Slow Active Suspension Control for Rollover Prevention by

Slow Active Suspension Control for Rollover Prevention by
Slow Active Suspension Control for Rollover
Prevention
by
Sarel Francois van der Westhuizen
Submitted in partial fulfilment of the requirements for the degree
Master of Engineering
In the Faculty of
Engineering, Built Environment and Information Technology
University of Pretoria
August 2012
© University of Pretoria
Abstract
Slow active suspension control for rollover prevention
Author:
Sarel Francois van der Westhuizen
Supervisor:
Prof. Pieter Schalk Els
Department:
Mechanical and Aeronautical Engineering
Degree:
Master of Engineering
Keywords:
Suspension control, Hydropneumatic suspension, Roll stability, Sports
Utility Vehicle, Rollover prevention
Abstract
Rollover prevention in Sports Utility Vehicles (SUV‟s) offers a great challenge in vehicle safety.
By reducing the body roll angle of the vehicle the load transfer will increase and thus decrease
the lateral force that can be generated by the tires. This decrease in the lateral force can cause
the vehicle to slide rather than to roll over. This study presents the possibility of using slow
active suspension control to reduce the body roll and thus reduce the rollover propensity of a
vehicle fitted with a hydro-pneumatic suspension system. The slow active control is obtained by
pumping oil into and draining oil out of each hydro-pneumatic suspension unit individually.
A real gas model for the suspension units as well as for the accumulator that supplies the oil is
incorporated in a validated full vehicle Adams model. This model is then used to simulate a
double lane change manoeuvre performed by a SUV at 60 km/h and it is shown that a significant
improvement in body roll can be obtained with relatively low energy requirements.
The proposed control is successfully implemented on a Land Rover Defender test vehicle. A
Proportional-Derivative (PD) controller is used to control on-off solenoid operated valves and
the flow is adjusted using the lateral acceleration as a parameter. Experimental results confirm
that a significant improvement in body roll is possible.
.
Opsomming
Stadige aktiewe suspensiebeheer om omrol te voorkom
Outeur:
Sarel Francois van der Westhuizen
Studieleier:
Prof. Pieter Schalk Els
Departement:
Meganiese en Lugvaartkundige Ingenieurswese
Graad:
Magister in Ingenieurswese
Sleutelwoorde:
Suspensiebeheer, hidropneumatiese suspensie,
Rolstabiliteit, Sportnutsvoertuig, Omrolvoorkoming
Opsomming
Omrolvoorkoming in Sportnutsvoertuie bied geweldige uitdagings in terme van
voertuigveiligheid. Deur die rolhoek van die voertuig te verminder word die laterale lasoordrag
verhoog en word die laterale krag wat die bande kan genereer minder. As die laterale krag
genoeg verminder sal die voertuig eerder gly as omrol. Die studie ondersoek die moontlikheid
om stadig-aktiewe suspensiebeheer op „n voertuig met „n hidropneumatiese suspensie te gebruik
om bakrol te verminder en dus die omrolgeneigdheid van die voertuig te verlaag. Die beheer
word toegepas deur olie in elke hidropneumaties suspensie-eenheid individueel in te pomp of te
dreineer.
„n Werklike gas model word gebruik om die supensie-eenhede asook die akkumulator, wat die
olie aan die suspensie voorsien, te modeleer. Hierdie modelle word in „n gevalideerde
volvoertuig ADAMS model geïnkorporeer en „n dubbel laanverwisseling word gesimuleer teen
60 km/h. Die resultate toon dat „n beduidende verbetering in die rolhoek moontlik is met
relatiewe lae energievereistes.
Die voorgestelde beheer is suksesvol op „n Land Rover Defender geïmplimenteer en „n
Proportioneele-Differensiaal (PD) beheerder word gebruik om die aan-af solenoїde kleppe te
beheer terwyl die vloei aangepas word na gelang van die laterale versnelling. Eksperimentele
resultate bevestig dat „n beduidende verbetering in bakrol moontlik is.
Acknowledgements
Acknowledgements
My thanks and appreciation to the following:







My Heavenly Father only through You this work was possible. As it says in Your Word:
“Our help is in the name of the LORD, who made heaven and earth.” (Psalm 124:8)
My wife Jenni for all her special love and support
Professor Els for giving me an opportunity, for his many hours of help and for sharing his
seemingly infinite knowledge, I hope that this relationship will still continue for many years
My parents and grandparents for their love and support (including financial support)
Theunis, Herman, Joachim, Carl, Cor-Jacques, Anria, Donna-Lee and Johan for everything
from helping with problems to making jokes and enjoying a good laugh
Eugene at Axiom Hydraulics for his willingness to help
Gerotek for the use of their facilities
Table of Contents
Table of Contents
Abbreviations ................................................................................................................................................. i
List of Symbols ............................................................................................................................................. ii
List of Tables ............................................................................................................................................... iv
List of figures ................................................................................................................................................ v
1.
Introduction ........................................................................................................................................... 1
2.
Literature Overview .............................................................................................................................. 4
2.1
Rollover......................................................................................................................................... 4
2.2
Handling........................................................................................................................................ 8
2.3
Methods to improve rollover and handling characteristics ......................................................... 12
2.3.1
Four wheel steering ............................................................................................................. 13
2.3.2
Passive interconnected suspensions .................................................................................... 13
2.3.3
Semi-Active and Active Suspension Systems..................................................................... 15
2.3.3.1 Four State Semi-Active Suspension (4S4)........................................................................... 15
2.3.3.2 Other Semi-Active Systems ................................................................................................ 19
2.3.4
Active Systems.................................................................................................................... 19
2.3.4.1
Active Anti Roll Bar on the 4S4 .......................................................................................... 19
2.3.4.2 Other Active Anti Roll Bars................................................................................................ 21
3.
2.3.5
Stability Control .................................................................................................................. 21
2.3.6
Tilting Vehicle .................................................................................................................... 22
2.4
Effect of height control on suspension characteristics ................................................................ 22
2.5
Conclusion .................................................................................................................................. 24
Simulation Results .............................................................................................................................. 25
3.1
Full Vehicle Model ..................................................................................................................... 25
3.2
System Requirements.................................................................................................................. 29
3.3
Hydraulic Circuit ........................................................................................................................ 30
3.4
Suspension Model ....................................................................................................................... 34
3.4.1 Ideal Gas Spring Model ............................................................................................................ 35
3.4.2 BWR Spring Model .................................................................................................................. 36
3.5
Control Strategies........................................................................................................................ 36
3.5.1
Control Strategy 1 ............................................................................................................... 37
3.5.2
Control Strategy 2 ............................................................................................................... 39
Table of Contents
3.5.3
PID Controller ..................................................................................................................... 42
3.5.4
On-off valve control ............................................................................................................ 44
3.5.4.1 60 Millisecond sampling increments .................................................................................. 44
3.5.4.2 90 Millisecond sampling increments .................................................................................. 47
3.6
4.
Conclusion .................................................................................................................................. 50
Experimental Work and Results ......................................................................................................... 51
4.1
Initial Verification Tests ............................................................................................................. 51
4.2
Voltage Controlled Current Source............................................................................................. 56
4.3
Proportional Valve Characterisation ........................................................................................... 59
4.4
PID Control Algorithm ............................................................................................................... 61
4.5
Volume Estimation ..................................................................................................................... 62
4.6
Vehicle Implementation and Experimental Results .................................................................... 65
4.6.1
Initial problems and modifications ..................................................................................... 65
4.6.1.1 Battery Power...................................................................................................................... 65
4.6.1.2 Volume Limit ...................................................................................................................... 66
4.6.1.3 Valve Response ................................................................................................................... 67
4.6.2
Experimental Results .......................................................................................................... 68
4.7
Simulation Verification ............................................................................................................... 73
4.8
Conclusion .................................................................................................................................. 77
5.
Conclusion .......................................................................................................................................... 78
6.
Recommendations for future work ..................................................................................................... 79
7.
Bibliography / References ................................................................................................................... 80
Appendix A
Derivation of the differential equation used to calculate the gas temperature in the
suspension ........................................................................................................................... 86
Appendix B
BWR and Nitrogen Constants ............................................................................................. 90
Appendix C
Equation for volume estimation .......................................................................................... 91
Abbreviations
Abbreviations
AARB
Active Anti-Roll Bar
ARB
Anti-Roll Bar
BWR
Benedict Webb Rubin
DC
Direct Current
CG
Centre of Gravity
DLC
Double Lane Change
ER
Electro-Rheological
FTF
Fixed Timing Fishhook
GPS
Global Positioning System
HIS
Hydraulic Interconnected Suspensions
ISO
International Organisation for Standardisation
MR
Magneto-Rheological
NHTSA
National Highway Traffic Safety Administration
PD
Proportional Derivative
PID
Proportional Integral Derivative
RRFF
Roll Rate Feedback Fishhook
SSF
Static Stability Factor
STC
Steering Tilt Control
SUV
Sports Utility Vehicle
USA
United States of America
VSC
Vehicle Stability Control
2WS
2 Wheel Steer
4S4
4 State Semi-active Suspension System
4WS
4 Wheel Steer
i
List of Symbols
List of Symbols
L
ΔP
̇
Piston area
BWR constant
BWR constant
Distance from CG to front axle or BWR constant (Context dependant)
BWR constant
Distance from CG to rear axle or BWR constant (Context dependant)
BWR constant
Cornering stiffness of the front tires
Cornering stiffness of the rear tires
Specific heat
Ideal gas specific heat
Displacement of the gas accumulator's piston
Upwards force exerted by pressurised gas
Vertical force on the outside wheel
Vertical force on the inside wheel
Lateral force
Acceleration due to gravity
Height of CG
Roll centre height
Current
Constant
PID controller gains
Understeer gradient
Roll stiffness of the suspension
Wheelbase
Sprung mass
Mass of the gas
Amount of substance
Constants for ideal gas specific heat
Pressure *
Maximum suspension pressure
Pressure difference
Maximum suspension oil flow
Radius of turn, Resistance or Specific Gas constant (Context dependant)
Track width
Temperature*
Atmospheric temperature
Forward speed, Voltage or Volume* (Context dependant)
Maximum suspension velocity
Change of volume
ii
List of Symbols
Wb
̇
Specific volume
Load (Vertical Force) on the front axle
Load (Vertical Force) on the rear axle
Weighting function
Rate of piston work
Suspension displacement
Suspension displacement at the static position
Greek Symbols
δ
Tire slip angle front
Tire slip angle rear
BWR constant
Bulk modulus
Steer angle of the front wheels
BWR constant
Heat capacity ratio
Thermal time constant
Roll angle of the body
Natural frequency
* Subscripts o = oil and g = gas
iii
List of Tables
List of Tables
Table 1
Table 2
Table 3
Table 4
Table 5
Lane change track dimensions (International Organisation for Standardisation, 1975) ......... 12
Weighted RMS of vertical acceleration for test runs on a Belgian paving (Cronje, 2008) ..... 20
Valve opening commands for different lateral accelerations .................................................. 69
RMS of the displacement for run 1 ......................................................................................... 71
RMS of the roll angle for two different runs........................................................................... 72
iv
List of figures
List of figures
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26
Figure 27
Figure 28
Figure 29
Figure 30
Figure 31
Figure 32
Figure 33
Figure 34
Figure 35
Figure 36
Pie chart of the fatal car crashes in South Africa during 2009 .................................................. 2
Pie chart of the fatalities in car crashes in South Africa during 2009 ....................................... 3
Roll over of a vehicle with a high CG (New Zealand Crash Investigators, 2010) ................... 4
Force analysis of a vehicle (seen from the rear) during cornering (Gillespie, 1992) ............... 6
Lateral forces generated by different vertical forces ................................................................. 6
NHTSA RRFF manoeuvre description (National Highway Traffic Safety Administration,
(2002) ........................................................................................................................................ 8
Constant Radius Test (Gillespie, 1992) .................................................................................... 9
Cornering of a bicycle model (Gillespie, 1992) ...................................................................... 10
Lane change track and cone placement ................................................................................... 11
Nominal fluid flow distribution in an idealised suspension modes (a) bounce, (b) roll,
(c)
pitch, and (d) articulation (Smith and Zhang, 2009) .............................................................. 14
(a) Conventional passive suspension system. (b) Electromagnetic suspension system.
