static modelling and stability analysis of non-slewing...

Static Modelling and Stability Analysis of

Non-Slewing Articulated Mobile Cranes

by

Jing Wu (20475615)

This thesis

is presented for the degree of

Master of Engineering by Research

of The University of Western Australia

in

School of Mechanical and Chemical Engineering

Western Australia, Australia, 2012

ii

Abstract

Non-slewing articulated mobile (NSAM) cranes are widely used in construction,

manufacturing, and mining industries in Australia. However, the occurrence of several

tipping accidents in Australia has raised concerns about their stability. This project aims to

explore the operating factors contributing to the NSAM crane tipping accident, examine the

inherent stability of the NSAM crane design, and suggest the potential development of a new

monitoring system to reduce the likelihood of the accidents. It does this using geometrical

modelling and theoretical static force analysis. A general static model for the stability study

of NSAM cranes on slopes with various orientations is developed and an investigation into

the tip-over and roll-over stabilities of the model under a number of static conditions is

presented in this thesis. Based on the developed model, the articulation angle, the slope

gradient, the orientation angle, and the height of the boom are the main operating factors

contributing to the NSAM crane tipping accidents. The results of the examination of the

inherent NSAM crane design suggests that having the articulation joints at the centre of the

wheel base is a suitable design for NSAM cranes for the maneuverability and tip-over

stability but not for the roll-over stability. After the explanation of the shortcomings of the

current monitoring system for NSAM cranes, this project suggests the potential development

of a new monitoring system based on the result of the developed model. Such a device would

likely increase the safety of these machines.

iii

Statement Candidate Contribution

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis and

not accepted by any other institutions.

I understand that my thesis may be made electronically available to the public.

iv

Acknowledgements

I would like to take this opportunity to express my deep gratitude and appreciation to those

people who have helped me to complete my Master of Engineering by Research program,

and to individuals to whom I am very much indebted and who, without their support, this

achievement would not have been possible.

First of all, special thanks to my supervisors, Professor Melinda Hodkiewicz and Research

Assistant Professor Andrew Louis Guzzomi, both of whom greatly contributed to the

successful outcome of this project. I thank them for their guidance, enthusiasm and support.

Also I wish to express my thanks to my former supervisor Dr Nathan Scott for his guidance

and support of this project at an earlier stage.

Moreover, the information and data provided by the Monadelphous is gratefully

acknowledged. Especially to Darryl Reeves, Brad McLean, Lee Rollings, and Michael

Pietrutie.

Many thanks to my friends, with them I have shared so much fun and so many good times

over the past two years in Western Australia. Many thanks to all the members of my family

for their support and encouragement. Finally, my greatest appreciations and thanks are

dedicated to my parents from whom I have taken the lesson of life. I am very proud of them.

v

Table of Contents

List of Figures ........................................................................................................... viii

List of Tables ................................................................................................................ x

List of Abbreviations.................................................................................................... xi

Nomenclature ..............................................................................................................xii

1 Introduction ........................................................................................................... 1

1.1 Motivation ...................................................................................................... 1

1.2 Scope and Objectives ...................................................................................... 2

1.3 Chapter Outline ............................................................................................... 2

1.4 The Significances of This Study ...................................................................... 3

2 Literature Review and Theory ............................................................................... 4

2.1 Chapter Aims .................................................................................................. 4

2.2 NSAM Crane .................................................................................................. 4

2.3 Literature Review............................................................................................ 6

2.4 Problem Statement ........................................................................................ 15

2.5 Hypothesis .................................................................................................... 15

2.6 Chapter Summary ......................................................................................... 17

3 Methodology ....................................................................................................... 18

3.1 Chapter Aims ................................................................................................ 18

3.2 Map of Methodology...................................................................................... 18

3.3 Model Development ...................................................................................... 20

3.4 Case Study .................................................................................................... 21

3.5 Chapter Summary ......................................................................................... 21

4 Theoretical Modeling .......................................................................................... 23

4.1 Chapter Aims ................................................................................................ 23

4.2 Approach of The Model Development .......................................................... 23

4.3 Assumptions ................................................................................................. 24

4.4 General Model Development......................................................................... 25

4.5 Specific Models Development ....................................................................... 32

4.5.1 Tip-over Stability on Level Ground ........................................................ 32

4.5.1.1 Without Articulation Angle ........................................................... 32

4.5.1.2 With Articulation Anlge ................................................................ 34

vi

4.5.2 Roll-over Stability Across a Side Slope .................................................. 36

4.5.2.1 Without Articulation Angle ........................................................... 36

4.5.2.2 With Articulation Anlge ................................................................ 38

4.6 Result Validation .......................................................................................... 42

4.7 Chapter Summary ......................................................................................... 46

5 Case Study .......................................................................................................... 47

5.1 Chapter Aims ................................................................................................ 47

5.2 Case Analysis ............................................................................................... 47

5.2.1 Articulaiton Angle ................................................................................. 49

5.2.2 Slope Gradient ....................................................................................... 51

5.2.3 Orientation Angle .................................................................................. 53

5.2.4 Height of the Load/Boom ....................................................................... 55

5.2.5 Attached Counter Weight ........................................................................ 56

5.3 Chapter Summary ......................................................................................... 58

6 Discussion ........................................................................................................... 59

6.1 Chapter Aims ................................................................................................ 59

6.2 Examine the Current Frame Design .............................................................. 59

6.2.1 Tip-over Stability ................................................................................... 60

6.2.2 Roll-over Stability.................................................................................. 66

6.3 A Potential Development of the Monitoring System ...................................... 72

6.3.1 Shortcomings of the Current Monitoring System .................................... 72

6.3.2 The design of the New Monitoring System for NSAM cranes ................ 73

6.4 Limitations of the Project .............................................................................. 77

6.4.1 Model Limitation ................................................................................... 77

6.4.2 Information Limitation ........................................................................... 78

6.4.3 Pratical Test Limitation .......................................................................... 78

6.5 Chapter Summary ......................................................................................... 78

7 Conclusion .......................................................................................................... 80

7.1 Thesis Summary ........................................................................................... 80

7.2 Future Work .................................................................................................. 82

References .................................................................................................................. 83

Appendix A: ............................................................................................................... 87

Appendix B: ................................................................................................................ 89

Appendix C: ................................................................................................................ 90

vii

PUBLICATIONS FROM CANDIDATURE ............................................................... 92

viii

List of figures

2-1 Schematic representation of a NSAM crane with component labels ................ 5

2-2 Schematic representation of stabilities of a NSAM crane ................................ 6

2-3 Schematic representation of a NSAM crane and a typical FELASV with

roll-OL denoted, a) NSAM crane ; b) FELASV ............................................ 12

2-4 Relation between 1l , 2l and the turning radii of the anterior and the

posterior bodies for: a) 1 2l l< ; b) 1 2l l= ; and c) 1 2l l> of a left turning

NSAM crane................................................................................................. 16

3-1 Map of methodology .................................................................................... 19

3-2 The flow chart of the Model Development .................................................... 20

4-1 Schematic of a NSAM crane on slope with orientation angle ( γ ) from 0 00 ~ 360 ...................................................................................................... 24

4-2 Schematic of a NSAM crane across a side slope with individual COG

locations, geometry and coordinated systems indicated ................................. 26

4-3 FBD of a NSAM crane on level ground in the: a) straight, and b)

articulated configurations.............................................................................. 33

4-4 Schematic of a straight NSAM crane across a side slope with COG

locations, geometry and coordinated systems indicated ................................. 36

4-5 Schematic of an articulated NSAM crane across a side slope with COG

(C) locations, geometry and coordinate systems indicated for the cases of:

a) anterior body higher than posterior body, and; b) posterior body higher

than anterior body ........................................................................................ 40

4-6 Schematic Representation of configurations according to Table 4-1 .............. 43

4-7 Distance from COG to OL as a function of orientation angle ......................... 44

5-1 Rollover accident (Universal crane, 2009) .................................................... 48

5-2 The relationship between the distance from the combined COG to the OL

and the articulation angle .............................................................................. 50


and the slope gradient ................................................................................... 52

5-4 Comparison of the distance from the COG to the OL between 00 and 040

articulation angle on a slope of 05 ................................................................. 54

ix


and the boom angle ....................................................................................... 55

5-6 The comparison of the distance from the combined COG to the OL when

counter weight is not attached, attached on anterior body, and attached on

posterior body ............................................................................................... 57

6-1 Schematic Representation Configurations according to Table 6-1: a)

5 6 3 4m b f rG l G l G l G l+ > + ; b) 5 6 3 4m b f rG l G l G l G l+ = + ; c)

5 6 3 4m b f rG l G l G l G l+ < + ............................................................................... 63

6-2 The relationship between the combined normal forces on the rear tyres

( RL RRN N+ ) and the distance from the rear drive axle to the centre of the

articulation joints ( 2l ) for three configurations .............................................. 64

6-3 Example One of the operation procedure of a NSAM crane .......................... 67

6-4 Example Two of the operation procedure of a NSAM crane ......................... 68

6-5 Schematic representation of configurations according to Table 6-3 ............... 69

6-6 The relationship between the ditance from the combined COG to the OL

and the orientation angle ............................................................................... 70

6-7 Example of current monitoring system on NSAM cranes (Robway, 2007) .... 72

6-8 The concept of the new design of the monitoring system .............................. 74

6-9 Roll angle 1β ................................................................................................ 75

6-10 Pitch angle 2β .............................................................................................. 75

B-1 Lifting chart of manual extension retracted of Franna AT-14 ........................ 89

C-1 The schematic representation of the NSAM crane with different ranges of

1l and 2l : a) 1 2l l> ; b) 1 2l l= ; and c) 1 2l l< ................................................... 90

x

List of Tables

2-1 The differences between the typical MB crane and NSAM crane .................... 8

2-2 Differences between the NSAM crane and FELASV ................................... 11

4-1 Example NSAM crane operting configuration values ................................... 43

5-1 The description and potential cause of an accident from the report ................ 48

5-2 Example input values for the study of roll-over accident ............................... 49

6-1 Example values for tip-over stability analysis ............................................... 62

6-2 Tip-over stability analysis result ................................................................... 65

6-3 Example NSAM crane operating configuration values .................................. 69

6-4 The variation of the distance from the combined COG to the OL under

different design geometries during the example operation procedures

shown in Figure 6.2.2.1 and Figure 6.2.2.2 ................................................... 71

6-5 The classification and resource of the input data ............................................ 74

xi

List of Abbreviations

NSAM Non-slewing articulated mobile

ASV Articulated steer vehicle

COG Centre of Gravity

DOF Degree of freedom

FBD Free body diagram

MB Mobile Boom

OL Overturn Line

SCL Slope Contour Line

xii

Nomenclature

FLA Contact point between ground and left front tire

FRA Contact point between ground and right front tire

RLA Contact point between ground and left back tire

RRA Contact point between ground and right back tire

b Half track width

C Centre of gravity (COG) of the total crane including the load

D Distance from the totG vector to the OL

mG Weight force of the load

cG Weight force of counter weight

bG Weight force of the boom

fG Weight force of the anterior body and the front drive axle

rG Weight force of the posterior body and the rear drive axle

TOTG Total weight force of the crane including the mass

hh Boom lifting point height

bh Boom COG height

fh Anterior body COG height

rh Posterior body COG height

1l Longitudinal distance from the front drive axle to the centre of articulation joints

2l Longitudinal distance from the rear drive axle to the centre of articulation joints

3l Longitudinal distance from the anterior body COG to the front drive axle

xiii

4l Longitudinal distance from the posterior body COG to the rear drive axle

5l Longitudinal distance from the load COG to the front drive axle

6l Longitudinal distance from the boom COG to the front drive axle

7l Distance between the load COG to the boom lifting point

FLN Normal force on left front tire

FRN Normal force on right front tire

RLN Normal force on left back tire

RRN Normal force on right back tire

1O Projection middle point of front drive axle

2O Projection middle point of rear drive axle

1OL Front tip-over line

2OL Rear tip-over line

3OL Left hand side roll-over line

4OL Right hand side roll-over line

1R Turning radius of anterior body

2R Turning radius of posterior body

r Tire radius

bW Wheel base

X Change of the orientation angle

α Slope gradient

θ Articulation angle

1β Roll angle

xiv

2β Pitch angle

γ Orientation angle

φ Boom angle

ϕ Coefficient of sliding friction

Introduction

1

1 Introduction

1.1 Motivation

Non-slewing articulated mobile (NSAM) cranes are commonly used in the construction,

mining and manufacturing industries for general purpose pick – and – carry of heavy

components because of their high-maneuverability. However, in recent years there have been

reports of a number of NSAM crane tipping accidents in Australia. They are:

• A 14 tonne NSAM crane tipped over on the south side of Willowdale crusher, WA on

26 June 2009 (Universal cranes, 2009);

• A 25 tonne NSAM crane tipped over in Brisbane, Queensland on 19 January 2010

(Universal cranes, 2010);

• A NSAM crane tipped over in North Rockhampton, Queensland on 18 May 2010

(Crane crushes, 2010);

• A NSAM crane tipped over in Brisbane, Queensland on 23 August 2010 (Crane tips

in Brisbane, 2010);

• Two NSAM cranes tipped over at mine site of Queensland in 2011 (Department of

Employment, Economic Development and Innovation, 2011).

