against price.

A total of seven plastics were highlighted from the chart.

• TPU (Ester, aromatic, 30% glass fiber) is typically used in automotive and industrialapplications, cams, gears as well as hydraulic applications. A commercial tradenamefor it is Desmopan © 192 and it is a thermoplastic block copolymer with high wearresistance and high mechanical strength for components subject to wear [37]. Abrasiontests performed on TPUs have shown that it has superior abrasion resistance comparedto other polymers such as Polytetrafluoroethylene (PTFE) and Nylon 11 [38].

• Polyamide 46 (super tough), designated Nylon 46 is known by its tradename Stanyl ©.Used in gears, cams, rollers, bearings and many other applications. Certain grades suchas Stanyl © HGR3-W and Stanyl © TW341 are well-suited for wear applications [39].

• Polyamide 66 (molding), designated Nylon 66. Has the advantage of being a self-lubricatingmaterial, although the addition of a lubricant is recommended for applications withhigh loads or high rotational speeds [40]. It has superb wear resistance properties andis used in gears, cams, rollers, bearings and similar applications.

• Polyamide 6 (toughened), designated Nylon 6. Just like Nylon 66, it has superb wearproperties and is used in similar applications. Graphite and molybdenum dioxideadditives can be used in the polymer in order to increase its wear resistance [40]. Glassfibers can also be added and it has been found [41] that a glass fiber content of 30%resulted in the lowest coefficient of friction and specific wear rate.

53


• POM (copolymer) is used in bearings, gears, electrical kettles and other applications.Characteristics include natural lubricity, exceptionally high mechanical strength, highresistance to repeated impacts and toughness [42]. Experimental tests [43] have shownthat POM shows a low specific wear rate and dynamic coefficient of friction comparedto other polymers such as PA 6, PA 66 and PBT (Polybutylene Terephthalate) whensliding against steel. The specific wear rate and dynamic coefficient of friction werereduced even further when the POM was modified with 20% PTFE.

• Polytrimethylene terephthalate (15 % glass fiber), designated PTT is used in structuralparts, automotive applications and various industrial applications. Wear additives canbe incorporated into the polymer in order to make it more suited for wear applications[44].

• Ebonite, sometimes known as Gear Fiber. Used in bowling balls, combs, buttons andsimilar applications. Experimental tests [45] involving a stainless steel pin sliding onvarious polymers showed that the wear rate of Gear fiber was lower compared to PTFE,but higher compared to glass fiber and Nylon.

It was then decided that PTT and Ebonite would be excluded from the list of potentialmaterials. Ebonite was removed since it was outperformed in terms of wear rate by Nylonand PTT was removed since information about it was more scarce compared to the otheralternatives and that it needs additives in order to be used in wear applications. Followingthis, the list of potential polymers was reduced to five materials: TPU, Nylon 46, Nylon 66,Nylon 6 and POM.

It was then decided to compare the nine remaining materials in a new chart. Once again, theinverse resistance to yielding and the price were the variables on each respective axis. Theresult is shown in Figure 4.15.

54


Figure 4.15: The nine remaining materials chart.

In Table 4.6, the relevant material data are presented for the nine materials. The data forthe materials’ respective resistance to yielding and prices were obtained from CES Edupack.Joining strategy was also added as a parameter.

Table 4.6: Material data for the remaining nine materials

Material Resistance to yielding [MPa] Price [SEKkg

] Joining strategy

Brass alloy 408-5400 41.1-50.5 Soldering, silver brazing, rivetting, friction welding [36]

Copper-beryllium alloy 200-845 147-167 Welding [36]

Bronze alloy 215-482 49.8-60.1 Welding [36]

Graphite 1301-43939 98.8-150 More suited to be used as filler material

TPU 1713-50653 36.2-36.6 Hot-plate, hot gas, ultrasonic welding [36]

Nylon 46 4953-9623 59.5-81 Laser, linear-vibration [46], spin, dielectric, ultrasonic welding [47]

Nylon 66 1505-3297 36.3-43.8 Linear vibration, hot-plate, orbital vibration [46], spin, dielectric, ultrasonic welding [47]

Nylon 6 1397-2826 34.8-40.1 Linear vibration, orbital vibration, hot-plate [46], friction stir [48], spin, dielectric, ultrasonic welding [47]

POM 480-1575 22.4-24.3 Friction, hot-plate, ultrasonic, laser welding [36]

In terms of cost, the material that stood out the most was the copper-beryllium alloy. Itscost compared to the other materials in combination with the fact that it is not typicallyapplied in wear applications lead to it being discarded. Graphite turned out to be ratherexpensive in relation to the other materials. As mentioned, it can be used as a filler material

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in wear applications. So an option for the tribo-system in question could be to use graphiteas filler material in order to provide self-lubricating abilities for the surface. If it were to beused as filler, the amount of graphite present in the bulk material would be rather small incomparison, and thereby the high kilogram price would would not matter as much.