Geysen et al (2010) ................................................................................................................. 15
Suspension Design (Holdmann and Holle, 1999) ................................................................... 16
Schematic diagram of the 4S4 (Els, 2006).............................................................................. 17
Soft and Stiff spring characteristics of the 4S4 (Els, 2006) ..................................................... 18
Damper characteristics of the 4S4 (Els,2006)......................................................................... 18
Average body roll angles for different ARB settings on the stiff suspension during a ........... 20
Average body roll angle vs. lateral acceleration during a constant radius test
(Cronje, 2008) ..................................................................................................................... 21
Tilting Vehicles (Rotpod, 2012) ............................................................................................. 22
Natural frequency as a function of spring load for for a mechanical, pneumatic and ............. 23
Spring rate as a function of spring load for a mechanical, pneumatic and a ........................... 23
Simulation model interaction (Cronje, 2008).......................................................................... 26
Schematic of the front suspension (Thoresson, 2007). .......................................................... 27
Front suspension in ADAMS model (Thoresson, 2007). ....................................................... 27
Schematic of the rear suspension (Thoresson, 2007). ............................................................ 28
Front suspension in ADAMS model (Thoresson, 2007). ....................................................... 28
Validation of the ADAMS model‟s handling dynamics for a DLC at 65km/h ....................... 29
Hydraulic circuit for a single suspension unit ......................................................................... 30
Performance graphs for SV10-24 valve (Hydraforce, 2012) ................................................. 31
Flow vs Pressure Drop for SV10-24 valve ............................................................................. 31
Flow vs Pressure graphs for the SV12-33 (Hydraforce, 2011) directional valve (left) and
the FPCC (Sun Hydraulics, 2011) proportional valve (right) ................................................. 32
Flow diagram of the hydraulic setup in the test vehicle .......................................................... 33
Suspension model interaction ................................................................................................. 34
Main principle of the suspension model ................................................................................. 36
Body roll angle for a DLC manoeuvre at 60 km/h .................................................................. 37
Suspension responses for a DLC manoeuvre at 60 km/h ........................................................ 38
Body roll angle for a DLC manoeuvre at 60 km/h .................................................................. 39
v
List of figures
Figure 37
Figure 38
Figure 39
Figure 40
Figure 41
Figure 42
Figure 43
Figure 44
Figure 45
Figure 46
Figure 47
Figure 48
Figure 49
Figure 50
Figure 51
Figure 52
Figure 53
Figure 54
Figure 55
Figure 56
Figure 57
Figure 58
Figure 59
Figure 60
Figure 61
Figure 62
Figure 63
Figure 64
Figure 65
Figure 66
Figure 67
Figure 68
Figure 69
Figure 70
Figure 71
Figure 72
Figure 73
Figure 74
Figure 75
Figure 76
Figure 77
Suspension responses for a DLC manoeuvre at 60 km/h ........................................................ 40
Suspension responses for a DLC manoeuvre at 60 km/h for unconstrained outflow ............. 41
Suspension responses for a DLC manoeuvre at 60 km/h for constrained outflow ................. 41
Body roll angle for a DLC manoeuvre at 60 km/h using a PID controlled proportional
valve ........................................................................................................................................ 42
Suspension responses for a DLC manoeuvre at 60 km/h for PID controlled proportional ..... 43
Body roll angle for a DLC manoeuvre at 60 km/h using a PID controlled on-off valve ........ 45
Suspension responses for a DLC manoeuvre at 60 km/h for on-off valves ............................ 45
Flow rates for each suspension unit ........................................................................................ 46
Total volume of oil pumped into the suspension .................................................................... 46
Total flow rate required........................................................................................................... 47
Body roll angle for a DLC manoeuvre at 60 km/h using a PID controlled on-off valve ........ 48
Suspension responses for a DLC manoeuvre at 60 km/h for on-off valves ............................ 48
Flow rates for each suspension unit ........................................................................................ 49
Total volume of oil pumped into the suspension .................................................................... 49
Total flow rate required........................................................................................................... 50
Comparison between the measured results and the simulation results with and without ....... 51
Comparison between simulation results of the ideal gas model with flow 12.8l/m and ......... 53
Simulation results of BWR equation model with flow 12.8l/m .............................................. 53
Specific volume during the simulation ................................................................................... 53
Measured and simulated results for Ideal gas and BWR model ............................................. 54
Simulation results of BWR equation model with flow 12.8l/m
(no friction & 50% damping) .................................................................................................. 54
Roll angles for a baseline and controlled DLC at 60km/h ...................................................... 56
Voltage controlled current source with a voltage divider in the reference voltage signal ...... 56
Comparative test between a 1Ω-10W coil resistor at R3 and two 1.5Ω-2W axial resistors in
parallel..................................................................................................................................... 57
Test setup with MR damper as load ........................................................................................ 58
Output signal for an input signal of 2-5V in 0.5V increments ................................................ 58
Input and output signal for an input signal of 5V ................................................................... 59
Valve test with a 50% command input. .................................................................................. 60
Valve test with a 60% command input. .................................................................................. 60
Valve test with a 70% command input. .................................................................................. 60
Valve test with a 80% command input. .................................................................................. 61
Flow vs Pressure curve obtained for different valve openings. .............................................. 61
Noise on the displacement Signals.......................................................................................... 62
PID signals for the averaged PID (left) and for the averaged displacement (right) ................ 62
Suspension displacements ....................................................................................................... 63
Estimated volume of oil in suspension.................................................................................... 64
Suspension displacements during fall test............................................................................... 64
Estimated volume of oil in suspension during fall test ........................................................... 65
10 l bladder type accumulator being charged to 7 MPa .......................................................... 66
Estimated Volume during a DLC at 60 km/h.......................................................................... 67
Valves for the rear suspension unit during characterisation ................................................... 68
vi
List of figures
Figure 78
Figure 79
Figure 80
Figure 81
Figure 82
Figure 83
Figure 84
Figure 85
Figure 86
Figure 87
Figure 88
Figure 89
Land Rover Defender test vehicle being prepared for testing ................................................. 70
Laser displacement sensor on the side of the vehicle.............................................................. 70
Suspension displacements for Run 1 during a DLC at 60km/h .............................................. 71
Body roll angle for DLC‟s at 60km/h ..................................................................................... 72
Vehicle path and speed for the baseline run and controlled run1 ........................................... 72
Simulated and experimental roll angle for a controlled DLC at 60 km/h ............................... 74
Simulated and Experimental controlled suspension displacement for a DLC at 60km/h ....... 74
Suspension displacement for average total inflow of 0.54 l/m during a DLC at 60km/h ....... 75
Suspension displacement for average total inflow of 1.35 l/m during a DLC at 60km/h ....... 75
Suspension displacement for average total inflow of 3.37 l/m during a DLC at 60km/h ....... 76
Suspension displacement for average total inflow of 6.75 l/m during a DLC at 60km/h ....... 76
Roll angle for different total flow magnitudes during a DLC at 60km/h ................................ 77
vii
Introduction
1.
Introduction
SUV‟s are becoming increasingly popular as family vehicles and are able to drive at reasonably high
speeds. These vehicles can give the driver a sense of safety because of their size and robustness and can
thus encourage reckless driving behaviour. In reality these vehicles generally have a high centre of
gravity (CG) and soft suspensions with large wheel travel to provide good off-road abilities and comfort,
which result in a vehicle that is prone to untripped rollover. These problems also occur in many other
vehicles used in construction, mining, military and agricultural applications.
Road accident statistics also show that SUV‟s are prone to rollover and that rollover is a very dangerous
type of accident:
According to the Governor’s Office of Consumer Affairs (2010) in Georgia, more than 40% of
Americans think that they are safer in a SUV than in a regular car and nearly 50% do not take into
account that loading increases the risk of rollover. This is shocking in the light that 37% of fatal crashes
reported in the study were due to SUV rollovers where only 15% of fatal accidents in passenger cars were
due to rollover. In 2006 SUVs also had the highest occupant fatality rate in rollover crashes namely 7.77
per 100,000 registered vehicles and single-vehicle rollover crashes made up 47% of driver deaths in
SUVs. In 2006, 65% of single vehicle crashes involved SUVs.
The rollover statistics for Pennsylvania shows similar trends. In 2008, 8.5% of light truck, van and SUV
accidents were due to rollover where 5% of passenger cars rolled over. Of these rollover cases the
occupant deaths were nearly 70% higher in SUVs than in passenger cars. (Edgar Snyder and
Associates, 2010)
In South Africa, rollover accidents made up 24% of the fatal crashes for 2009 and it made up 25% of the
fatalities for 2009 (see Figure 1 and Figure 2). This again shows the severity of a rollover accident.
(Road Traffic Management Corporation, 2009)
According to Takubo and Mizuno (2000) the particular use of SUV‟s in Japan make them more prone to
accidents.
SUV‟s are used to:
 Travel long distances for leisure
 Travel on crowded roads
 Travel unfamiliar roads to a holiday destination where the scenery can distract the driver
 Drive winding roads in recreational areas
 Drive children around
 Drive in places of heavy pedestrian traffic
This, combined with the fact that these vehicles are popular amongst younger people that often drive
more recklessly, and that the dynamics of these vehicles are worse than those of normal passenger cars,
results therein that these vehicles can be very dangerous to drive. The large side area of the vehicle
combined with general softer suspension makes it vulnerable to side winds while the high CG magnifies
the rolling motions during cornering. The high viewpoint of the driver also inspires confidence, because
the driver can see further, and the driver may become over confident.
1
Introduction
These are just a few examples of the very urgent need for better rollover stability or control in Sports
Utility and other high CG vehicles. From these statistics it becomes clear that rollover is a very
dangerous type of accident with a high fatality rate. This is because there is very little structural occupant
protection in vehicles in the case of a rollover accident compared to front and rear impacts.
South African Fatal Crashes 2009
Turn from wrong lane Person fell off vehicle
1%
0.33%
Animal
Turn in face of
0.48% Cyclist
oncoming traffic
2%
0.45%
Motorcycle
Approach at angle
0.45%
2%
Head-Rear end
Multiple vehicle
5%
1%
Sideswipe same
Unknown and other
direction
1%
2%
Sideswipe opposite
direction
Pedestrian
3%
35%
Collision - Fixed
object
4%
Overturned
24%
Figure 1
Hit and run 8%
Head on
11%
Pie chart of the fatal car crashes in South Africa during 2009
(Road Traffic Management Corporation, 2009)
2
Introduction
South African Fatalities 2009
Person fell off vehicle
Turn from wrong
1%
Animal
lane
0.48% Cyclist
0.33%
Turn in face of
2%
oncoming traffic
Motorcycle
0.45%
0.45%
Approach at angle
Multiple vehicle
3%
Head-Rear end
1%
5%
Unknown and other
Sideswipe same
1%
direction
2%
Pedestrian
Sideswipe opposite
28%
direction
4%
Collision - Fixed
object
4%
Overturned
25%
Head on
17%
Hit and run - mainly
pedestrian
7%
Figure 2
Pie chart of the fatalities in car crashes in South Africa during 2009
(Road Traffic Management Corporation, 2009)
This study will investigate the feasibility of using slow active suspension control, on a four state semi
active hydropneumatic suspension installed on a Land Rover Defender test vehicle, to improve the body
roll of the vehicle and thus decrease the vehicle‟s tendency to roll over. Oil is pumped into and drained
out of each suspension unit individually to counter compression and extension. Simulations are
performed using a validated ADAMS (MSC.Software, 2011) model. The suspension control is
implemented on a test vehicle and experimental tests are performed. The simulated an experimental data
obtained is then compared.
An overview of the relevant literature is given in Chapter 2. The simulation model, theoretical
development and simulation results used to determine the feasibility of slow active suspension control are
given in Chapter 3, while the experimental results and a comparison between the experimental and
simulation results are given in Chapter 4. A conclusion is given in Chapter 5 and recommendations for
future work in Chapter 6.
3
Literature Overview
2.
Literature Overview
This chapter summarises the relevant literature on rollover and handling, methods to measure rollover and
handling, methods to improve rollover and handling, characteristics of different suspensions and some
background on the simulation model used in this study. The semi-active suspension used in this study is
also described in this chapter.
