Modelling, Simulation and
Experimental Investigation of a
Rammer Compactor Machine
by
ANDERS JÖNSSON
Division of Computer Aided Design
Luleå University of Technology
SE-871 87 Luleå, Sweden
and
Department of Mechanical Engineering
Blekinge Institute of Technology
SE-371 79 Karlskrona, Sweden
Karlskrona 2001
Acknowledgements
This work was carried out at the Department of Mechanical Engineering,
Blekinge Institute of Technology, Karlskrona, Sweden. It was supervised by
Associate Professor Göran Broman. I wish to express my sincere
appreciation to my supervisor. Working together with Göran Broman has
been a grand privilege; his exemplary support and great knowledge will
continue to influence me in all future work.
I also wish to acknowledge my gratitude to Associate Professor Mikael
Jonsson and Professor Annika Stensson at the Division of Computer Aided
Design, Department of Mechanical Engineering, Luleå University of
Technology, Luleå, Sweden.
I would also like to thank all my colleagues and friends for valuable
discussions and their support during this work. Working together with the
staff of Svedala Compaction Equipment AB has been most inspiring. I
would particularly like to thank Anders Engström for his support.
The financial support from the Foundation of Knowledge and Competence
Development in Sweden is gratefully acknowledged.
And finally, I wish to express my thanks to my family – and particularly to
my beloved life-companion, Louise.
Anders Jönsson
2
Abstract
This licentiate thesis considers the modelling, simulation and experimental
investigation of a rammer compactor machine. The purpose is to develop an
efficient and verified method for simulation of rammer compactor machines
to be used in the product development process. The experience gained
through this work is also intended to be useful for studying other types of
dynamic compactor machines.
Rammer compactor machines perform impact soil compaction. This is more
efficient than static compaction. The machines are often used in places
where a high degree of compaction is needed, and where the space for
operation is limited. The complexity of this type of machine makes design
optimisation through traditional prototype testing impractical. This has
pointed to the need for a theoretical model and simulation procedure for
predicting the dynamic behaviour of the machine. To be useful for
optimisation the theoretical model and simulation procedure must be
verified.
By concurrently working with theoretical modelling, simulations,
experimental verifications, and optimisation an efficient analysis support for
product development is achieved. This co-ordination works both ways in an
iterative manner: experimental investigations are used to verify theoretical
models and simulations; and theoretical models and simulations are used to
design good experiments. This Complete Approach concept enables better
decisions to be made earlier on in the development process, resulting in a
decrease in time-to-market and improved quality.
In this thesis, the Complete Approach concept is applied to a rammer soil
compactor machine. An introductory iteration is described. The good
agreement between theoretical and experimental results indicates that the
theoretical model and simulation procedure should prove useful in
introductory optimisation studies. The thesis discusses reasons for the
remaining discrepancy and suggests improvements in both the theoretical
model and the experimental set-up for future iterations.
Keywords: Soil Compaction, Non-linear Dynamics, Theoretical Modelling, Numerical
Simulation, Experimental Verification, Complete Approach.
3
Thesis
This thesis comprises an introductory part and the following papers.
Paper A
A. Jönsson, G. Broman & A. Engström, Modelling of a Soil Compaction
Tamping Machine using Simulink, Proceedings of the MATLAB DSP
Conference, Espoo, Finland, 1999.
Paper B
G. Broman & A. Jönsson, The Nonlinear Behavior of a Rammer Soil
Compactor Machine, Proceedings of the EM2000 ASCE Fourteenth
Engineering Mechanics Conference, Austin, Texas, 2000.
Paper C
A. Jönsson & G. Broman, Experimental Investigation of a Rammer Soil
Compactor Machine on Linear Spring Foundation, Accepted to the
NAFEMS 2001 World Conference, Como, Italy, 2001.