An investigation conducted by the Department of Employment, Economic Development and

Innovation Australia (2010) into these accidents identified human factors associated with

inadequate ground preparations and driver training. However, the number of these events

suggests that design may be an issue.

Introduction

2

1.2 Scope and Objectives

The primary aims of the project are to:

• Explore what operating factors contribute to the tipping accidents of NSAM cranes;

• Examine the current frame design of NSAM cranes from a static stability perspective;

and

• Suggest a potential development of a control/monitoring system to assist the operators

to reduce the likelihood of NSAM crane tipping accidents.

1.3 Chapter Outline

The structure of this thesis is presented as follows:

Chapter 1 – The introduction defines the motivation, project scope and objectives, outlines

the frame of this thesis and illustrates the significance of this project.

Chapter 2 – A research background and literature review chapter, provides an introduction to

the NSAM cranes. This chapter reviews the work that has been done previously to understand

the stability of mobile boom (MB) cranes and articulated steer vehicles (ASVs). This chapter

also defines the main problems addressed and hypothesis posed in this project.

Chapter 3 – This model development chapter describes the methodology of this project and

explains the approach taken to the model the NSAM cranes.

Chapter 4 – This theoretical model development chapter - develops a general static model for

the stability analysis of the NSAM crane with different configurations and orientations. A

Introduction

3

number of individual models corresponding to specific configurations and/or orientation

angles are presented so as to validate the result obtained from the general model.

Chapter 5 – A case study chapter - investigates what operating factors contribute to the

tipping accidents of NSAM cranes. This involves the study of the impact of the articulation

angle, the slope gradient, the orientation, the height of the load/boom, and the counter weight

on the stability of NSAM cranes.

Chapter 6 – This is a discussion chapter that examines the current frame design from a

stability perspective. It discusses the potential development of a control/monitoring system to

indicate the real time COG position of the NSAM crane across the full range of operation.

This chapter also outlines the limitations of this project.

Chapter 7 – The conclusion chapter summarises the main findings of this project, and

suggests future work.

1.4 The Significance of This Study

This work is important as there have been a number of incidents related to the stability of

NSAM cranes reported in Australia, five in the last three years.

Although there is an established body of studies on the stability of a similar articulated

vehicle, ASVs, there appears to be no published investigations on the design of NSAM cranes

per se. This work investigates the factors which might contribute to the incidents. The

developed models will improve the understanding of designers and potentially lead to either

changes in design and/or development of monitoring systems on the unit to assist the

operators.

Background and Literature Review

4

2 Background and Literature Review

2.1 Chapter Aims

The aims of this chapter are to:

• Provide an introduction to the NSAM crane;

• Review the previous work on the stability of MB cranes and ASVs;

• Define the problem of this study; and

• State the hypothesis.

2.2 NSAM Crane

A NSAM crane is similar to a conventional mobile crane in that it is designed to travel on

public roads. However, NSAM cranes have no stabilising arms or slewing pivot. They are

designed to lift the load and carry it to its destination, within a small radius, then be able to

drive to the next job. Typically, a NSAM crane is comprised of:

• an extendable and luffing boom;

• an anterior (front) body;

• a front drive axle with tyres;

• a posterior (rear) body; and

• a rear drive axle with tyres.

An example is shown in Figure 2-1.


5

Figure 2-1: Schematic representation of a NSAM crane with component labels

The anterior and posterior bodies are connected by two co-linear (revolute) articulation joints.

Steering is achieved through a change of the articulation (yaw) angle (θ , normally between

040− and 040 ) of the two bodies of the vehicle using two symmetric hydraulic actuators. The

front and rear drive axles are connected to the bodies with a pair of semi elliptic leaf springs.

When in the lifting and carrying mode, the front axle is normally locked rigidly to the

anterior chassis while the rear axle is still suspended for the protection of the articulation

joints (Terex Lifting Australia, n.d.). NSAM cranes are mainly designed to be operated on

firm, flat and level ground (to within 1% gradient). However, according to AS 2550.5

(Standards Australia, 2002), they are permitted to operate on side slope of up to 05 (8.75%


6

gradient) with reduced rated capacity (Terex Lifting Australia, 2001). Construction and

mining sites seldom present such perfect operation conditions.

2.3 Literature Review

There is an established body of literature on vehicle stability. Generally, these studies can be

grouped into three categories according to the stability type. They are: 1) yaw, 2) tip-over,

and 3) roll-over. Figure 2-2 demonstrates these three stabilities with reference to a NSAM

crane.

Figure 2-2: Schematic representation of stabilities of a NSAM crane.


7

As the NSAM crane is a type of mobile boom (MB) crane comprising an articulated steer

vehicle revision of studies on the stability of MB cranes and ASVs might contribute to the

understanding of the stability of NSAM cranes. It is also of interest to see what monitoring

systems exist to inform vehicle operators of stability condition. Research and development

literature in these areas will be reviewed in the subsequent sections.

2.3.1 Stability of MB Cranes

Early work by Towarek (1998) studied the impact of flexible soil foundation on the dynamic

stability of the MB crane. Kiliçaslan et al. (1999) investigated the stability of MB cranes by

determining the maximum allowable loads and rates for a typical MB crane. In their study,

the boom and payload were moving upwards while the chassis orientation was kept fixed by

using outriggers. They used their software to simulate the hydraulic cylinder piston force of

the developed model and compared the simulated result to the result from the experimental

test with a 10 tonne MB crane. Their results showed that the motion time of the boom affects

the crane stability considerably: a faster piston speeds lowers the lifting capacity.

One recent study carried out by Fujioka et al. (2009) investigated the tip-over stability of MB

cranes with double-pendulum payloads. The aim of that study was to address a gap in the

research on the tip-over stability analysis of MB cranes. Their study was separated into three

steps. The first one was to conduct a static stability analysis of a single-pendulum boom crane.

This provided initial insight into the static stability of MB cranes by allowing the relationship

between the payload weight, crane configuration and the normal forces on the contact points.

Another step was to use a semi-dynamic method by including payload swing angles to study

the stability of MB cranes with swinging payload. The third step was to carry out a full


8

dynamic method by studying a dynamic multi-body simulation of a double-pendulum

payload. The results of the last two steps were verified by the experimental tests.

More recently Maleki and Singhose (2011) developed a nonlinear model of a typical slewing

boom crane. Based on the developed model, a number of possible motions corresponding to

the operator’s commands were analysed. It was believed that input shaping (Singhose, 2009)

could significantly reduce motion-induced oscillations. To examine that, a command-shaping

control technique was implemented in this study and its effectiveness was compared with the

result from the unshaped simulation. The theoretical predictions were verified by the

experimental results.

Those studies were conducted based on their developed model of MB cranes. However, due

to the differences between the typical MB cranes and NSAM cranes outlined in Table 2-1, the

models developed in those studies cannot be directly utilised in this project to investigate

static stability.

Table 2-1: The differences between the typical MB crane and NSAM crane

Typical MB crane NSAM crane

Steering Single-frame with wheel

steering

Dual-frame with articulated frame

steering

Slewing Can turn 0360 with the slewing

base No slewing function

Stability Area Area within the lines connecting

four rigid outriggers

Area within the lines connecting

four contact points on the wheels

(which is a function of articulation

angle)


9

It can be seen from Table 2-1 that NSAM cranes share some similar design features with the

ASV notably: 1) articulated frame steering; and 2) the articulation joints are located at the

centre of wheelbase. Thus, a review of the previous studies on the stability of ASVs may

provide insight into modeling NSAM cranes.

2.3.2 Stability of ASVs

Early work by Gibson et al. (1974) explored the concepts of a stability triangle, and

development of an overturn line (OL) for ASVs. According to Gibson et al. (1974), the OL is

the line connecting the lower contact point between the tyre on the rigid axle (the axle is

rigidly connected to the vehicle body) and ground and the centre of swing axle (the axle is

pivot connected to the vehicle body).

The stability triangle method can be traced back earlier to the work by Coombes (1968) for

conventional tractors with swing axles. Some shortcomings in that method for swing axle

tractors have recently been presented by Guzzomi (2012). By accounting for the kinematics

of the pivot joint on the swing axle, he shows that two types of roll-over initiation are

possible and that brake activation can hinder the progression into the next phase. In regard to

ASVs, the analysis of Gibson et al. (1974) focused on the relationship between the slope

angle at which roll-over occurs and the minimum stability point for a given articulation angle.

Further work in this area by Zhao et al. (1996) developed a new equation for the OL for

ASVs. They concluded that increasing the distance from the rigid axle and articulation joints

can increase the roll-over stability of the articulated vehicle.


10

More recently, at Waterloo University, there have been a large number of studies on the yaw

stability of ASVs. Azad et al. (2005a) investigated the yaw stability of an ASV with a rear-

mounted load. In their developed model, a torsional spring and damper were used to represent

the stiffness and damping in the hydraulic cylinders at the articulation joints. By the

simulation in ADAMS, the results show the dynamic yaw instability can be reduced or

delayed to higher speeds by increasing the stiffness or damping. Additionally, the same

researchers (2005b) examined the relationship between the different drive configurations and

the dynamic behavior of the vehicle during the instabilities. In that study, they simulated a

virtual prototype of an ASV with front-wheel drive, rear –wheel drive and four-wheel drive

in ADAMS and found that the drive configuration has no significant effect on the dynamic

behavior of ASVs during the instabilities. In addition, they studied the relationship between

the front and rear tyres characteristics and the snaking of ASVs (Azad et al., 2005c). That

study was separated into two steps. Firstly they simulated their model in ADAMS to analyse

the tyre slip angles, forces and moments, and the articulation angle. Then they changed the

cornering stiffness of the front and rear tyres and simulated the model again. The results

showed some changes in the rear tyres properties, such as that the use of narrower tyres could

reduce the yaw instability of ASVs.

Although the studies on ASVs do provide some insight, mainly in regard to the dynamic

stabilities associated with the yaw degree of freedom (DOF), there are a number of

differences between the NSAM crane and the ASV (even in the straight configuration with

zero articulation angle). They are listed in Table 2-2 based on Figure 2-3 (for an articulated

steer front-end-loader). In a traditional static model for the stability study of ASVs, the tip-

over and roll-over instability occurs when the combined COG vector exceeds the OLs.

However, according to Table 2-2, the axle connections and the OLs for ASVs and NSAM


11

cranes are different. The model for the stability analysis of the ASV is not suitable for the

NSAM crane and thus a new model for NSAM cranes must be developed.

Table 2-2: Differences between the NSAM crane and ASV

NSAM crane ASV

Operating

Condition

The boom can extend and lift. The

height of the lifted load is

dependent on the length of the rope

The bucket can lift. The height of

the supporting load is dependent

on the height of the bucket

Axle Connections

Front axle can be regarded as

rigidly connected to the anterior

body while rear axle is suspended

connected to the posterior body

One axle (in this case front) is

rigidly connected to the anterior

body while the other (in this case

rear) axle is pivot connected to

the posterior body

Roll-over Line

The line connecting the contact

point between the lower front tyre

and ground and the contact point

between the lower rear tyre and

ground

The line connecting the contact

point between the lower tyre on

the rigid axle and ground and the

centre of the swing axle.


12

Figure 2-3: Schematic representation of a NSAM crane and a typical ASV with roll-OL denoted, a) NSAM crane ; b) typical ASV (case shown is a front-end-loader).


