A tramming concept for a mechanical rock excavation machine
SARA BLOMQVIST
Master of Science Thesis Stockholm, Sweden 2015
A tramming concept for a mechanical rock excavation machine
Sara Blomqvist
Master of Science Thesis MMK 2015:52 MKN 139 KTH Industrial Engineering and Management
Machine Design SE-100 44 STOCKHOLM
Examensarbete MMK 2015:52 MKN 139
Ett trammningskoncept för en mekanisk bergavverkningsmaskin
Sara Blomqvist
Godkänt
2015-06-09
Examinator
Ulf Sellgren
Handledare
Ulf Sellgren
Uppdragsgivare
Svea Teknik AB
Kontaktperson
Jacob Wollberg
Sammanfattning
Denna rapport är resultatet av ett examensarbete på KTH i samarbete med Svea Teknik AB och Atlas Copco Mining and Rock Excavation.
Atlas Copco utvecklar för närvarande en familj av maskiner för mekanisk bergsbrytning.
Samtliga maskiner i familjen har två framdrivningsmetoder. Målet med detta projekt har varit att reducera antalet framdrivningsmetoder till en i en av dessa maskiner, Mobile minern.
Projektet har varit uppdelat i tre huvudfaser; bakgrundsstudier, konceptutveckling och dokumentation. Konceptutvecklingen har i sin tur varit uppdelad i fyra delar; generering, bedömning, utveckling och validering.
I projektet har inga fysiska prototyper, ritningar, komponentval, mjukvaruprogrammering, beräkningar av friktionsförluster eller detaljerade FEM-analyser gjorts.
Nio koncept togs fram. Dessa bedömdes med avseende på en produktspecifikation med hjälp av en viktad PUGH-matris. Det koncept som fick högst rankning i PUGH-matrisen var sex armar som används för att dra maskinen framåt. Konceptet utvecklades med avseende på applicerbarhet, hållbarhet och utmattning och slutade som ett koncept med fyra armar liknande saxlyftbord som lagts horisontellt. Funktionen har verifierats genom CAD-modeller, beräkning av säkerhetsfaktorer mot utmattning och FEM-modeller.
Den enda produktspecifikationen som inte uppnåddes var farten.
Nyckelord: Tramming, Propellering, Mekanisk bergavverkning
Master of Science Thesis MMK 2015:52 MKN 139
A tramming concept for a mechanical rock excavation machine
Sara Blomqvist
Approved
2015-06-09
Examiner
Ulf Sellgren
Supervisor
Ulf Sellgren
Commissioner
Svea Teknik AB
Contact person
Jacob Wollberg
Abstract
This report is the result of a thesis project at KTH in cooperation with Svea Teknik AB and Atlas Copco Mining and Rock Excavation.
Atlas Copco is currently developing a family of machines for mechanical rock excavation. All machines in the family have two propulsion methods. The goal of this project has been to reduce the number of propulsion methods down to one, in one of these machines, the Mobile miner.
The project has been divided into three main phases; background studies, concept development and documentation.
The concept development phase has in turn been divided into four parts; generation, evaluation, development and validation.
During the project no physical prototypes, drawings, component selections, software programming, calculations of friction losses or detailed FEM analysis were made.
Nine concepts were developed. These were assessed with respect to a product specification using a weighted PUGH-matrix. The concept that received the highest ranking in the PUGH-matrix was six arms that are used to pull the machine forward. The concept was developed with respect to applicability, durability and fatigue. This resulted in a concept with four arms similar to scissor lift tables placed horizontally. The function has been verified using CAD-models, calculation of safety factors against fatigue and FEM-models.
The only specification that was not achieved was the speed.
Keywords: Tramming, Propelling, Mechanical rock excavation
FOREWORD
I would like to thank my supervisors Ulf Sellgren and Jacob Wollberg for giving me the opportunity to undertake this project and for their support throughout these past few months. I would also like to thank the staff at Svea Teknik AB and Mikael Ramström for always being available and for answering all kinds of questions. Lastly I would like to give many thanks to David Viberg for brilliant company, lots of laughs and for being a great person to bounce ideas off of.
Sara Blomqvist Stockholm, May 2015
Nomenclature
This chapter presents the notations and abbreviations used in the report.
Notations
Symbol Description
vcs Stroke speed, for comparison of generated concepts [m/s]
sch Horizontal stroke, for comparison of generated concepts [m]
scv Vertical stroke, for comparison of generated concepts [m]
tc1−tc8 Time for one movement sequence for concept 1 to 9 [s]
vc1−vc8 Speed of Concept 1 to 9 [km/h]
vpc3 Vertical play, Concept 3 [m]
lf p Total length of the Mobile miner [mm]
dh Diameter of cutter head, Mobile miner [mm]
cm Distance from COGmto the centre of cutter head, Mobile miner [mm]
COGm Centre of gravity for the Main body and Head, Mobile miner COGb Centre of gravity for the Backup, Mobile miner
cb Distance from COGbto the centre of cutter head, Mobile miner [mm]
ct Distance from GOGt to the centre of cutter head Mobile miner [mm]
COGt Centre of gravity in the Mobile miner
mm Weight of the Main body, Mobile miner [ton]
mb Weight of the Backup, Mobile miner [ton]
Fa Total force from the weight of the Mobile miner on each arm [N]
m Total weight of the Mobile miner [ton]
Fg Gravitation force for the Mobile miner [N]
g Gravitation [m/s2]
Farm Force on each arm from the weight of the machine [N]
sa Stroke length of the arms [mm]
n Number of steps needed to walk the length of a plunge [ ] Rb Reaction force on caterpillar tracks in the Backup [N]
Fa1−a4 Reaction forces on arm 1-4 [N]
la1 Distance from support 1 in arm 1 and 2 to GOGt [mm]
la2 Distance from support 1 in arm 3 and 4 to GOGt [mm]
Fa Acting reaction force on arms [N]
l3 Distance from joint 1 to upper attachment point of machine [mm]
l4 Distance from joint 3 to joint 1 [mm]
l5 Distance from upper attachment point of machine to the ground [mm]
l6 Distance from upper attachment point of machine to the lower [mm]
ll Length of links [mm]
R1 Force in upper attachment point of machine [N]
R2 Force in lower attachment point of machine [N]
J1x Force in joint 1, x-direction [N]
J1y Force in joint 1, y-direction [N]
J2x Force in joint 2, x-direction [N]
C Force in cylinder in support 1 [N]
J4x Force in joint 4, x-direction [N]
J4y Force in joint 4, y-direction [N]
J5 Force in joint 5 [N]
J6x Force in joint 6, x-direction [N]
J6y Force in joint 6, y-direction [N]
α Angle between the upper link and the x-axis [rad]
l7 Distance between joint 1 and 5, x-direction [mm]
l8 Distance between joint 1 and 5, y-direction [mm]
µr Rolling resistance in the caterpillar tracks on the Backup [ ]
Fr Force from the rolling resistance in the caterpillar tracks on the Backup [N]
vcm Maximal speed of cylinder in support 1 [m/s]
s Safety factor against fatigue [ ]
λ Factor for technological volumetric dependence [ ] δ Factor for geometrical volumetric dependence [ ] κ Surface factor [ ]
σD Fatigue limit [ ]
φ Coefficient of restitution [ ] q Fillet sensitivity factor [ ]
Kt Shape factor [ ] σnom Nominal stress[ ]
