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 G˚ a˚ ard

Examiner: Jens Bergstr¨ om

Date: July 5, 2020

This Master’s thesis project was provided by Epiroc Rock Drills AB and conducted at Camatec Industriteknik AB in Karlstad, Sweden. The project is centered around the cutter wheel in the mechanical rock excavator Mobile Miner 40V. This cutter wheel is equipped with cutter discs that grind rock into debris as the wheel rotates and thrusts forward. The internal system consisting of a bearing constellation and the components in its vicinity has experienced a certain degree of wear in the form of scuffing and this was detected on the surfaces of some of the components in the system. The reasons for this occurrence are unknown and per the request of the thesis provider, this was to be determined. The thesis provider also requested a new Finite Element Analysis (FEA) model of the system along with feasible load cases that can be applied to said model. The project was deemed extensive and was therefore decided to be conducted by two students. This thesis covers the determination of the load cases as well 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 the internal 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-system with two components in sliding contact and the other consisted of the bearing constellation along with the outer-most section of the cutter wheel. The purpose of the first model was to use it to determine the contact pressure between the tribo-surfaces and by doing so, be able to determine the expected lubrication regime for the oil in the tribo-system. A material selection process was also conducted on the tribo-surface that had experienced the most severe surface damage. Additionally, minor reconstructions were made with the purpose of optimizing the system. The purpose of the second model was to apply the calculated load cases to the cutter disc attachments located on the outer-most section of the cutter wheel and 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 reconstructions and 60 different load cases for the FEA model. With the load cases, the largest contact pressures on the bearing roller elements was determined. In addition, the cause of the severe surface damage that had occurred in the system is believed to have been identified. Further work on the project work is believed to be required. Future work of interest are determining load 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 selection process and a criterion for the expected lubrication regime in the tribo-system based on tests performed with materials that are more identical to the ones in this project.

Keywords: Mechanical rock excavation, cutter wheel, cutter disc, reaction force, contact

pressure, scuffing, wear

Detta examensarbete tillhandah¨ olls av Epiroc Rock Drills AB och genomf¨ ordes hos Camatec Industriteknik AB i Karlstad, Sverige. Projektet ¨ ar centrerat kring cutterhjulet i maskinen Mobile Miner 40V som ¨ ar avsedd f¨ or mekanisk bergavverkning. Cutterhjulet ¨ ar utrustat med cutter discar som maler berget till mindre flisor genom att hjulet roterar och trycks fram˚ at. Det inre systemet best˚ aende av en lagring med n¨ arliggande komponenter har utsatts f¨ or en viss grad av n¨ otning i form av scuffing och detta uppt¨ acktes p˚ a ytorna hos vissa av komponenterna i systemet. De bakomliggande anledningarna f¨ or denna f¨ orekomst ¨ ar ok¨ anda och utifr˚ an beg¨ aran fr˚ an projektgivaren skulle dessa anledningar fastst¨ allas. Projektgivaren efters¨ okte ¨ aven en ny FEM-modell av systemet tillsammans med rimliga lastfall som ska kunna appliceras p˚ a modellen i fr˚ aga. Projektet ans˚ ags t¨ amligen omfattande och det bed¨ omdes d¨ arf¨ or att tv˚ a studenter kr¨ avdes f¨ or att genomf¨ ora arbetet. Denna uppsats behandlar framtagningen av lastfallen s˚ av¨ al som optimeringen av den nuvarande designen av systemet inuti cutterhjulet.

Under f¨ orstudien h¨ amtades relevant bakgrundsdata f¨ or cutterhjulet och det interna systemet.

Metoder och teorier som ans˚ ags vara potentiellt anv¨ andbara samlades ¨ aven in. Systemet i fr˚ aga delades in i tv˚ a separata modeller; en bestod av ett tribo-system best˚ aende av tv˚ a tribo-ytor i glidande kontakt och den andra bestod av lagringen tillsammans med den yttersta sektionen hos cutterhjulet. Syftet med den f¨ orstn¨ amnda modellen var att anv¨ anda den f¨ or att best¨ amma kontakttrycket mellan tribo-ytorna, och genom detta kunna fastst¨ alla den f¨ orv¨ antade sm¨ orjningsregimen hos oljan i tribo-systemet. En materialvalsprocess utf¨ ordes ¨ aven f¨ or tribo-ytan som hade utsatts f¨ or den mest allvarliga skadan. ¨ Aven sm¨ arre omkonstruktioner utf¨ ordes med syftet att optimera systemet. Syftet hos den andra modellen var att kunna applicera de ber¨ aknade lastfallen p˚ a cutter discarnas inf¨ astningar som ˚ aterfinns i den yttersta sektionen hos cutterhjulet och sedan best¨ amma kontakttrycken som uppst˚ ar p˚ a rullarna i lagren.