13

The above literature indicates that there is no publicly available literature that looks directly

at the static stability of NSAM cranes. However, some methodologies of the previous studies

contribute to this project. For example, the study conducted by Azad et al. (2005a) state a

hypothesis, which is the value of torsional spring stiffness or damping at the articulation joint

might contribute to the yaw instability of ASVs at lower speeds. They built a model that

allows the value of the spring stiffness or damping to be variable while keeping other

elements fixed. This technique uses the results from the simulation of the model to verify or

reject the hypothesis. Another methodology used by Fujioka et al. (2009) was to study the

relationship between the normal forces on the contact points and the crane operating

configurations. The third methodology can be learnt from Zhao et al (1996), which is to

investigate the stability of ASVs by studying the geometrical relation between the COG and

OL. The first methodology will contribute to the map of methodology in this project and the

others to the theory for modelling NSAM cranes.

2.3.3 Monitoring/Control System for ASVs

There have been several studies conducted on the development of the monitoring/control

system for MB cranes and ASVs. Typically, the monitoring systems designed for MB cranes

are mainly to prevent the tip-over accidents, while those devices designed for ASVs are from

the roll-over stability perspective. According to the listed incidents in Chapter 1, almost all

the NSAM crane tipping accidents are about roll-over stability. Hence, the next section

reviews the previous studies on the development of the monitoring/control system for ASVs.

An early warning device for four-wheel drive articulate logging machines with a pinned front

axle and rigid rear axle was developed by Gibson et al. (1981) based on their stability triangle


14

theory. The concept of this design collected the tipping forces data applied to the vehicle by a

number of mounted sensors, and the system modified the shape of the stability triangle of the

vehicle accordingly. Wray et al. (1984) developed two different types of warning devices for

front-end loaders. The first system was built based on the concept of calculating the angle at

which the loader would roll over by the input of the data from five sensors. The difference

between the theoretical result and the actual roll angle was divided into four different levels

and indicated by four different colour indicators, or levels of risk. This device was

implemented on three loaders for practical tests for about one year and was assessed as being

very helpful. Later, they built a second device that was cheaper and simpler. The concept of

the second device was to trigger the system when the normal force on one of the four wheels

reaches the threshold. This time, instead of using sensors, they utilised strain gauges to detect

the bending stress on the axles.

More recently, Azad (2006) demonstrated the shortcomings of some control systems that use

passive methods. Furthermore, he suggested some alternative solutions for dynamic yaw

instability, which are to develop different types of stability control systems: 1) an active

steering system with a classical controller; 2) an active torque vectoring device with a robust

full state feedback controller; and 3) a differential braking system with a robust variable

structure controller, to generate a stabilising yaw moment. The capabilities to stabilize the

vehicle of these suggested controllers were simulated with different operating conditions and

surfaces during the snaking mode.


15

2.4 Problem Statement

In Chapter One, a number of NSAM crane tipping accidents that had been reported were

listed. However, according to the literature review, two questions have thus far not been

answered:

1. What design factors contribute to the occurrences of NSAM crane tipping accidents?

2. Is it possible to reduce the likelihood of NSAM crane tipping accidents?

This study aims to answer these two questions. To help answer these questions, the

development of a static model for the stability study of NSAM cranes is required.

2.5 Hypothesis

There are a number of factors that could contribute to the increasing occurrences of NSAM

crane tipping accidents. Apart from operating factors suggested by the government

investigations (Department of Employment, Economic Development and Innovation

Australia, 2010), the inherent crane design may be relevant. In the literature review, it was

found that a NSAM crane adopts a traditional frame design similar to that of the ASV. That is,

to have the length between the front drive axle and the centre of the articulation joints ( 1l )

equal to the length between the rear drive axle and the centre of the articulation joints ( 2l ).

According to Azad (2006), the advantages of this key design feature are:

1 provides the greatest maneuverability. This can be explained by Figure 2-4;


16

2 for a four-wheel-drive vehicle, no centre differential is needed as the tyres on the

same side keep the same speed;

Figure 2-4: Relation between 1l , 2l and the turning radii of the anterior and the posterior bodies for: a) 1 2l l< ; b) 1 2l l= ; and c) 1 2l l> of a left turning NSAM crane

However, due to a number of differences between the NSAM crane and the ASV, this key

design feature might reduce the stability of NSAM cranes. Therefore, the null hypothesis and

alternative hypothesis are, respectively:

Null hypothesis:

Having the articulation joints at the centre of wheelbase is a good design for the stability of

NSAM cranes.

Alternative hypothesis:

Having the articulation joints at the centre of wheelbase is not a good design for the stability

of NSAM cranes.


17

2.6 Chapter Summary

In this chapter, a description of the NSAM crane was given. Reviews of previous work on the

stability of MB cranes and ASVs were conducted as there have been limited studies on

NSAM cranes and, more importantly, the NSAM crane is a type of MB crane and shares

some similar design features with the ASV. Although the models developed by previous

researchers for the stability of ASVs are not directly suitable to NSAM cranes, suitable

methodologies from the literature contribute to this project.

Methodology

18

3 Methodology

3.1 Chapter Aims

• Outline the methodology of this project;

• Explain the approach taken to the model development for the stability study of NSAM

cranes; and

• Demonstrate the aim of case study.

3.2 Methodology

The methodology for this study is shown in Figure 3-1.

Firstly, a general static model for the stability study of NSAM cranes is required. In this

model, the distance from the front axle to the articulation joints ( 1l ) and the distance from the

rear axle to the articulation joints ( 2l ) are variable. However, 1 2l l+ is fixed. Then different

operating conditions and orientations will be defined to examine whether 1 2l l= provides the

best stability for a NSAM crane under different operating conditions and orientations. If

1 2l l= provides the best stability for a NSAM crane, a suggestion for the development of a

control system will be given. Otherwise, additional suggestions, which may increase the

stability of NSAM cranes, will also be stated.

Methodology

19

Figure 3-1: Map of methodology

Methodology

20

3.3 Model Development

In the methodology, a most important step is the model development for the static stability

study. This involves several intermediate steps as shown in Figure 3-2.

Clarify Theory

State Assumptions

Develop General Model Develop Specific Model

Validate Result

Indentify Symbols

Figure 3-2: The flow chart of the Model Development

Firstly, the symbols necessary to describe a NSAM crane need to be identified. This has been

done in Chapter 2. Then the theory of the model development needs to be clarified. After that,

a number of assumptions are necessary. Based on these assumptions, a general static model

Methodology

21

for the stability study of NSAM cranes can be developed. Lastly, several specific models are

used to validate the result from the general model.

3.4 Case Study

After the model is developed and validated from a calculation perspective, a case study

section is introduced. This section not only examines the developed model for real operating

conditions and orientations, but also could conclude what operating factors contribute to the

NSAM crane tipping accidents. Hence, this section aims to study the impact of several factors

on the stability of NSAM cranes according to one representative tipping accident of NSAM

crane, they are:

• the articulation angle θ ;

• the slope gradient α ;

• the orientation angle γ ;

• the height of the carried load/boom φ ; and

• the counter weight cG .

3.5 Chapter Summary

This chapter outlines the methodology of this project, which is to use an analytical

engineering method to examine the current frame design of NSAM cranes. Based on the

stated research problem and hypothesis in Chapter 2, the development of a static model for

the stability study of NSAM cranes is required. The approach taken for the development of

this model is explained in that chapter. The aim of case study is demonstrated after that. By

Methodology

22

carrying out the case study section, the developed model can be used to investigate real

operating conditions. Ultimately some insight into the operating factors that may contribute

to the tipping accidents of NSAM cranes can be concluded.

Theoretical Modelling

23

4 Theoretical Modelling

4.1 Chapter Aims

• Introduce the approach taken to develop the general model for the stability study of

NSAM cranes;

• Outline the assumptions;

• Illustrate the process of the development of the general model;

• Describe the processes of the development of the specific models; and

• Validate the results.

4.2 Approach of the model development

The approach taken to model the stability of the NSAM cranes focuses on the determining

the geometric relationship between the combined COG (C, denoted as ) of the crane

including the load and the OLs with different parking orientation angle (γ ) from 0 00 ~ 360 .

Instability is assumed to occur when crosses the nearest OL downslope, given by D in

Figure 4-1.


24

Figure 4-1: Schematic of a NSAM crane on slope with orientation angle (γ ) from 0 00 ~ 360

4.3 Assumptions

Prior to the development of the theoretical model, it is important to outline a number of

assumptions. They are:

• The instability is caused statically by the combined COG exceeding the OL;

• The ground is assumed to be firm and flat, but not necessarily level;

• The articulation joints of NSAM cranes only permit the yaw degree of freedom;


25

• The crane bodies are assumed symmetric and rigid and can be geometrically

represented as lines and concentrated point masses. Thus the COGs of the boom, the

anterior and posterior bodies are located on the mid plane of the straight crane resting

on horizontal ground;

• Both the front and rear axles are assumed to be rigidly connected to the vehicle’s

anterior and posterior bodies respectively. It is expected that accounting for tyre and/

or suspension deflection may increase instability on the slope and thus the developed

model likely provides a conservative estimate;

• The weight forces of the boom ( bG ) and the anterior and the posterior bodies ( fG and

rG ) are assumed to be constant in magnitude and orientated parallel to the gravity

field;

• Wind force, deformation of the tyres and all inertial forces are neglected.

4.4 General Model Development

The schematic for a non-straight NSAM crane across a slope is shown in Figure 4-2.


26

Figure 4-2: Schematic of a NSAM crane across a side slope with individual COG locations, geometry and coordinated systems indicated


27

From Figure 4-2 a, it is possible to define the individual COG positions of the crane elements

in coordinate system 1 1 1 1O X Y Z .

Thus for the supported load:

1 5 7

7

1 5

( ) cos sincos

( )sin

X

Y

Z

m

m h

m

G l l lG h l

l lG

γ ααγ

+ − = − − +

(4.1)

the boom:

1 6

1 6

( ) cos

( )sin

X

Y

Z

b

b b

b

G l lG h

l lG

γ

γ

+ = − +

(4.2)

the anterior body:

1 3

1 3

( ) cos

( )sin

X

Y

Z

f

f f

f

G l lG h

l lG

γ

γ

− = − −

(4.3)

and finally, for the posterior body:

2 4

2 4

( ) cos( )

( )sin( )

X

Y

Z

r

r r

r

G l lG h

l lG

γ θ

γ θ

− − + = − +

(4.4)


28

The coordinates of the combined COG (C) in coordinate system 1 1 1 1O X Y Z for the total crane

can be found from the individual components. Thus, i ic

G XXG

=∑ , i ic

G YYG

=∑ , and

i ic

G ZZG

=∑ (Kleppner & Kolenkow, 1973) gives

1 5 7 1 6 1 3 2 4

7

1 5 1 6 1 3 2 4

(( ) cos sin ) ( ) cos ( ) cos ( ) cos( )

( cos )

( )sin ( )sin ( )sin ( )sin( )

m b f r

TOT

Xm h b b f f r r

YTOT

Z

m b f r

TOT

G l l l G l l G l l G l lG

CG h l G h G h G h

CG

C

G l l G l l G l l G l lG

γ α γ γ γ θ

α

γ γ γ γ θ

+ − + + + − − − +

− + + + = − + − + − − + − +

(4.5)

The coordinate of each tyre contact point in coordinate system 1 1 1 1O X Y Z can be found:

Thus, for the front left tyre:

1

1

cos sin0

( sin cos )

X

Y

Z

FL

FL

FL

A l bA

l bA

γ γ

γ γ

− = − +

(4.6)

for the front right tyre:

1

1

cos sin0

( sin cos )

X

Y

Z

FR

FR

FR

A l bA

l bA

γ γ

γ γ

+ = − −

(4.7)

for the rear left tyre:


29

2

2

( cos( ) sin( ))0

sin( ) cos( )

X

Y

Z

RL

RL

RL

A l bA

l bA

γ θ γ θ

γ θ γ θ

− + + + = + − +

(4.8)

and for the rear right tyre:

2

2

( cos( ) sin( ))0

sin( ) cos( )

X

Y

Z

RR

RR

RR

A l bA

l bA

γ θ γ θ

γ θ γ θ

− + − + = + + +

(4.9)