Db Diameter of bearing [mm]
Fb Force on bearing [N]
Pb Maximum allowed pressure on bearing [MPa]
lb Length of bearing [mm]
I Moment of inertia, Mobile miner [kgm2] T Torque needed to turn in a 5◦slope [Nm]
ns Number of screws, shaft for joint 1 [ ]
Fpl Maximum preload of screws, shaft for joint 1 [N]
µss Coefficient of friction steel against steel [ ] J6ymax Maximum force in joint 6 [N]
Abbreviations & Expressions
KTH Royal Institute of Technology (Kungliga Tekniska H¨ogskolan in swedish)
Mobile miner Mechanical rock excavation machine from Atlas Copco Tramming Method of propelling, similar to walking
CAD Computer-Aided Design
FEM Finite Element Method
Heading Excavation of rock, support of the cavity and mucking Head Anterior part of the mechanical rock excavation machines Cutter head Circular block which carries the indenters
Cutter Indenter
Slewing mechanism Mechanism for slewing the cutter head Apron Devise used for mucking
Muck Excavated earth or rock
Mucking Removal of excavated earth or rock
Main body The middle part of the mechanical rock excavation machines Gripper Hydraulic cylinder used to hold the mechanical rock
excavation machines
Backup The posterior part of the mechanical rock excavation machines
TBS Tunnel Bore System
Plunging Pushing the cutter head into the rock
COG Centre of gravity
Table of contents
1 Introduction 1
1.1 Background . . . 1
1.2 Purpose and delimitations . . . 2
1.3 Methodological choices . . . 2
2 Frame of reference 3 2.1 Mechanical rock excavation . . . 3
2.2 The Mobile miner . . . 5
2.3 The Reef miner . . . 6
2.4 The Tunnel Bore System (TBS) . . . 7
2.5 Excavation and tramming . . . 7
3 Methodology and Results 9 3.1 Product specification . . . 9
3.2 Generated concepts . . . 10
3.2.1 Concept 1 - Earth worm movement, 3 body parts . . . 10
3.2.2 Concept 2 - Earth worm movement, 2 body parts . . . 11
3.2.3 Concept 3 - Feet . . . 12
3.2.4 Concept 4 - Feet with no slewing mechanism . . . 13
3.2.5 Concept 5 - Arms . . . 14
3.2.6 Concept 6 - Arms with no slewing mechanism . . . 15
3.2.7 Concept 7 - Walking with 3 arms . . . 15
3.2.8 Concept 8 - Walking with 3 arms with no slewing mechanism . . . 16
3.2.9 Concept 9 - Omnidirectional wheels . . . 16
3.3 Concept evaluation . . . 17
3.4 Concept development . . . 19
3.4.1 Centre of gravity . . . 19
3.4.2 Linear motion . . . 20
3.4.3 Arm placement and load . . . 21
3.4.4 Dimensioning of the arms . . . 24
3.4.5 The final CAD-model . . . 33
3.5 Concept verification . . . 39
3.5.1 Fatigue . . . 39
3.5.2 Movement and size . . . 41
4 Discussion and conclusions 45 4.1 Discussion . . . 45
4.2 Conclusion . . . 47
5 Future work 49
6 References 51
Appendix A – Ansys setup Appendix B – Haigh-diagrams
1 Introduction
This chapter describes the background to and the purpose of this report.
1.1 Background
This report is a master thesis written as a result of a project conducted at Svea Teknik AB by a student of the master program Machine Design at the Royal Institute of Technology, KTH.
Svea Teknik AB is a technical consulting firm with a focus on product development.
They are developing parts for mechanical rock excavation machines at the request of Atlas Copco Mining and Rock Excavation [1]. An example of such a machine, the Mobile miner, is presented in Figure 1.
Figure 1: The Mobile miner [2]
Atlas Copco is currently developing a family of machines for mechanical rock exca- vation. These should be able to form the subsurface infrastructure and excavate ore at a performance level twice that of traditional methods, with the highest possible safety standard. Four machines are currently in the product family. One is ready for testing, two are being built and the fourth, the Mobile miner, is in an early concept stage. This project focuses on the fourth machine, the Mobile miner [1].
All machines in the product family are propelled by caterpillar tracks whilst out- side a tunnel and for turning within a tunnel. For straight movement within a tunnel the machine is pulled forward using hydraulic cylinders. The caterpillar tracks are heavy and expensive. There was therefore a desire to reduce the number of propelling methods down to one [3].
1.2 Purpose and delimitations
The purpose of this project was to generate a functional concept of tramming, i.e. pro- pelling, for the Mobile miner that can be further developed and potentially applied.
Different concepts of tramming was investigated during the project. The concepts only applies to one machine, the Mobile miner. The concept deemed most suitable was further investigated in terms of applicability, durability and fatigue. Time was the controlling factor in this project and was limited to 20 weeks, or 800 hours [4]. The project does not include the following:
• Physical prototypes
• Production preparation, tolerancing or detailed drawings
• Component selection
• Software programing for the hydraulic system
• Calculations of friction losses or their contribution to the loads
• Advanced FEM-analysis
1.3 Methodological choices
The project has been divided into three main parts; background study, concept devel- opment and documentation. The concept development phase was in turn divided into four sub-phases; generation, evaluation, development and verification.
All information necessary to solve the problem was gathered during the back- ground study as well as inspiration for the concepts.
The concept generation was performed by combining already existing solutions, found during the background study, with self-created ideas. The self-created ideas were generated through brainstorming etc. The generated concepts were then further developed till the extent that they could be evaluated in a PUGH-matrix. The PUGH- matrix method was chosen due to its simplicity and recognition. The highest scoring concept was further developed and investigated in terms of applicability, durability and fatigue. This was done as computer-aided design models, CAD-models, in Pro Engineer, calculations of static behaviour in MATLAB, modelling of static and dynamic behaviour in Adams and with finite element method, FEM, calculations, in Ansys. The softwares were selected since they were provided by Svea Teknik AB or by KTH. Some calculations were performed using Mathcad and Excel.
All components were dimensioned for infinite life using Haigh-diagrams [5].
The documentation of the project has been done continuously throughout the project but with an emphasis on the end.
2 Frame of reference
This chapter describes the theory of mechanical rock excavation, three of Atlas Copco’s me- chanical rock excavation machines, the excavation methods of these machines and the current tramming method.
2.1 Mechanical rock excavation
Mechanical rock excavation is an alternative method to the drill-and-blast method where a machine drills holes into the rock and fills them with a kind of plastic explo- sive. The explosive is then ignited in intervals. The drill-and-blast method is a cyclic heading whereas mechanical excavation is considered to be continuous, even though it too involves several steps [6].
