Conceptual Design of an Unloading System for Continuous Tracks

DEGREE PROJECT IN MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2017

How to increase the load capacity of tracks with the use of hydraulic cylinders

JONAS TORSTENSSON

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

Conceptual Design of an Unloading System for Continuous Tracks

How to increase the load capacity of tracks with the use of hydraulic cylinders

Jonas Torstensson

Master of Science Thesis MMK 2017:45 MKN 197 KTH Industrial Engineering and Management Department of Machine Design SE-100 44 Stockholm

Master of Science Thesis MMK 2017:45 MKN 197

Conceptual Design of an Unloading System for Continuous Tracks

Jonas Torstensson

KTH Industrial Engineering and Management

Approved Examiner Supervisor 2017-05-31 Ulf Sellgren Ulf Sellgren Commissioner Contact person Svea Teknik Jacob Wollberg

Abstract

This report presents the result of a Master thesis course done at the Machine Design department at KTH. The thesis was written at the company Svea Teknik in collaboration with the tunnel boring machine manufacturer Atlas Copco. The high longitudinal force needed when the Remote Vein Miner is boring is achieved by the friction when clamping the machine between the tunnels ceiling and ground using hydraulic cylinders mounted on the top and bottom of the machine. A new generation of machines doesn’t allow for the bottom cylinders to be ﬁtted on the machine. The pair of continuous tracks used to propel the machine must bear these loads but the tracks aren’t strong enough to alone support the weight of the boring machine. This creates the need for an unloading system which unloads the inner wheels of the track so they don’t fail. Concepts were generated using a morphological matrix with the load sharing unit broken down to sub functions with several solutions paired to each. The iterative process led to nine concepts, where two proved more promising than the others when they were subjected to a Pugh’s evaluation matrix. The two concepts were developed further where a feasibility analysis indicated that only one concept was feasible with the dimensions given in a CAD model together with the load provided by Atlas Copco. The remaining concept is based on hydraulic cylinders lifting the inner wheels of the track to unload them while the machine is boring. The machine is then resting on a skid mounted inside the track. A CAD model was made of the new concept and the new components strength was analyzed using FEM-models. Keywords: Hydraulic unloading system, continuous track, load capacity tracks

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Examensarbete MMK 2017:45 MKN 197

Konceptkonstruktion av ett avlastningssystem för bandenheter

Jonas Torstensson

KTH Industrial Engineering and Management

Godkänt Examinator Handledare 2017-05-31 Ulf Sellgren Ulf Sellgren Uppdragsgivare Kontaktperson Svea Teknik Jacob Wollberg

Sammanfattning

I denna uppsats presenteras resultatet av ett examensarbete för masterprogrammet Maskinkonstruktion på KTH. Arbetet utfördes på förtaget Svea Teknik tillsammans med tunnelborrmaskintillverkaren Atlas Copco. De stora longitudinella krafterna som krävs när tunnelborrmaskiner borrar erhålls med hjälp av hydraulcylindrar monterade både på ovan- och undersidan av maskinen som klämmer fast maskinen mellan tunnelns golv och tak. En ny generation maskiner från Atlas Copco tillåter inte hydraulcylindrar monterade framtill på undersidan av maskinen. Istället tar de båda bandenheterna som är avsedd att driva maskinen framåt upp dessa krafter. Bandenheterna är inte tillräckligt starka för dessa laster utan en avlastningslösning för hjulen inne i bandenheten behövs. Problemet delades upp i subfunktioner som sattes in i en morfologisk matris för att generera koncept. Den iterativa processen ledde till nio koncept där två av dem visades mest lovade efter en konceptutvärdering med hjälp av en Pugh’s matris. De båda koncepten arbetades vidare till en mer detaljerad nivå där en rimlighetsanalys visade att endast ett koncept var fysiskt möjligt att applicera med de givna begräsningarna som gavs av utrymmet i den givna CAD-modellen tillsammans med de givna lasterna. Det kvarstående konceptet baseras på hydrauliska kolvar som monteras på hjulen i bandenheten. Dessa förﬂyttar hjulen uppåt tills de inte är i kontakt med bandenhetens kedja längre. Kedjan vilar då på en stödstruktur som är stark nog för lasterna. En CAD-modell gjordes på konceptet och de nya komponenternas hållfasthet analyserades med hjälp av FEM-modeller. Nyckelord: Hydraulisk avlastare, bandenhet, lastkapacitet band

Acknowledgments

I would like to thank the employees of Svea Teknik and Atlas Copco for making this thesis possible, with special thanks to Jacob Wollberg, Bengt Johansson and Jerk Back. I would also like to thank Ulf Sellgren at KTH for being my supervisor. A huge thank you to my dear friends Oscar Hällfors and Elin Skoog for the years at KTH together. Your input writing this thesis while sharing an oﬃce with you has been invaluable. Most of all, thank you mother for always being there and thank you for all the support twin brother. I know what I can be. Let me tell you how I feel - I’m alright, I’m alive

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Contents

Abstract iii Sammanfattning v Acknowledgments vii Glossary xi Acronyms xiii Nomenclature xv

1 Introduction 1 1.1 Background ...... 1 1.2 Purpose ...... 2 1.3 Problem Description ...... 2 1.4 Scope ...... 3 1.5 Delimitations ...... 3 1.6 Product Design Speciﬁcation ...... 4 1.7 Methodology ...... 5

2 Frame of Reference 7 2.1 The Remote Vein Miner ...... 7 2.1.1 Tramming ...... 7 2.1.2 Boring ...... 9 2.2 Tracks ...... 9 2.2.1 External loads acting on the track ...... 10 2.3 Belleville Springs ...... 10

3 Concept Stage 13 3.1 Concept Generation ...... 13 3.2 Concept Evaluation ...... 14 3.3 Feasibility Analysis ...... 16 3.3.1 Compression Springs ...... 16 3.3.2 Belleville Springs ...... 17 3.3.3 Hydraulics ...... 19 3.4 Patent Search ...... 20

ix 4 Detailed Concept 21 4.1 The Skid ...... 22 4.2 The Fork ...... 23 4.3 The Frame ...... 24 4.4 The Cylinders ...... 27 4.5 PDS evaluation ...... 28

5 Discussion and Conclusion 31 5.1 Discussion ...... 31 5.1.1 Skid Discussion ...... 31 5.1.2 Fork Discussion ...... 32 5.1.3 Frame Discussion ...... 32 5.1.4 Cylinders Discussion ...... 32 5.1.5 Method Discussion ...... 32 5.2 Conclusion ...... 33

6 Future Work 35

References 37

Appendices 39 A The Elements of the Product Design Speciﬁcation ...... 39 B The Gantt chart ...... 43 C The Criteria of Pugh’s Evaluation Matrix ...... 47 D The MATLAB script used for calculation of the Belleville spring . . . . . 49 E Pictures of the ﬁnal design ...... 53

x Glossary

ANSYS A Finite Element Software used to numerically calculate solid mechanics Atlas Copco A Swedish company producing tunnel boring machines DIN 17222 A industrial standard specifying material data of steel used when manufacturing Belleville springs KTH Kungliga Tekniska Högskolan (Royal Institute of Technology), university in Stockholm, Sweden MATLAB A computer software used for writing scripts for solving mathe- matical problems

Acronyms

FEA Finite Element Analysis FEM Finite Element Method, a method used in solid mechanics to numerically analyze structures to see the stresses of the structure MTTF Mean Time to Failure, the mean time a system takes to fail MTTR Mean Time to Repair, the mean time it takes to repair the system PDS Product Design Speciﬁcation RVM Remote Vein Miner, a machine boring tunnels to mine minerals TBM Tunnel Boring Machine, a machine boring tunnels in a mine

xiii

Nomenclature

hBW Height of a Belleville spring washer Px Required axial load of each track tBW Thickness of a Belleville spring washer Py Required longitudinal load capacity of each track DiBW Inner diameter of a Belleville spring washer Pz Required horizontal load capacity

of each track DoBW Outer diameter of a Belleville spring washer g The gravitation acceleration con- 2 stant, set to g=9.81 m/s δ The deﬂection of a spring rsprocket The eﬀective radius of the hy- E Young’s modulus draulic motor in the tracks µ Poisson’s ratio TM The tracks max hydraulic motor torque, turn on spot + inclina- FBW The spring force from a Belleville tion spring