As the governing OL changes depending on the different orientation angle ( γ ) and the

articulation angle ( θ ), it is important to define the limit angles which define the zones

corresponding to each OL. To achieve this, the orientation angle ( γ ) that results in the COG

being in line with each down slope tyre is determined. This defines a region of applicability

for each OL. Hence:

2 4

1 5 1 6 1 3 2 4 1

( )sinarctan( )( ) ( ) ( ) ( ) cos

r TOTFL

m b f r TOT

G l l G bG l l G l l G l l G l l G l

θγ πθ

− += +

+ + + + − − − − (4.10)

2 4

1 5 1 6 1 3 2 4 1

( )sinarctan( )( ) ( ) ( ) ( ) cos

r TOTFR

m b f r TOT

G l l G bG l l G l l G l l G l l G l

θγ πθ

− −= +

+ + + + − − − − (4.11)

2 4 2

1 5 1 6 1 3 2 4 2

( )sin ( cos sin )arctan( )( ) ( ) ( ) ( ) cos ( cos sin )

r TOTRL

m b f r TOT

G l l G b lG l l G l l G l l G l l G l b

θ θ θγθ θ θ

− + −=

+ + + + − − − + + (4.12)

2 4 2

1 5 1 6 1 3 2 4 2

( )sin ( cos sin )arctan( )( ) ( ) ( ) ( ) cos ( sin cos )

r TOTRR

m b f r TOT

G l l G b lG l l G l l G l l G l l G b l

θ θ θγθ θ θ

− − +=

+ + + + − − − − − (4.13)


30

Therefore, the OL with different orientation angles can be represented as

02

3

1

40

2

(0 , )( , )( , )( , )( ,360 )

RL

RL FL

FL FR

FR RR

RR

OLOL

OL OLOLOL

γ γγ γ γγ γ γγ γ γγ γ

∈ ∈= ∈ ∈ ∈

(4.14)

According to Figure 4-2 b, it is possible to transfer the coordinates of the combined COG ( C )

and OLs from coordinate system 1 1 1 1O X Y Z to coordinate system 2 2 2 2O X Y Z and project them

on Panel 2 2 2O X Z . Hence, for C

cos sinPX YX

PZZ

C CCCCα α−

=

(4.15)

Then project 1OL , 2OL , 3OL and 4OL from coordinate system 1 1 1 1O X Y Z onto 2 2 2 2O X Y Z .

From the projected points, each OL can be determined as:

1 1 1 1P P P POL K X M= + (4.16)

2 2 2 2P P P POL K X M= + (4.17)

3 3 3 3P P P POL K X M= + (4.18)

4 4 4 4P P P POL K X M= + (4.19)

Where:

1cos

sin cosPK γ

γ α=


31

11 sinP lM

γ= −

2cos( )

sin( ) cosPK γ θ

γ θ α+

=+

22 sin( )P lM

γ θ=

+

2 1 23

2 2 1

( cos sin )sin ( cos sin )cos[( sin cos )sin ( cos sin )cos ]cos

P l b l b l bKl b b l b l

θ θ γ θ θ γθ θ γ θ θ γ α

+ + − − −=

− + − + +

2

1 2 1 23

2 1 2

sin ( ) cos sin( cos sin )cos ( sin cos )sin

P l l l l b bMl b l l b b

θ θ θθ θ γ θ θ γ

− + −=

+ + − − +

2 1 24

2 2 1

( cos sin )sin ( sin cos )cos[( sin cos )sin ( cos sin )cos ]cos

P l b l b l bKl b b l b l

θ θ γ θ θ γθ θ γ θ θ γ α

− + − − −=

+ − − − +

2

1 2 1 24

2 1 2

sin ( ) cos sin( cos sin )cos ( sin cos )sin

P l l l l b bMl b l l b b

θ θ θθ θ γ θ θ γ

+ + −=

− + − + −

Therefore, the distance from PC to the governing OL for different orientation angles can be

represented as

02

2

3

3

1

1

4

4

02

2

(0 , )

( , )

( , )

( , )

( ,360 )

P PP ZX RLP

P PP ZX RL FLP

P PP ZX FL FRP

P PP ZX FR RRP

P PP ZX RRP

M CCK

M CCK

M CD CK

M CCK

M CCK

γ γ

γ γ γ

γ γ γ

γ γ γ

γ γ

−+ ∈

−

+ ∈ −= + ∈ − + ∈ − + ∈

(4.20)

For typical NSAM cranes [ 40,40],θ ∈ − and [0,5]α ∈ .


32

4.5 Specific Models Development

In the previous section, a general expression for the distance from PC to the governing OL,

Equation (4.20), was obtained. This equation can be used to determine the stability condition

for NSAM cranes under different operating configurations and orientations. This section

develops a number of specific models. These additional models are separated for different

purposes. Section 4.5.1 considers an NSAM crane operating on level ground. The tip-over

stability analysis is carried out by understanding the relationship between the locations of the

articulation joints and the normal forces on the rear tyres based on the theoretical force

calculations under two operating conditions: 1) without articulation angle; and 2) with

articulation angle. These two models will be used in Chapter 6. In Section 4.5.2, the roll-over

stability of NSAM cranes on a side slope is explored. The analysis considers the geometric

relationship between the combined COG of the crane including the load and the OLs (which

is similar to the theory of the general model development) under five different orientations

and articulation angles: 1) without articulation angle; 2) the anterior body is higher than the

posterior body; and 3) the posterior body is higher than the anterior body. These three

independent models are used to confirm the robustness of the general model in this chapter

and the discussion in Chapter 6.

4.5.1 Tip-over Stability on Level Ground

In this section the two cases of tip-over stability without and with articulation angle are

presented.

4.5.1.1 Without Articulation Angle


33

Figure 4-3: FBD of a NSAM crane on level ground in the: a) straight, and b) articulated configurations.


34

A FBD of a NSAM crane without articulation angle on level ground and supporting a load is

shown in Figure 4-3 a.

From 1

0O ZM =∑

5 6 3 4( ) ( ) 0m b RL RR b f r bG l G l N N W G l G W l+ + + − − − = (4.21)

Therefore

4 5 6 3r m b fRL RR r

b

G l G l G l G lN N G

W+ + −

+ = − (4.22)

4.5.1.2 With Articulation Angle

A similar analysis can be conducted when a NSAM crane is with some non-zero articulation

angle on level ground and supporting a load as shown in Figure 4-3 b.

From1 1

0O ZM =∑

5 6 3 1 2 4

1 2 1 2

( ( ) )

( ) ( ) 0m b f r

RL RR

G l G l G l G l l l cosN l l cos bsin N l l cos bsin

θ

θ θ θ θ

+ − − + −

+ + − + + + = (4.23)

2 20O ZM =∑

1 5 2 1 6 2 1 3 2 4

1 2 1 2

[( ) ] [( ) ] [( ) ]

( ) ( ) 0m b f r

FL FR

G l l cos l G l l cos l G l l cos l G lN l cos l bsin N l cos l bsin

θ θ θ

θ θ θ θ

+ + + + + + − + +

− + − − + + = (4.24)


35

1 10O XM =∑

2 2 2 4( ) ( ) ( ) 0FL FR RL RR rN b N b N l sin bcos N l sin bcos G l l sinθ θ θ θ θ− + + + − − − = (4.25)

2 20O XM =∑

1 1

1 5 1 6 1 3

( ) ( )( ) ( ) ( ) 0

FL FR RL RR

m b f

N l sin bcos N l sin bcos N b N bG l l sin G l l sin G l l sin

θ θ θ θθ θ θ

+ + − + −− + − + − − =

(4.26)

From Equations (3), (4), (5) and (6), thus

4 1 2 6 5 3 2 12 2

1 1 2 2

( ) ( )( )( 2 )

r b m fRL RR r

G l l l Cos G l G l G l l l CosN N G

l Cos l l l Cosθ θ

θ θ+ + + − +

+ = −+ +

(4.27)

Note that 1 2bW l l= + . Equation (7) can be organised as follows

1 2 22

3 2 4 2 5RL RR r

K l KN N GK l K l K

++ = −

+ + (4.28)

Where

1 6 5 3 4( )(1 cos )b m f rK G l G l G l G l θ= + − − −

2 6 5 3 4( ) cosb m f b r bK G l G l G l W G l Wθ= + − +

3 2(1 cos )K θ= − −


36

4 2 (1 cos )bK W θ= −

25 cosbK W θ=

4.5.2 Roll-over Stability Across a Side Slope

4.5.2.1 Without Articulation Angle

When a NSAM crane is without articulation angle across a slope, the schematic showing

where the individual COGs (denoted as ) and combined COG ( C , denoted as ) are

located is that in Figure 4-4.

Figure 4-4: Schematic of a straight NSAM crane across a side slope with COG locations, geometry and coordinated systems indicated.


37

Again, according to i ic

G XXG

=∑ , i i

cG YYG

=∑ and i i

cG ZZ

G=∑ (Kleppner & Kolenkow,

1973). The coordinate of the combined COG (C) in coordinate system 1O XYZ can be

determined as follows

5 6 3 1 2 4

7

7

( )

( cos )

sin

m b f r

TOTX

m h b b f f r rY

TOTZ

m

TOT

G l G l G l G l l lG

CG h l G h G h G h

CG

CG l

G

α

α

− − + + + − − + + + =

−

(4.29)

It is possible to transfer C from coordinated system 1O XYZ to coordinate system ' ' 'FRA X Y Z as

5 6 3 1 2 4

'

7'

'

( )

( ) cossin

( )sincos

m b f r

TOTX

h m b b f f r r mY

TOTZ

h m b b f f r r

TOT

l G l G l G l l l GG

Ch G h G h G h G G l

C bG

Ch G h G h G h G

bG

αα

αα

− − + + + − + + + − = + + + + − +

(4.30)

Then project 'C on Panel ' 'FRX A Z as

5 6 3 1 2 4( )

( )sincos

m b f r

TOTPXPZ

m m b b f f r r

TOT


CC

h G h G h G h Gb

Gα

α

− − + + + − = + + + − +

(4.31)


38

Finally, the OL needs to be transferred from coordinate system 1O XYZ to coordinate system

' ' 'FRA X Y Z and projected onto Panel ' '

FRX A Z as

0PZ = (4.32)

Therefore the distance between the projected gravity vector ( PC ) and the projected OL ( PZ )

is

( )sincos m h b b f f r r

TOT

G h G h G h G hD b

Gα

α+ + +

= − (4.33)

4.5.2.2 With Articulation Angle

The two cases of a NSAM crane across a side slope analysed herein for the cases of: anterior

body higher than posterior body and posterior body higher than anterior body. These are

shown in Figure 4-5. Each case is analysed separately.

a. Anterior body higher than posterior body

The schematic for a non-straight NSAM crane across a slope with the anterior body higher

than the posterior body is shown in Figure 4-5 a.

The coordinate of the combined COG (C) in coordinate system 1O XYZ can be represented by


39

5 6 3 1 2 4

7

7 2 4

( ( ) cos )

( cos )

sin ( )sin

m b f r

TOTX

m h b b f f r rY

TOTZ

m r

TOT


CG h l G h G h G h

CG

CG l G l l

G

θ

α

α θ

− − + + + − − + + + = + −

−

(4.34)

It is possible to transfer C from coordinate system 1O XYZ to coordinate system ' ' 'FRA X Y Z by

applying

5 6 3 1 2 4

'

7 2 4'

'

2 4

( ( ) cos )

( ) cos ( )sin sinsin

( )sin ( )sin coscos

m b f r

TOTX

m h b b f f r r m rY

TOTZ

m h b b f f r r r

TOT


CG h G h G h G h G l G l l

C bG

CG h G h G h G h G l l

bG

θ

α θ αα

α θ αα

− − + + + − + + + − − − = + + + + + − − +

(4.35)

And to project 'C onto Panel ' 'FRX A Z as

5 6 3 1 2 4

2 4

( ( ) cos )

( )sin ( )sin coscos

m b f r

TOTPXPZ

m h b b f f r r r

TOT


CC

G h G h G h G h G l lb

G

θ

α θ αα

− − + + + − = + + + + − − +

(4.36)


40

Figure 4-5: Schematic of an articulated NSAM crane across a side slope with COG (C) locations, geometry and coordinate systems indicated for the cases of: a) anterior body higher

than posterior body, and; b) posterior body higher than anterior body.


