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DESCRIPTION
Magnetic wheeled climbing robotpassing corners and sharp edgesTRANSCRIPT
Semester Thesis
Magnetic wheeled climbing robotpassing corners and sharp edges
Lorenzo Bagutti
Wolfgang FischerAdviser
Prof. Dr. Roland Y. SiegwartAutonomous System Lab (ASL)
Swiss Federal Institute of Technology Zurich (ETH)
2009-05
Contents i
Contents
1 Abstract iii
2 Introduction 1
2.1 Motivation and Business-case . . . . . . . . . . . . . . . . . . . . 1
2.2 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3 State of the Art 3
3.1 Wheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.2 Magnetic wheeled vehicle with 2x2 wheels . . . . . . . . . . . . . 4
3.3 MagneBike . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.4 Wheel inside the wheel (Kawaguchi 1994) . . . . . . . . . . . . . 5
3.5 Limitations of current robots . . . . . . . . . . . . . . . . . . . . . 6
4 Basic Idea 8
4.1 Wheel parallel to wheel (WpW) . . . . . . . . . . . . . . . . . . . 8
4.2 Double-Tail-Structure (DTS) . . . . . . . . . . . . . . . . . . . . . 9
4.3 First proof of concept . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.4 Compatibility to MagneBike (Goal Project) . . . . . . . . . . . . 9
5 Fundamental parameters and decision 11
5.1 Morphological box . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6 Dimensioning 14
6.1 Wheel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.2 Motor Torque and Friciton Coefficient . . . . . . . . . . . . . . . 15
6.3 Belt gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7 Detailed Design 21
7.1 Structure, wheel parallel to wheel and lifter arm . . . . . . . . . . 21
7.2 Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
7.3 Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
7.4 Final Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Contents ii
8 Implemanetation and Testing 31
8.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
8.2 Wheel unit: final assembly . . . . . . . . . . . . . . . . . . . . . . 32
8.3 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
8.4 Further Improvement . . . . . . . . . . . . . . . . . . . . . . . . . 34
9 Conclusion and Outlook 39
References 40
A Appendix 42
A.1 Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
A.2 Planetary Gearhead . . . . . . . . . . . . . . . . . . . . . . . . . . 43
A.3 Belts and gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
A.4 Ball bearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
B Appendix 49
B.1 List of components . . . . . . . . . . . . . . . . . . . . . . . . . . 49
C Appendix 50
C.1 WpW gear calculation . . . . . . . . . . . . . . . . . . . . . . . . 50
1 Abstract iii
1 Abstract
The Autonomous System Lab (ASL) in collaboration with Alstom company have
successfully developed different concepts in the field of inspection robots. They
especially made progress in the concept of magnetic wheeled robots and the main
aim is to reduce the complexity and maintain a low number of DOF. With this
thesis new concepts are been applied and developed to solve the drawbacks of
the previous version of the “MagneBike”. The prototype is able to pass corners
and sharp edges with only 5 DOF and is compatible with the old design.
2 Introduction 1
2 Introduction
2.1 Motivation and Business-case
Nowadays, there are going on a lot of studies in the field of robotic for inspec-
tion. One of many environments where the robots are used is pipe inspection for
instance steam chest plants. In this sector the maintenance and inspection are a
main issue. In fact, this helps to guarantee high standards of safety and perfor-
mance. The conventional inspection methods require to disassembling complex,
large and heavy parts and not always all the spots are easily reachable. Moreover
all the operations need days or even weeks to be executed, this means high cost
for the company and gas turbine power plant is unusable. After these consid-
erations it is obvious that a company has huge interest in a better and faster
inspection procedure. Inspection robots help to guarantee this aim. They can be
placed in specific points to detect defects and also locally repaired,at least the
part with an error must be disassembled.
2.2 Specification
The aim of this thesis is to develop a new wheel unit for the “MagneBike” [9]
which is used for inspection of steam chests. In the new wheel unit the “double-
tail-concept” for passing sharp edges and the “wheel-parallel-to-wheel”(Wpw)
for passing corners have been integrated (see chapter 4). The environment is
generally metallic and has complex structure with narrow sections, high abrupt
diameter changes and inclined elements(see Fig.1). Here follows a list of the
specific requirements copied from [9]:
1. The wide range of inner diameters encountered. The diameter varies from
200mm (this defines the maximum robot space envelope) up to 700mm.
2. The local abrupt inner diameter changes, up to 50mm on Fig.1. These can
be seen as 90◦ convex or concave edge obstacles.
3. The complex arrangement and sequence of these obstacles such as triple
step or gap.
4. The environment is composed of horizontal pipe elements, as well as vertical
2.2 Specification 2
elements. Generally any inclination can be encountered (see the gravity
vector orientation): climbing ability is then required.
5. The locomotion system has to be able to maneuver in narrow locations
and to be able to travel on circumferential paths, which can also have any
orientation regarding gravity.
,
Figure 1: 3D CAD model of a typical environment [9],
A magnetic wheeled robot is suitable for the inspection of the above environment.
However, corrosion, abrasion and lubrication produce dirt, which reduces the
magnetic force and friction coefficient of the wheels on the surface. The new
wheel unit needs to carry more payload, have a better obstacle-passing capability,
higher speed and lower cost.
A miniaturized prototype corresponding to the above mentioned requirements
has already been developed (see Fig. 6 (b)). It integrates two unit of wheel-
parallel-to-wheel and an extra motorized arm.
3 State of the Art 3
3 State of the Art
In a ferromagnetic environment, inspection robots with permanent magnetic
wheels are the principle choice. They do not need an external power source and
they can stay in place. A system with these characteristics has the advantage of
being simple to control and having a low number of DOFs.
This chapter introduces the state of the art in the inspection with magnetic
wheeled robots.