µt Friction coeﬃcient between the Fflat The load of where a Belleville ground and the track’s shoes spring washer is ﬂattened mfront The weight of the front wagon of h0 Cup height of a Belleville the Remote Vein Miner, a machine spring boring tunnels to mine minerals (RVM) Nsprings Number of springs stacked in a Belleville spring stack Pwz The forces acting on the joint connecting the front and back wagon κ The quota of the spring thick- of the RVM ness and height of a Belleville spring mequiv The equivalent mass acting on the tracks when the RVM is tram- σuts The maximum stress of a material ming before it breaks

xv Lstack The height of a Belleville spring pskid,b Pressure transferred from the skid stack to the chain

δtot Total horizontal displacement of the track’s inner wheel

ηmin Ratio of the pre-tension length as a quota of the cup height in a Belleville spring

ηmax Ratio of the maximum deﬂection length as a quota of the cup height in a Belleville spring hpre The cup height of a pre-tensioned Belleville spring

δBW,max The maximum allowed deﬂection of a Belleville spring psystem Hydraulic system pressure dpiston Diameter of a hydraulic piston pop,max The maximum operation pressure of a hydraulic cylinder

αg The tilt angle of the ground

Lb The width of the mounting surface of the track’s inner wheels

Lh The height of the mounting surface of the track’s inner wheels

Fsm The maximum force the spring in Concept 2 needs to withstand

PzF Z Total load capacity of the tracks using the hydraulic cylinder FZ 250 -80 50 01 201 32

PyF Z Total allowable side load of the system using hydraulic cylinders FZ 250 -80 50 01 201 32

Askid,b Area of the surface where skid is in contact with the chain xvi Chapter 1

Introduction

This thesis describes the process of creating a conceptual design of an unloading system for continuous tracks used in the Tunnel Boring Machine, a machine boring tunnels in a mine (TBM) developed by Atlas Copco. This chapter formulates the problem and speciﬁes the criteria needed to be met for an acceptable design. The methodologies used in the this master thesis work are also presented in this chapter.

1.1 Background

RVM manufactured by Atlas Copco uses the vehicle propulsion system “continuous tracks” (or tracks) shown in figure 1.1. The machine operates by clamping itself between the ground and ceiling of the tunnel using hydraulic stingers and jacks. The cutter head is then pushed forward, boring through the tunnel wall. The stingers and jacks are then unclamped and the machine trams forward in the newly bored part of the tunnel. Close enough to the wall, the machine clamps itself again to repeat the cycle. The combined force of the machine’s own weight and stingers is too high for the tracks to bear. Atlas Copco’s existing tunnel boring machines have support legs (jacks) which lift the machine to relieve the tracks from the high load. However, with the current design of their new RVM, there’s no room to fit jacks in front of the tracks. Atlas Copco wants to find a solution where the load capacity of the tracks, when the tracks are stationary, is increased without increasing the outer dimensions of the vehicle. Several concepts of how the tracks can increase their load capacity should be generated and evaluated. One should be picked to design a detailed concept with a complete CAD model and general dimensioning which proves that the concept is feasible to be implemented in the machine.

1 Chapter 1. Introduction

Stingers

Jack Track

Figure 1.1. Side view of the RVM

1.2 Purpose

Due to the RVM’s limited space in front of the tracks, it’s not possible to ﬁt jacks to unload the tracks. This is the solution used on Atlas Copco’s previous tunnel boring machines. To bear the combined gravitational and stinger forces, the load capacity of the tracks must be increased.

1.3 Problem Description

The tracks used in the RVM shown in ﬁgure 1.2 consist of a chain wrapped around a frame with a total of six wheels mounted on the frame. The rear wheel supplies torque to the chain which propels the machine. The front wheel tensions the chain and the four smaller wheels in the middle absorb the vertical forces from the ground. According to the industrial contact at Atlas Copco, the weakest link is the four inner wheels which indicates that increasing the load capacity of the inner wheels or creating an unload mechanism of the wheels would increase the overall loading capacity of the tracks. The highest load the track is exposed to is during the boring operation when the tracks aren’t moving. Hence, a solution where the inner wheels are unloaded and limits the tracks propulsion is allowed. General calculations should be performed to prove the concept’s feasibility and crucial parts should be designed in detail to expose new weak spots.

2 1.4. Scope

Chain pre-tension spring

Rear wheel

Inner wheels Front wheel Figure 1.2. The tracks used in the RVM

1.4 Scope

To create a conceptual design of an unloading system which increases the loading capacity of the tracks in Atlas Copco’s remote vein miner without increasing the outer dimensions of the machine. The project will be performed from January to May 2016.

1.5 Delimitations

One of the several concepts generated should be chosen for a more in depth study. Since the concept could be applied on a range of tunnel boring machines, the design will be kept at a not too detailed level and only rough calculations with specific forces will be performed. The thesis won’t go further than the concept stage since the available time for the project would not allow for an acceptable design if time would be spent on other areas. More ground for the delimitations are available in the Product Design Specification (PDS) in appendix A. The conceptual design does not include • Analyzing the market for commercial purposes • Packing for transport, storage or commercial purposes • Weight optimizing • Testing or plan for testing the final design

3 Chapter 1. Introduction

• Disposal of machine when reaching end of life • The interface between the tracks and the machine • End of Life - specifications Some of the tunnel boring machines available from Atlas Copco are protected by confi- dentiality. The machine RVM will be used as the frame-of-reference machine in careful consultation with Atlas Copco to make sure no confidential information is used in the thesis which obstructs the report from being published.

1.6 Product Design Speciﬁcation

The partial PDS presented in appendix A was composed using parts of the Total Design method [1]. Due to the delimitations speciﬁed in chapter 1.5 and after consultation with the industrial supervisor some of the elements in the PDS were disregarded. Figure 1.3 shows the elements of a complete PDS with the disregarded elements crossed over.

Figure 1.3. The elements of a complete PDS with the disregarded elements of the conceptual design crossed over

4 1.7. Methodology

1.7 Methodology

This thesis was done according to the Stage Gate method [2] which breaks down the process into smaller goals. Popular design methods such as design for manufacturing [3] and design for assembly [4] have been proven effective when larger quantities are produced but due to the production level of the RVM and this project’s delimitation, these methods were not applied. The Stage-Gate-System [2] is used to assure the success of an innovative project where gates are set as quality checkpoints. At each checkpoint, a decision of go or no go is made based on the project’s quality compared to the requirement specification. If a no go is decided, the project should move back to a previous stage to meet the quality requirements. A Stage Gate flow chart of the project is presented in figure 1.4 where arrows illustrating the iterative part of the planning report and the customer approval. However, this iterative step applies to every gate, where you have to go back to previous stages if the requirements of the gate haven’t been fulfilled.

Define and Planning Planning and Problem Defining Frame describe Report and Supervisor Yes (planning) Defined Correct? Customer Yes (Problem) of Reference problem Seminar

Planning no Problem defined no

Feasibility Concept Concept Background Analysis Evaluation Generation Search

Adjust Design Customer Customer Create detailed to Customer s Yes Consultation Approval CAD model Wishes

Final Corrections Final Finish Report and Make Numeric and Report Hand Presentation Presentation Analysis(FEA) in and Opposition

Figure 1.4. General methodology and work ﬂow throughout the thesis.

The ﬁrst stage to Deﬁne and describe problem was done to be eligible a supervisor from KTH. A planing report containing the Stage Gate-chart, the Gantt-chart and the problem description was done and accepted both by the academic and industrial supervisors.

5 Chapter 1. Introduction

With the problem description as a base, the frame of reference could be defined by listing all knowledge needed to be gathered to solve the task. The background search was done using the knowledge database provided by the library of KTH and by searching for relevant literature at the library. The database and product data sheets provided by Atlas Copco were also used. Course literature from the courses of solid mechanics, component design, advanced manufacturing were also used when searching for usable information. The methods used for the concept generation and evaluation are presented in chapter 3.1 respectively chapter 3.2. The feasibility analysis was done using the skills the literature gathered during the background search. The concepts were then presented to the customer (Customer Consultation) to be able to make changes according to their wishes. A detailed CAD-model was designed after the concept was approved by customer. The designing of the CAD-model was an iterative step together with the Finite Element Analysis (FEA) until acceptable stress levels were obtained. The thesis was then handed to the academic supervisor who sent it to an opponent for review. A public oral presentation was done at KTH and the opponent presented the suggestions of how the thesis and work could be improved. Corrections of the thesis were then done before handing it in to the examiner for final grading. Each stage functions as a key point which breaks down the project into smaller sections to make it more manageable. A Gantt chart was created with the Stage Gate chart as a base. The Gantt chart shown in appendix B has specific dates for each checkpoint with the work process divided into weeks. The purpose of the Gantt chart is to create an easy method of regularly following the time plan, making sure deadlines are kept.