2.1
Rollover
Roll over is defined as a vehicle rotation of 90˚ around the longitudinal or lateral axis but during dynamic
testing rollover is generally defined as two or more wheels lifting more than 51mm off the ground for
more than 0.5s (Ponticel, 2003). There are two types of rollover namely tripped rollover and untripped
rollover. In many cases the moment around the roll axis (due to the centrifugal force on the CG and the
lateral force generated by the tire) in vehicles with a high CG like SUV‟s can become large enough to
cause untripped rollover. The magnitude of this moment can be reduced by lowering the CG, reducing
the centrifugal force on the CG or reducing the lateral force generated by the tyre. The centrifugal force
can be reduced by reducing the speed of the vehicle when cornering and the lateral force by changing the
load transfer (described later on). If the lateral force that the tires can generate is reduced sufficiently the
vehicle will slide rather than to roll over untripped. Sliding is not desirable because the vehicle will not
follow the desired path but it is preferable to rolling over. Although sliding can cause tripped rollover it
dissipates energy and thus reduces the vehicle speed which in turn reduces the probability of rollover.
Therefore this study will focus on reducing the risk of untripped rollover which occurs when the vehicle
rolls over without hitting an obstacle. Figure 3 shows a vehicle where static rollover starts to occur when
the CG passes the point of contact with the ground (Point A). From this it becomes clear that the higher
the CG, the smaller the angle necessary for roll over.
Static rollover starts
to occur
Force applied to
cause rollover
Mass
Mass
Lateral force by tire
A
Figure 3
A
Roll over of a vehicle with a high CG (New Zealand Crash Investigators, 2010)
4
Literature Overview
When cornering at high speeds, lateral acceleration is generated which causes a centrifugal force to act on
the CG (Fy in Figure 4), one can see here that the magnitude of the moment around A will increase as the
height of the CG increases. The roll centre of the vehicle is the point where the lateral forces are
transferred from the axle to the body of the vehicle. The difference between the vertical force on the
inside and the outside wheels can be determined using the following equation given by Gillespie (1992):
(1)
Where:
Vertical force on the outside wheel
Vertical force on the inside wheel
Lateral Force
Roll centre height
Roll stiffness of the suspension
Track width
Roll angle of the body (+ is clockwise, when looking at the rear of the vehicle)
The first part of the equation
is a transfer of the lateral load due to the cornering forces and can
only be improved by widening the track of the vehicle or by lowering the CG. Although ride height
control is not the focus of this study, slow active ride height control can be easily implemented using the
same hydraulic and control hardware developed in this study, but with changes to the algorithms.
The second part
is a transfer of the lateral load due to body roll. It can be seen here that if the roll
angle is reduced the load transfer will be smaller and the vehicles tendency to roll over will be less due to
the moment of the mass around point A in Figure 4. However to reduce the roll angle,
needs to
increase which increases the load transfer and this, due to the non-linearity between the vertical force and
the lateral force, reduces the lateral force that the tyres can generate. If the lateral force is reduced enough
the vehicle will slide rather than roll over. Figure 5 indicates a typical lateral tyre force vs. vertical tyre
force graph for a constant slip angle. It shows two cases; one where both wheels experience a vertical
force of 4 kN and the other where one wheel experiences a vertical force of 3 kN and the other 5 kN. One
can see that the total lateral force generated for the first case is about 5 kN and for the second case 4.9 kN,
thus there is a decrease in the lateral force due to the load transfer between the wheels. (Gillespie, 1992)
A popular method to characterise rollover resistance is the Static Stability Factor (SSF). The SSF is
defined as the half of the track width divided by the height of the CG if the nomenclature of Figure 4 is
used the SSF will be:
(2)
(National Highway Traffic Safety Administration, 2012)
5
Literature Overview
CG
A
Figure 4
Force analysis of a vehicle (seen from the rear) during cornering (Gillespie, 1992)
Vertical Force vs. Lateral Force for a Constant Slip Angle
Lateral Force [kN]
3
X: 5
Y: 2.847
2.5
X: 4
Y: 2.524
2
X: 3
Y: 2.045
1.5
1
Lateral Force vs. Vertical Force
Load Case 1: Left = 4 kN Right = 4 kN
Load Case 2: Left = 3 kN Right = 5 kN
0.5
0
0
1
2
3
4
5
6
7
8
9
Vertical Force [kN]
Figure 5
Lateral forces generated by different vertical forces
6
Literature Overview
Ungoren et.al. (2001) evaluates the effect of a Vehicle Stability Control (VSC) system on the rollover
propensity of a SUV using CarSim (Mechanical Simulation, 2012a) and TruckSim (Mechanical
Simulation, 2012b). According to the National Highway Traffic Safety Administration (NHTSA) of the
United States of America the SSF is the most reliable measure of the vehicle‟s tendency towards
untripped rollover. The authors use an evaluation method where the disturbances are modelled as a worst
case while the control input is optimised for the disturbance inputs. The authors come to the conclusion
that the vehicle‟s tendency to roll over can be reduced by a VSC system. This shows that the dynamics of
a vehicle with undesirable geometry like an SUV can be improved by other means than to change the
geometry.
When cornering in a passively suspended vehicle, the sprung mass shifts to the outside of the vehicle‟s
centreline. This has a negative effect on the roll stability of the vehicle. In terms of mass distribution it
would be preferable to have the vehicle lean into the corner to move the CG to the inside of the vehicles
centreline. This will create a moment that will act against the centrifugal force that can cause rollover
(Sampson and Cebon, 2003). The effect of this is very small but if the inside of the vehicle body is
lowered this will also lower the CG which might have a bigger effect on the rollover propensity. This
will have a desirable effect if cornering is only done in one direction, but if the weight suddenly shifts to
the lowered suspension units as will be the case in a dynamic handling manoeuvre it can cause rollover.
Thus it is not desirable to lower the units under normal or even hard driving conditions but it might be
useful in an extreme case where rollover is about to occur. In order to do this a robust algorithm is
needed that can predict rollover accurately. Ozaki (2002) concluded that the basic driving stability is
equal for inward as well as for outward roll.
These are just a few examples that finding a universal method to define rollover propensity and handling
poses a great challenge. This is made even more difficult by the fact that control systems can change the
rollover propensity or handling characteristics of a vehicle.
A popular manoeuvre to measure rollover resistance is the Fishhook Manoeuvre and the National
Highway Traffic Safety Administration (2002) describe two variants of the manoeuvre namely the
Fixed Timing Fishhook (FTF) and the Roll Rate Feedback Fishhook (RRFF). The single difference
between the two manoeuvres is that the dwell times between steering inputs are fixed for the FTF
manoeuvre and that it is determined by the roll motion of the vehicle in the case of the RRFF manoeuvre.
For these tests the vehicle is driven at a speed slightly higher than the desired entrance speed, the
accelerator is then released and when the vehicle reaches the desired speed the steer robot engages the
manoeuvre. The steer robot will give a steer input 6.5 times the steer input needed to obtain 0.3g lateral
acceleration at 80km/h then after the determined dwell time it will give a countersteer input. All steer
inputs should be done at 720 degrees per second. The Steering input and roll rate feedback for the RRFF
manoeuvre is shown in Figure 6. The entry speed is increased until rollover takes place which is defined
as 2 wheels lifting more than 51mm of the ground for more than 0.5 seconds. This test requires a wide
enough track so that the manoeuvre can be performed without the risk of going of the track. Due to the
lack of a wide enough track it was not possible to perform the Fishhook Manoeuvre during this study.
7
Literature Overview
Figure 6
2.2
NHTSA RRFF manoeuvre description (National Highway Traffic Safety Administration,
(2002)
Handling
The quality of the handling of a vehicle is determined by the ease with which a human can control the
vehicle, in other words a vehicle that is easy to control has good handling and a vehicle that is hard to
control has poor handling. There is currently no universally accepted method that can quantify the
controllability of a vehicle seeing that various human beings will experience the controllability of a
vehicle in different ways.
Uys et al. (2006a) investigated the possibility of a single, unambiguous objective criterion for handling.
It is shown from literature that there is no single criterion to define handling, and experimental work is
done where four drivers of different ages and gender drive three different vehicles. A one to one
relationship is observed between the lateral acceleration and the roll angle in the case of all the test
drivers. It is concluded that roll angle is a favourable criteria to optimise the suspension settings for a
prescribed road, to determine when to switch over between a hard and a soft suspension and to measure
handling.
It was shown in 2.1 that that a reduction in roll angle can decrease the tendency to roll over for a vehicle
with a high CG. Thus if an improvement in the roll angle is obtained during a handling manoeuvre this
will also indicate an improvement in the roll over tendency of the vehicle.
The handling of a vehicle can be divided into two categories namely steady state handling and dynamic
handling. Steady state handling is somewhat easier to quantify than dynamic handling but does not give a
8
Literature Overview
Steer Angle [δ]
very good indication of how the vehicle will handle in a dynamic situation. Steady state handling can be
tested with a constant radius test. It is however important that this test is used as a comparative test and
that these tests are done around the same circle on the same surface. During this test the vehicle is driven
around a circle maintaining a constant radius by changing the steer angle. The speed is increased until the
vehicle can no longer keep to the prescribed path. The steering angle vs. speed indicates whether the
vehicle under steers or oversteers. Gillespie (1992) recommends a minimum radius of 30m for the circle
as shown in Figure 7.
Understeer
Neutral Steer
Oversteer
Critical Speed
Characteristic Speed
Speed
Figure 7
Constant Radius Test (Gillespie, 1992)
Steering characteristics such as over- and understeer can be derived using a simplified bicycle model. In
this model the difference between the steer angles of the front wheels is seen as negligible. Thus the two
wheels are represented as one wheel with a cornering force equal to the sum of the forces of both wheels
at a steer angle . The same assumption is made for the rear wheels (see Figure 8). Body roll and lateral
load transfer is ignored. The steer angle (in degrees) is then given by the following equation:
(
)
(3)
Where:
(
(
)
)
9
Literature Overview
(
)
Neutral-, under- and Oversteer can now be defined as:
i)
Neutral steer is when the no change in the steering angle is necessary to stay on the prescribed path
(constant radius turn) as the speed increases or decreases.
(4)
ii)
Understeer is when the steering angle needs to increase during a constant radius turn as the speed
increases.
(5)
iii) Oversteer is when the steering angle needs to decrease with an increase of speed during a constant
radius turn.
(6)
L/R
αf
αf
δ
δ
αR
b
R
L
αR
c
Figure 8
Cornering of a bicycle model (Gillespie, 1992)
10
Literature Overview
The vehicle‟s handling characteristics (oversteer and understeer) can be changed by increasing the front
or rear load transfer as indicated previously (Par. 2.1 and Figure 5) load transfer decreases lateral force.
For example more lateral load transfer at the rear axle will result in a bigger rear slip angle and thus more
oversteer, a vehicle that understeers will understeer less, a neutral vehicle will oversteer and a vehicle that
oversteers will oversteer more (Gillespie, 1992) & (Cronjé, 2008). Thus by controlling the suspension
characteristics the vehicle can be forced into over- or understeer. The geometry and roll stiffness also
play a role and as a result of the CG being far above the roll axis in an SUV, the CG causes a moment
around the roll axis and this causes the vehicle body to roll outwards excessively. The inclination of the
roll axis will also affect the lateral forces on the front and rear wheels. Having a roll axis that is lower at
the front will decrease the lateral force on the rear wheels and increase it at the front wheels, this will help
to obtain a vehicle that understeers rather than to oversteer (Higuchi et. al., 2001). Controlling the
inclination of the roll axis might improve handling during dynamic manuoevres where the inclination can
change.
Dynamic handling is often quantified using the Severe Double Lane Change (DLC) manoeuvre. The DLC
manoeuvre is defined by the International Organisation for Standardisation (1975) as: “A dynamic
process consisting of driving a vehicle from its initial lane to another lane parallel to the initial lane as fast
as possible, and possibly returning to the initial lane.”. Similar to the constant radius test this test is to be
used as a comparative test where all the tests are done on the same surface. The track dimensions and
cone placements are shown in Figure 9 and Table 1.
