static modelling and stability analysis of non-slewing...
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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.
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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.
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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.
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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
5-3 The relationship between the distance from the combined COG to the OL
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
5-5 The relationship between the distance from the combined COG to the OL
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
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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
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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.
Background and Literature Review
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%
Background and Literature Review
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.
Background and Literature Review
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
Background and Literature Review
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)
Background and Literature Review
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.
Background and Literature Review
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
Background and Literature Review
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.
Background and Literature Review
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).
Background and Literature Review
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
Background and Literature Review
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.
Background and Literature Review
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;
Background and Literature Review
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.
Background and Literature Review
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.
Theoretical Modelling
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;
Theoretical Modelling
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.
Theoretical Modelling
26
Figure 4-2: Schematic of a NSAM crane across a side slope with individual COG locations, geometry and coordinated systems indicated
Theoretical Modelling
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)
Theoretical Modelling
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:
Theoretical Modelling
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)
Theoretical Modelling
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=
Theoretical Modelling
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 ∈ .
Theoretical Modelling
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
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33
Figure 4-3: FBD of a NSAM crane on level ground in the: a) straight, and b) articulated configurations.
Theoretical Modelling
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)
Theoretical Modelling
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= − −
Theoretical Modelling
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.
Theoretical Modelling
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
l G l G l G l l l GG
CC
h G h G h G h Gb
Gα
α
− − + + + − = + + + − +
(4.31)
Theoretical Modelling
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
Theoretical Modelling
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
G l G l G l G l l lG
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
G l G l G l G l l lG
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
G l G l G l G l l lG
CC
G h G h G h G h G l lb
G
θ
α θ αα
− − + + + − = + + + + − − +
(4.36)
Theoretical Modelling
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.
Theoretical Modelling
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.
Theoretical Modelling
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
Theoretical Modelling
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
Theoretical Modelling
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 .
Theoretical Modelling
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.
Theoretical Modelling
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+ = +
The maximum combined normal force on the rear tyres
( 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+ < +
The maximum combined normal force on the rear tyres
( 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
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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
l G l G l G l l l GG
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
l G l G l G l l l GG
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
l G l G l G l l l GG
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