In mechanical rock excavation the rock is harvested by inducing stresses exceeding the rocks strength which fractures the rock. There are two main methods for inducing these stresses; penetrating the surface with a drag bit and moving it across the surface, see Figure 2, or by pressing an indenter into the rock and, in some cases, letting it roll over the rock surface, see Figure 3 [7].
Figure 2: Drag bits. To the left: sharp drag bit, to the right: blunt drag bit [7]
Figure 3: Indenter [7]
As long as the drag bit is sharp, the main part of the force acting on it has the same direction as the motion, see Figure 2. As the drag bit becomes blunted from wear the impact from the normal force increases rapidly [7].
When an indenter is pressed into the rock’s surface it fractures the rock beneath, see Figure 3. This leads to tensile cracks that expands and, ultimately, propagates the surface [7].
Drag bits needs less force to break the rock compared to indenters. However, since drag bits are vulnerable to wear they are generally applied exclusively in weak, non- abrasive rock [7].
Using indenters, there are two methods for cutting the rock, conventional cutting and undercutting, see Figure 4 [6].
Figure 4: Conventional cutting, to the left, and undercutting, to the right [7]
In the conventional method the indenter is simply rolled over the surface. In the undercut method the process starts from a pre drilled edge and cuts the rock from the side [6]. The advantage of the undercutting method is that it generates the tensile tension, required to fracture the rock, with less applied force than the conventional method [7].However, there is no appropriate method to control the size of the har- vested rocks, which complicates the mucking, i.e. the removal of excavated material [3].
2.2 The Mobile miner
The Mobile miner is a mechanical excavation machine from Atlas Copco, still in a con- ceptual phase [3]. It is comprised of three main parts, see Figure 5.
Figure 5: The Mobile miner [2]
The anterior part, called the Head, consists of the cutter head, which carries the in- denters, or cutters, and an apparatus for changing the direction of the cutter head, the slewing mechanism. It also has an apron used for gathering excavated rock, muck [8].
The middle part, called the Main body, has vertically mounted hydraulic cylinders, called grippers, for fixating the machine in the tunnel and horizontal cylinders that can push the Head forward [8].
The posterior part of the machine, called the Backup, contains engines, hydraulic pumps etc. The Backup is propelled by caterpillar tracks [8].
The Mobile miner uses a conventional cutting application, with cutters that can ro- tate in relation to the cutter head which, in turn, rotates in relation to the machine [3].
The vertical position of the Head can be altered with hydraulic cylinders, see Figure 5. The Head and the cylinders are attached to a circular plate. By sliding along this plate the cutter head is slewed [3].
Some requirements for the Mobile miner are listed in Table 2.
Table 2: Requirements for the Mobile miner [8]
Machine specification Value Unit
Geotechnical
Friction coeff. Grippers/tunnel walls 0.33 Cutter head
Diameter 4 m
Width 1.5 m
Main dimensions
Weight excl. Backup 270 ton
Weight incl. Backup 310 ton
Cutter head boom
Extension stroke 1.5 m
Undercarriage
Traction speed [3] 1 km/h
2.3 The Reef miner
The Reef miner, see Figure 6, is a mechanical rock excavation machine similar to the Mobile miner, see Chapter 2.2. The main difference is that the cutter head is horizontal and that it is equipped with bolting devices and cabins. The bolting devices, see Figure 6, inserts bolts into the tunnel roof to ensure that it does not collapse [3].
Figure 6: Reef Miner [10]
2.4 The Tunnel Bore System (TBS)
The TBS is the largest machine in the family. The Head is very similar to the Mobile miner. The rest of the machine contains roof support equipment, safety chamber etc., see Figure 7 [3].
Figure 7: The TBS [11]
2.5 Excavation and tramming
The excavation method is fairly similar for all of the machines. The procedure is as follows: [3]
1. The machine is fixated by pressing the grippers on the Main body onto the floor and roof of the tunnel.
2. The cutter head is pressed into the rock using cylinders between the Main body and the Head. The head, for some of the machines, rests on cylinders connected to skids. This is called plunging.
3. The cutter head is pulled back and repositioned to the side and/or height wise.
4. Step 2 and 3 is repeated until the desired tunnel profile is achieved. When the last cut has been made the cutter head is left in the plunged position.
5. The grippers on the Head are pushed onto the floor and roof of the tunnel.
6. The grippers on the Main body is loosened.
7. The cylinders, previously used for plunging, now pulls the Main body and the Backup forward. As the machine moves, the muck is scoped up by the apron and transported under the machine using a conveyor. The muck is transported behind the machine where it is taken away.
8. The sequence is repeated.
The machines have two different tramming methods. The first is described in step 5 - 7 above. Using this method, the machine cannot turn and it needs to be in a tunnel for roof support. The second tramming method is crawling using caterpillar tracks attached beneath the Main body [3].
3 Methodology and Results
This chapter explains the methods used during this project and the results.
3.1 Product specification
The generated concepts had certain criteria that should be met. These criteria are listed in Table 3. In the right hand column it is stated whether the criteria is a wish or a demand. This refers to if the specification value was demanded by Atlas Copco and Svea Teknik AB or if it was simply a wish.
Table 3: Product specification [8]
Specification Value Unit Wish or demand
Contact between machine and tunnel
Max. applied ground force contact pressure 3 MPa D Tunnel shape
Minimum inner curve radius 18 m W
Minimum outer curve radius 24 m W
Height centre 4.5 m D
Width 3.5 m D
Width half way up 4.5 m D
Machine movement
Extension stroke 1.5 m W
Max incline 5 deg W
Max decline 5 deg W
Forces
Total force applied, all grippers pressurized 13.5 MN D
Corresponding force holding capacity 4 MN D
Speed
Traction speed [3] 1 km/h W
3.2 Generated concepts
Several concepts were derived for the specifications listed in Chapter 3.1. The preemi- nent concepts are presented in this chapter.
All hydraulic cylinders are assumed to have a maximum stroke speed, vcs, of 0.2 m/s [9], to allow for comparison between the concepts. The stroke of the horizontal cylinders, sch, are all 1500 mm so that the machine can travel between faces in one movement sequence. The stroke of the vertical cylinders, scv, are assumed to be 50 mm.
3.2.1 Concept 1 - Earth worm movement, 3 body parts
The first concept, see Figure 8, is based on the same tramming principle as the existing solution, see Chapter 2.5.
