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Mesh Mounting Concept for a Mechanical Rock Excavation Machine
Elin Skoog
Master of Science Thesis MMK 2017:91 MKN 206
KTH Industrial Engineering and Management
Machine Design
SE-100 44 STOCKHOLM
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Examensarbete MMK 2017:91 MKN 206
Nätmonteringskoncept för
en Mekanisk Bergavverkningsmaskin
Elin Skoog
Godkänt
2017-06-09
Examinator
Ulf Sellgren
Handledare
Ulf Sellgren
Uppdragsgivare
Svea Teknik AB
Kontaktperson
Jacob Wollberg
Sammanfattning
Denna rapport är resultatet av ett examensarbete som utförts på Institutionen för
Maskinkonstruktion på KTH. Projektet gjordes med Svea Teknik AB i samarbete med Atlas
Copco Rock Drills AB och deras avdelning för Gruv- och Bergbrytningsteknik i Örebro.
Atlas Copco håller för närvarande på att utveckla en ny TBM för mekanisk bergavverkning, som
har fått namnet RVM (Remote Vein Miner). När bergavverkning sker så induceras spänningar
och sprickor i berget som omger tunneln och det är därför nödvändigt att förstärka tunneln så att
den inte rasar samman. I detta fall så sker denna förstärkning genom att borra hål i tunnelväggen
och sätta in bergbultar, och samtidigt klä väggarna med ett skyddande nät. När operatörerna utför
detta arbete så befinner de sig i en del av tunneln som inte är säkrad och de är således utsatta för
säkerhetsrisker. Det är därför av intresse att göra denna nätmonteringsprocess automatiserad.
Syftet med detta projekt var att utveckla en konceptkonstruktion för näthanteringen- och
monteringen för RVM-maskinen som innebär mindre manuellt arbete av operatörerna, alltså att
ersätta den nuvarande semi-manuella näthanteringslösningen med en lösning som istället kan
automatiseras och fjärrstyras.
Brainstormning användes för att ta fram 6 stycken olika koncept, 4 gällande näthanteringen och
2 för bulthanteringen. Dessa koncept utvärderades i två separata Pugh matriser. De två koncept
som ansågs vara de mest lovande, bultkarusellen och en armkonstruktion för hantering av
nätrullar, utvecklades vidare. CAD-modeller av de inkluderade komponenterna och systemen
gjordes och användes för att verifiera armens räckvidd och att den uppfyllde att hålla sig inom
maskinens platsbegränsningar. De hydrauliska cylindrarna dimensionerades utifrån krafter som
erhölls från en ADAMS-simulering.
Den slutgiltiga konstruktionen uppfyllde alla specificerade krav, men ansågs vara väldigt
komplex och det ansågs osäkert hur och om den skulle klara av den mycket tuffa miljön i
tunnelgången.
Nyckelord: nätmontering, stängselnät, bergförstärkning, tunnelförstärkning
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Master of Science Thesis MMK 2017:91 MKN 206
Mesh Mounting Concept for a
Mechanical Rock Excavation Machine
Elin Skoog
Approved
2017-06-09
Examiner
Ulf Sellgren
Supervisor
Ulf Sellgren
Commissioner
Svea Teknik AB
Contact person
Jacob Wollberg
Abstract
This report is the result of a Master’s Thesis done at the Machine Design Department at the
Royal Institute of Technology. The project was carried out at Svea Teknik AB in cooperation
with Atlas Copco Rock Drills AB and the Mining and Rock Excavation division in Örebro.
Atlas Copco is currently developing a new TBM for mechanical rock excavation, which have
been named the RVM (Remote Vein Miner. When doing the excavation, stresses and cracks are
induced in the tunnel walls and roof, why it is necessary to reinforce the tunnel so that is does
not collapse. In this case this is done by drilling holes and inserting rock bolts into the tunnel
walls, and at the same time clothe the walls with a chain link mesh. The operators that are doing
this are working in an unsecured part of the tunnel and are hence exposed to a safety risk. It is
therefore of interest to make this mesh mounting procedure automated.
The project’s purpose was to develop a design concept for the mesh handling and mounting for
the RVM that require less manual hands-on work by the operators, i.e. replacing the existing
semi-manual mesh handling to a solution that instead can be automatized and remote controlled.
Brainstorming was used to generate 6 different concepts, 4 for the mesh handling and 2 for the
bolt handling, which were evaluated in two separate Pugh’s evaluation matrices. The two
concepts that was deemed most promising, the bolt carrousel and an arm handling solution for
mesh rolls, were further developed. CAD models of the included components and systems were
made and used to verify the arm’s range and that it fulfilled all of the constraints related to the
spatial limitations on the machine. The hydraulic cylinders were dimensioned with forces
obtained from an ADAMS simulation.
The final conceptual design did fulfil the requirements, but was considered to be very complex
and concerns were made regarding how it would handle the harsh environment in the tunnel.
Keywords: mesh mounting, chain link mesh, rock reinforcement, mine tunnel support
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FOREWORD
Firstly, I want to thank Svea Teknik for giving me the opportunity to take on this project with
them and for their support and help during the semester. I would also like to thank Fredrik Saf
and Jan Olsson at Atlas Copco in Örebro for their help in answering questions and providing me
with all necessary information, and for taking time to show me around their production site. I
really enjoyed that.
Lastly, I want to acknowledge my friends and fellow Master’s Thesis colleagues Oscar Hällfors
and Jonas Torstensson, whom I have shared office with this last semester. Thanks for the
brilliant company, many laughs and all the fun, passionate and interesting discussions we have
had together.
Elin Skoog
Stockholm, June 2017
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NOMENCLATURE
Abbreviations
KTH Kungliga Tekniska Högskolan/Royal Institute of Technology
TBM Tunnel Boring Machine
RVM Remote Vein Miner
CAD Computer Aided Design
CAE Computer Aided Engineering
WBS Work Breakdown Structure
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TABLE OF CONTENTS
1 INTRODUCTION ......................................................................................................... 13
1.1 Background .............................................................................................................. 13
1.2 Project description ................................................................................................... 14
1.3 Delimitations ............................................................................................................ 15
1.4 Method ..................................................................................................................... 15
2 FRAME OF REFERENCE .......................................................................................... 17
2.1 Rock Reinforcement ................................................................................................ 17
2.2 The Mining Method ................................................................................................. 17
2.3 The RVM ................................................................................................................. 19
2.3.1 General .............................................................................................................. 19
2.3.2 Drilling and Bolting .......................................................................................... 20
2.3.3 The Mesh .......................................................................................................... 22
2.4 State of the art .......................................................................................................... 23
3 CONCEPT DEVELOPMENT ..................................................................................... 25
3.1 Requirement specification ....................................................................................... 25
3.2 Concept generation .................................................................................................. 26
3.2.1 Morphological Matrix ....................................................................................... 26
3.3.2 Concept Feasibility ........................................................................................... 27
3.2.3 Concept 1 – Vertically standing mesh rolls ...................................................... 29
3.2.4 Concept 2 – One horizontal laying roll ............................................................. 30
3.2.5 Concept 3 – Horizontal half roll ....................................................................... 31
3.2.6 Concept 4 – Small mesh rolls ........................................................................... 32
3.2.7 Concept 5 - Bolt Conveyor Belt ........................................................................ 34
3.2.8 Concept 6 - Bolt Carrousel ............................................................................... 36
3.3 Concept evaluation ................................................................................................... 38
3.3.1 The Evaluation .................................................................................................. 38
3.3.2 Evaluation Discussion ....................................................................................... 39
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4 DETAILED CONCEPT ............................................................................................... 41
4.1 Overview of Final Concept ...................................................................................... 41
4.2 The Mesh Mounting ................................................................................................. 42
4.3 CAD models............................................................................................................. 43
4.3.1 The Arm ............................................................................................................ 43
4.3.2 Arm Components .............................................................................................. 48
4.3.3 The Platform ..................................................................................................... 49
4.3.4 The Bolt Carrousel ............................................................................................ 50
4.3.5 The Adapter ...................................................................................................... 51
4.4 Cylinder dimensioning ............................................................................................. 52
5 DISCUSSION AND CONCLUSION .......................................................................... 55
5.1 Discussion ................................................................................................................ 55
5.2 Conclusion ............................................................................................................... 56
6 RECOMMENDATIONS AND FUTURE WORK .................................................... 57
7 REFERENCES .............................................................................................................. 59
APPENDIX A – FREE BODY DIAGRAM ................................................................... 61
APPENDIX B – MATLAB CODE ................................................................................. 63
APPENDIX C – COORDINATES TO ADAMS ........................................................... 65
APPENDIX D – ADAMS RESULTS ............................................................................. 66
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1 INTRODUCTION
This chapter presents background information to the subject and includes the project
description with the purpose, as well as the limitations and methods used.
1.1 Background
Svea Teknik AB is a technical consultant company based in Stockholm. They have during
several years been taking on development and design projects for Atlas Copco Rock
Drills AB and the division for Underground Rock Excavation located in Örebro which is
developing new Tunnel Boring Machines (TBMs) for mechanical underground rock
excavation. Some of these projects have been offered as master’s thesis projects to
machine design students at the Royal Institute of Technology. This report is the result of
such a project.
Mechanical rock excavation is a continuous excavation method unlike the old traditional
drill and blast method. Instead of drilling holes, insert explosives and blast, this
excavation method does not use explosives but instead a machine with a circular
cutterhead with cutting discs placed in front. The cutterhead rotates and is pressed against
the tunnel face at enormous pressure, making the cutter discs roll on the rock surface and
in that way inducing stresses in the surface which makes the rock break into small pieces.