6 Chapter 2

Frame of Reference

This chapter introduces the frame of reference needed to design and properly specify the concepts in chapter 3. The forces acting on the RVM as well as the loads on the tracks are deﬁned together with theory of Belleville springs.

2.1 The Remote Vein Miner

This chapter describes the external forces acting on the RVM. The loads acting on the tracks are divided into two load cases. One while the machine is tramming and the other while the cutter head is operating.

2.1.1 Tramming

The RVM shown in figure 1.1 consists of two wagons which are connected by an axial joint. The front wagon pulls the rear wagon while the machine is tramming. The free body diagram in figure 2.1 shows the load acting on the tracks while the RVM is tramming. The rear wagon is cut off and replaced by forces acting on the joint. Atlas Copco provides data on what loads act on the tracks as a sum of the weight of the front wagon mfront and the forces acting on the joint Pwz giving the equation 2.2. The following equations for the forces in figure 2.1 can be derived:

Fg = mfrontg (2.1) F + P m g P = g w,z = equivalent (2.2) z 2 2

TM Px = (2.3) rsprocket

7 Chapter 2. Frame of Reference

Fg Fg

rsprocket

Pw,z Pw,z

P w,x P y Py TM Px Pz Pz Pz

Figure 2.1. Side view (left) and front view (right) free body diagram of the RVM while tramming

Where g is the gravity acceleration and rsprocket is the eﬀective radius the sprocket of the hydraulic motor which acts on the track’s chain. Machine speciﬁcations are listed in table 2.1.

Table 2.1. Machine data

Weight mfront of the front wagon of the RVM 160 000 kg The equivalent weight on the tracks mequiv 200 000 kg Max hydraulic motor torque TM 222 764 N m Track sprocket radius rsprocket 615.5 mm Friction coeﬃcient between ground and tracks µt 0.7 Maximum tilt angle of the ground αg 5°

The load Py is given by the maximum tilt angle of the ground αg. The tilt angle is shown in ﬁgure 2.2 and was provided by Atlas Copco. By assuming the load is distributed evenly over the two tracks of the RVM, equation 2.4 can be used to calculate the side load Py while tramming.

Pw,z

Py αg Pz Py

Figure 2.2. Front view of the RVM showing the ground tilt angle αg where the machine is tramming

Py = sin αgPz (2.4)

8 2.2. Tracks

The data in table 2.1 together with equations 2.2, 2.3 and 2.3 were used to calculate the speciﬁc loads. The result is presented in table 2.2.

2.1.2 Boring

The machine is clamped between the ground and the ceiling of the tunnel when it’s boring, as shown in ﬁgure 2.3. The rear wagon is disconnected from the front when the machine is boring due to heavy vibrations propagating through the joint. The horizontal load Pz

10x Pstinger,z 10x Pstinger,y

10x Pstinger,x

Fg FL,z FL,x

FL,x

rsprocket

Py P T y 2x Pjack,x M P Pjack,z P jack,y P x Pz jack,yPz

Figure 2.3. Side view (left) and front view (right) free body diagram of the RVM while boring and side load Py acting on the tracks were given by Atlas Copco and the longitudinal load Px is calculated using equation 2.5 and the data in table 2.1. The result is presented in table 2.2. The tracks are equipped with brakes which are used while boring to compensate for the high longitudinal forces. Px = Pzµ (2.5)

Table 2.2. The speciﬁc external forces acting on the track

Tramming Boring Px 0.086 MN 1.75 MN Py 0.196 MN 0.5 MN Pz 0.918 MN 2.5 MN

2.2 Tracks

The tracks used in the RVM are provided by Titan Intertractor GmbH with the product id WWC161013. One track is mounted on each side of the machine (see ﬁgure 1.1) with a hydraulic motor mounted on the track’s rear wheel (see ﬁgure 1.2).

9 Chapter 2. Frame of Reference

2.2.1 External loads acting on the track

The forces shown in figure 2.1 (tramming) and figure 2.3 (boring) are assumed to be evenly distributed over the chain as shown in figure 2.4.

Px Py

Figure 2.4. The external forces acting on the tracks

The forces for both the tramming and boring load case for each component are all listed in table 2.2

2.3 Belleville Springs

Belleville springs can be used when dealing with high loads, limited space and short movement [5]. In contrary to a traditional helical spring, the conical shaped disc of the Belleville spring has a nonlinear force-deflection relationship [5]. A near constant region of force for a 65-135% deflection from flat can be achieved by having a ratio κ=1.414 of the spring cup height h0 and spring thickness tBW [5], where h0 is the spring cup height and tBW the thickness of washer (equation 2.6). The dimensions are shown in figure 2.5. The spring stiffness nears linear with declining κ and can be considered as linear as κ nears zero.

The force FBW of the spring is given as a function of the deflection δ, Young’s modulus E and Poisson’s ratio µ. The function is presented in equation 2.7, 2.8 and 2.9. The load Fflat of where the spring is flattened out (i.e. δ = h0 ≈ hBW − tBW ) is given by equation 2.10 where hBW is the total spring height also shown in figure 2.5.

h κ = 0 (2.6) tBW 4Eδ h δ) 3i FBW = 2 2 (h0 − δ)(h0 − )t + t (2.7) K1Do(1 − µ ) 2

10 2.3. Belleville Springs

SECTION A-A Di bw 0 h h

t Do bw

A A

Figure 2.5. The dimensions of a Belleville spring

2 6 h(Rd − 1) i K1 = 2 (2.8) π ln Rd Rd

Do Rd = (2.9) Di 3 4Eh0t Fflat = 2 2 (2.10) K1Do(1 − µ ) The maximum stresses of a Belleville spring are concentrated at the inner and outer edges of the cone. These can be calculated using the equations 2.11 to 2.17 [5].

4Eδ h δ i σc = − 2 2 K2 h0 − + K3t (2.11) K1Do(1 − µ ) 2

4Eδ h δ i σti = 2 2 − K2 h0 − + K3t (2.12) K1Do(1 − µ ) 2 4Eδ h δ i σto = 2 2 K4 h0 − + K5t (2.13) K1Do(1 − µ ) 2

6 hRd − 1 i K2 = − 1 (2.14) π ln Rd ln Rd

6 hRd − 1i K3 = (2.15) π ln Rd 2

11 Chapter 2. Frame of Reference

Rd ln Rd − (Rd − 1) Rd K4 = 2 (2.16) ln Rd (Rd − 1)

Rd K5 = (2.17) 2(Rd − 1) To increase the length of the deflection δ, the springs can be stacked as shown in figure 2.6. The flattening force Fflat is kept but the new spring stiffness gives linear relationship with the number of springs stacked, δstacked = δNsprings, where Nsprings is the number of stacked springs [5].

Figure 2.6. A method of stacking four Belleville springs to increase the deﬂection four times while keeping the ﬂattening out force

The height of a pre-tensioned spring can be described as the relaxed spring height hBW minus the fraction ηmin of the relaxed spring height it has been pre-tensioned:

hpre = hBW (1 − ηmin) (2.18)

The fraction ηmax of the relaxed spring height hBW deﬁnes the maximum allowed deﬂection δBW,max as: δBW,max = hBW ηmax (2.19)

The number of springs required to achieve a total deﬂection δtot can be calculated using the pre-tension ηmin and the maximum deﬂection ηmax:

Nsprings = δtothBW (ηmax − ηmin) (2.20)

An estimation of the total spring stack height Lstack is presented in equation 2.21 where tBW is substituted using equation 2.6 and hpre using equation 2.18. 1 L = N (h + t) = N h 1 − η + (2.21) stack springs pre springs BW min κ

12 Chapter 3

Concept Stage

This chapter presents how the concepts were generated and the evaluation process of the concepts. The two most promising concepts were then worked in more detail to see if they were feasible in relation to the PDS. A patent search comparing the remaining concept with existing solutions was done before proceeding with creating a more detailed model.