Figure 8: Concept 1
Only one of the three main parts of the machine would be moved at a time, this whilst kept above ground. With the part numbers referring to the arrows in Figure 8, the sequence for moving would be:
1. Pull up vertical cylinders, part 1, on the Head
2. Push the Head forward with the horizontal cylinders, part 2 3. Lower the vertical cylinders, part 1, on the Head to the ground 4. Pull up vertical cylinders, part 3, on the Main body
5. Push/pull the Main body forward with the horizontal cylinders, part 2 and 4 6. Lower the vertical cylinders, part 3, on the Main body to the ground
7. Pull up vertical cylinders, part 5, on the Backup
8. Pull the Backup forward with the horizontal cylinders, part 4 9. Lower the vertical cylinders, part 5, on the Backup to the ground 10. Repeat sequence
The time for one movement sequence, tc1, and the machine’s speed, vc1, is calcu- lated in equation 1 and 2.
tc1 = scv vcs
+ sch vcs
+2·scv vcs
+sch vcs
+2·scv vcs
+sch vcs
+scv vcs
=24 s (1)
vc1= sch
tc1 =0.225 km/h (2)
The horizontal cylinders, part 2 and 4 in Figure 8, are connected to controllable rotational joints so that the machine can turn whilst moving by pushing the Head in an appropriate angle.
For reversing the anterior and posterior part numbers are interchanged in the move- ment sequence described above.
If the strain on the horizontal cylinders is too great the machine parts can be sup- ported by keeping the vertical cylinders, part 1, 3 and 5, on the ground whilst mov- ing. The machine would then slide over the floor just like in the existing solution, see Chapter 2.5. Another solution could be to support the horizontal cylinders, part 2 and 4, with some sort of a link system.
3.2.2 Concept 2 - Earth worm movement, 2 body parts
The second concept has the same general principle as the first but with only two, of the machine’s three, main parts involved in the movement. The moving part of the machine could no longer be held up over the ground but the speed of the tramming would be enhanced.
The time for one movement sequence, tc2, and the machine’s speed, vc2, is calcu- lated in equation 3 and 4.
tc2= scv vcs
+sch vcs
+2·scv vcs
+ sch vcs
+ scv vcs
=16 s (3)
vc2= sch
tc2 =0.338 km/h (4)
3.2.3 Concept 3 - Feet
The third concept is inspired by a product from Columbia Industries, used for moving various heavy objects [12]. The concept is presented in Figure 9 below.
In this concept, and all following concepts, only the movement of the Main body and Head is considered. The caterpillar tracks on the Backup are preserved.
Figure 9: Concept 3
The Main body is connected to feet via vertical cylinders, part 1 in Figure 9. The feet consist of a horizontal cylinder, part 2, and a liner guiding, part 3.
With the part numbers referring to the arrows in Figure 9, the sequence for moving would be:
1. Lift the Main body using the vertical cylinders, part 1
2. Push the machine forward with the horizontal cylinders, part 2, letting them slide over the linear guiding
3. Put the Main body back on the ground 4. Pull the horizontal cylinders, part 2, back 5. Repeat sequence
The time for one movement sequence, tc3, and the machine’s speed, vc3, is calcu- lated in equation 5 and 6.
tc3 = scv vcs
+ sch vcs
+ scv vcs
+ sch vcs
=15.5 s (5)
vc3= sch
tc3 =0.348 km/h (6)
The vertical cylinders, part 1, can be rotated so that the machine can turn. For doing so, these cylinders also need to be connected to a linear guiding so as to enable the machine to move in an arc, see Figure 10.
Figure 10: Vertical play, Concept 3
Assuming the feet are mounted as in Figure 10 the required vertical play, vpc3, is calculated as in Equation 7.
vpc3=2174− r
21742−sch 2
2
=133 mm (7)
3.2.4 Concept 4 - Feet with no slewing mechanism
The fourth concept has the same tramming solution as Concept 3 but the separate steer- ing for the Head, the slewing mechanism described in Chapter 2.2, has been eliminated.
The idea is that the entire machine would be repositioned between plunges. The plung- ing movement could also be performed by the feet.
The time for one movement sequence, tc4, and the speed, vc4, would be the same as for Concept 3.
3.2.5 Concept 5 - Arms
The fifth concept consists of six arms mounted on the side of the Main body, see Fig- ure 11. The arms are two hydraulic cylinders mounted horizontally with a cylinder mounted vertically in one end and a rotary actuator in the other.
Figure 11: Concept 5
With the part numbers referring to the arrows in Figure 11 the sequence for moving would be:
1. Pull up three of the vertical cylinders, parts number 1
2. Extend the corresponding horizontal cylinders, parts number 2 3. Lower the vertical cylinders, parts number 1, to the ground 4. Pull up the other three vertical cylinders, parts number 3
5. Pull the corresponding horizontal cylinders, parts number 4, forward.
6. Lower the vertical cylinders, parts number 3, to the ground
7. Drag/push the machine forward using the horizontal cylinders, parts number 2 and 4
8. Repeat sequence
The time for one movement sequence, tc5, and the machine’s speed, vc5, is calcu- lated in equation 8 and 9.
tc5 =scv vcs
+sch vcs
+scv vcs
·2+ sch vcs
=23.5 s (8)
vc5= sch
tc5 =0.23 km/h (9)
This concept would most likely require the same gripper cylinders as the original design, see Chapter 2.5, so as to not subject the horizontal cylinders to too high side forces.
3.2.6 Concept 6 - Arms with no slewing mechanism
The fifth concept could be modified so as to eliminate the slewing mechanism. Just as for Concept 4, the entire machine could be repositioned between plunges. The plunging movement of the Head would most likely have to be done separately.
The time for one movement sequence, tc6, and the speed, vc6, would be the same as for Concept 5.
3.2.7 Concept 7 - Walking with 3 arms
The seventh concept, see Figure 12, has the same basic principle as the fifth but only three arms are in contact with the ground whilst the machine is moving.
Figure 12: Concept 7
With the part numbers referring to the arrows in Figure 12 the sequence for moving would be:
1. With three of the horizontal cylinders, parts number 2, and the corresponding vertical cylinders, parts number 1, extended, pull up the other three vertical cylinders, parts number 3.
2. Pull the Main body forward using the horizontal cylinders, parts number 2. At the same time, extend the other three horizontal cylinders, parts number 4.
3. Lower the vertical cylinders, parts number 3, to the ground.
4. Repeat sequence but start with parts number 4 as extended.
The movement is hence more fluent and much faster than the other concepts as can be seen in equation 10 and 11 where the time for one movement sequence, tc7, and the speed, vc7, is calculated.
tc7= scv vcs
+ sch vcs
+ scv vcs
=8 s (10)
vc7= sch
tc7 =0.675 km/h (11)
3.2.8 Concept 8 - Walking with 3 arms with no slewing mechanism
Concept 7 could also be modified so as to eliminate the slewing mechanism. Just as for Concept 4 and 6, the entire machine could be repositioned between plunges.
The time for one movement sequence, tc8, and the speed, vc8, would be the same as for Concept 7.
3.2.9 Concept 9 - Omnidirectional wheels
In the ninth concept the machine would be fitted with omnidirectional wheels [13]
such as the one presented in Figure 13.
Figure 13: Omnidirectional wheel [14]
If conventional wheels were applied the corresponding shafts would have to be rotated in order to turn the machine. Since the load from the machine weight is so great this would result in the need for large components and most probably, large wear. Omnidirectional wheels enable movement in all directions, including turning, without having to change the direction of the wheels.