3.1 Wheels
Magnetic wheels allow to drive the unit in different places in despite of the gravity
force. This is the reason why they are widely used on metallic surface.
As described in [5], the magnetic wheels consist of a NdFeB ring magnet, mag-
netised in axial direction and two steel discs attached to each side. (Fig.2). The
permanent magnet is never in contact with the surface, only the steel discs touch
the ground.
This configuration guarantees a magnetic flux through the discs, providing a
contact force which hold the robot on the metallic surface.
The magnets and disc chosen for this work, reach magnetic forces of approx-
imately 125N . However, the magnetic force is reduced significantly when the
wheel is tilted. According to [11], the force is reduced to 75% at 5◦, to 55% at
10◦ and even 45% at a tilling angle of 15◦. This results are important to keep
in mind especially when the robot unit drives on curved surface, where a full
contact with it cannot be guaranteed.
The friction between the wheel and surface plays also an important role in the
movement of the robot. To apply the necessary traction, the friction coefficient
must be higher enough, in fact for a steel on steel contact, the coefficient µ is
maximal 0.3. This is the reason why an extra thin rubber film is added to the
wheel, which result in an improvement of µ = 0.6. However, the rubber film
reduces the magnetic force of the wheel. Therefore, the layer must not be thicker
than 0.1mm to limit the force reduction to 20%.
3.2 Magnetic wheeled vehicle with 2x2 wheels 4
,
Figure 2: Magnetic wheel structure: permanent magnet disc (blue), ferromag-netic discs (red) and magnetic flow (arrow) [8]
,
3.2 Magnetic wheeled vehicle with 2x2 wheels
The previous configuration of the MagneBike robot, as the name suggests,looks
like a motorbike, where 2 wheels are aligned. This set up has the advantage to be
independent on the pipe diameter, but it has the main drawback to be laterally
unstable on inclined and vertical surface as explained in [9]. There is another
approach with two units and in each one will be mounted two wheels, to have a
final structure similar to a car (as shown in 3).
It guarantees a better stabilization on the laterally instability of the MagneBike.
However, the main problem is that the magnetic wheels are not in perfect contact
with the surface, especially in the pipe case. As explained in the previous section
3.1, if the wheel is not perfect perpendicular to the surface the magnetic force
will decrease, which possibly results in losing its contact. There is the possibility
to implement a complex passive mechanism with virtual center of rotation on the
wheel-to-surface contact point (Fig.3 a). This solution allows a maximal magnetic
adhesion, but the system requirs too much space and moreover it is complex and
heavy.
3.3 MagneBike
ASL group is looking for new opportunities and concepts in the investigation of
internal metallic pipe. They presented the MagneBike in [10] which is composed
by two identical wheel units with one powered wheel and one rotatory lifter and
a stabilization arm each. The result is a system with 5DOF in an configuration
3.4 Wheel inside the wheel (Kawaguchi 1994) 5
,
Figure 3: 2 to 4 wheels arrangements: matrix of top view regarding side andfront views [9]
,
like a bike. The Magnetbike has the ability to pass sharp concave corners and
convex edges. However, its complexity and requirement on control is still higher
than for a tripod configuration.
3.4 Wheel inside the wheel (Kawaguchi 1994)
Kawaguchi proposed another solution for internal pipe inspection robot [6] using
a different concept of magnetic wheel. The solution suggested is a wheel inside
the wheel. The wheel unit is formed from a magnet axle, outer tires and magnetic
inner wheel as shown in Fig.4 (a). This dual magnetic wheel allows the robot
to travel over bumps which are lower than half the diameter of the outer wheel
as shown in Fig.4 (b). Moreover, the following concept helps to get rid of the
magnetic force more easily that a magnetic wheel. This is because the inner wheel
can climb inside the locked outer tire in Fig.4 (b). Wheel inside wheel has also
less problem with the rust. In fact, it is easily removed by wheel rotation when
the outer tire moves away from the magnet. The main problem of this system is
when the robot climb a wall and needs to pass a corner. In this case there is the
3.5 Limitations of current robots 6
risk to fall down.
,(a)
(b)
Figure 4: (a) Magnetic Wheel Concept, (b) Magnetic Wheels Climb a SharpObstacle [[6]].
,
3.5 Limitations of current robots
The Magnebike in [9] has satisfied the major requirements for an inspection of
steam chest environment. However, a few problems are still not solved:
1. low playload, robustness, mobility
2. difficulty and complexity of the control
3. very low security margin when passing edges, especially sharp edges.
3.5 Limitations of current robots 7
With this thesis we try to overcome these difficulties applying on MagneBike new
concepts which are already tried in a miniaturized prototype with great results.
4 Basic Idea 8
4 Basic Idea
Within this chapter we discuss additional requirements that have been tested in
the previous prototype.
4.1 Wheel parallel to wheel (WpW)
The objective of the WpW is passively rolling through corners without using
an additional DOF, and it must have a lower complexity but (almost) similar
mobility.
The WpW is made of a magnetic wheel (see also 3.1), a bigger disc, in which an
axle is attached to the magnetic wheel, can roll in a axial guiding element. The
advantage of wheel inside to wheel (see chapter 3.4) is that the magnetic wheel is
in direct contact with the surface and it does not need to be enclosed in another
wheel.
As explained in chapter 3.4 the main issue for using such configuration is to help
the robot to detach the wheels when it handles a corner. Then bigger magnetic
force is generated (Fig.5).
,
Figure 5: WpW configuration and sequence when passing a corner [2],
4.2 Double-Tail-Structure (DTS) 9
4.2 Double-Tail-Structure (DTS)
The old MagneBike lost the contact with the surface when it was passing sharp
edge. The fall of the entire robot and damages at the unit were the consequence.
