DYNAMIC MODELLING OF A BACKHOE-LOADER MODELLING OF A BACKHOE-LOADER. ... Bu çalşmanıın amac bir...
Transcript of DYNAMIC MODELLING OF A BACKHOE-LOADER MODELLING OF A BACKHOE-LOADER. ... Bu çalşmanıın amac bir...
DYNAMIC MODELLING OF A BACKHOE-LOADER
A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
OF MIDDLE EAST TECHNICAL UNIVERSITY
BY
BORAN KILIÇ
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OF MASTER OF SCIENCE IN
MECHANICAL ENGINEERING
SEPTEMBER 2009
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Approval of the thesis:
DYNAMIC MODELLING OF A BACKHOE-LOADER submitted by BORAN KILIÇ in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department, Middle East Technical University by, Prof. Dr. Canan Özgen ________________ Dean, Graduate School of Natural and Applied Sciences Prof. Dr. Suha Oral ________________ Head of Department, Mechanical Engineering Prof. Dr. Tuna Balkan ________________ Supervisor, Mechanical Engineering Dept., METU Prof. Dr. Eres Söylemez ________________ Co-Supervisor, Mechanical Engineering Dept., METU Examining Committee Members: Prof. Dr. Y. Samim Ünlüsoy ________________ Mechanical Engineering Dept., METU Prof. Dr. Tuna Balkan ________________ Mechanical Engineering Dept., METU Prof. Dr. Eres Söylemez ________________ Mechanical Engineering Dept., METU Asst. Prof. Yiğit Yazıcıoğlu ________________ Mechanical Engineering Dept., METU Ferhan Fıçıcı, M.Sc. ________________ Team Leader of R&D, Hidromek Inc. Date: ________________
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I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work.
Name, Last name : Boran KILIÇ
Signature :
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ABSTRACT
DYNAMIC MODELLING OF A BACKHOE-LOADER
Kılıç, Boran
M.S., Department of Mechanical Engineering
Supervisor : Prof. Dr. Tuna Balkan
Co-Supervisor : Prof. Dr. Eres Söylemez
September 2009, 82 pages
The aim of this study is to develop a dynamic model of the loader system of a
backhoe-loader. Rigid bodies and joints in the loader mechanism and loader
hydraulic system components are modelled and analyzed in the same environment
using the physical modelling toolboxes inside the commercially available simulation
software, MATLAB/Simulink. Interaction between the bodies and response of the
hydraulic system are obtained by co-operating the mechanical and hydraulic
analyses. System variables such as pressure, flow and displacement are measured on
a physical machine and then compared with the simulation results. Simulation results
are consistent with the measurement results. The main result of this work is the
ability to determine the dynamic loads on the joints and attachments of the backhoe-
loader. In addition to that, prototyping time and costs can be highly reduced by
implementing this model in the design process.
Keywords: Mobile Hydraulics, Backhoe-loader, Modelling
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ÖZ
KAZICI-YÜKLEYİCİ İŞ MAKİNASININ DİNAMİK MODELLENMESİ
Kılıç, Boran
Yüksek Lisans, Makina Mühendisliği Bölümü
Tez Yöneticisi : Prof. Dr. Tuna Balkan
Ortak Tez Yöneticisi : Prof. Dr. Eres Söylemez
Eylül 2009, 82 sayfa
Bu çalışmanın amacı bir kazıcı-yükleyici iş makinasının yükleyici sisteminin
dinamik modelini geliştirmektir. Makinanın yükleyici mekanizmasını oluşturan rijit
parçalar ve bağlantı elemanları ile yükleyici hidrolik sistemi, MATLAB/Simulink
benzetim programının içindeki fiziksel modelleme araçları kullanılarak
modellenmiştir. Parçalar arasındaki etkileşim ve hidrolik sistemin tepkisi, dinamik ve
hidrolik sistem analizlerinin eş zamanlı çözülmesi ile elde edilmiştir. Makina
üzerinde yapılan ölçümlerle elde edilen basınç, debi, pozisyon gibi farklı sistem
değişkenleri, benzetim sonuçları ile karşılaştırılmıştır. Karşılaştırma sonucunda
benzetim sonuçlarının ölçüm sonuçları ile tutarlı olduğu elde edilmiştir. Bu
çalışmanın temel çıktısı, kazıcı-yükleyici üzerindeki mafsallara ve rijit parçalara
gelen dinamik yüklerdir. Aynı zamanda, bu modelin tasarım aşamasında
kullanılmasıyla prototip zaman ve maliyetlerinin düşürülmesi mümkün olacaktır.
Anahtar kelimeler: Mobil Hidrolik, Kazıcı-yükleyici, Modelleme
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To My Love Seda
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ACKNOWLEDGMENTS
I wish to express my deepest gratitude to my supervisor Prof. Dr. Tuna BALKAN for
his guidance, advice, criticism, encouragements and insight throughout the research.
I would like to state my sincere thanks to my co-supervisor Prof. Dr. Eres
SÖYLEMEZ for his guidance, motivation, supervision and patience.
I would like to thank my colleagues Ferhan FIÇICI, Cevdet Can UZER, Tarık
OLĞAR, Erkal ÖZBAYRAMOĞLU, Koray Serdar TEKİN and Durmuş Ali
GÖZTAŞ for their suggestions and comments.
I would also like to express my appreciation to Hasan Basri BOZKURT, general
manager of Hidromek Inc., for his support.
I wish to offer very special thanks to my love Seda YILDIRIM for her
encouragement and spiritual support during the study.
Finally, I would like to express my thanks to my parents for their support and
continuous faith in me.
This study is supported by Hidromek Inc.
TABLE OF CONTENTS
ABSTRACT................................................................................................................ iv
ACKNOWLEDGMENTS .........................................................................................vii
TABLE OF CONTENTS..........................................................................................viii
LIST OF FIGURES ..................................................................................................... x
LIST OF SYMBOLS AND ABBREVIATIONS .....................................................xiii
CHAPTERS
1. INTRODUCTION .......................................................................................... 1
1.1 Background and Motivations ................................................................... 1
1.2 Literature Survey...................................................................................... 6
1.2.1 Model-Based Design ..................................................................... 6
1.2.2 Hydraulic and Mechanical Models................................................ 7
1.2.3 Friction Models ........................................................................... 13
1.3 Research Objective................................................................................. 16
1.4 Thesis Outline ........................................................................................ 16
2. HYDRAULIC SYSTEM MODELLING ..................................................... 17
2.1 Engine Model ......................................................................................... 18
2.2 Pump Model ........................................................................................... 21
2.3 Directional Control Valve Model .......................................................... 23
2.4 Cylinder Model ...................................................................................... 26
2.5 Relief and Check Valve Models ............................................................ 31
2.6 Hydraulic Pipeline Model ...................................................................... 34
2.7 Hydraulic Fluid Properties ..................................................................... 36
3. MECHANICAL SYSTEM MODELLING .................................................. 39
3.1 Determination of Mass and Inertia Tensor Properties of the Parts ........ 41
3.2 Implementation of Loader Mechanism to the SimMechanics Model.... 42
3.3 Introduction of Friction.......................................................................... 45
3.4 Co-Simulation of Hydraulic and Mechanical Models ........................... 47
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4. VERIFICATION OF THE MODEL ............................................................ 49
4.1 Measurement Instrumentation................................................................ 49
4.2 Measurement Points ............................................................................... 53
4.3 Comparison of the Results ..................................................................... 57
5. CASE STUDY.............................................................................................. 64
6. DISCUSSION, CONCLUSION AND RECOMMENDATIONS................ 76
6.1 Discussion and Conclusion .................................................................... 76
6.2 Recommendations for Future Work....................................................... 77
REFERENCES........................................................................................................... 79
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LIST OF FIGURES
FIGURES
Figure 1.1 - HMK 102B Energy Series Backhoe-Loader General View..................... 2
Figure 1.2 - Cutaway View of a Mobile 6/3 Open-Center Valve ................................ 3
Figure 1.3 - Cutaway View of a Mobile 6/3 Closed-Center Valve.............................. 3
Figure 1.4 - V Diagram of New Product Development Process .................................. 7
Figure 1.5 - SimMechanics model of the 12MXT MECALAC excavator .................. 8
Figure 1.6 - SimMechanics animation of Terex O&K RH 200 model ........................ 9
Figure 1.7 - PVG 32 Simulink Model........................................................................ 10
Figure 1.8 - Wheel Loader Simulink Model .............................................................. 11
Figure 1.9 - ADAMS Model of a Wheel Loader ....................................................... 12
Figure 1.10 - Coulomb plus Viscous Friction Curve ................................................. 13
Figure 1.11 - Friction Curve including the Stribeck Effect ....................................... 14
Figure 1.12 - Measured Friction Force for a Typical Hydraulic Cylinder................. 15
Figure 2.1 - Loader Hydraulic Circuit Diagram of HMK 102B Backhoe-Loader..... 17
Figure 2.2 - Diesel Engine Torque Curve at Full Throttle......................................... 19
Figure 2.3 - Diesel Engine Model .............................................................................. 19
Figure 2.4 - Rigid Coupling Subsystem Model ......................................................... 20
Figure 2.5 - Pump Model Parameters ........................................................................ 22
Figure 2.6 – Section View and Symbol of 6/3 Directional Control Valve ................ 24
Figure 2.7 - SimHydraulics Model the 6/3 Directional Control Valve...................... 24
Figure 2.8 - Underlapped Orifice Model Parameters................................................. 26
Figure 2.9 - Hydraulic Cylinder Subsystem Model ................................................... 27
Figure 2.10 - Translational Hard Stop Model ............................................................ 28
Figure 2.11 - Lift Cylinder Model Parameters........................................................... 29
Figure 2.12 - Bucket Cylinder Model Parameters ..................................................... 30
Figure 2.13 - Direct Acting Pressure Relief Valve .................................................... 31
Figure 2.14 - Main Relief Valve Model Parameters .................................................. 33
Figure 2.15 - Check Valve Model Parameters ........................................................... 34
Figure 2.16 - Hydraulic Pipeline Model .................................................................... 34
Figure 2.17 - Pipeline Model Parameters................................................................... 36
