1. UNIVERSITÀ DEGLI STUDI DI SALERNO
Dipartimento di Ingegneria Industriale
Master of Science in Mechanical Engineering
“Functional simulation of a pneumatic
Breaker by using original modelling and multi-
body software”
Supervisors Student
Ch.mo Prof. Adolfo Senatore Nicola Melone
Ch.mo Prof. Ivan Arsie Matr. 0622300467
Assistant supervisors
Ing. Liselott Ericsson , Linkoping Universitet
Ing. Thomas Lilja, Atlas Copco
ACCADEMIC Year 2015/2016
1
3. Abstract
This Thesis is just the beginning of a process that the company hopes to give good results. Overall,
the current breaker is the second complete pneumatic machine modelled with such approach, thus
there are limitations and wide margins for improving the current study. After some discussion
about the working principles of a general percussive machine, explanation about this breaker and
the software itself will follow.
In fact, in a worldwide market with many competitors, the Atlas Copco’s hand-held pneumatic
department located in Kalmar ( Sweden ), brings to its costumers a new conception of pneumatic
breaker. More hitting power, higher performances and low air consumption are results that alone
show how great has been the design of this machine, that can be used for vertical heavy work as:
concrete demolition, asphalt breaking, digging hard clay/frozen ground. Compared with the actual
breakers on the market, this new percussive tool proved itself to be the best also from a vibration
level and noise points of view.
After the initial design the company wants to improve the machine, going deep in the under-
standing of the processes related to its internal phenomena. During the manufacturing and the
set-up phases, the practical work came along the simulations made in Dymola, a software created
by the widely-known Dassault Systemes. The model built in Dymola is limited to the hammer
mechanism, which does not allow the company further analyses as: the feed force required by the
operator, analysis of the stress waves in the chisel and the interaction chisel-ground. In order to
do so, this Thesis work has been charged with the aim to expand the current model to the study
of the interacting systems. The software used throughout this work is Hopsan NG.
Developed at the Division of Fluid Power Technology of the Department of Mechanical Engi-
neering at Link¨oping University, this software is widely used by the same company in ¨Orebro (
Sweden ) in the mining and underground area. Here they use Hopsan to simulate and reproduce
a lot of complicated systems related to hydraulic applications. Indeed, the company has improved
its default hydraulic library astonishingly and together with FEM software etc., is fundamental in
the hydraulic field. Last but not the least, this software is free whereas Dymola is quite expansive.
On these basis, the Kalmar’s pneumatic department wants to test the Hopsan capabilities in re-
producing pneumatic systems.
This Thesis ends showing the results obtained and the comparison with Dymola that will be dis-
cussed in details, in addition with the measurements made by the company on the real machine to
validate the virtual model built.
3
5. Acknowledgements
This work has been an experience that gave me a lot of knowledge about being part of a such big
company, about my future and myself. This is the end of one beautiful and unforgettable year in
Sweden, country to which I hope to say only ”see you soon” and not ”good bye”.
I want to say ”Thank you!” to all my colleagues that helped me in this work especially the com-
pany members, in particular my mentor Thomas Lilja. I learnt a lot from him and he was never
tired of all my questions and mistakes. Then, I want to say also thanks to ¨Olof Ostensson and
Per Forsberg that, with Thomas, after the job interview gave me the possibility to do this work
and introduced me in a really friendly, funny and amazing work environment that I hope to find
everywhere I will work.
In this long experience another thank goes to my Italian supervisor Adolfo Senatore that, to-
gether with my Erasmus coordinator Ivan Arsie, has always been willing to help me with the
bureaucracy and all the problems arisen all along this experience. They simplified a lot my Eras-
mus and I feel really lucky to have had professors like them.
Another important support that I cannot do without, comes from my family. Thank to them I
reached another important goal in my life and I will never stop to make them proud of me, not
only in this special situation but in every moment of my life.
Last but not the least, I want to thank all the people and friends met in this experience who have
told me to never give up in many situations. For this reason and more, deserve to be mentioned
also my girlfriend who helped me despite the distance and never let me alone.
A famous quote at the beginning of each chapter will come along with you during the reading
of this work, with the hope to make it less heavy to read.
Kalmar, July 2016
Nicola Melone
9. Chapter 1
Aim
”What you get by achieving your goals is
not as important as what you become by
achieving your goals”
Zig Ziglar
The overall aim of this Thesis is to develop a simulation model in the area of drilling and road
construction projects, using the new Hopsan NG software. The model will simulate one of the
latest Atlas Copco’s pneumatic breaker, including simulation of the stroke mechanism of the piston
controlled by pneumatic pressure and the vibration level that the operator of the machine will be
exposed to. During the development of the simulation program the model will be calibrated against
physical prototypes to fine-tune it, aiming at introducing design changes without need of building
new physical prototypes.
The approach used is to build the percussive mechanism as done in Dymola ( multi-engineering
modelling and simulation software ) and validate it with the measurements. Then, extend the
model including the operator feed force and the interaction of the piston with the tool and the
material that is to be demolished.
One important limitation is the 1D modelling approach that Hopsan allows in order to simulate
whatsoever system. The real breaker will have motion not only in the crushing direction, but also
in other directions. The main consequence of this is the different vibration level that the simulation
will not be able to reproduce. Precisely, in the latter only the working direction will be included
thus the vibration level will be the optimum one to aim to. Another limitation is given by the few
measurements of the stress waves released by the piston to the tool using different materials. Thus,
the material modelled does not match from all the point of views what is actually being crushed
by the breaker, e.g. the penetration rate.
The fluid used is pressurised air, so a compressible flow is to be simulated while it is filling up
and discharging the different volumes involved. The latter might be constant or variable over each
cycle. Their dynamics is not well implemented in the available components, especially the filling of
channels which have at the both end different pressures. In this case the channels are substituted
by simple lumped volumes, whose dynamics of course is different. To overcome this limit several
solutions will be introduced as done in Dymola, with the aim to match the breaker’s performances
measured during the tests made by the company itself.
9
11. Chapter 2
Introduction
”Everything must be made as simple as
possible. But not simpler”
Albert Einstein
2.1 What this work is about
The task of this master Thesis includes modelling of a virtual machine based on an existing pneu-
matic breaker. Apart from the stroke mechanism, the surrounding systems like the hand/arms
system, simulating the operator, as well as the material the machine is working on, will be in-
cluded. Today the simulation work is performed through the software Dymola/Modelica. At the
University of Link¨oping a new version of modelica/C++ based software Hopsan NG, evolution of
the former Hopsan software, have been developed. In Hopsan NG it is now possible to simulate also
pneumatic systems. With the aim to strengthen their simulation capability, the division above-
mentioned would like to study Hopsan NG possibilities not only for the percussive mechanism alone,
but also for the complete system that is interacting with the feed force supplied by the operator
and the material that is intended to be demolished.
The research has been developed at Construction Tools, one of the four divisions of Atlas Copco’s
Construction Technique business area, located in Kalmar in Sweden. This division has 140 em-
ployees mainly involved in production of hydraulic breakers and internal combustion engine driven
breakers and drill. They are responsible also for the development of hand-held compaction equip-
ment and pneumatic driven breakers and drills manufactured in India and Bulgaria.
2.2 Atlas Copco - Presentation
Atlas Copco Group is a global industrial group of companies, that develop and manufacture in-
dustrial tools, air compressors ( of which it is the world’s leading producer ) and construction and
mining equipment. This is a Swedish company that was founded in 1873. The main company’s
divisions focused on design, manufacturing and marketing of a large range of products are:
• Compressor Technique: Provides industrial compressors, vacuum solutions, gas and process
compressors and expanders, air and gas treatment equipment and air management systems;
11
12. • Mining and Rock Excavation Technique: Provides equipment for drilling and rock excavation,
a complete range of related consumables and service through a global network. The business
area innovates for surface and underground mining, infrastructure, civil works, well drilling
and geotechnical applications;
• Industrial Technique: Provides industrial power tools and systems, industrial assembly so-
lutions, quality assurance products, software and service through a global network. The
business area innovates for customers in the automotive and general industries, maintenance
and vehicle service;
• Construction Technique: Provides construction and demolition tools, portable compressors,
pumps, generators, lighting towers, compaction and paving equipment through a global net-
work. Construction Technique innovates for sustainable productivity in infrastructure, civil
works, oil and gas, energy, drilling and road construction projects.
Figure 2.1: Atlas Copco’s divisions
12
13. Chapter 3
Hand-held Tools and Vibrations:
Some theory about measurements and
related safety hazards
”If you want to find the secrets of the
universe, think in terms of energy,
frequency and vibration.”
Nikola Tesla
3.1 Hand-held tools at Atlas Copco
The name Hand-held Tools is referred to a large variety of products which are directly tactile
controlled by the operator. The pneumatic breaker involved in this work belongs to the group of
the hand-held percussion machines, widely used throughout industry. The direct control by the
operator exposes him permanently to harmful vibrations, which leads to a variety of disorders.
This is one field of study that got underway in the last 20 years along the design and manufacture of
these kind of machines. Even though widely used due to their convenience in service, high efficiency
and adaptability for various operation processes, a common problem associated with a systematic
use of such machines are the severe vibrations resulting in injury to the operator. Therefore, the
hand-transmitted vibrations have gained increasing attention in the literature and is now regarded
as one of the most important occupational hazards.