An idea to help the robot to overcome this case is adding an active lifter arm
or tail. The tail moves in the direction of the surface and fixes the robot before
moving through a sharp edge. When the robot lose the front unit , the arm
still keeps attached the rear unit and moreover the robot can continue driving
regardless of the front unit. When it reaches the edge the front unit falls on the
top surface. Now the robot is safely attached and the lifter arm can be removed
from the wall. Fig.[?] (b) shows the sequence when the robot is passing a sharp
edge.
4.3 First proof of concept
The ASL group has already implemented the previous described requirements in
a prototype 6 (a). The following results are reported from [2]:
1. Field tests with the MagneBike + support of its industrialization.The prob-
lems that will be solved with the new design cannot be neglected: No robust
solution for lifter force control found yet; limited payload; slow speed.
2. Successful demonstration of edge-passing-sequence with a conceptual pro-
totype (50% size) .
3. Field tests with the MagneBike show that speed and payload are limited.
4. The functionality of passive corner-passing principles is also proven (WpW).
4.4 Compatibility to MagneBike (Goal Project)
The aim of the project is to develop a new prototype of the old MagneBike where
the previous ideas are integrated. These specifications must be compatible with
the old model or a least with only little change in the structure.
4.4 Compatibility to MagneBike (Goal Project) 10
,(a)
(b)
Figure 6: (a) Double-tail-structure (DTS) , (b) sequence when passing a sharpedge. [2]
,
5 Fundamental parameters and decision 11
5 Fundamental parameters and decision
This chapter treats important decisions that have been made during the analyse
phase of the project.
5.1 Morphological box
Before we start with the creation of a 3D CAD model and afterwards a prototype,
an analysis of the functions and core variation parameters in the design have
been searched and evaluated. After this first analysis we have detected four main
functions:
1. Drive wheel: how the robot must be driven and where the motor/motors
must be placed.
2. Drive arm: where the motor to lift the arm must be placed and how.
3. Cogwheel/ gear belt: which of those solution is better for the new concept.
4. Wheel position: Where the wheels must be placed.
These functions have been summarized in a morphological box and for each func-
tion a few solutions have been proposed, as shown in Tab.1.
Drive Wheel 1 Motor + Differential gear + Servo 2 MotorsDrive Arm Structure Arm
Cogwheel/Gear belt
Wheels Position
Table 1: Morphological box
After analysing the various combinations, we decided to integrate the following
functions. The prototype will have each wheel motorized. The variant with the
5.1 Morphological box 12
differential gear has been rejected, due to the complexity of the system as shown
in Fig.7 and also the higher space necessity of the system. The gears have played
a big role in the decision of the design of the new robot. We chose the belt gears
cause of their simplicity in assemblage, cost, installation space and also for the
weight. To save more space the motor for the arm will be included in the own
structure and also in this case belt gears will been utilized. The position of the
wheels was another important issue. We opted for a solution where the wheels
are inside of the structure because a better stability of the configuration but also
a better use of the space will be reached.
Servo
Differential gears
Arm
Belt gears
WpW
Figure 7: Complexity of the differential gear solution
5.1.1 Wheel parallel to wheel
In addition to the previous configuration, a wheel parallel to wheel should be
integrated in the final prototype . The system has been described in the chapter
4.1. In the previous section 5.1, we take the decision to place the wheel inside
the structure, due to limited space the wheel parallel to wheel system must have
a narrow size. The bigger limitation is given from the height of the structure,
where we have 50.26mm high, as shown in Fig.12. Respect to the old model, we
have a variation of ∆h = 4.81mm.
5.1.2 Extra arm
The arm must help to pass edge safely and to bring back the wheels after they
have lost contact passing an edge. The critical issue of the arm, is the structure,
5.1 Morphological box 13
as according to the previous section 5.1, where a motor must be placed in it. We
considered some solutions but at the end we decided to produce something less
complicate. Since the decision to use belts for the traction, we have a limitation
on the design of the arm. In fact we can have a straight structure, a bounded
solution will be better to pass the edge but this kind of configuration is not
possible with the use of belt. To overcome this drawback, we put an extra wheel
at the end of the arm with the possibility to change its angle.
6 Dimensioning 14
6 Dimensioning
In this chapter there are some dimensioning issues reported. It is important to
consider that for the following project one of the goal is to have a similar structure
like the old version but, also to integrate new functions.
6.1 Wheel
This section will explain the characteristics of the magnetic wheel and the choice
that have been taken. In order to have an optimal magnetic flow through the
wheel, it must be easily to center. This guarantees a better attach force between
the surface and the wheel. The new concept counts two magnetic wheels for
wheel unit, this means, according to the old design (see table 5), a force of 125N
per wheel instead of 250N and the diameter of wheel stays the same as in the old
concept. Due to the budget limitation, old magnetic disc and wheel rim in steel
have been used.The following table 2 are summarized the material composition
and size of the magnetic wheel. Two cases of wheel rim have been considered, one
of these as an optimized structure as a result of an asymmetric wheel as shown
in Fig.8 (a), whereas the second concept is symmetric (Fig.8 (b)).
Material weight [g] ext. diam-eter [mm]
int. diame-ter [mm]
thickness[mm]
Magnetwheel
NdFeB 74 55 20 3
Symmetricwheel rim
St32 60 60 39.4 5
Asymmetricwheel rim
St32 64 60 20 5
Wheeltire/tape
- - - 0.1
Table 2: Composition, material and size of the magnetic wheel
An experiment was carried out to determine if the following configuration of
the magnetic wheel can generate the necessary force of 125N . The experiment
consisted to place the magnetic wheel over a metallic surface and calculating
with a dynamometer the necessary force to detach the wheel form it. The test
was repeated and each time an extra layer of tape has been added. Table 3
6.2 Motor Torque and Friciton Coefficient 15
,(a) (b)
Figure 8: (a) Asymmetric magnetic wheel, (b) Symmetric magnetic wheel.,
and 4 summarize the results of the above described test (either asymmetric or
symmetric wheel). In conclusion, the results satisfied the requirements of the
model.