Figure 2.18 - Hydraulic Fluid Properties ................................................................... 37
Figure 2.19 - Simulink Loader Hydraulic System Model.......................................... 38
Figure 3.1 - Loader Mechanism of the HMK 102B Backhoe-Loader ....................... 40
Figure 3.2 - 2D Drawing of the Loader Mechanism.................................................. 40
Figure 3.3 - Mass and Inertia Tensor Properties of the Front Arm............................ 42
Figure 3.4 - SimMechanics Visualization of the Loader Mechanism........................ 44
Figure 3.5 - Cylinder Friction Parameters ................................................................. 46
Figure 3.6 - Cylinder Friction Force vs. Rod Velocity Graph at Different Pressures 46
Figure 3.7 - Solution Cycle for Co-Simulation.......................................................... 47
Figure 3.8 - Mechanical System Model ..................................................................... 48
Figure 4.1 - Hydrotechnik Multi-System 5050.......................................................... 50
Figure 4.2 - Hydrotechnik 0-600 bar Pressure Sensor ............................................... 51
Figure 4.3 - Hydrotechnik 16-600 l/min Flow Rate Sensor....................................... 52
Figure 4.4 - Hydrotechnik Rotational Speed Sensor.................................................. 52
Figure 4.5 - OPKON Linear Variable Displacement Transducer .............................. 53
Figure 4.6 - Installation of the Pressure and Flow Rate Sensors ............................... 55
Figure 4.7 - Installation of the Flow Rate Sensor ...................................................... 55
Figure 4.8 - Installation of the Rotational Speed Sensor ........................................... 56
Figure 4.9 - Installation of the Linear Variable Displacement Transducer................ 56
Figure 4.10 - Lift Spool Position Input ...................................................................... 58
Figure 4.11 - Throttle Input........................................................................................ 58
Figure 4.12 - Engine Rotational Speed ...................................................................... 59
Figure 4.13 - Lift Cylinder Head Side Flow Rate...................................................... 60
Figure 4.14 - Lift Cylinder Head Side Pressure......................................................... 61
Figure 4.15 - Lift Cylinder Rod Side Pressure........................................................... 62
Figure 4.16 - Lift Cylinder Rod Displacement .......................................................... 63
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Figure 5.1 - Lift Spool Position Input for Case Study ............................................... 65
Figure 5.2 - Engine Throttle Input for Case Study .................................................... 65
Figure 5.3 - Engine Rotational Speed-Case Study..................................................... 66
Figure 5.4 - Engine Output Torque-Case Study......................................................... 67
Figure 5.5 - Lift Cylinder Head Side Pressure- Case Study ...................................... 68
Figure 5.6 - Lift Cylinder Head Side Flow Rate-Case Study .................................... 68
Figure 5.7 - Lift Cylinder Rod Displacement-Case Study......................................... 69
Figure 5.8 - Bucket COG Coordinates....................................................................... 70
Figure 5.9 - Forces on the Loader Mechanism .......................................................... 71
Figure 5.10 - Reaction Force Between Lift Cylinder and Front Arm in X Direction 72
Figure 5.11 - Reaction Force Between Lift Cylinder and Front Arm in Y Direction 73
Figure 5.12 - Reaction Force Between Chassis and Front Arm in X Direction......... 73
Figure 5.13 - Reaction Force Between Chassis and Front Arm in Y Direction......... 74
Figure 5.14 - Reaction Forces on the Front Arm ....................................................... 74
LIST OF SYMBOLS AND ABBREVIATIONS
SYMBOLS
cv : Transition Coefficient
f : Friction Factor for Pipeline
fc : Coulomb Friction Coefficient
fL : Friction Factor at Laminar Border
fT : Friction Factor at Turbulent Border
fv : Viscous Friction Coefficient
g : Gravitational Acceleration
gN : Gap Between the Slider and the Case in the Negative Direction
gP : Gap Between the Slider and the Case in the Positive Direction
h : Orifice opening
hl : Head Loss
hmax : Spool Maximum Displacement
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kHP : Hagen-Poiseuille Coefficient
kleak : Leakage Coefficient
n : Gas Specific Heat Ratio
q : Flow Rate
qleak : Pump Leakage Flow
t : Time
v : Body Velocity
vC : Case Terminal Velocity
vf : Average Hydraulic Fluid Velocity
vR : Rod Terminal Velocity
x : Piston Displacement from Initial Position
xC : Case Terminal Displacement
xO : Piston Initial Displacement
xR : Rod Terminal Displacement
xS : Spool Displacement from Initial Position
xSO : Initial Opening
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A : Piston Area
A(h) : Instantaneous Orifice Passage Area
Amax : Orifice Maximum Area
AP : Pipe Cross-Sectional Area
CD : Flow Discharge Coefficient
DH : Instantaneous Orifice Hydraulic Diameter
Dn : Damping Coefficient at Negative Cylinder End
DP : Damping Coefficient at Positive Cylinder End
Dpipe : Pipe Hydraulic Diameter
Dpump : Pump Displacement
F : Force
Ff : Friction Force
Fpr : Preload Force
Fx : Force in X Direction
Fy : Force in Y Direction
Jpump : Rotational Inertia of the Coupling and Pump Internal Components
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Kbrk : Breakaway Friction Force Increase Coefficient
Kn : Contact Stiffness at Negative Cylinder End
KP : Contact Stiffness at Positive Cylinder End
Ks : Shape Factor Characterizing the Pipe Cross Section
L : Pipe Geometrical Length
Leq : Equivalent Length of Local Resistances
P : Pressure Differential Across the Component
Pa : Atmospheric Pressure
PA, PB : Gage Pressures at the Component Ports
Pcrack : Relief or Check Valve Preset Pressure
Pmax : Relief or Check Valve Pressure at Maximum Opening
Pnom : Pump Nominal Pressure
Pp : Gauge Pressure at the Outlet of the Pump
Psystem : Maximum System Pressure
Pt : Gauge Pressure at the Inlet of the Pump
Re : Reynolds Number
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ReL : Maximum Reynolds Number at Laminar Flow
ReT : Minimum Reynolds Number at Turbulent Flow
TE : Output Torque of the Diesel Engine
TP : Torque at the Pump Driving Shaft
VG : Gas Volume at Atmospheric Pressure
VL : Volume of Liquid
α : Relative Gas Content at Atmospheric Pressure
β : Bulk Modulus of Hydraulic Oil
βl : Pure Liquid Bulk Modulus
δ : Relative Displacement Between the Piston and the Case
ηmech : Pump Mechanical Efficiency
ηv : Pump Volumetric Efficiency
μ : Hydraulic Fluid Dynamic Viscosity
ν : Hydraulic Fluid Kinematic Viscosity
νnom : Nominal Hydraulic Fluid Kinematic Viscosity
ρ : Hydraulic Fluid Density
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ω : Angular Velocity
ωnom : Pump Nominal Angular Velocity
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ABBREVIATIONS
ARV : Anti-shock Relief Valve
COG : Center of Gravity
FEA : Finite Element Analysis
HIL : Hardware-in-the-Loop
LVDT : Linear Variable Displacement Transducer
STL : Stereolithographic
CHAPTER 1
1INTRODUCTION
1.1 Background and Motivations
Earth-moving machines are used for engineering projects such as roads, dams, open
pit excavation, quarries, trenching, recycling, landscaping and building sites [1].
Among various types of earth-moving machines, backhoe-loader (Figure 1.1) is one
of the most commonly used machines. There are two main systems in this machine:
loader and backhoe. While the loader system is used for lifting, transporting and
dumping the material; backhoe system is used for digging and excavating operations.
Loader remains in place when the machine is used as an excavator and vice versa. A
backhoe work cycle normally consists of excavating, elevating, swinging and
discharging of material. A loader work cycle normally includes filling, elevating,
transporting and discharging of material [2].
Backhoe-loader is propelled by an internal combustion engine. A rigid chassis
supports the loader and backhoe attachments. Attachment movements are provided
by hydraulic cylinders. A hydraulic pump, which is connected directly to the internal
combustion engine, supplies the necessary oil flow for these cylinders. Directional
control valves enable the operator to control the direction and velocity of the
cylinders. Hydraulic components are connected by appropriate hoses, pipes and
fittings.
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Figure 1.1 - HMK 102B Energy Series Backhoe-Loader General View
Since backhoe and loader systems are not used simultaneously in practice, they are
considered as independent systems from each other [3]. Only hydraulic and
mechanical models of the loader system are developed in this work.
Hydraulic systems of backhoe-loaders can be classified into two main groups named
as open-center hydraulic system (Figure 1.2) and closed-center hydraulic system
(Figure 1.3).
In open-center hydraulic systems, a constant displacement pump is used to supply
oil. Directional control valve’s neutral position is open to the tank; that is, when there
is not any input to the control lever, oil flows through the valve and returns to the
tank. When the control lever is moved, flow path from pump to tank closes
proportionally and pump to actuator path opens accordingly in the same proportion
[4]. A pressure relief valve is used in these systems in order to prevent any excessive
pressure increases.
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Figure 1.2 - Cutaway View of a Mobile 6/3 Open-Center Valve [5]
Figure 1.3 - Cutaway View of a Mobile 6/3 Closed-Center Valve [5]
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On the other hand, in closed-center hydraulic systems, neutral position of the
directional control valve is closed, therefore when the control lever is not moved, oil
cannot flow through the valve and pressure builds up in the system. In order to
prevent high energy loss, variable displacement pump with load sense signal input is
used in these systems.
Open-center systems are simpler and cheaper systems when compared to closed-
center hydraulic systems, however energy loss in open-center systems is higher.
Hydraulic system modelled in this work is an open-center system.
Loader mechanism of the backhoe-loader is a two degree of freedom mechanism
with 11 linkages. This mechanism is actuated by four cylinders in total and the
mechanism is completely symmetric with respect to the longitudinal axis of the
machine.
Digging depth and dump height of the machine are determined by the loader
mechanism. Moreover, bucket and arm breakout forces and lift capacity are directly
related to this loader mechanism in addition to the cylinder sizes and maximum
system pressure.
Construction equipment industry has been in a rapid growth in the last 10-15 years.
Parallel to that, construction equipment manufacturers are in a very competitive race.
Since customers prefer the most durable, reliable machines, design of the machine
plays one of the most important roles in this competition. In order to design and
manufacture such a machine, designer must be well aware of the forces on the
structure of the machine. Therefore, predicting or measuring the loads on the
machine should be one of the first steps in designing process. This necessity leads
engineers to model the machine thoroughly including the hydraulic and mechanical
systems in order to determine the forces on the structure.