This excavated material, called the muck, is then transported on a conveyor belt system
through the body of the machine to the end where it can be collected for further transport.
[1]
An example of a TBM can be seen in figure 1, illustrating one of Atlas Copco’s more
recent machines called the Reef Miner.
Figure 1. The Reef Miner [2]
Even though this mechanical excavation method is claimed to be kinder to the rock mass
than the drill and blast-method, it still induces cracks in the rock and the tunnel is still in
need of reinforcement to obtain a sufficient load-bearing capacity and prevent it from
collapsing. This is especially important when the rock quality is bad, and it is of
importance that as little as possible of the roof and the tunnel walls are unsupported
during on-going excavation. The reinforcement can be done in different ways, one of
which is to insert rock bolts in the tunnel walls and roof. Holes are drilled at certain
places and then rock bolts are being inserted. The bolts distribute the stresses in the rock
and make it self-supporting, comparable to an arch bridge.
When doing this, sometimes also the walls and the roof of the tunnel are being clad with a
metal mesh (welded or chain link fence), which is fastened in between the tunnel face and
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the bolt bearing plate, as shown in figure 2. In addition to the reinforced support that the
mesh provides, another strong motivation for doing this is to make the tunnel a safe
working environment for the machine operators. The bolts secure larger rock blocks and
the mesh protects the operators and the machine itself from smaller falling stones. [1]
Figure 2. Chain link mesh fastened on a tunnel wall [3]
On Atlas Copco’s newest TBM that is currently under development, the mounting of this
mesh is today a semi-automatic process where the operators can control the procedures of
drilling and bolting while standing under a protective roof or in a cabin. However, this
current solution requires that the two operators need to do manual work about every half
hour to refill bolts and locate the mesh segments. While doing this, the operators are
working in an unsecured part of the tunnel and are exposed to a safety risk. It is therefore
of great interest for the mining company to reduce the number of times that the operators
need to do the manual tasks. [4]
This is also in agreement with the direction in which the development in the mining
technology in general is heading. To improve the productivity, lower the labour costs and
hence achieve higher economical profits for the mining companies together with the
safety concerns for the mine workers are the driving factors for developing
robotic/automatized systems. Automated systems would also mean improved precision
and the outcome of the work would be more predictable, more exact and would lead to a
safer mining process which gets increasingly important the deeper the mines go. The
vision is to have fully automatized mine systems in the near future. [5]
So as a step in this development process towards full automatization, Atlas Copco is
interested in reducing the time that the operators spend manually working on the machine
from intervals of every half hour to once per working shift. [4]
1.2 Project description
This project’s purpose was to develop a design concept for the mesh handling and
mounting for the RVM that require less manual hands-on work by the operator, i.e.
replacing the existing semi-manual mesh handling to a solution that instead can be
automatized and remote controlled. The drilling and bolting process is also included in
the mesh mounting procedure. The objective was to reduce the time that the machine
operators need to be working in unsafe area and therefore reduce the risks that they are
exposed to.
Only the mounting of the mesh on the tunnel walls was included in the task, since the
mesh in the roof already will be in place because of the mining technique.
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1.3 Delimitations
Due to the project’s restricted time frame of 20 weeks (corresponding to about 800 work
hours) and the initial knowledge of the author some limitations needed to be done.
As stated previously in the project description, only the mounting of mesh on the
tunnel walls had to be considered since the mesh in the roof already will be in
place.
The project is on a conceptual design stage, and no detailed design nor advanced
FEA will be carried out.
No physical prototype will be produced and no detailed drawings.
The task does not include any design of control systems or software programming.
No detailed selection of materials.
To further limit the scope it was decided that changes to the existing drilling and
bolting unit would be kept to a minimum, the same applies to other close by
components and systems.
1.4 Method
The project consists of three main parts; the introduction, a background study with the
concept development and the documentation. The project has been broken down in a
Work Breakdown Structure (WBS), see figure 3. The WBS divides the project into the
different activities (called work packages) that are needed to achieve the top deliverables
which are the second level under the project name. [6]
Figure 3. Project’s Work Breakdown Structure
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The project planning and outline follows the Stage-Gate model, which is shown in figure
4, where the different stages of the project (in blue) are set and are followed by decision
gates (in red). At these decision gates, the previous stage has to be approved before the
project may proceed to the next stage. [7]
Figure 4. Stage-Gate Process
The requirements for the design were set in discussions with the customer. Brainstorming
was used to generate different concepts with possible solutions, which were developed to
a point where they could be fairly evaluated in a Pugh’s evaluation matrix. The concepts
with the highest score and hence seemingly the most promising concepts were developed
further to the final product. The development of the final concept was an iterative process
where the design was being refined until all requirements were fulfilled.
The 3D computer-aided design models (CAD models) were made in the program
ProEngineer Wildfire 4.0, since it is the software used by the customer. Matlab was used
for calculations of static forces and ADAMS was used for verification and a dynamic
simulation. The documentation has been done quite continuously during the project, but
been more focused towards the last weeks.
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2 FRAME OF REFERENCE
This chapter presents the topics that were covered during the pre-study to provide some
theoretical background information that are relevant in order to understand the project
task. Also the result of the state of the art-search that was used in the concept generation
and development phase is presented here.
2.1 Rock Reinforcement
The method of this continuous mechanical excavation with TBMs are generally said to be
kinder to the rock mass than the method of drilling and blasting. However, mechanical
excavation does have much higher advance rates that require much earlier load-bearing
capacity than with the drill and blast method. [1] The stresses in the rock that existed
prior to the excavation redistributes when boring a tunnel or mine. The vertical load
before the excavation is carried out is equal to the weight of rock mass above, and thus is
increasing the deeper into the ground the excavation proceeds. [8] Support systems are
therefore needed in order to stabilize the tunnel and prevent it from shrinking or
collapsing. This support of the tunnel can sometimes be carried out behind the machine,
but in this case that would mean at least 20 meters behind the cutterhead and the tunnel
face. That would leave much of the tunnel walls and roof to be unsupported during quite
some time. That is the reason to instead place the drilling and bolting unit in the middle of
the machine, as close to the cutterhead as possible, as shown in figure 6. [1], [8]
It exist two types of rock reinforcement possibilities, which are rock bolts and shotcrete.
[8] In this case with the new machine, it will use rock bolts of the type Split-Set which are
a type of friction bolts that are described more in detail in section 2.3.2 below. [9] The
main parameters in reinforcement design are size (the diameter) and length of the bolts
and the spacing between them. The purpose of the rock bolts are to knit the rock mass
together so that it becomes self-supporting. Movements and deformations that occur in
the rock mass makes the bolt to elongate, which creates tension in the bolt. This tension
transfers to the rock mass as compression stress and thus assists the rock mass to support
itself by increasing the confinement. This means that rock bolts need to have good tensile
capacity since they are normally under tension. [10]
In order to prevent so called fallout of smaller rock blocks and stones between the bolts, a
chain link mesh may also be mounted as a skin support. [8]
2.2 The Mining Method
It exist many different methods for excavating ore in underground mines, which have
been developed during the history of mining. This section briefly explains the specific
method used at the location that the RVM is being made for, which is necessary in order
to understand why the roof does not need to be clad with mesh as well as the walls, which
is normally the case.
The method is called underhand cut and fill, and is illustrated in figure 5. The excavation
is done in horizontal layers, starting from the top and going downwards. When one layer
has been mined have about 20 cm of muck been left on the floor of the stope. In this
muck are Dywidag reinforcement bolts with bearing plates installed vertically in a pre-
determined pattern, and the bolts are kept in place with a thin steel wire attached between
them and the walls. On top of the muck has a metal mesh been placed so that the bolts are
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inserted through it. When the layer has been finished are the mined-out stope being
backfilled with a paste mixture of the muck from the excavation and cement. This fill is
left to cure for about three days and when finished does it have excellent compressive
strength properties. That makes it possible to excavate another layer underneath the
previous one, and in that way keep excavating downwards. The mining are thus being
carried out beneath the reinforced cemented backfill that will not fall in the case of a rock
burst, which provides safety for the miners. The floor of that first layer becomes the roof
of the next layer beneath. [12]
Figure 5. Cross section view of vein
The mining direction could also be carried out in the opposite direction, i.e. going
upwards, and that is instead called overhand cut and fill. [12]
Many factors have to be taken into consideration when deciding what method should be
the most suitable to use when excavating ore, which of the most important ones are the
geometry of the ore body and the existing ground conditions and structure of the rock.
The cut and fill-method are especially suitable for when the ore body is steeply dipping
vertically. [13]
Layer 1
Layer 2
Dywidag bolt
with bearing plate
Mesh
Muck
Fill paste
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2.3 The RVM
This new machine from Atlas Copco is called the Remote Vein Miner (RVM), shown in
figure 6 below, is still in the development phase. It is approximately 20 meters long and
will weigh about 200 ton. [4]
2.3.1 General
In the front of the machine is the cutterhead with the cutting discs on the circumference
that rotates and simultaneously is pressed with huge force against the tunnel face to
execute the excavation. The head is moveable in both vertical direction, rotational to the
sides and back and forth as indicated by the arrows in the figure 6. The crushed stone,
called the muck, is then collected with help of the apron onto a conveyor belt system that
goes in the bottom of the machine all the way through to the rear where it can be collected
for further transport. The other two main parts of the machine are called the main body
and the power module. The main body primarily contains the hydraulic systems that
steers and pushes the cutterhead, and also holds the hydraulic system for the grippers and
jacks that vertically extend from the top and bottom and fixates the machine against the
tunnel floor and roof. This is so that the machine does not move backwards during
excavation. The second part, the power module, contains components such as the
hydraulic pumps, electric engines, drums for the electric cables and hydraulic hoses.