Resultaten fr˚ an arbetet best˚ ar av fem potentiella materialval, tv˚ a konstruktions¨ andringar och 60 olika lastfall f¨ or FEM-modellen. Genom att applicera lastfallen best¨ amdes de st¨ orsta kontakttrycken p˚ a lagrens rullar. Ut¨ over detta anses det att anledningen f¨ or den allvarliga ytskadan som hade skett i systemet har identifierats. Det anses att fortsatt arbete kr¨ avs f¨ or projektet. Kompletterande arbete som anses vara av intresse ¨ ar lastfall som inkluderar flera cutter discar i ingrepp samtidigt med berget, konstruktionsl¨ osningar f¨ or tillf¨ orsel och bortf¨ orsel av oljan, en mer djupg˚ aende materialvalsprocess och ett kriterium f¨ or f¨ orv¨ antad sm¨ orjningsregim hos tribo-systemet baserat p˚ a tester utf¨ orda med material som ¨ ar mer identiska med dem som f¨ orekommer i projektet.

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

scuffing, n¨ otning

Firstly, I would like to express my sincere gratitude to Epiroc Rock Drills AB for providing such a challenging, interesting and, above all, fun thesis project. I would also like to thank Camatec Industriteknik AB for the opportunity to conduct this project and for providing a stimulating working environment with helpful people as well as software licenses. Thanks to Joakim Bengtsson, Jonas Andersson, Daniel W¨ annlund and Michael Olofsson for the help throughout the project work. A special thanks to G¨ oran Karlsson for providing the necessary data and information regarding the project and for taking the time to assist whenever it was needed. Lastly, a huge thank you to my supervisor from Camatec, Peter Wigarthsson, for the valuable advice on how to approach the project and for the interesting conversations about everything from boundary conditions in Ansys to string theory.

I would also like to thank my supervisor from Karlstad University, Anders G˚ a˚ ard, for the lengthy 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 project

with me.

Abstract i

Sammanfattning ii

Acknowledgements iii

1 Introduction 1

1.1 Background . . . . 1

1.2 Problem description . . . . 2

1.3 Purpose . . . . 3

1.4 Goal . . . . 4

1.5 Declaration of confidentiality . . . . 4

1.6 Delimitations . . . . 4

2 Theory 5 2.1 Contact mechanics . . . . 5

2.2 Equivalent static force . . . . 5

2.3 Centripetal force . . . . 6

2.4 Sliding wear . . . . 6

2.4.1 Lubrication . . . . 8

2.5 Rolling wear . . . . 13

2.6 Models for determining load cases in mechanical excavation machines . . . . 14

3 Method 18 3.1 Project plan . . . . 18

3.2 Background data . . . . 19

3.3 Establishing useful theories and models . . . . 20

3.4 FEA model . . . . 23

3.5 Determining the load cases . . . . 24

3.6 Construction alterations . . . . 31

3.7 Materials selection . . . . 33

4 Results 37 4.1 Scuffing between Component 1 and Component 2 . . . . 37

4.1.1 Determining the expected contact pressure . . . . 37

4.1.2 Expected lubrication regime . . . . 42

4.1.3 Dry sliding . . . . 42

4.2 Load cases . . . . 44

4.3 Construction alterations . . . . 48

5 Discussion 59

5.1 Scuffing between Component 1 and Component 2 . . . . 59

5.1.1 Density of Component 1 in Ansys . . . . 59

5.1.2 Centripetal force . . . . 59

5.1.3 Oscillating impact motion and dynamic impact factor . . . . 60

5.1.4 Sliding/impact model and equation . . . . 60

5.1.5 Generalised Stribeck curve . . . . 61

5.1.6 Low contact pressure - dry sliding . . . . 61

5.1.7 Surface roughness . . . . 62

5.2 Load cases for the C-model . . . . 63

5.2.1 CSM model . . . . 65

5.3 Materials selection . . . . 66

5.4 Construction alterations . . . . 67

5.5 Future work . . . . 68

6 Conclusion 69

References 70

Appendix A 75

Appendix B 76

1 Introduction

1.1 Background

Camatec Industriteknik AB is a consultancy engineering company with expertise in several technical areas. One of their costumers is the company Epiroc Rock Drills AB, one of the leading productivity companies in the mining and infrastructure industries. Mining is a process where different types of rock are excavated through the use of various techniques.

The four basic mechanisms include spalling, fusion and vaporization, mechanical stress and chemical reactions [1]. Mining is performed with two purposes. One is to create tunnels or networks of tunnels in which people and vehicles can be and travel through. The other purpose 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 primitive tools or with black powder. With new inventions, machine-driven devices were introduced and black powder was replaced with dynamite [2].

The use of explosives cause vibrations and residual stresses in the rock, which in turn increases the need for rock reinforcement. Because of this, there is a high market demand of mechanical rock excavation means that are at least as effective as the use of explosives. In order to fill this need, Epiroc have developed the machines in the Mobile Miner series. The machines in 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 flexibility in comparison to TBMs because of their smaller turning radius. When using explosives to excavate tunnels, a number of different machines have to be used in order to complete certain tasks. There needs to be loaders and trucks for the gathering and transportation of rock debris, as well as machines for rock reinforcement. However, the machines in the Mobile Miner series implement these separate functions into one unit, which makes continuous operation possible and thereby vastly increasing efficiency. The machines excavate rock with the use of a large rotating cutter wheel equipped with cutter discs that grind the rock into debris. 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 height

as low as 2.2 meters. In the Mobile Miner 40V the wheel is instead oriented vertically, which

provides a tunnel height of 4 meters. Illustrations of the two Mobile Miner machines are

shown in Figure 1.1.