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MATLAB®, commercially available software used in this work, is a powerful
simulation software with various toolboxes embedded inside the software. One of
these toolboxes, Simulink® is an environment for multidomain simulation and model
based design for dynamic systems. It lets the user to design, simulate, implement,
and test different time-varying systems including the physical systems such as
hydraulic or mechanical systems. It is possible to use only Simulink to simulate a
multidomain dynamic physical system by first deriving the differential equations of
the system and then solving them in Simulink. However, it is mostly very time
consuming and tough to obtain the system equations of multidomain systems,
especially when the number of the components in the system and their complexity
are high.
Simscape™ extends the capabilities of Simulink by introducing the tools and
libraries for modelling the physical systems. There are standard mechanical,
hydraulic, electrical and thermal component blocks inside the Simscape libraries;
however, these blocks use the simplest correlations for simulation.
On the other hand, SimHydraulics® increases the level of complexity by providing
more detailed component blocks for modelling hydraulic components in the
Simulink environment. In SimHydraulics library, there are over 50 different blocks
which include linear and rotary actuators, pumps, valves, pipelines. One of the most
important advantages of this toolbox is that a SimHydraulics model can be connected
to a mechanical system for a multidomain simulation. Moreover, a SimHydraulics
system model closely resembles the hydraulic schematic, which lets the user to
understand and analyze the model much more efficiently.
Similarly, SimMechanics™ toolbox extends Simscape’s mechanical system
modelling capabilities by introducing tools for modelling three-dimensional
mechanical systems within the Simulink environment. Instead of deriving,
programming and solving multi-body dynamics equations, rigid bodies and joints can
be easily modelled with standard blocks inside the SimMechanics library.
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1.2 Literature Survey
Results of the literature survey are given in this section. Firstly, importance of the
model based design and details of the different design processes are given. Then,
hydraulic and mechanical models found in literature are shown in detail. Finally,
various friction models are given.
1.2.1 Model-Based Design
Forsberg et al. [6] presented a V diagram, which represents a systematic design and
validation process for a construction machine (Figure 1.4). In the left part of the
diagram, which is the initial part of the process, machine specifications are
determined according to the machine requirements and machine is divided into
systems. These systems are then separated into small subsystems in order to simplify
the design process. Once the subsystems are implemented, they are tested and
integrated to each other in order to obtain systems. Similarly, these systems are tested
and integrated. Development process is finalized by testing of the machine.
Prabhu [7] proposed two different types of design processes: traditional design
process and model-based design process. In the traditional design process, engineers
work on their own subsystems or systems, and interact with other system engineers
by exchanging design documents. However, since the construction machines consist
of various engineering disciplines, they are highly non-linear systems and therefore
each system affects the other systems. In addition to that, in this approach, engineers
have to build physical prototypes, test these prototypes and optimize the design on
these prototypes. This is a very costly and time-consuming process.
In the model-based design process, dynamic behaviour of the machine can be
obtained in the system design step before building the physical prototype. This gives
the design engineers a great flexibility in the design process. Moreover, in this
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approach, interactions between different disciplines such as hydraulics, mechanics,
heat transfer and electronics may also be implemented into the model [7].
Figure 1.4 - V Diagram of New Product Development Process [6]
1.2.2 Hydraulic and Mechanical Models
There are several works done on the dynamic modelling of construction machines;
however, none of them is for backhoe-loaders. Among these models, excavator
models have the greatest percentage. Koivo et al. [8] presented a dynamic model of
an excavator during digging operation. In this work, they combined the equation of
motions of each link with the equations for the forces and torques acting on the links
in order to obtain the dynamic model in Newton-Euler formulation. Since the
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developed model was going to be used in automated motion, developed equations are
in the form similar to the ones of robotic manipulators. In addition to that, a
numerical simulation was performed in C language programming environment with
real excavator parameters. However, this dynamic model lacks the hydraulic system
of the excavator.
Sleiman et al. [9] developed a dynamic mechanical model of a 12MXT MECALAC
excavator using SimMechanics in MATLAB/Simulink platform (Figure 1.5).
Hydraulic cylinders were modelled as two separate bodies connected by a prismatic
joint. Since this model also lacks the hydraulic part of the excavator, net cylinder
forces were applied to the joints as an input to the model.
Figure 1.5 - SimMechanics model of the 12MXT MECALAC excavator [9]
Similarly, McAree et al. [10] proposed a method to calculate the forward dynamics
of multi-body mechanisms. In their study, body accelerations are first evaluated by
implementing the known body positions, relative body velocities and hydraulic
cylinder forces. These accelerations are then integrated in order to obtain the bodies’
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new positions and velocities. In addition to that, a SimMechanics model of a Terex
O&K RH 200 500 ton hydraulic mining excavator was developed in order to verify
the method described above (Figure 1.6).
Figure 1.6 - SimMechanics animation of Terex O&K RH 200 model [10]
Frankel [11] developed a mathematical model of a Sauer Danfoss PVG 32 valve
block while developing a testbed for a haptic backhoe. Hardware-in-the-Loop (HIL)
simulator was used to measure input and output data. Using system identification
techniques with this data, he obtained the valve parameters for the mathematical
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model. A Simulink model was constructed to simulate this mathematical model
(Figure 1.7).
Figure 1.7 - PVG 32 Simulink Model [11]
All the dynamic models described above lack the multi-domain system simulation.
They either include only mechanical system or only hydraulic system. On the other
hand, Prabhu [12] presented a multi-domain model for a wheel loader, which
includes hydraulics, mechanics, drivetrain and internal combustion engine. He used
MATLAB/Simulink environment in the modelling process since this software
enables the user to model various complex systems via specialized physical
modelling toolboxes such as SimMechanics, SimHydraulics and SimDriveline. In his
paper, he focused on a typical wheel loader application, hopper charging. He also
gave some requirements such as lift system response, propulsion system response
and simultaneous lift and propulsion. He described the model in system level for
each discipline and integrated these systems to obtain the whole machine model
given in Figure 1.8. Then, by using this model and predetermined scenarios, he
checked whether the machine meets the requirements given above.
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This paper shows that MATLAB/Simulink environment is one of the most powerful
solutions for the multi-domain system modelling; however, it lacks the verification
of the model with the measurement of the system variables on the actual machine. In
that model, standard blocks in the software library are used for modelling the
directional control valve and the cylinders. These standard blocks represent less
advanced models, which may lead to less accurate results in the analysis.
Figure 1.8 - Wheel Loader Simulink Model [12]
There are also studies in which other commercially available software such as
MSC.ADAMS® and LMS.AMESim® were used in dynamic modelling. Ericsson et
al. [13] developed a dynamic model of a VOLVO wheel loader in ADAMS in order
to calculate the digging forces during loading application (Figure 1.9). This dynamic
model was verified with cylinder pressure measurements on physical machine.
Similarly, Park et al. [14] used ADAMS to model a crawler type excavator with a
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flexible boom attachment and verified their model with pressure, displacement and
acceleration measurements. However, both of these models lack the hydraulic system
model.
One of the most comprehensive studies on multi-domain system modelling was
performed by Frank [15]. In the design process of an electrical hybrid wheel loader, a
complete LMS.AMESim® model of the machine was developed. This model
includes internal combustion engine, hydraulic, mechanical and electrical systems as
well as the drivetrain. A particle based gravel model was also used during simulation.
Simulation results were validated by actual measurements.
Figure 1.9 - ADAMS Model of a Wheel Loader [13]
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1.2.3 Friction Models
In hydraulic construction machines, friction exists in hydraulic cylinders, in revolute
joints and also in hydraulic valves. However, according to the experimental studies
conducted by Tafazoli, it was shown that cylinder friction is dominant and all other
frictions can be neglected in the system [16], [17]. A common approach is to use a
friction model which includes Coulomb and viscous frictions illustrated in Figure
1.10. Experimental measurement techniques were used in order to obtain the friction
parameters [18]. This common form of friction model is parameterized as:
0)sgn( vvfvfF vcf (1.1)
Figure 1.10 - Coulomb plus Viscous Friction Curve
Apart from the basic friction model described above, there are some studies in which
Stribeck effect [20] is included in the friction model. Sulc [21] used an analytical
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friction model which includes Coulomb and viscous frictions with the Stribeck effect
during the non-linear modelling and control of a hydraulic actuator. This friction
model is illustrated in Figure 1.11.
Figure 1.11 - Friction Curve including the Stribeck Effect
Similarly, Rahmfeld et al. [22] also used the Stribeck effect in their friction model.
They measured the cylinder pressures on both sides in addition with the cylinder
force and the rod linear displacement. Hydraulic cylinder used in this study has a
stroke of 0.5 m and maximum cylinder force of 100 kN. Cylinder rod acceleration is
evaluated from the measured rod linear displacement. Then, Equation (1.2) was used
to determine the friction force.
(1.2) ..
xmFApApF KBKAf
14
where Ff is the friction force, F is the cylinder force, m is the mass in motion in the
cylinder, x is the cylinder rod linear position, pA is the A side cylinder pressure, pB is
the B side cylinder pressure, AK is the differential cylinder piston area and α is the
differential cylinder area ratio.
This measured friction force is plotted and a very similar graph to the theoretical
friction curve given in Figure 1.11 was obtained (Figure 1.12). This curve was used
to determine the parameters in the analytic friction model.
Figure 1.12 - Measured Friction Force for a Typical Hydraulic Cylinder [22]
15
16
1.3 Research Objective
The aim of this study is to develop a dynamic model of the loader system of a
backhoe-loader. The main results of this work will be the dynamic loads on the joints
and attachments of the machine. In addition to that, effect of any change in
mechanical or hydraulic systems can be analyzed in a more cost-saving and faster
manner with the help of this model.
In this study, hydraulic and mechanical system models are developed in trial licensed
versions of MATLAB/SimHydraulics® and MATLAB/SimMechanics©, respectively.
Interaction between the mechanical bodies and the response of the hydraulic system
are obtained by co-operating the dynamic mechanical and hydraulic analyses in
MATLAB/Simulink® environment.
1.4 Thesis Outline
This chapter gives a brief introduction on the hydraulic and mechanical systems used
in backhoe-loaders. In addition to that, literature survey conducted on hydraulic and
mechanical models as well as the friction is also given in this chapter.
Following two chapters describe the modelling process of the hydraulic and
mechanical systems, respectively. In the fourth chapter, details of the measurement
instrumentation and measurement points are given. Comparison of the simulation
and measurement results are also presented in the fourth chapter.