3.1 Concept Generation

To generate concepts of the task given in chapter 1.4, a morphological matrix [6] was used. The task of the concept was broken down into sub functions and several solutions for each subfunction were generated by brainstorming and analyzing available commercial products. Simple sketches were done for each solution and inserted in the matrix to foster creativity. The matrix is presented in ﬁgure 3.1. Concepts were generated by pairing one random solution from each sub function. If the concept looked feasible, it was sketched in a low level of detail to be used in a concept evaluation. Intuitive concepts, where a solution had emerged during the background search and designing of the morphological matrix were also added to the list of generated concepts just at the methodology states [7]. The following concepts were generated and are presented in ﬁgure 3.2: • Concept 1: Pillars situated between the inner wheels which moves down with hydraulic cylinders to unload the wheels • Concept 2: The inner wheels are mounted on springs which are compressed enough for a skid to hit the ground unloading the inner wheels • Concept 3: A skid mounted on an electric motor which rotates the ACME screw, making the skid move down to unload the inner wheels

13 Chapter 3. Concept Stage

Morphological Matrix Solu�ons Subfunc�ons 1 2 3 4 5

Mo�on Piston Scissor li� Elas�c ACME Screw Gear rack

Energy Hydraulic Spring Electric motor Pneuma�c

Unloading structure Skid Pillars Reinforced wheels

Moving part Pillars/skid Wheels

Figure 3.1. The morphological matrix used to generate concepts

• Concept 4: A scissor lift moves a skid with a pneumatic cylinder unloading the inner wheels • Concept 5: Springs mounted on the inner wheels which are compressed until the wheels hit unloading cylinders situated above the inner wheels • Concept 6: Investigating the possibility to reinforce the wheels/bearings to increase load capacity • Concept 7: Hydraulic cylinders moving a skid to unload the inner wheels • Concept 8: Moving a skid by using a gear rack and an electric motor • Concept 9: Mounting hydraulic cylinders on the inner wheels to move them up until the skid unloads the wheels

3.2 Concept Evaluation

The concepts generated in chapter 3.1 were evaluated using Pugh’s Evaluation Matrix [7] to systematically and in an unbiased way decide what concept to proceed with. The evaluation criteria were created by studying the PDS and all criteria are speciﬁed in appendix C. Each concept generated in chapter 3.1 was inserted in the matrix shown in ﬁgure 3.3. A datum concept (Concept 1) was set and the rest of the concepts were benchmarked on each criterion. A value of "+" was given if the concept was deemed as better performing and a "-" if it performed worse. An "S" was given if the concept performed as good as the datum. The method of controlled convergence [7] was used when the weaknesses of the most promising concepts were studied to see if alterations of the concept could be made to

14 3.2. Concept Evaluation

Concept 1 Concept 2

Concept 3 Concept 4

Concept 5 Concept 6

Concept 7 Concept 8

Concept 9

Figure 3.2. Sketches of the generated concepts to evaluate

Pugh's Evalua�on Matrix + for be�er than datum - for worse than datum S for same than datum

Key Criteria Concept 1 Concept 2 Concept 3 Concept 4 Concept 5 Concept 6 Concept 7 Concept 8 Concept 9 Sta�c load D + -- + - S- + Ground pressure + + + - - + + + Cycle Time s + + + + S SS Environmental Eﬀects A + -- + S S- S Sustainability + - S + + S -S Maintenance T- SS -- SS S Cost -- S- -S -S Complexity U s -- -- S- S Size s + -S + - -- M

Sum Posi�ves 0 4 3 2 4 3 1 1 2 Sum Nega�ves 0 2 5 4 4 5 1 6 1 Sum Sames 0 3 1 3 1 1 7 2 6

Figure 3.3. Pugh’s evaluation matrix used to evaluate the generated concepts make these weaknesses into strengths. The altered concepts were added to the evaluation matrix as new ones in a new column to the far right. Concept 2 and Concept 9, shown in ﬁgure 3.2 were deemed the most promising and a more detailed conceptual design was done to be able to perform a feasibility analysis.

15 Chapter 3. Concept Stage

The decision was a compromise between the concepts having scored the most positives and the least negatives together with the fact that the two concepts had fundamentally diﬀerent sub solutions.

3.3 Feasibility Analysis

A feasibility analysis was performed on the two concepts chosen to proceed with. The inner wheels are set to require 30 mm of horizontal displacement δtot to be unloaded. The space where the hydraulic cylinders and springs of Concept 2 and Concept 9 can be fitted is limited by the surface defined by the dimensions Lh and Lb shown in figure 3.4. These dimensions are listed in table 3.1

Lb h L

Figure 3.4. The limited space of Lb and Lh of the inner wheels available for ﬁtting hydraulic cylinders or springs

Table 3.1. Dimensions of the mounting surface of the track’s inner wheel

Lh 220 mm Lb 65 mm

3.3.1 Compression Springs

Concept 2 is designed to use springs to unload the inner wheels when their max allowed load is reached. Three compression springs with a maximum outer diameter of 65 mm can be ﬁtted on each side of the inner wheel on the surface deﬁned by Lb and Lh. The max spring force Fsm for each spring can be approximated with equation 3.1, only considering

16 3.3. Feasibility Analysis

the vertical force Pz. P F = z (3.1) sm 24 The strongest spring provided by [8] with an outside diameter smaller than 65 mm is

Table 3.2. The maximum spring force when using three compression springs on each side of the inner wheel

Required spring force Fsm 40.9 kN Standard compression spring [8] 3.9 kN Die spring [8]([9]) 27.8 kN (12.7 kN)

listed in table 3.2. The die spring made from rectangular wire oﬀers a tougher spring with higher load capacity in relation to its outside diameter but it is still not strong enough for the required load capacity (see table 3.2) which indicates that compression springs are too weak for the limited space in the tracks.

3.3.2 Belleville Springs

A Belleville spring can be designed to be fitted in Concept 2 by using the theory in chapter 2.3. Equation 2.10 can be rewritten as equation 3.2 by using the material data of DIN 17222 spring steel specified in table 3.3 to get the spring thickness tBW as a function of the flattening spring force Fflat and outer diameter DoBW .

! 1 D2F t = o flat (3.2) 1072 κ

Assuming an even distribution of the horizontal load Pz with four wheels on each track and four springs on each wheel, the load on each spring Fflat can be calculated. The maximum outer diameter of the spring is deﬁned as the width of the surface in ﬁgure 3.4 (DoBW = Lb). The dimensions and load used in the analysis are presented in table 3.3.

Table 3.3. Requirements of the Belleville spring designed in ﬁrst feasibility analysis, material properties according to DIN 17222

E 207 GPa µ 0.3 DoBW /DiBW 2 DoBW 65 mm Fflat 81.8 kN FBW (δ=0.75hBW ) 61.4 kN σuts 1810 MPa (SS-EN 1.4021) [10]

17 Chapter 3. Concept Stage

The theory in chapter 2.3 needs to be applied for dynamic loads where the deflection is limited due to fatigue. The Belleville spring manufacturer Lesjöfors supplies springs for dynamic loads with a recommendation of a maximum deflection between 20-75% of the cup height h0 [8]. The spring is estimated to have a linear spring rate since κ<1 [5] and together with the limited deflection, the new force Fflat needs to be adjusted according to equation 3.3. P 0.75F = z (3.3) flat 16 The maximum spring stresses given by equations 2.11- 2.17 can be calculated as a function of κ. Figure 3.5 shows a plot for the maximum stresses using the deflection δ = 0.75h0 and the dimensions in table 3.3. The MATLAB script is available in appendix D.

4500 σ c σ 4000 ti σ to σ 3500 uts

3000 [MPa]

σ 2500

Stress 2000

1500

1000

500 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Quota κ = h /t 0 BW

Figure 3.5. Graph showing the maximum stresses of a Belleville spring as a function of the quota κ

Comparing the stresses in ﬁgure 3.5 and the ultimate strength in table 3.3 gives a maximum value κ=0.105. The spring thickness tBW is calculated for this κ using equation 3.2 and then used in equation 2.21 together with δtot=30 mm to calculate the minimum required stack height Lstack for the total load Pz. The result is presented in table 3.4.

18 3.3. Feasibility Analysis

Table 3.4. Dimensions of the Belleville spring from the static analysis

tBW 7.01 mm h0 0.74 mm δBW,max 0.56 mm Nsprings 54 pcs Lstack 413 mm

The spring stack height Lstack in table 3.4 is too tall to ﬁt inside the tracks indicating using Belleville springs being an unfeasible solution in this application.