The three polyamides have been described as quite similar in terms of mechanical propertiesand this is not surprising since they are merely different grades. Despite this, Nylon 66 hasbeen acknowledged of being stiffer and exhibiting better wear resistance compared to Nylon 6.This is attributed to their difference in chemical structure. In addition to this, the mechanicalresistance of Nylon 46 is superior to that of Nylon 66 [49]. The mechanical resistance refersto the polymers behaviour under the influence of mechanical forces. This includes elasticity,hardness, wear resistance and other properties [50]. Additionally, its fatigue resistance is also50 times better [49]. Reinforcement of the polymers could be a possible solution to increasethe wear resistance. It has been shown [51] that glass-fiber reinforcement (GFR) of Nylon46 and Nylon 66 resulted in Nylon 66 with 30% GFR exhibiting a specific wear rate of theorder 10−7 mm3

Nmm, while Nylon 46 with 30% GFR showed a specific wear rate of the order

10−6 mm3

Nmm. The superior grade therefore seem to depend on if glass-fiber reinforcement is

implemented, although the least suitable grade in both cases is Nylon 6. Therefore, thisgrade was discarded. Just like the Nylon grades, POM is also frequently used in various wearapplications. As can be seen from Figure 4.15 and Table 4.6, POM is a cheaper alternativeto all three grades of Nylon. However, dry sliding pin-on-disc wear tests [52] have shown that,when sliding against a tool steel, the specific wear rate of POM was measured as high as inthe order of 10−3 mm3

Nm, while for Nylon 66 the specific wear rate was in the order of 10−6

mm3

Nm. The choice between Nylon 46 and POM then turned into a choice between whether

what was deemed to be of higher importance between wear resistance and price.

The five most prominent materials remaining following further investigation of the materialproperties included:

• Brass, CuZn30Al5Mn4Fe2, cast (high-tensile manganese bronze)

• Bronze, CuAl10Fe5Ni5, C95820, cast (aluminum bronze)

• Nylon 46

• POM

• TPU

As mentioned, using graphite as filler material would provide the selected material withself-lubricating properties. However, brass alloys, Nylon grades and POM grades are alreadyinherently self-lubricating, so the material that would benefit most from an addition of

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graphite fillers would be the bronze alloy. In the case of graphite being added into Nylon66, this has not only been shown to be true, but it has also been shown that the additionof graphite can worsen its friction and wear characteristics [53]. Additives such as Siloxane,Molybdenum disulfide (MoS2) and carbon nanotubes reduced its wear rate, on the other hand.In the same study, it was also shown that TPU benefits greatly in terms of wear resistancewhen additives such as graphite, MoS2 and larger amounts of PTFE are incorporated.Molybdenum disulfide can be used to reduce wear and friction in many applications. Similarto graphite, it can form single layer stacked with very low interlaminar forces that can easilyslip with respect to the others. Experimental studies [54] with Nylon reinforced with MoS2

showed the best anti-friction and anti-wear performance in comparison to two other wearresistant materials, namely PTFE and POM.

Given the advantages that the remaining materials offer for the system, the final materialselection was given as a list of options instead of one single material choice. The five optionswere as follows:

Option 1: Brass, CuZn30Al5Mn4Fe2

The brass alloy offers a self-lubricating ability, in combination with good mechanical propertiessuch as Young’s modulus, hardness and compressive strength [36]. Graphite fillers would notbe needed due to its self-lubricating ability and the manufacturing cost would therefore notincrease as a result. The segments can be joined through to use of soldering, silver brazing,rivetting or friction welding. Both soldering and brazing are flexible joining processes andespecially cheap for smaller bath sizes, such as the component in this particular system.

Option 2: Bronze, CuAl10Fe5Ni5

The bronze alloy would offer higher strength compared to the brass alloy [36]. In order tocompete with the other materials’ wear resistant properties, graphite bushings would bebeneficial to include. The price per kilogram for bronze is higher than for brass and addinggraphite filler would further increase manufacturing cost and time. Joining of the segmentswould be accomplished by welding.

Option 3: Nylon 46

The most expensive choice out of the three plastics. It does, however, offer better wearresistance compared to POM. Incorporating additives such as MoS2 would further increaseits wear resistance. Vibration welding would be a sufficient joining method. The cost ofequipment is high, but tooling costs are low and the process is fast [36]. Another option

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could be laser welding, under the assumption that the ends of the segments are made thinnercompared to the rest of the bulk, as shown in Figure 4.16.