Details of the case study are given the fifth chapter. Moreover, comparison of the
static forces with the dynamic simulation forces is given in that chapter.
In addition to the brief summary of this work, findings of this study are given in the
last chapter. Moreover, possible future work on this subject is discussed.
CHAPTER 2
2HYDRAULIC SYSTEM MODELLING
As stated in the introduction section, backhoe and loader systems are not used
simultaneously in practice, therefore hydraulic systems of these two systems are
considered as independent from each other and only loader hydraulic system is
modelled in this work.
Figure 2.1 - Loader Hydraulic Circuit Diagram of HMK 102B Backhoe-Loader
17
Figure 2.1 illustrates the open-center loader hydraulic system circuit diagram of the
backhoe-loader modelled in this work. This system includes a prime mover, which is
the diesel engine in this case, a constant displacement pump, a directional control
valve, cylinders, relief and check valves and a hydraulic tank.
Standard blocks in the SimHydraulics library are used for modelling the pump, check
valve, relief valve, pipeline and hydraulic fluid. On the other hand, in modelling the
engine, directional control valve and hydraulic cylinder, custom subsystems are built
using the standard SimHydraulics, Simscape and Simulink blocks. All of the
equations given in this chapter are the equations used by the standard blocks under
the SimHydraulics library. These equations are given in order to show that the blocks
used in this model are compatible with the components on the physical machine and
they provide the complexity of the system.
2.1 Engine Model
Diesel engine power is transmitted to the pump with a rigid coupling. Therefore,
rotational speed of the engine and pump are same. Engine torque-speed characteristic
is modelled with the “Lookup Table” block under the Simulink library. Table of
engine rotational speed and engine torque values at full throttle are entered into the
block. This block computes the engine torque output for a given engine rotational
speed by linear interpolation or extrapolation. Figure 2.2 gives the engine torque
curve against engine rotational speed at full throttle of the Perkins Tier 3 engine used
in this machine. As can be seen from this curve, speed regulating governor sharply
decreases the output torque of the engine to zero at maximum engine speed, which is
2260 rev/min. It is assumed that engine output torque is linearly proportional to the
throttle. Therefore, a throttle input ratio changing between 0 and 1 is multiplied with
the engine output torque to obtain the engine output torque. Saturation blocks are
used to restrict the throttle input to go below 0 or above 1 and to prevent the engine
speed from going below low idle speed. Diesel engine model is given in Figure 2.3.
18
800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 24000
50
100
150
200
250
300
350
400
450
Rotational Speed (rpm)
Tor
que
(Nm
)
Diesel Engine Torque vs. Speed Curve at Full Throttle
Figure 2.2 - Diesel Engine Torque Curve at Full Throttle
1
Shaft
Torque-Speed Curveof the
Diesel Engine atFull Throttle
T
TorqueActuator
Throttle Saturation
Rotational Inertia of the Rigid Coupling andPump Internal Components
MD
Rigid Coupling
v
Motion Sensor
Low Idle SpeedSaturation
torque_engine
Goto
EngineTorque
EngineSpeed
Env
60/(2*pi)
Conversion fromrad/s to rpm
1Throttle
Figure 2.3 - Diesel Engine Model
19
A subsystem called “Rigid Coupling” (Figure 2.4) is constructed to simulate the
connection between the engine and the pump. In this subsystem “Torque Sensor”
block is used to measure the torque consumed by the hydraulic pump. This torque
value is subtracted from the engine output torque by using the “Torque Actuator1”
block. The “Inertia” block models the rigid rotating bodies which are simply the
coupling and the pump internal components. “Motion Sensor1” senses the rotational
speed of the coupling. This rotational speed is fed back to the hydraulic pump via
“Angular Velocity Source” block.
In summary, equations used by the MATLAB/Simulink blocks during the diesel
engine-rigid coupling-hydraulic pump system can be given as:
(2.1)
pumpPE JTT
dt
d
(2.2)
2
M
1
D
Motion Sensor1
RC
T
Torque Sensor
T
Torque Actuator1
PSS
PSS
AngularVelocity Source
vS
CR
torque_pump
Goto
Figure 2.4 - Rigid Coupling Subsystem Model
20
2.2 Pump Model
David Brown constant displacement external gear pump is modelled with the
standard “Fixed-Displacement Pump” block available under the SimHydraulics
library. Efficiency and internal leakage of the pump are taken into account during
simulations. “Fixed-Displacement Pump” block uses the following equations [23]:
pumpleakpump PkDq (2.3)
mech
pumppump PDT
(2.4)
HPleak
kk (2.5)
nom
nomvnompump
HP P
Dk
)1( (2.6)
TPpump PPP (2.7)
If the mechanical efficiency of the pump is not known, it can be calculated from
v
totalmech
(2.8)
Leakage flow in the pump is assumed to be linearly proportional to the pressure
difference across the pump and it is determined by the Hagen-Poiseuille formula
given as
leakHP
leakpump qk
qd
lP
4
128 (2.9)
21
where d and l are the geometric parameters of the leakage path. Leakage flow in the
pump can be calculated when pressure and flow are equal to nominal pressure and
nominal flow of the pump, respectively.
)1( vnompumpleak Dq (2.10)
Once leakage flow is determined, Hagen-Poiseuille coefficient can be calculated by
the following equation:
nom
nomvnompumpHP P
Dk
)1( (2.11)
The effect of fluid compressibility is neglected during pump modelling. Moreover, it
is assumed that leakage inside the pump is linearly proportional to the pump pressure
differential. Parameters used in pump modelling are given in Figure 2.5.
Figure 2.5 - Pump Model Parameters
22
2.3 Directional Control Valve Model
HUSCO 6000 series two-section mobile directional control valve is used in the
machine. This valve is an open-center type 6/3 (6 way/3 position) mechanically
controlled valve. Each section is connected in series to each other. Levers are used
for controlling the spool in the valve. Spool diameter and spool stroke are 20 mm and
8.73 mm, respectively. A load hold check valve is installed into the pump port in
order to prevent hydraulic oil from flowing in the opposite direction of the pump
flow.
Spool is held in its neutral position with springs on both sides when there is not any
input to the control levers. As can be seen in Figure 2.6, a by-pass (high pressure
carry-over) passage from P to T1, which lets the hydraulic fluid to pass through other
sections, is available in the neutral position of the valve. P to A, P to B, A to T and B
to T passages are all closed in the neutral position where A and B are cylinder ports,
P is the pump port and T is the return (tank) port. In this neutral position, all the
passages except for P to T1 are overlapped, whereas P to T1 passage is underlapped.
When the control lever is moved, passages from pump to cylinder and cylinder to
tank (P to A and B to T, or vice versa) open proportionally. As these passages open,
pump to by-pass passage closes at the same proportion.
New SimHydraulics subsystems are built for each section of this valve. As it can be
seen in Figure 2.7, each subsystem has six variable area orifices, which represent
each passage in the valve. Standard “Variable Orifice” block available in the
SimHydraulics library is used for this passage modelling. Each orifice is connected
to the same spool opening, S. Initial opening of P to T1 and P to T2 orifices are given
positive values in order to make the orifice underlapped. Other initial openings have
negative values, therefore they are overlapped orifices. Variable orifice is
parameterized by maximum passage area and orifice opening. The passage area is
assumed to be linearly dependent on the spool displacement.
23
Figure 2.6 – Section View and Symbol of 6/3 Directional Control Valve
Figure 2.7 - SimHydraulics Model the 6/3 Directional Control Valve
24
Laminar and turbulent flow regimes are taken into account by calculating the
Reynolds number and comparing its value with the critical Reynolds number in each
solution step. Equations used by “Variable Orifice” block in determining the flow
rate are as follows:
crH
DL
crd
forPD
AC
forPsignPAC
q
ReRe2
ReRe)(2
(2.12)
SSO xxh (2.13)
00
0)( max
max
hfor
hforh
Ah
hA (2.14)
ba PPP (2.15)
)(Re
hA
Dq H (2.16)
2
Re
cr
DDL
CC (2.17)
)(4 hADh (2.18)
It is assumed that the transition between the laminar and turbulent regimes is sharp at
critical Reynolds number. In addition to that, leakage inside the valve and effects due
to the fluid inertia are neglected during directional control valve modelling. Model
25
parameters used in underlapped orifices are given in Figure 2.8. For overlapped
orifices, all the parameters except for the initial opening value are same as the
underlapped orifice parameters. Overlapped orifice initial opening is -1 mm.
“Saturation” blocks are also used to restrict the spool position input between -8.73
mm and 8.73 mm.
Figure 2.8 - Underlapped Orifice Model Parameters
2.4 Cylinder Model
“Double-Acting Hydraulic Cylinder” block in SimHydraulics library is not used
since it is not possible to specify the initial pressure in this block. Instead of that, a
new cylinder subsystem (Figure 2.9) is constructed with the Simscape library blocks.
“Translational Hydro-Mechanical Converter” blocks are used to convert hydraulic
energy to mechanical energy in both directions of the cylinder. “Piston Chamber”
blocks simulate the fluid compressibility in the cylinder chamber. Stroke of the
cylinder is limited with the “Translational Hard Stop” block. “Ideal Translational
Motion Sensor” is also added to the subsystem in order to measure the instantaneous
26
position of the piston and this position is fed back to the “Piston Chamber” blocks for
the fluid compressibility calculations.
4
B
3 A
2
R1
C
RC
Translational HardStop
CAR
TranslationalHydro-Mechanical
Converter1
CA R
TranslationalHydro-Mechanical
Converter
P A
Piston Chamber B
P A
Piston Chamber A
R
C
V
P
Ideal TranslationalMotion Sensor
Figure 2.9 - Hydraulic Cylinder Subsystem Model
By taking the piston area as an input, “Translational Hydro-Mechanical Converter”
block uses the following very basic equations for transforming hydraulic energy in to
mechanical energy [24].
)( CR vvAq (2.19)
PAF (2.20)
“Translational Hard Stop” block restricts the motion of the piston at the lower and
upper ends of the cylinder. Contact between the piston and cylinder head is modelled
27
with a spring damper system in order to simulate the elastic impact and energy loss
behaviour of the end stops. Figure 2.10 shows a simple model of this block.