4
Contents
1
Introduction............................................................................................6
1.1
1.2
1.3
1.4
Compaction of Soil......................................................................6
Compactor Machines...................................................................7
Non-linear Dynamics...................................................................8
Product Development ..................................................................9
2
Aim and Scope of the Present Work ..................................................12
3
Summary of Papers..............................................................................15
3.1
3.2
3.3
Paper A ......................................................................................15
Paper B ......................................................................................15
Paper C ......................................................................................16
4
Conclusions...........................................................................................17
5
References .............................................................................................18
Enclosures
Paper A
A. Jönsson, G. Broman & A. Engström, Modelling of a Soil Compaction Tamping
Machine using Simulink, Proceedings of the MATLAB DSP Conference, Espoo,
Finland, 1999.
Paper B
G. Broman & A. Jönsson, The Nonlinear Behavior of a Rammer Soil Compactor
Machine, Proceedings of the EM2000 ASCE Fourteenth Engineering Mechanics
Conference, Austin, Texas, 2000.
Paper C
A. Jönsson & G. Broman, Experimental Investigation of a Rammer Soil Compactor
Machine on Linear Spring Foundation, Accepted for the NAFEMS 2001 World
Conference, Como, Italy, 2001.
5
1
Introduction
1.1
Compaction of Soil
Soil has been used as a construction material since early civilisations for
constructing roads, canals, embankments for dwellings and fortifications [1].
The knowledge of how to use the material was initially passed on from
generation to generation by word of mouth. Later on, the written word
became important as a means of increasing knowledge about soil properties
and handling. The Dschou-Li, a book about the customs of the Dschou
Dynasty written in China about 3000 B.C., contains instructions for the
construction of roads and bridges [2]. The Ten Books on Architecture is one
of the oldest purely technical texts describing soil-based construction. This
text was written by the Roman engineer Vitruvius in the first century B.C.
[3].
During the mid-1600s, France initiated a large civil engineering program for
roads, canals and border fortification systems. This resulted in the first
engineering school in Europe, Ecole des Ponts et Chaussées, established in
Paris in 1747. This school was to influence all future scientific development
in civil engineering. The building of railway lines at the beginning of the
1800s raised demands on the underlying structure and demonstrated the need
for a scientific approach. During the first half of the 1900s, soil compaction
tests and the relationship between density, moisture, strength,
compressibility and other soil properties were studied and developed; see,
for example, [4,5].
There have been major developments in construction equipment since the
early days of civil engineering. In ancient times, humans and animals were
used for compaction and hauling. Developments were rapid during the
industrial revolution; and in 1859, M. Louis Lemoine of Bordeaux, France,
was granted a patent for a steamroller. In 1906, a patent was issued for a socalled sheep foot roller, which increased the efficiency of soil compaction.
Compaction was limited to the surface layer because it was believed that the
fill would settle by itself.
6
The evolution of the infrastructure brought about by mainroads during the
1920s resulted in the use of higher embankments. The latter required the fill
to be compacted from the ground to the surface. This necessitated larger and
heavier compaction equipment with a higher capacity.
1.2
Compactor Machines
Compactor machines are designed to consolidate earth and paving materials
to sustain loads greater than those sustained where there is no compaction.
The machines range in size from small hand-held tampers to large machines
weighing more than 50 tons. Static loading for compaction is an old
technique. To make the compaction more effective many machines include
vibratory action so that compaction is achieved by impact force rather than
sheer weight; see, for example, [6-11]. All early works focused on
experimental investigations. This is not sufficient, however, to support an
efficient product development process. For more extensive parameter
studies, theoretical models are also needed.
Theoretical modelling of soils and compactor machines started to appear in
the 1950’s [12-14]. By using modern computers for simulations, it is
possible to simulate more complex behaviours [15-19]. Most of the
simulations performed during the last decades have focused on vibratory
rollers.
Published descriptions of measurements on rammer compactor machines are
rare. In 1963, Borchert [20] made some measurements on large rammer
compactors. Filz and Brandon [21] performed force measurements on a
rammer compactor in 1993.
The design of compactor machines now concentrates to a high degree on
modifications of established designs to increase speed, efficiency, accuracy,
and operator comfort and safety. An introductory optimisation study of a
rammer compactor machine has been performed by Broman et al. [22].
The need for civil engineering equipment is still an important feature of
modern society since major changes occur in the infrastructure all the time.