The drilling and bolting unit together with the mesh handling system will be placed in
between these two main parts, which figure 6 does not show but the placement is
indicated with the red arrow. The space is better illustrated further ahead in the report in
figure 14 chapter 3.3.2 where the used CAD model is shown and explained. [4], [9]
Figure 6. The RVM with named parts
The excavation cycle for the RVM is similar to the cycle for most TBMs, and is carried
out in the following steps.
The rotating cutterhead with the cutter discs are used to excavate the rock in front of the
machine by being pressed very hard towards the face. To prevent the machine from
moving backwards in the tunnel due to this huge pressing force are vertically mounted
hydraulic cylinders, called stingers, and jacks being extended from the main body and
Placement of the mesh
handling system
Apron
Power module
Cutterhead
Main body
Stingers
Conveyor belt
Rear
tracks
Front
tracks
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that clamps the machine between the tunnel roof and floor. When one full stroke and the
desired tunnel profile has been finished by moving the cutter head, the machine retracts
the stingers and jacks and moves forward by using the front and rear tracks. The working
cycle is then repeated. As can be understood from this mode of procedure, this kind of
gripper TBMs are only suitable for use in hard solid rock that can withstand the high
forces from the stingers and jacks. [1]
This mechanical underground excavation machine is being designed to manage tunnel
profiles ranging from 3.9-5.0 m in height and 3.2-4.5 m in width, see figure 7. The
machine with its components itself should stay inside a rectangular cross-section shape of
2.0x3.6 m. [4]
Figure 7. Simplified cross-section view with max and min tunnel profile with dimensions and approximate
bolt positions [mm]
2.3.2 Drilling and Bolting
The bolts have to be placed with a centre distance of maximum 1.2 meters both vertically
and horizontally on the wall. Since the maximum stroke length for the machine is 0.6
meters, this means that the bolting in the horizontal direction only has to be done every
second stroke on each side. The bolting can hence be done on alternating sides of the
machine for each stroke, as shown in figure 8, which is how the existing drilling and
bolting unit work. The one unit handles the bolting on both sides by being rotatable. [9]
The red arrow indicating the machine’s direction of travel.
Figure 8. Top view of the machine with bolt placement in the tunnel [mm]
39005000
2000
3200
4500
3600
1200
600
Max.
Min.
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This means that 3 bolts are required in the vertical direction when doing the minimum
tunnel profile and 4 when doing the maximum profile, see figure 7. The bolts are installed
more or less perpendicular to the to the tunnel wall, with the lower and upper bolt
installed at an angle of 30°-45°. The mesh shall cover the tunnel walls starting from a
maximum of 0.9 meters off the floor up to the corner of the profile, see figure 9. [9]
Figure 9. Placement of the mesh (blue) on the tunnel wall [mm]
The currently semi-automatic solution for the mesh handling and mounting procedure
require the operators to do manual work once every stroke the machine does, to refill
bolts in the magazine and locate the mesh. The time it takes for the machine to carry out
one full cycle is 30 minutes, which hence also is the time for the manual task intervals. It
is this interval that the customer wishes to be reduced to once per work shift of 8 hours
(corresponding to 16 cycles). [4] This gives the total wall area to cover per shift 57.6
m2/78.7 m
2.
The bolts used are of friction type, and are called Split Set stabilizers and have a diameter
of 39 mm and length 1800 mm. [9] Figure 10 shows the bolt, which basically is a slotted
tube made of thin metal. As can be seen, one end of the tube is tapered for easier insertion
into the drilled hole, and the other end have a welded ring flange to hold the bearing plate.
[14] The drilled hole is 37 mm, smaller than the bolt [9], meaning that when the bolt is
forced into the hole the bolt diameter will be compressed slightly which is made possible
because of the slotted design. This ensures a tight fit and forces exerted in the radial
direction along the length of the bolt in contact with the rock provides friction that holds
the rock together. [14]
The domed bearing plates, also shown in figure 10, have the dimensions 150x150x4 mm,
and the hole is slightly larger than the diameter of the diameter of the bolt, which means
that the plate can adapt to irregularities of the tunnel wall. The hanger on the plate can be
used to support/attach loads for example cables, tubing and pipes. [14]
Figure 10. Split Set stabilizers SS-39 [14]
Max. 900
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2.3.3 The Mesh
The mesh used in this project is illustrated in figure 11 and is a regular metal chain link
mesh where the holes have the dimensions 50x50 mm and the wire thickness is 3 mm. [9]
This type of mesh has very high load bearing capacity, however it is quite hard to handle
during installation due to its flexibility. [11]
Figure 11. Metal chain link mesh [16]
The mounting of the mesh is carried out by an operator that manually places a section of
mesh on a holder that keeps it in the correct place on the wall in order for the bolting unit
to be able to place the bolts and secure it. The sections are placed vertically (seen from
the side) from the upper corner and down. One section is 1500 mm wide because the
chain link mesh must overlap the previous mesh sheet with at least 150 mm. It is in this
seam the bolts are placed, as illustrated in figure 12, and in that way secures two mesh
sides at the same time. The overlap is necessary due to safety concerns. [9]
The weight for the mesh has been estimated from data for a regular existing fence of the
type “Gunnebostängsel”. A roll with the dimensions 1.5x4.1 meters weigh about 15 kg
which corresponds to 2.4 kg/m2 mesh. [9] To estimate the diameter for mesh rolls the
circumference of a circle, equation 1, was used. Since the total required length of the
mesh for different cases are known, could the required outer diameter be calculated by
adding the circumference for several layers, see figure 13.
Ltot = ∑Di· π (1)
Di = d1 + d2 +…+ dn. The distance between the layer diameters was set to 16 mm and an
inner rod to which the mesh is wrapped around to be 25 mm.
Figure 13. Illustration of cross-section of mesh roll [mm]
150
mm Figure 12. Placement of the rock bolt through two mesh sections, without the restraining plate [mm]
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This gave the dimensions that were used when doing the CAD models, and are presented
in table 1.
Table 1. Calculated diameters for mesh roll
Required mesh length
[min. profile/max. profile]
Calculated diameter for roll
[min. profile/max. profile]
One single roll
(both sides) 48 m/65.6 m 0.70 m/0.83 m
Two half rolls
(one for each side) 24 m/32.8 m 0.50 m/0.60 m
16 rolls
(on roll per stroke) 3 m/4.1 m 0.20 m/0.20 m
Previous tests done by the customer have shown that one problem that occur when
mounting the mesh is to stretch the mesh sections sufficiently in order to reduce the slack
from the wall and also to position the mesh correctly. [9]
2.4 State of the art
A search for already existing automatic solutions for mesh mounting in the underground
mining industry was carried out, both for inspirational purposes to the concept generation
and also not to reinvent the wheel. The search resulted above all in numerous different
patents in the area, which were briefly studied. Generally about the found patents can be
said that it exists both separate more mobile stand-alone systems away from the mining
machine itself which can be used together with different machines, as well as whole units
attached to more specific machines. The patented solutions contain ways for not exposing
the operators to direct risks while working with the mesh mounting, as they are working
in the secured area of the tunnel. Most of the patents contains configurations of booms
and/or arm systems that places reels of wire mesh in position for a bolting unit to bolt the
mesh to the walls and/or roof. Two examples of more recently granted patents that are
using different arm solutions are a patent from 2014 called “Method and apparatus for
lining tunnel walls or tunnel ceilings with protective nets” [17] and another one called
“Mesh handling apparatus and related methods” from 2015. [18]
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3 CONCEPT DEVELOPMENT
This chapter describes the structured working process of the concept development phase,
which started with defining the requirement specification and then progressed to the
concept generation and evaluation.
3.1 Requirement specification
The previous explained and presented information from chapter 2.3 has been summarized
in table 2 below and are the criteria that the design should meet to fulfil the purpose of the
project. Where it is relevant it has been stated if the criteria was a demand or a wish from
the customer. The available space is more clearly shown in figure 14.
Table 2. Requirement specification
Description Value Wish or
demand
General
Operator’s manual interval 1 per shift á 8
hours D
Fit on the available space on the machine 2.0x2.6 m
(cross-section) D
Keep changes to other systems to a minimum W
Mesh mounted from max. 0.90 m up from
tunnel floor up to corner
D
Tunnel profile (cross-section)
Minimum width 3.2 m D
Minimum height 3.9 m D
Maximum width 4.5 m D
Maximum height 5.0 m D
Machine data
Dimensions 2.0 m x 3.60 m
Distance between floor and tunnel ground
(space for muck handling system) 0.90 m
Available space on machine for the design,
including space occupied by bolting unit
(length x width)
- whereof space in front of bolting unit
(frame not included)
- whereof space behind bolting unit
(frame not included)
5.0 m x 2.0 m
1.7 m x 2.0 m
2.1 m x 2.0 m
D
Bolts and bearing plates
Number/stroke (min. profile) 3 D
Number/stroke (max. profile) 4 D
Total for one shift (min.) 48 D
Total for one shift (max.) 64 D
26
3.2 Concept generation
When the project had been defined and the requirement specification had been
formulated, the project continued with the concept generation phase. With the help of the
state-of the-art-search, this phase started with brainstorming sessions and the making of a
morphological matrix, see table 3 below.