Equations used by “Translational Hard Stop” block are given as:
(2.21)
nCRnn
Pn
PCRPP
HS
gforvvDK
ggfor
gforvvDK
F
)(
0
)(
CR xx (2.22)
dt
dxv R
R (2.23)
dt
dxv C
C (2.24)
Figure 2.10 - Translational Hard Stop Model [23]
28
“Piston Chamber” block simulates the fluid compressibility in the hydraulic cylinder
by using the hydraulic oil bulk modulus property defined in Section 2.7 with the
following equation:
dt
dpxxAq O
)(
(2.25)
Pressure built up in the cylinder is calculated when there is no input to the directional
control valve. Then, this pressure value is given as the initial pressure in the “Piston
Chamber” block.
Figure 2.11 - Lift Cylinder Model Parameters
29
Figure 2.12 - Bucket Cylinder Model Parameters
It is assumed that there is not any internal or external leakage present in the hydraulic
cylinders. Since the standard double-acting cylinder block in SimHydraulics library
is not used, a new input window is constructed for specifying the cylinder model
parameters. Lift cylinder and bucket cylinder model parameters are given in Figure
2.11 and Figure 2.12, respectively.
30
2.5 Relief and Check Valve Models
There are two different relief valves in this loader hydraulic system. First one is the
main relief valve (primary relief valve), which avoids the main system from
excessive pressure and prevents any failure of the hydraulic components.
In the neutral position of the directional control valves, cylinder ports are isolated
from the pump flow path, therefore main relief valve is not able to prevent over
pressure present in the cylinders in that condition. In order to avoid this over pressure
in the cylinder ports, anti-shock relief valves (secondary relief valve) are used in this
system. Another advantage of these relief valves is that each cylinder port maximum
pressure can be set at different values independent from the main relief valve set
pressure.
Figure 2.13 - Direct Acting Pressure Relief Valve [24]
31
Both of these relief valves are direct acting type (Figure 2.13). The poppet, which is
the moving regulating element, is held in its fluid blocking position with a spring
when the system pressure is lower than the set value. Poppet starts to move when the
system pressure reaches to the preset value, which determined by the spring preload
force. This pressure at which the poppet starts to move is called the cracking pressure
of the valve. If the system pressure increases further, poppet moves from its blocking
position and lets the fluid to flow to the reservoir.
Moreover, a check valve is used in parallel to the anti-shock relief valve (ARV) in
order to avoid cavitation in the cylinder. When the cylinder pressure drops below the
tank line pressure, hydraulic fluid flows to the cylinder from the tank through the
check valve and prevents the further decrease in cylinder pressure. A subsystem
called “ARV” is implemented into the hydraulic system model to simulate the anti-
shock and anti-cavitation valve group.
Standard “Pressure Relief Valve” and “Check Valve” blocks under the
SimHydraulics library are used for modelling the relief valve and check valve,
respectively. Laminar and turbulent flow regimes are taken into account by
calculating the Reynolds number and comparing its value with the critical Reynolds
number in each solution step similar to the procedure described in directional control
valve modelling section. Equations used by “Pressure Relief Valve” and “Check
Valve” are given as:
crH
DL
crd
forPD
AC
forPsignPAC
q
ReRe2
ReRe)(2
(2.26)
(2.27)
maxmax
max 0)()(
ppforA
pppforppkpA crackcrack
32
crackPP
Ak
max
max (2.28)
BA ppp (2.29)
)(Re
PA
Dq H (2.30)
2
Re
cr
DDL
CC (2.31)
)(4 PADh (2.32)
It is assumed that the transition between the laminar and turbulent regimes is sharp at
critical Reynolds number. In addition to that, leakage inside the valve and effects due
to the fluid inertia are neglected during relief and check valve modelling. Parameters
used in relief valve and check valve models are given in Figure 2.14 and Figure 2.15,
respectively.
Figure 2.14 - Main Relief Valve Model Parameters
33
Figure 2.15 - Check Valve Model Parameters
2.6 Hydraulic Pipeline Model
Pump, directional control valve and cylinders are connected to each other with hoses,
pipes and fittings. All the pipeline components have circular cross-section. Fittings,
bendings, junctions and other local resistances are converted to their equivalent
lengths and added to the pipe length.
Figure 2.16 - Hydraulic Pipeline Model [23]
34
Figure 2.16 shows the SimHydraulics model of the hydraulic pipeline used in this
thesis. It consists of two standard “Resistive Tube” blocks and a “Constant Volume
Chamber” block to simulate the friction losses and fluid compressibility,
respectively. Equations used by “Constant Volume Chamber” have already been
discussed in Chapter 2.4 during cylinder modelling. Frictional pressure loss along the
pipe is determined with the Darcy’s equation [26]. This equation given below is also
used by “Resistive Tube” block.
g
v
D
LLfh
f
pipe
eql 2
2
(2.33)
and by using Equation (2.33), pressure loss along the pipe is calculated by:
lhgP (2.34)
Haaland approximation [27] is used by the “Resistive Tube” block to calculate the
friction factor in turbulent regime with the following equations:
T
pipe
TLLLT
LTL
LS
for
D
r
forff
f
forK
f
ReRe
7.3Re
9.6log8.1
1
ReReRe)Re(ReReRe
ReReRe
211.1
10
(2.35)
P
Pipe
A
DqRe (2.36)
35
It is assumed that the fluid flow is fully developed along the pipe length and effects
due to the fluid inertia are not taken into account. Parameters used in the pipeline
between the directional control valve and the lift cylinder bore side are given in
Figure 2.17. All the parameters of the pipelines are the same except for the pipe
length. Pipeline lengths between the directional control valve-cylinder bore side and
directional control valve-cylinder rod side are 1000 mm and 1500 mm, respectively.
Figure 2.17 - Pipeline Model Parameters
2.7 Hydraulic Fluid Properties
Shell Tellus T46 hydraulic oil is used in this system. This oil has a kinematic
viscosity of 46 mm2/s at 40oC oil temperature. Therefore, it is ISO VG 46 compliant
oil. This oil is modelled with “Hydraulic Fluid” block in SimHydraulics library.
Throughout the analysis, oil temperature is kept constant at 60oC, which is the
optimum working temperature. Fluid properties are given in Figure 2.18.
36
Since air is 10,000 times more compressible than hydraulic oil, trapped air inside the
oil drastically affect the bulk modulus of the oil. As can be seen from the above
figure, it is assumed that relative amount of trapped air inside the hydraulic oil is
0.005. Change in bulk modulus due to the trapped air is calculated with the following
equation inside the SimHydraulics environment [23]:
l
n
n
a
na
n
a
a
l
PPn
P
PP
P
1
1
1
)(
1
1
(2.37)
Figure 2.18 - Hydraulic Fluid Properties
The Simulink subsystem, which includes the hydraulic component models described
in this chapter, can be found in Figure 2.19.
37
4Bucket_B3Bucket_A2
Lift_B
1
Lift_A
Signal 1
Throttle ControlSystem&Relief
Flowrate
f(x)=0
SolverConfiguration
PSS
PSS
Scope8
Scope1
Saturation1
Saturation
AB
Pump Hose
PSS
AB
Main Relief Valve
S
P
T
Main Gear Pump
AB
Lift Cylinder Flowrate
Lift_B HoseAB
Lift_A Hose
S
T
P
A
B
T1
Lift Valve
Lift Spool to Bucket Spool Flowrate
Signal 1
Lift Spool Control
Lift Cylinder Pressure
SignalPhy sical
Ideal Pressure Sensor3
SignalPhy sical
Ideal Pressure Sensor2
Signal Phy sical
Ideal Pressure Sensor1
Signal Phy sical
Ideal Pressure Sensor Sig
nal
In
Ou
t
Ideal Flowrate Sensor4
Signal
In
Out
Ideal Flowrate Sensor3
Signal
InOut
Ideal Flowrate Sensor1
Sig
nal
Ou
t
Ideal Flowrate Sensor
In
Sig
nal
In
Ou
tIdeal FlowrateSensor2
ISO VG 46Hydraulic Tank Volume
V P R
Hydraulic Tank
Throttle Shaf t
Diesel Engine
AB
Check Valve
AB
Bucket_B HoseA
B
Bucket_A Hose
CV
ARV1
S
T
P
P_T1
A
B
T1
Bucket Valve
0
Bucket Spool Control
Bucket Cylinder Pressure
Bucket Cylinder Flowrate
CV
ARV
Relief
Sy stem
Volume
38
Figure 2.19 - Simulink Loader Hydraulic System Model
CHAPTER 3
3MECHANICAL SYSTEM MODELLING
Loader mechanism used in this machine is a two degree of freedom mechanism
actuated by four hydraulic cylinders operating in parallel (Figure 3.1). There are 10
dynamic mechanical parts and 24 revolute joints in this loader mechanism.
This mechanism is completely symmetrical with respect to the longitudinal axis of
the machine. In order to model the mechanical system in three dimensions, flexibility
of the attachments and clearances inside the revolute joints must be specified.
Otherwise, the system becomes statically unstable system and this may lead to
inconsistent results in the simulation. Because of that, it is assumed that there is not
any motion present in the lateral axis of the machine and the mechanism motion is
planar. Therefore, three-dimensional system is reduced into two-dimensional planar
system.
Standard rigid body and joint blocks under the SimMechanics library are used in
mechanical system modelling.
In this chapter, firstly the procedure to determine the mass and inertia properties of
the mechanical parts is explained. After that, an initial mechanism position is chosen
and the mechanism is implemented into the SimMechanics model by specifying the
coordinates of the joints at this predetermined initial position. Details of the friction
model used in this system are also given in this chapter. Mechanical part names used
throughout this chapter are illustrated in Figure 3.2.
39
Figure 3.1 - Loader Mechanism of the HMK 102B Backhoe-Loader
Figure 3.2 - 2D Drawing of the Loader Mechanism
40
3.1 Determination of Mass and Inertia Tensor Properties of the Parts
A CAD assembly can be imported directly into SimMechanics with a translator
while preserving the joint types as well as the mass and inertia of each part in the
assembly. This is a useful tool if the parts in the CAD assembly do not contain sub-
assemblies. If they do so, it becomes ineffective to use this translator since
inappropriate bodies are created in the SimMechanics model. Because of that, direct
import method is not used in this work.
3D drawings of the loader mechanism parts are created in Pro/ENGINEER®. The
advantage of using a 3D computer aided drawing software is that the software lets
the user to determine the mass and inertia properties of the part. In this section, the
procedure for obtaining the mass and inertia matrix of the front arm is described as
an example. Same procedure is followed for the other parts in the mechanical system.