Figure 4.16: Requirement for laser welding of the polymer.

Just like with vibration welding, the equipment costs are high and the thinner end segmentswould make molding more costly.

Option 4: POM

Cheaper alternative compared to Nylon, while at the same time being self-lubricating andoffering good wear resistance. Just like with Nylon 46, laser welding is a possibility. Hotplate welding is a moderately cheap process, effective for joining larger components and couldbe applied as well [36].

Option 5: TPU

Like Nylon, additives could be added in order to increase its wear resistance. Graphite, MoS2

and PTFE would increase cost, but also increase its durability. It is the second cheapestalternative out of the materials, while at the same time offering higher strength and stiffnesscompared to Nylon 46 and POM. Hot plate welding is an option for joining of the segments.It can also be joined through hot gas welding, a process similar to gas welding of metals. Theequipment cost and set up time are both low, making it an economically beneficial process[36].

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5 Discussion

5.1 Scuffing between Component 1 and Component 2

The results from the calculations to determine the expected wear mechanism and the severityyielded two possible outcomes. For lubricated sliding, it was determined that the expectedlubrication regime would be elastohydrodynamic lubrication. From studies performed on thelubrication regimes, this regime was described as a much more preferred one compared to themixed lubrication regime where severe wear or wear through scuffing is mostly expected [15].For dry sliding, it was determined that there would be severe wear in the system [16], due toa high enough applied load and a sliding velocity not high enough to cause the steel surfacesto oxidize fast enough to form a protective oxide layer on the surfaces [5].

5.1.1 Density of Component 1 in Ansys

The models used in both the Two-ring case model and the C-model were simplified versionsof the actual parts. It was described that the density used for Component 1 in the Two-ringcase model was ρComponent1 = 9656 kg

m3 . This is significantly larger compared to commondensities of different steel grades [17]. The reasoning behind the high density value wassimply to achieve the correct mass of the real part. The simplified model of Component 1was forced to have a lower volume than its real counterpart and as such, the density had tobe increased in order to compensate for the volume loss.

5.1.2 Centripetal force

In terms of determining the centripetal force affecting the system, Component 1 was seenas an arbitrary ring rotating around a center point. For rotating rings with relatively shortlengths, when observing individual segments of the ring, these segments are exposed to radialand hoop stresses. The centripetal force acts as a radial stress component that causes the ringto expand and be forced further outwards. The variables that determine the centripetal forceare the ring’s mass, velocity and radius of curvature. As can be seen in Eq. 2.7, the faster thering rotates, the larger the centripetal force will be. This would then cause the ring to expandand be pushed further outward. Component 1 is a relatively large part but its rotationalspeed is not high. During test drives with the Mobile Miner, the cutter wheel rotated with 7RPM and Component 1 rotated with only half of that rotational speed. It was consideredthat such a small rotational speed would only produce an almost insignificant centripetalforce contribution to the system. As such, the force was considered to be irrelevant for thecalculations in the thesis work and other theories and factors were instead pursued.

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5.1.3 Oscillating impact motion and dynamic impact factor

Figure 4.4 revealed the radial displacements of Component 1 and Component 1RHS duringexcavation operation. It became apparent that the parts did move radially during operation,but they moved very slowly. There seemed to be no indication that either of the partsmade any sudden radial movements that could be likened to them being pushed upwardsand then returning down to impact the surfaces of Component 2 and Component 2RHS.The most likely explanation seem to be that instead of Component 1 and Component 1RHSviolently oscillating up and down, all the associated parts in the cutter wheel assembly moveas a unit and thereby not providing the sensors with any irregular radial displacements toregister. Another possible explanation could be the dimensions of the two parts. Their largesizes imply that there could be a degree of asymmetry in the parts. They are rigid steelcomponents so elastic deformations should be insignificant, but manufacturing of such largecomponents makes it difficult to ensure (near) perfect rotational symmetry. Therefore, apossibility is that the parts are not perfectly round, but instead display different diameterswhen measuring around their circumference and are thereby oval-shaped, if only slightly. Ifthe asymmetric discrepancies were to be large enough, this would then mean that the sensorsmeasuring the clearance between Component 1 and Component 2 or Component 1RHS andComponent 2RHS would detect radial displacements as Component 1 and Component 1RHSrotate. Something that strengthens this theory is the fact that the radial displacements ofComponent 1 and Component 1RHS both follow a periodic pattern. Neither part make anysudden radial movements, which would indicate that the radial displacements measured bythe sensors are merely caused by the components’ presumed oval-shaped dimensions.