3.2.1 Morphological Matrix
The task was first broken down to two separate main parts, which were the storage and
handling of the bolts and the mesh respectively. Then different independent primary
functions that were relevant in the design process were identified to be cutting
mechanisms for the mesh, stretching mechanism for the mesh and mean to deliver the
bolt to the drill and bolt unit. The matrix works by combining the solutions for each
different sub-functions in different ways, several complete solutions can be obtained. [19]
Table 3. Morphological matrix
Solution
Sub-
function
1
2
3
4
5
6
Storage of
bolts
Standing
Lying
Groups
Separate
plate and
bolt
Handling
of bolts
Hangar
Carrousel
Robot arm
Perforated
plate
Mesh
storage
One big roll
Vertical
One big roll
Horizontal
Half rolls
Vertical
Half rolls
Horizontal
Single
rolls
Vertical
Single
rolls
Horizontal
27
Mesh
mounting
Arm
Elevator
- moving
whole roll
Elevator
- Drag free
end
Cutting
mechanism
Scissors/
Shears
Punch
Knife
Saw
Drag/
pull
Laser
Stretch
mesh
section
Add arm with
hook on
existing
bolting unit
External
controlled
arm
Support
internally
inside mesh
roll
Frame
Hooks on
floor
Feed bolts
to bolting
unit/
magazine
Replace
whole
magazine
Refill
magazine
one at a
time
Feed
directly
from
storage
3.3.2 Concept Feasibility
The CAD model of the RVM obtained from the customer was simplified in order to
remove components and information not relevant to the task, as well for illustrational
purposes to be able to clearly present the rendered concepts. The model was also
important in order to get a good understanding of the geometrical constraints. The
simplified CAD model is shown in figure 14.
Figure 14. 3D CAD-model of the RVM, skew side view and top view respectively
28
The grey floor space does not represent an actual existing floor, but are showing the lower
limit for the available space. The compartment underneath this grey “floor” is occupied
by the conveyor belt system for the muck transport.
The board walks are retractable floor boards that will be used by the operators to reach
the different compartments of the machine, for example when refilling mesh and bolts at
the start of each shift, or when doing maintenance and reparation work.
The main restricting factor is the spatial limitations on the machine and the space given
on the sides from the excavated tunnel. Bigger tunnel profile gives more room, however it
does also require a larger amount of mesh and bolts that need to be carried on the
machine during the working shift. The operator’s cabin was decided to be removed, since
it will not be necessary when the processes are being remote controlled. That liberated
space could instead provide room to storage of bolts, bearing plates and mesh rolls.
Using the morphological matrix, brainstorming sessions and sketching on paper resulted
in numerous alternatives and possible combinations of placement and configurations of
the handling of the mesh and bolts. However, many of them had to be dismissed early
mostly due to one or a combination of the following factors:
Spatial limitations
The mesh sections should be mounted in front of the drilling and bolting unit, as
shown by the red arrow in figure 15, which also limits the possibilities. The
dashed arrow indicates the machine direction of travel.
Figure 15. Top view of machine, red arrow marking the mesh section to be bolted to the wall
If the mesh storage and handling system were to be placed behind the unit it
would mean that there would be a long distance to get the mesh section in correct
position for the bolting. Moving the drill and bolting unit would bring on
significant changes to other systems, which was not desired from the project
limitations.
The alternative with storing the bolts in laying position were also disregarded,
because of their length. The magazine of the bolt unit is loaded in upright position
and there would be no space to turn the lying bolts up to get them in correct
position for refilling.
Bolt/drill
unit
29
The following presented 6 different concepts; four for the mesh handling and two for the
bolt handling, were the ones considered to have the most potential and hence worth to be
developed further in order to be able to evaluate them fairly. In the figures 16, 18 and 20
have the bolting unit been hidden for clarity reasons.
3.2.3 Concept 1 – Vertically standing mesh rolls
This idea uses two vertically standing mesh rolls, one for the right and left tunnel wall
respectively, that cover the whole length of the wall that should be clad with mesh, see
figure 16. The right green roll shows the position for the minimum profile, and the left
larger green roll shows the case for the maximum profile.
Figure 16. Illustrational model of concept 1 with vertical rolls, front view
The rolls each contain 10 m mesh which corresponds to the amount required for one
working shift and by using equation 1 this results in a roll diameter of 40 cm. The steering
mechanism consists of hydraulic cylinders placed on the frame supporting the bolting
unit. There is one individual steering mechanism for each side, they are identical and only
mirrored. To be adaptable to different tunnel profiles, the movement is steerable and
extendable both vertically, in-out direction and rotationally around its own axis as
indicated by the arrows in figure 16. To fit inside the dimensions of the machine and at
the same time reach the walls when excavating the maximum tunnel profile, double-
acting telescopic hydraulic cylinders would be used. The mesh rolls would each weigh
maximum 95 kg, which is not an issue to handle and lift with a hydraulic system.
Figure 17. Illustrational model of concept 1 with vertical rolls, top view
Frame
30
This solution mean that there would be no issue with holding and stretching out the
previous mesh section to be able to drill and bolt in the mesh overlap. The mesh section in
this case would be continuous during the shift and therefore there would not be necessary
to cut in correct lengths. When the RVM is tramming (i.e. moving forward with the help
of the tracks) the mesh unrolls with the movement. When the machine is tramming the
rolls would be placed as in figure 17, retracted as indicated with the red arrows so they do
not touch the tunnel wall and risk breaking.
To fit the vertically standing rolls within the required 2.6 m height of the machine, the
rolls need to hang below the floor surface which is 0.9 m above the ground level. This
would not disturb the conveyor belt system for the muck underneath because the rolls
would hang outside of that system which is located in the middle. However when
excavating the larger profile the roll needs to be 4.1 m, which would not meet the
requirement to fit inside the height of 2.6 meters.
This concept as mentioned has got some advantages, but the main disadvantages besides
that it does not fit within the required size, is mainly the inflexibility; it cannot handle
changing profile heights during one shift without manual interaction from the operators
that would need to change the roll to one with a different height. Also the handling of the
large mesh rolls could be quite unmanageable, and also the bolts protruding from the roof
might affect negatively and hinder the mesh from unrolling or similar.
3.2.4 Concept 2 – One horizontal laying roll
The second concept for the mesh handling has a link arm system placed on the frame of
the drilling and bolting unit that holds only one single big mesh roll which is placed
horizontally, see figure 18. The link arm system consists of two jointed arms, whereof the
upper arm is extendable, and can be controlled by two hydraulic cylinders. The mesh roll
then needs to be 1500 mm wide as previously explained in chapter 2.3.3 and it contains
all the mesh required for both sides for one working shift (total of 65.6 m for the
maximum profile) which according to table 1 corresponds to a roll diameter of 83 cm.
Figure 18. Illustrational model of concept 2 with one horizontal laying roll, front view
31
A gripping claw mechanism on the end of the arm grips the mesh roll and lift it and keep
it in place for the bolting unit. The platform on which the arm system is mounted, marked
with the red arrow in figure 19, can rotate around its own axis to reach and locate the
mesh on alternating sides. The blue arrow shows that the mesh roll needs to be able to
move horizontally in order to reach to the bolting unit.
Figure 19. Illustrational model of concept 2 with one horizontal laying roll, top view
To be able to move the roll horizontally and position it outside of the bolting unit, a
motorized linear motion slide guide is used which is marked in figure 19 with the red
arrow.
To make this a fully functional concept, a cutting mechanism needs to be implemented, to
get the correct lengths on the mesh sections. Also the issue with stretching of the mesh
will need a solution. The need of this cutting and stretching solution adds complexity to
the design.
This concept does fit inside the required 2.0x2.6 meters and is more flexible regarding
adaption to different tunnel sizes, however it is disadvantageous because the mesh roll
also in this case still is quite unmanageable due to its size. The roll will weigh about 240
kg and since the diameter is bigger than the width floor boards which are 60 cm would
cause troubles when transporting the roll into position on the machine.
3.2.5 Concept 3 – Horizontal half roll
This concept is developed from the same idea as concept 2, using link arm system and
hydraulic cylinders to position the mesh roll in place for the bolting unit. Instead of only
one roll for all the required mesh it uses two half rolls mounted on two similar but
separate arms. This would simplify the handling of the mesh rolls because of their more
manageable size; the dimensions would be 1500 mm long, diameter 600 mm (from table
1) and weight about 120 kg each.
32
This concept is shown below in figure 20, where the left roll shows the position for the
minimum tunnel profile and the right roll shows the position for the maximum profile.
Figure 20. Illustrational model of concept 3 with two horizontal laying rolls, front view
The platform in this case will not need to be rotatable, however overall is this concept
more complex since both arms for each side would need to have the cutting mechanism
and solution for the stretching as in the previous concept.
This would also fit inside of the available space.
Figure 21. Illustrational model of concept 3 with two horizontal laying rolls, top view
3.2.6 Concept 4 – Small mesh rolls
This concept originated with the intention to avoid the additional complexity that the
cutting and stretching adds to the two previous presented concepts. In this concept the
mesh is pre-prepared in rolls with the correct dimensions before the start of the shift, and
uses one roll for each stroke. The roll diameter would be 20 cm for each of the 16 rolls
required during one whole shift. The storage placement of the rolls is shown in figure 22,
33
in front of the bolting unit’s frame. The figure also shows the link arm position in the case
of the maximum tunnel profile.
Figure 22. Illustrational model of concept 4 with small rolls, front view
Figure 23 shows the position for the minimum profile, with the mesh rolls in the storage
area hidden.
Figure 23. Position of the arm for minimum profile, front view
As in the previous concepts also this consists of a link arm system placed on the frame
and is steered with two hydraulic cylinders. The arm is as in concept 2 attached to a
platform that is rotatable around its axis as the arrow indicates, meaning that it handles
the positioning of the mesh for both sides.
34
Also the motorized linear sliding guide as in previous concepts is needed to enable the
movement horizontally, see figure 24.