Firstly, center of gravity (COG) is found according to the default coordinate system
of the front arm drawing. A new coordinate system is constructed at this located
center of gravity. Then, a line is drawn between the chassis-front arm connection
point and front arm-bucket connection point. X axis of the coordinate system at the
COG is aligned with this line as shown in Figure 3.3. Similarly, while keeping the
position of the coordinate system constant, Y axis of the COG coordinate system is
aligned with the line which is perpendicular to line used in defining the X axis.
Therefore, position and orientation of the coordinate system at the COG are specified
completely.
The inertia tensor of a body in SimMechanics is defined with respect to that body's
COG coordinate system [28]. Orientations of the COG coordinate systems in
SimMechanics and Pro/ENGINEER should coincide with each other in order to
obtain an accurate model. The moment of inertia tensor of a body does not change as
the body rotates since the COG coordinate system of the body is fixed rigidly on that
body.
41
Density of the material is defined as 7850 kg/m3. Mass and moment of inertia tensor
at the coordinate system specified above are determined by Pro/ENGINEER. Inertia
tensor, I, is a 3x3 matrix.
Figure 3.3 - Mass and Inertia Tensor Properties of the Front Arm
3.2 Implementation of Loader Mechanism to the SimMechanics Model
It is assumed that a coordinate system is placed in the center of the revolute joint
connecting the chassis and the front arm and it is the origin of the mechanism. While
the X axis of this coordinate system is in the longitudinal direction of the machine, Y
axis is in the vertical direction of the machine. In AutoCAD®, a two dimensional
computer-aided drawing software, all the revolute joint coordinates are determined
42
with respect to the coordinate system described above at the predetermined initial
position given in Figure 3.2. Lengths of the hydraulic cylinders are also calculated
from the two-dimensional drawing. In this initial position, extension of the lift and
bucket cylinders are 47 mm and 288 mm, respectively. Bucket is parallel to the
ground in this position. Gravity is defined as 9.81 m/s2 in the –y direction of the
global coordinate system, which points downwards.
In order to model the rigid moving parts in the system, “Body” blocks in
SimMechanics library are used. Mass and moment of inertia tensor properties
determined in Pro/ENGINEER are specified for each part. Positions and rotations of
the coordinate systems located at the center of gravities of the moving parts are also
implemented into the model.
“Ground” blocks in SimMechanics library are used to model the connection between
the loader mechanism parts and the machine chassis. This block represents a point
which is not moving throughout the simulation. Front arm, lift cylinder and Part 4
body blocks are connected to the “Ground” blocks with “Revolute Joint” blocks,
which represent one rotational degree of freedom between two bodies.
Hydraulic cylinder is modelled with two separate bodies, bore and rod, connected
with a prismatic joint. “Prismatic Joint” block represents single translational degree
of freedom along the axis in which the rod translates. Initial distance between the
cylinder bore bottom end and the piston is consistent with the initial stroke defined in
Section 2.4 in hydraulic modelling of the cylinder. Since the mechanical system is
reduced to planar 2D, cross-sectional area of the hydraulic cylinders are multiplied
by two in order to represent the hydraulic cylinders working in parallel to each other.
In order to obtain a better visualization of the mechanical model, external graphics
file is used to visualize the body geometry. Firstly, in Pro/ENGINEER, three-
dimensional drawings of each part are exported into Stereolithographic (STL) file
format to specify the three-dimensional surface geometry or shape of that body. COG
43
coordinate system is used in exporting the STL file. Then, these STL files are
embedded into the body blocks in SimMechanics. Coordinate system of the STL file
is attached to the COG coordinate system for each body in SimMechanics.
SimMechanics visualization of the loader mechanism, which illustrates the
mechanical parts, center of gravities of these parts and coordinate systems on these
parts, is given in Figure 3.4.
Figure 3.4 - SimMechanics Visualization of the Loader Mechanism
44
3.3 Introduction of Friction
Friction is a difficult phenomenon to simulate since it is highly non-linear and hard
to predict. In this work, only the friction inside the hydraulic cylinder is modelled
parallel to the studies done on this subject. Friction in the revolute joints and the
friction between the spool and the valve casing are neglected in this study.
Standard “Cylinder Friction” block in SimHydraulics library is used to model the
friction in the hydraulic cylinder between the cylinder bore and rod. Friction force is
the sum of Coulomb and viscous frictions including the Stribeck effect and its value
changes with varying velocity and pressure. Coulomb friction force increases as the
pressure inside the cylinders pushes harder on the seal. The preload force due to the
seal squeeze during assembly and the force proportional to pressure are also included
in Coulomb friction. Viscous friction force is directly proportional to the relative
velocity between the moving bodies. Equation used by the “Cylinder Friction” block
in friction force estimation is given as [23]:
vfvsignvcKppfFF vvbrkBAcprf exp)11()(( (3.1)
As can be interpreted from Equation (3.2), there is a discontinuity at zero velocity. In
order to overcome this problem, a small region |v| ≤ vth is implemented around zero
velocity, where friction force is assumed to be linearly proportional to velocity.
Therefore, computational efficiency is increased.
Rahmfeld et al. [22] measured the friction force in a hydraulic cylinder. According to
that study, 3 kN is the highest value of the friction force measured in the hydraulic
cylinder, which has a maximum cylinder force of 100 kN. Therefore, according to
this study, maximum friction force in the hydraulic cylinder is approximately 3 % of
the maximum cylinder force. Similarly, same friction force ratio is used in this thesis
and parameters used in the “Cylinder Friction” block are selected accordingly.
Parameters used in cylinder friction model are given in Figure 3.5. According to
45
these parameters, friction forces at different cylinder pressures are calculated and
plotted in Figure 3.6.
Figure 3.5 - Cylinder Friction Parameters
Cylinder Friction Force vs. Rod Velocity
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
-0,4 -0,3 -0,2 -0,1 0 0,1 0,2 0,3 0,4
Velocity (m/s)
Fo
rce (
kN
)
P=50 bar P=100 bar P=150 bar P=200 bar
Figure 3.6 - Cylinder Friction Force vs. Rod Velocity Graph at Different Pressures
46
47
3.4 Co-Simulation of Hydraulic and Mechanical Models
Connection between the SimHydraulics and SimMechanics models are obtained by
introducing the “Prismatic Translational Interface” elements between the hydraulic
and mechanical models of the cylinders. Firstly, hydraulic system model calculates
the pressure built up in the cylinders while keeping the position and velocity of the
cylinder constant. This pressure is converted into the cylinder force and fed to the
mechanical model. Mechanical model uses forward dynamics to determine the
positions and velocities of the bodies by using the cylinder forces. New position and
velocity of the hydraulic cylinder is computed and fed back to the hydraulic system
model. In each solution step, the cycle given in Figure 3.7 is repeated and therefore
co-simulation of hydraulic and mechanical models is obtained.
Figure 3.7 - Solution Cycle for Co-Simulation
B F
Revolute9
BF
Revolute8
BF
Revolute7
BF
Revolute6
BF
Revolute5
B F
Revolute4
B F
Revolute3
BF
Revolute2
BF
Revolute11
BF
Revolute10
B F
Revolute1
BF
Revolute
BF
Prismatic1
B FP Prismatic -
TranslationalInterface1
B FP Prismatic -
TranslationalInterface
B F
Prismatic
Position_lift
CS
1C
S2
Part 4 CS
1C
S2
Part 3
CS1CS2
CS3
Part 2
CS2CS1
CS3
Part 1
Env
MachineEnvironment
CS1 CS2
Lift Cylinder Rod
Front Arm
A
C
B
R
t C ctiLif ylinder Fri on
CS1 CS2
Lift Cylinder Bore
R
B
C
A
R
B
C
A
Lift Cylinder
Joint Sensor2
Joint Sensor1
Joint Sensor
Lift_A
Lift_B
Bucket_A
Bucket_B
Hydraulic System
CS1
CS2
CS3
CS4
CS5
Force_chassis
Force_arm
Chasis
Chasis Connection Point
Chasis ConnectionPoint 2
CS1 CS2CS1 CS2
Bucket CylinderBore
Bucket Cylinder Rod
A
C
B
R
Bucket Cylinder Friction
R
B
C
A
R
B
C
A
Bucket Cylinder
CS1 CS2
Bucket
48
Figure 3.8 - Mechanical System Model
CHAPTER 4
4VERIFICATION OF THE MODEL
Various measurements are made on the actual physical machine in order to verify the
simulation model. During the measurements, control valve position input and engine
throttle input are arranged as identical to the inputs used in the simulation. Measured
system variables are
Engine rotational speed
Lift cylinder head side pressure
Lift cylinder rod side pressure
Lift cylinder head side flow rate
Lift cylinder rod position
In this chapter, firstly, instrumentation used in measurements is explained in detail.
After that, measurement points are illustrated. Finally, comparison of the simulation
and measurement results are given.
4.1 Measurement Instrumentation
It is important to collect all the data with one data acquisition system in order to
eliminate the possible time shifts for different measurement point data. Hydrotechnik
Multi-System 5050 data acquisition system (Figure 4.1) is used in this work.
49
Figure 4.1 - Hydrotechnik Multi-System 5050
This data acquisition system has four analog and two digital measuring inputs. This
system is a compact and robust data acquisition system with a maximum scanning
rate of 0.1 ms.
Cylinder pressure measurements are conducted with Hydrotechnik 0-600 bar
pressure sensors, which generate 0 to 20 mA signal output by using piezo-resistive
measuring principle (Figure 4.2). These sensors have a response time of 1 ms with an
accuracy of ±0.75 bar.
50
Hydrotechnik 16-600 l/min flow rate sensor (Figure 4.3) is used to measure the flow
rate in the lift cylinder of the loader system. It is a turbine type flow rate sensor with
an inductive sensor installed on the turbine casing in order to measure the rotational
speed of the turbine. This measured rotational speed is converted to the flow rate
with a response time of 40 ms. Accuracy of the sensor is ±1 l/min. Ports for pressure
and temperature measurements are also available on the casing of the flow rate
sensor.
Hydrotechnik rotational speed sensor (Figure 4.4) is used to measure the rotational
speed of the diesel engine. A reflector is placed on the surface of the rotating part of
the engine in order to obtain a correct measurement.