0 tape layer 1 tape layer 2 tape layers 3 tape layersForce [kg] 13 12-13 10 10
Table 3: Symmetric wheel test
0 tape layer 1 tape layer 2 tape layers 3 tape layersForce [kg] 11 10 7 5
Table 4: Asymmetric wheel test
6.2 Motor Torque and Friciton Coefficient
6.2.1 Model
We use the old concept characteristics as explained in [9] for the calculation of
our model: Tab.5 summarises the characteristics of the old unit.
We also assume that the mass of the new model will be around 5kg and the new
concept of the unit wheel has two wheels instead of one. This means that the
magnetic force generated by the old wheel must be divided in two. This means
6.2 Motor Torque and Friciton Coefficient 16
Size: L×W ×H 180× 130× 220mm3
Height of the center of mass: zCM 65mmWheel Distance: LW 120mmWheel Diameter: 2r 60mmMass: m 3.5kgMass repartition: Wheels: 23%, actuators: 18%, gears: 17%,
Structure, housing, electtronic: 42%Max. magnetic wheel force: Fmag 250N(NdFeB magnets)Wheel torque: Tw cont/int 2.1Nm (cont.), 6.7Nm (int.)Lifter torque: Tl int 7.7Nm (int.)Steering torque: Tsteer cont/int 2.33Nm (cont.), 4.1Nm (int.)Operating voltage: 24V (actuators), 5V (electronic)Power( @ max.speed): 4.6W (hor.), 6.7W (vert.)Communication: RS232 @ 115′200baudMaximum speed: vrobot max 2.7m/minSteering rotation speed: ws 33◦/sControl mode: Remote control with on board motor con-
trollers
Table 5: Old robot characteristics [[9]]
that our new wheel must have a force of around Fmag = 125N . An experiment
has been carried out to determine if the design of the new wheel reaches the
required force. (see also 6.1).
Mass: m 5kgMax. magnetic wheel force: Fmag 125N(NdFeB magnets)
Table 6: Assumption robot characteristics
6.2.2 MATLAB calculation
According to the previous characteristics shown in Tab.5, Tab.6 and using a
MATLAB file developed by ASL [3], the necessary torque to drive the robot
has been calculated. Before describing the model that has been developed in
the MATLAB file, an excursus over the magnetic wheel and forces applied on it
would be made. As it can be seen in Fig.9, the normal force (FN = FR + Fmag)
is the sum of magnetic force (Fmag) and reaction force (FR). Fig.9 (B) shows
the case where the FR is negative, the wheel is still attached to the ground and
is able to provide traction. The limit case is reached, when the reaction force
6.2 Motor Torque and Friciton Coefficient 17
is stronger than the magnetic (Fig9 (C)). When a wheel is in contact with two
surfaces, as shown in Fig.9 (D), two cases can be observed. To estimate if the
robot is able to move , we consider the following two factors: 1) The actuator
torque (T = r ∗ FT ) has to be big enough to provide the necessary force to move
the robot (FT ). 2) The friction coefficient µmin = FT/FN has to be below the
maximal obtained value of µ.
,
Figure 9: Forces and torque on a magnetic wheel [3],
The MATLAB file considers a model based on a vehicle with two wheel pairs
passing a concave corner. The two worst cases occur when one wheel is in con-
tact with two surfaces.To get rid of the unwanted magnetic force the vehicle needs
a huge traction force. In Fig.10the used equation for the two cases is shown. The
first the robot approaches a wall and in the second case it leaves the corner. The
model uses 4 equations, three for the force- and moment-equilibriums and the 4th
one for the torque distribution between the front and back wheels. These equa-
tions are reunited into a matrix equation and solved in MATLAB. The model
takes the variable ϕ into account , which describes the position of the robot re-
spect to the gravity vector and an axis that passes through the gravity middle
point. Fig.11 reports the four basic positions with the respective ϕ value.
Tot. magnetic force per two wheels [N] 250Gravity force [N] 5 · 9.81Length between wheels [m] 120 · 10−3
Wheel radius [m] 30 · 10−3
Height of the center of mass [m] 30 · 10−3
Table 7: Initial values for the MATLAB model
6.2 Motor Torque and Friciton Coefficient 18
,
Figure 10: 2D-model of a magnetic wheeled vehicle in concave corners [3],
,
Figure 11: Different positions of the robot,
6.3 Belt gears 19
The results obtained from the model are the following:
• Case 1: approach the wall
– The maximal torque occurs when the robot approaches the wall hor-
izontal (ϕ = 270◦) with a value of T = 5490.5[mNm] per wheels pair
(Twheel = 2745, 25[mNm] per wheel).
– The worst case for friction coefficient occurs when the robot comes
down from the wall (ϕ = 0◦), µ = 0.54 over the first wheel.
• Case2: leave the wall
– The maximal torque occurs when the robot leaves the wall and climbs
in the direction of the roof (ϕ = 180◦), T = 4485.8[mNm] per wheels
pair (Twheel = 2242, 9[mNm] per wheel).
– The worst case for friction coefficient occurs in the same case of the
torque (ϕ = 180◦), µ = 0.93 over the second wheel.
In addition at these case, the necessary torque to make wheels slip has been
calculated: Twheel = 125N · 30mm · 0.8 = 3000[mNm]. To find the this result
the force is multiplied with the radius of the wheel and the friction coefficient.
After the following consideration the motor can be evaluated and we decided to
use the motor from an old prototype [4] in order to save money. Maxon motor
A Max 22 (Ø22mm,Graphite Brushes, 6 Watt) and the planetary gearhead GP
22C (Ø22mm, 0.5 − 2.0Nm, Ceramic Version), see also Appendix A.1 and A.2,
must support the previous critical torques. As reported in the Appendix A.2 the
stall torque generate from the motor is equal to 6751, 269[mNm] and is strong
enough to support the critical force.