Figure 24. Illustrational model of concept 4 with small rolls, top view
At the start of the shift are 15 rolls (5x3) placed in the storage and the 16th
and last roll is
directly placed on the arm with the grippers.
Inside each of the rolls are a beam fastened to the edge of the mesh which when mounted
on the tunnel wall will help stretch and hold out the mesh until the next section is placed.
3.2.7 Concept 5 - Bolt Conveyor Belt
Placing the mesh handling in front of the drilling and bolting unit gives the possibility to
use all of the rear space to the storage and handling of bolts and bearing plates. This suits
well with the placement of the existing bolt unit with the bolt magazine. Concept 5 and 6
are describing the two generated concepts for the bolt handling part.
This first idea is inspired by regular tool clips that are normally used for holding
workshop tools, brooms or other object in place on a tool board or on a wall. Gripper
clips like this exist in numerous different configurations and some examples are shown in
figure 25.
Figure 25. Tool clips from Lesjöfors (a and b) [20], and gripper clip from Hardware World (right) [21]
a
b c
35
If combining and integrating this gripping solution with a quite flexible rubber band, the
resulting belt could be driven around a metal frame, as shown in figure 26. The 60
grippers (shown as indents in the black rubber band) would each hold one bolt with plate
which would be kept in place with gripping force and friction.
Figure 26. Required dimensions for the frame to hold 60 bolts [mm]
To be able to hang the bolts as close together as possible to reduce the required space, the
bolts will be hanging on slightly different heights as shown in figure 27.
Figure 27. Bolts hanging on altering heights
The belt can be controlled so that is rotates around the frame, carrying the bolts with it as
it moves similar to the function of conveyor belt systems. One bolt at a time then rotates
into a specific position where a device with grippers called the adapter is placed. The
adapter is basically two claws that grips the bolt, turns and delivers it into the magazine of
the drill and bolting unit. Since the bolts hang on varying heights the adapter would also
need to be controllable vertically. The magazine has place for 4 bolts, sufficient for one
stroke for the large tunnel profile. So at the start of each shift the operator places 4 bolts
with bearing plates in the magazine directly, and 60 more in each of the holders in the
band. After one stroke and the magazine is empty, the bolting unit is positioned in its
original (vertical) start position, to be refilled. The operator steers the driving belt so that
one bolt at a time reaches the position where it can be taken by the adaptor and placed in
the magazine, and this is repeated four times until the magazine is full and ready for
bolting the other side.
1500
1800
36
Generally the tool clips are not dimensioned for such heavy objects as the bolt and plate
which in this case would weigh about 4 kg, but by changing the dimensions of the hangar
and/or material would be able to achieve sufficient load capacity without breaking.
This concept mean almost no modification to the drill and bolt unit, however it does
require high precision both for the transport band and the adapter. The two individually
controlled systems have to work together to obtain the complete working solution. To be
able to hold the required amount of bolts it is not very space efficient, see figure 28,
where the location of the frame on the machine is shown. Also, a quite thorough search
for an already existing product with a combination of hook and rubber band like this has
not given any results. This means that if this method would be used, it would require
some time, engineering skills and money to develop this seemingly new product.
Figure 28. Top view of placement on the machine
3.2.8 Concept 6 - Bolt Carrousel
One negative aspect of the previous explained bolt handling concept was that it takes up
almost all available area behind the drilling and bolting unit and it is also close to the
sides of the machine which might hinder operators when refilling mesh and/or bolts,
during reparations and maintenance work.
Another concept called the bolt carrousel is illustrated in figure 29 on the next page was
developed specifically with the intension to provide a more space efficient solution. It
consists of a middle large dividing plate that in turn has place for 10 smaller dividing
plates that each are attached to arms (yellow in figure) which are mounted to a common
centre. The arm and the large dividing plate are provided with bearings so that they can
rotate around the centre. The bolts are placed in the cut-outs in the smaller dividing plates
and supported from the below by a plate attached to each of the arms.
37
Figure 29. The bolt carrousel and components
To be able to contain 60 bolts (4 bolts are directly placed in the bolt magazine by the
operator at the start of the working shift as with the previous concept), the dimension of
the large dividing plate is Ø1200 mm and the small Ø320 mm respectively. The
restricting factor for the size are in this case the space that the bearing plates on the bolts
take up, so also here the bolts could be placed at alternating heights in order to make the
design somewhat more compact.
Figure 30 is showing the placement on the machine, as well as the placement of the
adapter.
Figure 30. Placement on machine, top view
As mentioned, the yellow arm assembly has a mechanism that makes it rotatable around
the centre and in that way place a bolt in position for an adapter to grip it and bring it into
Adapter
Bolt magazine
38
the bolt magazine on the bolt unit. The same design for the adapter as in the previous
concept can be used.
3.3 Concept evaluation
In the section the evaluation of the concepts are explained and discussed.
3.3.1 The Evaluation
The concepts in the previous chapter was being evaluated in a Pugh Evaluation Matrix,
table 4. [22] Since the two parts could be considered independent of each other, one
evaluation was made for the mesh concepts and another one for the bolt handling. The
evaluation of the concepts criteria were decided together with the requirement
specification as well as discussion with the customer.
For the mesh handling, concept number 1 was set as the datum reference to which the
other three mesh concepts were compared. For each of the evaluation criteria stated in
table 4 and 5 each concept were given the score +1 if considered to perform better than
the reference, 0 if equal and -1 if the concept was considered worse.
Table 4. Pugh evaluation matrix for mesh handling concepts
Evaluation criteria Concept 1
Reference Concept 2 Concept 3 Concept 4
Work for both max. and min.
tunnel profile 0 +1 +1 +1
Adaption between profiles
- Flexibility 0 +1 +1 +1
Handling and change/refill of
mesh roll 0 0 +1 +1
Availability for operator 0 +1 +1 +1
Complexity 0 -1 -1 0
Robustness 0 0 -1 -1
Modifications of surrounding
systems and components
0
0
0
0
Number of parts/subsystems 0 -1 -1 -1
∑+ 0 3 4 4
∑- 0 2 3 2
Total score: 0 1 1 2
39
For the bolt concepts the datum reference was decided to be concept 5.
Table 5. Pugh evaluation matrix for bolt handling concepts
Evaluation criteria Concept 5
Reference
Concept 6
Work for both max. and min. tunnel
profile 0 0
Adaption between profiles
– flexibility 0 0
Refill bolts 0 0
Availability for operator 0 +1
Required space/size 0 +1
Complexity 0 0
Robustness 0 -1
Modifications of surrounding systems
and components 0 0
Number of parts/subsystems
0 -1
∑+ 0 2
∑- 0 2
Total score: 0 0
3.3.2 Evaluation Discussion
Concerning the mesh handling it can be seen from the Pugh evaluation that concept
number 4 scored the highest, even though the difference is small between the different
concepts. However did concept 4 have more positives (equal as concept 3) but did have
fewer negatives. It was thus decided that concept 4 did have the most potential and
therefore was the concept to progress with and develop further.
The evaluation for the bolt handling turned out to be indecisive, as the two concepts both
scored equal (0 points). The evaluation matrix showed that concept 6, the bolt carrousel,
did score better than concept 5 in two aspects regarding the availability for operators and
the space it takes up on the machine but worse in two other aspects regarding the
robustness and number of parts. However, the two factors regarding the space were
considered more important for the design and hence weigh more than the others. Also
with concept 5 was taken into consideration the negatively contributing aspect of the
extra added development required for the belt/clip combination. This lead to the decision
to go further with concept 6, the bolt carrousel.
40
41
4 DETAILED CONCEPT
This chapter presents the further development of the chosen concepts from the previous
chapter, and the resulting final concept.
4.1 Overview of Final Concept
Figure 31 and 32 are showing the whole solution of the two combined concepts when
positioned on the machine.
Figure 31. Overview of final concept and placement, side view
It can be seen that the components do fit inside the limited space, as was demanded from
the requirement specification.
Figure 32. Overview of final concept and placement, zoomed in on mesh and bolt handling parts
In the following sections 4.2-4.4 are the included components described.
42
4.2 The Mesh Mounting
As mentioned, 16 rolls are required during one working shift, 8 mounted on each side of
the tunnel. At the start of each shift places the operator 15 rolls in the storage area shown
in figure 32, and one roll is directly placed in the gripper arm that locates the mesh. Each
of the rolls has been prepared on beforehand to have the right dimensions. The top edge
of the mesh section is fastened to a metal rod that protrude about 10 cm on each side,
shown in figure 33, and the mesh is rolled up around the rod.
Figure 33. The gripping arm
The protruding metal rods becomes handles that the claws grips to lift the roll to locate it
on the tunnel wall, and the rod will also provide the stretching function by hindering the
corner of the mesh to fall down as the red arrow in figure 34 is showing. Mesh section
number 1 have been mounted first, and then when the machine has carried out two strokes
are section 2 placed and bolted in place, overlapping the previous section. This continues
as the excavation keeps progressing forward. The rod will hence be left on the tunnel wall
as the machine excavates its way forward.
Figure 34. Mesh placement on the tunnel wall
The grippers are slightly bigger than the rod diameter so that the roll can rotate even
though the grippers are closed. The mesh mounting on the wall starts with the lowest bolt,
and when that one is fastened the mesh will unroll automatically as the arm moves
upward to insert the next bolts. As mentioned in the frame of reference-chapter, the bolts
are being placed in the overlap between the previous mesh section and the one currently
mounted. When getting to the last and uppermost bolt, the rod is located just below or just
above the previous rod, and the bolt is inserted so that the bearing plate cover both the
rods to keep them in place. This is also shown in figure 34.