Originally these kind of machines did not have any vibration protections or safety devices until
health problems have arisen to the people working with them. From the introduction of a silencer
in 1950s and use of ergonomic handles in the 1970s, the focus on safety working conditions in
using such machines starts to take over their standard design and use. Indeed, after some years
of standardizations and rules, the EU directive 2002/44/EC on hand-arm vibrations commit the
measurement of the levels of exposure to mechanical vibrations to each employer in according with
the EU guidelines on this matter. The obligation of stating the vibrations level and the relation
between this value and the maximum allowed working hours defined by the same EU directives,
pushed the companies in more research in order to solve this problem. The aim is to give at their
13
14. costumer reliable products not only on the standard performances as power and consumption, but
also the vibration exposure which might limit the daily productivity. The latter is influenced by
the possible incurable damages which may affect the operators involved. Less vibrations leads to
more working hours for each worker, therefore less of them are needed for the same work, ending
up in an opportunity to increase both the income and the productivity.
The figure 3.1 shows the main hand-held Atlas Copco’s hammers on the market. There are three
different solution: hydraulic, pneumatic or petrol-driven breakers. The challenges to overcome are
different, but basically the working principles are the same. Some energy source is used to push
a piston against a tool that in turn crashes the material in contact with it. Depending on the
conditions in which the customer is used to work, the energy source can be different.
• Hydraulic breaker: hydraulic equipment offers the best power-to-weight ratio of any system.
With no exhaust from the tool it is possible to use them both indoor and outdoor, whether
it is cold or hot, dusty or wet or even water;
• Petrol-driven breaker: this is a portable machine, easy to start and virtually with no set-up
time. Since it is petrol-driven, it does not require any compressors, hoses or cable, it can just
be grabbed and brought everywhere;
• Pneumatic breaker: compressors are needed to supply air at this machine, which consequently
does not need a real fuel. Can be design to be smaller and lighter than the other two machines
and it is easy to control.
In this Master Thesis a deep look in a new concept of pneumatic breaker is given, along with the
need of software for simulating its behaviour. The motion of the piston defines different working
phases. The control of the machine is completely designed in its hardware, thus once has been built
it must be able to adjust itself to a different working conditions and problems. As the design is
really critical, simulations are needed to make it as good as possible.
14
15. Figure 3.1: Atlas Copco - Hand-held products - Examples of breakers
3.2 Human vibrations
Human vibration [1] is defined as the effect of mechanical vibration on the human body. During a
normal daily life, people are exposed to vibrations of one or other sort e.g. in buses, trains and cars.
Many people are also exposed to other vibrations during their working day, for example vibrations
produced by hand-tools, machineries, or heavy vehicles.
There are two types of human vibration: whole-body vibration and hand-arm vibration. The first
is transmitted generally through the supporting surfaces ( feet, back, buttocks etc. ); the latter is
transmitted to the hands and arms. This split of the vibrations reflects the different problems they
are involved in and consequently the approach used to study them.
Exposure to Whole-body vibration can either cause permanent physical damage to the lower spinal
region ( ischemic lumbago ), or disturb the central nervous system in the form of fatigue, insomnia,
headache and ”shakiness”. However, the latter symptoms usually disappear after a period of rest.
Daily exposure to Hand-arm vibration over a number of years can cause permanent physical
damage resulting in what is common known as ”white-finger syndrome”, or can damage the joints
and muscles of the wrist and/or elbow.
15
16. Figure 3.2: Whole-body disturbance
Figure 3.3: White finger syndrome
3.3 Vibration control and protection
In a blow-rate percussive machine, as the one studied in this dissertation, vibrations are mainly
generated by its moving parts. Damping them is an ongoing study, which involves different tech-
niques and problems. It is very important both that the method used to dampen the vibrations
introduces resonance frequencies which lie outside the range of frequencies to which the human
body is sensitive, and that those frequencies of the machine which do lie within the human sensi-
tivity range are efficiently damped [2].
The main groups of method studied and available for protecting the operator from hand-transmitted
vibrations are:
• Reduce the intensity of the sources of harmful vibrations through the proper
design of the machine. This way is highlighted since is crucial in the studied breaker, as
will be showed later.
• Vibration isolation. This is attained through two approaches: isolation of the machine handle
from the vibrating source and isolation of the hand from the vibrating handle ( e.g. achieved
by using gloves or operator substitution by a guided machine or robot, etc. ). However simple
passive systems of vibration isolation are usually effective only in a high-frequency range and
cannot provide high static stiffness. The latter point is important, because high static stiffness
results in a better control of the working point when hand-held machine are considered.
• The third method involves a dynamic absorption of vibration, through a dynamic absorber
16
17. tuned to the driving frequency and attached to the machine. In the case where the magnitudes
of the second and/or third harmonics are still large, additional dynamic absorbers might be
used. Clearly this method has one straight shortcoming, increase the weight of the machine.
The final trade-off to be considered is that high static stiffness with the presence of only the low
frequencies ( passive damping ) is preferable in order to have a better controllability, low stiffness
with the presence of only the high frequencies gives good isolation.
17
18. 3.4 Measurement parameters and quantification of the vibration
level
The term vibration is usually referred to a whatsoever body that is being forced to oscillate about
its reference ( stationary ) position. Displacement is, therefore, one parameter which can be used
to describe the magnitude of a vibration. Also the velocity and acceleration can be used instead,
which differ each other just for the phase while the magnitude of the vibration is the same ( figure
3.4 ).
Figure 3.4: Parameters to measure the vibration level [3]
The ISO (International Standards Organisation) standards for human vibration measurement re-
quire that acceleration must be the parameter used to measure vibration levels. The main used
quantities are [1]:
1. The Instantaneous root mean square value ( RMS value ) of a vibration is obtained
by taking an exponential average of the acceleration values measured during a certain time
interval
RMS = aeq =
1
T
·
T
0
a2(t)dt (3.1)
Waveforms made by summing known simple waveforms have an RMS that is the root of the
sum of squares of the RMS values: RMStotal = RMS2
1 + RMS2
2 + ... + RMS2
n.
2. The RMS value is therefore often referred to as the equivalent acceleration value, aeq(m
s2 ).
This parameter can also be expressed on a logarithmic scale (decibels, dB) with reference to
a scale where an acceleration of aref = 10−6 m
s2 corresponds to 0 dB. This is achieved by using
the following equation:
aeq(dB) = 20log10[
aeq(m/s2)
aref (m/s2)
] (3.2)
3. The maximum peak value is the maximum instantaneous acceleration measured during
the measurement time, T. It is useful indicator of the magnitude of short duration shocks.
18
19. 4. The crest factor defines the ratio between the Maximum peak value and the RMS value for
the measurement time, T. The more impulsive (or more random) a vibration is, the higher
is its crest factor. Because Impulsive vibrations are considered to be more harmful than
non-impulsive vibrations, the crest factor is a good indicator of the harmful content of a
vibration.
The sensitivity of the human body to mechanical vibration is known to be dependent on both
the frequency and the direction of excitation. These factors need to be taken into account if the
harmful effects of a vibration are to be assessed. The ISO has devised the three weighting curves,
shown here, which can be used to take the aforementioned factors into account when assessing the
harmfulness of a vibration (see ISO Standards 5439 and 2631 part 1). For the human vibration
Figure 3.5: Weighting filter amplification [1]
measurements the vibrations of interest are within the frequency range that goes from 0.1 Hz -1
500 Hz. Those vibrations occurring between 1 Hz - 80 Hz are of particular interest when measuring
exposure to whole-body vibration, and those occurring between 6.5 Hz -1 000 Hz are of special
interest when measuring exposure to hand-arm vibration.
Vibration levels
The frequency-weighted RMS acceleration values (aeq) associated with occupational exposure to
hand-arm vibrations normally range from 2 − 50m/s2, whilst those encountered in whole-body
19
20. vibration range from 0, 1−40m/s2. The ISO standard 2631 for whole-body vibration distinguishes
Figure 3.6: Daily vibrations [1]
three main human criteria ( figure 3.7 ) which can be used to assess vibrations in different situations:
• The preservation of working efficiency (the ’fatigue decreased proficiency boundary’);
• The preservation of health or safety (’exposure limit’);
• The preservation of comfort (’reduced comfort boundary’).
In order to assess a vibration which takes place in more than one direction simultaneously the ISO
2631 suggests that the effect of such a vibration can be calculated by taking the vector sum, a, of
the three weighted acceleration values, ax and ay and az as follows:
a = (1.4ax)2 + (1.4ay)2 + (az)2 (3.3)
The ISO Standard 5349(1986) for hand-arm vibration does not define the limits for safe exposure,
it only provides guidelines for the measurement and assessment of hand-arm vibration. Annex A
of the ISO 5349 provides information which allows one to predict the probability of white-finger
syndrome as a function of the frequency-weighted energy equivalent RMS acceleration value for
daily period of 4h and the exposure time in years ( see figure 3.8 ).