5.1.4 Sliding/impact model and equation

Eq. 2.13 was one of few models found for the wear mechanism sliding/impact wear. It relatesseveral variables from both the sliding wear field and the less explored impact wear field[19]. Given that the particular wear mechanism has not been studied nearly as in-depth asother more established wear mechanisms, there was uncertainty from the author’s perspectiveabout its validity. A positive aspect was considered to be that the model incorporatesdynamic factors such as number of impact cycles, N , and the ratio between the initialcontact area, Ai and the contact area after N cycles, A. Rather than studying the respectivecontributions from sliding and impact separately, this model combines both in the sameequation - something that other models found did not do. One negative aspect was the factthat the test rig consisted of a rotating plate made out of sintered bronze. Wear data obtainedfrom tests depend heavily on the particular materials used and can vary considerably whenchanging one or both of the materials. Since both components in the tribo-system in theTwo-ring case are made out of steel alloys, there was too much uncertainty about whether ornot the model would be applicable for that particular system. Finally, the equation requiresdata that was impossible for the author to determine. The initial contact area could be

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estimated with the aid of the Two-ring case model, but the area after N cycles would eitherneed experimental measurements from the actual surface of Component 2, which the authordid not have access to, or it would require an accurate dynamic FEA wear model, somethingthat was outside the scope of the thesis work. The two wear coefficients k and n wouldmost likely also not be valid given the system’s material combination and would need tobe determined experimentally, which was also outside the scope of this thesis work. It wasdetermined that using this model would lead to too many uncertain assumptions.

5.1.5 Generalised Stribeck curve

The Generalised Stribeck curve shown that was introduced in Section 2.4.1 shows thelubrication regimes for lubricated AISI-52100 steel contact pairs [15]. This curve was chosensince the expected lubrication regimes for the system depends on the lubrication numberwhich involves variables that was considered to be relevant for the sliding wear of thetribo-system in the Two-ring case. It is very similar to the lambda ratio [5]. Both equationsare dependent on the surface roughness and the lubricant film thickness, i.e. the relationshipbetween the oil viscosity, the sliding velocity and the applied load derived from the contactpressure. The curve provided the criteria necessary for the author to determine which theexpected lubrication regime would be depending on the value of the contact pressure thatwas determined during the thesis work. A possible error with using this particular diagramfor this thesis work could be found in the test setup used when for determining the diagram.As mentioned, the contact pair consisted of AISI-52100 steel alloys. The steel alloys usedin the Two-ring case tribo-system were of different steel grades. It was expected that thelubrication regimes’ positions and the transitions between them would have been different ifthe same test had been performed on the exact steel grades in the Two-ring case, but giventhat the materials in question are from the same material group as the steel used in the test,it was assumed that the differences would not be very significant. The lubricant used in thetest was not specified and was therefore also a possible error factor.

5.1.6 Low contact pressure - dry sliding

The wear-mechanism map for dry sliding was used in Section 4.1.3 in order to determine thewear mechanism if the tribo-system was assumed to be insufficiently lubricated [16]. Thiswas done with the intention of ascertaining which of the two criteria correlated better withthe obtained results from the test-drives with the machine - either the criterion for lubricatedsliding (the lubrication number and the Generalised Stribeck curve) or the wear-mechanismmap for dry sliding.

By using the criterion for lubricated sliding, the results indicated that the contact pressurecaused by the weight of Component 1 would not be enough to penetrate the lubricant oilfilm. It was predicted that the lubrication would be in the elastohydrodynamic regime and

61


not in the mixed lubrication regime, which had been proven to be the regime in which most,if not all, scuffing occur with the sliding of steel surfaces [15]. This would then mean thatthe tribo-system would not experience serious surface damage as it did during test-running.

The criterion for dry sliding was instead applied and the results showed that the combinationof the contact pressure and the sliding velocity would be enough to cause the surfaces in thetribo-system the experience severe wear, as shown in Figure 4.8. This would mean that theoxide layers on the steel surfaces would be penetrated by the applied load and the slidingvelocity would not be high enough for a thick enough oxide layer to be formed. There wouldinstead be steel-to-steel contact and the worn material would then be steel debris instead ofoxides [5]. This result correlates better with the real case where serious wear through scuffingwas experienced. The reason for the surface damage obtained in the tribo-system withComponent 1 and Component 2 (as well as the tribo-system between Component 1RHS andComponent 2RHS) was then strongly believed to be the result of poor lubrication in the system.

The material used for the test where the wear-regime map for dry sliding was determinedwas a medium-carbon steel [16]. Similar to the test where the Generalised Stribeck curvewas determined, the material used in the test is not the same material as the ones in thecurrent tribo-system. The steel used in the test had not been modified by e.g. surface coatingprocesses or similar techniques, but determining how different the wear-regime map would beif the steel grades in the current system had been used was difficult. Therefore it was onceagain assumed that the referenced work could be used for the calculations presented in thereport, despite the uncertainty about how much of an impact that a different steel gradecombination would have.