41

Start by transferring the OL from coordinate system 1O XYZ to coordinate system ' ' 'FRA X Y Z

and project it on Panel ' 'FRX A Z as

2

1 2

( sin cos )coscos sin

P Pl b bZ Xl l bθ θ α

θ θ+ −

= −+ −

(4.37)

Note that 1 2bW l l= + , the distance between projected gravity vector ( PC ) and projected OL

( PZ ) is

6P PX ZD K C C= + (4.38)

Where

26

2

( sin cos )cossin (1 cos )b

l b bKW b l

θ θ αθ θ

+ −= −

− − −

5 6 3 4 2( cos (1 cos ))m b f r bPX

TOT

G l G l G l G W l lC

Gθ θ− − + + − − −

=

2 4( )sin ( )sin coscosh m b b f f r r rP

ZTOT

h G h G h G h G G l lC b

Gα θ α

α+ + + + −

= − +

b. Posterior body higher than anterior body

The schematic for an articulated NSAM crane across a slope with the posterior body higher

than the anterior body is shown in Figure 4-5 b.


42

Following a similar procedure to that in Section 4.5.2.2a (detailed calculation procedure is

included in APPENDIX A), the distance between projected gravity vector ( PC ) and projected

OL ( PZ ) is

7P PX ZD K C C= − + (4.39)

Where

27

2

( sin cos )cossin (1 cos )b

l b bKW b l

θ θ αθ θ

− +=

+ − −

5 6 3 4 2( cos (1 cos ))m b f r bPX

TOT

G l G l G l G W l lC

Gθ θ− − + + − − −

=

2 4( )sin cos ( )sincosr h m b b f f r rP

ZTOT

G l l h G h G h G h GC b

Gθ α α

α− − + + +

= +

4.6 Result Validation

Equation (4.20) is the general equation to determine the distance from the combined COG to

the critical OL for different articulation angles. Equation (4.33), (4.38), and (4.39) are the

specific equations to determine the distance from the combined COG to the OL when a

NSAM crane is straight, non-straight with anterior higher than the posterior body, non-

straight with posterior body higher than anterior body on a slope. For the validation of

Equation (4.20) from a calculation perspective, the example parameters are used and reported

in Table 4-1. These values were chosen since they seemed representative of this type of crane.

Figure 4-6 accompanies Table 4-1. Using these input values and logging the cases in


43

MATLAB, the relationship between the distance (D) from combined COG to the nearest

downslope OL and the orientation angle (γ ) were calculated and reported in Figure 4-7.

Table 4-1: Example NSAM crane operating configuration values

[ ]mG kg :4410 1[ ]l mm :1950 [ ]hh mm :6000

[ ]bG kg :2000 2[ ]l mm :1950 [ ]bh mm :4200

[ ]fG kg :4000 3[ ]l mm :500 [ ]fh mm :800

[ ]rG kg :10000 4[ ]l mm :500 [ ]rh mm :800

[ ] : 20410TOTG kg 5[ ]l mm :3600 [deg]γ : 0 0[ 360 ,360 ]−

[ ] :1220b mm 6[ ]l mm :500 [deg]α : 05

7[ ]l mm :1000 [deg]θ : 0 0 00 ; 10 ; 40± ±

Figure 4-6: Schematic Representation of configurations according to Table 4-1


44

Figure 4-7: Distance from COG to OL as a function of orientation angle

Figure 4-7 is obtained from Equation 4.20. This plot depicts how the stability of the NSAM

crane is related to the articulation angle and the orientation angle. Generally, different

orientation angles result in different OL and different articulation angles change the COG of

the crane. Thus, when the orientation angle and the articulation angle change, they will

change the distance from the COG to the OL. When the distance approaches to 0, the crane

will be more likely to tip/roll over. In the case of Table 4-1, since the posterior body is

heavier than the anterior body and the carried load, when the articulation angle increases, it

shifts the COG of the crane further to the OL between 0

70 and 0

120 and between 0

70− and

0

120− orientation angles. This gives more stability to the crane. However, for other

orientations, the COGs are closer to the OL. This increases the tip/roll over accident

likelihood. In additional, from the plot, it is evident that most NSAM crane tip-over/roll-over

accidents occur when the articulation angle exceeds 010 .


45

Consider the chosen case is for 040θ = ± and 05α = . As expected the graph is symmetrical

about the 0 00 (360 )γ = orientation and:

1) When across the slope without articulation angle ( 090γ = or 0270γ = with 00θ = ), the

distance from the combined COG to the OL ( D ) is 1019 mm. This is the same as the

result of Equation (4.33), when 2 1.95l = m ( 2 2ll = );

2) When across the slope with the anterior body higher than the posterior body at 040

articulation angle ( 090γ = with 040θ = − or 0270γ = with 040θ = ), the distance from the

combined COG to the OL ( D ) is ~843 mm. This is the same as the result of Equation

(4.38), when 2 1.95l = m ( 2 2ll = );

3) When across the slope with posterior body higher than the anterior body at 040

articulation angle ( 090γ = with 040θ = or 0270γ = with 040θ = − ), the distance from

the combined COG to the OL ( D ) is 1194 mm. This is the same as the result of Equation

(4.39), when 2 1.95l = m ( 2 2ll = ).

Therefore, the results of the specific models are same as the results of the general models

when α , γ , and θ are at the specific angles. Therefore, the validity of the general model is

confirmed.


46

4.7 Chapter Summary

In this chapter, a general model for the stability study of NSAM cranes under different

configurations and orientations is developed by understanding the geometric relationship

between the combined COG and the determined OL based on a number of assumptions. Then

seven specific models are built for the validation of the result (Equation 4.20) from the

general model. According to the match of the results, the general model is validated for

subsequent use in the following chapters.

Case Study

47

5 Case Study

5.1 Chapter Aims

In Chapter 4, a general static stability model was developed and validated by a number of

specific static stability models from the calculation perspective. However, whether this model

can explain the stability of NSAM cranes in the real environment is still unknown. Therefore,

in this chapter, a reported tipping accident is investigated using the developed models. This

provides a better understanding of the causes of this accident and may contribute to reduce

the likelihood of NSAM crane tipping accidents in the future.

5.2 Case Analysis

A number of tipping accidents were listed in Chapter 1. This section studies one

representative accident. The description and suggestion from the report are summarised in

Table 5-1. Figure 5-1 is the photo of the accident. The reason for choosing this incident to be

the case study is because it is the more complete of the incidents and provides sufficient

information for analysis. Using MATLAB, it is possible to study the impacts of the

articulation angle, the slope gradient, the orientation angle, the height of the carried load, and

the counter weight on the stability of NSAM cranes.

Case Study

48

Table 5-1: The description and potential cause of an accident from the report (Universal cranes, 2009)

Model Description Suggestion From The Report

14T

The mobile crane was positioned at

approximately 090 to the truck. The crane

took a 10t load and reversed until the load

was clear of the truck tray. As the crane

turned right at maximum articulation angle,

it tipped over onto its right hand side.

1) Reduce the lifted load according

to the instruction from the crane

make (Terex Lifting Australia,

2001);

2) Keep the load as low as

possible; and

3) Attach the counter weight.

Figure 5-1: Rollover accident (Universal cranes, 2009)

Case Study

49

Although the information of this accident is the most complete compared with the other cases,

the detailed data is limited. However, it is possible to gain a physical understanding of the

causes of this accident by assigning some example values shown in Table 5-2. These example

input values refer to the layout (Titan Cranes Limited, 2010) and the lifting chart

(APPENDIX B) of a 14 tonne Franna crane and the description given in Table 5-1.

Table 5-2: Example input values for the study of roll-over accident

[ ]mG kg :10000 1[ ]l mm :1900 [ ]hh mm :5300

[ ]bG kg :2000 2[ ]l mm :1900 [ ]bh mm :4343

[ ]fG kg :4000 3[ ]l mm :500 [ ]fh mm :800

[ ]rG kg :10000 4[ ]l mm :500 [ ]rh mm :800

[ ] :cG kg 2000 5[ ]l mm :1200 [deg]γ : 0 0[ 360 ,360 ]−

[ ]b mm : 1220 6[ ]l mm :-60 [deg]α : 05

7[ ]l mm :4200 [deg]θ : 040

[deg] :ϕ 040

5.2.1 Articulation Angle

It is interesting to find that, according to the lifting chart of a 14 tonne NSAM crane (Titan

Cranes Limited, 2010), the lifting capacity is different for a certain model of NSAM cranes

when the articulation angle is less than 010 and greater than 010 . The reason for this can be

found by studying Figure 5-2, which shows the different distance from the COG to the OL

with different articulation angles ( 00 , 010+ , and 040+ ) when a 14 tonne NSAM crane is on a

05 slope.

Case Study

50

Figure 5-2: The relationship between the distance from the combined COG to the OL and the articulation angle

From Figure 5-2:

1) As the articulation angle increases, the tip-over stability decreases. When the articulation

angle increases from 00 to 010 , the tip over stability decreases by 8mm (1.25%).

However, when the articulation angle increases from 00 to 040 , the tip over stability

decreases by 125.5mm (19.6%);

2) As the articulation angle increases, the roll-over stability decreases. When the articulation

angle increases from 00 to 010 , the roll-over stability decreases by 16.3mm (1.68%).

Case Study

51

However, when the articulation angle increases from 00 to 040 , the roll-over stability

decreases by 137.2mm (14.1%).

Therefore, the impact of the articulation angle on the stability of NSAM cranes is significant.

In the current design of NSAM cranes, there is a monitoring system that can demonstrate the

real time articulation angle during the operation. However, depending on the operating

experience or work pressure, some operators might take a risk leading to a tipping accident.

5.2.2 Slope Gradient

According to the Information bulletin for operation on side slope (Terex Lifting Australia,

2001), NSAM cranes are permitted to operate on side slopes of up to 05 (8.75% gradient). It

is of interest to understand what the impact of the slope gradient on the stability of NSAM

cranes is. This can be explained by interpreting the results displayed in Figure 5-3. This

figure, compares the stability of a 14 tonne NSAM crane when it is on different slope

gradients ( 00 , 05 , and 015 ) with 040+ articulation angle.

Case Study

52

Figure 5-3: The relationship between the distance from the combined COG to the OL and the slope gradient

From Figure 5-3, as the slope gradient increases, the stability of NSAM cranes decreases

dramatically. When the slope gradient increases from 00 to 05 , the tip over stability

decreases from 763.3mm to 516mm (32.4%) and the roll over stability decreases from

1082mm to 833.8 mm (22.9%). However, when the slope gradient increases from 00 to 015 ,

the crane is to tip over and the roll over stability decrease from 1082mm to 319.8mm (70.4%).

Therefore, the impact of the slope gradient on the stability of NSAM crane is significant.

Currently, there is a conventional spirit type level indicator mounted on the dashboard which

can help the operator know the slope gradient. However, as it is a passive device requiring

monitoring by the drive, it cannot prevent the tipping accidents; it may even be a distraction.

It is possible that a NSAM crane may lift a load on level ground by using the standard lifting

Case Study

53

chart but the ground may not always be level during the carry operation. Such an operation

may contribute to a tipping accident.

5.2.3 Orientation Angle

As introduced in Chapter 2, the combination of different orientation angles and articulation

angles leads to the determination of the OL for NSAM cranes on a slope. Therefore, the

orientation angle is another important factor that affects the stability of NSAM cranes on a

slope. Section 5.2.1 studied the impact of the articulation angle on the stability of NSAM

cranes, thus this section mainly aims to study the impact of the orientation angle on the

stability of NSAM cranes.

According to the description of this tipping accident, this 14 tonne NSAM crane rolled over

onto its right hand side when it was turning right at the articulation angle of 040 . Typically,

when a NSAM crane turns on a slope, both the anterior body and the posterior body move

because the steering hydraulic cylinders act on both bodies. Based on a dynamic balance

model, it would be possible to determine the change of the orientation angle by inputting the

example values (Table 5-2) when the crane is turning right at 040 articulation angle. However,

this study is based on a static analysis, the dynamic study is beyond the current scope, though

recognised as a logical future step in the research of NSAM crane stability. Therefore, it is

assumed that the change of the orientation angle is X ( 0 00 40X< < ) when this 14 tonne

NSAM crane was turning at 040 articulation angle. The detailed value of X will be

acknowledged by the approach introduced in Chapter 6.