3.3.3 Hydraulics

Concept 9 uses two hydraulic cylinders per inner wheel and unloads the wheels completely while boring, meaning each cylinder needs to withstand one eight each of Px and Pz while tramming and no load while boring. The piston diameter dpiston in the cylinders can be calculated using the equation 3.4 where the hydraulic system pressure psystem was decided together with the industrial supervisor. The same displacement δtot used for the springs is used as the cylinder stroke length. The result is presented in table 3.5. π P p d2 = z (3.4) system piston 4 8

Table 3.5. Hydraulic operating pressure and calculated piston diameter for Concept 9

psystem 150 bar dpiston 102.1 mm

Hydraulic cylinders are in general very sensitive to side loads [11]. The cylinders need to withstand the side load caused by Px. The hydraulic component manufacturer Roemheld recommends a maximum side load of 3% of the cylinder’s force at maximum operating pressure pop,max for cylinders up to 50 mm stroke length [12]. This condition gives equation 3.5 when assuming Px is evenly distributed over the cylinders. P π x < 0.03p d2 (3.5) 8 op,max piston 4 The result from equation 3.5 when using data taken from [12] is presented in table 3.6. The result in table 3.5 and 3.6 indicates that Concept 9 is feasible.

Table 3.6. Side load data and result for the hydraulic system

pop,max 500 bar dpiston 33.7 mm

19 Chapter 3. Concept Stage

3.4 Patent Search

The patent database Derwent innovations index was searched for existing products similar to Concept 9 to avoid future problems when producing the concept. Keywords describing the system were used together with ﬁlters suitable for the application. The hits were then read through to make sure the new concept wasn’t clashing with any of them. Table 3.7 lists keywords, subject ﬁlter and number of hits that were scanned through.

Table 3.7. Patent search result

Keywords Subject Hits Track load capacity Transportation 172 Unload system + track load capacity Mining and mineral, Agriculture 18 Actuator loaded wheels Engineering 57

The patent search resulted in no clashes of Concept 9 with existing patents.

20 Chapter 4

Detailed Concept

This chapter presents a more detailed model of the chosen concept. An overview of the complete CAD model is shown in ﬁgure 4.1. Two hydraulic cylinders are used on each inner wheel which unloads the wheels while the RVM is boring. To make room for the inner wheel closest to the front wheel, a new fork connecting the pre-tension spring with the front wheel was designed. A FEA was performed to validate the strength of the fork and skid. The Finite Element Method, a method used in solid mechanics to numerically analyze structures to see the stresses of the structure (FEM) software ANSYS was used. Structural steel with a Young’s modulus E=200 GPa and a Poisson’s ratio µ=0.3 were used in the FEA. The plates protecting the components situated inside the tracks are hidden in ﬁgure 4.1. Figures showing these plates are available in appendix E.

Skid Cylinders Fork

Figure 4.1. Detailed CAD model of the chosen concept using hydraulic cylinders and a skid to distribute the load

21 Chapter 4. Detailed Concept

4.1 The Skid

The longitudinal forces are assumed to be distributed through the track’s chain and motor since the track’s own brake is used while boring. Since the inner wheels are fully unloaded, the pair of skids takes the force from Py and Pz. Figure 4.2 shows the green highlighted surfaces where these loads were applied on the top surfaces for the FEA model and the bottom surface Askid,b was set as fixed. The mesh was refined in the max stress areas and the result converged with a maximum element size of 5 mm. The forces Py and Pz used are specified in table 2.2. Figure 4.3 shows the final designs’ stresses.

Top surfaces

Askid,b

Figure 4.2. Boundary surfaces used in the FEM simulation of the skid

Figure 4.3. FEM simulation of the skid

22 4.2. The Fork

General calculations of the forces transferred from the skid to the chain were made to examine the stresses in the chain. The area of the skid Askid,b is listed together with the transferred pressure pskid,b in table 4.1.

Table 4.1. Skid dimensions and transferred pressure from the skid to the chain

2 Askid,b 0.117 m pskid,b 13.2 MPa

4.2 The Fork

The new and more compact fork was subjected to a FEM simulation to validate its strength. A worst-case scenario was setup with the machine tipping forward, meaning all its own weight is applied to the track’s front wheel. Figure 4.4 shows the surfaces used as boundary conditions for the FEM simulation. The surface connecting the fork to the pre-tension spring (green surface to the left in figure 4.4) was set with the boundary condition fixed and the force of Pz for tramming defined in table 2.2 was applied to the front surfaces of the fork, to the right in figure 4.4.

Figure 4.4. Two views of the fork showing the surfaces used for boundary conditions in the FEM simulation

The result of the FEA is shown in ﬁgure 4.5 with the old fork to the left with the same boundary conditions used in FEA of the new fork. The areas with max equivalent stress of 201 MPa is greatly reduced on the new fork indicating an improvement in strength of the new fork compared to the old one. The local stress concentrations shown in the new fork converged with a reﬁned mesh size in this area.

23 Chapter 4. Detailed Concept

Figure 4.5. FEA of the old (left) and new (right) fork

4.3 The Frame

The horizontal load Pz and the side load Py are assumed to be evenly distributed along the four small inner wheels and the longitudinal force (Px) is distributed to the hydraulic motor as shown in ﬁgure 4.6

Pz Figure 4.6. The internal load distribution of the frame

The blue surface in ﬁgure 4.7 shows the surfaces making up the interface between the tracks and the machine. The interface was considered as out of scope and thereby no changes or analyzes were done to this interface. When analyzing the frame, the surfaces were regarded as frictionless supports, meaning the surfaces had zero displacement in its normal direction and were allowed to strain along its own plane. The CAD model was imported as an assembly where all the parts that were in contact with each other were set as "bounded" in ANSYS, meaning the software considered them

24 4.3. The Frame as one solid when calculating the stresses.

Frictionless support

Figure 4.7. The surfaces making the interface between the machine and the tracks

Figure 4.9 shows the FEA done on the original frame that was provided by Atlas Copco and one done on the frame that was designed for the new concept. Both models showed high stress concentrations in three sharp corners where welds are supposed to be. Cross frame 1 in figure 4.9 showed high stress concentrations both in the original frame and the concept frame (upper circle in the detailed view) where it is joined with the rest of the frame. The mesh size shown in figure 4.8 was reduced in these parts but no convergence of the stress was obtained due to the sharp corner. An attempt on making the bottom of Cross frame 1 stronger (where the stress concentration is situated) using the arch geometry cross frame 2 was made but wasn’t feasible due to the hole in the middle of the plate needed for the chain pre-tension spring (see figure 1.2). The stress concentration areas are situated in welded joints which is highly problematic. To solve this problem, the industrial supervisor recommends consulting a weld expert before proceeding with manufacturing. The stress concentrations could be reduced with smooth transitions in the corners.

Figure 4.8. Mesh used in the FEM model of the original (left) and concept (right) frame

25 Chapter 4. Detailed Concept

An extra cross frame part Cross frame 2b in ﬁgure 4.8 was added compared to the new frame to make the frame stronger. By adding this cross frame, the stresses in both cross frame 2a and cross frame 2b could be kept below 380 MPa. The parts were also made thicker to reinforce the frame.

Frame provided by Atlas Copco M MPa

Cross frame 1

Cross frame 2 Concept 9 frame

MPa

Cross frame 2b

Cross frame 2a

Figure 4.9. Bottom view FEA of the original and concept frame using the boring loads in table 2.2

26 4.4. The Cylinders

4.4 The Cylinders

Several product catalogs of hydraulic component suppliers [13], [14], [15] were unsuccess- fully scanned to find cylinders compact enough to fit inside the tracks with the diameter specified in table 3.5. The strongest cylinder compact enough to fit was FZ 250 -80 50 01 201 32 [14] from Merkle AHP. The CAD model provided by the manufacturer website was imported to the CAD model (shown in figure 4.1). The small gap between the inner wheels and the chain shown in figure 4.10 allows the inner wheels to be fully unloaded while the machine is boring. The cylinders move the inner wheels, lifting the machine a distance δtot (minus the small gap) off the skid when changing operating mode from boring to tramming. The exploded view in figure 4.11 shows the adapter plate which was designed to allow the cylinder to be mounted on the frame.