Rods
Rod that make up the handles
1 2 3
43
By using beam bending theory could the deflection at the free end of the rod be
calculated. The rod was approximated to be a cantilevered beam with uniform load. The
equation for the deflection y is
𝑦 =𝑄𝑙3
8𝐸𝐼 (2)
where Q is the total load, l the length of the rod, E the modulus of elasticity for the
material, and I is the moment of inertia. I for a circular cross section is defined as
𝐼 =𝜋𝑑4
64 (3)
where d is the rod diameter. [23] Setting the rod diameter to 25 mm, the length 1600 mm
and the E-modulus to be 205 GPa [23], this resulted in a deflection of about 20 mm,
which was considered acceptable.
4.3 CAD models
The development phase has been an iterative process, where the design has been changed
and improved continuously when evaluations have shown necessary, until all
requirements were fulfilled.
4.3.1 The Arm
Figure 35 is showing the 3D model for the arm that handles the mesh placement which
was developed in ProE.
Figure 35. The arm configuration with named parts
The arm with the grippers must be able to reach all of the mesh rolls when placed in the
storage, and also reach the top and bottom position on the wall for both the minimum and
the maximum tunnel profile. At the same time it should not collide with the drilling and
bolting unit or any of the other surrounding components. A geometrical investigation was
done in order to verify that these demands were satisfied.
Cylinder 2
Cylinder 1
Platform
Arm 2
Arm 1
Gripper
Universal joint
Connector to linear
sliding guide
44
Figure 36. The two most difficult rolls to reach in the storage
Figure 22-23 in chapter 3.2.6 shows the positions for minimum and maximum tunnel
profile. The lengths of respective parts were found by iterating the design until all the
conditions were fulfilled, which was verified with the CAD model. The arm with the
grippers must be able to reach every one of the mesh rolls which are placed in storage.
The lowest and uppermost roll closest to the arm turned out to be the positions that were
the hardest to satisfy, but were achieved as shown in figure 36.
Arm 2 is a 2-part telescopic arm. To dimension the arms and the hydraulic cylinders (both
to size and stroke lengths) a slightly simplified free body diagram was drawn, with
corresponding derived equilibrium equations, see Appendix A. There are two equations
for equilibrium in x and y-direction and one for torque equilibrium in the right direction
around the point in the figure marked with a black dot for each body respectively. The
platform gave no information about the system and was thus not included, which gave 12
unknowns and 12 equations and a fully determined system. The centre of mass for the
parts was estimated to always be in the middle of each component.
The final lengths are listed in table 6.
Table 6. . Lengths of the arm parts
Dimension Length [mm]
Larm,1 985
Larm,2 min: 1740 max: 2730
Lcyl,1 min: 435 max: 695
Lcyl,2 min: 535 max: 850
X1 230
X2 15
X3 425
X4 678
X5 110
X6 105
X7 172
45
The masses for the parts Arm 1 and Arm 2 are known from the CAD-model, material set
to steel with density 𝜌 = 7800 kg m3⁄ . The mass for the two cylinders have been
estimated with data from existing hydraulic cylinders with approximated diameters and
stroke lengths. The used masses are listed in table 7.
Table 7. Masses for the parts
Part Mass [kg]
Arm 1 30
Arm 2 55
Cylinder 1 7
Cylinder 2 6
Load 75
Platform 100
In the load mass are included one mesh roll with the inner rod, the sliding guide presented
further on as well as the weight for the grippers and their actuators. With Newton’s
second law,
𝐹 = 𝑚𝑎 (16)
and knowing the gravitational acceleration 𝑔 = 9.81 m s2⁄ , can the forces be defined by
the following equations
𝐹𝑎𝑟𝑚,1 = 𝑚𝑎𝑟𝑚1 ∙ 𝑔 (17)
𝐹𝑎𝑟𝑚2 = 𝑚𝑎𝑟𝑚2 ∙ 𝑔 (18)
𝐹𝑚𝑐,𝑐𝑦𝑙1 = 𝑚𝑐𝑦𝑙1 ∙ 𝑔 (19)
𝐹𝑚𝑐,𝑐𝑦𝑙2 = 𝑚𝑐𝑦𝑙2 ∙ 𝑔 (20)
𝐹𝑙𝑜𝑎𝑑 = 𝑚𝑙𝑜𝑎𝑑 ∙ 𝑔 (21)
The magnitude of the force R1 was calculates with Pythagoras’ theorem
𝑅1 = √𝑅1𝑋2 + 𝑅1𝑌
2 (22)
and correspondingly for R2, R3, R4, R5 and R6. The equation system was solved in Matlab,
see appendix A for the code.
When this analytical model had been set up was the arm modelled in ADAMS using the
same lengths, see figure 35 and Appendix C.
Figure 37. ADAMS model to the left and CAD model to the right, in start position
46
The analytical and the ADAMS models were compared in the low start position also
shown in figure 35 above. The required angles and lengths to be able to execute the
Matlab calculation were taken directly from the CAD model and presented in table 8. The
length for Arm 2 was set to 2730 mm, meaning fully extended, since this gives the
highest forces.
Table 8. Angles and cylinder lengths used in Matlab
α β γ θ Lcyl,1 Lcyl,2
56° 64° 66° 60° 679 mm 535 mm
The obtained forces from both models are presented and compared in table 9, and the
difference of has been commented on later in the discussion chapter.
Table 9. Forces in the low position
Force
Analytical model
[kN]
ADAMS model
[kN]
Difference [%]
R1X -3.61 3.57
R1Y -5.90 5.84
R1 6.92 6.84 1.2
R2X -3.61 -3.57
R2Y -7.60 -7.47
R2 8.41 8.28 1.5
R3X -3.61 -3.57
R3Y -7.54 -7.47
R3 8.36 8.28 0.9
R4X 3.32 3.26
R4Y 5.47 5.42
R4 6.40 6.32 1.3
R5X 3.32 -3.26
R5Y 6.81 -6.76
R5 7.60 7.50 1.3
R6X 3.32 3.26
R6Y 5.54 5.49
R6 6.46 6.38 1.3
The results coincide quite well, and were thus considered to be reliable.
The arm motion was simulated in order to obtain the maximum forces in the joints and
the required forces from the cylinders, which were needed for the dimensioning. The
simulation time was set to be 10 seconds, and the motion of the arm was defined so that
only cylinder 1 was acting during the first 6.5 seconds, in order to raise Arm 2 to about
horizontal position. Then cylinder 2 starts to move Arm 1 while the motion of cylinder
1/Arm 2 continues until both cylinders reaches their full stroke length and the arm stops
in the high position shown. This simulation should represent a realistic motion and get the
forces in the worst occurring case.
47
Figure 38 is showing the end (high) position of the arm.
Figure 38. ADAMS model to the left and CAD model to right, end position
The analysis was made static, meaning that no considerations were taken to the dynamic
effects that occur due to the parts’ inertia etc. This was to be able to compare the
simulation results with the analytical model. The resulting time plot of the forces in each
joint are shown in figure 39.
Figure 39. Time plot of the simulated forces in ADAMS
It can be seen that the highest force of about 16.6 kN is occurring in joint 5, which is the
joint between Arm 1 and Arm 2, and occurring when the arm is approximately in the
position shown in figure 40.
Figure 40. Worst case position
48
The maximum obtained forces in each cylinder are presented in table10.
4.3.2 Arm Components
The outermost part of the arm has the holder with the grippers that can pick up the mesh
rolls. A basic concept model was created for the grippers, which are identical for both
sides of the holder. The opening and closing motion is achieved by a mechanical rack and
pinion mechanism. The two pinions are attached to one claw each and the opening and
closing of the gripper is achieved when the rack is being pushed or pulled by an electric
actuator which make the pinions turn and generate the desired motion.
Figure 41. The gripper
Furthermore is the holder attached to the extendable arm with an universal joint
mechanism that makes it possible to adapt the position of the roll to the wall for example
in case when the wall is not flat, when the machine is not placed correctly in the tunnel or
when in a turn. The motion vertically and horizontally are steered by two linear electric
actuators that are mounted to two sides of the inner telescope arm that each controls the
motion in each direction.
Figure 42. Detailed picture on linear sliding guide and universal joint
The holder also has a motorized linear sliding guide to provide the motion horizontally so
that the roll gets in position for the drill and bolt unit. The length for the guide needs to be
1500 mm which can be obtained from the CAD model. Figure 42 is showing a detailed
view of the head of the link arm system, the connection to the linear sliding guide.
Actuators
Universal
joint
Linear
sliding guide
49
4.3.3 The Platform
The platform on which the arm is standing is rotatable so that the arm can work on both
sides of the machine in the tunnel. Figure 43 are showing the set up that consists of two
parts. The grey upper part is resting on shaft that is attached to the blue lower part. The
shaft is a bit longer than the sides of the upper part, so that they do not touch when
assembled. The shaft is provided with a bearing which makes the two parts rotatable
relative each other. The rotations is achieved by an electric motor mounted to the lower
blue part which has a driving pinion connected to an internal gear which is attached to the
upper part.
Figure 43. Cross-section view of the platform on the bolt unit frame
The platform is also controllable up and down, and the motion in this vertical direction is
created by having a single-acting hydraulic cylinder beneath, also shown in figure 43,
which makes it function similar to a column type lifting table. The cylinder does not need
to be double acting since the weight from the platform itself and the arm will work as
counterforce and press it back down when the pressure is released. The stroke length for
the cylinder is 190 mm and the required diameter is calculated in section 4.4. The load
that the cylinder must be able to lift are the total load of the platform, the arm with all its
components including the hydraulic system and one mesh roll. This has been estimated to
add up to no more than 350 kg.
Internal gear ring
Motor
Hydraulic
cylinder
Load
Bearing
Space
50
4.3.4 The Bolt Carrousel
For the bolt handling the chosen concept was the bolt carrousel, illustrated in figure 44.