(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 Mobile Miner 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 bearing constellation consisting of a radial bearing with a thrust bearing on both sides. Currently, the design of the cutter wheel assembly is not optimal as there is a presence of wear within the construction that occurs at a rate that exceeds what is considered acceptable. The bearings in the bearing constellation and a number of components in contact with them contain surfaces which, to different degrees, have been exposed to tribological phenomena such as scuffing.

The phenomena scuffing is characterized by macroscopically observable changes in the surface

texture, with features related to the direction of relative motion [5]. In this particular case,

the presence of scuffing has led to severe chip formation, which in turn has affected adjacent surfaces and caused them to wear unexpectedly fast. The hydraulic system that provides the feed of the lubricant oil is also affected by the chip formation. In Figure 1.3, two surfaces that 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 Element Analysis (FEA) model using different load cases. However, test running of the machine in the Kvarntorp Mine in ¨ Orebro yielded unexpected results in the form of high wear, as mentioned earlier. The thesis project providers therefore believe this indicates that the numerical model used as validation when developing the current version of the machine contains an unknown amount of discrepancies. As of today, it remains unknown if it is the FEA model that is inadequate, or if it is the assumed load cases or a combination of both. Hence, because of this, it is desired that the work presented in this report leads to an altered construction of the cutter wheel with a longer expected life-time compared to the current design. The new construction is to be based on a new FEA model along with applied load cases that better correspond 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 cutter

wheel has been worn the way it has and using this new knowledge, try to work out solutions

to improve the system’s performance. The FEA model with assumed load cases developed

during the project work is expected to provide a theoretical basis for the mechanical influences

that affect the system as the machine is operating. Given that the working principle with

machines in the Mobile Miner series diverges considerably from traditional mining operations

such as the use of explosives, and to a lesser extent TBMs, they could potentially offer

costumers more value compared to the other alternatives.

1.4 Goal

The project consists of two sub-goals that need to be achieved in order to reach the main goal. One of the sub-goals consists of developing an FEA model containing the relevant parts in the cutter wheel in the software Ansys. It should be possible to make changes to the construction of the individual parts so that the user may test how these changes affect the results of the simulations. Another sub-goal consists of establishing a feasible estimation of the 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 scenarios should affect the cutter wheel, it is relevant to include a combination of the most extreme loads in the estimation of the load cases. By accomplishing these sub-goals, the main goal can then be achieved. The main goal of this project is to establish the reason or reasons why components in the system have suffered such serious surface damage and then, with this knowledge, optimize the current design of the cutter wheel so that the expected life-time of the machine increases as much as possible. This includes conducting construction alterations to one or several components in the vicinity of the bearing constellation, making appropriate material selections where it is deemed necessary and designing to ensure that contact surfaces are 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 not disclose 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 illustrated in 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 ideally smooth and horizontal.

• The load cases were determined by assuming that only one cutter disc at a time made

contact with the rock wall.

2 Theory

2.1 Contact mechanics

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

1 d ^∗ = 1

d ₁ + 1

d ₂ (2.1)

Where d ₁ [m] is the diameter of the concave part (set as a negative value) and d ₂ [m] is the diameter of the convex part. In addition, an effective elastic modulus, E ^∗ [P a], is also determined according to Eq. 2.2,

1

E ^∗ = 1 − ν ₁ ²

E ₁ + 1 − ν ₂ ²

E ₂ (2.2)

Where ν 1 and E 1 [P a] are the Poisson’s ratio and elastic modulus of material 1, respectively, and ν ₂ and E ₂ [P a] are the Poisson’s ratio and elastic modulus of material 2, respectively. For cylinder-to-cylinder contact, the width of the contact surface that forms is defined according to Eq. 2.3,

b =

r 2F d ^∗

πLE ^∗ (2.3)

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

p _max = 2F πbL =

r 2F E ^∗

πLd ^∗ (2.4)

2.2 Equivalent static force

Many systems contain features that can be approximated as a body with a certain mass

impacting another body with a certain velocity. What this means is that the impacted body

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

n = 1 + r

1 + 2h

δ _static (2.5)

Where δ _static [m] is the static deflection of the member. This approximation with the use of the 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 times the gravitational constant g, in order to obtain the approximated maximum dynamic load P _max [N ] that the member is exposed to, according to Eq. 2.6,

P max = nmg (2.6)

2.3 Centripetal force

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

F _c = ma _c = m v ²

r (2.7)

Where m [kg] is the mass of the object that is moving with a tangential speed v [ ^m _s ] along a circular path with radius of curvature r [m]. The centripetal acceleration, a c [ ^m _s 2 ], is proportional to the square of the tangential speed and inversely proportional to the radius of curvature.