Most civil engineering projects have high associated costs. This means that
an increase in efficiency during the construction phase is usually highly
advantageous from an economical point of view.
7
1.3
Non-linear Dynamics
The classical study of a mechanical system often starts with the use of
Newton’s Law F=ma. For the three centuries after the publication of
Newton’s Principia in 1687 (a reproduction in Swedish can be found in [23])
it was believed that the behaviour of every system described by particles
could be predicted indefinitely if their initial conditions were known.
However, it has also been recognised for some time that complex systems
exist that cannot be studied deterministically, for example, turbulent flow.
The problem is the large number of degrees of freedom, and the complexity
of the relationships between the particles. Systems with different kinds of
non-linearities have also proved difficult to simulate due to the problem of
finding analytical solutions.
The introduction of fast computers has recently increased the study of nonlinear systems. These studies have revealed that even very simple systems
can exhibit highly complex behaviour that cannot be predicted far into the
future. Such motions have been labelled chaotic. Their topicality value as a
research area is increasing with the growing capacity of computer
simulations. In current publications, chaotic is defined as the motions in
deterministic systems whose time history has a sensitive dependence on
initial conditions [24]. Some examples of systems known to exhibit chaotic
vibrations are: systems with sliding friction, non-linear acoustic systems,
feedback control devices, flow-induced problems, and mechanical systems
with play or backlash.
Impact compactor machines are included in the last group. Broman and
Jönsson have proved that the rammer machine of this work is capable of
exhibiting chaotic behaviour; see paper B. The study of non-linear systems is
often more complicated than that of linear systems; and the intuition gained
from many years of studies of linear systems can often be misleading when it
comes to studying non-linear systems.
Understanding non-linear systems places greater demands on the underlying
theoretical knowledge of the system when doing simulations since the
system is often sensitive to parameter changes. By slightly changing a
parameter value, completely different behaviour can be produced; such is not
8
the case for linear systems. Ignoring non-linearities will in some cases give a
completely false description of the real system.
1.4
Product Development
High quality, low price and short time-to-market are essential aspects of the
modern manufacturing industry. Customer requirements are rising at the
same time as the products are becoming more and more complex.
Suggestions for a successful product development process can be found
widely in a large number of publications; see, for example, [25-27].
Although there is a great variety of strategies, a common conclusion is that
changes in product design introduced late in the product development
process are extremely costly and should be avoided.
The paradox of the design process is that knowledge about the problem and
its potential solutions is gained throughout the process and, conversely,
design freedom is lost as the project proceeds. This is demonstrated
schematically in figure 1.
100
Knowledge about
the design problem
Per cent
Design
freedom
0
Time into design process
Figure 1. The design process paradox, reproduced from [25].
During the design process, design decisions constrain the design, as
illustrated by the “Design freedom” curve. The “Knowledge about the design
problem” curve is a learning curve for the problem. It is obvious that the
learning curve should be as steep as possible so that maximum knowledge
9
about the problem is obtained as early as possible in the design process,
while the freedom of design is still large.
Modern simulation techniques enable one to test many different design
concepts early on in the design process. Of course, simulation procedures
must be verified in some way if they are to be useful as a basis for design
decisions.
At the Department of Mechanical Engineering at Blekinge Institute of
Technology, a concept for modelling, simulation, verification, and
optimisation has been implemented in both research and education; see
figure 2.
Simulation
Theoretical
Modelling
Project
Coordination
Experimental
Verification
Optimisation
(Re)designing
Market Changes
New Technology
New/Modified
Product
Figure 2. Complete Approach for analysis support in product development.
In short, theoretical models describing interesting product characteristics are
developed. The models are used for simulations. Adjustments are made
between the modelling and simulation parts until the simulation yields
reasonable results. The simulations are then verified experimentally.
Theoretical models and simulations are also used to design good
experiments. This process is repeated until good agreement is achieved
between theoretical and experimental results.
10
Simulation of the theoretical models can then be used as an effective tool for
optimisation in the product development process. Should optimisation entail
design changes that significantly change the relevance of the assumptions of
the theoretical models, the entire procedure is repeated. In this way,
increasingly detailed descriptions of the product are created where necessary
alongside development of the product.