Figure 4.2 - Hydrotechnik 0-600 bar Pressure Sensor
51
Figure 4.3 - Hydrotechnik 16-600 l/min Flow Rate Sensor
Figure 4.4 - Hydrotechnik Rotational Speed Sensor
52
Lift cylinder position is measured with an OPKON linear variable displacement
transducer (Figure 4.5). It has 800 mm maximum stroke with an accuracy of ±0.5
mm. This transducer has 0-10 V regulated output signal and it can be connected
directly to Hydrotechnik Multi-System 5050 data acquisition system.
Figure 4.5 - OPKON Linear Variable Displacement Transducer
4.2 Measurement Points
As stated in the mechanical modelling chapter, loader mechanism on the machine is
completely symmetrical with respect to the longitudinal axis of the machine.
Position, velocity and acceleration of the cylinders on the left and right side of the
machine are identical. Similarly, flow rate and pressure built up in these cylinders are
53
same. Therefore, it is sufficient to measure the system parameters only for one
cylinder.
In order to measure pressure built up in the lift cylinder, pressure sensors are
installed on the head and rod side of the left-hand side lift cylinder. In addition to
that, flow rate sensor is mounted between the main control valve and the head side of
the lift cylinder. Installation of pressure sensors and flow rate sensor is given in
Figure 4.6 and Figure 4.7.
Diesel engine rotational speed is measured directly from the crank pulley of the
engine. Rotational speed sensor is placed as directly facing the surface of the crank
pulley. A reflector is also installed on the pulley in order to minimize the reading
errors. Figure 4.8 shows the installation of the rotational speed sensor and the
reflector on the machine.
Due to the installation problems, linear variable displacement transducer (LVDT) is
placed on to the right-hand side cylinder. Body of the LVDT is stabilized on to the
bore of the cylinder with clamps. Rod side of the LVDT is mounted to the pin, which
connects the front arm and the lift cylinder. Intense care is taken to keep the LVDT
parallel to the lift cylinder during the test in order to obtain a correct measurement of
the rod displacement. Installation of the LVDT can be seen in Figure 4.9.
54
Figure 4.6 - Installation of the Pressure and Flow Rate Sensors
Figure 4.7 - Installation of the Flow Rate Sensor
55
Figure 4.8 - Installation of the Rotational Speed Sensor
Figure 4.9 - Installation of the Linear Variable Displacement Transducer
56
4.3 Comparison of the Results
Verification of the model is made for one case, which is lifting the empty bucket
from predetermined position to its maximum height at full engine throttle while
keeping the bucket cylinder length constant.
Firstly, input for the simulation and measurement is determined. There are three
inputs for this system: lift spool position, bucket spool position and engine throttle.
Directional control valve is mechanically controlled in physical machine, therefore
lift spool and bucket spool positions are controlled directly by the spool position
input in the model.
Lift spool position is kept at zero during the first three seconds. At t=3 s, a ramp
input is given and in two seconds position of the spool is increased linearly to
8.73 mm, which is the maximum spool displacement. After t=5 s, spool position
input is kept constant at this maximum value until the end of the simulation. It is
illustrated in Figure 4.10. There is no input to bucket spool position; therefore it stays
at zero during the simulation. As it is seen from Figure 4.11, a ramp input is given to
the throttle control at t=0.7 s. It reaches the full throttle value in 1.3 seconds and
stays at this full throttle value throughout the simulation.
ODE15s variable-step solver is used in the simulation. It takes approximately 29
seconds to run this simulation on a Core2Duo 2.5 GHz computer.
Before starting the measurement, hydraulic oil temperature is increased to 60oC,
which is also the temperature of hydraulic oil in simulation. Firstly, machine is
adjusted to the initial position described in Chapter 3.2. Then, inputs identical to the
ones in simulation are given to the machine and system parameters are recorded.
Total simulation and measurement time is 10 seconds.
57
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
7
8
8.73
Time (second)
Po
siti
on
(m
m)
Lift Spool Position vs. Time
Figure 4.10 - Lift Spool Position Input
0 1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (second)
Th
rott
le
Throttle Opening Ratio vs. Time
Figure 4.11 - Throttle Input
58
Figure 4.12 gives the engine rotational speed graph for simulation and measurement.
Simulation results show a good agreement with the measurement. Engine speed
starts from low idle speed, 870 rpm, and increases to the maximum engine speed,
2260 rpm, in two seconds. After that, it stays at this maximum speed value. It can be
interpreted that the engine model, which includes the engine torque characteristics
and the inertia of the shaft and pump internal components, works well.
0 1 2 3 4 5 6 7 8 9 10800
1000
1200
1400
1600
1800
2000
2200
2400
Time (second)
Sp
eed
(rp
m)
Engine Rotational Speed vs. Time
Simulation
Measurement
Figure 4.12 - Engine Rotational Speed
Flow rate between the directional control valve and the head side of the lift cylinder
is plotted for simulation and measurement in Figure 4.13. In the first three seconds,
since there is no input to the spool position, flow rate is zero. With the ramp input of
lift spool position at t=3 s, flow rate through the lift cylinder starts to increase and
59
reaches its maximum value, 145 l/min. At t=7 s, lift cylinder piston reaches the end
stroke, pressure builds up in the cylinder and as this pressure reaches the pressure
setting of the main relief valve, lift cylinder flow rate decreases sharply to zero since
all the fluid supplied by the pump goes directly to the tank through the main relief
valve. Consequently, movement of the piston stops. Lift cylinder flow rate remains
zero until the end of the analysis.
As can be seen from the same graph, flow rate decreases slightly as the pressure of
the system increases. This is a result of the increasing internal leakage in the pump
due to the increasing pump pressure. Since the simulation and measurement results in
this region are parallel to each other, it can be concluded that the internal leakage
behaviour of the pump is modelled correctly. There is a slight deviation between the
simulation and measurement results in the increasing and decreasing flow rate
sections; however, this level of accuracy is enough for this study.
0 1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
Time (second)
Flo
w R
ate
(l/m
in)
Lift Cylinder Head Side Flow Rate vs. Time
Simulation
Measurement
Figure 4.13 - Lift Cylinder Head Side Flow Rate
60
Figure 4.14 gives the simulation and measurement results of the lift cylinder head
side pressure on the same graph. Weights of the parts in the loader system create an
initial pressure in the head side of the lift cylinder. This initial pressure is defined
correctly in the model. With the introduction of the lift spool input at t=3 s, pressure
in the head side of the lift cylinder starts to increase until the lift cylinder piston
reaches the end of the cylinder stroke. When the piston movement is restricted due to
the cylinder stroke limit, pressure increases sharply to the main relief valve setting
pressure and it remains at that value until the end of the analysis.
As Figure 4.14 and Figure 4.15 show, stiction inside the cylinder causes the head and
rod side pressures to increase suddenly just before the piston of the cylinder starts to
move at t=3.5 s. In general, simulation results are consistent with the measurement
results.
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
140
160
180
200
220
240
Time (second)
Pre
ssu
re (
bar
)
Lift Cylinder Head Side Pressure vs. Time
Simulation
Measurement
Figure 4.14 - Lift Cylinder Head Side Pressure
61
Lift cylinder rod side pressure are also plotted for simulation and measurement
(Figure 4.15). As stated before, there is a pressure increase at t=3.5 s due to the
stiction in the lift cylinder. Measurement pressure values are approximately 1 bar
higher than the simulation pressure values. This may be due to the lack of the
hydraulic oil cooler resistance in the model. Except for that difference, simulation
results follow the same trajectory with the measurement results.
0 1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12
14
16
18
20
22
24
Time (second)
Pre
ssu
re (
bar
)
Lift Cylinder Rod Side Pressure vs. Time
Simulation
Measurement
Figure 4.15 - Lift Cylinder Rod Side Pressure
Figure 4.16 illustrates the lift cylinder rod displacement in simulation and
measurement. Lift cylinder rod displacement is at its initial value, 47mm, during the
first three seconds of the analysis. As the lift spool position input starts to increase at
62
63
t=3 s, lift cylinder rod displacement also starts to increase until it reaches the stroke
limit at t= 7 s. Model shows quite a good agreement with the measurement results.
0 1 2 3 4 5 6 7 8 9 100
50
100
150
200
250
300
350
400
450
500
550
600
650
700
750
800
Time (second)
Dis
pla
cem
ent
(mm
)
Lift Cylinder Rod Displacement vs. Time
Simulation
Measurement
Figure 4.16 - Lift Cylinder Rod Displacement
CHAPTER 5
5CASE STUDY
In this chapter, results of the case study are presented. Dynamic reaction forces on
the front arm and chassis are obtained from the simulation. Then, these forces are
compared with the static forces used in structural analysis of the attachments.
In this case study, the most critical case is considered. It is assumed that an additional
weight is present in the bucket. Maximum allowable lift capacity of this machine,
1000 kg, is used as the mass of this additional weight. It is assumed that the weight is
uniformly distributed in the bucket. Therefore, mass of the bucket is increased by
1000 kg in the model. Similarly, inertia matrix of the bucket is tuned accordingly in
order to represent the actual physical conditions of the machine.
Lift spool position input and throttle input are identical to the inputs given in the
previous chapter. These inputs are illustrated in Figure 5.1 and Figure 5.2. Bucket
spool position input is held at zero. Similarly, initial position of the mechanical
system is the same with the one in Chapter 4.
System variables such as lift cylinder pressure, lift cylinder flow rate, lift cylinder
rod displacement, engine rotational speed, engine output torque are obtained from the
simulation. In addition to that, dynamic reaction forces between the lift cylinder rod
and the front arm are measured in the simulation.
It takes approximately 12 seconds to run this simulation with the ODE15s variable-
step solver on a Core2Duo 2.5 GHz computer.
64
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
7
8
8.73
Time (second)
Pos
ition
(m
m)
Lift Spool Position vs. Time
Figure 5.1 - Lift Spool Position Input for Case Study
0 1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (second)
Th
rott
le
Throttle Opening Ratio vs. Time
Figure 5.2 - Engine Throttle Input for Case Study
65
As can be seen in Figure 5.3, engine reaches its maximum rotational speed in less
than two seconds and stays at this value throughout the simulation.
0 1 2 3 4 5 6 7 8 9 10800
1000
1200
1400
1600
1800
2000
2200
2400
Time (second)
Spe
ed (
rpm
)
Engine Rotational Speed vs. Time
Figure 5.3 - Engine Rotational Speed-Case Study
Figure 5.4 gives the engine output torque curve for this simulation. Engine output
torque stays constant at the start of the simulation, since the engine throttle input is
constant. With the ramp throttle input at t=0.7 s, engine output torque starts to
increase. At t=1.7 s, engine reaches its maximum rotational speed and therefore
governor reduces the output torque of the engine and holds the engine speed
constant. When the attachments start to move, the pressure in the system increases
and therefore it increases the engine output torque. After reaching the end of stroke
in the lift cylinder, engine torque output stays constant at 265 Nm due to the constant
227 bar system pressure.