20
21. In order to assess the long-term effect of a certain amount of hours T of daily exposure, one must
calculate the RMS value aeq, which would produce an equivalent amount of energy in a 4 hour
period of exposure:
aeq,4h = aeq · T/4 (3.4)
In practice under these guidelines, once that each National Standardization Board ( N.S.B. ) has
stated the maximum frequency-weighted acceleration aL that can be tolerated for a maximum
continuous period TL, if aeq is the actual level of vibration,the allowed exposure time can be
calculated as follows:
a2
eq · Tallowed = a2
L · TL ==> Tallowed ≤
k
aeq
(3.5)
To end this discussion, it is worth mention that ISO standards recommend that human-vibration
signals are analysed in 1/3-octave frequency bands over the range of interest ( e.g. for hand-arm
vibration is 8-1000 Hz ). An octave is a frequency band where the upper frequency limit is twice
the lower limit. An octave has three 1/3-octave bands of equal width on a logarithmic scale. The
band-width of a 1/3-octave band is 23% of its centre frequency .
Finally, in order to contextualize the machine that will be showed later, the figure 3.10 shows an
example of what is the maximum admissible vibration levels allowed for different machines. The
black circle highlights the limit for the current pneumatic breaker.
21
27. Chapter 4
Basic principles of percussive rock
destruction
“Rocks and minerals: the oldest
storytellers”
A.D. Posey
4.1 Introduction
The three basic principles of percussive rock destruction [5] are showed below:
Figure 4.1: [5] Basic drilling principles: A - hammer=>rod=>bit; B - hammer=>bit; C - direct
impact principle
• In the principle A a hammer impacts a rod which is long in comparison with the hammer.
During the impact a stress wave is generated in the rod. This stress wave propagates toward
27
28. the bit, where it is partly reflected. Under the combined action of the incident and reflected
stress wave the bit is forced into the rock, which is thereby crushed;
• In the principle B there is no rod in between the hammer and the bit. Thus the hammer
impacts the bit itself, and the bit is forced into the rock which is crushed;
• In the principle C the bit is attached to the hammer to form a single tool, which directly
impacts and thereby crushes the rock.
The principle A is frequently applied in modern conventional rock drills, while B is applied in most
modern down-the-hole drills. C has only limited application today, but together with B has a very
long history, since they were applied in manual drilling long ago.
28
29. 4.2 Shock waves - Generation and Reflection
4.2.1 Generation - One dimensional stress waves
As reported in the figure 4.2, the impact between a piston ( which represents what before we called
hammer, that in general is a type of striker used in the percussive machines ) and a bar generates
a compressive wave that travels in both elements. Once reached the free end of the piston it is
Figure 4.2: Compressive shock wave - generation
reflected as a tensile stress which neutralize the first compressive one, as soon as reaches the impact
surface again. If the length of the piston is L, the final wave in the bar will have a length of 2L.
When the wave at the elements’s interface changes its sign from negative to positive, the force
acting between them drops to zero.
Must be remarked that this is valid as long as two cylindrical-shaped elements are considered
made by the same material and same average cross-sectional area. Indeed a simply change in
geometry, e.g. different cross section, leads to a multiple reflections that complicate the wave
analysis. However, the main part of the wave with higher magnitude involved in the destruction
process is long always twice the piston’s length.
Based on the one dimensional stress waves theory [6] , considering a rod of steel with cross section
area A in which at time t there is a stress σ(x, t) at the position x along the rod itself, the strain
(x, t) is given by:
=
σ
Es
(4.1)
where Es is the Young modulus for the steel. The strain is by definition the space differential of
the particle displacement u(x, t):
=
δu
δx
(4.2)
Consider an infinitesimal bar element of length dx at the position x, the net force on this element
is given by:
A{σ(x + dx, t) − σ(x, t))} = {
∂σ
∂x
}Adx = {
∂2u
∂2x
}EsAdx (4.3)
29
30. This force must equal the acceleration force
{
∂2u
∂t2
}ρsAdx (4.4)
The final equation obtained is:
{
∂2u
∂2x
}cs − {
∂2u
∂t2
} = 0 (4.5)
cs is the one-dimensional stress wave velocity in the steel.
The general solution of this equation gives the following expression for the velocity and the corre-
spondent stress at time t at the position x in the rod:
u(x, t) = u+(x − cst) + u−(x + cst) (4.6)
σ(x, t) = σ+(x − cst) + σ−(x + cst) (4.7)
Using the equations 4.1, 4.2, 4.6 and 4.7 the particle velocity is found to be equal to:
˙u =
cs(−σ+ − σ−)
Es
(4.8)
Looking at the figure 4.2 with a piston and a rod made of same material and equal cylindrical-shaped
section, the generation of a compressive stress wave can be studied in seven stages.
1. The piston has not yet struck the bar;
2. The piston has just struck the bar;
3. A compressive wave with the same amplitude σ0 is emerging and travelling both in the piston
and in the rod at the velocity cs. The rear end of the piston does not yet ”know” that there
has been an impact so it still travels with the velocity v towards the bar. The particle velocity
now is
˙u =
csσ0
Es
(4.9)
As the blow surfaces of the piston and the bar move with equal velocity, it follows that
v − ˙u = ˙u (4.10)
Using the equations 4.9 and 4.10 it yields:
σ0 =
vEs
2cs
and ˙u =
v
2
(4.11)
4. At the time t =
Lp
cs
after the impact, where Lp is the piston’s length, the compressive stress
wave in the piston reaches the rear end. Since this end by definition is free of stress a tensile
wave with the amplitude σ0 emerges from it. Travelling in the opposite direction cancels the
compressive one. In this case the particle velocity is still given by 4.11 and travels in the
opposite direction of the tensile wave. The two waves together correspond to the particle
velocity v;
5. The tensile stress waves travels through the piston;
30
31. 6. The tensile wave reaches the impact surface of the piston at time tp =
2Lp
cs
and cannot be
transmitted to the bar. Considering that the piston’s impact end has travelled during tp
at the velocity v/2, the stress wave displacement δ can be calculated multiplying these two
quantities
δ = tp · v/2 =
vLp
cs
(4.12)
7. The compressive wave in the rod travels towards the other end of the rod and its length is
the double of the piston length.
Can be demonstrated [7] that if the piston has a larger section of the rod, same impact velocity
and same mass, the free end of the piston will be moved towards the rod with a velocity
v1 =
v(Ap − A)
Ap + A
(4.13)
The impact thus generates a compressive wave σ1 during the next time interval tp
σ1 =
σ0(Ap − A)
Ap + A
(4.14)
The stress wave amplitude decreases with the same factor every time interval tp.
A third case might be that the piston has a cross section area A smaller than the bar, this result in
a negative velocity v1 and the piston recoils away from the rod with this velocity. The force-time
graphs for the first two cases are reported in the figure 4.3. The recoil velocity is a negative effect
of the impact. Can be demonstrated that the 80% of the recoil energy trapped in the piston is
found as an internal vibration energy and only the 20% as centre-of-mass motion energy.
31
33. 4.2.2 Reflection
According to the previous explanation, it is useful to remark how the stress wave reflection takes
place as it will be important in the explanation of the rock component. Considering the propaga-
tion of the wave in a bar, but the following reasoning is the same for whatsoever element, when it
reaches the opposite end of it different reflections might take places, depending on current bound-
ary condition. The two extreme cases are showed below [5]:
Free end
Figure 4.4: Compressive shock wave - reflection free end
In this case the condition that must be satisfied is to balance the pressure fo the surroundings.
It might be called open boundary condition, the particle velocity at the free end doubles and the
wave is reflected with the opposite sign.
Fixed end
Figure 4.5: Compressive shock wave - reflection fixed end
If the end of the rod is fixed, the condition to satisfy is to have zero velocity. Thus, the wave is
reflected with same sign to cancel out the current particle velocity.
33
34. 4.3 Rock behaviour - Assumptions
The assumption commonly made is that the force F is a linear function of the penetration x and it
is independent of the penetration velocity as long as the latter is positive [8], [9]:
Figure 4.6: Rock stiffness
F = k1 · x (4.15)
The rock can be characterised with two stiffness, one regarding the penetration k1 and one regarding
its elastic unloading when the force from the tool is ended k2. The energy required to penetrate
the rock and the losses can be expressed as:
Win =
F2
2 · k1
(4.16)
Wlost =
F2
2 · k2
(4.17)
The energy of rock destruction consists of several components such as: (a) energy of created sur-
faces, (b) energy transmitted from the loaded area as elastic waves, (c) energy associated with
fluid flow between pores and (d) kinetic energy of fragments of rock. It Has been demonstrated by
Simon [10] that all above components of energy are relatively small compared with the component
(b), that is the only useful part. However, all the above-mentioned components are necessary and
inevitable. The reason is that to initiate a fracture an appreciable amount of elastic energy must
be stored within a volume much larger than the fracture zone that will result. After the fracture
initiation, cracks propagate with high velocity and very rapid unloading occurs at the tips of the
cracks with consequent dissipation of elastic energy [11].
Under the above-stated assumptions, it is possible to calculate the rock energy transmission effi-
ciency as:
η = (1 −
k1
k2
) · 100 (4.18)
4.3.1 Rock behaviour - Implementation
As showed above the rock has two stiffness that characterize two different situations. Moreover, it
has been showed how the wave in the rod, piston etc. can be reflected depending on the current
34
35. situation. About the rock model implemented in Hopsan the situation to consider is an ”hybrid”.
Looking the figure 4.7, far well explained and proved with experiments in this Thesis work [12], the
penetration can be assumed as an open boundary condition, whereas the fixed boundary condition
can be applied when the tool is not able anymore to crack the rock.