5.1.7 Surface roughness

It was unknown about the reason or reasons as to why the system had suffered such serioussurface damage through scuffing. The thesis author estimated that one of the reasons couldhave been the surface roughness of either one or both of the surfaces in contact. The lambdaratio in Eq. 2.9 reveals the relationship between the minimum lubricant film thickness andthe roughness of a surface [5]. The minimum lubricant film thickness depends on the oil’sviscosity, the applied load and the sliding velocity [13]. The applied load and the slidingvelocity are variables that depend on the weight of Component 1 and its rotational speed,respectively, and can not be altered. The oil had been selected specifically for this systemand had been proven to achieve its purpose in prior projects. This means that hmin could beexpected to be relatively fixed during excavation procedures with the machine. That wouldleave the surface roughness as the free variable. As mentioned, higher values of the lambdaratio is preferred when the intention is to reduce wear in a particular system. For λ > 3 thetribo-surfaces are completely separated by the lubricant film and no metal-to-metal contact

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occurs, resulting in little to no wear [5]. In order for the tribo-system consisting of Component1 and Component 2 to to achieve as high of a lambda value as possible, their respectiveroughness values Ra1 and Ra2 should be reduced as much as possible. The manufacturingtime and cost of a produced detail is inversely proportional to its roughness. Making sure thatComponent 1 and Component 2 have sufficiently smooth surfaces would then require moreresources. In the current system Component 1 has an average roughness of Ra1 = 0.8 µm andComponent 2 has an average roughness of Ra2 = 1.6 µm. These values are already relativelylow considering the large size of the parts, but reducing the roughness of Component 2 toRa2 = 0.8 µm is nevertheless a recommendation.

5.2 Load cases for the C-model

The exact values of the contact pressures on the roller elements could not be publishedin the results due to the confidentiality of the thesis work. Instead, the results presentedshowed how the different cutter wheel and cutter disc configurations affected the contactpressures. From Table 4.3, it could be seen that the cutter disc angles γleft = 137.38 °and γright = 42.62 ° contribute with the largest radial roller contact pressure in five out ofsix excavation procedures and the largest thrust roller contact pressure in four out of sixexcavation procedures. Both cutter discs are the left-side and right-side members of the samecutter disc pair and have the same configuration angle with respect to the cutter wheel, onlythat one is positive and the other is negative. It seems like the configuration γleft = 137.38 °is the critical disc configuration angle for procedures 1− 2, when the cutter wheel is rotatedto the left (referring to Figure 3.6). Based on the ratios between the forces Qz and Qx, thiscould indicate that there is a limit for when this ratio leads to the highest contact pressureson the roller elements. For procedures 1 − 2 it is in the range −0.545 ≤ Qz

Qx≤ −0.353.

For procedures 3 − 4, the cutter wheel is oriented perpendicular to the rock wall. Thecritical disc configurations are γleft = 137.38 ° and γright = 42.62 ° and the limit is instead−1.043 ≤ Qz

Qx≤ 1.043. Finally for procedures 5− 6 when the cutter wheel is rotated to the

right, there are four different critical angles and the Qz

Qxratio limit is much larger compared

to the other cases. It is in the range −1.52 ≤ Qz

Qx≤ 2.333. For most of the cases, the largest

contact pressures formed when Qx was larger than Qz. Therefore, it seems that generally, theforce Qx that causes bending moments in the cutter discs attachments lead to larger contactpressures inside the bearing constellation in comparison to the compressive force Qz.

In Table 4.4, the differences between the mean contact pressure values obtained from applyingthe forces Qz and Qx to the left-side cutter discs and the right-side cutter discs are presented.It can be seen that applying the forces on the left-side cutter discs lead to larger contactpressures in the radial roller elements in all but one of the excavation procedures. Conversely,applying the forces to the right-side discs lead to larger contact pressures in the thrust rollerelements in all but two of the procedures. In procedures 1− 2, the cutter wheel is oriented

63


to the left (referring to Figure 3.6) and then thrusts towards the rock wall. The reactionforces from the left-side cutter discs then lead to larger contact pressures on both radialand thrust rollers. Conversely, in procedures 5− 6, when the cutter wheel is oriented to theright, the reaction forces from the right-side cutter discs lead to larger contact pressures onthe roller elements, with the exception of procedure five where the left-side discs lead tolarger contact pressures on the radial roller. The author believes this can be connected tothe aforementioned Qz

Qxratio. When the cutter wheel is rotated to the left, the right-side

cutter discs are generally directed close-to perpendicularly to the rock wall. In other words,the forces Qz, the force that is directed parallel with the cutter disc, will be much larger incomparison to the forces Qx that are the force contributions in bending moments acting onthe cutter disc attachments. The left-side cutter discs, on the other hand, will generally beoriented more tangentially to the rock wall. As a result the contribution from Qx will belarger than the contribution from Qz. As discussed earlier, the Qz

Qxratios revealed that for

procedures 1− 2, the limit of the fraction was −0.545 ≤ Qz

Qx≤ −0.353. In other words, the

largest contact pressures on the rollers were achieved when −2.833Qz ≤ Qx ≤ −1.835Qz.