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

two bodies are in contact with each other under the influence of a certain normal force and the 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 relation to each other is known as the sliding speed.

When studying tribological fields such as wear, the presence of asperities is an important contributing factor [5]. A tribo-surface in contact with another tribo-surface in relative motion has on a microscopic level an uneven surface with higher and lower areas. These areas form peaks and valleys, respectively, on the surface that are known as asperities. When tribo-surfaces come into contact on a macroscopic level, what really happens is the highest asperity peaks of the respective surfaces come into contact and start to deform plastically as the normal load forcing the two tribo-surfaces together increases. As the asperities are deformed, the surfaces move closer to each other and more asperities subsequently come into contact. The more the asperities deform plastically, the larger the real area of contact between the tribo-surfaces will be.

When the subject of sliding wear of tribo-surfaces is studied, one of the most central theories regarding the wear of the surfaces is known as the Archard wear equation [5], as shown in Eq.

2.8,

Q = K W

H (2.8)

Where Q [ ^mm _mm ³ ] is the volume of material worn per sliding distance, W [N ] is the normal load and H [M P a] is the hardness of the softer surface. The coefficient K is often times known as the wear coefficient and is of great importance as it provides an indication of how severe wear processes will be in different systems.

From Eq. 2.8 it can be understood that the wear rate is proportional to K, meaning that

if lower wear rates in a system are desired, as is often the case, there should be effort put

into making sure that the value of K is reduced for said system. One phenomena that

has a significant impact on the wear coefficient is the so called tribological compatibility

of the system [5]. The tribological compatibility of a system refers to a reluctance of the

two tribo-surfaces to form a strong interfacial bond. The stronger the interfacial bond, the

more material would be removed upon relative dry (unlubricated) sliding of the surfaces and

as such, the system would have a higher wear rate. The term metallurgical compatibility

can be seen as being inversely proportional to the tribological compatibility between two

materials. For example two identical materials would have the highest possible metallurgical

compatibility, but the lowest tribological compatibility. In Figure 2.1 it is illustrated how the

compatibility influences the value of the wear coefficient.

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

As can be deducted from Figure 2.1, the more identical the two materials in the tribo-system are, 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 relative motion. One purpose is to reduce the friction of the tribo-system by reducing the frictional forces between the surfaces. The lubricant serves as a thin film with low shear strength that separates the tribo-surfaces. Another purpose is to reduce the wear in the system. This is possible due to the fact that the lubricant reduces surface contact. The lubricant also seals against 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 the surface temperature and oxygen levels in the system [12].

Many different materials can be used as a lubricant in a system, including gases, liquids or solids. There are four types of lubrication [5]:

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

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

• Boundary - Oil or grease molecules are adsorbed at asperity tips. The molecules

generally separate the surfaces, although a certain degree of asperity contact may still

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

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

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

λ = h _min

σ ^∗ (2.9)

gives an indication of how likely and how severe asperity interactions will be in lubricated sliding. 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 film thickness is too small to prevent increasingly severe surface damage. The middle-ground for the value of lambda, i.e. when 1 < λ < 3, represents a lubrication condition where some asperity 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 peaks and valleys from the mean line through the profile. The mean line is the line of best fit with equal 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 shown that when the roughness value increases, the critical normal load required for the lubrication to transition into boundary lubrication and scuffing decreases.

As stated previously, having a satisfactory amount of lubrication in a system is in many cases

desirable and if the amount of lubrication is not adequate or if there is no lubricant present

at all, gross surface damage can occur. An example of such surface damage is the phenomena

of scuffing that has occurred in some of the components in the cutter wheel assembly in the

Mobile Miner 40V. Scuffing is characterized by macroscopically observable changes in the

surface texture, with features related to the direction of relative motion [5], as can clearly be

seen in Figure 1.3. An inadequate amount of lubrication is not necessarily the only reason

why scuffing occurs in a system where surfaces slide against each other. It can also occur

even if there is a lubricant separating the surfaces. If the normal force acting on the surfaces

is high enough and if the sliding speed is high enough, the lubricant will no longer be able to

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

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

L = η _i V ₊

¯

pRa _t (2.10)

where η _i [P a ∗ s] is the inlet viscosity of the lubricant and ¯ p [P a] is the mean contact pressure.

The sum velocity, V ₊ [ ^m _s ] is defined in Eq. 2.11 as

V ₊ = V ₁ + V ₂ (2.11)

where V ₁ and V ₂ are the respective velocities of the tribo-surfaces. The Combined Center Line Average (CLA) surface roughness, Ra t [m] is defined in Eq. 2.12 as

Ra _t = q

Ra ² ₁ + Ra ² ₂ (2.12)

where Ra ₁ and Ra ₂ are the respective surface roughness values of the tribo-surfaces. In Figure

2.2, a generalised Stribeck curve is shown with three lubrication regimes. Depending on the

value of the lubrication number, the system will operate under either boundary lubrication,

mixed lubrication or elastohydrodynamic lubrication.