Case Study

54

Based on the developed model, Figure 5-4 shows the comparison of the distance from the OG

to the OL between 00 and 040 articulation angle on a slope of 05 . From this figure, it is

evident that the orientation angle ( γ ) when the accident occurred was between 0 0229 X+ and

0 0280 X+ (dashed area in Figure 5-4).

Figure 5-4: Comparison of the distance from the COG to the OL between 00 and 040articulation angle on a slope of 05

If the operator can monitor in real time the orientation, perhaps with a device similar to that

proposed by Wray et al. (1984). They could have time to decide whether to carry out their

work. However, currently no monitoring system for detecting the orientation angle has been

developed.

Case Study

55

5.2.4 Height of the Load/Boom

In the investigation reports of some NSAM crane tipping accidents, the causes are attributed

to the operators not keeping the load as low as possible during the operation. However, it is

the length of the rope 7l that needs to be minimised. Thus the boom should be kept as low as

possible. The reason can be explained by Figure 5-5, which compares the different distances

from combined COG to the OL when a 14 tonne NSAM crane on 05 slope with the boom at

040 , 050 , and 060 angle and the load is maintained at 1100mm height from the ground.

Figure 5-5: The relationship between the distance from the combined COG to the OL and the

boom angle

Figure 5-5 shows that, for a given load height, increasing the boom angle decreases the

stability of NSAM cranes when operating on side slope. This is logical since, ignoring

Case Study

56

dynamic effects, the load will maintain vertical orientation and thus, even on a constant angle

slope, for a higher boom, the COG of the load will be further away from the boom’s centre

line. This in turn shifts the combined COG of the crane further down slope and closer to an

OL. Although the distance away from the centerlines is independent of the mass of the load,

the effect on the combined COG is more significant for heavier loads. Therefore, the boom

should be kept as low as possible when in the carrying mode. If the boom angle cannot be

kept at 00 during operation, the slope gradient should be ensured to be within 05 .

5.2.5 Attached Counter Weight

A NSAM crane accident report (Universal cranes, 2010) implies that not having the counter

weight attached on the anterior/posterior body is a potential cause. However, according to the

model developed in this thesis, the counter weight does not assist greatly in increasing the

roll-over stability, but only the tip-over stability. This can be explained by Figure 5-6, which

compares the distance from the combined COG to the OL when a 14 tonne NSAM crane is

non-straight with 040+ articulation angle on a slope of 05 with no counterweight attached,

attached on the anterior body, and attached on the posterior body.

Case Study

57

Figure 5-6: The comparison of the distance from the combined COG to the OL when counter

weight is not attached, attached on anterior body, and attached on posterior body

According to Figure 5-6:

1 If the counter weight is attached on the anterior body, the stability of NSAM cranes

cannot be increased; and

2 If the counter weight is attached on the posterior body, it helps to increase the tip-over

stability but assist to a lesser extent the roll-over stability.

Case Study

58

5.3 Chapter Summary

In this chapter, the impacts of the articulation angle, the slope gradient, the orientation angle,

the height of the carried load, and the counter weight on the stability of NSAM cranes were

studied. The results show that the articulation angle, the slope gradient, the orientation angle,

and the height of the boom play an important role in the tipping accidents of NSAM cranes.

However the height of the carried load and the counter weight appear to be unlikely causes of

the NSAM crane tipping accidents.

Discussion

59

6 Discussion

6.1 Chapter Aim

• Examine the current frame design of NSAM cranes;

• Investigate a potential development of a monitoring system to assist the NSAM crane

operators; and

• Discuss the limitation of this project.

6.2 Examine the Current Frame Design of NSAM cranes

Chapter 2 stated the hypothesis that having the articulation joints at the centre of the

wheelbase ( 1 2l l= ) is not a good design for NSAM cranes from the stability perspective. To

verify this hypothesis, the development of a general model for the static stability study of

NSAM cranes was required and carried out in Chapter 4. After that, five specific static

models were developed in the same chapter. Among them, the specific models 3, 4, and 5

validated the results from the general model. However, the specific models 1 and 2 were

developed to contribute to the examination of the current frame design in this section directly.

This section aims to examine whether having the articulation joints at the centre of the

wheelbase is a good design for NSAM cranes from the stability perspective. It is assumed the

values for the wheelbase ( bW ), the distance from the lifting point, the boom and anterior

COGs to the front axle ( 5l , 6l and 3l ), and the distance from the posterior body COG to the

rear axle ( 4l ) remain fixed when the front and the rear axles positions are shifted

(APPENDIX C). This involves the use of the results from both the general model from the

geometry perspective and the specific models 1 and 2 from the force perspective.

Discussion

60

6.2.1 Tip-over stability

As noted by Fujioka et al (2009), the normal force on the contact points is a critical basis to

examine the tip-over stability of MB cranes. For a NSAM crane, it would seems that a good

design for ensuring the tip-over stability of NSAM cranes is to have variation of the

combined normal force on the rear tyres ( RL RRN N+ ) as small as possible as the articulation

angle ( θ ) changes. This may increase the predictability of ensuring instability during

operation. Therefore, this section aims to examine the tip-over stability of NSAM cranes by

exploring what ratio of the distance from the front axle to the articulation joints and the

distance from the rear axle to the articulation joints provides the smallest variation of the

combined normal force on the rear tyres ( RL RRN N+ ) as the articulation angle (θ ) changes.

Equations (4.22) and (4.28) are the results from the Specific Models 1 and 2. They describe

the relationship between the combined normal force on the rear tyres ( RL RRN N+ ), the

distance from the front drive axle to the articulation joints ( 1l ) and the distance from the rear

drive axle to the articulation joints ( 2l ). These pertain to when a NSAM crane is on level

ground.

From Equation (4.22), the combined normal force on the rear tyres ( RL RRN N+ ) is

independent of the distance from the front drive axle to the articulation joints ( 1l ) and the

distance from the rear drive axle to the articulation joints ( 2l ). This is quite unremarkable and

is expected since, without articulation, changes in their values do not influence the contact

locations.

Discussion

61

On the other hand, from Equation (4.28), the combined normal force on the rear tyres

( RL RRN N+ ) is a function of the lifting configuration, orientation and design geometry of the

crane ( 1K in Equation (4.28)). During operation, the distance from the boom COG to the front

axle ( 6l ), the distance from the boom lifting point to the front axle ( 5l ), and the weight of the

load ( mG ) are variables, thus 1K is variable. As the articulation angle ( θ ) is typically

between 040− and 040 , three basic configurations can be indentified:

1) The moments of the boom and the load to the front axle are larger than the moments

of the front half to the front axle and the rear half to the rear axle

( 6 5 3 4b m f rG l G l G l G l+ > + );

2) The moments of the boom and the load to the front axle equal to the moments of the

front half to the front axle and the rear half to the rear axle ( 6 5 3 4b m f rG l G l G l G l+ = + );

and

3) The moments of the boom and the load to the front axle are smaller than the moments

of the front half to the front axle and the rear half to the rear axle

( 6 5 3 4b m f rG l G l G l G l+ < + ).

According to Equation (4.28), it is possible to investigate the relationship between the

distance from the rear drive axle to the centre of articulation joints ( 2l ), the articulation angle

(θ ) and the combined normal force on the rear tyres ( RL RRN N+ ), when all other parameters

( bW , 3l , 4l , 5l , 6l , mG , bG , fG , and rG ) remain constant. Consider the example values listed

in Table 6-1. Using these input values and logging the cases in MATLAB, the relationships

are depicted in Figure 6-2.

Discussion

62

Table 6-1: Example values for tip-over stability analysis (Terex Cranes, 2004)

EXAMPLE VALUES 5mG l

[ ]N m⋅ 6bG l

[ ]N m⋅ 3fG l

[ ]N m⋅ 4rG l

[ ]N m⋅ bW

[ ]m θ[deg]

2l [ ]m

CO

NFI

GU

RA

TIO

NS 5 6

3 4

m b

f r

G l G lG l G l

+> +

52.09 10×

43.2 10×

42 10×

45 10× 3.9

40

40θ

−≤ ≤ 2

0.5

3.4l≤ ≤ 5 6

3 4

m b

f r

G l G lG l G l

+= +

43.8 10×

5 6

3 4

m b

f r

G l G lG l G l

+< +

0

Note: the example values are according to Figure 6-1 and the range of 2l is determined in

APPENDIX C

Discussion

63

Figure 6-1: Schematic Representation Configurations according to Table 6-1: a) 5 6 3 4m b f rG l G l G l G l+ > + ; b) 5 6 3 4m b f rG l G l G l G l+ = + ; and c) 5 6 3 4m b f rG l G l G l G l+ < +

Discussion

64

Figure 6-2: The relationship between the combined normal force on the rear tyres ( RL RRN N+ ) and the distance from the rear drive axle to the centre of the articulation joints

( 2l ) for three configurations.

Discussion

65

As expected, for a symmetric vehicle (with COG on mid plane), the variations are also

symmetrical. The main attributes of the trends can be tabulated as in Table 6-2.

Table 6-2: Tip-over stability analysis result

SUMMARY

CA

SES

6 5 3 4b m f rG l G l G l G l+ > +

The maximum combined normal force on the rear tyres

( RL RRN N+ ) with different articulation angles (θ ) are on

the left of 2 2bWl = and they all pass through the point

4 5 6 3( , )2

r m b fbr

b

G l G l G l G lW GW

+ + −− .

6 5 3 4b m f rG l G l G l G l+ = +


( RL RRN N+ ) with different articulation angles (θ ) are at

2 2bWl = , and they all pass through the point

42( , )2

b rr

b

W G lGW

− .

6 5 3 4b m f rG l G l G l G l+ < +


( RL RRN N+ ) with different articulation angles (θ ) are on

the right of 2 2bWl = and they all pass through the point

4 5 6 6 3( , )2

r m fbr

b

G l G l G l G lW GW

+ + −− .

Assuming a NSAM crane is carrying a load on level ground, the lifting configuration

( 5 6 6mG l G l+ ) usually remains while the articulation angle (θ ) changes. From Table 6-2, when

the longitudinal distance from the rear drive axle to the centre of articulation joints is half of

Discussion

66

the distance between the axles ( 2 2bWl = ), the combined normal force on the rear tyres

( RL RRN N+ ) is independent of the articulation angle (θ ). Therefore, from the combined

normal force on the rear tyre’s perspective, having the articulation joints at the centre of the

wheelbase ( 1 2l l= ) is a good design for NSAM cranes.

6.2.2 Roll-over Stability

According to Zhao et al (1996), the variation of the distance from the combined COG to the

OL is a key condition to test the roll-over stability of ASVs. Therefore, a good design for

ensuring the roll-over stability of NSAM cranes is to have the variation of the distance from

the combined COG to the OL (D) as small as possible as the articulation angle (θ ) changes.

This renders the instability less dependent on orientation and hence may increase the driver’s

ability to perceive instability. Hence this section aims to analyse the roll-over stability of

NSAM cranes by exploring what ratio of the distance from the front axle to the articulation

joints ( 1l ) and the distance from the rear axle to the articulation joints ( 2l ) provides the

smallest variation of the distance from the combined COG to the OL (D) as the articulation

angle (θ ) changes.

Equation (4.20) is the result of the general model. This expression determines the distance

from the combined COG to the OL under different operating configurations and orientations.

In Chapter 5, all the studies were carried out based on having the articulation joints at the

centre of the wheelbase ( 1 2l l= ). However, this section aims to study the impact of the

different combination of the distance from the front drive axle to the articulation joints ( 1l )

Discussion

67

and the distance from the rear drive axle to the articulation joints ( 2l ) when the length of the

wheelbase is fixed.

From Equations (4.20), the distance from the combined COG to the OL is a function of the

operating configuration and orientation. Two operation procedures shown in Figure 6-3 and

Figure 6-4 are illustrated here. In both case, the truck is parked on a slope of 05 with 090

orientation angle.

During Procedure One: 1) a NSAM crane approaches the flatbed truck from the entry arriving

at 090 to the truck; 2) lifts a load from the truck bed with a certain configuration (Table 6-3)

with 040− articulation angle and turns the articulation angle to 040+ ; 3) reverses the crane

until straight with 090 orientation angle (dashed arrow); and 4) moves forward and turns left

to leave the site with 040− articulation angle.

