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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x

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’

8

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

9

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

13

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

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Machines.

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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

including Hydraulics, Proceedings of the 5th National Hydraulic Pneumatic

Congress and Exhibition, İzmir, pp. 359-375, 2009.

[5] Bosch Rexroth AG, www.boschrexroth.com, last visited on August 2009.

[6] Forsberg K., Mooz H., The Relationship of Systems Engineering to the

Project Life Cycle, Engineering Management Journal, 4(3), pp. 36-43, 1992.

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