The tensile wave is first reflected as the rock is penetrated (letter ”c” ); when the force available
from the tool is decreasing and not able to keep crashing the material a compressive wave ( closed
boundary condition, letter ”d” ) is detected. So, the rock is assumed to be acting as spring, which
is squeezed in a first moment and then released.
Figure 4.7: Rock model with equivalent stiffness
35
36. 4.4 Energy released through mechanical interaction
The essential problem to be solved in the design of a percussive drill is the transmission way of
the energy produced by rapidly repeated impacts of a piston to one end of a long, slender, drill
column, and effectively utilizing this energy to shatter the rock at the other end of the column.
The energy transfer in this mechanical contact occurs via impact-induced elastic waves through the
bodies. The energy contained in such a strain wave is given by:
Energy =
A · c
E
t
0
σ2
dt (4.19)
where σ is the stress and A the cross-sectional area of the rod.
Since the energy is dependent on σ2 it is possible to transmit an equivalent amount of energy at
high stress level and relatively short wavelength or at low stress level and longer wavelength. It
Has been verified experimentally by Atlas Copco as showed in the video [13], but it is also possible
to find theoretical proves, that the second method is more efficient for the energy transmission. It
means higher penetration and longer life of the piston, bar and all the elements involved in the
contact. Of course the level of the stress must be enough high to crush the rock, e.g. for the
concrete ( that is one of the material worked with this breaker ) must be at least 150 MPa. High
stress-level waveforms might be used for cracking hard rocks, but this leads to an increase in energy
losses in the system, plastic deformation and fatigue, with consequent reduction in the service life
of the drill rods.
By considering the tool used in the current breaker, its fatigue limit is 300 MPa. Thus, it would be
desirable to have long wave with a stress level between 150 and 300 MPa. As can be seen the design
and control of the waveform is of great significance both from the viewpoints of rock penetration
performance and the life of the drill rods.
The control of the stress waveform is obtained by the design of the geometrical shape of the piston
and by variation in its striking velocity. Variations of the impact velocity of the piston produce
a direct variation in the amplitude of the stress wave, while the piston geometry determines the
profile of the stress wave, i.e. the manner in which the wave amplitude changes in a single pulse
[7].
36
37. 4.5 Stress waveforms - Examples
In the following plots obtained from the software Hopsan NG that will be discussed afterwards, is
showed what so far has been said about the stress waveform, in particular the stress magnitude
measured at the half of the length of the tool used for this kind of breakers ( technically called chisel
). The impact velocity used in the figure 4.8 is 9.7 m/s, that is what reasonably might be found
in actual operations with the breaker that is going to be presented. The simplified geometries
considered to obtain these results are reported at the end of this chapter, the cross-sectional areas
are all circular. The chisel shape ( figure 4.10 ) is not the one used in reality, but what must be
taken in according to the standard tests to measure the performances of the hand-held machines.
In reality the conditions are little bit different, but the results are still valid.
Discussion of the results
The figures 4.8 and 4.9 show waveforms really different from the one in the figure 4.3. The profiles
are jagged and with different peaks due to the considered geometry, of course it is easier treat one-
dimensional stress waves and it is well known that such an approach features limitations. Leaving
at the readers a proper detailed study, it is necessary to know that the conditions to apply this
theory for the current machine has some limitations.It must be verified that the length of each
component is much bigger than its cross section diameter ( or equivalent cross section diameter ).
This is not exactly the case, because between the chisel and the piston in this machine there is
an intermediate-short body called anvil, whose length is comparable with its average cross section
diameter.
In the figure 4.8 it is clear how the different piston shape influences the waveform, meanwhile in
the figure 4.9 how a different piston velocity modifies the magnitude of the wave. The curves show
distortions because of the multiple reflections that take place, due to the different cross-sectional
areas of the components involved and their internal damping caused by the material they are made
by ( in this case is steel for all ). It is important to remark what as said about the energy content of
the wave. As the energy released by the piston is the same but their length is different, the shortest
piston releases a wave that is shorter as well and has an high-level stress. The maximum value is
close to 300 MPa that means in reality the component’s life might be compromised. In reality the
final cross-sectional area of the chisel is wedge-shaped, thus the real stress would be higher. The
waveform of the actual piston used in the breaker instead, is longer and most of its part is above
the 150 MPa ( that as said before is the lower limit to break the concrete ).
It is clearly showed that the longer piston must be preferred to deliver better working conditions,
also because the longer is the useful part of the wave the easier is the rock destruction.
37
38. Figure 4.8: Stress waveforms - Two different piston geometry
Figure 4.9: Stress waveforms - Same piston and different impact velocities
38
40. 4.6 Rtex 25 - New concept of pneumatic breaker
Figure 4.11: Rtex25 - Pneumatic breaker
The Rtex25 represents a new concept of pneumatic breaker made by Atlas Copco’s pneumatic
department located in Kalmar ( in Sweden ). The innovations of this new product can be found
throughout its structure and its operation. A pneumatic breaker is so called because of the pres-
surised fluid used to make it work, that is air. Thus, a compressor is needed as power source. Some
features of this breaker are shared by others of the same class that use different power source, e.g.
petrol-driven breakers or hydraulic breakers.
The Rtex 25 weighs 25 kg and, as will be showed afterwards, it is able to release at least 70J of
energy, an amount normally available with breaker whose weight is at least 30 kg. Here comes
up the first feature of this product, that is perform the same work with less fatigue required by
the operator, or do the same work in less time increasing the productivity. This result has been
reached modifying one the most important elements that composes this breaker, the piston. The
piston, indeed, is the one showed in the chapter 4.5. It has been seen that the longer is piston’s
length and the bigger is the interaction time between the piston and the chisel in turn in contact
with the material to crush. Various tests and video have been made by the company [13] along
with simulations ( that will be showed in this work ), to prove that the longer is the primary wave
released by the piston the easier is the destruction of the rock, because the power produced is more
useful and less of it is lost.
Slimmed silencer, wide range of chisels, solid body design and built-in lubricator, results in less
maintenance, longer machine life and easy operator’s prospective to see where he is working on.
The main parts of the breaker are showed in the figure 4.12.
It is important to point out the fundamental element called anvil, that separates the piston
from the chisel, because its function is really crucial for two main reason:
1. It avoids that dust and particles go from the surrounding up into the machine during the
40
41. Figure 4.12: Rtex25 - Main parts
normal operation, preventing wear corrosion and more maintenance;
2. During the mechanical interaction to transmit the shock wave, the reflections from the rock
travel back to the chisel which, without the anvil, would bounce back hitting the piston.
This would create an enormous amount of vibrations felt by the operator through the handle.
Moreover the pressure in the breaker’s chambers would be affected a lot, resulting in a further
increase in vibrations and noise. It has been showed how dangerous is a long and permanent
exposure to this kind of vibrations, thus everything would have ended up in less effective hours
of working, to avoid permanent damage to the operator, or the use of some damping systems
that would have increased the breaker’s mass, complicating its design and compromised its
slender shape, which are the key factors of the breaker itself. However, it is not case thank to
the anvil. Indeed, when the chisel bounces back it hits the anvil and in turn the vibrations
are transmitted to the breaker’s main body that dampens them. What the operator feels in
this case is a vibration-level much lower than before. So, as mentioned in the chapter 3.2,
a good design of the machine can reduce the vibration level. In this case the situation is
handled so well that no dynamic absorber is needed in order to stay within the limits for the
vibration regarding this machine ( see figure 3.10 ).
Other important features play a relevant rule about the low vibration level of the machine and will
be presented later, when the working principles of the machine are going to be discussed.
Last but not the least, the air consumption of this breaker is much lower than the other breakers
41
42. available on the market with the same power. It has said before indeed, that this new machine is
more than simply comparable with others whose weight is around 30 kg in order to have the same
energy level. If normally the air has two inlet, in both the upper and lower chamber to create a
pressure difference required to move the piston, in this machine there is only one inlet. The same
air is used for each cycle to push the piston down during the working stroke and to raise it up
during the return stroke.
42
43. 4.6.1 Functioning principles
The use of simulation for these kind of machines is really important, because it is not possible
adjust the machine once it has been built. Its behaviour differs if the material to work changes, so
different feed force by the operator and different vibrations level are expected. As a consequence,
the simulation help the goal to reach a robust desing.
The functioning principles of the machine are discussed below.
4.6.1.1 Positioning of the chisel and full throttle sequence
Figure 4.13: Rtex25 - Starting the machine
Pushing the trigger down, more o less at the half of its possible stroke, the machine starts to
work at low power level. The inlet valve is not fully open creating a restriction in the inlet orifice.
This allows the operator to position the chisel in the right working point, since the air is flowing a
low rate and consequently the power is low as well. This makes easier moving the breaker precisely
before to use its maximum power.
While the air is coming in, the upper chamber is pressurised and in it there are two channels: one is
always open to pressurise the so-called ”I-duct” ( which function will be later discussed ), whereas
the ”pilot-duct” is pressurised partly both during the working and the return stroke. In the same
time also the oil chamber receives the air flow.
Internal dosing feeder
When the trigger is released the upper chamber is connected to the atmosphere, the air in the
oil chamber faces a lower pressure in the upper chamber. It is drawn in it by suction, passing
through a bronze brush and being mixed with some oil allows the lubrication of the machine. This
43
44. oil then goes to the exhaust along with the air.