The Complete Approach enables better decisions to be made earlier on in the
development process, resulting in decreased time-to-market and improved
quality. When a completely new product is developed, a number of complete
iterations are usually needed. When a new variant of a product is developed,
much prior work can be re-used. The Complete Approach concept gives the
company a framework with which to structure such experience.
11
2
Aim and Scope of the Present Work
The aim of this work is an efficient and verified method for simulating
rammer compactor machines to be used in the product development process.
The experience gained should also be useful in studying other types of
dynamic compactor machines.
The complexity of the machine makes design optimisation through
traditional prototype testing impractical. This has pointed to the need for a
theoretical model and simulation procedure for prediction of the dynamic
behaviour of the machine as well as for a procedure for optimisation. In this
work, a model of a rammer compactor machine is described. The model is
used for simulations. The simulation results are compared with measured
results.
The rammer compactor machine LT70 from Svedala Compaction Equipment
AB, Karlskrona, Sweden, is studied. Many other manufacturers and models
of rammer compactor machines exist. All such machines are basically
designed in the same way. A sketch of the machine showing the main parts
is presented in figure 3.
Cam disc
Engine
Engine house
Connecting rod
Cylinder
Piston
Foot
Soil
Figure 3. Principal sketch of a rammer soil compactor machine.
12
Although the mechanism seems to be rather simple, the machine conceals
considerable inherent complexity. Descriptions of the soil and the interaction
between the machine and the soil are also non-trivial problems. To make
efficient simulations, simplifications must be made. The simplified model
used in this work is shown in figure 4. All assumptions, simplifications and
notations are described in the enclosed papers.
M
u3
Engine
m3 , J
r
Piston
m2
φ
u2
ci
ki
u1
Foot
m1
Soil
cs
Replacement
ks
Figure 4. Theoretical model of the rammer
machine and soil replacement.
The most questionable simplification of the combined system is the
representation of the soil as a linear spring and a viscous damper. However,
since the aim of the present work is an efficient model of the machine itself,
this simplification is justifiable. Parallel work is currently being carried out
to find better soil models. Combining the machine model suggested in this
work with other soil models should not present any major difficulties.
13
The dynamic system is non-linear due to the angle of the cam disc and the
jumping behaviour, which makes it hard to solve the equations analytically.
Standard ordinary differential equation solvers in Matlab and Simulink are
used for the simulations.
14
3
Summary of Papers
The three papers included in this thesis represent a description of how to
work iteratively with modelling, simulations and measurements.
3.1
Paper A
In this paper, a theoretical model for the dynamic behaviour of a rammer
compactor machine is described, and a simulation procedure is established.
The model was suggested by Moshin [14] and has been applied also in
papers B, C and [28-30]. The soil is modelled by a linear spring and a
viscous damper. In this paper the foot of the machine and the soil
replacement are not allowed to lose contact with each other. In contrast to
earlier works on compactor machines of this kind [12, 14, 28], the equations
of motion are solved numerically for an arbitrary time period in this work.
This also makes it possible to study the transient and non-harmonic
behaviour of the machine, and to reach a steady state. The Matlab toolbox
Simulink is used to solve the equations of motion. Experimental results from
[28], where the rammer compactor machine was run on simulated soil
material, are used for a preliminary verification. The agreement between the
simulation and the experiment is good, which implies that the level of detail
in the theoretical model is sufficient for further studies.
3.2
Paper B
In this paper, the complexity of the theoretical model used in paper A is
increased by allowing the foot of the machine to lose contact with the soil
replacement. The contact conditions between the foot of the machine and the
soil replacement are investigated and described. The simulation procedure is
complemented by these conditions. The differential equations of the model
are solved numerically by using Matlab. The dynamic behaviour is analysed
for different driving torque values. Simulation results are presented as time
series, phase plane diagrams, mappings and bifurcation diagrams. The results
show that the system is highly non-linear and indicate that harmonic, subharmonic and chaotic behaviour are present within the parameter variations
used. This phenomenon has also been observed while operating the machine
under real-life conditions. The parameter sensitivity emphasises the need to
include such simulations in the product development process.