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

Several other diagrams found during the project’s pre-study were similar in that they provided a 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 wear would not be reliable since the test specimen used for the IRG Transition Diagram had an unknown 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-mechanism map presented in Figure 2.3 depicts the measured wear mechanisms depending on the normalized pressure, e F , and the sliding velocity, v. The test was performed with a pin-on-disc configuration 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 carbon

content ranges from 0.3% to 0.6% and their manganese content ranges between 0.6−1.65% [17].

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

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

Sliding wear is a field that has garnered a relatively large amount of research over the years since it was first studied. However, one type of wear mechanism related to sliding wear has not been studied as extensively and the mechanism is known as impact wear. Impact wear is reminiscent of erosive wear, but the difference lies in how the particles strike the worn surface. In erosive wear, several hard particles strike a surface either carried by a gas stream or entrained in a flowing liquid, while in impact wear a single body wears down a surface through percussion, i.e. repetitive contact [18]. Depending on from which angle the abrasive particle strikes the worn surface, this percussive motion can either include only a force component normal to the worn surface or it can also include a shear component. As a result of the small amount of research invested in the wear mechanism, wear data is scarce and no extensively applied modeling techniques are available. One of the models that has been 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 bronze

plate in a percussive manner. The model defines the worn volume, W [m ³ ], according to Eq.

2.13 as

W = ( kP N x

H + kN exp (n))( A _i

A ) ^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 [ _m ^kg 2 ] is the hardness

• n is an impact wear coefficient

• A i [m ² ] is the initial contact area

• A [m ² ] is the contact area after N cycles

• j is a constant

Another study [20] conducted on the wear behaviour for different complex impact-sliding motions in impact wear has shown that the amount of surface damage sustained depends on which type of impact-sliding motion is used. It was shown that a unidirectional motion leads to the most severe surface damage, compared to a reciprocating motion and a combined motion. 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 at least one of the tribo-surfaces moving in relation to the other by a rolling motion, rolling wear will 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 depending on a number of factors the bearing will have a certain life expectancy. The rating life, L ₁₀ of a bearing is defined as ”the fatigue life of 90% of a sufficiently large group of identical bearings operating under identical conditions can be expected to attain or exceed” [21]. It is measured in millions of revolutions, is determined in accordance to ISO 281 [22] and is calculated according to Eq. 2.14 as

L ₁₀ = ( C

P ) ^p (2.14)

where C [kN ] is the basic dynamic load rating and p = 3 for ball bearings and p = ¹⁰ ₃ for roller bearings. P [kN ] is the equivalent dynamic bearing load determined from Eq. 2.15,

P = XF _r + Y F _a (2.15)

where

• F r [kN ] is the actual radial bearing load

• F a [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 give a 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 is defined as the load that results in a certain value of contact stress at the center of contact in the most heavily loaded rolling element. For roller bearings this contact stress is σ _H = 4000 M P a. The total residual strain arising from these contact stresses are approximately equal to 0, 0001 of the diameter of the rolling element. It should be noted that the static load rating should be of importance only if the bearing is subjected to static loading, i.e. either when it is not rotating and is subjected to continuous high load or intermittent peak loads or if its rotational speed is less than 10 RP M 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 F _r , which only causes radial displacement of the roller elements in relation to each other. For thrust and thrust-radial bearings, the static load rating instead corresponds to the force F _a , which only causes axial displacement of the roller elements in relation to each other. Under static loading conditions, the damage of the roller bearings is present in the form of the working surface plastic strain. The strain of 0, 0001 that the contact stress σ _H causes should not be higher than the allowable contact stress, [σ] _H [25].

2.6 Models for determining load cases in mechanical excavation machines

The cutter wheel in the present study is designed to excavate rock through continuous

grinding that leads to spalling of rock debris. The cutter wheel is driven by a hydraulic motor

and the cutter discs that are mounted around the circumference of the outer-most section

of the cutter wheel (see Figure 1.2) rotate along with the cutter wheel. The Mobile Miner

40V excavates rock by a certain procedure. An assembly of hydraulic cylinders provide the

cutter wheel with several degrees of freedom. With the use of these cylinders, the wheel

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

Several models for predicting resulting cutter disc forces in tunneling machines exist, although

most of these studies have been conducted on TBMs. The front face of TBMs is a flat plane

equipped with cutter discs. They excavate rock by rotating the front, allowing the cutter discs

to 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 perpendicular

to the rock wall and all of the discs are always in contact with the wall. One of the models

developed for TBMs [26], named the CSM model, is based on a large data base of full-scale

linear cutting tests performed on rock samples. This model takes into account properties such

as tensile and compressive strength of the rock being excavated, cutter disc geometry and

penetration depth. Recently, this model was altered [27] by using different cutting conditions

and linear cutting machines. It has been argued that the previous model needed modification

factors in order to predict more accurate results. A schematic view of the forces acting on

the cutter disc can be seen in Figure 2.4. The contributions of the normal force, F N , and

the rolling force, F R, both lead to a resultant force, F T .