The movement would be fluent. The speed would be dependent on the capacity of the wheel and the engine.
With this concept the machine would need to be fitted with the same kind of grip- pers as the existing solution, see Chapter 2.5.
3.3 Concept evaluation
The concepts described in Chapter 3.2 have been evaluated with respect to the features described in Table 4.
Table 4: Concept evaluation criteria’s
Feature Assessment criteria
Forward movement Ability, speed
Backwards movement Ability, speed
Turning Radius, speed
Turning whilst moving Radius, speed
Parallel movement Ability
Elimination of slewing mechanism Ability
Moving in incline/decline Ability, speed Turning in incline/decline Ability
Lifting the machine Ability, Speed
Serviceability Accessibility, required time, time between services etc.
Price Manufacturing method, mass and material price,
component price etc.
Reliability Use of standard components, simple design etc.
Weight Mass
Manoeuvrability Operability, ability to steer to a specific point Redundancy Alternative propulsion possibilities
The features presented in Table 4, form the basis for a PUGH-matrix, see Table 5.
Weights, from 1 to 5, have been added in agreement with Atlas Copco and Svea Teknik AB, the more important the feature the higher the weight. The weights are multiplied to each concept’s rating for the corresponding feature to create the score. The concept’s rating are -1 for worse than the benchmark concept, 0 for as good as and 1 for better.
All scores are then added into a final sum. The benchmark concept is the Mobile miner as it is originally designed, see Chapter 2.2 and 3.1.
Table 5: PUGH-matrix
Criteria Weight Benchmark Concept1 Concept2 Concept3 4Concept Concept5 Concept6 Concept7 Concept8 Concept9
Forward movement 5 0 -1 -1 -1 -1 -1 -1 -1 -1 0
Backwards movement 5 0 -1 -1 -1 -1 -1 -1 -1 -1 0
Turning 4 0 -1 -1 1 1 1 1 1 1 1
Turning whilst moving 2 0 1 1 1 1 1 1 1 1 1
Parallel movement 1 0 0 0 1 1 1 1 1 1 1
Elimination of slewing mech- anism
3 0 0 0 0 1 0 1 0 1 0
Moving in incline/decline 3 0 0 -1 1 1 1 1 1 1 1
Turning in incline/decline 1 0 0 -1 0 0 1 1 1 1 1
Lifting the machine 2 0 0 0 0 0 1 1 1 1 0
Serviceability 4 0 1 -1 -1 -1 1 1 1 1 -1
Price 3 0 1 1 0 0 0 0 0 0 0
Reliability 5 0 1 1 1 1 1 1 1 1 -1
Weight 2 0 1 1 0 0 1 1 1 1 1
Manoeuvrability 4 0 -1 -1 1 1 1 1 1 1 1
Redundancy 2 0 -1 -1 1 1 1 1 1 1 0
Sum: 46 0 -4 -16 7 10 20 23 30 33 8
After discussions of the PUGH-matrix with Atlas Copco and Svea Teknik AB, Con- cept 8, with some modifications, was considered most suitable and was hence further developed [9].
3.4 Concept development
After rendering Concept 8 the most suitable, see Chapter 3.3, it was further developed.
That process is described in this chapter.
After discussions with Atlas Copco it was concluded that the machine can be sup- ported by the caterpillar tracks on the Backup, see Figure 14 [9]. The machine therefore only needs two arms, not three as described in Chapter 3.2.7, to stand on at a time.
Thus, the total of only four, not six, arms are needed.
Figure 14: The Mobile miner [2]
3.4.1 Centre of gravity
To derive the forces acting on the movement mechanism the location of the centre of gravity, COG, for the machine parts had to be established.
The Main body of the Mobile miner is assumed to be so similar to the Main body of the TBS that the geometry of the TBS can be used to identify the COG in the Mobile miner. The TBS is scaled down with the ratio between the cutter head’s diameters as the dimensioning value. Furthermore, the Backup on the Mobile miner’s drawings is smaller than the Backup on the smaller machine, the Reef miner. The Reef miner has cabins which the Mobile miner does not, but the Mobile miner is assumed to require larger, or more, pumps etc. The Backup on the Mobile miner is hence assumed to be of the same size as the Reef miner’s. The total length of the machine, lf p, with the Head retracted, is then 17930 mm [15].
When the cutter head in the TBS is fully retracted the COG for the Main body and Head is located 4710 mm from the centre of the cutter head [16]. The TBS’ cutter head has a diameter of 4500 mm [16] and the Mobile miner’s cutter head has a diameter, dh, of 4000 mm [8].
The location, cm, of the COG for the Main body and Head, COGm, in the Mobile miner in relation to the centre of the cutter head is calculated in equation 12.
cm= 4710·4000
4500 =4186.7 mm (12)
The COG in the Backup, COGb, is located in its volumetric centre, 14170 mm from the centre of the cutter head, cb [15].
The location, ct, of the COG for both the Backup and the Main body, COGt, in relation to the centre of the cutter head is calculated in equation 13.
ct= cm·mm +cb·mb
mm+mb =5784 mm (13)
, where mmis the weight of the Main body and Head and mbis the weight of the Backup, see Chapter 2.2.
A schematic drawing of the Mobile miner with COGm, COGb and COGt marked is presented in Figure 15.
Figure 15: Schematic drawing of Mobile miner 3.4.2 Linear motion
The linear motion in Concept 8 is performed by hydraulic cylinders, see Chapter 3.2.7.
Hydraulic cylinders can withstand a relatively small force in the direction perpen- dicular to the motion it actuates [9]. Since the horizontal cylinders in Concept 8 are perpendicular to the gravitation force from the machine, they will need to be unnec- essarily large in relation to what would have been needed to only pull the machine forward. To avoid this, a different solution for the linear motion was generated, see Figure 16.
Figure 16: Concept for linear motion
The concept works as a scissor lifting table placed horizontally. The machine will be attached to support 1 and the foot will be placed on the ground. As the piston is pressed out of the cylinder support 1, i.e. the machine, will move to the right in Figure 16 and vice versa when the piston is pressed in to the cylinder. Joint number 2 and 5 are connected to linear bearings in support 1 and 2 respectively.
3.4.3 Arm placement and load
Assuming that a pair of arms should be able to carry the entire weight of the machine each arm would be required to carry half of that. The force from the weight of the machine, Fg, and the total force on each arm, Farm, is calculated in equations 14 and 15.