A Boring SECTION A-A

Gap Contact

A B Tramming SECTION B-B δ

Figure 4.10. Close up of how the cylinders lift the machine oﬀ from the skid when changing from boring to tramming

The data for the cylinder is presented in table 4.2 and shows that a system of eight cylinders achieve a total load capacity PzF Z greater than the tramming load Pz speciﬁed in table 2.2. The total allowable side load for the cylinders PyF Z is not suﬃcient compared

27 Chapter 4. Detailed Concept

No Name Quan�ty 1 M10x70 Socket Head Cap Screw 8 2 FZ 250 -80 50 01 201 32 1 3 M16x70 Socket Head Cap Screw 4 4 Cylinder Adapter Plate WW 1 5 Cylinder Bracket S009053_JT 1

Figure 4.11. Exploded view of how the cylinders are mounted to the frame

to the Py for tramming also shown in table 2.2. The system operating pressure psystem was set to the max pressure pop,max to achieve these loads.

Table 4.2. Data for Cylinder FZ 250 -80 50 01 201 32

pop,max 250 bar psystem 250 bar dpiston 80 mm PzF Z 1.01 MN PyF Z 0.03 MN

4.5 PDS evaluation

The ﬁnal design was evaluated in regard to the PDS in appendix A and the result is presented in table 4.3.

28 4.5. PDS evaluation

Table 4.3. Evaluation of the ﬁnal concept compared to the PDS

Static vertical load Pz Yes Static side load Py Boring Yes, Tramming No Cycle time Not confirmed Ambient temperature working Yes, according to hydraulic component data sheet Ambient temperature storage Yes, according to hydraulic component data sheet Vibrations Yes, the loads compensate for dynamic effects Dirty and wet environment Yes, the components are insensitive to dirt and moisture Life in service Yes, the components are maintenance friendly and dimensioned to last Shipping and size Yes, the design respects the dimension specification Aesthetics and appearance No, the level of detail does not include aesthetics Material Yes, structural steel was used for the design Standards Yes, standardized components were used except for the newly designed fork and skid Ergonomics Yes, standard tools are used for maintenance and no springs were used Quality and reliability Not evaluated Shelf life Yes, the components used will last the 6 month shelf life Timescale Yes, the deadline for May 2017 was met Safety Yes, the unloading operation is au- tonomous Patents Yes, no patent clashes were found Documentation Yes, the thesis together with the CAD- model documents the design extensively Sustainability Partially, hydraulic fluid is normally fossil fluids. Main components are made out of structural steel with no conflict minerals

Chapter 5

Discussion and Conclusion

This chapter includes a discussion regarding the design of the concept with its strengths and weaknesses. The result of the main new components described in chapter 4 is discussed and compared to the PDS in appendix A. The methods used in the project are discussed and the conclusion sums up the result of this thesis.

5.1 Discussion

Even in a quite low level of detail of the CAD model (piping, wiring, welds joints were not included) there were quite a lot of diﬃculties to ﬁnd room for the cylinders in the frame. Parts in the frame were moved which led to other parts needing adjustments. The model was built as a bottom-up assembly [16]. In hindsight, a lot of advantages could have been found with a top-down assembly [16] when changing a dimension of one part meant dimensional changes on several other parts. Even though the patent search performed in chapter 3.4 didn’t show any patent clashes, there’s still a need for a more detailed search of existing patents. Experts in patents and patent search should be consulted before manufacturing the concept.

5.1.1 Skid Discussion

The FEA done in chapter 4.1 indicates that the skid is strong enough for the high loads the skid needs to sustain when the machine is boring. The stresses are in the same order as the yield strength of conventional construction steel. This suggests that a more in-depth study of how the dynamic forces aﬀect the life length of the structure regarding fatigue. The loads in chapter 2.1 given by Atlas Copco are supposed to compensate for dynamic eﬀects but a more in-depth study might still be needed. The track’s chain was assumed to be strong enough for the loads in table 2.2. The

31 Chapter 5. Discussion and Conclusion pressure in table 4.1 indicates a tolerable level but this needs to be conﬁrmed by the track manufacturer.

5.1.2 Fork Discussion

The new fork creates more space for the cylinders to be ﬁtted in the frame and the FEA done with the tipping over scenario indicates that the fork is strong enough for the task. Manufacturing cost and complexity of the new fork is increased but compared to adding more tracks it is still found to be a proﬁtable choice.

5.1.3 Frame Discussion

The stress concentration where Cross frame 1 in ﬁgure 4.9 is joined with the rest of the frame needs to be resolved. As earlier suggested, an expert in welding should be consulted to decide acceptable stress levels and how to reduce them. Furthermore, the stress level of 380 MPa limits the choice of material to a higher quality steel compared to conventional construction steel with a yield strength of 235 MPa. Just as with the skid, a more in-depth study of fatigue may be needed.

5.1.4 Cylinders Discussion

The cylinders were compact enough to ﬁt inside the track with some modiﬁcations of the frame. The level of detail in the given CAD model did not include electric components, wires or pipes. The placements of such parts are now needed to be adjusted to the new design of the frame.

The cylinders used in chapter 4.4 are too weak for the side load Py when tramming. Either should linear guides be added connecting the inner wheels to the frame to take these side loads or the cylinders should be changed to larger ones.

5.1.5 Method Discussion

The following reﬂections of the methods used in the thesis could be done • The tedious work of creating the PDS (appendix A) was of great support when questions about prioritizes arose while designing the concepts • Both the Stage Gate ﬂow chart and the Gantt chart proved to be of great help to meet deadlines • The Gantt chart had to be revised several times and details were added to keep it true to the project. Working with an outdated Gantt chart would defeat the purpose of using it for structure your work and keeping deadlines

32 5.2. Conclusion

• The Morphological Matrix was the root for coming up with the final concept. The early idea of having a skid mounted on the hydraulic cylinders to lift the machine when it was boring proved to be less effective than the later generated and finally chosen concept of the moving inner wheels. • The Pugh’s Evaluation Matrix proved to be a good way of systematically evaluate the concepts. • The controlled convergence method was the ground for coming up with the final concept. The method could be even more effective when working in groups allowing for more creative thinking.

5.2 Conclusion

In conclusion, the concepts fulﬁll the PDS in appendix A with some deviations: • The cylinders used aren’t strong enough for the side loads when the machine is tramming. • The frame is showing stress concentrations in welded corners. The stresses need to be reduced or moved out of the joint.

• The desired hydraulic operating pressure psystem was exceeded with the chosen cylinders. • The concept’s level of detail did not include specifying a hydraulic pump or piping. • Environmental effects: – How moist and dirt affect the hydraulic cylinders hasn’t be investigated. – How dirt between the skid and the chain affect its performance hasn’t investigated. – Ambient temperature hasn’t been studied. The hydraulic oil must be compatible with these temperatures. • The hydraulic cylinder’s life in service isn’t specified. However, service and replace- ment of the cylinders is easy with the service slots in the frame. • The quality and reliability haven’t been investigated. The specified availability specified in the PDS still needs to be verified. • Regarding sustainability, no conflict minerals have been found in the design. How- ever, the use of hydraulics implies the use of fossil oil.

Chapter 6

Future Work

The concept could be developed further to make it a better and more detailed solution. The following parts are recommended to develop further: • Add linear guides to reduce the side load of the hydraulic cylinders

• Reducing the clearance δtot and creating more space for a larger diameter for the spring could allow the use of Belleville springs using the theory in chapter 2.3. Using springs instead of hydraulic components could create a less complex design • Create a more detailed design of the concept including source and distribution for hydraulic power (pump and piping) • Solving the stress concentration in cross frame 1. Mimicking the bottom geometry of cross frame 2 is possibly a solution

References

[1] S. Pugh, Total design - integrated methods for successful product engineering. Wokingham: Addison-Wesley, 1990, pp. 44–66. [2] R. G. Cooper, “Stage-gate systems: A new tool for managing new products”, Business Horizons, pp. 44–45, 1990. [3] S. El Wakil, Processes and design for manufacturing. Boston, PWS Publishing Company, 1998, pp. 14–15. [4] ——, Processes and design for manufacturing. Boston, PWS Publishing Company, 1998, pp. 430–459. [5] P. R. Childs, Mechanical design engineering handbook. Burlington: Elsevier Science, 2013, pp. 664–671. [6] G. Pahl, W. Beitz, J. Feldhusen, and K. Wallace, Engineering design : A systematic approach. Springer London, 2007, pp. 169–186. [7] S. Pugh, Total design - integrated methods for successful product engineering. Wokingham: Addison-Wesley, 1990, pp. 67–89. [8] Lesjöfors AB, Spring catalogue 13, http://www.lesjoforsab.com/teknisk- information/standard_stock_springs_catalogue_13_- _english_id1107. pdf accessed 2017-04-20, 2017. [9] Danly IEM, Jis springs, http://www.daytonlamina.com/sites/default/files/ doc/DanlyIEM-JIS-Springs.pdf accessed 2017-04-20, 2017. [10] K. Björk, Formler och tabeller för mekanisk konstruktion. Karl Björks Förlag HB, 1999, p. 53. [11] E. Parr, Hydraulics and pneumatics: A technician’s and engineer’s guide. United Kingdom, Butterworth Heinemann, 2013, p. 125. [12] ROEMHELD, Block cylinders double acting, max. operating pressure 500 bar, [http://www.roemheld.com/en/roemheld.aspx?cmd=PDF&Article=1549100& csid=4912&sm=Kolbendurchm=100 accessed 2017-04-20], 2017. [13] ——, Roemheld product catalogue,[http://www.roemheld.com/en/roemheld. aspx?cmd=PDFS accessed 2017-04-20], 2017. [14] AHP Merkle, Product catalogue,[https://ahp.partcommunity.com/3d- cad- models/ahp-merkle/?info=ahp accessed 2017-04-20], 2017.