15
3.3
Paper C
In this paper, the theoretical model of paper A is thoroughly investigated
experimentally, and the resulting introductory iteration of the Complete
Approach concept is described. In the experimental set-up, the rammer foot
is attached to a linear spring foundation. This eliminates uncertainties
associated with soil modelling, and makes possible a check of the model of
the machine itself. The good agreement between theoretical and
experimental results indicates that the theoretical model and simulation
procedure are potentially useful in introductory optimisation studies.
Possible reasons for the remaining discrepancy are discussed, and
suggestions are given for improvements in both the theoretical model and the
experimental set-up for coming iterations.
16
4
Conclusions
In this work an efficient and verified method for simulation of a rammer
compactor machine is presented. The method has been developed by using a
structural approach called Complete Approach, which includes theoretical
modelling, simulation, experimental verification, and optimisation. In this
way, a deeper understanding of the system has been gained.
The results of the simulations and the measurements deviate by
approximately ten per cent; a highly satisfactory result considering the
complexity of the machine studied, and the significant simplifications
introduced. The presented model and simulation procedure constitute a
useful support in product development of compactor machines.
Although there is good agreement between simulation results and
experimental results, suggestions for improvements in both the theoretical
model and the experimental set-up have been given, and additional work in
the future is recommended.
Suggested improvements relate primarily to the modelling of internal
dissipation. In the present model, all internal dissipation is represented by a
viscous damper between the foot and the piston of the machine. It is
sometimes possible to estimate an equivalent damping constant, giving the
same dissipated energy per cycle as the combined friction and viscous
dissipation that are present in reality. Since the friction dissipation seems to
be significant compared to the truly viscous dissipation in this machine, a
new equivalent damping constant must be estimated for each new operating
condition. Considering this, the theoretical model can be improved by
including a friction element between the foot and the piston.
If necessary, stiffness, damping and friction between the foot and the house
can also be included. The experimental set-up can be improved by adding a
damper to the soil replacement foundation to produce a closer resemblance
to real operating conditions. It is also recommended that a more
sophisticated theoretical model of the soil is introduced, which includes the
non-linear behaviour of real soil materials.
17
5
References
1
WEBER, W. G. Jr., History of Embankment Construction, State of
the Art Report 8, Transportation Research Board, National Research
Council, Washington, D.C., 1990.
2
SPECK, A., Der Kunststrassenbau, Ernst, Berlin, 1950.
3
GRANGER, F., Translation of Vitruvius’
Architechture, Putnam, New York, N.Y., 1934.
4
PROCTOR, R. R., Fundamental Principles of Soil Compaction,
Engineering News Record, Vol. 111, No. 9, pp. 245-248, 1933.
5
HOGENTOLER, C. A., Essentials of Soil Compaction, Proceedings –
Highway Research Board, Washington, pp. 309-316, 1936.
6
STEUERMANN, S., A New Soil Compacting Device, Engineering
News Record, pp. 87-88, July, 1939.
7
BERNHARD, R. K., Static and Dynamic Soil Compaction,
Proceedings from the Annual Meeting/Highway Research Board,
1951.
8
FORSSBLAD, L., Jordpackning genom vibrering, Teknisk Tidskrift,
No. 30, 1955.
9
LEWIS, W. A., A Study of Some of the Factors Likely to Affect the
Performance of Impact Compactors on Soil, Proceedings of the 4th
International Conference on Soil Mechanics and Foundations,
London, 1957.
10
LEWIS, W. A., Recent Research into the Compaction of Soil by
Vibratory Compaction Equipment, Proceedings of the 5th International
Conference on Soil Mechanics and Foundations, Paris, 1961.
18
Ten
Books
on
11
D’ Appolonia, D. J., Sand Compaction with Vibratory Rollers,
Journal of the Soil Mechanics and Foundations Division / Proceedings
of ASCE, Vol. 95, January, pp. 263-284, 1969.