Fg=m·g (14)
, where m is the total weight of the machine and g is the gravitation, 9.81 m/s2. Farm= Fg
2 =1520550 N (15)
Assuming that the same kind of hydraulic cylinders are needed for the arms as for other purposes in the machine, the minimum piston diameter needed is calculated in equation 16 [8].
r Farm
16 MPa·π ·2≈0.35 m=350 mm (16)
If the machine is to be fitted with only four arms, and therefore also only stand on two at a time, they have to be attached in front of COGt to ensure that the machine does not tip over. Since the radius of the cutter head is 2000 mm[8], the distance from the COGt to the edge of the cutter head is 3784 mm, see Figure 15 in Chapter 3.4.1. If a stroke of 1500 mm is desired this leaves 784 mm for material in and space between the arms. Since the minimum piston diameter is 350 mm, see equation 16, 784 mm could not possibly be enough space. Consequently the stroke length has to be reduced. Since this concept allows for an almost continuous propulsion this does not greatly affect the speed. It will, however, significantly enhance the mobility of the machine since the shortening of the arms will make the machine fit easier in the tunnel.
Each plunge into the rock is 1500 mm deep. Even though this distance no longer can be reached with one step it would still be preferable to do so in a whole number of steps so as to simplify the control and utilize the entire stroke i.e. the stroke, sa, must satisfy equation 17.
sa=1500
n (17)
, where the number of steps, n, is a natural number.
Assuming that the width of each support in the arms must be 500 mm, to fit the cylinders and to manage the load, and that the feet always must be at least 300 mm from the edge of the cutter head, in order to fit the apron etc., the maximum stroke length is calculated as in equation 18.
3784−500·2−300
2 =743.35 mm (18)
Thus the maximum stroke length must satisfy equation 19.
743.35> 1500
n (19)
From which follows that the stroke length, sa, must be 500 mm.
From Figures 17 and 18 below, the reaction forces from the caterpillar tracks on the Backup, Rb, and the arms, Ra1−Ra4, can be calculated, see equations 14 to 22.
Figure 17: Free body diagram of the entire machine, arm 1 and 2 is in contact with the ground
Figure 18: Free body diagram of the entire machine, arm 3 and 4 is in contact with the ground
Fa1=Fa2= Fg· (cb−ct)
2· (cb−ct+la1) (20) , where la1 is the distance from COGt to the centre of Support 2, see Figure 17.
Fa3=Fa4= Fg· (cb−ct)
2· (cb−ct+la2) (21) , where la2 is the distance from COGt to the centre of Support 2, see Figure 18.
Rb =Fg−2·Fa (22)
, where Fa is the reaction force currently acting on the arms.
From equations 20 and 21, it is clear that the shorter the distances la1 and la2, the higher the loads Fa1, Fa2, Fa3, Fa4. Thus the rear arms, arm 1 and 2, will be subjected to the highest loads, yet always less than half that of the total weight of the machine.
Since the machine is fitted with an apron just behind the Head, it would be preferable to keep the arms as far away from the Head as possible yet in front of COGt. The centre of Support 1 in the hind arms are therefore placed in line with COGt.
3.4.4 Dimensioning of the arms
To dimension the arms the forces acting on each part of them had to be derived. In order to do so, a free body diagram was drawn, see Figure 19.
Figure 19: Free body diagram of arm
With l7 and l8 as displayed in equations 23 and 24, the forces in Figure 19 can be described as in equations 25 to 35, assuming all parts are weightless.
l7=ll·cos(α) (23)
l8=ll·sin(α) (24)
J5=0 (25)
J6x=J5 (26)
J6y=Fa1 (27)
J1y= J6y·l7−J6x·l8+J5·l8
l7 (28)
J1x= J1y·l7−J5·l8
l8 (29)
J2x=J1x−J5+J6x (30)
J4x=J2x−J6x (31)
R2= J2x· (l8+l3) −J1x·l3
l6 (32)
R1=R2+J1x−J2x (33)
C=Fa1−J1y (34)
J4y=J1y (35)
The caterpillar tracks on the Backup has separate drive but the arms should be able to pull the Backup if this system fails or if the caterpillar tracks gets stuck etc. After discussions with engineers at Svea Teknik AB, the rolling resistance in the caterpillar tracks, µr, was estimated to 0.35. The force from the rolling resistance, Fr, is calculated in equation 36 [17].
Fr =Rb·µr (36)
This force will be horizontal and always in the opposite direction of the motion.
The free body diagram is now altered as displayed in Figure 20.
Figure 20: Free body diagram of arm with rolling resistance from caterpillar tracks
The only alternations to the system of equations will be to equations 25 and 26, see equations 37 and 38.
J5= −Frl5
l8 (37)
J6x=J5+Fr (38)
The forces were calculated for all positions of the arm using some suitable assump- tions for the lengths of the components. The results are presented in Figures 21 and 22.
Figure 21: Calculated forces, no rolling resistance
Figure 22: Calculated forces, rolling resistance
Using the same lengths, the arm was modelled in Adams, see Figures 23 and 24.
Figure 23: Adams setup, zoomed
As can be seen in Figure 23, revolute joints are placed between support 1 and the upper link, the sliding block in support 1 and the lower link, support 1 and the cylin- der in support 1, the upper link and the lower link, the sliding block in support 2 and the upper link and between support 2 and the lower link. A spherical joint is placed between the piston in support 2 and the ground. Translational joints are placed be- tween the sliding block in support 1 and support 1, the piston and cylinder in support 1, the sliding block in support 2 and support 2 and the piston and cylinder in support 2. A fixed joint has been placed between support 2 and the cylinder in support 2.
Figure 24: Adams setup
As can be seen from Figure 24, the Backup and caterpillar tracks are represented by links. Revolute joints are placed between the Backup and the upper and lower edge of support 1 and between the Backup and caterpillar track. A translational joint is placed between the caterpillar track and the ground. A fixed joint is placed between two parts of the Backup.
The motion was first modelled very slowly so as to simulate static conditions like the ones calculated. The results are presented in Figures 25 and 26.
Figure 25: Simulated forces, no rolling resistance, static conditions
Figure 26: Simulated forces, rolling resistance, static conditions
The maximum and minimum for each force is presented in Table 6 and 7, to visu- alize the differences between the calculated and the simulated forces.
Table 6: Maximum and minimum forces, no rolling resistance Force Max calc Max sim Diff Min calc Min sim Diff
[MN] [MN] [MN] [MN]
J1x 1.0699 1.0698 0.009% 0.38045 0.38045 0.000%
J1y 1.4596 1.4596 0.000% 1.3806 1.3806 0.000%
J2x 1.0699 1.0698 0.009% 0.38045 0.38045 0.000%
J4x 1.0699 1.0698 0.009% 0.38045 0.38045 0.000%
J4y 1.4596 1.4596 0.000% 1.3806 1.3806 0.000%
J5 0 0 0.000% 0 0 0.000%
J6x 0 0 0.000% 0 0 0.000%
J6y 1.4596 1.4596 0.000% 1.3806 1.3806 0.000%
R1 0.87394 0.87389 0.006% 0.38045 0.38045 0.000%
R2 0.87394 0.87389 0.006% 0.38045 0.38045 0.000%
C 0 0 0.000% 0 0 0.000%
Table 7: Maximum and minimum forces, rolling resistance Force Max calc Max sim Diff Min calc Min sim Diff
[MN] [MN] [MN] [MN]
J1x 1.181 1.1809 0.008% 0.30564 0.30564 0.000%
J1y 1.7945 1.7945 0.000% 1.1248 1.1248 0.000%
J2x 1.2683 1.2682 0.008% 0.21837 0.21837 0.000%
J4x 1.3795 1.3793 0.015% 0.14356 0.14356 0.000%
J4y 1.7945 1.7945 0.000% 1.1248 1.1248 0.000%
J5 0.19843 0.19842 0.005% -0.19843 -0.19842 0.005%
J6x 0.11115 0.11115 0.000% -0.11115 -0.11114 0.009%
J6y 1.4596 1.4596 0.000% 1.3806 1.3806 0.000%
R1 0.94875 0.94869 0.006% 0.30564 0.30564 0.000%
R2 1.036 1.036 0.000% 0.21837 0.21837 0.000%
C 0.33484 0.33484 0.000% -0.33484 -0.33484 0.000%
As can be seen from Table 6 and 7 the results from the calculations and the model coincide well. Both the model and the calculations are therefore deemed reliable.