4.6.1.2 Phase 1 - Working stroke
Figure 4.14: Rtex25 - Working stroke
The pressure difference in the two chambers pushes the piston down. As soon as the holes,
indicated by the dashed arrow, are exposed to the pressurised air during the piston downwards
motion, the pilot is being pressurised. The pilot channel ends up in the main valve, whose piston’s
extreme cross-sectional areas are highlighted by black circle. As the working pressure is the same
on both of its sides ( as the I-duct is always pressurised ) but the involved areas are different,
the force balance makes this small piston move to the left, opening the channel that allows the
pressurised air from the I-duct to flow in the lower chamber.
Just before that the piston hits the anvil, the lower chamber’s pressure starts to increase in order
to push up the piston again as soon as the hit is over. The timing of the main valve is really
important, because if the pressure in the lower chamber were too high before the hit takes place,
the piston would be decelerated losing useful energy; if the pressure were too low the frequency of
the machine would be decreased ( Power=Energy*Frequency ).
4.6.1.3 Phase 2 - Return stroke
Pushing up the piston, the holes above-indicated by the dashed arrow are firstly closed by the upper
section of the piston and then opened again, connecting the pilot with the mid volume around the
longest section of the piston in which reigns the atmospheric pressure. The pilot is being discharged
44
45. Figure 4.15: Rtex25 - Return stroke
while the piston is moving upwards and air in the upper chamber flows back to the hose, which
in this case acts as an accumulator. Now the pilot is at the atmospheric pressure while the I-duct
is still pressurised, thus the piston of the main valve faces a force directed to the right side. This
movement closes the channel from the I-duct to the lower chamber and let the flow from the main
45
46. valve go to the exhaust. Almost at the same time, but a little bit later, another channel in the
lower chamber is getting opened by the motion of the piston in order to discharge it and make the
process starts over again.
4.6.1.4 Piston cushioning
Figure 4.16: Rtex25 - Air cushion
Before to start a new working stroke the piston must be braked and it is accomplished via
air cushioning ( figure 4.16 ). During the normal working conditions the upper air cushioning is
not acting. It takes over in extreme cases, for instance working on a steel plate in order to avoid
metallic contact. In the lower chamber it is active when the operator is not applying enough feed
force, leading the piston striking under the point defined by the ideal stroke ( figure 4.18 ). This
expedient avoids metallic contact and leads to a further vibrations reduction. Moreover the hose,
which acts as an accumulator and connects the breaker to the compressor, is very long and this
gives little variations in pressure in the upper chamber when the piston is coming upwards after the
hit. Little variations in pressure in the I-duct and in the all volumes and channels of the machine,
results in much less vibrations felt by the operator.
In an ordinary breaker the pressure above and below the piston is constantly shifting in both places.
The constant change in pressure adds more vibrations.
46
47. 4.6.2 Feed force and striking position
Figure 4.17: Rtex25 - Floating striking position
Figure 4.18: Rtex25 - Ideal stroke
As shows the picture 4.18, the stroke of the piston is measured ideally considering the anvil in
contact with the housing. The striking point in the figure 4.17 instead is different and also not
stable in reality, as it changes cycle by cycle. The variation of the striking point theoretically is
not a desirable working condition, because the operator will feel the handle more oscillating and
47
48. the breaker becomes difficult to control. If the striking point varies and the piston hits the anvil
in the floating-point-spot, the cushioning in the lower chamber would be really high in order to
avoid the metallic contact between the piston and the housing. This would lead to an increase in
pressure in the lower chamber that would affect the whole breaker’s behaviour. The pressure in
the lower chamber would be really high with high oscillations and this would give more vibrations.
However for different reasons this situation is the ideal one compared to other possible scenarios,
as explained in the paragraph 8.4.5.
In reality by the way, the minimum feed force to avoid the floating point cannot be really reached, at
most might be ”adjusted” to the current material. Ideally the operator feed force should be within
the range of 21-25 kgf ( 206-245 N ) to keep the anvil in a ”controlled” floating-striking position,
avoiding the air cushioning in the lower chamber to impair the working machine’s performances.
After each blow the shock waves is transferred to the chisel, in which other reflections will take place
caused by the interaction with the ground. This oscillations then are transferred to the structure of
the machine through the anvil. The latter starts to oscillates between the housing and the chisel,
hitting them continuously. The chisel’s mass used in the tests and in the simulation is almost 6 kg,
the breaker’s mass is 23 kg, while the anvil’s weight is 340 grams. Thus, the anvil can be imagined
behaving as a ”maracas”.
The figure 4.8 in the chapter 4.5 shows the primary wave released by the piston, but after that
as already said, a lot of reflections take place in the chisel through the interactions with the rock
and with the anvil as well. Each reflection that represents a compressive wave helps the cracking
process of the rock, if and only if the stress ( or equally the force ) magnitude is enough to crush
it.
The operator feed force must balance the pressure in the upper chamber the whole time. However,
in the lower chamber during the return stroke there is a pressure acting on the housing down-
wards, which acts helping the operator. In the volume around the anvil there is a pressure given
by trapped air, as a small leakage has been designed between this volume and the lower chamber.
In the chapter ”Results and comparison” will be clarified how to approximate the calculations to
obtain the operator feed force.
The figure 4.19 shows how the striking point changes when a variable force is applied, taking as
an example the current model made in Hopsan where the machine is being simulated ( without
the anvil ). It is clear how the impact position is more stable, with less oscillation and closer to
zero if higher force is applied. A more detailed analysis on the feed force will be presented in the
paragraph 8.3.
48
51. Chapter 5
Simulation - Introduction to Hopsan
NG
”Whenever a theory appears to you as the
only possible one, take this as a sign that
you have neither understood the theory nor
the problem which it was intended to
solve.”
Karl Poppet
5.1 Introduction - Different simulation approaches
Simulation is a very powerful analysis tool that supports the development and design of products
throughout the industry world. It turns to be really useful at the early stage of a design process
for evaluating ideas and designs. In this Thesis it refers to computer simulation of mechanical and
pneumatic systems. The idea is to model as more precisely as possible complex systems made by
relative simple subsystems, while the surroundings is modelled in a more general way.
The continuously growth of the computers’s capacity and simulation tools has made possible the
resolution of models further complex over the time. Thus, make less approximations when a
particular system is studied gives more knowledge about the process itself and allows the use of
smaller safety coefficient. More complex equations might be solved and more reasonable results
might be obtained.
For breakers as the one treated during this work, simulation is a very necessary tool to consider
in order to reduce the need of prototype testing. Its characteristics are to a large extent built
into the hardware, which makes it difficult to tune the machine while running. It is important to
get a robust design that will run under different working conditions, such as rocks with different
degrees of hardness. Computer-based simulations therefore offer a powerful tool for the designers
to evaluate and tune the design to achieve the desired properties. The principal requirements that
must be fulfilled to obtain efficient demolition are:
• A correct feed force to ensure contact with the rock;
• A correct impact speed between the striker and the working part in contact with the rock;
51
52. • The ”right” amount of energy must be transferred to ensure the penetration in the rock.
Modelling and simulation tools can generally be divided into two main types [14]: programs with
a high degree of generality and programs that are specialised for a specific engineering domain ( as
Hopsan NG ).
Centralized solver
This kind of solver uses the same approach, so the same tool, for modelling the total system.
It offers high generality, but has usually fewer features to support modelling. When equations with
strong non-linearities and stiff differential equations must be dealt with, conventional technique like
this must use small time step in order to be able to avoid numerical problems. To avoid this another
solution can be to model the system neglecting the dynamics regarding the non-linear components,
but even this approach may be affected by other complications. Even if there are routines able to
handle non-linear and stiff equations implicitly, they have to have some information of the dynamics
of the system, e.g. represented by the so-called Jacobian matrix. If the dynamics changes very fast
these routines have problems, moreover it is difficult to realize what it is going wrong during the
resolution and where are located the problems.
In general the basic principle of this solver is form an expression to relate the different states of
every component in a system in addition to their variations over the time.
Distributed solver
With a distributed solver the system can be described by parallel processes, where each com-
ponent or group of components can be simulated in parallel on separate processors. In this way the
processing will be also physically distributed. The approach of modelling each subsystem with a
tool developed for the engineering domain of the subsystem, makes the modelling more convenient.
Acting like that, follows the obligation to connected together each subsystems in one single model
( considering that theoretically each subsystem uses a different solver ). Different solvers that ex-
change data during the simulation can be used ( so called co-simulation ).
Naturally the choice between these two different approaches depends on what must be simulated.
It is clear that if the sub-models are similar, is more efficient use the same solver avoiding the
data transfer between the sub-models. On the other hand, if their dynamics are dissimilar, the
centralized solver has huge problems to handle the total system at the same time. Thus, in this
case, using different solvers is clearly more convenient.
52
53. Figure 5.1: Centralised solver vs. Distributed solver
5.2 Fluid power system - Use of distributed modelling - Hopsan
NG
In the fluid power systems the equations to be solved are very stiff and have non-linearities. This
leads without hesitations to choose a distributed modelling approach that is what the software
employed ( Hopsan NG ) is based on to simulate the above-discussed pneumatic breaker. This
software is developed at the Department of Fluid and Mechanical Engineering Systems at Link¨oping
University [15]. The philosophy behind the software is to utilise a time delay in the propagation of
information between different parts in a system. This can be done introducing line element between
components, so-called Unit Transmission Line (UTLs) [14]. The components can be of two different
type:
1. C-type ( the UTLs element for instance ) : components such as volumes, pistons and pipes
in which the characteristics, which have the same dimension as the effort variables, are calcu-
lated. This components is the key to model time-delays assuming that the delay is lossless.