6.3 Belt gears
The belts and gears have been calculated with Mulco company tool 1. The tool
needs the following parameters to choose the right belt’s length and width:
• Art of gearing: The teeth of the belt must support more or less force. For
the following unit the teeth should be smaller and also the belt should be
as thiner as possible.
1Mulco website: http://www.mulco.net/
6.3 Belt gears 20
• Position of the gears:due to our structure, the position of the gears is con-
ditioned from it. Moreover, we choose to add a tension gear for tending the
belt better. In the structure we have a fix position of the motor. We de-
cide to increase of 4.81mm (see Fig.12)the length of the old “MagneBike’s”
structure in order to fit the belt better.
• Number of teeth: We took different numbers of teeth per gear. The bigger
gear (32 teeth) would be on the axis of the wheel. This choice will help the
robot while climbing or in case of big torsion. However, this will be a dis-
advantage regarding the velocity of the robot when it drives in a horizontal
plane. On the motor axis we have a 18 teeth gear, whereas for spanning
the belt we use an extra wheel with 25 teeth. This results in a reduction
i = 32/18 and it results in a torque Twheel = frac2.7 · 3218 = 4.8[Nm].
• Revolutions per minute: The Motor Amax-22 does around 8000rpm. The
planetary gear has got a reduction of 561 : 1, so the revolution pro minute
is 15rpm.
• Torsion: the maximal continuous torque is around 2Nm.
• Torsion on extra wheel 0Nm
However the company offers only a limited size of the belt length, so the program
help in choice of the position of the gears. In conclusion, we opted for a AT3
GenIII belt; this type of belt is characterized by the larger tooth shear strength
resulting from the larger tooth volume and the stronger tension members.
7 Detailed Design 21
7 Detailed Design
7.1 Structure, wheel parallel to wheel and lifter arm
7.1.1 Structure
The structure remain almost the same as the old “MagneBike”, only the length
has been extended to fit the present belt size of 201mm (other length available2: 150, 201, 252, etc). A 3rd structure in the middle has been included to place
the ball bearings of the wheel axes. As shown in Fig.12 the bottom part of the
structure has been cut to facilitate the assembly of the the wheel’s shafts.
,
Figure 12: Structure of the wheel unit,
7.1.2 Wheel parallel to wheel
In the developing of the WpW a new system to drive the outer wheel has been
taken into account. As explained in chapter 4.1, the outer wheel rolls in a disc
with a smaller diameter. In the new development, the outer wheel is equipped
2http://www.mulco.net/
7.1 Structure, wheel parallel to wheel and lifter arm 22
with an additional gear. When the unit drives trough a corner the outer wheel is
in direct contact with the wall and the floor, the gear helps the magnetic wheel
to roll in an easier manner. The other surface is an additional help to support
the radial force.
,
Figure 13: 1) Gear teeth, 2) inner and outer disc surfaces, 3) outer wheel, 4)magnetic wheel, 5) protection disc and 6)inner disc
,
The parameters for the calculation of the gears are reported in the appendix C.
7.1.3 Arm
The lifter arm/tail structure is composed of two parallel arms which include place
for the ball bearings at their bottom part. Like in the main structure, we have
cut the arms to facilitate the assembly for all the unit.
The motor is inserted in an aluminum tube and fixed on it. In the tube a cut
is done to help when the lock ring is applied to close better around the motor.
The extremities of the tube-motor structure are fixed with the arms. The small
wheel is placed in the middle of the tube-motor structure and it can be arranged
in different angles. When the unit loses the contact with the surface because of a
7.2 Bearings 23
sharp edge, the arm needs to help to keep the robot attached and with this small
wheel it is able to continue. Two ball bearings in a O-configuration are enclosed
with the following specification Di = 4, Do = 8andb = 3.
Figure 14: Arm Structure
1 Arms structure2 Small wheel structure3 Tube-motor lock ring4 Motor MAXON A-max 225 Tube,Øint = 22,Øext = 25,
Al Mg Si 0.5
7.2 Bearings
The wheels are the critical point for the bearings, especially in the situation where
the unit detaches from the surface. In this situation a force of 250N is generated.
Another requirement is their size and therefore we are searching something which
is as small as possible. The ball bearings need to carry the radial force more than
the axial. When the wheel unit is detached to a horizontal plane, the force is
radial distributed over four ball bearings. In another case, where the robot is
attached to a vertical surface, the gravity force is axial applied over two bearings
(Fig.15).
SKF 618/6 ball bearings have been used to calculate the structural safety factor
fs. After the calculation, see also appendix A.4 fs = 5.5 is obtained but for save
money we decide to buy the bearing from Conrad 3. However, the company does
not give the specification for this bearings. We assume that they will satisfy the
fs because the bearings are similar to the considered ones.
3http://www.conrad.ch
7.3 Axes 24
,
Figure 15: The two cases where the force have an effect on ball bearings,
7.3 Axes
7.3.1 Arm and wheels motor
The wheel motor axis consists of a motor and a synchronising pulley for the
transmission of the motor torque. The pulley is in AlCuMgPb and fixed on the
shaft of the motor with a hex key. Whereas the arm motor axis includes the
motor and a pulley without any teeth, therefore a wire will be connected to move
the arm and the pulley is glued on the motor axis.
,
Figure 16: 1) MAXON motor A-max22, 2)Synchronising pulley 18 teeth for AT3GENIII belt (similar composition for arm motor but with a pulley without anyteeth).