The arm was modelled with a cylinder speed more closely corresponding to what was assumed possible in reality. The cylinders maximum speed, vcm, is 0.2 m/s [9].
The position of the piston, in relation to the cylinder, over time was modelled as a sinus curve, see Figure 27.
Figure 27: Piston position and speed
As can be seen in Figure 27 the speed of the piston peaks at 0.2 m/s .
The loads were also altered so as to simulate a five degree slope, the maximum allowed according to the specifications see Chapter 3.1. The gravitation force from the machine was split into an x- and a y-component equal to 0.13252 MN and 1.5148 MN respectively. This set-up constitutes the worst case scenario and the forces subjected to the different joints are presented in Figure 28.
Figure 28: Dynamically simulated forces
The maximum and minimum for all forces are presented in Table 8.
Table 8: Maximum and minimum forces
Force Max Min
[MN] [MN]
J1x 1.3485 0.41185 J1y 1.3174 0.63968 J2x 1.5705 0.45066 J4x 1.8538 0.48263 J4y 1.3174 0.63972 J5 0.50539 0.070629 J6x 0.28309 0.032598 J6y 1.4556 1.3748 R1 1.0613 0.41043 R2 1.2825 0.4517 C 0.81582 0.06168
To give a sense of the necessary dimensions of the components some preliminary fatigue calculations were performed using the results displayed in Table 8. This was done with a safety factor, s, that was set to 1.5, see equation 39 [18].
s= λ·δ·κ·σD
φ(1+q·σnom(Kt−1)) (39) , where λ is the factor for technological volumetric dependence as a function of the dimensions, δ is the factor for geometrical volumetric dependence as a function of the diameter and the tensile strength of the material, κ is the surface factor as a function of the tensile strength and the surface roughness, σD is the fatigue limit, φ is the coeffi- cient of restitution, q is the fillet sensitivity factor as a function of the fillet radius and the tensile strength, Kt is the shape factor and σnom is the nominal stress.
Two kinds of steel have been chosen, SS2225-05 for the casted parts and SS2541-04 for the shafts, see Table 9. The materials have been selected since they are used in other similar components of the machine.
Table 9: Materials
Material σD bending, σD bending, Rm ReL Rs= 0,[MPa] Rs= −1,[MPa] [MPa] [MPa] SS2225-05 830 [18] ±480 [18] 1000 [18] 700 [19]
SS2541-04 1040 [18] ±600 [18] 1200 [18] 800 [20]
For the components in need of bearings, equation 40 was used to realize the neces- sary diameters. A journal bearing material called JM7-15 [21] was selected, see Table 10, since it can withstand large loads and it has the same supplier as other bearing materials used in the machine.
Db=
Fb Pb
Lb (40)
, where Db is some bearing diameter available from the supplier [21], Fb is the total load on the bearing, see Table 8, Pb is the maximum allowed pressure, see Table 10, and Lb is some bearing length available from the supplier [21].
Table 10: JM7-15 [21]
Feature Value Unit Max speed 0.3 m/s Max pressure 90 MPa
When dimensioning the linear bearings in the supports, equation 40 was also used but with the diameter as the width.
After discussions with engineers at Svea Teknik AB and some investigations of other cylinders the length of the cylinder in support 1 was assumed to be 270 mm longer than the stroke length needed.
A suitable slew drive that can achieve the rotation of the arms was found [22].
Assuming that the distance from the front arms to the COGt, i.e. the longest distance from an arm’s attachment point to the COGt, is 2.2 m the moment of inertia for the machine, I, is approximately 6.7·105 kgm2. The torque needed to turn whilst in a 5◦slope, , T, is calculated as in equation 41.
T=sin(5◦) ·Fg=1.1503·105 Nm (41) These needs would be filled with the model WD-H 0645/3-00001 [22] and still give an acceptable acceleration, see equation 42.
T
I =3.2◦/s2 (42)
3.4.5 The final CAD-model
The process of deriving the final CAD-model was iterative. The result is presented in Figures 29 and 30. No bearings are included in the model.
Figure 29: Final CAD-model, size
Figure 30: Final CAD-model
Support 1 consists of two, almost identical, halves, see Figure 31. The only differ- ence is the holes in the side that should be cut out for tubes for the hydraulic cylinder.
The two halves can be casted in the same mould and the holes can be drilled after as- sembly. The two halves are assembled with screws and nuts. The walls of the square holes are lined with plates of bearing material JM7-15[21], not shown in the figure.
The top of the support halves are fixed with two plates, shaped as partial circles, and four screws. These plates will be casted. The top of the support is screwed on to a shaft connected to the slew drive. The slew drive is connected to the machine. On the bottom of the support the male part of a journal bearing, connecting the arm to the machine, is mounted. Both the slew drive shaft and the male of the journal bearing will be lathed. The screws have not been dimensioned.
Figure 31: Support 1
The hydraulic cylinder is placed inside support 1, see Figure 32. It is connected to the support by a shaft which is fastened with screws and lids on both sides. The screws in the figure is M6 but has not been dimensioned. The cavity in the support is slightly larger than the cylinder so that it is free to move and will hence only be subjected to loads in the axial direction of the piston. The piston is attached to the sliding block either by welding or by screws. The sliding block has two extrusions that fit into a track in the support to hold the sliding block in place. The sliding block will be manufactured by milling and lathing.
Figure 32: Support 1, contents
Support 2, see Figure 33, is going to be casted. Just as for support 1 the square hole is lined with plates of the bearing material JM7-15 [21]. The sliding block, like the one in support 1 but without the extrusion, will be placed in the square hole. A hydraulic cylinder is connected to the bottom of the support using screws. The piston is connected to a plate through a spherical bearing, not included in the model.
Figure 33: Support 2
The upper and lower links are almost identical with the exception of screw holes in the lower links, see Figure 34. All four links can hence be casted in the same mould and the holes drilled after. The links are connected to the sliding blocks through bearings, not included in the figure. They are fixed using lids and screws. The upper and lower links are connected via a shaft that is fastened to the lower link trough a lid and screws.