12
BATHELT, U., Das Arbeitsverhalten des Rüttelverdichters auf
plastisch-elastischem Untergrund, Bautechnik Archiv, Heft 12, Verlag
von Wilhelm Ernst & Sohn, Berlin, 1956.
13
RICHART, F. E. Jr., J. R. HALL Jr., and R. D WOODS, Vibration of
Soils and Foundations, Prentice-Hall, Inc., 1970.
14
MOSHIN, S. H., Untersuchungen des dynamischen Verhaltens von
Stampfsystemen, Baumaschine und Bautechnik, Jahrgang 14, Heft 1,
pp. 11-17, 1967.
15
YOO, T. and E. T. SELIG, Dynamics of Vibratory-Roller
Compaction, Journal of the Geotechnical Engineering Division,
GT10, pp. 1211-1231, 1977.
16
PIETZSCH, D. and W. POPPY, Simulation of Soil Compaction with
Vibratory Rollers, Journal of Terramechanics, Vol. 29, No. 6, pp. 585597, 1992.
17
TATEYAMA, K. and T. FUJIYAMA, Study on the Vibratory RollerGround Interaction and its Application to the Control of a Roller,
Proceedings of the 5th Asia-Pacific Regional Conference ISTVS,
1998.
18
ADAM, D., Continuous Compaction Control(CCC) with Vibrating
Rollers, Doctoral Thesis, Civil Engineering Department, Technical
University of Vienna, 1996.
19
KOPF, F., Continuous Compaction Control(CCC) during Compaction
of Soils by means of Dynamic Rollers with different kinds of
Excitation, Doctoral Thesis, Faculty of Civil Engineering, Technical
University of Vienna, 1999.
19
20
BORCHERT, G., Untersuchungen am Elektrostampfer-200kg, Großer
Beleg TU Dresden, Institut für Fördertechnik und Baumaschinen,
1963.
21
FILZ, G. M. and T. L. BRANDON, Compactor Force and Energy
Measurements, Geotechnical Testing Journal, Vol. 16, No. 4, pp. 442449, 1993.
22
BROMAN, G., A. JÖNSSON, T. ENGLUND and J. WALL,
Introductory Optimisation Study of a Rammer Soil Compactor
Machine, Proceedings of the NAFEMS World Congress, Como, Italy,
2001.
23
CHARLIER, C. V. L., Naturvetenskapens Matematiska Principer, A
reproduction of: NEWTON, I., Philosophiae Naturalis Principia
Mathematica, 1686, C W K Gleerups förlag, Lund, 1927.
24
MOON, F. C., Chaotic and Fractal Dynamics: An Introduction for
Applied Scientists and Engineers, John Wiley & Sons, Inc., 1992.
25
ULLMAN, D. G., The Mechanical Design Process, McGraw-Hill,
Inc., 1992.
26
PAHL, G. and W. BEITZ, Engineering Design. A Systematic
Approach, Springer, 1996.
27
ULRICH, K. T. and S. D. EPPINGER, Product Design and
Development, McGraw-Hill, Inc., 1995.
28
BORG, J. and A. ENGSTRÖM, Dynamic Behaviour of a Soil
Compaction Tamping Machine, Master Thesis, Department of
Mechanical Engineering, University of Karlskrona/Ronneby,
Karlskrona, Sweden, 1997.
29
JÖNSSON, A. and G. BROMAN, Dynamic Characteristics of a Soil
Compaction Tamping Machine, Presented at the Swedish Days of
Mechanics 1999, Royal Institute of Technology, Stockholm, Sweden,
1999.
20
30
ARBIN, U., T. ENGLUND and J. WALL, Modelling and Optimising
a Rammer Soil Compactor Machine, Master Thesis, Department of
Mechanical Engineering, Blekinge Institute of Technology,
Karlskrona, Sweden, 2000.
21
Paper A
Modelling of a Soil Compaction Tamping Machine using Simulink
22
Paper B
The Nonlinear Behavior of a Rammer Soil Compactor Machine
23
Paper C
Experimental Investigation of a Rammer Soil
Compactor Machine on Linear Spring Foundation
24