The purpose of the bolt carrousel is to rotate the bolt into position where the adapter can
reach one at a time and deliver it to the bolt magazine.
Figure 44. Illustrative sketch of the bolt carrousel with components (not to scale), cross-section view [mm]
The bolt carrousel consists of a middle shaft with 10 protruding fixed arms. On each arm
is a support plate fasted that has 6 holes where the bolts with bearing plates are being
placed, see figure 29. In figure 44 above only two bolts per arm is shown for clarity. A bit
higher up on the shaft is a larger dividing plate attached which in turn has place for 10
smaller dividing plates that hold 6 bolts each. The small dividing plates as well as the
support plate are provided with ball bearings that makes it possible to rotate the bolt
holders around their own axis. The shaft is mounted through a frame and has ball bearings
that allows it to rotate. The large dividing plate is fixed to the shaft and rotates together
with it. An electric motor located on the floor under the carousel itself (inside of the
frame) is by gear transmission connected to the shaft which generates the rotational
motion.
As mentioned are the bolts place in holes in the support plate. The holes are smaller than
the diameter of the welded flange which hinders it from falling through. To be able to
place the bolts closer together so are the bearing plates placed at slightly different heights
so that the plates overlap.
~550
~525
51
Figure 45. Detailed picture on support plate
4.3.5 The Adapter
The adapter is the device needed as a link between the bolt carrousel and the bolting unit.
It consists of two grippers that grabs the bolt that is put into location by the bolt carrousel.
Two grippers are being used not because the bolt and plate weight so much but to
increase the stability and accuracy of the motion. As previously explained are the bolts
standing in the support plates in holes, which is why the adapter need to be controllable
vertically to be able to lift the bolt before rotating into the bolt magazine. The basic idea
of the adaptor is shown in figure 46.
Figure 46. Basic configuration of the adapter
The bolt are approximately 500 mm up from the machine floor. Figure 47 and 48 are
showing the placement for both the mesh rolls and the bolt carrousel on the machine, the
bolting unit is outlined in red in the middle.
52
Figure 47. Side view of placement on the machine
Figure 48. Top view of placement
4.4 Cylinder dimensioning
Table 10 is the maximum forces in respective joint obtained from the ADAMS
simulation, figure 39.
Table 10. Maximum forces in the joints
Force Value [kN]
R1 14.2
R2 15.6
R3 15.6
R4 15.3
R5 16.6
R6 15.3
53
The required diameters for the hydraulic cylinders was calculated using the highest force
at respective place in equation 23 and 24. The pressure p in the system is 150 bar [4], A
denotes the area and R are the magnitude of the forces.
𝐴𝑚𝑖𝑛1 =
𝑅6
𝑝 (23)
𝐴𝑚𝑖𝑛2 =
𝑅2
𝑝 (24)
Together with the formula for the area of a circle,
𝐴𝑚𝑖𝑛 =𝜋
4𝑑𝑚𝑖𝑛
2 (25)
this gives the diameters 𝑑𝑐𝑦𝑙 = 36 mm for both cylinder 1 and 2.
However both the cylinders are double-acting, meaning that they can produce force in
both push and pull direction. The hydraulic fluid acts on both sides of the piston, and as
shown in figure 49 the pull area (side a) is smaller because of the lost area where the rod
is placed and therefore does the outer diameter need to be somewhat bigger to be able to
achieve the required forces.
𝐴𝑚𝑖𝑛 =𝜋
4(𝑑𝑏
2 − 𝑑𝑎2) (26)
Taking data from existing cylinders, see figure 50, [24] it is calculated with equation 24-
26 that the size db = 40 mm and rod diameter da = 20 mm does not suffice to provide
enough force. The chosen size is therefore chosen to be db = 50 mm and da = 32 mm.
Figure 49. Cylinder cross-section
Figure 50. Draft from data sheet of hydraulic cylinders from Stacke Hydraulik [24]
What also needs to be taken into consideration when choosing cylinders are the required
stroke lengths. Small cylinder diameters with relatively long stroke length will be at risk
of buckling. For the above mentioned cylinders a table with maximum recommended
54
stroke lengths do exist which have been used here. [25] The stroke lengths needed for the
cylinders are 𝑙𝑠𝑡𝑟𝑜𝑘𝑒1 = 260 mm and 𝑙𝑠𝑡𝑟𝑜𝑘𝑒2 = 315 mm. From the table at the working
pressure of 16 MPa, which is the closest to the system’s pressure of 150 bar, can be seen
that the maximum stroke lengths are 660 mm, which means that neither of the cylinders
should be in the risk for buckling.
Figure 51. Extract from table for maximum stroke lengths [25]
For cylinder number 3, which lifts the platform with the arm, the load was estimated to
maximum 350 kg. Setting a safety factor of 1.5, this gives 525 kg that the dimensioning
are based upon. Using the same approach and equations as in the previous case for
cylinder 1 and 2, this results in a minimum diameter of 21 mm . Also here the buckling
needs to be taken into consideration. The required stroke length for cylinder 3 is 190 mm,
which leads to choosing a cylinder that is at least db,3 = 25 mm and da,3 = 16 mm.
55
5 DISCUSSION AND CONCLUSION
Here are the results from the previous chapter discussed together with the overall
conclusion of the project. The chapter also includes some personal reflections form the
author.
5.1 Discussion
This project task was to come up with a conceptual design solution for an automated
mesh mounting procedure to the new RVM machine from developed by Atlas Copco.
One of the main factors during the concept generation was to try to keep at concepts as
simple as possible. Due to the hard environmental conditions in the tunnels is it essential
to have robust and insensitive systems that are not affected by vibrations, dust, changing
temperatures that can range from 30°C to about 70°C, moisture and so on. This proved to
be a challenging task, and the concepts finally presented were more complex than
intended. A lot of time was spent on brainstorming and searching for inspiration online.
The concepts that were chosen for evaluation were quite similar to each other, and no
really clear winner did stand out in either of the cases. Nevertheless, the seemingly most
promising concepts were developed as far as the time restriction allowed.
This conceptual design solution presented here in the project are based upon two quite
individual parts; the mesh mounting and the bolting. One of the main restrictions was that
the bolting unit should not be moved or altered. This led to the implementation and
development of several different sub-systems that were needed I order to obtain a fully
working solution for both parts, which was the reason that the overall solution became
complicated.
The final concept did fulfil all the spatial limitations and could manage and fit the
required amount of both mesh, rock bolts and bearing plates.
The CAD models in this project were not developed or dimensioned very much in detail
since this was a project on a conceptual design level, and focus has been put on creating
and developing the overall general design for the different parts and to together form a
workable concept.
The placement of the mesh on the tunnel wall in this design is probably not optimal, since
the inner rod of the rolls are being left on the walls. However, this was discussed with the
industrial supervisor and did not considered to be a problem since the tunnel will be
backfilled when finished. What might become problematic though, are to overlap the two
closely placed rods with the bearing plate. It is believed that the inserted bolt and plate
would have no problem to keep the weight of the rods, but the accuracy when drilling
might not be so good so the possibility that the plate misses the rods are impending.
Another aspect to consider is that the tunnel wall is not completely flat, and protruding
rock and irregularities could affect and hinder the correct placement.
56
5.2 Conclusion
This combined solution with the bolt carrousel and the arm design for the handling of the
mesh rolls presented in this report is could have the potential to work if implemented on
the real physical machine. The presented concept does fulfil the requirement
specification, however it does consist of many different parts that need to work together
with quite high accuracy and is quite complex. This does need a lot of further
development work, analyses and tests in the real operation conditions to be able to assure
a fully working solution. The author’s main concern are regarding how the mechanical
parts and necessary control systems will react to the difficult working environment in the
tunnel, especially the vibrations, dirt and moisture.
57
6 RECOMMENDATIONS AND FUTURE WORK
Here are presented some recommendations for future work if this design were to be
further developed.
After this project does the author strongly believe that it is necessary to integrate the
drilling and bolting unit in the development work for the mesh handling, in order to get a
good overall solution and get rid of some of the subsystems that makes this design
complex.
However, if this design is to be further developed there are some things that are advisable
to investigate in order to simplify and reduce the number of different subsystems.
Redesigning of the existing drill and bolt unit could make it possible to directly move the
bolts from the bolt carrousel and into the magazine, which would result in the removal of
the adapter. Furthermore is it recommendable to redesign the frame to the drill and bolt
unit so that the third hydraulic cylinder that actuates the vertical motion of the arm’s
platform could be removed. This would also mean to re-dimension the link arm system
itself. Simplifications like these are believed to increase the robustness and reliability of
the system a lot.
There is also advisable to look further into how the placement of the mesh on the wall
could be done better, without leaving the rods attached and how to make the placement
even more adaptable to irregularities in the tunnel wall.
The gripper on the arm could be improved by adding a mechanism so that it would be
possible to control the unwinding of the mesh better, in order to prevent any potential
tangling.
Also some kind of cover/roof/sides to both the bolt carrousel and some kind of protection
to the mesh arm would be advisable, to protect the components and system from the
difficult environment as much as possible.
58
59
7 REFERENCES
[1] Maidl, B., Maidl, U., Thewes, M.“Handbook of Tunnel Engineering, Volume I:
Structures and Methods”, Wilhelm Ernst & Sohn, Berlin, 2013.
[2] Leonida, C. “MM’s Top 10 technologies”, http://www.miningmagazine.com/
equipment/mine-development/mms-top-10-technologies-1/, 2015, (accessed 2017-02-17)
[3] https://www.geobrugg.com/en/MINAX-804-7878.html (accessed 2017-02-20)
[4] Saf, F, Atlas Copco, Örebro, [interview], 170130
[5] Darling, P., Lever, P. “Mining Engineering Handbook”, Society for Mining,
Metallurgy and Exploration Inc., USA, 2011.