The model equation become decoupled by the delays and much easier to solve. It is easy to
imagine for a steel bar, as it has a certain length and it takes a while for the compressive
wave to go from one end to another one of the material. In hydraulics and pneumatics ( the
latter showed in the paragraph 5.4 ) a good candidates for delay line are components that
contain some amount of medium, because the delay is caused by waves travelling through the
medium itself;
53
54. 2. Q-type: components such as valves and orifices. Flows variables ( such as flow, speed and
electric current ) are calculated and the characteristics are adjusted to become efforts variables
( such as pressure, force or electric potential ) in the C-type. An orifice ( Q-type ) does not
really contain any air/oil, it is just a infinitesimally small point. So, there can be no delay of
waves and it is modelled as Q-type component.
These components are combined into a system and solved using the method of characteristics.
54
55. 5.3 Method of characteristics
5.3.1 Introduction
As explained in details in the papers [14] [16], this method can be employed to solve both the
mechanical part as well as hydraulic or pneumatic part of a system. This represents a distributed
way of solving equations using also separate processors (a). This method can be used to simulate
pipelines with distributed parameters, short line regarded as lumped parameter and for pure in-
tegration. In the latter case is demonstrated that this method coincides, in the fashion to treat
the equations, with the trapezoidal rule for integration, that is a numerical method always stable
(b). The (a) and (b) properties enable a faster resolution of the simulations, compared with the
conventional approach.
In whatsoever hydraulic/pneumatic system there is always between every hydraulic/pneumatic
component such as valves and cylinders, a pipe or a volume. Extended in the flow direction, they
can all be considered as transmission lines. Each physical component is represented by subrou-
tine and they are then connected to form the complete system. The information transfer between
the components travels at speed of sound. Consequently, there is no immediate communication
between components that are separated by some distance. No big system of equations must be
solved, instead it will end up in solving very small systems of equations.
5.3.2 Wave propagation
To simplify the explanation a transmission lines is considered. More appropriate details can be
found in [14]. From the distributed transmission line in figure 5.2 the well known four-pole equation
Figure 5.2: Hydraulic transmission line
can be derived, in the frequency domain:
AL BL
CL DL]
·
Q1
P1
=
−Q2
P2
55
56. where
AL = DL = coshTs N(s)
BL = −(
1
ZcN(s)
)sinhTs N(s)
CL = −ZCN(s)sinhTs N(s)
ZC =
ρ · a
A
(5.1)
Zc is the characteristic impedance and a is the speed of sound in the medium in which the wave
travels, in this case the oil in the pipe. If the frequency dependent friction factor N(s) is neglected,
the relations between flows and pressures at the both ends of the line become:
p1(t + T) = p2(t) + Zcq2(t) + ZcQ1(t + T)
p2(t + T) = p1(t) + Zcq1(t) + ZcQ2(t + T) (5.2)
where T is the time taken by the wave to go from one end of the transmission line to the other one
T =
L
a
(5.3)
A problem that arises with this approach comes from the principle to assume a time delay of at
least one time step between two Q-type components. This means that if the time delay in the real
systems is less then the time step used in the simulation, a non-physical inductance will appear
between them, so-called parasitic inductance. This is however not a large issue, because in reality
there are always time-delay, so this inductance is normally of second order.
As the transmission lines are used between components, they enable them to solve their own equa-
tions accelerating the simulation without any numerical stability-related problems. Moreover, if
for example a component containing a certain number of state variables is considered and solved
with a centralised numerical solver, the size of the problem grows more than linear to the number
of states in that component. Using transmission lines, the time needed for a simulation is directly
proportional to the number of states in that component.
Finally, this approach has its appeal in the fact that it is possible to keep track not only of the
different states in a system, but also how the information propagates in the system itself.
Transmission line and the waves of information: c1 and c2
If the old information from the other end of the line is denoted c, the equation 5.2 can be written
as
p1(t + T) = Zcq1(t + T) + c1(t)
p2(t + T) = Zcq2(t) + c2(t) (5.4)
where the waves of information from one end of the line to the other one are written as
c1(t + T) = p2(t) + Zcq2(t)
c2(t + T) = p1(t) + Zcq1(t) (5.5)
56
57. Combining the equations in 5.5 with the ones in 5.4 the characteristics can be calculated as
c1(t + T) = c2(t) + 2 · Zcq2(t)
c2(t + T) = c1(t) + 2 · Zcq1(t) (5.6)
The system works in the following way. Take for example the figure 5.2 and it is decided that c1
is the incident wave and c2 the reflected one. If the left end is closed, q1 is zero and the reflected
wave c2 will be equal to c1 ( equations 5.5 ) thus no energy has been added or lost. If an orifice
had been placed on the left end and it was connected to a tank, a negative q1 would have been
the effect. The wave c2 would then have smaller amplitude than c1 after the reflection. The latter
means that energy would have been lost in the view of the transmission line.
57
58. 5.4 Hopsan NG - Pneumatic components
In order to build whatsoever simulation model in Hopsan, the company in collaboration with the
Link¨oping’s university has modelled the following components creating a library on their own (
figure 5.3 ). It is possible simulate the filling/emptying of volumes connected mechanically with
Figure 5.3: Pneumatic Components
piston or mechanic elements via valves and orifices. The light blue indicates that the connection
involved is between pneumatic components, instead the dark blue ( as in the ”pneumatic mechanic
connection” component ) means that is possible have two separated connections with two mechani-
cal elements. Therefore, this component is an interface between the mechanical parts of the system
and the pneumatic ones, as in the middle it has the light blue colour. Moreover, when the colour
is surrounded by a grey circle it means that more the one connection is permitted by that port. In
this case more pneumatic Q-components can be connected to this one.
The ”Orifice and Leakage” components instead have two inwards triangle and two outwards one.
The first are used to take some quantity as a reference to move the piston inside the component;
the latter instead gives as output the movement of the piston inside the component itself.
Missing component
Another thing must be highlighted about the available pneumatic library in Hopsan NG, since
an important component used in modelling the hydraulic systems is not available in the pneumatic
library yet. In the pneumatic field the most important difference compared with the hydraulic field
is that the fluid treated is air, which is compressible. This does not allow to use the hypothesis
of incompressible fluid, that complicates the resolution of the equations involved. A long line,
which can be represented by the pilot duct showed in the figure 4.14, is alternatively filled up
and discharge with air. In order to study the process with a compressible fluid using Hopsan, the
differential equations involved must be solved discretizing the volume in small parts and for each
handle the equations for each part. The process is so complicated and moreover the company’s
58
59. attention on the pneumatic modelling is relatively new, that a component like this is not available
yet.
Indeed, this software was born to study hydraulic systems, whose library is quite big and able to
cover, so far, a lot of necessities.
By the way, theoretically it would be possible to simulate a long line of a fluid like air, by using
in sequence a desired number of ”pneumatic volumes” as the one showed in the figure 5.3. As
mentioned in the paragraph 5.3.2, a component like this has a length equal to the product of the
time step times the sound’s velocity. If for example air at 6 bar is considered the sound velocity can
be approximately stated to be around 600 m/s; the time step used to simulate the current breaker
is 4e−7s. This means that the length of such component would be around 2e−4m == 0.2mm. If
we consider that the breaker’s height is not more the 80 centimetres and the pilot duct’s length is
long as the breaker’s height, the number of volumes needed would be 4000. As the simulation time
would be increased a lot because of the high number of components ( e.g. the actual simulation
model has not more than 40 components ), this solution is quite far to be considered reasonable.
However, there are other ways to easily overcome this problem as explained in the following chapter,
but of course the modelled system will be a little bit ”distorted” from the reality.
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60. 5.5 Dymola vs. Hopsan
5.5.1 Dymola introduction
Dymola is a very powerful simulation tool that can be used in many areas: automotive, aerospace,
robotics, process etc. As the knowledge of the author is not so deep in this software, the discussion
will be directly applied at the feature the company is interested in for studying this new pneumatic
machine, leaving to the interested people the will to examine in depth the software itself [17].
The company has built the model in Dymola in order to design the actual breaker, with the aim to
forecast the results if some changes would have taken place in the machine and evaluate different
design solutions. However, now that the breaker is released on the market, in order to add improve-
ments and get a better understanding of the real processes involved, Dymola has revealed some
not trivial shortcomings. Moreover, also the cost aspect has been considered and it is by no means
negligible. Dymola indeed is an expansive software, instead Hopsan is completely free. Thus, it is
possible download the software and build whatsoever component or library the user needs, as Atlas
Copco has done. Indeed, the above-showed components are not present in the default version of
the software, but they have been build by the company itself.
5.5.2 Dymola-Problems and Hopsan-Features
The same problem discussed in Hopsan about the simulation of a long line of compressible fluid is
encountered in Dymola. Initially with Hopsan the same expedient has been used to overcome this
problem as it has already been done in Dymola. However the author used a different approach,
after he had realized that it is not straightforward to handle the model in this way.