,
7.3 Axes 25
7.3.2 Wheels
Thee wheel axes are set in the structure and they lean on ball bearings. All parts
of this axis, excluding the ball bearings, are realized with 3D prototyping. All the
acetal resin parts are fixed with an adhesive bond. The wheels are mounted onto
the axes and through them, the torque is transmitted to the surface to propel
the vehicle.
Figure 17: Wheel axis with WpW
1 Pulley, z = 32 for AT3 GENIII belt2 Distance bush3 Protection disc4 Magnetic wheel, Fm ≈ 125N5 Intern disc and axis6 Ball bearings, Conrad 6x12x47 Shaft,Ø6mm X 10 Cr Ni S 18 9 1.4305 grinding h88 Rims9 Rubber
7.3.3 Tension gear
Figure 18: Tension gear axis
1 Structure2 Shaft,Ø4mm X 10 Cr Ni S 18 9 1.4305 grinding h83 Distance bush4 Pulley, z = 25 for AT3 GENIII belt5 Ball bearings, Conrad 4x8x3
7.3 Axes 26
The tension gear has the function to tighten the belt. Long holes are included in
the structure to have the possibility to tend the belt more easily. The bearings
are placed in a O-configuration. The structure, pulley and distance rings are
made with stereolithography process.
7.3.4 Arm
The arm’s axes are fixed on the structure with an adhesive bond. After analysing
our arm’s structure, we opted for a two fixed bearings. In fact, the structure would
tend to bend and the arm will lose its position. The parts are 3D printed and
bonded with glue.
Figure 19: Arm shafts
1 Structure2 Shaft,Ø6mm X 10 Cr Ni S
18 9 1.4305 grinding h83 Distance bush4 Ball bearings, Conrad
6x12x45 Pulley without teeth6 Closing disc
7.4 Final Model 27
7.4 Final Model
In this section different views of the wheel unit and final robots are shown.
7.4.1 Wheel unit
,
Figure 20: Wheel unit: side-view,
7.4 Final Model 28
,
Figure 21: Wheel unit: front-view,
,
Figure 22: Wheel unit: top-view,
7.4 Final Model 29
Figure 23: Wheel unit: section
1 Wheel parallel to wheel2 Pulley, z = 32 for AT3 GENIII
belt3 Arm structure4 Pulley, z = 25 for spanning the
AT3 GENIII belt5 Pulley, z = 18 for AT3 GENIII
belt6 Pulley for the wire
7.4.2 Final robots
Some 3D-CAD images of the final robot.
,
Figure 24: Final robot,
7.4 Final Model 30
,
Figure 25: Final robot: possible rotation of the front wheel unit,
8 Implemanetation and Testing 31
8 Implemanetation and Testing
In the previous chapter, we designed the prototype of the new wheel unit. In this
chapter, the implementation and testing are discussed.
8.1 Implementation
For the implementation of the previous concepts and structures, available norm
parts were used but also stereolithography printed parts were made. Sterolithog-
raphy or also 3D-printing is an excellent solution to produce parts in a short time.
However, the quality of the components can not be compared to metal pieces,
but it is still a reasonable choice for prototyping.
A list of components can be found in appendix B.
8.1.1 WpW’s shaft implementation
All the parts beside the bearings and the external disc of the WpW system were
mounted onto the shaft using an adhesive bound. By assembling the shaft to the
structure, a few walls of the bearing pocket have been damaged, because it was
too thin. A possible solution would be to create a metal structure instead of a
solidified resin or to just make the walls thicker.
Figure 26: WpW’s shaft
8.1.2 Lifter arm implementation
Also in this case the shafts and all the components excluded the bearings were
glued. The lifter arm would be mounted over the shaft, which is fixed in the
8.2 Wheel unit: final assembly 32
structure of the wheel unit.
Whereas the motor and all the components of the front part of the lifter arm
were fixed with M2 screws and bolts.
Figure 27: Lifter arm
8.2 Wheel unit: final assembly
In the following tab.?? are summarized the new dimensions of the wheel unit and
after a few shots of the final prototype are displayed.
Width ≈ 134mmHight ≈ 141mm
Length without arm ≈ 72mmLength with arm extended ≈ 176mm
Weight ≈ 1.3kg
Table 8: Size new unit.
8.3 Testing
In this section we’re going to discuss the tests which have been carried during
the project. However, at the present time we were unable to test the new func-
tions like passing through sharp edges and corners, because of the delays with
the Mulco supplier for the belts. Despite this, we have tried if the WpW’s was
rolling by pushing the unit by hands. The unit moves but we encounter some
problems .After rolling the unit forward and back, some teeth of the WpW sys-
tem were broken, most probably it is caused by the resistance of the material (3D
prototyping). So, for the next prototype it’d be interesting to test it without the
8.3 Testing 33
Figure 28: Wheel unit prototype
8.4 Further Improvement 34
gears and test if the contact between the two surfaces produces enough friction.
Another experiment was to test the resistance of the robot when we try to detach
it from the surface. We have considered a few cases where the robot can approach
in the real environment. The first one is a flat surface, the second is the surface
outside of a tube and the last one inside of it. On the tab.9 are summarized the
results, in the 3rd case we obtained an unexpected one. The wheels are not strong
enough to guarantee a constant contact when the unit travels inside a tube. This
problem is due to the wheel parallel wheel system, while the outer wheels are in
contact with the surface, the magnetic wheels are detached from it. A possible
solution would be to consider the shape of the smaller tube diameter and design
the new outer wheels in consideration of it.
21− 24[kg] 11− 14[kg] 5− 7[kg]
Table 9: Test:detach the unit from different surfaces
Further tests can be done when the belts will be available. For instance the ones
regarding passing corners and approaching sharp edges.
8.4 Further Improvement
After an analysis of the structure of the unit, we figured out that using a short
belt would be better. In this way we can reduce the size of the bigger gear and
also the belt-gears system would be more compact. This helps us also for the
creation of a wheel unit chassis with the scope to protect it from the dust or
possible contamination inside the gears, which could cause a malfunction.