37 References

[15] Parker Hannifin Corporation, Cylinder product catalogue,[https://www.parker. com/literature/Industrial%20Cylinder/cylinder/cat/english/HY08-1114- 6_NA_2H-3H%20.pdf accessed 2017-04-20], 2017. [16] D. D. Gajski, S. Abdi, and A. Gerstlaue, Embedded system design modeling, synthesis and verification. London New York: Springer Dordrech Heidelberg, 2009, pp. 35–38. [17] B. Bali, U. Naeher, D. Ruppen, and P. Schütte, “Conflict minerals 3tg: Mining production, applications and recycling”, Current Opinion in Green and Sustainable Chemistry, no. 1, pp. 8–12, 2016.

38 Appendix A

The Elements of the Product Design Speciﬁcation

This chapter extends the summary of the PDS in chapter 1.6 treating the complete list of elements [1]. The elements were used to create the Pugh’s Matrix in chapter 3.1 • Performance The static load capacity and cycle time is presented in table A.1

Table A.1. Static load when operating

Static vertical load Pz 2.5 MN Static side load Py 0.5 MN Cycle time (tramming - ready to bore - tramming) 10 seconds

• Environment Ambient temperature working: 0 ◦C to 35 ◦C Ambient temperature storage: −5 ◦C to 70 ◦C Vibrations: The static load supplied by Atlas Copco Pz and Px are dimensioned for dynamic loads Dirty and wet environment. • Life in Service The machine should operate 24 hours a day, 5 days a week. Total life in service: 1500 h • Target Product Cost The alternative to an unloading system is adding more tracks. Therefore, the cost of the unloading system should not exceed that of adding more tracks.

39 Appendix A. The Elements of the Product Design Specification

• Competition No competition is considered since Atlas Copco reports that no other solutions are available on the market. • Shipping The RVM needs to be transported down the mine shaft in an elevator. As long as the unload sharing unit fulfills the requirement of fitting within the tracks, this should not be a problem. • Packing Packing is considered as out of scope. • Quantity When the concept is realized, the quantity will be very low. Approximately 1-3 machines. • Size The design should fit inside the tracks of the RVM. • Weight Regarding the he large weight of the machine (160 tonnes) and the size constraints, the weight of the design is subordinate. • Aesthetics and Appearance Flat surfaces should be colored with the Atlas Copco yellow color. The design should appear robust and give the impression of handling the rough mine environment. • Materials Steel alloys are used for structural frames. These are in general preferred over aluminum and other metals on these machines according to Atlas Copco Hydraulic components may be used. • Product life span This section is subordinate since only one machine is planned to be manufactured. • Standards and Specifications European standard components should be used when possible but customized parts may be designed to find a solution. • Ergonomics When using springs (pre-tensioned), the design should allow for a safe assembly. Maintenance should be possible using standard tools. • Customer The customer of the design is Atlas Copco who wants to integrate the solution in their machine (the RVM). • Quality and Reliability

40 The RVM availability is set at 80%. The availability is calculated using Mean Time to Failure, the mean time a system takes to fail (MTTF) and Mean Time to Repair, the mean time it takes to repair the system (MTTR):

MTTF Availability = (A.1) MTTF + MTTR

• Shelf life The design should survive 6 months’ shelf life. • Processes Atlas Copco has a high level of in-house process competence, including welding, milling, turning, grinding, casting, hydraulic tubing and electric wiring making this speciﬁcation subordinate. • Time-Scales The concept design should be completed no later than May 2017. • Testing How the product should be tested is considered as outside of the conceptual design scope. • Safety No human contact when the unloading system operational. It should be safe to move around the machine while the machine is tramming. • Company Constraints No company constraints are considered in this project since this is considered as a small and low quantity part of the machine. • Market Constraints Since the customer is considered to be Atlas Copco and the RVM project is underway, no more market constraints will be taken in to consideration. • Patents, Literature and Product Data Possible patent clashes should be investigated. • Legal Legal parts regarding miss-use and defects are outside of the scope of the conceptual design stage. • Installation The unloading system should be applicable to the RVM tracks but alteration of the track’s frame is allowed to achieve the target load. • Documentation The design is documented extensively in the master thesis.

41 Appendix A. The Elements of the Product Design Specification

• Disposal The disposal of the unloading system is regarded as outside of the scope of the conceptual design stage. • Sustainability Even though [1] does not handle the matter of sustainability, with today’s challenges of global warming the author considers this to be something that must be regarded. Fossil ﬂuid and material should be kept to a minimum and conﬂict minerals [17] should be avoided as far as possible.

42 Appendix B

The Gantt chart

The Gantt chart shown in B.1 was used as a base for scheduling when each part of the project was supposed to be done. The progress bars were ﬁlled with blue as progress was made. This was done at least every Friday when the chart was uploaded to the workspace shared with the academic supervisor.

43 Appendix B. The Gantt chart

44 Figure B.1. Gantt chart for the project 45

Appendix C

The Criteria of Pugh’s Evaluation Matrix

The following criteria were used in chapter 3.1 to evaluate the previously generated concepts. The PDS described in chapter 1.6 was used as a base for creating the criteria. • Static load performance Can the concept effectively take the horizontal load? Can the concept effectively take the side load? Is the mechanism suitable for taking high static load? Since the frame in its current state needs to be reinforced the load distributer needs to be compatible with frame reinforcements. • Track chain pressure An even load distribution acting on the track’s chain is required to reduce the stress of the chain. • Cycle time The cycle time set to 10 seconds needs to be met • Environmental effects Both the storage and operating temperature spans need to be met. The RVM uses water to cool the cutter head and reduce the dust created when cutting. This creates a dirty and wet environment. The load distributor needs to endure the dusty and dirty environment in the mine. • Sustainability Does the concept have any environmentally harmful material or conflict minerals [17]? • Maintenance

47 Appendix C. The Criteria of Pugh’s Evaluation Matrix

Does the maintenance take the RVM out of service for longer periods of time? Is the availability met? (80%) • Cost Is the estimated development and production cost higher than the datum concept? Does the concept require a lot of expensive custom made parts? • Complexity Does the concept use energy mediums (hydraulic, electric, mechanic) than the datum? How complex is the concept regarding number of parts used in assembling? Does the concept involve complex control units? Is manufacturing of the concept feasible with respect to the manufacturing cost? • Size How large are the dimensions of the concept? One main requirement is that the concept should ﬁt inside the tracks.

48 Appendix D

The MATLAB script used for calculation of the Belleville spring

MATLAB script used for calculating Belleville springs, hydraulic pressure and cylinder diameter. The chosen cylinders’ load capacity and side load capacity are also calculated.