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

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

F T _Rost,M = KT ∗ F T _Rost (2.16)

where F T _Rost,M [N ] is the modified resultant force, KT is a modification factor and F T _Rost [N ] is the resultant force obtained with the use of the CSM model. F T Rost is determined according to Eq. 2.17,

F T _Rost = Z φ

0

T P ^θ Rdθ = Z φ

0

T P ⁰ ( θ

φ ) ^ψ Rdθ = P ⁰ RT φ

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 a contact 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 − p

R ) (2.19)

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

P ⁰ = C ³ s

sσ _c ² σ t

φ √

RT (2.20)

where C is a constant in the semi-theoretical CSM prediction model that is usually taken as

2.12. The variable s [m] is the disc cutter spacing and σ _c [P a] and σ _t [P a] are the uniaxial

compressive strength and Brazilian tensile strength of the rock, respectively.

3 Method

3.1 Project plan

This particular phase was the first of the entire project work and it was conducted in collaboration with K. Xie [6] as well as the project’s supervisor from Camatec. The purpose of this phase was to establish a project plan with an associated project timeline that both participants 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 in order to be able to proceed with their respective goals. Therefore it was decided that four different major activities needed to be completed in order to obtain the FEA model. The activities were defined as:

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

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

• Determine which forces act on the cutter wheel during excavation. With these forces determined, calculate the force components that should affect each cutter disc. Acquire a 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 establishing which criteria to use, the simulation results can be compared to this and it can then be determined what the results indicate for the system.

Given the limited time scope of the thesis projects, it was determined that the activities had to distributed to some extent between the two participants. The author of this report was to be responsible for the third activity listed above, i.e. determining the different load cases of the system. K.Xie [6] was to be responsible for the second activity; the development of the FEA model in Ansys. The two remaining activities were considered to be linked to the respective pre-studies of the projects and therefore it was decided that both participants would conduct these activities. The information regarding the Mobile Miner 40V was essential for both projects 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 able

to pursue the individual goal of the thesis work. In order to be able to optimize the current

design of the cutter wheel, the areas in need of rework would have to be identified. After

personal communication with G. Karlsson, Camatec (February 2020), the author decided on

some key areas to focus the work on. These were listed as:

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

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

• Materials selection - Another important factor from a tribological point of view.

Choosing appropriate materials for surfaces that are in contact can potentially increase the lifetime of the system drastically.

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

3.2 Background data

The Mobile Miner 40V in its entirety is shown to the right in Figure 1.1. A CAD model of the cutter wheel, which this thesis project is based on, is shown in Figure 1.2. The interior of the cutter wheel contains several components and systems. The system relevant for this thesis work is the bearing constellation with the components that are in its vicinity. It is in this system 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 the worn components are classified information, these components have therefore been assigned other names in this report and their models have been simplified (except in Section 3.6 and 3.7). The two rotation symmetric steel components, named Component 1 and Component 2, are shown as an assembly in a section view in Figure 3.1. Component 1 has an internal diameter of 1930 ^+2.2 _+1.6 mm, while Component 2 has an external diameter of 1930 ⁰ _−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.

The bearing constellation consists of a radial bearing in combination with a thrust bearing on each side. With the cutter wheel being oriented vertically, the bearing constellation is not located in line with the cutter wheel’s center of gravity (COG). The assembly of bearing components are positioned with a certain distance to the left of the COG and as such, have an inherent moment arm. The outer ring of the radial bearing is attached to the outer-most section of the cutter wheel by interference fit. So when the hydraulic motor drives the outer-most section and causes it to rotate, the outer ring of the radial bearing rotates along with it. Since it is a radial bearing, its main purpose is to absorb the radial reaction forces that originate from the cutter discs. The thrust bearings on either side of the radial bearing serve the purpose of keeping the radial bearing in place as it experiences bending moments caused by the reaction forces originating from the cutter discs that would otherwise cause the radial bearing to bend.

Component 1 is mounted on the outer surface of Component 2 with a certain clearance fit. Lubricant oil flows into the system through an inlet hole located slightly to the left of Component 2 in Figure 3.1 and at the top. The oil then flows down along the components in the cutter wheel and flows out through an outlet hole located at the bottom. During excavation, Component 1 rotates in relation to the outer ring of the radial bearing, while Component 2 is fixed in place. Due to gravity, a certain surface area of Component 1 will always be in contact with Component 2. The size of this surface area is determined by the size of the clearance fit and the gravitational force of Component 1. Both Component 1 and Component 2 are located on the left side of the radial bearing. On the right side of the bearing, two identical (although mirrored) components are located. The same contact sliding conditions apply for these two components, but the wear damage they had suffered was not as severe as for Component 1 and Component 2. That is why the majority of this thesis work is focused on the components on the left side of the radial bearing and not the components on 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-diameter surface of Component 2 will always be in contact. It is also known that Component 1 will rotate in relation to the outer ring of the radial bearing. It will therefore slide on Component 2 whenever the cutter wheel is rotating. From this, it is obvious that this particular tribo-system will be demonstrate sliding wear. Component 1 has a certain mass and its gravitational force can 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 [ ^m _s ], according to Eq. 3.1,

v = r _Component1 ω (3.1)