For procedures 3− 4, the cutter wheel is oriented perpendicular to the rock wall (referringto Figure 3.6) and is then thrust forward. The results show that the reaction forces fromthe left-side cutter discs lead to larger contact pressures in the radial bearing rollers andthe reaction forces from the right-side cutter discs lead to larger contact pressures in thethrust bearing rollers. The author believes this can be connected to the fact that the bearingconstellation’s Center Of Gravity (COG) is located a certain distance to the left of the cutterwheel COG. This means that the bearing constellation is located closer to the left-side cutterdiscs compared to the right-side cutter discs, as can be seen in Figure 3.3b. Reaction forcesentering the cutter wheel from the left-side discs therefore travel almost laterally to thebearing constellation and there will only be a minor bending moment affecting the radialbearing since the moment arm will be short. On the other hand, for reaction forces enteringfrom the right-hand discs, the lateral distance for the forces to travel will be the same as forthe left-side case, but the moment arm will instead be much longer. These forces will therebylead to larger bending moments that will cause the outer ring of the bearing to bend into oneof the thrust bearings while at the same time losing contact with the thrust bearing on theopposite side. The thrust bearing it bends towards and compresses against will as a resultof this experience a large contact pressure; as indicated by the data from the excavationprocedures 3− 4 in Table 4.4. The limit fraction Qz

Qxfor the largest radial bearing rollers in

procedures 3 − 4 was −1.043 ≤ Qz

Qx≤ −0.811. So the largest radial bearing roller contact

pressures were achieved when −1.233Qz ≤ Qx ≤ −0.959Qz. The limit fraction Qz

Qxfor the

largest thrust bearing rollers in procedures 3− 4 was 0.811 ≤ Qz

Qx≤ 1.043. The largest thrust

bearing roller contact pressures were achieved when 0.959Qz ≤ Qx ≤ 1.233Qz.

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In procedures 5− 6, the opposite seems to hold true to some extent. In those procedures,the left-side cutter discs are generally directed close-to perpendicularly to the rock wall andthe right-side discs are generally directed more tangentially to the rock wall. From Table 4.4it can be distinguished that for both cases, the right-side cutter discs produce the largestcontact pressures on the thrust bearings and also on the radial rollers when β = 25 °. Justlike for procedures 1− 2, this is thought to be due to the ratio Qz

Qx. For the thrust bearings,

the limit is 0.23 ≤ Qz

Qx≤ 0.701 and the largest thrust bearing roller contact pressures were

achieved when 1.427Qz ≤ Qx ≤ 4.349Qz. The only discrepancy to this reasoning is thefraction limit for the radial bearing rollers, which is −1.52 ≤ Qz

Qx≤ 2.333. The largest radial

roller contact pressures were then achieved when −0.658Qz ≤ Qx ≤ 0.429Qz.

For the simulations in Ansys that were used to determine the values of Qz and Qx, the meshsize was not optimized. Optimizing the mesh size in order to obtain more accurate resultswould have lead to severely longer computational times. Because of the vast number of loadcases that needed to be simulated and that only one Ansys license was available, the meshsize needed to be larger than first anticipated. There was also time constraints that neededto be accounted for and as a result of this, the simulations had to be conducted with largerelement sizes. This provided the author with contact pressures that were most likely notentirely accurate, however it was still considered that relationships such as the Qz

Qxratio were

usable. Also the relation between the determined contact pressures would still be the same,since all the contact pressures were simulated with larger element sizes.

5.2.1 CSM model

The CSM model was introduced in Section 2.6. The model has been used for predictingreaction forces in cutter discs in TBMs [26] and the altered version of the model [27] wasdescribed more thoroughly in that section. The reaction forces affecting the cutter discs aredependent on factors such as the uniaxial compressive strength and Brazilian tensile strengthof the rock being excavated, as well as the cutter penetration depth, cutter disc spacing andtip width. The model was considered to be useful for this thesis work, since the cutter discsused for the model are similar to the ones used in the Mobile Miner 40V. The cutter discsin the Mobile Miner rotate with the cutter wheel and as such follow a circular path, whileperiodically coming into contact with the rock wall. This is slightly different compared tothe linear cutting tests used for the development of the CSM model where the cutter discsare always in contact with the rock, but it was considered that the basic principle of the twoprocesses were similar enough for the model to be applicable for this thesis work.