Driving
direction
Lane
offset
Section
1
1
2
Section
2
Figure 9
2a
Section
5
Section
4
3
Driving
direction
1a
Section
3
Section
6
7
8
9
10
11
7a
8a
9a
10a
11a
Lane
offset
3a
4
5
6
4a
5a
6a
Lane change track and cone placement
(International Organisation for Standardisation, 1975)
11
Literature Overview
Table 1
Lane change track dimensions (International Organisation for Standardisation, 1975)
Section
1
2
3
4
5
6
Lane offset
Width
1.1 x vehicle width + 0.25m
Not Applicable
1.2 x vehicle width + 0.25m
Not Applicable
1.3 x vehicle width + 0.25m
1.3 x vehicle width + 0.25m
3.5m
Length
15m
30m
25m
25m
15m
15m
The standard requires the test to comply with the following requirements:





The lane change track must be marked by cones as shown in Figure 9
The track limit must be tangential to the base circle of the cone as shown in Figure 9.
The measuring distance starts at the beginning of section 1 and finishes at the end of section 5.
The lane change must be done by a skilled driver.
A passage is faultless when none of the cones positioned as specified have been displaced.
(International Organisation for Standardisation, 1975)
Note that the lane change indicated in Figure 9 is mirrored from that given in the standard because it is
applied to a right hand drive vehicle.
Several other handling tests exist as well, for example: The J-turn and Sine Sweep.
Other methods to quantify the handling of a vehicle is also possible for instance to measure the biological
reactions of the driver, and then to use this to determine the workload the driver is experiencing. This test
method was used by Abe and Manning (2009) to determine the controllability of a vehicle with
oversteer characteristics compared to that of a vehicle with understeer characteristics. It was found that a
vehicle with moderate understeer characteristics is easier to control. This test method does however
require some medical knowledge as well as the appropriate equipment and is not easily executable
without the appropriate expertise.
2.3
Methods to improve rollover and handling characteristics
There are various methods to improve handling including changes to the physical dimensions or
aerodynamics of the vehicle. The handling can also be improved by changing the suspension
characteristics either passively, semi-actively or actively. SUV‟s drive relatively slow and aerodynamic
downforce is largely dependent on the speed of the vehicle therefore this will not be considered here.
Changing the physical dimensions of the vehicle will also not be considered seeing that most of these
dimensions are constrained due to some requirement other than handling.
Thus methods to improve handling that do not necessarily require changes to the geometry of the vehicle
will be considered here. Any factor influencing the cornering force will directly affect the directional
response of the vehicle. The suspension is one of the primary contributors to these influences. One of
these influences is the load transfer that is largely determined by the suspension and can increase or
decrease the lateral force possible (Dukkipati et al., 2008). Optimising a passive suspension for handling
12
Literature Overview
results in a vehicle with poor ride comfort and similarly good ride comfort results in poor handling, for
this reason the tendency is to implement some form of control on suspensions to give good ride comfort
and good handling in the relevant circumstances.
Shim and Velusamy (2010) categorises active roll control in the following four main categories: four
wheel steering, active suspensions, active roll bars and differential braking.
2.3.1 Four wheel steering
Shaout et al. (2000) developed a nonlinear controller for a four wheel steering (4WS) vehicle. A single
track nonlinear vehicle model is used and a linear quadratic regulator model is used to control the 4WS.
It is concluded that the control is robust and effective in the presence of noise and shows an improvement
in handling. No experimental data is given and no comment is made on the improvement of handling
compared to a two wheel steer (2WS) vehicle.
Hakima and Ameli (2010) modelled a four wheel steer vehicle with an electronic stability program using
the brakes to generate a corrective yaw moment using a 3 degree of freedom model. The steering is
controlled using a fuzzy logic controller. The simulation results show that the system can improve the
vehicle‟s handling and directional stability significantly. No experimental verification is given.
2.3.2
Passive interconnected suspensions
Interconnected suspensions are a popular method to overcome the ride handling compromise. Smith.
and Walker (2005) defines an interconnected suspension as a system where a displacement at one wheel
station can produce forces at other wheel stations. Concepts of hydraulic interconnected suspensions
(HIS) is found as early as 1927, (Hawley, 1927), and interconnected suspensions were widely used
during 1950 to the 1970s for ride comfort improvement. In the later years the emphasis of these
suspension systems moved to vehicle roll. Most of these systems were based on two wheel
interconnections however, having a drawback due to the loose coupling between modal pairs. The
advantage in four wheel interconnected systems lies in their ability to provide features such as increased
roll stiffness together with reduced articulation stiffness and decoupled roll and bounce damping in a
passive system. Wilde et al (2005) simulated and tested a kinetic suspension using a fishhook test. The
performance was determined by the maximum speed the vehicle can maintain during the manoeuvre
without a rim touching the ground or two wheels lifting more than two inches (51 mm) of the ground.
The vehicle‟s speed improved from 43mph (69 km/h) to 60 mph (97 km/h). Figure 10 shows the different
flow distributions on a schematic of the kinetic suspension used. (Smith and Zhang, 2009)
13
Literature Overview
Figure 10
Nominal fluid flow distribution in an idealised suspension modes (a) bounce, (b) roll, (c)
pitch, and (d) articulation (Smith and Zhang, 2009)
14
Literature Overview
2.3.3
Semi-Active and Active Suspension Systems
Figure 11
(a) Conventional passive suspension system. (b) Electromagnetic suspension system.
Geysen et al (2010)
According to Fischer and Isermann (2004) it is important to keep the unsprung mass resonance
frequency near 10Hz to increase the tire‟s contact with the road and thus increase the handling. On the
other hand it is preferable to have the sprung mass resonant frequency at 1Hz for good ride comfort. This
means that a passive system always results in some compromise between handling and ride comfort.
Active and semi-active suspensions attempts to solve or reduce this compromise. Semi-active suspension
systems adapts the damping or suspension stiffness to the demand where active suspension systems
provides an extra force input in addition to the possible passive system. Active suspension systems have
high power requirements. Semi-active dampers conventionally consist of a damper with a bypass that
can be opened and closed to provide different states of damping. One variation of active or semi-active
dampers are magneto-rheological (MR) dampers, these dampers offer stable hysteretic behaviour over a
broad temperature range, a broad bandwidth and can have fast response times. Active suspension
systems can be hydraulic, hydro-pneumatic, pneumatic, electro-mechanical, etcetera. Due to their
complexity, high costs and high energy demand the commercial availability of these systems are limited.
Figure 11 shows a passive suspension compared to an active electromagnetic suspension.
2.3.3.1 Four State Semi-Active Suspension (4S4)
According to Theron and Els (2003) a vehicle‟s passive suspension always has to make some
compromise between handling and ride comfort. Good ride comfort will require a soft suspension with
good wheel travel to minimise the disturbances carried trough from the wheels to the occupants. For
optimal handling the suspension needs to be stiff to minimise body roll as explained in the previous
section. With controllable suspensions the characteristics of the suspension can be changed while the
vehicle is driving, this can vastly reduce or maybe even eliminate the compromise between ride comfort
and handling. According to Wallentowitz and Holdman (2010), two spring stages are sufficient to
overcome this compromise. A soft spring is used to obtain optimal ride comfort while a stiff spring is
used during handling manoeuvres and braking. This phenomenon is illustrated in Figure 12.
15
Literature Overview
Figure 12
Suspension Design (Holdmann and Holle, 1999)
The four state semi-active suspension system (4S4) was developed by Els (2006) which uses semi-active
hydropneumatic springs and hydraulic dampers. The 4S4 was optimised to give optimal ride comfort (soft
springs and low damping) and to give optimal handling (hard springs and high damping) on its specific
settings. The ride comfort was optimised by minimising the vertical acceleration and the handling by
minimising the body roll angle when performing a DLC. The 4S4 can switch between hard and soft
spring settings and between high and low damping in less than 100 milliseconds. This is done
automatically based on acceleration measured on the vehicle body. The switching is done by opening or
closing solenoid valves (See par. 3.3). A schematic diagram of a 4S4 unit can be seen in Figure 13. The
wheel displacement relative to the vehicle body results in the displacement of the piston in the main strut
which is filled with oil. The oil then flows through the damper packs or valves until the oil pressure and
the pressure of the accumulator equalises. If valves 3 and 4 are closed the suspension is on the stiff spring
setting where only the 0.1 litre nitrogen accumulator is used as a pneumatic spring. If valves 3 and 4 are
open it is on the soft spring setting where both the 0.4 litre and the 0.1 litre accumulators serve as a
pneumatic spring. If valve 1 and 2 are closed the system has high damping because the oil flow is forced
to flow through the damper pack, and if they are open the system has low damping because the oil flow
can flow past the damper pack through the open valves. Two valves were used at 3 and 4 due to the high
flow requirement and a faster response time is possible using two smaller valves compared to that of a
larger single valve.
16
Literature Overview
The 4S4 can change the driving characteristics of the vehicle from ride comfort mode to handling mode in
a fraction of a second. It also has the added advantage that the power required is mainly that of the
solenoid valves which results in a fraction of the power requirement of a fully active suspension. This
suspension has been implemented successfully on a Land Rover Defender 110 at the University of
Pretoria and experimental results of a DLC has shown improvements in the roll angle as high as 78% for
the handling setting compared to the baseline vehicle. The comfort setting gave a 50 % to 80%
improvement in ride comfort compared to the handling setting when driving over a Belgian paving. The
suspension characteristics for the different settings of the 4S4 are shown in Figure 14 and Figure 15
Figure 13
Schematic diagram of the 4S4 (Els, 2006)
17
Literature Overview
Figure 14
Soft and Stiff spring characteristics of the 4S4 (Els, 2006)
Damper Characteristics
20
15
Force [kN]
10
5
0
-5
Stiff Spring - Low Damping
Stiff Spring - High Damping
Soft Spring - Low Damping
Baseline Land Rover Rear Damper
-10
-15
-0.8
Figure 15
-0.6
-0.4
-0.2
0
Speed [m/s]
0.2
0.4
0.6
0.8
Damper characteristics of the 4S4 (Els,2006)
18
Literature Overview
2.3.3.2 Other Semi-Active Systems
Choi et al. (2001) carried out field tests on a semi active electro-rheological (ER) suspension system. It
is unclear what type of springs was used but the vehicle was fitted with ER dampers. The results showed
an improvement in the ride quality over bumps and a reduction in roll angle during a sinusoidal test which
shows that the steering stability has increased.
Nell and Steyn (2003) describes the development of a two-state semi-active translational damper
implemented on a 6x6 high mobility off-road vehicle. The semi-active dampers consisted of the vehicle‟s
original dampers fitted with a controllable bypass valve to provide a second state. Experimental tests
included driving over Belgian paving and a rough suspension track for ride comfort and for handling the
severe double lane change manoeuvre was performed. Experimental results showed an improvement in
ride comfort as well as handling for the low and high damping settings respectively. The speed through
the double lane change was improved by 9.4%, the roll velocity decreased by 9.6 % and the yaw velocity
increased by 6%.
Ha et al. (2009) used a 6 degree of freedom model to simulate the dynamics of a 6 wheeled military
vehicle. The vehicle, equipped with gas springs and semi-active MR dampers, is compared to the vehicle
with its passive suspension. It is concluded that the steering stability can be improved and an
improvement in body roll angle is also shown when driving over a random road surface and a bump at 50
km/h. No validation of the simulation results is given.
Dong et al. (2010) concludes that the performance of a MR damper is highly dependent on the algorithm
used to control the damper. And thus good hardware without proper control will not necessarily improve
the vehicles handling.
2.3.4
Active Systems
Geysen et al (2010), states that active hydraulic systems are commonly used due to their high force
density, availability and the maturity of the technology but hydraulic systems can have relatively low
efficiencies (pressure losses and flexible pipes) and a small operational bandwidth. An alternative to a
hydraulic system is an active electromagnetic suspension system which allows for both the elimination of
the road disturbances and active roll and pitch control. If a mechanical spring is used it also does not
require continuous power as with a hydraulic system and can operate over a larger bandwidth. These
systems however require a relatively high current at 12 V and are expensive to implement. (See Figure
11)
De Bruyne et al. (2011) use advanced vehicle state and parameter estimation to obtain the necessary
parameters to implement skyhook control on an active suspension. The states and parameters are
estimated using 4 suspension displacement sensors, 3 vertical accelerometers on the vehicle body and
some longitudinal and lateral accelerometers. It was found that a significant reduction in body roll is
possible during a slalom manoeuvre.