%MATLAB script for Master Thesis Machine Design % RVM tracks Jonas Torstensson 2017-02-10 % Calculating RVM forces on the track clear all;close all;clc m_equv=200e3 ;% Equivalent mass of RVM while tramming[kg] T_max=222764;% Max torque of the hydraulic motor in the tracks[Nm] mu_t=0.7 ;% Friction coefficient between the tracks and the ground g=9.818 ;% Gravity constant[m/s^2] P_yboring=0.5e6;%Forces iny-direction while boring r_sprocket=615.5e-3;% Radius of track sprocket[m] alfa_g=5;% Ground tilt angle[deg] P_ztram=m_equv*g/2;% Load on each track inz-direction P_xtram=T_max/r_sprocket; disp(['P_xtram=',num2str(P_xtram *10^-6),'[MN]']) P_ytram=P_ztram*sind(alfa_g); disp(['P_ytram=',num2str(P_ytram *10^-6),'[MN]']) disp(['P_ztram=',num2str(P_ztram *10^-6),'[MN]']) P_zboring=2.5e6 ;%Vertical load on track when boring[Nm] P_xboring=mu_t*P_zboring; disp(['P_xboring=',num2str(P_xboring *10^-6),'[MN]'])

%% Approximating the hydraulic cylinders size disp('');disp('Hydraulics'); n_wheels=4;% Number of wheels per track

49 Appendix D. The MATLAB script used for calculation of the Belleville spring n_cylperwheel=2; p_popmax=300e5;% max hydraulic pressure specified by the manufacturer of ... the specific cylinder range(Roemheld) P_zwheel=P_ztram/n_wheels;% Load on each wheel (4 per track) P_zwheel_side=P_zwheel/n_cylperwheel;% Pressure on each side of the wheels p_max=250e5 ;% Max system pressure A=P_zwheel_side/p_max; r_piston= sqrt(A/pi);% Cylinder radius for max system pressure in regard ... to P_z P_y_cyl=P_ytram/(n_wheels*n_cylperwheel); r_piston_sl=sqrt(P_y_cyl/(0.03*8*pi*p_popmax));% Min piston radius ... considering the side load and condition of max 3% of max pressure load disp(['Load on each cylinder while tramming P__y_cyl= ... ',num2str(P_y_cyl*10^-3),' kN',' P_z_cyl= ... ',num2str(P_zwheel_side*1e-3),' kN']) disp(['Min piston diameterd=', num2str(r_piston *2e3),' mm for tramming']) disp(['Side load min piston diameterd=', num2str(r_piston_sl *2e3),' mm ... for tramming']) disp(['Using system pressure',num2str(p_max *1e-5),' bar and ... ',num2str(n_wheels),' wheels per track and ... ',num2str(n_cylperwheel),' cylinder per wheel'])

%% Ground pressuredisp disp('');disp('Check ground pressure'); A_ideal=541255.05e-6;%Area of track below the small wheels %A_skid=(127884.28+127883.41)*1e-6;% Area where the skid would act on ... the track. A_skid=2*116886.41e-6;% P_tot_bor=sqrt(P_xboring^2 + P_yboring^2 + P_zboring^2); p_ideal_bore=P_tot_bor/A_ideal; disp(['Ideal ground pressure when boring p_ideal= ... ',num2str(p_ideal_bore*1e-6),' MPa']); p_track_boring=P_tot_bor/A_skid; disp(['Track pressure when boring p_track_boring= ... ',num2str(p_track_boring*1e-6),' MPa']); %% Compression spring F_sm=P_ztram/24; disp('');disp('Compression springs') disp(['Compression spring force F_sm=',num2str(F_sm *1e-3),' kN']) %% Belleville spring disp('');disp('Belleville Spring dimensioning'); D_o=65e-3 ;% outer diameter of spring[m] E=207e9;% Youngs modulus for spring steel[Pa] mu=0.3 ;% Poissons ratio for spring steel D_i=D_o/2; %F_flat=2*62.5/(3*0.75) *1e3;% Force for the spring to flatten out F_flat=P_ztram/(.75*16); Sigma_uts=1810e6;% Ultimate strength ofSS-EN1.4021 delta_tot=30e-3;%Required displacement for the wheels(spring stack) eta_min=0.2;% Pre tension quote from h_0 %htquote=0.01:0.1:1.414;% the quotah/t set to givea(near) constant ... force for the defelction

50 kappa=[0.03:0.005: 0.4]; t=1/1072 * ( (D_o^2 * F_flat)./(kappa)).^0.25;% Assuming constant spring ... force anda D_o/D_i=2 %disp(['thicknsesst=',num2str(t *1e3),' mm']) h=t.*kappa; %disp(['heighth=',num2str(h *1e3),' mm']) delta_min=.65*h;delta_max=1.35*h; Delta_delta=delta_max-delta_min; %disp(['Delta_delta=',num2str(Delta_delta *1e3),' mm']) tot_h=h+t; N=4;% Number of springs Stack_height=N*tot_h;% Stack height usingN springs %disp(['Stack_height=',num2str(Stack_height *1e3),' mm']) %disp(['Total deflection delta=',num2str(N *Delta_delta*1e3),' mm']) L_0faktor=.8*2*(1+1/1.414); L_0t=.8*(1+1/1.414)*h; % Calculating the stresses in the spring %t=[1:0.1:2]*t; R_d=D_o/D_i; K_1=6/(pi*log(R_d)) *( (R_d-1)^2 /R_d^2); K_2=6/(pi*log(R_d))*( (R_d-1)/log(R_d) -1); K_3=6/(pi*log(R_d))*( (R_d-1)/2); K_4=((R_d*log(R_d)-(R_d-1))/log(R_d))* R_d/ ((R_d-1)^2); K_5=R_d/(2*(R_d-1)); delta_max=0.75*h; sigma_c= 4*E.*delta_max/(K_1*D_o^2*(1-mu^2)) .*( ... K_2.*(h-delta_max./2)+K_3.*t); sigma_ti=4*E.*delta_max/(K_1*D_o^2*(1-mu^2)) ... .*(-K_2.*(h-delta_max./2)+K_3.*t); sigma_to=4*E.*delta_max/(K_1*D_o^2*(1-mu^2)) ... .*(K_4.*(h-delta_max./2)+K_5.*t); %disp(['Stress sigma_c=',num2str(sigma_c *1e-6),' MPa']) hold on plotc=plot(kappa,sigma_c*1e-6,'LineWidth',1.7); plotti=plot(kappa,sigma_ti*1e-6,'LineWidth',1.1); plotto=plot(kappa,sigma_to*1e-6); plotuts=plot([kappa(1) kappa(end)], [Sigma_uts*1e-6 Sigma_uts*1e-6],'--'); legend('\sigma_c','\sigma_t_i','\sigma_t_o','\sigma_u_t_s'); xlabel('Quota\kappa= h_B_W/t_B_W'); ylabel('Stress\sigma[MPa]'); grid on no=find(kappa==0.105); delta_no=h(no)*0.75;%Maximum deflection of one spring req_N=delta_tot/(delta_no);% Requirered number of springs for the ... deflection delta_tot with the chosen kappa(no) %stack_Height=ceil(req_N)*tot_h(no)*(1-.2); stack_Height=ceil(req_N)*h(no)*(1-eta_min+1/kappa(no)); disp(['Minimum kappa', num2str(kappa(no))]) disp(['Thicknesst=', num2str(t(no) *1e3),' mm']) disp(['Cup heighth=', num2str(h(no) *1e3),' mm']) disp(['Spring height L_0=', num2str(tot_h(no) *1e3),' mm']) disp(['Max deflection of one spring delta=', num2str(delta_no *1e3),' mm']) disp(['Required number of springs=', num2str(ceil(req_N)),' pcs'])% ... req_N rounded up!

51 Appendix D. The MATLAB script used for calculation of the Belleville spring disp(['Stack height L_stack=', num2str(stack_Height *1e3),' mm'])

%% CylinderFZ 250 -80 50 01 201 32 d_FZpist=80e-3 ;% Piston diameter for the chosen cylinder[m] p_FZop=250e5;%(max) operating pressure of the cylinder[Pa] n_FZ=8 ;% Total number of pistons mounted on the track A_FZp=d_FZpist^2 *pi/4;% Piston area of the piston[m^2] F_zFZtot=p_FZop*A_FZp * n_FZ;% Total load capacity of the cylinders disp(['Total load capacity of theFZ Cylinders P_tot= ... ',num2str(F_zFZtot*1e-6),'MN']) F_yFZtot=F_zFZtot*0.03;% Total allowable side load for theFZ cylinder disp(['Total load capacity of theFZ Cylinders P_tot= ... ',num2str(F_yFZtot*1e-6),'MN'])

52 Appendix E

Pictures of the ﬁnal design

This chapter shows pictures of how the track’s plates protecting the components inside are mounted.

Figure E.1. Front view of the ﬁnal design of the track

53 Appendix E. Pictures of the final design

Figure E.2. Tilted front view of the ﬁnal design of the track

Figure E.3. Back view (interface to machine) of the ﬁnal design of the track

TRITA MMK 2017:45 MKN 197