The model was used for preliminary load case calculations for the most simple case thatconsisted of a single cutter disc oriented parallel to the cutter wheel and normal to therock wall. The cutter disc is thrust forward by a certain thrust force. The thrust force, in

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combination with the reaction rolling force resulting from the rotating motion of the cutterwheel, results in the three forces shown in Figure 2.4. By inserting the values of the variablesin Eqs. 2.17-2.20, the resultant force was determined. The value obtained was within areasonable limit when compared with the thrust force and the force from the torque of thecutter wheel. However, it was then discovered that the model would be more difficult toapply for other load cases. The reason for this was the variation of the configurations of thecutter discs in the Mobile Miner. According to Eq. 2.17, the resultant force is determinedby integrating the pressure distribution function along the rock-cutter contact angle, whilethe contact area between the disc and the rock is constant. If the disc cutter is orientedperpendicular to the surface, this would hold true even when the cutter disc penetratesdeeper into the rock. However, if the disc was tilted with a certain angle (rotated around thex-axis in Figure 2.4), the contact area would increase proportionally to the penetration depth.There is a possibility that the equation could have been modified in order to be applied totilted cutter discs such as the ones in the Mobile Miner 40V but due to time constraints themodel was not used to determine the load cases in this thesis project.


The hardness range limit for the materials selection section was set as 10 − 150 HV . Aspointed out in Section 3.7, this could exclude a number of materials with higher hardnessvalues that could have been applicable for the tribo-system. Two studies were mentioned[30, 31] which showed that when sliding against a steel surface, silicon nitride exhibited alow wear rate, but the steel showed an even lower wear rate. This would then indicate a lowmetallurgical compatibility between the surfaces and then per definition a high tribologicalcompatibility. High tribological compatibility is desired in systems where the wear rate isdesired to be kept low [5], so that would indicate that silicon nitride could have been amaterial selection option. The reason why the hardness limit used in CES Edupack was keptto the previously presented values was that if the hardness limit had been increased highenough to include these types of technical ceramics, the amount of other materials from othergroups present in the charts would then increase drastically. As brought up in Section 3.7,the general rule of thumb is that the softer surface is usually the surface that suffer moresevere wear in a sliding tribo-system. In other words, a vast majority of the materials thatthen would have been made available in the materials selection charts would have been poormaterial choices. Choosing from them would have then resulted in Component 1 experiencingmore wear in the system, instead of the ring made out of the selected material. There isnaturally a possibility that a number of materials excluded from the materials chart by thehardness limit would have turned out to be excellent choices for the system - silicon nitridebeing one of them. Due to time constraints with the thesis work, however, the author decidedthat the time needed to conduct a larger material selection would most likely be too much tobe able to arrive at a satisfactory result. So in order to reduce to vast number of materials

66


and thereby making the materials selection more realistic to accomplish, the hardness limitwas kept as 10− 150 HV .

Ferrous steel alloys was also intentionally left out when selecting the material groups toexamine. The reason for this was that the author considered steel grades from that familyto be too similar to s275jr, the steel grade that Component 1 is made out of, in terms ofcomposition. Once again, the factors of metallurgical and tribological compatibility wereconsidered [5]. It was considered that there would exist a number of suitable materials fromthe remaining material groups to examine further, rather than selecting among steel gradesthat would be more metallurgically compatible with Component 1. It was considered thatmany steel grades in the ferrous alloys family would result in higher adhesive forces betweenthe tribo-surfaces due to the metallurgical compatibility and thereby resulting in a higherwear rate.

A property of the materials chosen as options to consider is the maximum service temperature.The brass alloy and particularly the bronze alloy seem to be able to function well at highertemperatures without sustaining severe changes in properties, as can be seen in the materialproperties data sheets in Appendix B. The plastics, on the other hand, have lower maximumservice temperatures - below 100 °C. As mentioned in Section 4.1, the operating temperaturein the tribo-system is in the range of 40− 50 °C. It is unknown how much the temperaturerises between the tribo-surfaces during sliding. The lubricant in the system, provided thatthere is an adequate amount of it present, contributes to lowering this temperature [12]. Ifthe amount of lubricant present would be scarce, the safer material choice would be the brassalloy or the bronze alloy, due to their higher maximum service temperatures. The brass alloyin particular would provide additional lubrication due to its self-lubricating property.