2.3.4.1 Active Anti Roll Bar on the 4S4
Anti-roll bars (ARB) control the roll stiffness independent of the vertical stiffness of the vehicles
suspension. An Active Anti-Roll Bar (AARB) is an anti-roll bar that is controlled by some means to
actively increase or decrease the roll stiffness of the vehicle when necessary. This enables the control of
the of the body roll angle of the vehicle as well as the load transfer during cornering.
19
Literature Overview
Cronje (2008) implemented a hydraulically controlled AARB on a Land Rover Defender test vehicle at
the University of Pretoria. The AARB was controlled using a hydraulic actuator with a MOOG hydraulic
servo valve with a maximum flow rate of 19 l/min. The displacement of the actuator was measured using
a string displacement meter and the displacement data was then used to control the AARB. The servo
valve was controlled with a Zwick Roell K7500 servo controller.
In conjunction with the 4S4 (See par. 2.3.3.1) it was possible to test the effect of the AARB on soft and
hard suspension settings. It was found that a significant improvement in the body roll angle is possible
using an AARB in during a DLC (See Figure 16) and a constant radius test (see Figure 17). The AARB
was designed to keep the body roll angle at a minimum up to 0.4g where after body roll is allowed to
warn the driver that the vehicle is reaching its limits. It was also found that the AARB had no significant
effect on the ride comfort of the vehicle when driving over a rough road as can be seen in Table 2. Cronje
concluded that an AARB can dramatically improve the handling of an off-road vehicle without sacrificing
the ride comfort.
Average Body Roll Angle for a DLC at 70 km/h
Without ARB
With ARB
With AARB
1
0.8
0.6
Roll angle (Deg)
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
5
6
7
8
9
10
11
12
13
Time (s)
Figure 16
Average body roll angles for different ARB settings on the stiff suspension during a
DLC at 70 km/h (Cronje, 2008)
Table 2
Weighted RMS of vertical acceleration for test runs on a Belgian paving (Cronje, 2008)
Suspension setting
Soft
Soft
Soft
ARB setting
Disconnected
Connected (Passive)
Active
Weighted RMS:
1.43 m/s2
1.41 m/s2
1.44 m/s2
20
Literature Overview
Average Body Roll Angle vs. Lateral Acceleration for a Constant Radius Test
3.5
Stiff suspension, ARB disconnected
Stiff suspension, ARB connected
Stiff suspension, AARB
Average body roll angle (Deg)
3
2.5
2
1.5
1
0.5
0
-0.5
-1
0
1
2
3
4
5
6
7
8
Lateral acceleration (m/s 2)
Figure 17
Average body roll angle vs. lateral acceleration during a constant radius test (Cronje, 2008)
2.3.4.2 Other Active Anti Roll Bars
Sampson and Cebon (2003) designed an active roll control system that can generate a roll moment
between the sprung and unsprung mass at each axle. It consists of a stiff U-shaped anti roll bar connected
to the trailing arms of the suspension and to the vehicle frame via a pair of double acting hydraulic
actuators. A lumped mass is added to the truck to simulate a fully laden trailer. It is concluded that an
improvement of between 26% and 46% in roll stability is possible over a passive suspension. Only
simulation results are presented here and no experimental validation is given.
Cimba et al (2006) designed an active torsion bar system that utilises an anti-roll bar actuated by a
hydraulic actuator. The system cancels the body roll up to a lateral acceleration of 5g where the system
reaches saturation and the vehicle body will begin to roll at a rate similar to a passive suspension.
Simulations were done and some of the results were then verified with experimental tests. The results
show that an overall reduction in body roll of up to 73% may be possible.
2.3.5
Stability Control
Jo et al. (2008) investigates the use of a vehicle stability control system to prevent accidents from
occurring. This system uses the vehicle‟s differential brake system to generate a yaw moment to improve
the vehicle stability. Other control systems such as four wheel steer, active front wheel steer, rear wheel
steering and differential traction is also mentioned. The satisfactory performance of the system is verified
with a CarSim model as well as with experimental results. During the experimental test a single lane
change at 90km/h with a SUV is done and a significant improvement in the yaw rate was obtained with
the control system.
21
Literature Overview
2.3.6
Tilting Vehicle
Gohl et al. (2004) implemented Steering Tilt Control (STC) on a narrow tilting vehicle. Tilting the
vehicle moves the centre of gravity to the inside of the corner during cornering. This reduces the vehicles
tendency to roll over due to the moment around the outside wheels being reduced. Without the STC the
vehicle tipped over and with it was stable during cornering, thus it improved the stability of the vehicle
but no quantitative value is given. It is however stated that this principle is more effective on narrow
vehicles. Figure 18 shows an example of a tilting vehicle.
Figure 18
2.4
Tilting Vehicles (Rotpod, 2012)
Effect of height control on suspension characteristics
A passive suspension is designed to give some compromise between ride, handling and rollover for the
range of different vehicle loads. Throughout the load range the suspension should allow enough travel for
the suspension in both directions to avoid hitting the bump stops that have a negative effect on ride
comfort. A linear passive suspension has a constant spring constant k, and the natural frequency
is
given by:
√
(7)
From the equation it becomes clear that if the mass M increases, the natural frequency becomes lower or
in other words the suspension becomes softer (see Figure 19). Not only does this have a negative effect
on the handling but it also decreases the suspension travel and therefore increases the possibility of hitting
the bump stops of the suspension. Therefore this suspension will always operate under some form of
compromise depending on the load of the vehicle. The hydropneumatic suspension shares the favourable
22
Literature Overview
characteristic of that of a pneumatic suspension that the force increases nonlinearly as the displacement
increases.
To address the problem of changes in vehicle mass level control can be used. This can be done with
different approaches. Mechanical level control exists but is rarely used. Level control on pneumatic
suspensions is done by increasing the amount of gas where in hydropneumatic suspensions the amount of
oil is changed. In both cases the pressure of the gas increases but in the case of the pneumatic suspension
the volume of the gas stays constant while the mass increases. In the case of the hydropneumatic
suspension the mass of gas stays the same and the volume decreases. For this reason there is a
progressive behaviour in the spring rate vs. the sprung mass (Figure 20) for hydropneumatic suspensions
(higher mass means higher spring rate). The advantage of doing level control with a hydropneumatic
suspension is that the flow required is much lower than that of a pneumatic suspension due to the ideally
incompressibility of the oil. (Bauer, 2011)
Figure 19
Natural frequency as a function of spring load for for a mechanical, pneumatic and
a hydropneumatic suspension (Bauer, 2011)
Figure 20
Spring rate as a function of spring load for a mechanical, pneumatic and a
hydropneumatic suspension (Bauer, 2011)
23
Literature Overview
2.5
Conclusion
There are various methods to improve the handling and rollover propensity of a vehicle. Four wheel steer
is a feasible alternative but requires a robust algorithm to be able to use it for commercial purposes. It
will also require a rear steering system which will add extra weight and costs. Tilting might also improve
the vehicles rollover propensity to some extend but is less effective on normal vehicles. Stability control
is another feasible alternative but is already widely in use commercially and many new vehicles are sold
standard with stability control.
Cronje (2008) obtained satisfactory results for handling improvement using an AARB and found that it
had a negligible effect on the ride comfort, but this is an expensive solution due to the expensive servo
valve and servo controller. The AARB also has the downside that extra components and weight needs to
be added on to the vehicle and it can only control the roll stiffness and lateral load transfer on the rear
axle, thus it has highly limited uses.
It might be possible to achieve the same by controlling the suspension displacement utilising the existing
height control on the 4S4 suspension. Bauer (2011) concluded that handling can be improved for
different load cases with level control (similar to slow active suspension displacement control) on a
hydropneumatic suspension. Not only will this be less expensive than an AARB, it will also require less
extra weight and equipment, give the possibility to control load transfer in all directions, control the CG
height and allow for tilting.
From the literature it became clear that active suspension has many advantages but that their large power
consumption is a shortcoming. Using slow active suspension displacement control where the suspension
is a single acting hyropneumatic actuator, will reduce the power requirement seeing that power will only
be required to pump oil into the suspension. Oil will be drained form the suspension utilising the pressure
difference between the oil in the suspension and the atmosphere. Slow active suspension control seems
like a feasible method with added advantages over active suspension control and will be investigated in
this study.
The simulation model, theoretical development and simulation results used to determine the feasibility of
slow active suspension control are given in Chapter 3, while the experimental results and a comparison
between the experimental and simulation results are given in Chapter 4. A conclusion is given in Chapter
5 and recommendations for future work in Chapter 6.
24
Simulation Results
3.
Simulation Results
The test vehicle used in the following simulations is a Land Rover Defender 110, fitted with the 4S4
suspension as described in par. 2.3.3.1.
In order to determine the feasibility of slow active roll control, using height adjustment of the 4S4 struts,
several simulations have been done. In the simulations the aim was to minimise the displacement of each
suspension unit by pumping oil into the system from a pressurised accumulator when the suspension is
compressed, and to allow oil to flow out of the suspension to atmospheric pressure when the suspension
unit is extended. Initial simulations were done with simple suspension models and as the project
progressed the models were updated and improved to incorporate additional parameters.
In this chapter the vehicle model, some key requirements for slow active suspension control and the
results of the initial simulations will be discussed. All the simulation result shown in this chapter were
simulated using an ideal gas suspension model and the valve characteristic of the SV10-24 valves as
described in par. 3.3, seeing that none of the final system specifications was available at the time. The
baseline and controlled runs were done with the same model each time to make sure that the improvement
is not due to other model parameters, but due to the suspension control.
3.1
Full Vehicle Model
A full vehicle model of the Land Rover Defender 110 test vehicle used in this study was developed by
Thoresson (2007) in ADAMS/View (MSC.Software, 2011). This model has 15 unconstrained degrees
of freedom. It also has 16 moving parts, 6 spherical joints, 8 revolute joints, 7 Hooke‟s joints and a
motion defined by the steering driver. The model was modified by Uys et al (2007), Cronje (2008) and
Botha (2011) to add the additional changes made to the test vehicle. The ADAMS/View model is linked
with Simulink and Matlab (MathWorks, 2012) using the ADAMS/Control interface. Adams/View
exports the vehicle dynamics variables to Simulink (MathWorks, 2011). These variables are then used
to do calculations and the relevant variables are sent back to ADAMS/View (See Figure 21). An example
of this is the suspension forces that are calculated using a Matlab model and then sent back to ADAMS
via Simulink.
An extensive amount of work has been done to get an accurate model that verifies well with experimental
results. The Hydro-pneumatic 4S4 suspension units fitted to the test vehicle has been modelled as an
adiabatic process using the ideal gas law. It also takes into account non-linear friction, damping and the
bulk modulus of the oil derived from experimental results. The model makes use of the Pacejka 89 tyre
model (Pacejka, 2002). The longitudinal behaviour of the tyre and vehicle is not taken into account to
make the model less computationally expensive. The more important vertical and lateral dynamics is
however taken into account. The body torsion is taken into account by dividing the vehicle body in two
rigid bodies and connecting them with a revolute joint and a torsional spring. The bump and rebound
stops are modelled as non-linear force elements. The suspension bushings are modelled using kinematic
joints with torsional spring characteristics. The CG, and moments of inertia has been determined
experimentally and is also incorporated in the model (Uys et al, 2006b). See Figure 22 to Figure 25 for
the suspension layout in the ADAMS model.
25
Simulation Results
The model has been fully validated against 16 measured channels during experimental testing and very
good correlation was obtained. The vertical verification was done by driving over discrete bumps and the
dynamic verification was done by performing a DLC at 65km/h. Some of the relevant results are shown
in Figure 26.
A validated model as described above is extremely valuable for the initial development of a new project.
This model will be modified to determine the feasibility of slow active suspension control on a SUV.
ADAMS
Simulink
Matlab
Figure 21
Simulation model interaction (Cronje, 2008).
V
e
h
i
c
l
e
D
y
n
a
m
i
c
s
C
o
m
p
o
n
e
n
t
C
h
a
r
a
c
t
e
r
i
s
t
i
c
s
26
Simulation Results
Vehicle Front body
Wheel
Leading Arm
Pan hard rod
Leading Arm
Wheel
Legend
Hooke’s Joint
Spherical Joint
Revolute Joint
Front Axle
Steering
Arm
Steering
Arm
Steering link
Figure 22
Schematic of the front suspension (Thoresson, 2007).