where r Component1 [m] is the inner radius of Component 1. These two tribo-surfaces will have a certain surface area - the contact surface. Contact pressure, p [P a], is defined according to Eq. 3.2 as

p = F

A (3.2)

where F [N ] is the applied force and A [m ² ] is the true contact area. The value of the applied force 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. When solids 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 should mean that Hertz contact theory could potentially be used to determine the contact pressure between the surfaces. The condition that needed to be fulfilled to be able to use the theory was that the radius of the concave surface (in this tribo-system the inner radius surface of Component 1) must be far greater than the radius of the convex surface (in this tribo-system the outer radius of Component 2). Since the components each have large diameters and are assembled with a clearance fit, this condition was ultimately not met. As such, Hertz contact theory could not be used. Instead, the contact pressure had to be determined numerically with the use of a simplified model in Ansys depicting the tribo-system. This model was named 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 Component 2. The red circle indicates that the largest clearance will be at the bottom due to gravity and their differences in diameter.

Component 1 was assigned a density of ρ _Component1 = 9656 _m ^kg 3 - significantly larger than

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

contact pressure between the surfaces could be determined. However, other forces were also thought to be involved in the system. Component 1, having a certain mass, rotating around its axis with a certain velocity would mean that it should be exposed to a centripetal force. If such a force was determined to be large enough to be significant, it would have an 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 and Component 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 there existed forces in the opposite direction large enough to overcome Component 1’s gravitational force in the system, it would thereby cause it to lift off from Component 2’s surface. If those forces then were to be removed, Component 1 would fall downwards and impact Component 2. It was thought to be a possibility that this oscillating impact motion where Component 1 lifts from Component 2’s surface and falls back down and impacts it could be present in the tribo-system. The force from this impact would then have an effect on the contact pressure that arises between the surfaces. Since such a force would be a dynamic force, a certain correlation between it and its corresponding static force would be needed in order to make the 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 deflection of Component 2, it was approximated as a beam with length L [m] and a constant flexural rigidity, EI [P a ∗ m ⁴ ], where E [P a] is its Young’s modulus and I [m ⁴ ] is its second moment of area. The equation to use in order to determine the deflection would be the Euler-Bernoulli equation defined in Eq. 3.3 as

EI d ⁴ w

dx ⁴ = q(x) (3.3)

where w(x) [m] is the static deflection (same as δ static ), q(x) [ ^N _m ] 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 occurred

on the surfaces of Component 1 and Component 2, as shown in Figure 1.3. As such, a

criteria was needed to be able to obtain an estimation as to how much wear is expected

in the tribo-system upon altering of certain variables. The generalised Stribeck curve in

Figure 2.2 was chosen as a useful tool for this. As explained in Section 2.4.1, the boundary

lubrication regime indicates that asperity tips adsorb oil or grease molecules and partially

separates the surfaces. In mixed lubrication, some asperity contact occurs but it had been

shown that this particular regime was the one that almost exclusively featured scuffing. In

elastohydrodynamic lubrication, the film is very thin and local pressures are high, which

causes elastic deformation of the surfaces, but from the same study it was shown [15] that this

regime featured virtually negligible wear. Because of this, the priority became to try to ensure

that the lubrication type of the tribo-system in question would be in the elastohydrodynamic

regime in order to reduce the wear generated. The lubrication number, L, in Eq. 2.10 then

became the determining factor in which regime the tribo-system was expected to be. The variables involved were the inlet viscosity of the lubricant, sum velocity and combined surface roughness 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 in this thesis work. For further details about the development of the FEA model, the reader is referred to that thesis report.

Two separate models were created; the aforementioned Two-ring case (see Figure 3.2) and the C-model. The Two-ring case model was used for the tribo-system consisting of Component 1 and Component 2 in order to determine the contact pressure between the surfaces. The C-model was used to determine the contact pressures on the rollers in the radial bearing and

the 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 to

this model.

3.5 Determining the load cases

One of the major activities of the thesis work included determining the load cases that the cutter wheel is expected to be exposed to. In order to obtain feasible load cases, the possible external factors for the cutter wheel had to be taken into consideration. In reality, the rock surface being excavated is not particularly smooth, but rather coarse and dented. If the load cases were to be more precise, the uneven surface of the rock wall would need to be factored into the calculations. However, due to the uncertainty about just how coarse the surfaces being excavated are and how to implement this into the calculations in a reasonable way, it was decided early on that this would not be taken into consideration when determining the load 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 are mounted in pairs along the circumference of the outer-most section of the wheel, amounting to a total of 16 pairs of cutter discs. The discs are identical in terms of dimensions, but they are oriented in different configurations in relation to the cutter wheel. The angle of the cutter discs on the left side of the cutter wheel is termed γ _{lef t} and the angle of the cutter discs on the right side of the cutter wheel is termed γ _right . These angles are measured in reference to the 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 1

in Table 3.1, (b) is configuration 2, (c) is configuration 3, (d) is configuration 4 and (e) is

configuration 5.