Figure 6-3: Example One of the operation procedure of a NSAM crane

Discussion

68

During Procedure Two: 1) a NSAM crane approaches the flatbed truck from the entry

arriving at 090 to the truck; 2) lifts a load from the truck bed with a certain configuration

(Table 6-3) with 040+ articulation angle and turns the articulation angle to 040− ; 3) reverses

the crane until straight with 00 orientation angle (dashed arrow); and 4) moves forward and

turns right to leave the site with 040+ articulation angle.

Figure 6-4: Example Two of the operation procedure of a NSAM crane

According to the case study in Chapter 5, in both example operation procedures, Step 2 is the

most dangerous operation as this step changes both articulation angle and orientation angle

under load. Therefore, it is necessary to investigate the variation of the distance from the

combined COG to the OL during this step. Table 6-3 shows the example operating

configuration and Figure 6-5 accompanies Table 6-3.

Discussion

69

Table 6-3: Example NSAM crane operating configuration values

[ ]mG kg :4410 1[ ]l mm :1950 [ ]hh mm :6000

[ ]bG kg :2000 2[ ]l mm :1950 [ ]bh mm :4200

[ ]fG kg :4000 3[ ]l mm :500 [ ]fh mm :800

[ ]rG kg :10000 4[ ]l mm :500 [ ]rh mm :800

[ ] : 20410TOTG kg 5[ ]l mm :3600 [deg]γ : 0 0[ 360 ,360 ]−

[ ] :1220b mm 6[ ]l mm :500 [deg]α : 05

7[ ]l mm :1000 [deg]θ : 0 0 00 ; 10 ; 40± ±

Figure 6-5: Schematic representation of configurations according to Table 6-3

Using MATLAB, Figure 6-6 shows how the distance of the combined COG to the OL varies

as a function of different operating configurations and different design geometries.

Discussion

70

Figure 6-6: The relationship between the distance from the combined COG to the OL and the orientation angle

When a NSAM crane turns on a slope, there are changes in orientation of both the anterior

and posterior bodies. Since the modeling of this is beyond the scope of this study, the

following assumptions have been made. The change of the orientation angle 0

X (the angle

between the boom and the slope contour line, SCL) is assumed to have a defined value for

selected cases of 1l and 2l . These defined values are selected by considering the orientations

that result in the overturn line being parallel with the SCL resulting in minimum stability.

These defined values of 0

X are:

1) 0 034X = when 116 bl W= and 2

56 bl W= ;

2) 0 027X = when 113 bl W= and 2

23 bl W= ;

3) 0 020X = when 112 bl W= and 2

12 bl W= ;

Discussion

71

4) 0 013X = when 123 bl W= and 2

13 bl W= ; and

5) 0 06X = when 156 bl W= and 2

16 bl W= .

The detailed value will be acknowledged in the next section. Table 6-4 illustrates the

variations of the distance from the combined COG to the OL when the orientation angle

changes from 0270− to 0 090 X− and the distance from the combined COG to the OL when

the orientation angle changes from 090 to 0 0270 X− + .

Table 6-4: The variation of the distance from the combined COG to the OL under different design geometries during the example operation procedures shown in Figure 6-3 and Figure

6-4

1

2

1 ;656

b

b

l W

l W

=

=

1

2

1 ;323

b

b

l W

l W

=

=

1

2

1 ;212

b

b

l W

l W

=

=

1

2

2 ;313

b

b

l W

l W

=

=

1

2

5 ;616

b

b

l W

l W

=

=

Proc

edur

e

One

(608.3mm-

1297mm=

-688.7mm)

(53.1%)

(691.3mm-

1237mm=

-545.7mm)

(44.1%)

(784.8mm-

1152mm=

-367.2mm)

(31.9%)

(887.1mm-

1042mm=

-154.9mm)

(14.9%)

(996.8mm-

912.4mm=

84.4mm)

(9.3%)

Two

(1549mm-

442.2mm=

1106mm)

(71.4%)

(1394mm-

580.1mm=

813.9mm)

(58.4%)

(1239mm-

725.3mm=

513.7mm)

(41.5%)

(1082mm-

867.5mm=

214.5mm)

(19.8%)

(924.3mm-

997.8mm=

-73.5mm)

(7.4%)

From Table 6-4, the variation of the distance from the combined COG to the OL (D)

decreases as the distance from the rear axle to the articulation joints ( 2l ) decreases. Therefore,

from the roll-over stability perspective, it is beneficial to have the distance from the rear axle

to the articulation joints ( 2l ) shorter than half of the wheelbase ( bW ).

Discussion

72

6.3 Potential Development of a Monitoring System

6.3.1 Shortcomings of A Current Monitoring System on NSAM Cranes

There is a commercially available monitoring system for NSAM cranes developed by

Robway (2007). Figure 6-7 shows the operator interface of the current monitoring system on

NSAM cranes.

Figure 6-7: Example of current monitoring system on NSAM cranes (Robway, 2007)

Typically, the functions of the current monitoring system are to monitor:

• The boom length;

• The boom angle;

• The radius from the head of the boom to the boom pivot;

• The weight of the load;

• The length of the rope;

• The articulation angle;

Discussion

73

• The roll (inclination) angle; and

• The pitch (inclination) angle.

The information provided by the current monitoring system may help operators reduce the

likelihood of tip-over accidents during the lifting mode. However, according to the review of

NSAM crane tipping accidents in Chapter 1, almost all of the accidents occurred during the

carrying mode. This is because when a NSAM crane is traveling with a load, the articulation

angle, the slope gradient, and the orientation angle are not constant. Additionally, there are

dynamic effects. This makes the stability situation when a NAM crane is in carrying mode

more complicated than that when the crane is in the lifting mode and stationary. Without

providing the physical concept of the location of the combined COG to the operators, the

likelihood of the NSAM crane tipping accidents is likely very high. Therefore, an extension

to the monitoring system which could provide real time geometry relationship between the

combined COG to the OL for the operators is suggested here.

6.3.2 The Design of the new Monitoring System for NSAM Cranes

As the recommended traveling speed for NSAM cranes when carry a load is limited to

1.44km/h (Terex Lifting Australia, n.d.), it is possible to develop a preliminary monitoring

system based on the developed static model in Chapter 4. It is recommended that a future

study investigate the significance of accelerations at low speeds and also constant speed

turning (which give rise to centripetal accelerations). However this is considered beyond the

scope of the current study. The basic concept of the new monitoring system is to input the

required real time data from the current monitoring system into Equation (4.20). The

calculation could be done by the microcomputer interfaced in the system. The method would

Discussion

74

be based on the distance from the combined COG to the OL to the operators. The concept is

shown in Figure 6-8. A system similar to that developed by Way et al. (1984) could then be

used to provide a simple indication to the operator.

Figure 6-8: The concept of the new design of the monitoring system

In this concept, an important step is to input the required data into the system. From Equation

(4.20), three types of data are required: 1) constant data; 2) measured data; and 3) calculated

data. They are shown in Table 6-5.

Table 6-5: The classification and resource of the input data

Data Resource

Constant Data: bG ; fG ; rG ; 1l ; 2l ; 3l ; 4l ; fh ; rh ; and b. Crane Manufacturers

Measured Date: mG ; TOTG ; 5l ; 6l ; 7l ; hh ; bh ; and θ . Current Monitoring System

Calculated Data: α ; and γ . New Monitoring System

Discussion

75

In Table 6-5, two important measured data are the orientation angle γ the slope gradient α .

These two data cannot be accessed directly from the existing monitoring system. However,

they can be determined by knowing the roll angle 1β (Figure 6-9) and the pitch angle 2β

(Figure 6-10) . 1β and 2β are provided by the current monitoring system.

Figure 6-9: Roll angle 1β

Figure 6-10: Pitch angle 2β

By the following method, the value of γ can be determined.

Firstly, the roll angle 1β is 0 degrees when the left hand and right hand contact points of the

anterior body are at the same height on the slope (i.e. on the same contour line). If the left

hand side of the anterior body is higher than the right hand side, the roll angle 1β is negative,

alternatively, the roll angle 1β is positive. The pitch angle 2β is 0 degrees when the anterior

body and the posterior body are at the same height on the slope (i.e. the crane is level). If the

anterior body is higher than the posterior body, the pitch angle 2β is positive, otherwise, the

pitch angle 2β is negative. According to the trigonometric relationship between the

Discussion

76

orientation angle γ , the slope gradient α , the roll angle 1β and the pitch angle γ , two

equations are shown as Equations 6.1 and 6.2.

1sinα γ β− = (6.1)

2cosα γ β= (6.2)

Thus:

1

2

tan βγβ

− = (6.3)

Therefore:

11 2

2

12

2

11 2

2

01 2

01 2

arctan 0 0

arctan 0

2 arctan 0 0

90 0 0

270 0 0

when and

when

when and

when and

when and

β β βββπ ββ

γ βπ β ββ

β β

β β

− ≤ >

− < =

− ≥ > < = > =

(6.4)

And the slope gradient can be determined by the following expression.

2

cosβαγ

= (6.5)

Based on this concept of new monitoring system, operators could have a physical

understanding of the distance from the combined COG to the OL. Such a device would help

warn operators of the potential danger associated with their operation and configuration.

Although the design of this improved device is possible in the future, more work is needed to

design a robust system.

Discussion

77

6.4 Limitations of the Project

6.4.1 Model Limitation

In this study, the general static model for the stability study of NSAM cranes was developed

based on a number of theoretical assumptions outlined in Chapter 4. However, as real

conditions are not always the same as the theoretical assumptions, some differences might

change the result. Some such implications are explained here.

• It was assumed the ground is firm and flat. However, in the real environment, it is

difficult to ensure the ground is always firm and flat. Uneven ground and non-rigid

ground may cause different slope gradients for all four wheels of NSAM cranes. This

will result in the error of the final result. Accounting for these effects would likely

decrease stability;

• Both the front and rear axles are assumed to be rigidly connected to the vehicle’s

bodies. However, in reality, when lifting a load, only the front axle is rigidly

connected to the anterior body, but the rear axle is usually suspended connected to the

posterior body. It should also be noted that the operator is responsible for locking the

front axle and hence may not always do this during operation. Thus this extra

flexibility would likely allow the COG of the posterior body to not to be located mid

plane due to the body tilt. This also affects the distance from the combined COG to

the OL. Tyre flexibility may have a similar effect;

• It is also assumed that the carried load is static when attached to the boom. However,

during operation, due to inertia effects, the load most likely swings like a pendulum

(Fujioka, 2010). The swinging motion would cause dynamic force components on the

boom and may be a significant factor influencing the stability of these cranes. This

Discussion

78

aspect is not included here, as only a static analysis is performed. The inclusion of this

effect however is recommended; and

• In theory, the limited traveling speed for NSAM cranes should be 1.44km/h. However,

in practice, the speed may be different due to accelerations resulting from turning,

traversing humps, take-off and slowing down.

6.4.2 Information Limitation

Some detailed information, for example, the exact locations of the COGs of the boom, the

anterior body and the posterior body cannot be accessed because these data are intellectual

properties owned by the crane manufacturer. In this study, these data are assumed for the

calculation purpose and the explanation of the results.

6.4.3 Practical Test Limitation

This study is only based on the theoretical model development and calculation. It is

acknowledged that experimental verification of the theory is beneficial. However, due to the

time limitations, safety issues and research budget, no practical tests have been carried out yet,

this will be the subject of future work.

6.5 Chapter Summary

In this chapter, the current frame design of NSAM cranes was examined by using the

developed model of this study. The values for the wheelbase, the distance from the lifting

point, the boom and the anterior body COGs to the front axle, and the distance from the

Discussion

79

posterior body COG to the rear axle were assumed to remain fixed when the front and the

rear axle positions are shifted. This examination was carried out by understanding both the

force relationship and the geometry relationship between the stability of a NSAM crane and

the different combinations of the distance from the front axle to the articulation joints and the

distance from the rear axle to the articulation joints.

In the force relationship study, the result showed it is a good design to have the articulation

joints at the centre of the wheelbase. However, in the geometry relationship study, the result

showed having the articulation joints at the centre of the wheelbase is not a suitable design

for NSAM cranes from roll-over stability perspective. It seems better to have the articulation

joints closer to the rear axle.

A development of a potential monitoring system was described. The concept of the new

monitoring system is to integrate some additional data with the existing data from the current

monitoring system to a new display through application of the theory developed in this thesis.