Figure 23
Front suspension in ADAMS model (Thoresson, 2007).
27
Simulation Results
Vehicle Front body
Vehicle Rear body
Legend
Hooke’s Joint
Trailing
Arm
A-Arm
Trailing
Arm
Spherical Joint
Revolute Joint
Rear Axle
Wheel
Wheel
Figure 24
Schematic of the rear suspension (Thoresson, 2007).
Figure 25
Front suspension in ADAMS model (Thoresson, 2007).
28
Simulation Results
Figure 26
3.2
Validation of the ADAMS model’s handling dynamics for a DLC at 65km/h
(Thoresson, 2007)
System Requirements
Before any simulations were done a worst case flow requirement was calculated using the model
described in par. 3.1. To determine the maximum flow needed to keep the suspension level on the stiff
suspension setting the maximum vertical velocity of the suspension was obtained for a DLC at
.
⁄ . The flow of the oil is then
The right front wheel had the highest maximum velocity of
obtained from this velocity by multiplying it with the piston area of the 4S4 which equates to
.
To determine the system requirements, the maximum pressure in the suspension during the double lane
change at
was determined. It was found that the right rear wheel reached the highest pressure
during the manoeuvre namely
.
It was decided to use a system pressure of
so that a pressure difference in excess of than
will exist. To determine the return flow from the suspension to the oil reservoir the minimum pressure in
the suspension during the manoeuvre was determined as
.
This will give a minimum pressure difference of
between the atmosphere and the suspension.
Repeating the same analysis for the soft suspension setting a
was found.
29
Simulation Results
It must be noted that these are the peak flow requirements that are necessary only for a short amount of
time when the suspension velocity is at its highest. The oil flow requirement should decrease once the
suspension is controlled because the control would counter the movement of the suspension. Taking this
into account the values seemed reasonable to continue with the design of the slow active roll control
system.
3.3
Hydraulic Circuit
The hydraulic circuit for a single suspension unit is shown in Figure 27 and the full circuit is shown in
⁄
Figure 31. Oil is supplied by a Stone KP40 gear pump (Stone Hydraulics, 2012) at
, the
pressurised oil is then stored in a
bladder type accumulator which supplies oil to the suspension when
the strut is extended. The SV12-33 directional valves can connect the suspension strut with either the
accumulator to add oil or the reservoir to drain oil. The FPCC is a proportional valve used to control the
in and out flow and is opened relative to the magnitude of the lateral acceleration of the vehicle. The
SV10-24 valves were kept open during the suspension control. It would be preferable to remove these
valves to reduce the flow losses, but these valves are integrated in the suspension units and could
therefore not be removed. P2 on the diagram corresponds to P2 in Figure 13 and is the pressure generated
by the vertical wheel force. P5 depends on the pressure the pump is able to supply (Max 12.5 MPa with
the battery setup in the test vehicle but the pump can supply up to 20 MPa). The pump is switched on and
off using the accumulator pressure as a decision value.
Resevoir
Stone KP40 Pump
4 cc/rev
12 l/min @ 3000 rpm
Accumulator
5.7 l
SV12-33
3-Way
Normally
Closed Valve
FPCC
Proportional
Flow Control
Normally
Closed Valve
SV 10-24
2-Way
Normally
Closed Valve
4S4
Suspension
Unit
10 l
P5 < 20 MPa
P2
Patm = 100 kPa
Figure 27
Hydraulic circuit for a single suspension unit
The SV10-24 valves are manufactured by HydraForce (2012) and are solenoid operated, 2-way normally
closed valves. The performance graphs, as given by the manufacturer, are shown in Figure 28. From the
given graphs, Figure 29 was generated to obtain a flow rate for the specific pressure drop in the
suspension model. This graph was then used to determine the flow through the valve during the initial
simulations. Later during the simulations it became clear that, although these on-off valves will work,
they will only function optimally under certain circumstances (for a specific lateral acceleration) and
therefore it was decided to introduce the proportional valves.
The SV12-33 valves are manufactured by Hydraforce (2011). These valves can handle oil flow of over
and have a reaction time of
. These valves have a leakage of
at
.
The FPCC valves are manufactured by Sun Hydraulics (2011) and can control oil flow between
and
. Laboratory tests have shown that these valves have a response time of 30ms. These valves
30
Simulation Results
at
. The graphs shown in Figure 30 were used in the
have a maximum leakage of
model to simulate the SV 12-33 and FPCC valves (Figure 77 in par. 4.6.1.3 shows the valves in the test
vehicle).
Figure 28
Performance graphs for SV10-24 valve (Hydraforce, 2012)
Flow vs Pressure Drop
-3
Pressure Drop [Pa]
2
x 10
1.5
1
0.5
0
0
0.5
1
1.5
3
Flow [m /s]
Figure 29
2
2.5
7
x 10
Flow vs Pressure Drop for SV10-24 valve
31
Simulation Results
SV 12-33 Valve
Figure 30
FPCC Valve
Flow vs Pressure graphs for the SV12-33 (Hydraforce, 2011) directional valve (left) and the
FPCC (Sun Hydraulics, 2011) proportional valve (right)
32
Simulation Results
Figure 31
Flow diagram of the hydraulic setup in the test vehicle
33
Simulation Results
3.4
Suspension Model
The suspension is modelled using MATLAB (MathWorks, 2012)/Simulink (MathWorks, 2011) and
provides the ADAMS (MSC.Software, 2011) vehicle model with a suspension force. The total
suspension force consists of four forces namely: damper force, friction force, spring force and the
bumpstop force (see Figure 32). The damper force is defined using piecewise quadratic approximations
giving damping force as a function of velocity. Friction is determined using a lookup table giving friction
as a function of velocity. The force generated by the gas spring is calculated using either the ideal gas
equation or the Bennedict Webb Rubin (BWR) real gas equation. The gas model receives a displacement
value from the ADAMS vehicle model and then calculates the spring force. The effect of the bump stops
are modelled using first order polynomials giving the bumpstop force as a function of displacement.
Suspension Force
ADAMS
Suspension Force
Velocity and
Displacement
Simulink
Suspension Force
Velocity
Friction
Bumpstop Force
Spring Force
Displacement
Velocity
Friction Force
Figure 32
Displacement
Matlab
M-file
Damper force
Damper Force
Velocity and
Displacement
Bumpstop
Spring force
Suspension model interaction
34
Simulation Results
3.4.1 Ideal Gas Spring Model
For the initial feasibility study the ideal gas suspension model was modified so that oil can be pumped
into or drained from the suspension units. The flow into and out of the suspension is proportional to the
pressure difference between the accumulator and the suspension unit‟s cylinder. A ΔP is determined
between the accumulator and the suspension for the inflow and between the suspension and atmospheric
pressure for the outflow. A lookup table of the valve‟s characteristics is used to determine the flow
(Figure 29).
The added or drained oil is simulated using the ideal gas law which states:
(8)
Which can be rewritten as follows
(9)
From equation 9 one can see that reducing the volume will increase the pressure and will result in
increased suspension force.
It is assumed that the oil is incompressible and when oil is pumped into the suspension the volume for the
gas in the suspension is reduced by the amount of oil added to the suspension. Similarly when oil is
allowed to flow out the volume for the gas is increased by the amount of the oil that has flown out. For
each time increment a new flow rate is determined using the internal pressure (P2 in Figure 31) and the
external pressure which is 20 Mpa for the inflow and 100 kPa for the outflow. The flow rate is
determined using the lookup table of Figure 29 or Figure 30 and is then multiplied by the time increment
to obtain the volume of oil that was pumped in or out for that time increment. In Figure 33 one can see
that if d decreases, F will increase. When F increases the mass will move up to increase d until F=Mg.
Using this principle the suspension model obtains parameter values from the ADAMS model via
Simulink and then calculates a force which is then sent back via Simulink to the ADAMS model (see
Figure 32).
35
Simulation Results
(10)
Mg
(11)
F
d
Gas
Replacing 10 & 11 into 8 we get:
A
Vg
(12)
Oil
Wheel
Figure 33
Main principle of the suspension model
3.4.2 BWR Spring Model
During the first experimental testing concerns about the accuracy of the ideal gas law in this application
arose. Subsequently the Benedict Webb Rubin (BWR) real gas equation was introduced. This model
works on the same principle as the ideal gas model but here the gas in the suspension as well as the gas in
the accumulator is modelled using the BWR equation. Thus the accumulator pressure is not a fixed value
as in the case of the ideal gas model but takes into account the flow of the pump and the flow out of the
accumulator to get a more accurate pressure difference to model the flow. This model is described in par.
4.1 and Appendices A and B.
3.5
Control Strategies
To determine a suitable control strategy for roll angle control, different ideas were implemented and
simulated for a DLC manoeuvre at 60 km/h. All these simulations were done using the Ideal gas
suspension model and the 4S4 in handling mode. One of the main challenges is the non-linearity caused
by the fact that the 4S4 is only a single acting cylinder. This means that an increase in ride height can be
well controlled, but a decrease is heavily reliant on the pressure in the suspension strut.
36
Simulation Results
3.5.1
Control Strategy 1
In control strategy 1, oil is drained from the suspension units that experiences positive displacement
(extended), and when a unit experiences a negative displacement (compressed) oil is pumped in. The oil
is added and drained with valve opening directly proportional to the magnitude of the suspension
displacement up to 50mm positive or negative displacement and from there on it is added or drained at
maximum rate. The results are shown in Figure 34 and Figure 35. The suspension control was only
activated after 0.8 seconds, after the vehicle has reached 60km/h.
The working principle of the algorithm is shown below:
| |
| |
( )
2
Controlled (Strategy 1)
Baseline (4S 4 Handling)
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
Figure 34
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Body roll angle for a DLC manoeuvre at 60 km/h
37
1.9
2
Simulation Results
2
2
1.9
Controlled (Strategy 1)
Baseline (4S 4 Handling)
1.9
Controlled (Strategy 1)
Baseline (4S 4 Handling)
1.8
Oil added [m3] x 100
1.8
Oil added [m3] x 100
1.7
1.7
1.6
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1
1
1.1
1.2
1.3
1.4
2
1.5
1.6
1.7
1.8
1
1.9 1
2 1.1
1.2
1.3
1.4
1.6
1.7
1.8
2
1.9
Controlled (Strategy 1)
Baseline (4S 4 Handling)
1.9
1.8
Controlled (Strategy 1)
Baseline (4S 4 Handling)
Oil added [m3] x 100
1.8
Oil added [m3] x 100
1.7
1.7
1.6
1.6
Figure 35
1.5
1.4
Suspension responses for a DLC manoeuvre
at 60 km/h
1.5
1.4
1.3
1.3
1.2
1.1
1
1.5
1
Looking at the results it becomes apparent that a sudden shift of the vehicles weight, to the side of the
1.2
suspension where oil has previously been drained, results
in large body roll angles. The weight shifts too
1.1
fast for the system to counter the compression of the
units. A good example can be seen just before 6
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9 1
2 1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
seconds on the right rear suspension graph and on the roll angle graph (Figure 34) where the roll angle of
the vehicle makes a very sharp and high peak.
38
2
1.9
Simulation Results
3.5.2
Control Strategy 2
For this strategy the oil is only drained out of the suspension unit until the original amount of oil (when
the vehicle is static) in the unit is reached. This simulation was run for 12 seconds to see if the
suspension units settle down at a displacement of 0 after the double lane change. The results for the 4S4
in handling mode are shown in Figure 36 and Figure 37.
The working principle of the algorithm is shown below:
Suspension Extended
(Outflow Control)
| |
( )
Suspension Compressed
(Inflow Control)
| |
( )
2
Controlled (Strategy 2)
Baseline (4S 4 Handling)
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
Figure 36
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
Body roll angle for a DLC manoeuvre at 60 km/h
39
Simulation Results
2
2
1.9
1.9
1.8
Controlled (Strategy 2)
Baseline (4S 4 Handling)
1.8
Controlled (Strategy 2)
Baseline (4S 4 Handling)
1.7
Oil added [m3] x 100
1.7
Oil added [m3] x 100
1.6
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1
2
2
1.9
1.9
1
2
1.1
1.2
1.3
1.4
1.8
Controlled (Strategy 2)
Baseline (4S 4 Handling)
1.8
Controlled (Strategy 2)
Baseline (4S 4 Handling)
1.7
Oil added [m3] x 100
1.7
Oil added [m3] x 100
1.6
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1
Figure 37
1
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1
1
2
1.1
1.2
1.3
1.4
Suspension responses for a DLC manoeuvre at 60 km/h
The results for the suspension show a significant improvement. There is also an improvement in the body
roll of the vehicle. Although these results show an improvement the on-going oscillation after 8 seconds
in the body roll angle (Figure 36) is of some concern. Thus control strategy 2 does not give satisfactory
results even though there is a significant improvement.