What the company is really interested in, is the simulation of the floating-hitting point. In Dymola
the model does not allow this study, moreover there is no chisel or anvil body modelled. To simulate
the percussive mechanism the software allows the user to set a piston’s rebound velocity after the
hit. In the final Hopsan’s model instead, the whole system is being simulated. A variable feed
force can be applied either to simulate the fixed-hitting point and the floating-hitting condition.
As the real system is modelled, the vibration study can be approached as well. Furthermore a rock
component will be used to simulate the real material, studying the rate of penetration and the
rock-chisel interaction.
As the floating-striking-point model in Hopsan is quite complex, also a fixed-striking model as in
Dymola has been built. This let the straightforward implementation of simple changes in the last
one before to approach at the more complex floating model.
60
61. Chapter 6
Hopsan NG - Models: Fixed/Floating
hitting point
”If you can’t understand it without an
explanation, you can’t understand it with
an explanation”
Haruki Murakami
6.1 Fixed-hitting-point system
6.1.1 Introduction
The first phase of this work deals with the model of an ideal system regarding only the percussive
mechanism, in which are not considered the feed force given by the operator, the chisel and the
material. In order to do this a special component has been used ( figure 6.1 )
Figure 6.1: Rock/Rebound component
The main concern in this stage is to make the percussive mechanism works, that is realize correctly
the dynamic of the piston before to approach at the complete ( and more complex ) system. The
parameters to set inside this component are the average area and the length of both the piston and
the chisel, but most important the recoil velocity for the piston after the hit. As showed in the
chapter 4.2, depending on the respective cross-sectional area of the piston and the chisel, the first
after the hit might have a certain recoil velocity. Based on the company’s experience, the coefficient
61
62. has been set to 0.1 both in Dymola and in Hopsan. Thus, using the recoil velocity of the piston is
0.1 times the impact one.
Modelling problem: Approximation of the long channels
One big issue regards the modelling of long channel filled up by compressed air. This problem
has been already mentioned in the chapter 5.5. In both the software the problem has been solved
with different ”tricks”. Basically instead of a long line which has at its ends a drop pressure that
forces the air to flow in it, a simple volume is used and the process involved is to fill this volume.
Naturally the dynamics regarding the air is completely different, as a ”static” air in a volume sub-
stitute a dynamic fluid flowing in a line. In Dymola the solution applied is to change the position of
the orifices involved in the filling/discharging processes regarding the pilot and the lower chamber.
This solution makes the model tricky to handle if, for instance, a bigger breaker must be simulated.
The Rtex 25 will be come along with other two breakers, once smaller Rtex 15 and the other one
bigger Rtex 35 ( the numbers represent their weight in kilograms ). These new machines have the
same working principles but different geometry. The time to set-up the model might be long as
every time the position of the orifices must be guessed to find what are supposed to be the real
performances of the breaker. Moreover, the Rtex 15 and 35 are still in their designing phase and
no prototype is still ready, thus the guess has no fundamental at all.
In Hopsan the geometry of the breaker remains the same, while the approximation to time properly
the valve with respect to the filling of the pilot channel has been solved using an heavier piston in
the valve itself. The latter piston can be set up with a different mass to control the dynamics of
the valve, contrasting the too fast filling process for the pilot channel in the simulation in order
to open and close the valve when expected. The mass has been set up for the Rtex 25 and then
using some mathematical relation, the piston’s mass for the other two different breakers can be
estimated. These formulas in addition to the goodness of the resulting pressure profile in the lower
chamber, leads to a less time to prepare new models. This process will be explained afterwards (
paragraph 8.6 ) and it is quite straightforward as well.
6.1.2 Hopsan model
The figure 6.2 shows a simplified view of what has really built in Hopsan. The author decided to
simplify the explanation showing a schematic view of the process, because of the likely difficulty
encountered by the reader in facing the real model. The showed model, indeed, will not work if
launched like it is because important linking components are missing. These components involve
only the simulation process, but can be neglected to explain the design idea behind the modelling
of this machine.
General scheme
The various parts of the breaker are lumped together in subsystem. Following the legend, the
red line represents the high pressure line. From the inlet the air flows into the upper chamber and
then into the main valve. During the working stroke, when the pressure in the pilot is at a proper
level, the piston in the main valve is being moved to the left ( figure 4.14 ) and from the I-duct the
air goes into the lower chamber. After the strike the piston bounces back and its motion opens an
62
63. Figure 6.2: Hopsan scheme: fixed hitting point model
orifice that connects the lower chamber and the pilot to the exhaust.
Both the upper and lower chamber are simulated with those two components called ”pneumatic
mechanical connection” with walls that surround a dead volume. As this system is ideal and neither
vibrations of the housing nor real recoil velocity for the piston are considered, a fixed boundary
condition can be applied to simulate the housing itself ( see the component called ”fixed” figure
6.2 ), which consequently is stiff.
Design of the Lower chamber and striking point
The quadratic component with a red circle does not represent anything, it is just needed to link
the piston and the rebound component ( the light blue arrow ) through the green connector. The
latter one has two different ports on the piston side. One is a continue line used to connect one
of the wall of the lower chamber; the other connection works differently. The first one means that
the upper wall of the lower chamber follows the bottom surface of the piston during its motion.
This is due to the fact that also in reality the distance between this piston surface and the housing
determines the lower chamber volume. This wall has the same cross sectional area of the piston at
63
64. which is connected. The other part of the connector has a separation, this means that after the
hit the piston is moving independently from the following component. Now this component is this
light blue arrow, but later on will be the anvil. So after the hit and using that separation, the
model simulates what actually happens, that is the piston moves upwards and the anvil on its own.
Now the anvil, the chisel and the rock are replaced by the rebound component. Thus, after the hit
the piston bounces back from it with a certain recoil velocity.
Design of the upper chamber and the main valve
For the upper chamber one connector is used. Since there is no feed force because we have supposed
the housing to be stiff, one mechanical connection fixes one side of this chamber whereas the other
one follows continuously the piston’s motion. How the main valve has to work depends on the
piston position. A dashed blue arrow is used to pass inside the subsystem the piston’s position, so
that can be used to set the piston in the main valve as it is in reality. This valve is a 3/2 valve (
three ports and two positions ):
• The first position can be assumed to be the one which allows the flow to go from the I-duct
into the main valve ( first port ) and then to the lower chamber ( second port ), in both cases
the flow path is highlighted with a red line;
• The second position is the one which let the flow from the main valve to go to the exhaust (
third port ), the flow path is the blue line.
64
65. 6.2 Floating-hitting-point system
6.2.1 Introduction
In this model instead the whole system is considered. The rock’s behaviour is supposed to assume
the same features characterising the steel balls ( in the next chapter will discussed briefly ), that is
the material used by the company to measure the breaker’s performances. If the rock is too hard
it increases the recoil velocity of the piston if the chisel’s length is not appropriate, so it ends up
in more vibrations. Thus, the rock component in Hopsan must be set properly and its modelling
is showed in the following chapter.
About the complete model, a study about the right feed force that is to be applied has been done.
In reality the operator is not able to give more than 24-25 kgf ( 235-245 N ). In the real test of
the machine to be able to measure its performances in a standard fashion in order to have stable
conditions, the feed force applied is 56 kgf ( 549 N ) by using straps. This value has been chosen
both from an heuristic point of view and the from behaviour of old company’s machines. What
practically change is that during the tests the striking point has almost no variation, in order to have
the breaker working in a stationary state. Thus, we can consider almost 56 kgf as an ideal operator
force to achieve the fixed-hitting-point condition ( but will be clear in the paragraph 8.4.5 that this
working condition is not ideal at all ). As in reality the real feeding is lower, the floating point
is the actual situation. The result is that the piston has a longer stroke, higher impact velocity,
lower frequency and less vibrations on the machine. The latter point will be clearly explained in
the chapter regarding the vibration analysis 8.4.
65
66. 6.2.2 Hopsan model
Figure 6.3: Hopsan scheme: floating hitting point model
This model considers the feed force and also the chisel. The component used to model the chisel
is divided in five sections and between the fourth and the fifth, a sensor is connected to measure the
force magnitude related to wave released by the piston and its subsequent reflections. Dividing this
value by the current area of the chisel the stress is retrieved. In reality during the tests, in the same
position is located the strain gauge to measure the stress waves in the chisel via the measurement
of its strain.
Design of the Lower chamber, Housing and striking point
The housing is modelled with one mass ( called ”breaker mass” ), in which all the machine is
lumped together ( the housing and the two handles are one mass in the simulation ). In reality the
vibrations are damped by the structure itself that is a distributed body, instead here everything is
represented by a point whose weight is equal to the breaker’s one ( except the chisel and the piston
). This ”point” is subjected to the force coming from the chambers and the hit from the anvil as
well. This is another approximation especially from the vibration point of view. The lower chamber
has not anymore a fixed part, but it is connected to the housing by an element called ”breaker
66
67. mass link”, that represent the material coloured with yellow in the figure 4.12 that encloses the
anvil. It must be pointed out again that the model showed is not the one that can be simulated
in Hopsan in a proper way. The view is schematic to show the basic modelling idea on which the
actual model is built on.