During the assembling some parts have been damaged, as already mentioned in
8.4 Further Improvement 35
the section 8.1.1, so the 3D prototyping is not the best solution for a final unit.
The creation of the metal parts could be a possible solution. Another choice could
be the increase of the thickness, but this can cause some problems especially on
the WpW’s shaft, where the distances are limited.
Another problem we noticed was the collision between the tension gear (25 teeth)
and the encoder of the motor, whose elimination was necessary. Another approach
would be to increase the width of the unit. Like this we could also solve the
problem of the thickness.
8.4 Further Improvement 36
8.4.1 New wheel unit with differential gears
In the chapter 5 is explained that the decision of the differential gear was not
considered, because the complexity of the system and more over due to the lack
of space between the wheels. This is true for a classical system has shown in
Fig.8.4.1.
Figure 29: classical differential gearbox(www.howstuffworks.com)
Figure 30: differential gearbox for thenew wheel unit
8.4 Further Improvement 37
,
Figure 31: New unit with differential gearbox: side view,
8.4 Further Improvement 38
,
Figure 32: New unit with differential gearbox: front view,
9 Conclusion and Outlook 39
9 Conclusion and Outlook
As already explained in the testing section 8.3, the minimal requirement of the
project has not been reached, because some delays with suppliers of the ball bear-
ings and especially with Mulco company for the belts. At the present time, the
belts still not arrived. The testing was an important step to see if the new func-
tions of the robot, to pass corners and sharp edges, were working. Despite of this
problem, a few conclusion can be done. A final prototype has been developed,
although without the belts. It helped us to visualize some problems that they
can be solved in a future improvement. A chassis will be necessary for protect
the unit from dust. In the present version would be not optimal only to enclose
the structure in a chassis. This is caused by the big belt gears in the wheel axis.
Another point is the length of the belt, if these could be reduced then the size
of the big belt gears will also be smaller. Moreover, all the belt system will be
smaller and compact and this will facilitate the creation of a chassis.
A new wheel unit will be soon developed. However, it will include the differential
gears system. At the end of my thesis a new system, more compact, has been
found. Moreover the new wheel unit will get rid of the belts and so it will be
easy to test.
References 40
References
[1] R. Fernandez-Rodrıguez, V. Felieu, and A. Gonzalez-Rodrıguez. ”A Pro-
posed Wall Climbing Robot For Oil Thank Inspection”.
[2] W. Fischer, G. Caprari, and R. Siegwart. ”Preseentation G3:New locomotion
concept for stem chest inspection and similar applications”. ASL, 2008.
[3] W. Fischer, F. Tache, R. Siegwart, R. Moser, and F. Mondada. ”Magnetic
wheeled robot with high mobility but only 2 DOF to control”. Proceedings
of the 11th International Conference on Climbing and Walking Robots and
the Support Technologies for Monile Machines Coimbra,Portugal, 2008.
[4] F. Frohlicher, W. Fischer, F. Tache, and R. Siegwart. ”Entwicklung eines ein-
fachten Radantriebes fur den kleinen Kletterroboter ”Raccon” auf einer fer-
romagnetischen Oberflache”. Studienarbeit Autonomous Systems Lab, 2006.
[5] W. Guy. ”US Patent Nr. 3690393: Magnetic Wheel”. 1973.
[6] Y. Kawaguchi, I. Yoshida, H. Kurumatani, T. Kikuta, and Y. Yamada. ”In-
ternal Pipe Inspection Robot”. IEEE International Conference on Robotic
and Automation, 1995.
[7] Meier. ”Dimensionieren”.
[8] M. Oeschger, W. Fischer, G. Caprari, and R. Siegwart. ”Improvement of
a compact inspection robot with magnetic wheels”. Master Thesis Au-
tonomous Systems Lab, 2008.
[9] F. Tache, W. Fischer, G. Caprari, R. Siegwart, R. Moser, and F. Mondada.
”Magnebike: A magnetic Wheeled Robot With High Mobility for Inspecting
Complex Shaped Structures”. Unpublished.
[10] F. Tache, W. Fischer, G. Caprari, R. Siegwart, R. Moser, and F. Mondada.
”Adapted Magnetic Wheel Unit for Compact Robots Inspecting Complex
Shaped Pipe Structures”. Proc. of the IEEE/ASME International Confer-
ence on Advanced Intelligent Mechatronics (AIM 2007), Zurich, Switzerland,
2007.
References 41
[11] F. Tache, W. Fischer, G. Caprari, R. Siegwart, R. Moser, and F. Mon-
dada. ”Compact Magnetic Wheeled Robot With High Mobility for Inspect-
ing Complex Shaped Pipe Structures”. Proc. of the IEEE/RSJ 2007 Inter-
national Conference on Intelligent Robots and Systems (IROS 2007), San
Diego, USA, 2007.
A Appendix 42
A Appendix
A.1 MotorMain page Downloads
A-max 22 Ø22 mm, Graphite Brushes, 6 Watt
ø 2 ø 22 ø 2
6.5 31.9 16
Dimensions in mmThis schematic is not drawn to scale.