It is important to take note of the difference in the results between control strategy 1 and control strategy
2. To drain too much oil out of the system seems to have more losses than gains. This principle is shown
in Figure 38 and Figure 39 where a Proportional–Integral–Derivative (PID) controller was used to control
the flow. In the Figure 38 the oil was drained with no limit, where in the Figure 39 the oil was only
drained until the amount of oil in the suspension unit was equal to that of the static position.
40
1.5
1.6
1.7
1.5
1.6
1.7
Simulation Results
2
Controlled (PID)
Baseline (4S 4 Handling)
1.9
Small gain
1.8
Oil added [m3] x 100
1.7
1.6
1.5
1.4
1.3
1.2
Large loss
1.1
1
Figure 38
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.8
1.9
Suspension responses for a DLC manoeuvre at 60 km/h for unconstrained outflow
2
No loss
1.9
Controlled (PID)
Baseline (4S 4 Handling)
1.8
Oil added [m3] x 100
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
Figure 39
Small gain
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Suspension responses for a DLC manoeuvre at 60 km/h for constrained outflow
41
Simulation Results
3.5.3
PID Controller
The PID controller made use of the following method to control the valve opening for oil inflow also
using the volume limit on the outflow:
∫
|
|
Suspension Extended
(Outflow Control)
|
|
Suspension Compressed
(Inflow Control)
Where is the displacement of the suspension unit with compression negative and extension positive.
The aim is to keep the suspension displacement zero as this will result in zero body roll and pitch.
2
1.9
Controlled (PID)
Baseline (4S 4 Handling)
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
Figure 40
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
Body roll angle for a DLC manoeuvre at 60 km/h using a PID controlled proportional valve
To obtain the optimal results it was attempted to optimise the gains of the PID controller with an
optimisation algorithm. The algorithm did however not converge satisfactorily but did show that the
results improve with larger gains for
and . The optimisation was not investigated further because
42
Simulation Results
this was not the final design, but the improvement with larger gains showed that the valves spend very
little time being opened proportionally and are almost always fully open or fully closed. This means that
on-off valves, which are generally cheaper that proportional valves, can be used.
The results for
,
and
is shown in Figure 40 and Figure 41. The PID
controller gave satisfying results in terms of the body roll angle, but the displacement does not converge
to zero due to the large gain on the derivative. Due to the PID decision value being low relative to the
gains, the controller is insensitive to changes in the gains.
2
2
1.9
Controlled (PID)
Baseline (4S 4 Handling)
1.9
Controlled (PID)
Baseline (4S 4 Handling)
1.8
Oil added [m3] x 100
1.8
Oil added [m3] x 100
1.7
1.7
1.6
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
2
1
1.9
1
2
1.1
1.2
1.3
1.4
1.5
1.6
1.8
1.9
2
1.9
Controlled (PID)
Baseline (4S 4 Handling)
1.9
Controlled (PID)
Baseline (4S 4 Handling)
1.8
Oil added [m3] x 100
1.8
Oil added [m3] x 100
1.7
1.7
1.6
1.6
Figure1.541
Suspension responses for a DLC manoeuvre at
1.560 km/h for PID controlled proportional
valves
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1
1.7
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1
1.9
1
1.1
2
1.2
1.3
1.4
1.5
1.6
1.7
43
1.8
1.9
Simulation Results
3.5.4 On-off valve control
The on-off PID controller makes use of the following method to control the on-off valve for oil flow:
∫
(
)
(
)
Suspension Extended
(Outflow Control)
Suspension Compressed
(Inflow Control)
|
|
Suspension Neutral
(No Control)
The same gains as with the proportional valve is used namely,
,
and
.
It was however found that the improvement is small once the gains are larger than the decision value (0.5
in this case). Compression is taken as negative and extension as positive.
3.5.4.1 60 Millisecond sampling increments
The characteristics of the SV10-24 valves manufactured by Hydraforce (2011) are used in the model for
these simulations. The valve response is not modelled but to compensate for the response time of the
valves a sampling time of 60 milliseconds is used which is double the response time indicated by the
manufacturer. This is done by obtaining an average value of the PID for the previous 60 milliseconds,
and then this value is used as the parameter to determine the switching signal for the valves.
Figure 42 and Figure 43 shows that there is a significant improvement in the roll angle as well as the
suspension displacements. This shows that at higher speeds and hard cornering proportional control is
not necessary. The oscillation in the roll angle after 7 seconds is of some concern but has been improved
by using one proportional valve to reduce the total flow to each valve as can be seen in Figure 44. This
proportional valve was modelled to reduce the flow to 10% of the original after 7 seconds but a strategy
to control the proportional valve should be investigated.
Figure 44 shows that the valves rarely need to switch within 60 milliseconds from the initial switch. This
means that the response time of the valve should be sufficient for the control. The total volume and flow
rate shown in Figure 45 and Figure 46 is also acceptable.
44
Simulation Results
2
Controlled (PID & On-Off Valve)
Baseline (4S 4 Handling)
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
Figure 42
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
Body roll angle for a DLC manoeuvre at 60 km/h using a PID controlled on-off valve
2
2
1.8
Controlled (PID & On-Off Valve)
Baseline (4S 4 Handling)
1.6
3
Oil added [m ] x 100
1.4
1
1
1.5
1.6
Controlled (PID & On-Off Valve)
Baseline (4S 4 Handling)
1.4
Oil added [m3] x 100
1
2
1
1.5
2
2
2
1.8
Controlled (PID & On-Off Valve)
Baseline (4S 4 Handling)
1.6
3
Oil added [m ] x 100
1.4
1.8
1.6
Controlled (PID & On-Off Valve)
Baseline (4S 4 Handling)
1.4
Oil added [m3] x 100
1.2
1.2
1
1.8
1.2
1.2
Figure 43
1
1
1.5
2
1
1
1.5
2
Suspension responses for a DLC manoeuvre at 60 km/h for on-off valves
45
Simulation Results
Figure 44
Flow rates for each suspension unit
Figure 45
Total volume of oil pumped into the suspension
46
Simulation Results
Figure 46
Total flow rate required
3.5.4.2 90 Millisecond sampling increments
To determine the effect if the valves responded slower a sample time of 90 milliseconds was taken which
is 3 times the response time of the valves. In Figure 47 the second positive peak at 6 s is smaller where
the negative peak has increased. This shows that the specific time at which the control signal is sampled
will have an effect on the performance of the system. The results are still satisfactorily and the
improvement is still significant. There is however a larger on going oscillation in the body roll angle due
to the slower system response, as can be seen after 7 seconds. The response of the suspension (Figure 48)
is not as good as with the lower sampling time but still results in a significant improvement over the
baseline suspension. The flow requirements shown in Figure 49 to Figure 51 stay similar to that of the 60
ms sampling time.
47
Simulation Results
2
Controlled (PID & On-Off Valve)
Baseline (4S 4 Handling)
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
Figure 47
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
Body roll angle for a DLC manoeuvre at 60 km/h using a PID controlled on-off valve
2
2
1.8
1.6
Controlled (PID & On-Off Valve)
Baseline (4S 4 Handling)
1.4
Oil added [m3] x 100
1.2
1
1.8
1.6
Controlled (PID & On-Off Valve)
Baseline (4S 4 Handling)
1.4
Oil added [m3] x 100
1.2
1
1.5
1
2
2
2
1.8
1.8
1.6
Controlled (PID & On-Off Valve)
Baseline (4S 4 Handling)
1.4
Oil added [m3] x 100
1
1
1.5
2
1.6
Controlled (PID & On-Off Valve)
Baseline (4S 4 Handling)
1.4
Oil added [m3] x 100
1.2
1.2
Figure 48
1
1
1.5
2
1
1
1.5
2
Suspension responses for a DLC manoeuvre at 60 km/h for on-off valves
48
Simulation Results
Figure 49
Flow rates for each suspension unit
Figure 50
Total volume of oil pumped into the suspension
49
Simulation Results
Figure 51
3.6
Total flow rate required
Conclusion
From the simulation results it seems feasible to continue to implement slow active roll control on a
vehicle to improve the handling and rollover propensity of the vehicle. The flow requirements seem
within reach and this system will allow for many other advantages over that of an AARB. Although the
model is not yet given the correct input parameters due to most of it still being unknown, the
improvement looks to be significant and therefore it was decided to continue with the hardware
implementation of slow active suspension control on the test vehicle.
The experimental results and a comparison between the experimental and simulation results will be given
in Chapter 4. A conclusion is given in Chapter 5 and recommendations for future work in Chapter 6.
50
Experimental Work and Results
4.
Experimental Work and Results
In this chapter the system, proposed in chapter 3, is implemented and experimental tests are performed.
The initial verification tests, voltage controlled current source developed and the valve characterisation is
discussed in par. 4.1 to 4.5 where the vehicle is stationary in the lab. The problems experienced and the
performance of the system during track tests is discussed (Par. 4.6) and the model is updated with the
known parameters and then compared to the experimental results (Par. 4.7).
4.1
Initial Verification Tests
In order to obtain an indication to the accuracy of the model two verification tests were done where the
displacement was measured to verify with the simulation results. The first test consisted of opening the
⁄
valves of the front suspension units for 0.5s while the pump supplies oil at
to raise the front,
as is shown in Figure 52. For the second test the valves for all four suspension units were opened for 1.5
⁄
s to raise while the pump supplies oil at
, the valves were then closed for 1 second and opened
to lower the suspension for 2 s (see Figure 56). Both these tests were done while the vehicle was
stationary on a solid surface without any external disturbances.
During the initial simulations poor correlation with the experimental results were obtained, which initially
looked like the gas is modelled too compressible, but the problem was narrowed down to be the friction in
the model as well as the friction taken into account in the damping. As there is always some form of
friction present in any system the force measurements done to determine the damping of the suspension
also had a component due to friction. In order to improve the correlation the friction was removed from
the model. The results are shown in Figure 52 and it is clear that the friction caused a greater deviation
from the measured experimental results.
Front Left Displacement
Front Right Displacement
35
30
30
25
20
Displacement [mm]
Displacement [mm]
25
20
15
10
10
5
5
Measured
Simulated with Friction
Simulated without Friction
0
-5
15
6
Figure 52
6.5
7
7.5
8
Time [s]
8.5
9
9.5
10
Measured
Simulated with Friction
Simulated without Friction
0
-5
6
6.5
7
7.5
8
Time [s]
8.5
9
9.5
10
Comparison between the measured results and the simulation results with and without
friction
Initial simulations were performed using the original ideal gas law suspension model, developed by
Thoresson (2007). These results showed that a significant improvement in body roll is achievable but
some concerns regarding the accuracy of the ideal gas law in this application arose. The concerns were
51
Experimental Work and Results
that calculation errors could be introduced due to the fact that the ideal gas law does not take the
intermolecular forces at small intermolecular distances into account. It therefore over estimates the
compressibility at either high pressures or low temperatures, of which the former is present when working
with hydropneumatic suspensions (Sontag and Van Wylen, 1991). In the initial verification test the
ideal gas model correlated well with the measured results, but this is done at low pressures while the
vehicle is standing still (see Figure 53). Subsequently the BWR real gas equation was introduced (Otis
and Pourmovahed, 1985) (See Eq. 13).
(
)
(13)
A new specific volume and temperature is calculated for each time step to enable the calculation of the
pressure by means of the BWR equation (See Appendix A for the temperature equation and Appendix B
for the BWR constants). During the simulation of the DLC the flow requirements for the ideal gas model
was found to be much higher than that of the BWR model. This is likely due to the above mentioned
problems and the BWR model is expected to deliver more accurate results.