On the ”breaker mass” component the feed force is applied. Also the anvil has a connection with
the ”breaker mass link”. The connection chosen assures that the anvil is moving on its own and
it is free to hit both the chisel and the housing. As explained in the chapter 4.6.1 the anvil has
the task to transmit the vibrations coming from the ground to the housing in order to dampen
them. The anvil has overall three links, one to the piston, another to the chisel and third one to
the housing that and all of them are not continuous, because its motion is independent from them.
This gives the possibility to simulate the floating point using the position of the housing as an
absolute reference. Defined by the geometry the ideal distance between the anvil and the top of the
housing, when the piston strikes the current position of the anvil is recorded, that is its distance
from the top of the housing. Subtracting from this value the ideal distance, the striking point is
retrieved.
The position of the housing is also the reference system used to measure the penetration in the
rock. In the figure 6.3 is sketched the directions of reference adopted, in which the motion ( x ),
the velocity ( ˙x ) and the acceleration ( ¨x ) are positive if directed upwards.
Design of the Upper chamber and the operator feed force
The upper chamber now has one straight connection with the housing as well. The feed force
chosen at 6 bar is 40 kg, which gives a configuration setting equal to the fixed-hitting-point condi-
tion that in reality is achieved with 56 kg. In the paragraph 8.3 will be showed the analysis that
has been carried out to understand how the feed force affects the breaker’s performances.
67
68. 6.3 Different operating conditions - tuning phase
When the company had to patent the breaker, different tests have been carried out at different
working ( relative ) pressures 6, 7 and 8 bar ( the one used in reality to run normally the machine
is 6 bar ). In the model the situations at 6 and 8 bar are considered as two extremes to tune some
parameters regarding both the minimum feed force to apply to have stable working conditions and
the losses. About the latter in particular, the most important parameter is called Discharging
coefficient ( Cd ). This coefficient decreases the actual area through which the air flows in the
various orifices: Areal = Cd · Aideal. Practically can be seen as a parameter that considers the
turbulence in the flow. If the same setting at 6 bar were used at 8, the model would give higher
power and efficiency than the real machine. A linear relation has been used so far to change
automatically the discharge coefficient in relation with the working pressure, taking in account
indirectly the turbulence and the losses found in reality. In this way the situation at 7 bar has been
simulated as an intermediate case via a simple interpolation.
The losses have been added ( see figure 6.4 ) at the inlet valve ( yellow circle ), at the section that
allows the flow to go from the I-duct to the main valve ( green circle ), at the one in charge to
connect the main valve to the lower chamber ( purple circle ) and at the two ones regarding the
filling and the discharge of the pilot channel ( blue circle ). These orifices have a crucial rule and
they seem the best to be chosen, also because they involve changes in section through which the air
must flow. The latter point is the main reason of losses due to the turbulence in the flow. The table
6.1 shows the parameters used as extremes to interpolate the ”Cd” coefficient when the operating
pressure change from 6 bar to 8 bar. When the soft start will be explained ( chapter 8.8 ) the ”Cd”
coefficient in all the critical points is the same used at 6 bar.
Table 6.1: Discharge coefficient - Settings to interpolate linearly vs. Operating pressure
Cd
6 bar 8 bar
Inlet 1 0,55
I-duct to Main valve 1 0,55
Main valve to Lower chamber 0,86 0,6
Pilot 1 0,6
68
71. Chapter 7
Modelling of the rock material
”As with all my work, whether it’s a leaf
on a rock or ice on a rock, I’m trying to
get beneath the surface appearance of
things. Working the surface of a stone is
an attempt to understand the internal
energy of the stone.”
Andy Goldsworthy
7.1 Introduction
It has been already described in the chapter 4.3 how the ground is modelled in Hopsan, that is
using two different stiffness. One is related with the penetration ( k1 ) and the other with the
elastic unloading ( k2 ), the latter when the energy of the wave released to the ground is not
enough to keep crashing the material. Different settings have been tried, comparing them with the
measurements performed on the real machine.
The set-up for these measurements is reported in the figure 7.1, which is the same used to measure
the vibrations as well.
• two accelerometers have been positioned respective on the handle that has not the trigger
and on the housing;
• the strain gauge for the energy measurements is not really visible as it is positioned at the
half of the chisel’s length and it is hidden in the hole in the ground;
• two straps are used to apply 56 kgf ( 549 N ) of feed force as the a normal operator cannot
feed more than 24-25 kgf ( 235-245 N ).
In order to evaluate the performances of a general hand-held power tool like the machine treated in
this work, the feed force to apply must be high enough to guarantee zero-hitting-point condition.
This is a situation in which the breaker works in a stable conditions, in other words its stroke,
impact velocity and operating frequencies have small variations from blow to blow. The chisel used
in this case is the longest one ( see table 8.1 ). It is four times as long as the piston and the strain
71
73. gauge is mounted at the half of its length. Since the piston primary wave is double the piston’s
length, the wave itself is not altered by its following reflections that will take place. Consequently
also the reflections following the primary wave will be detected without interferences. Thus, it is
possible integrate the primary wave to calculate the energy delivered by the piston and also to
study its shape.
In order to evaluate the vibration level of the machine instead, the real feed force must be applied
and an operator is running the machine. The set up is the same but the absence of the strain
gauge, because the chisel mounted now is the real one that is too short to keep it undamaged due
to the vibrations that normally occur while running the machine. Now the situation is going to be
as the real one.
Some details about the equipment used are showed below:
• Air ( relative ) pressure 6 bar;
• Sample frequency - Energy measurements : 200 kHz;
• Sample frequency - Vibration measurements : 65 kHz;
• Strain gauge: Ub 3V excitation, amplification factor 200, gauge factor k 2.095; sensitivity
V/microstrain=k*Ub*Amplification.
73
74. 7.1.1 Standard test procedure
The machine used in reality to perform the measurement is one coming from the series production.
The measurements must respect the standard ISO 8662, which in part is explained in the paper
[18] written by a working group of the PNEUROP Tools Committee. The test is called Dynaload
and it is the way used to measure the performances for percussive tools. The device consists of a
metallic cylinder filled with steel balls on which the hand-held power tool is brought to bear and
which absorbs the energy transmitted by the tool ( 7.2 ). The device can either be fixed to a surface
or buried below the working floor level. The Dynaload device absorbs the blow energy from the
power tool. Much of the shock wave is absorbed by the steel balls, however some 15 % to 20 % is
reflected back to the power tool, as would be the case in a normal working situation. The Dynaload
should be constructed to be of an appropriate size depending on the hand-held power tools to be
tested. Three preferred sizes are in use, i.e. cylinder diameters of 20mm, 40mm and 60mm, and
are related to the requirement for absorbed power capabilities. For more information about the
maintenance and all the details to be aware of, the interested reader is invited to look at the paper
mentioned before
Figure 7.2: General scheme - Dynaload
Example of a measurement - piston primary wave
74
75. Regarding the energy measurements, two tests have been carried out and for each an average
of the stress waves has been done on a time range of 1 seconds. Since the frequency of the breaker
is around 13 Hz, twelve waves have been average out and the results is reported in the figure
7.3. In Hopsan with equal sampling frequency the same procedure has been applied ( figure 7.4 )
considering one second of simulation as well.
The black line in both cases represents the average wave that can be considered as a reference
for further comparisons. In the simulation the deviation from the average wave is smaller compared
with the one in reality and for both however the highest peak is almost constant. The highest peak
in reality is followed by a lot ripples, which cover a wider range compared with the result in the
simulation. The reason lays in the motion of the anvil, which is quite different from the reality due
to the vibrations occurring also in the other two directions and not only along the vertical one (
more details in the paragraph 7.2.2 ). The latter is the only present in Hopsan, thus the model in
the software is perfectly vertical during the running ( indeed, Hopsan allows only a 1D modelling
).
75
76. Figure 7.3: Stress waves obtained from one of the two tests
Figure 7.4: Stress waves from Hopsan - k1=1e8 N/m - k2=1.5e10
76
77. 7.2 Final configuration for the ground
Before to show the results, some remarks must be pointed out. While this work was on going the
company did not have the time to perform more measurements on different materials apart the
steel balls. Consequently a problem has risen. The steel balls have their own working period and
after that they must be replaced with new ones. During the test there is not a real penetration in
them, but only a compression and then an elastic unloading so the breaker remains in the same
position all the time. In Hopsan instead the penetration is included in the model, thus the breaker
is going down in the material as well.
The figure 7.5 shows different cases analysed. Two curves are retrieved from as many measurements
Figure 7.5: Different possible settings for simulating the steel balls
and others characterise different stiffness for the rock model set in Hopsan, in which some of them
are constant whereas other are variable. In the latter case has been decided to set 5 MPa as the
absolute threshold limit to change the stiffness, in particular it takes the highest value when the
absolute value of the stress is bigger than 5 MPa. The results can be read in the three areas
highlighted, which are characterized by a specific event. The intervals which define these areas are
the theoretical ones calculated simply from geometrical considerations.
1. Piston primary wave : It is the wave released by the piston, that is practically the same
both comparing the measurements and the simulations with themselves. This let us say that
the working condition of the breaker is really stable as the energy released by the piston is
constant whatever is the rock model used. This is clear both looking at the magnitude of
the waves and at their duration. In particular can be notice that even if in the simulation
there are two main peaks higher than in reality, the shape in between is almost on the same
level of the measurements. This might be explained considering some losses due to the anvil
77