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

Table 3.1: The configurations of the cutter discs

Configuration γ _{lef t} [ °] γ _right [ °]

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 from

different angles. As a result of this, the reaction force components that they are exposed to

will 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 cutter

wheel has a number of degrees of freedom due to a number of hydraulic cylinders. It can

thrust forward with a thrust force which leads to a reaction thrust force, F _r , but depending

on the rotation of the cutter wheel and the configurations of the cutter discs, it will also

experience a reaction side force, F _a . It can also tilt upwards and downwards with certain

angles, according to Figure 3.5.

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 cutter discs. It rotates around an axis normal to its rotational axis, pointed upwards. From the starting configuration where it is placed parallel to the machine, it can then be rotated between −25 ° to 25° relative to the machine, as shown in Figure 3.6.

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

This angle was termed β and is the angle of the cutter wheel relative to the rest of the machine as the cutter wheel is rotated. During operation, five different configurations of the cutter 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 cutter wheel is oriented according to one of the configurations listed in Table 3.2 and it then thrusts forward with a certain thrust force from a hydraulic cylinder. The cutter wheel’s orientation is fixed when thrusting forward and the wheel always thrusts in a direction parallel to the rest 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 is

fixed when thrusting and the direction of the thrust motion is always parallel to the Mobil

Miner. Viewed from above.

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

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

Procedure β[ °] F _r [kN ] F _a [kN ]

1 -25 F _r1 F _a1

2 -14 F _r2 F _a2

3 0 F _r3 F _a3

4 0 F _r4 F _a4

5 14 F _r5 F _a5

6 25 F _r6 F _a6

So far, there are three angle variables of importance in determining the load cases - the angle configuration of the cutter wheel, β, and the angle configuration of the left and right cutter discs, γ _{lef t} and γ _right , respectively. There is also another factor influencing the reaction forces that the cutter discs are exposed to. Initially, during the beginning of the excavation, only one or two cutter discs will be in contact with the rock at a time since the wheel at that point just started to make contact with the rock. As the cutter wheel excavates the rock by thrusting forward, the wheel will progressively penetrate deeper into the rock. Because of this, the wheel’s contact area with the rock will increase and more cutter discs will be in contact with the rock at all times. The thrust force will be the same in all the cases, but the 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 the thrust force will be divided among the cutter discs. In the case of only one cutter disc being in 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 the

case where the reaction forces affecting a cutter disc are at a maximum. Therefore, it was

determined that the most relevant excavation case would be the case where only one cutter

disc is in contact with the rock wall, since that case would arguably result in the highest

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

As mentioned, the cutter discs experience reaction thrust forces and reaction side forces. The reaction force from the thrust force will be directed parallel to the cutter wheel, while the reaction 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 variable γ _right . The forces F represent the resultant forces.

Figure 3.8: The thrust force results in two reaction forces. The reaction force F _r is always directed parallel to the cutter wheel (not included in the figure) while the reaction force F _a is always 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 reaction

forces affecting the cutter disc had to be explored further. As mentioned previously, one

reaction force is parallel to the cutter wheel, F _r , and one reaction force is perpendicular to the

cutter wheel, F _a . From these forces, two equivalent forces, Q _z and Q _x , could be determined,

as illustrated in Figure 3.9.

Figure 3.9: The forces Q z and Q x .

The force Q _z represents the equivalent reaction force parallel to the cutter disc and the force Q _x represents the equivalent reaction force perpendicular to the cutter disc. The force Q _z is compressive while the force Q _x leads to a bending moment at the cutter disc’s attachment plates. Through trigonometric means, the forces Q _z and Q _x could then be determined. Using the cutter discs as reference, the forces F _r and F _a both contribute to the magnitudes of the forces Q _z and Q _x . 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 Q _z and Q _x .

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

Q _xa = F _a cos (γ − ( π

2 )) (3.4)

Q _za = F _a sin (γ − ( π

2 )) (3.5)

Q _xr = F _r sin (( π

2 ) − γ) (3.6)

Q zr = F r cos (( π

2 ) − γ) (3.7)

In order to obtain the values of Q z and Q x , Eqs. 3.8 and 3.9 were used:

Q _z = Q _za + Q _zr (3.8)

Q _x = Q _xa + Q _xr (3.9)

Every individual load case would have certain values of the forces Q _z and Q _x and all of these cases were to be applied in the C-model in Ansys. With the C-model, the contact pressures on the rollers in the radial bearing and the thrust bearings could be determined. Depending on 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 work was the bearing constellation and the components in its vicinity. The bearing constellation consists of one radial bearing and two thrust bearings manufactured specifically for this particular application. As such, these components could not be altered in any way. This left the author with limited options in how the system would have to be redesigned in order to reduce the stress distributions experienced by the components. Despite this, other solutions were possible, including reconstructions with the purpose of simplifying assembling of the cutter 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 order

to properly demonstrate the reasoning behind this construction alteration, a more detailed

illustration would be needed. Component 2 is not only in contact with Component 1, but

also a solid ring. The contact between Component 1’s and Component 2’s surfaces is a sliding

contact, but as illustrated in Figure 3.11, the solid ring is mounted onto Component 2 with

an interference fit and no sliding occurs.