Price in Order No. pc(s) excl. VAT
110164 EUR 36.12
Motor data
Assigned power rating W 6
Nominal voltage V 24
No load speed min-¹ 10500
Stall torque mNm 24.3
Max. continuous torque mNm 6.97
Speed / torque gradient min-¹ / mNm-¹ 445
No load current mA 23.7
Starting current A 1.14
Terminal resistance Ohm 21
Max. permissible speed min-¹ 9800
Nominal current (max. continuous current) A 0.35
Max. efficiency % 73.1
Torque constant mNm / A-¹ 21.2
Speed constant min-¹ / V-¹ 450
Mechanical time constant ns 19.1
Rotor inertia gcm² 4.13
Terminal inductance mH 1.37
Thermal resistance housing-ambient KW-¹ 20
Thermal resistance winding-housing KW-¹ 6.0
Thermal time constant winding s 9.78
Motor lenght mm 31.9
Weight g 54
Operating range diagram
n[min-1] 6 W
9800
0
6.97 24.3 M[mNm]
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A.2 Planetary Gearhead 43
A.2 Planetary GearheadMain page Downloads
Planetary Gearhead GP 22 C Ø22 mm, 0.5 - 2.0 Nm, Ceramic Version
ø 4 ø 22
14.85 45.5
Dimensions in mmThis schematic is not drawn to scale.
Price in Order No. pc(s) excl. VAT
144001 EUR 97.37
Gear data
Reduction 561:1
No. of stages 4
Max. continuous torque Nm 1.8
Sense of rotation, drive to output =
Max. efficiency % 49
Average backlash no load ° 2
Mass inertia gcm² 0.4
Gearhead length L1 mm 45.5
Weight g 81
Max. motor shaft diameter mm 3.2
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The calculation for the torque generate from the motor: is the multiplication of
the stall torque or the maximal continuous torqueA.1 with the planetary gearhead
reduction and maximal efficiency.
• Stall torque: 24.3× 0.49× 561 = 6751.269[mNm]
• Continuous Torque: 6.97× 0.49× 561 = 1951.9833[mNm]
A.3 Belts and gears 44
A.3 Belts and gears
A.3 Belts and gears 45
A.3 Belts and gears 46
A.4 Ball bearing 47
A.4 Ball bearing
,Deep groove ball bearings, single row, unsealed
Principal dimensions Basic load ratings Fatigue Speed ratings Mass Designationdynamic static load Reference Limiting
limit speed speed
d D B C C0 Pu
mm kN kN r/min kg -
6 13 3,5 0,884 0,345 0,015 110000 67000 0,0020 618/6
,
Figure 33: SKF 618/6
This calculation refers to a wheel unit with two wheels and four ball bearings.
The magnetic force FM = 250N is distributed over four ball bearings in radial
direction.
FR =FM
4= 62.5 (A.1)
The gravitational force in axial direction is distributed over two bearings. FG =
5kg · 10 ms2 = 50N
FA =FG
2= 25 (A.2)
From the script “Dimensionieren” written by Prof. Meier [7] is the static equiv-
alent strain formula:
P0 = X0 ·FR + Y0 ·FA (A.3)
and to find X0 and Y0 the following tab.34 is used.
The values of C0 and f0 are given by the producer of ball bearings(see tab.33).
f0 ·FA
C0
=25 · 11
345≈ 0.8 (A.4)
A.4 Ball bearing 48
,
Figure 34:,
The data are inserted in the equation A.4 and the result must be interpolated
with the data from the tab. 34. We obtain the following value of e = 0.27. WithFA
FR= 0.4 ≤ e so are X0 = 1 and Y0 = 0.
P0 = 1 · 62.5 + 0 · 25 (A.5)
The structural safety factor is:
fs =C0
P0
≈ 5.5 (A.6)
This mean that the structural safety is more then sufficient.
B Appendix 49
B Appendix
B.1 List of components
Nr. Part # Comment1 Maxon Motor A-Max 22 and
Planetary gearhead GP 223
2 Magnet Ring NdFeB 2 di = 20mm, do = 55mm, b = 3mm3 Rim St32 2 di = 20mm, do = 60mm, b = 5mm4 Rim St32 2 di = 39.40mm, do = 60mm, b = 5mm5 Shaft 2 X10CrNiS18/9/1.4305, Ø = 6mm, l =
46mm6 Shaft 1 X10CrNiS18/9/1.4305, Ø = 6mm, l =
44mm7 Shaft 1 X10CrNiS18/9/1.4305, Ø = 6mm, l =
36mm8 Shaft 2 X10CrNiS18/9/1.4305, Ø = 4mm, l =
13.85mm9 Shaft 1 X10CrNiS18/9/1.4305, Ø = 4mm, l =
73mm10 Tube 1 AlMgSi0.5,di = 22mm, do = 25mm,
l = 95mm11 Ball bearing 6 Conrad: di = 6mm, do = 12mm, b =
4mm12 Ball bearing 6 Conrad: di = 4mm, do = 8mm, b =
3mm13 Pulley 32 teeth 2 3D Prototyping14 Pulley 25 teeth 2 3D Prototyping15 Pulley 18 teeth 216 Belt 2 AT3 GenIII, b = 6mm, l = 201mm
Table 10:
C Appendix 50
C Appendix
C.1 WpW gear calculation
,
Figure 35: Gear parameters (http://en.wikipedia.org/wiki/Gear)
C.1.1 General parmaters
• Module m = 1
• Angle of action α = 20◦
• Width tooth b = 2.5mm
• Foot radius %F = 0.38 ∗m = 0.38mm
• Circular pitch p = m ∗ π = 3.142mm
• Circular thickness s = p/2 = 1.571mm
C.1 WpW gear calculation 51
C.1.2 Inner wheel
• Number of teeth z = 15
• Outside diameter da = m ∗ (z + 2) = 17.0mm
• Pitch diameter d = z ∗m = 15.0mm
• Base diameter db = z ∗m ∗ cos(α) = 14.1mm
• Root diameter df = m ∗ (z − 2.5) = 12.5mm
C.1.3 Outer wheel
• Number of teeth z = 25
• Outside diameter da = m ∗ (z + 2) = 22.5mm
• Pitch diameter d = z ∗m = 23.5mm
• Base diameter db = z ∗m ∗ cos(α) = 25.0mm
• Root diameter df = m ∗ (z − 2.5) = 27mm