The links are connected to the supports through shafts and kept in place using lids.
The lids and shafts will be lathed.
Figure 34: Links
Since there is limited room for screw heads on the shafts connecting the links to the machine the necessary number of screws, ns, were calculated, see equation 43.
ns =
qJ1x2 +J1y2
Fpl·µss (43)
, where Fplis the maximum preload for screws of grade 12.9 [23] and µss is the coeffi- cient of friction between steel and steel, equal to 0.78 [24]. The forces acting in joint 1, J1xand J1yare taken from Table 11 see Chapter 3.5.1.
The largest diameter of the screws that will fit, with regards to the socket wrench diameter for hexagonal screw heads [25], is M12.
The number of screws needed, ns, was hence calculated to 10.4. Since the maximum forces only occur very shortly, the number was rounded down to 10.
All parts are presented in Figure 35.
Figure 35: Final CAD-model, exploded
Regards have been taken to the diameter of socket wrenches [25] for all counter bores in the model.
3.5 Concept verification
To verify the function of the concept it has been tested in regards to fatigue life, move- ment and size.
3.5.1 Fatigue
The movement of the final CAD-model was simulated in Adams, in the same setup as the previous models, see Chapter 3.4.3. The results are presented in Figure 36.
Figure 36: Forces in final CAD-model
To realize the stresses in the different components simplified versions of the CAD- models were put in to Ansys and subjected to the loads presented in Table 11. These are not the largest forces since not all maximum forces occur at the same time, see Figure 36.
Table 11: Loads, worst case scenario Force Value [MN]
J1x 0.94898
J1y 0.75649
J2x 1.1121
J4x 1.228
J4y 0.85783
J5 0.27907
J6x 0.1159
J6y 0.82538
R1 0.69583
R2 0.9157
C 0.57371
As can be seen from Table 11, only the forces in the x- and y-plane are considered.
This is to simplify the modelling and the calculations and because the loads in the z- plane are comparatively small. Only the worst case scenario was modelled and only one model for each kind of part was produced. For example only one link was mod- elled, the lower link, since it would be subjected to larger loads than the upper link.
Images of the arrangements and the results are attached in Appendix A. The maximal equivalent stresses and the components materials are presented in Table 12.
Table 12: Maximal stresses and component material Component Max stress [MPa] Material
Support 1 349 SS2225-05
Link 385 SS2225-05
Shaft for joint 1 312 SS2541-04 Shaft for joint 4 657 SS2541-04
Shaft to machine 320 SS2541-04
Sliding block 1 859 SS2541-04
Shaft for cylinder in support 1 206 SS2541-04
Support 2 78.8 SS2225-05
To verify that the components will not fail due to fatigue a Haigh-diagram was made for each part subjected to stresses above 250 MPa. In all reductions the shape factor, Kt, was set to 1 since the highest stress in the part was known. The minimum stress was always set to 0 since the arm will be raised above the ground between steps and will then essentially be unloaded. In the CAD-models used in the Ansys models all rounds and small holes have been excluded since the number of nodes in the student license is limited. There are hence some extreme stress concentrations. In the Haigh-diagrams, the stresses presented two steps away from such a concentration, in the yellow zone, were used, see Appendix A and Table 12. The Haigh-diagrams are attached in Appendix B. The safety factors against fatigue, s, corresponding to these diagrams are presented in Table 13. The safety factors have been calculated according to equation 44 [5].
s= OB
OA (44)
, where OB is the vector from origo to the intersection between R and the reduced Haigh-diagram and OA is the vector from origo to the stress, see Appendix B.
Table 13: Safety factor
Component s
Support 1 1.68 Link 1.69 Shaft for joint 1 3.18 Shaft for joint 4 1.51 Shaft to machine 3.10 Sliding block 1 1.29
3.5.2 Movement and size
To ensure that the machine can fit in the tunnel and move as required, a CAD-model of the Main body and Head was created. Firstly the arms should fit on the machine. Since the size of the other components on the machine, such as the apron, grippers and cylin- ders for plunging, is not yet decided this cannot be completely determined. However, as can be seen in Figures 37 and 38 there is potential room for such components.
Figure 37: Machine seen from the side
Figure 38: Machine seen from above
Secondly, the machine should fit in the tunnel. As can be seen from Figure 38, it does since the tunnel is 4500 mm wide half way up from the floor to the roof [8].
The machine can be moved in a circle with its centre in almost any point depend- ing on how the movement is programmed. The minimal inner curve radius is hence entirely dependent on the length of the Main body and Head. In Figure 39 the arms are placed in a 45◦angle to the Main body and the machine still fits in the tunnel.
Figure 39: Machine seen from above, 45◦
The machine could also be moved parallel however not with an entire stroke length of the arms, see Figure 40.
Figure 40: Machine seen from above, parallel
The final stroke length of the hydraulic cylinder in support 1 is 370 mm and the stroke length of the arm is 500 mm. Assuming that the cylinders speed is 0.2 m/s [9], the speed of the machine would be as calculated in equation 45 excluding the time needed to place the foot on the ground.
0.5
0.37 0.2
=0.27 m/s (45)
However, the average speed when running simulations in Adams was 0.17 m/s since the cylinder was accelerating and decelerating.
The maximum allowed ground pressure is 3 MPa, see Chapter 3.1. The diameter of the feet are 500 mm. The ground pressure is calculated in equation 46.
J6ymax
π0.52 ≈1 MPa (46)
, where J6ymax is the maximal value of J6y, see Table 11, which is equal to the normal force acting on the foot see equation 27 in Chapter 3.4.4.
The mass of each arm, excluding the shaft to the slew drive and the slew drive, is 5670 kg. This has been asessed using Pro Engineer.
4 Discussion and conclusions
In this chapter the methods and results of this project are discussed and the conclusion pre- sented.
4.1 Discussion
The concept meets all product specifications, see Chapter 3.1, except the tramming speed. It is however possible that the piston in the hydraulic cylinder in support 1 could be moved faster than 0.2 m/s but that would increase the loads. Another way of increasing the speed would be to elongate the arms thus making the stroke length of the hydraulic cylinder in support 1, shorter. This would however have a negative effect on the mobility of the machine and make the placement of the arms, and sur- rounding components, more difficult. The attachment points of the cylinder in sup- port 1 could also be moved to some entirely different location so that the cylinder, for example, acts more closely to joint 4. This could make the stroke length of cylinder shorter and hence increase the speed of the arms. This would however increase the load on the cylinder and, most likely, the length of the arm.
The mobility of the machine would be enhanced with arms instead of the original tramming mechanism, see Chapters 2.5 and 3.5.2. The software needed to steer the machine would, however, most likely be complicated.
The assumed length of the cylinder in support 1 might be a bit too short, see Chap- ter 3.4.5. Since the stresses in support 1 are low in regards to fatigue life, see Table 13 in Chapter 3.5.1, the mounting could be raised and placed on the inside of the shaft for joint 1, see Figure 41.
Figure 41: Placement of cylinder, support 1