66
0 1 2 3 4 5 6 7 8 9 100
50
100
150
200
250
300
Time (second)
Tor
que
(Nm
)
Engine Output Torque vs. Time
Figure 5.4 - Engine Output Torque-Case Study
Lift cylinder head side pressure given in Figure 5.5. As expected, initial pressure
built up in the cylinder due to the weights of the bodies is higher when compared to
the pressure in the previous chapter. With the lift spool movement at t=3 s, pressure
increases suddenly due to the stiction inside the cylinder. Pressure increases
uniformly until the piston reaches the end of stroke. When the piston reaches stroke
end, pressure increases sharply; however, the main relief valve prevents the pressure
to increase any more.
Similarly, flow rate inside the lift cylinder starts to increase with the spool position
input at t=3 s. When the piston reaches the end of stroke, flow rate decreases as
expected. If the flow rate values of this case and the case without the additional
weight are compared, it can be seen that flow rate decrease with the increasing
pressure due to the decreasing efficiency is higher in this case since the leakage
inside the pump is modelled as linearly proportional to the pump pressure.
67
0 1 2 3 4 5 6 7 8 9 1040
60
80
100
120
140
160
180
200
220
240
Time (second)
Pre
ssur
e (b
ar)
Lift Cylinder Head Side Pressure vs. Time
Figure 5.5 - Lift Cylinder Head Side Pressure- Case Study
0 1 2 3 4 5 6 7 8 9 100
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
Time (second)
Flo
w R
ate
(l/m
in)
Lift Cylinder Head Side Flow Rate vs. Time
Figure 5.6 - Lift Cylinder Head Side Flow Rate-Case Study
68
Lift cylinder rod displacement curve shows a similar characteristic with the one in
the verification chapter; however, during the extension of the piston, the slope of the
curve, which is the piston velocity, is smaller in this case due to the lower pump
volumetric efficiency at higher pump pressure.
0 1 2 3 4 5 6 7 8 9 100
50
100
150
200
250
300
350
400
450
500
550
600
650
700
750
800
Time (second)
Dis
plac
emen
t (m
m)
Lift Cylinder Rod Displacement vs. Time
Figure 5.7 - Lift Cylinder Rod Displacement-Case Study
In Figure 5.8, bucket center of gravity coordinates in x and y directions with respect
to the origin located at the connection point between the front arm and the machine
chassis are illustrated. As can be seen from the graph, during the lift operation, COG
of the bucket first moves in the positive x-direction; however, when it reaches a
certain height, it starts to move in the negative x-direction. This graph helps the user
to visualize the motion of the bucket.
69
2200 2300 2400 2500 2600 2700 2800 2900 3000-1500
-1000
-500
0
500
1000
1500
2000
2500
X-Coordinate (mm)
Y-C
oord
inat
e (m
m)
Bucket COG Y-Coordinate vs. X-Coordinate
Figure 5.8 - Bucket COG Coordinates
Figure 5.9 illustrates the components of the reaction forces on the front arm and the
machine chassis when the lift cylinder piston reaches the end of stroke. F1 is the
resultant force on the machine chassis in the revolute joint between the machine
chassis and front arm. It is computed by applying the maximum static lift cylinder
force when the lift cylinder is fully extracted. F2 is the maximum lift cylinder static
force.
Maximum static force applied by the cylinder is defined simply as the maximum
system pressure multiplied by the cross-sectional area of the cylinder and can be
given as:
APF system (5.1)
70
cosFFx (5.2)
sinFFy (5.3)
where θ is the angle between the resultant force and the horizontal plane as it is given
in Figure 5.9.
Figure 5.9 - Forces on the Loader Mechanism
71
Reaction forces in the X and Y directions measured on the front arm in the revolute
joint between the lift cylinder and front arm are given in Figure 5.10 and Figure 5.11,
respectively. As it is illustrated, reaction forces increase drastically when the lift
cylinder piston reaches the stroke end and hits the cylinder bore. As can be seen in
Figure 5.12 and Figure 5.13, reaction forces on the machine chassis in the revolute
joint between the front arm and the chassis show a similar behavior.
In addition to that, in Figure 5.14, reaction force on the front arm in the revolute joint
between the front arm and lift cylinder in Y direction, F2y, is plotted against the same
reaction force in X direction, F2x. It can be seen that a similar behaviour to the bucket
COG coordinates curve illustrated in Figure 5.8 is observed for the reaction forces on
the front arm.
0 1 2 3 4 5 6 7 8 9 10-350
-300
-250
-200
-150
-100
-50
0
50
100
150
Time (second)
For
ce (
kN)
Reaction Force Between Lift Cylinder and Front Arm in X Direction vs. Time
Figure 5.10 - Reaction Force Between Lift Cylinder and Front Arm in X Direction
72
0 1 2 3 4 5 6 7 8 9 10-500
-400
-300
-200
-100
0
100
200
Time (second)
For
ce (
kN)
Reaction Force Between Lift Cylinder and Front Arm in Y Direction vs. Time
Figure 5.11 - Reaction Force Between Lift Cylinder and Front Arm in Y Direction
0 1 2 3 4 5 6 7 8 9 10-400
-300
-200
-100
0
100
200
Time (second)
For
ce (
kN)
Reaction Force Between Chassis and Front Arm in X Direction vs. Time
Figure 5.12 - Reaction Force Between Chassis and Front Arm in X Direction
73
0 1 2 3 4 5 6 7 8 9 10-400
-300
-200
-100
0
100
200
Time (second)
For
ce (
kN)
Reaction Force Between Chassis and Front Arm in Y Direction vs. Time
Figure 5.13 - Reaction Force Between Chassis and Front Arm in Y Direction
76 78 80 82 84 86 88 90 920
20
40
60
80
100
120
Force in X-Direction (kN)
For
ce in
Y-D
irect
ion
(kN
)
Reaction Force on the Front Arm in the Revolute Joint Between Front Arm and Lift Cylinder
Figure 5.14 - Reaction Forces on the Front Arm
74
75
Maximum values of the dynamic forces obtained from the simulation are compared
with the maximum static forces for F1 and F2 in Table 5.1. For this case study, it is
found that the maximum dynamic resultant force for F1 is 67.5% higher than the
maximum static resultant force. Similarly, there is 87.4% difference between the
dynamic and static resultant forces for F2.
Table 5.1 – Comparison of Maximum Static Forces with Maximum Dynamic Forces
Maximum Static Force(kN)
Maximum Dynamic Force(kN)
F1x 210,6 352,8
F1y 229,0 383,5
F1 311,1 521,1
F2x 173,5 325,0
F2y 230,9 432,7
F2 288,8 541,2
CHAPTER 6
6DISCUSSION, CONCLUSION AND RECOMMENDATIONS
6.1 Discussion and Conclusion
In this study, a dynamic model is developed to perform the hydraulic and mechanical
simulation of the loader system of a backhoe-loader. By developing such a model, it
is aimed to calculate the dynamic forces on the bodies and joints of the loader
system. In addition to that, implementing the model-based design process explained
in this study, it is expected to reduce the cost and time of the design process.
Instead of deriving and programming the hydraulic and mechanical system
equations, physical simulation toolboxes inside MATLAB environment are used to
model the hydraulic and mechanical systems of the machine. Hydraulic system
response due to the dynamic motion of the rigid parts is obtained by co-operating the
mechanical and hydraulic simulations in Simulink platform.
Pump, check valve, relief valve, pipeline and hydraulic fluid are modelled with the
standard blocks in the SimHydraulics library. On the other hand, custom subsystems
are built using the standard SimHydraulics blocks in order to model the diesel
engine, directional control valve and hydraulic cylinder.
Three-dimensional loader mechanism is reduced to two-dimensional planar system.
After determining the mass and inertia properties of the rigid bodies in the system,
mechanical system is implemented into the SimMechanics model with the
predetermined mechanism position. Friction is introduced only in the hydraulic
76
cylinders. Friction in the revolute joints and the friction between the spool and the
valve casing are neglected in this study.
Dynamic system model is verified with the flow, pressure, rotational speed and
position measurements performed on the physical machine. It is presented that the
simulation results are consistent with the measurement results.
A case study is performed in order to compare the maximum dynamic forces
obtained from the simulation with the maximum static forces currently used for the
structural analysis of the attachments. It is found that the dynamic forces on the rigid
bodies and the machine chassis are higher than the static forces.
In conclusion, this dynamic machine model, which includes the hydraulic and
mechanical systems, can be used in determining the dynamic loads on the joints and
attachments of the backhoe-loader. Then, these dynamic loads may be used as an
alternative loading condition for the stress analyses of the attachments. In addition to
that, this model may be integrated into the design process in order to reduce
prototyping time and costs during the design process.
6.2 Recommendations for Future Work
Dynamic forces obtained in this study can be used for the structural analyses of the
critical attachments such as front arm and machine chassis. Loading conditions of the
finite element analysis (FEA) can be defined according to these dynamic force
values.
Backhoe system of the machine can also be modelled for a further study in digging
operations; however, the followed procedure may remain exactly the same.
77
Friction in the revolute joints can be added to the mechanical system model for a
more accurate analysis. In addition to that, friction coefficients in the hydraulic
cylinder can be determined with a method similar to the one explained by Rahmfeld
et al. [22].
Hydraulic components such as hydraulic oil cooler, bendings and fittings, which are
not modelled in this work, can be included in the model for a further study on the
hydraulic system.
A control system may be implemented into this model for future works on trajectory
planning and autonomous motion of the machines. In conjunction with that, a
realistic simulator for machine operator training may be developed by using this
model.
78
REFERENCES
[1] SAE J1116 REV. NOV2004: Categories of Off-Road Self-Propelled Work
Machines.
[2] ISO 6165:2006: Earth-moving machinery – Basic types – Identifications and
terms and definitions.
[3] Avallone E. A., Baumaister T III., Marks’ Standard Handbook for
Mechanical Engineers, 10th edition, McGraw-Hill International editions,
1997.
[4] Kılıç B., Balkan T., Söylemez E., Dynamic Analysis of a Backhoe-Loader
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