The construction alterations performed were minor in terms of changes to the dimensions ofthe parts in question. The main reasoning behind the adjustments, however, was to providebenefits without affecting the functions of other parts in the assembly or the assemblingprocess. The adjustment in Figure 4.9 provided the solid ring with a larger contact surface.With an increase in the contact area, a smaller part of the solid ring would be exposed topotential bending effects, making it more rigid. Also, given that the chamfered edge wasleft intact, the process of mounting the solid ring onto Component 2 would be unaffected.With the new construction seen in Figure 4.10, the length of the revolved bulk material wasadded by 3 mm and then chamfered. Since the large parts of the cutter wheel assembly aremounted by lowering down the respective parts with an overhead crane, this constructionsolution would simplify the mounting process. The added bulk material would not come intocontact with any other parts either.

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Additional construction adjustments were considered. These were going to be made with thepurpose of improving the lubricant flow in the bearing constellation assembly and the nearbycomponents. Both the inlet hole of the lubricant oil located at the top of Component 2 andthe outlet hole at the bottom of Component 2 were to be reconstructed in order to makesure that the lubricant flow was improved compared to the current design. However, due totime constraints these changes did not happen.

5.5 Future work

The work presented in this Master’s thesis is believed to have laid the groundwork for futurework to be conducted regarding the subject. The following should be considered:

• Reconstruct the inlet and outlet pipes for the lubricant oil in Component 2 in order toensure that the entire system is sufficiently lubricated during excavation.

• Search for and use studies where either wear-mechanism maps or transition diagramshave been developed by using tests with materials identical or more similar to thematerials used in the tribo-system of Component 1 and Component 2.

• Consider other additional forces that could possibly affect the load cases, such asvibration forces.

• Include load cases where not only one cutter disc is making contact with the rock wallat a time. In reality, up to four pairs of cutter discs can be in contact with the rockwall simultaneously. The reaction forces will be divided among the cutter discs, buthow will this affect the contact pressures?

• Run the simulations of the load cases with the C-model in Ansys with smaller elementsizes in order to achieve more accurate results.

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6 Conclusion

Based on the work in this Master’s thesis, the following conclusions can be drawn:

• The scuffing that had occurred in the tribo-system consisting of Component 1 andComponent 2 during test-runs was most likely due to insufficient lubrication in thesystem. With an adequate amount of lubricating oil in the system, the lubricationregime would be Elastohydrodynamic lubrication.

• The cutter disc configurations γleft = 137.38 ° and γright = 42.62 ° result in the largestbearing roller contact pressures for when the cutter wheel is rotated to the left andis thrust forward and when it is oriented perpendicular to the rock wall and is thrustforward.

• When the cutter wheel is rotated to the right and is thrust forward, four different cutterdisc configurations lead to the largest roller element contact pressures.

• The fraction Qz

Qxbetween the reaction forces Qz (force component directed parallel to

the cutter disc) and Qx (force component directed perpendicular to the cutter disc)that are absorbed by the cutter discs seems to hold a significance. Qx generally hashigher impact on the experienced contact pressures in the bearing constellation’s rollerelement than Qz.

– For excavation procedure 1, the largest contact pressures on both the radial andthrust bearing rollers were achieved when Qx = −2.833Qz.

– For excavation procedure 1, the largest contact pressures on both the radial andthrust bearing rollers were achieved when Qx = −1.835Qz.

– For excavation procedures 3− 4, the largest contact pressure on the radial bearingrollers was achieved when −1.233Qz ≤ Qx ≤ −0.959Qz. The largest contactpressure on the thrust bearing rollers was achieved when 0.959Qz ≤ Qx ≤ 1.233Qz.

– For excavation procedure 5, the largest contact pressures was achieved whenQx = −0.658Qz for radial bearing rollers and Qx = 4.348Qz for thrust bearingrollers.

– For excavation procedure 5, the largest contact pressures was achieved whenQx = 0.429Qz for radial bearing rollers and Qx = 1.427Qz for thrust bearingrollers.

• Five new material options for Component 2 were chosen: a bronze alloy, a brass alloy,TPU, Nylon 46 and POM copolymer.

• Two minor reconstructions were suggested with the purpose of improving the rigidityof a component and to simplify the assembling process.

69


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Appendix A

Figure A.1: The Mathematica code used to determine the static deflection of the beamelement.

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Appendix B

Figure B.1: Some properties of the copper-beryllium alloy [36].

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Figure B.2: Some properties of the bronze alloy [36].

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Figure B.3: Some properties of the brass alloy [36].

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Figure B.4: Some properties of the TPU thermoplastic [36].

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Figure B.5: Some properties of the Nylon 6 thermoplastic [36].

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Figure B.8: Some properties of Graphite [36].

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Figure B.9: Some properties of the POM thermoplastic [36].

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