This could provide a real time physical understanding of the stability situation of NSAM

cranes for the operators. Eventually, this might reduce the likelihood of roll-over accidents

during the carrying mode. Finally, the limitations of the project were discussed in terms of

the information limitation, and the practical test limitation of this study.

Conclusion

80

7 Conclusion

This study addressed a gap in the research on the stability study of NSAM cranes by: 1)

exploring what operating factors contribute to the tipping accidents of NSAM cranes; 2)

examining the current frame design of NSAM cranes from a static stability perspective; and 3)

suggesting the potential development of a monitoring system to assist operators to reduce the

likelihood of NSAM crane tipping accidents. This chapter summarises the key achievements

and some topics are introduced that can be considered as potential future studies in this area.

7.1 Thesis Summary

The development of a general static model for the stability study of NSAM cranes was

presented. This model was developed based on a number of assumptions and validated by

some specific models. The result of the general model showed the stability of NSAM crane

on a slope by determining the distance from the combined centre of gravity to the overturn

line. Theoretically, the instability increases as this distance decreases. Depending on which

overturn line is encroached determines whether the instability leads to a tip-over or a roll-

over.

A representative tipping accident of a 14 tonne NSAM crane was studied. Based on the

limited description and suggested causes from the investigation report, a more detailed

analysis of the potential causes was carried out using the static model in this thesis. The result

suggests that the articulation angle, the slope gradient, the orientation angle, and the height of

the boom are the main operating factors contributing to the instability accidents of NSAM

Conclusion

81

cranes. However, the height of the carried load and the counter weight provide minimal

assistant to increase the stability of NSAM cranes on a slope.

An examination of the current frame design of NSAM cranes was conducted. This

examination was mainly to investigate whether having the articulation joints at the centre of

wheelbase is a good design for NSAM cranes from stability perspective. Both tip-over and

roll-over stabilities were investigated. In the tip-over stability analysis, the investigation was

based on the understanding of the relationship between 1) the combined normal force on the

rear tyres and 2) the different combinations of the distance from the front axle to the

articulation joints and the distance from the rear axle to the articulation joints. The result

suggests it is a good design to have the articulation joints at the centre of the wheelbase in

terms of the tip-over stability. In the roll-over stability analysis, the study explored the

relationship between the distance from the combined centre of gravity to the overturn line and

the different combinations of the distance from the front axle to the articulation joints and the

distance from the rear axle to the articulation joints. The result suggests it is not a suitable

design to have the articulation joints at the centre of the wheelbase. The roll-over stability can

be increased by having the articulation joints closer to the rear axle.

The potential development of a new monitoring system was also introduced. It is believed

that the current monitoring system provides a limited ability to ensure the stability when a

NSAM crane is in carrying mode. Due to the lack of the real time physical understanding of

the stability situation of the crane, the operators might take a risk that may lead to an

instability accident. The new design aims to improve this problem and potentially reduce the

likelihood of the tipping accidents of NSAM cranes.

Conclusion

82

Finally, the limitations of this project were outlined. This involves the limitations of the

model development, the information access, and the practical test. The model limitation was

due to the differences between the theoretical assumptions and real environment such as

uneven ground. The limitations associated with information access concerning design

parameters were a result of the design intellectual properties owned by NSAM crane

manufacturer. Experimental testing was not feasible due to the time period, the research

budget, and the associated safety issues.

7.2 Future Work

A number of works are proposed to do in the future. They are:

• Develop a full model of the crane in a simulation package, for instance, Adams. This

full model could be used for cross-validation of the static model developed in this

work. The specific models and general model are essentially developed based on the

same procedure, and therefore, the used of another model for cross-validation would

be useful. In addition, different factors ignored in this study (in particular, the

dynamic effects) could also be investigated using this full model;

• Compare the results of this study with those obtained from a dynamic model to

ascertain the limits of applicability;

• Carry out experimental tests to examine the result from a dynamic model; and

• Develop a new monitoring system for NSAM cranes to indicate stability conditions to

the operator and ultimately reduce the number of instability accidents that occur on

slopes.

83

Reference

Azad, NL, McPhee, J & Khajepour, A 2005a, ‘Off-road lateral stability analysis of an

articulated steer vehicle with a rear-mounted load’, International Journal of Vehicle Systems

Modelling and Testing, vol. 1, no. 1/2/3, pp. 106-130.

Azad, NL, McPhee, J & Khajepour, A 2005b, ‘The effects of drive configuration on

undesirable behaviors of articulated steer vehicles’, in Proceedings of IEEE Vehicle Power

and Propulsion (VPP) Conference, Chicago, Illinois, USA, pp. 221-226.

Azad, NL, McPhee, J & Khajepour, A 2005c, ‘The effects of front and rear tyres

characteristics on the snaking behavior of articulated steer vehicles’, in Proceedings of IEEE

Vehicle Power and Propulsion (VPP) Conference, Chicago, Illinois, UWA, pp. 274-279.

Azad, NL 2006, Dynamic modeling and stability controller development for articulated steer

vehicles. Ph.D thesis, University of Waterloo.

Coombes, GB 1968, Slope stability of tractors. Farm Machine Design Engineering,

September 1968, pp.18-33.

Crane crushes 2010. Available from: <http://www.vertikal.net/en/news/story/10124>. [19

May 2010].

Crane tips in Brisbane 2010. Available from: <http://www.vertikal.net/en/news/story/10653>.

[23 August 2010].

Department of Employment, Economic Development and Innovation 2011, Mines safety alert

263 – Non-slewing articulated mobile cranes tipping, Queensland Government, Available

from: <http: // mines.industry.qld.gov.au/mining/safety-alerts-bulletins.htm>. [7 April 2011].

http://www.vertikal.net/en/news/story/10124%3e.%20%5b19�

http://www.vertikal.net/en/news/story/10653�

84

Fujioka, DD, Rauch, A, Singhose, WE & Jones, T 2009, ‘Tip-over stability analysis of

mobile boom cranes with double-pendulum payloads’, in American Control Conference, St.

Louis, Missouri, pp. 3136–3141.

Fujioka, DD 2010, Tip-over stability analysis for mobile boom granes with single-and

double-pendulum payloads. Master thesis, Georgia Institute of Technology.

Gibson, HG & Biller, CJ 1974, ‘Side-slope stability of logging tractors and forwarders’,

Transactions of the ASAE, vol.17, no.2, pp.245-250.

Gibson, HG, Thorner, BC & Thomas, JW 1981, Slope stability warning device for articulated

tractors, US Patent 4284987.

Guzzomi, AL 2012, A revised kineto-static model for Phase I tractor rollover, Biosystems

Engineering, 113(2012) pp.65-75.

Kiliçaslan, S, Balkan, T & Ider, S 1999, ‘Tipping loads of mobile cranes with flexible booms’,

Journal of Sound and Vibration, vol. 223, no. 4, pp. 645–657.

Kleppner, D & Kolenkow, R 1973, An Introduction to Mechanics (2nd ed.), McGraw-Hill.

Maleki, E & Singhose, W 2011, ‘Dynamics and control of a small-scale boom crane’, Journal

of Computational and Nonlinear Dynamics, vol. 6, no. 3, pp. 31015. Available from: ASME

Digital Library. [2 March 2011].

Robway 2007, RCI-1512 rated capacity indicator. Available from:

<http://www.robway.com.au/products-1500.php>. [30 August 2007].

Singhose, W 2009, ‘Command shaping for flexible systems: A review of the first 50 years’,

International Journal of Precision Engineering and Manufacturing, vol. 10, no. 4, pp. 153-168.

http://www.robway.com.au/products-1500.php�

85

Standards Australia 2002, Cranes, hoists and winches – safe use: part 5: Mobile cranes. AS

2550.5-2002. Available from: Standards Australia Online. [24 July 2002].

Terex Lifting Australia n.d., Operators manual: AT-14 H07D RHD. Available from:

<http://www.franna.com.au>.

Terex Lifting Australia 2001, Information bulletin: Operating on side slopes. Available from:

<http://www.franna.com.au>. [09 October 2001].

Terex Lifting Australia 2004, AT-15 Crane with OM906 2000 AT-15 Series Ⅱ. [08

September 2004].

Terex Cranes. 2004, Franna AT-15 Radius Chart. Available from:

<http://esvc000710.wic055u.server-web.com/service_technical_informations.htm>. [8

September 2004].

Titan Cranes Limited 2010, Franna AT-14: 14 tonne all terrain crane. Available from:

<http://www.titancranes.co.nz/fleet/docs/669.pdf>. [26 July 2010].

Towarek, Z 1998, ‘The dynamic stability of a crane standing on soil during the rotation of the

boom’, International Journal of Mechanical Sciences, vol. 40, no. 6, pp. 557-574.

Universal cranes 2009, Lifting Matters: July 2009. Available from:

<http://universalcranes.com.au/liftingmatters.php>. [July 2009].

Universal cranes 2010, Lifting Matters: February 2010. Available from:

<http://universalcranes.com.au/liftingmatters.php>. [February 2010].

Wray, G, Nazalewicz, J & Kwitowski, AJ 1984, ‘ Stability indicators for front end loaders,’

the 8th international conference ISTVS, Cambridge, pp. 655-671.

http://www.franna.com.au/�

http://www.franna.com.au/�

http://www.titancranes.co.nz/fleet/docs/669.pdf�

http://universal/�

http://universal/�

86

Zhao, D, Wu, G, Wang, D & Cheng, Y 1996, ‘The accurate position of the first order vertical

overturning axis of articulated vehicle’, Transactions of the Chinese Society of Agricultural,

vol.27, no.1, pp.11-15. (in Chinese)

87

APPENDIX A

The detailed calculation procedure in Section 4.5.2.2b is shown as follows.

C in coordinate system 1O XYZ can be determined by the follows

5 6 3 1 2 4

7

7 2 4

( ( ) cos )

( cos )

sin ( )sin

m b f r

TOTX

h m b b f f r rY

TOTZ

m r

TOT


Ch l G h G h G h G

CG

CG l G l l

G

θ

α

α θ

− − + + + − − + + + = − + −

(A.1)

Transfer C from coordinate system 1O XYZ to coordinate system ' ' 'FLA X Y Z as

5 6 3 1 2 4

'

2 4 7'

'

2 4

( ( ) cos )

( ) cos ( )sin sinsin

( )sin cos ( )sincos

m b f r

TOTX

h m b b f f r r r mY

TOTZ

r h m b b f f r r

TOT


Ch G h G h G h G G l l G l

C bG

CG l l h G h G h G h G

bG

θ

α θ αα

θ α αα

− − + + + − + + + + − − = + − − + + + +

(A.2)

Project 'C on Panel ' 'FLX A Z as

5 6 3 1 2 4

2 4

( ( ) cos )

( )sin cos ( )sincos

m b f r

TOTPXPZ

r h m b b f f r r

TOT


CC

G l l h G h G h G h Gb

G

θ

θ α αα

− − + + + − = − − + + + +

(A.3)

88

Transfer Overturn Line Z from coordinate system 1O XYZ to coordinate system ' ' 'FLA X Y Z and

project it on Panel ' 'FLX A Z as

2

1 2

( sin cos )coscos sin

P Pl b bZ Xl l bθ θ α

θ θ− +

=+ +

(A.4)

89

APPENDIX B

Figure B-1: Lifting chart of manual extension retracted of Franna AT-14 (Titan Cranes Limited, 2010)

90

APPENDIX C

Figure C-1: The schematic representation of the NSAM crane with different ranges of 1land 2l : a) 1 2l l> ; b) 1 2l l= ; c) 1 2l l<

91

From Figure B-1, the range of 2l can be determined as follows

2

1

1 2b

l rl rl W l

≥ ≥ = −

(C.1)

Therefore,

2 br l W r≤ ≤ −

(C.2)

92

PUBLICATIONS FROM CANDIDATURE

At the time of publication of this thesis, some of the content had been submitted to journals:

JOURNAL PAPERS:

Article: Static stability analysis of non-slewing articulated mobile cranes

Author(s): Wu, J, Guzzomi, AL, Hodkiewicz, M

Journal: Australian Journal of Mechanical Engineering

Status: Submitted

Article: A general articulation angle stability model for non-slewing articulated mobile

cranes on slopes

Author(s): Wu, J, Guzzomi, AL, Hodkiewicz, M

Journal: Australian Journal of Mechanical Engineering

Status: Submitted

static modelling and stability analysis of non-slewing...

Documents