[6] Petersen, C. “The Practical Guide to Project Management”, PMP & Bookboon.com,
2013.
[7] Cooper, R.G., “Perspective: The Stage-Gate Idea-to-Launch Process, Update, What’s
New and NexGen Systems”, 2008.
[8] Bickel, J.O., Kuesel, T.R., King, E.H.,“Tunnel Engineering Handbook”, Chapman &
Hall, 1996.
[9] Olsson, J, Atlas Copco, Örebro, [interview], 170308
[10] He, L., An, X.M., Zhao, Y., “Fully Grouted Rock Bolts: An Analytical
Investigation”, Springer-Verlag, Wien, 2014.
[11] Hoek, E., Wood, D. F., “Support in Underground Hard Rock Mines”, Canadia
Institute of Mining and Metallurgy, Montreal, 1987.
[12] Williams, T.J., Brady, T.M. “Underhand Cut and Fill Mining as Practiced in Three
Deep Hard Rock Mines in the United States”, National Institute for Occupational Safety
and Health.
[13] Pakalnis, R., et al., “Design Spans – Underhand Cut and Fill Mining”, Canadian
Institute of Mining, Metallurgy and Petroleum (CIM), Toronto, 2005.
[14] Split Set, datasheet, http://www.splitset.com/pdf/Form_16516_ASS_39.pdf
(accessed 2017-03-15)
[15] Bickel, J.O., Kuesel, T.R., King, E.L.,“Tunnel Engineering Handbook”, Chapman &
Hall, 1996.
[16] http://www.vectordiary.com/illustrator/wire-fence-tutorial/ (accessed 2017-02-20)
[17] Brown, S., “Method and apparatus for lining tunnel walls or tunnel ceilings with
protective nets”, US8662796B2, 2014. From Google Patents
60
[18] Burgess, Timothy D., et.al, “Mesh handling apparatus and related methods”,
US9194231B2, 2015. From Google Patents
[19] Weber, R.G., Condoor, S.S., “Conceptual Design Using a Synergistically
Compatible Morphological Matrix”, Frontiers in Education Conference, 1998.
[20] http://springs.lesjoforsab.se/tco-38-50-fzb (accessed 2017-04-30)
[21] https://www.hardwareworld.com/cpfkl6d/Workshop-Tool-Organizer-Hooks-Clips,
(accessed 2017-04-30)
[22] Pugh, S., “Total design – integrated methods for successful product engineering”,
Addison-Wesley Publishing Company, Wokingham, 1991.
[23] “Maskinelement handbok”, Maskinkonstruktion, KTH, 2008.
[24] http://www.stackehydraulik.com/sites/default/files/product-media/da0101_0.pdf
(accessed 2017-04-30)
[25] http://www.stackehydraulik.com/sites/default/files/knacktabell_0.pdf (accessed
2017-05-10)
61
APPENDIX A – FREE BODY DIAGRAM
Derived equilibrium equations
For Arm 1:
𝑅1𝑌 + 𝑅4𝑌 − 𝐹𝑎𝑟𝑚1 − 𝑅3𝑌 − 𝑅5𝑌 = 0 (4)
𝑅1𝑋 + 𝑅4𝑋 − 𝑅3𝑋 − 𝑅5𝑋 = 0 (5)
𝑅4𝑋(𝑥3 sin 𝛼 + 𝑥5 cos 𝛼) − 𝑅4𝑌(𝑥3 cos 𝛼 −𝑥5 sin 𝛼) + 𝐹𝑎𝑟𝑚1
𝑙𝑎𝑟𝑚1
2cos 𝛼
+ 𝑅3𝑌(𝑥4 cos 𝛼 + 𝑥6 sin 𝛼) − 𝑅3𝑋(𝑥4 sin 𝛼 − 𝑥6 cos 𝛼) +
+𝑅5𝑌 ∙ 𝑙𝑎𝑟𝑚1 cos 𝛼 − 𝑅5𝑋 ∙ 𝑙𝑎𝑟𝑚1 sin 𝛼 = 0
(6)
Cylinder 1:
−𝑅4𝑌 − 𝐹𝑚𝑐,𝑐𝑦𝑙1 + 𝑅6𝑌 = 0 (7)
62
−𝑅4𝑋 + 𝑅6𝑋 = 0 (8)
𝐹𝑚𝑐,𝑐𝑦𝑙1 ∙
𝑙𝑐𝑦𝑙1
2cos 𝜃 + 𝑅6𝑋 ∙ 𝑙𝑐𝑦𝑙1 sin 𝜃 − 𝑅6𝑌 ∙ 𝑙𝑐𝑦𝑙1 cos 𝜃 = 0 (9)
Cylinder 2:
−𝑅2𝑌 − 𝐹𝑚𝑐,𝑐𝑦𝑙2 + 𝑅3𝑌 = 0 (10)
−𝑅2𝑋 + 𝑅3𝑋 = 0 (11)
𝐹𝑚𝑐,𝑐𝑦𝑙2 ∙
𝑙𝑐𝑦𝑙2
2cos 𝛽 − 𝑅3𝑌 ∙ 𝑙𝑐𝑦𝑙2 cos 𝛽 + 𝑅3𝑋 ∙ 𝑙𝑐𝑦𝑙2 sin 𝛽 = 0 (12)
Arm 2:
−𝑅6𝑌 + 𝑅5𝑌 − 𝐹𝑎𝑟𝑚2 − 𝐹𝑙𝑜𝑎𝑑 = 0 (13)
−𝑅6𝑋 + 𝑅5𝑋 = 0 (14)
−𝑅5𝑌 ∙ 𝑥7 𝑐𝑜𝑠 𝛾 − 𝑅5𝑋 ∙ 𝑥7 𝑠𝑖𝑛 𝛾 + 𝐹𝑎𝑟𝑚2
𝑙𝑎𝑟𝑚2
2𝑐𝑜𝑠 𝛾 + 𝐹𝑙𝑜𝑎𝑑 ∙ 𝑙𝑎𝑟𝑚2 𝑐𝑜𝑠 𝛾 = 0 (15)
63
APPENDIX B – MATLAB CODE
% Link arms equations case 2
clear all, close all, clc
%parameters alpha = 59.6; %angle between ground and arm 1 beta = 68.7; %angle between ground and cylinder 2 gamma = 2.2; %angle arm 2 and ground
theta = 77.1; %angle between cylinder 1 and arm
g = 9.81;
%lengths from CAD x1 = 230e-3; x2 = 55e-3; x3 = 410e-3; x4 = 670e-3; x5 = 110e-3; x6 = 105e-3; x7 = sqrt(235^2 - 80^2)*10^-3;
%masses m_arm1 = 30; m_arm2 = 55; m_cyl1 = 7; m_cyl2 = 6; m_load = 75;
%lenght l_arm1 = 880e-3; l_arm2 = 2730e-3; %max lenght ger stˆrst krafter
l_cyl1 = 450e-3;
l_cyl2 = 548e-3;
F_arm1 = m_arm1 * g; F_arm2 = m_arm2 * g; F_mccyl1 = m_cyl1 * g; F_mccyl2 = m_cyl2 * g; F_load = m_load * g;
%equation system A = [0 0 0 -1 0 1 0 0 0 0 0 0; 0 0 -1 0 1 0 0 0 0 0 0 0; 0 0 0 0 l_cyl2*sind(beta) l_cyl2*cosd(beta) 0 0 0 0 0 0;
0 1 0 0 0 -1 0 1 0 -1 0 0; 1 0 0 0 -1 0 1 0 -1 0 0 0; 0 0 0 0 -(x4*sind(alpha)-x6*cosd(alpha))
(x4*cosd(alpha)+x6*sind(alpha)) (x3*sind(alpha)+x5*cosd(alpha)) -
(x3*cosd(alpha)-x5*sind(alpha)) -l_arm1*sind(alpha) l_arm1*cosd(alpha)
0 0;
64
0 0 0 0 0 0 0 -1 0 0 0 1; 0 0 0 0 0 0 -1 0 0 0 1 0; 0 0 0 0 0 0 0 0 0 0 l_cyl1*sind(theta) -l_cyl1*cosd(theta); 0 0 0 0 0 0 0 0 0 1 0 -1; 0 0 0 0 0 0 0 0 1 0 -1 0; 0 0 0 0 0 0 0 0 -x7*sind(gamma) -x7*cosd(gamma) 0 0];
B = [F_mccyl2; 0; -F_mccyl2*l_cyl2/2*cosd(beta); F_arm1; 0; -F_arm1*l_arm1/2*cosd(alpha); F_mccyl1; 0;
-F_mccyl1*l_cyl1/2*cosd(theta); F_arm2+F_load; 0; -F_arm2*l_arm2/2*cosd(gamma)-F_load*l_arm2*cosd(gamma)];
x = A\B
R1 = sqrt(x(1)^2+x(2)^2) R2 = sqrt(x(3)^2+x(4)^2) R3 = sqrt(x(5)^2+x(6)^2) R4 = sqrt(x(7)^2+x(8)^2) R5 = sqrt(x(9)^2+x(10)^2) R6 = sqrt(x(11)^2+x(12)^2)
65
APPENDIX C – COORDINATES TO ADAMS
66
APPENDIX D – ADAMS RESULTS
The obtained resulting forces R1, R2, R3, R4, R5 and R6 from the ADAMS simulation in
the corresponding joints .
67
Force components in the X- and Y-direction in each joint.