The BWR model correlates well with the measured values as can be seen in Figure 54. The pump
⁄
delivers
depending on the voltage of the battery and the flow losses in the system. It was
⁄
found that both models correlate with the measured results at a flow of
. Both models do
however deviate quite substantially from the measurements if the displacement becomes negative. As
described in par. 3.4 the damping is modelled as a function of the suspension velocity. Thus the model
cannot distinguish between movement due to height control and movement due to road inputs. The
damper effect can be modelled more accurately if the flow through the dampers is calculated using fluid
mechanics, this is however computationally very expensive and it was therefore not implemented.
In the model the suspension is lowered by increasing the volume of the gas, this lowers the pressure
which then gives a lower suspension force. In reaction to this the Adams model lowers the vehicle body
at the suspension unit to obtain an equilibrium of forces. But due to the damping not being able to
distinguish the nature of the movement it generates a force to resist the movement. The damping thus
causes the suspension to lower more slowly than the rate at which the oil is removed (gas volume is
increased). This causes the gas to expand more than in reality which then predicts a smaller suspension
force than in reality. This happens for each time step and the net effect after a few time steps is that the
suspension lowers more and faster than in reality. The effect of the damping on the specific volume can
be seen in Figure 55 where the rapid increase in the specific volume of the gas can be seen once the
displacement becomes negative (Figure 56). In Figure 56 it can be seen that the simulation results
overshoot the measured results when the suspension is lowered.
There is some discrepancy between the measured and simulated results while the displacement is positive
as well, this is also due to the damping. The oil is pumped into the suspension at the main strut (P2) in
Figure 13. In the simulation it is modelled as the equivalent to the oil being pumped in at the accumulator
(P1). This has the effect that the damping resists the displacement, where in reality it can allow for faster
raising. The model is modelled in this way; because the ADAMS (MSC.Software, 2011) model requires
a force input from the suspension m-file (Mathworks, 2012) as is shown in Figure 32 and Figure 33.
Figure 57 shows the results where the damping in the system has been set to half its original value. An
52
Experimental Work and Results
improvement is visible at the end of the raising (8s) but during the raising process it becomes clear that
the gas expands too much because there is less damping resisting it. Reducing the damping will give
inaccurate results during a dynamic manoeuvre where the damping in the suspension plays a major role.
Front Right Displacement
45
40
40
35
35
Displacement [mm]
Displacement [mm]
Front Left Displacement
45
30
25
20
15
10
Measured
Ideal Gas
5
30
25
20
15
10
0
0
-5
-5
-10
2
2.5
3
3.5
4
4.5
5
-10
5.5
Measured
Ideal Gas
5
2
2.5
3
3.5
Time [s]
Figure 53
4.5
5
5.5
Comparison between simulation results of the ideal gas model with flow 12.8l/m and
experimental results
Front Left Displacement
Front Right Displacement
35
35
30
30
25
25
Displacement [mm]
Displacement [mm]
4
Time [s]
20
15
10
5
20
15
10
5
Measured
Simulated
0
6
6.5
7
7.5
8
8.5
9
9.5
Measured
Simulated
0
10
6
6.5
7
7.5
Time [s]
Figure 54
8
8.5
9
9.5
10
Time [s]
Simulation results of BWR equation model with flow 12.8l/m
Specific Volume
0.08
Front Left
Front Right
Rear Left
Rear Right
0.07
v [m3/kg]
0.06
0.05
0.04
0.03
0.02
0
Figure 55
1
2
3
4
5
Time [s]
6
7
8
9
10
Specific volume during the simulation
53
Experimental Work and Results
Front Left Displacement
40
40
Measured
Ideal Gas
BWR
0
-20
-40
-60
-80
Measured
Ideal Gas
BWR
20
Displacement [mm]
20
Displacement [mm]
Front Right Displacement
0
-20
-40
-60
2
3
4
5
6
Time [s]
7
8
9
-80
10
2
3
Rear Left Displacement
20
Displacement [mm]
Displacement [mm]
-60
-100
Figure 56
6
Time [s]
7
8
9
Measured
Ideal Gas
BWR
-120
10
2
3
4
5
6
Time [s]
7
8
9
10
Measured and simulated results for Ideal gas and BWR model
Front Left Displacement
Front Left Displacement
35
35
30
30
25
25
Displacement [mm]
Displacement [mm]
10
-60
-100
5
9
-40
-80
4
8
-20
-80
3
7
0
-40
2
6
Time [s]
Rear Right Displacement
-20
-120
5
20
Measured
Ideal Gas
BWR
0
4
20
15
10
5
20
15
10
5
Measured
Simulated
0
6
6.5
Figure 57
7
7.5
8
Time [s]
8.5
9
9.5
10
Measured
Simulated
0
6
6.5
7
7.5
8
Time [s]
8.5
9
9.5
10
Simulation results of BWR equation model with flow 12.8l/m (no friction & 50% damping)
54
Experimental Work and Results
The lessons learned from the initial verification tests are now incorporated in the model and the BWR
model is used to simulate a DLC manoeuvre at 60 km/h. The suspension displacement is controlled by
adding or removing oil from each suspension unit. Oil is supplied from an accumulator (which is also
modelled using the BWR equation) at a maximum pressure of 12.5 MPa. The maximum accumulator
pressure was initially chosen as 20 MPa but initial tests on the vehicle have shown that the battery driven
pump delivers a maximum pressure of 12.5 MPa. A PID controller as shown below is used to choose
between pumping oil in, draining it or to close the valve. The gains used were the same as used in par
3.5.4. After looking at the data of the previous simulations it was found that the lateral acceleration
becomes higher than 0.1g when entering a DLC. Thus in order to control the oil flow, the model selects
between high or low flow using the lateral acceleration as input. Initial simulations showed that it has a
negative effect on the handling to pump out too much oil from a suspension unit in order to keep the
displacement zero. Therefore oil is only pumped out until a little less than the original amount of oil is
left in the suspension. Simulations with this model again showed that a substantial improvement is
possible on the body roll angle of the vehicle as can be seen in Figure 58. The working principle of the
control algorithm used is shown below:
∫
(
|
)
(
)
|
55
Experimental Work and Results
Roll Angle
4
Baseline (Simulated)
Controlled (Simulated)
3
Roll Angle [deg]
2
1
0
-1
-2
-3
-4
0
1
2
3
4
5
6
7
8
9
Time [s]
Figure 58
4.2
Roll angles for a baseline and controlled DLC at 60km/h
Voltage Controlled Current Source
In order to control the FPCC (Sun hydraulics, 2011) proportional valve (see Par. 3.3) using the PC/104
(Diamond Systems, 2012) available on the Land Rover test vehicle a voltage controlled current source is
needed. An amplifier that serves this purpose is available from the valve manufacturer but it is expensive
and the possibility of another solution was researched.
Valve Coil
6.4 - 9.4Ω
+12V
Vref
R6
68kΩ
R5
15kΩ
LM324N
C1
0.1 µF
+
STP36NF06
-
R2
1kΩ
R1
1kΩ
Figure 59
C2
10 nF
R4
1.5Ω
R3
1.5Ω
Voltage controlled current source with a voltage divider in the reference voltage signal
56
Experimental Work and Results
A voltage controlled current source was developed and tested in conjunction with another student who
intends to use this current source to control a magneto-rheological (MR) damper. The PC/104 used in the
test vehicle can deliver voltage between +5 and -5 volt on its analogue output channels, therefore it was
decided that the current source should deliver a current of 0 - 1.15A for a voltage input of 0 – 5V. The
coil of the valve can have a resistance as high as 9.4Ω when it heats up to 50ºC. Therefore a restriction
on the maximum total resistance for R3+R4 of 1Ω was determined (see Figure 59), to enable sufficient
current from the 12V power supply (
).
In order to get the required input to output ratio the reference voltage to the operational amplifier is
lowered by adding a voltage divider (R5 & R6) in the reference signal as can be seen in Figure 59. The
resistors
and
has been given a high resistances so that the required current is low. The operational
amplifier measures the voltage difference over R3+R4 and if the current is too low it closes the gate of the
power MOSFET and if it is too high it opens the gate, thus controlling the current.
Due to the relatively high current passing through R3+R4 axial film resistors will have to be used in
parallel due to their low power rating. A coil resistor, which generally has higher power ratings, can also
be used. Using a single coil resistor will have the advantage that the manufacturing will be easier but the
inductance of the coil might increase the response time. Comparative tests were done with axial film and
coil resistors, and the results showed that there is no quantifiable difference between the response times
and a coil resistor can be used (see Figure 60). The resistors used at R3 and R4 in the final design are
1.5Ω, 2W axial film resistors and were used due to availability at the time (see Figure 59).
Voltage Controlled Current Source
Signal [mV or mA]
2000
1500
1000
500
Input Signal Axial [mV]
Output Signal Axial [mA]
Input Signal Coil [mV]
Output Signal Coil [mA]
0
-500
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
Time [s]
Figure 60
Comparative test between a 1Ω-10W coil resistor at R3 and two 1.5Ω-2W axial resistors in
parallel.
The response for different input signals, and the valve coil as the load, is shown in Figure 62. The
response show that there is a linear relationship between the input and output where 0V input will give a
0A output and a 5V input will give a 1.2A output. Although the sampling frequency (1000Hz) was too
low in Figure 63 one can still see that the response time is under 4ms for maximum input command which
is sufficient for the intended purpose.
57
Experimental Work and Results
Test setup with MR damper as load
Figure 61
Voltage Controlled Current Source With Voltage Divider
1400
Output Signal [mA]
1200
1000
800
600
400
200
0
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Input Signal [mV]
Figure 62
Output signal for an input signal of 2-5V in 0.5V increments
58
Experimental Work and Results
Voltage Controlled Current Source With Voltage Divider
Input Signal
Output Signal
6000
X: 9.878
Y: 5355
Signal [mV or mA]
5000
4000
3000
2000
X: 9.879
Y: 1244
1000
X: 9.876
Y: -49.96
0
X: 9.876
Y: -169.4
9.872
9.873
9.874
9.875
9.876
9.877
9.878
9.879
9.88
9.881
9.882
Time [s]
Figure 63
4.3
Input and output signal for an input signal of 5V
Proportional Valve Characterisation
To determine the flow obtained at different valve opening commands, the valve is given a determined
percentage of its command input for 0.5 seconds to raise the suspension and then it is given the same
command input for 1 second to lower the suspension. Using this data, the average flow can be
determined as it is indicated in the legends of Figure 64 to Figure 67. From these results it is seen that the
proportional valve responds faster than the directional valve and thus there is a slight increase in the
height just before the suspension is lowered. This increase in height is due to the proportional valve
opening before the directional valve was able to switch from inflow to outflow. This was rectified by
adding a delay on the proportional valve so that it starts to open 70 ms after the directional valve so that
both open fully at the same time. From the data one can also see that an input of less than 50% gives
negligible small flow and therefore it was not included in the characterisation. Flow above 80% is more
than 200% higher than the expected required flow and it will also not be included in this characterisation
measurements.
Using the data in Figure 64 to Figure 67 for the inflow and the pressure data recorded of the suspensions
and the accumulator, a pressure vs. flow graph is generated (see Figure 68). The data obtained here is not
sufficient to get an accurate indication of the flow curve of the valve, the valve needs to be opened longer
over a broader range of ΔP. This however is not possible with the valves installed in the vehicle and the
characterisation will need to be done on a hydraulic test bench. The average flow does give a relatively
good indication as to what flow to expect at different valve openings and it was decided that this will be
sufficient.
59
Experimental Work and Results
Height Adjustment for Right Rear with Valve 50 % open
15
Displacement
Displacement
Displacement
Displacement
Displacement [mm]
10
left front
right front
left rear
right rear Flow Up = 2.3434 [l/m] Flow Down = 2.125 [l/m]
5
0
-5
-10
0
2
4
6
8
10
12
14
Time [s]
Figure 64
Valve test with a 50% command input.
Height Adjustment for Right Rear with Valve 60 % open
40
Displacement
Displacement
Displacement
Displacement
35
Displacement [mm]
30
left front
right front
left rear
right rear Flow Up = 7.7045 [l/m] Flow Down = 4.956 [l/m]
25
20
15
10
5
0
-5
-10
0
2
4
6
8
10
12
14
Time [s]
Figure 65
Valve test with a 60% command input.
Height Adjustment for Right Rear with Valve 70 % open
70
Displacement
Displacement
Displacement
Displacement
60
Displacement [mm]
50
left front
right front
left rear
right rear Flow Up = 13.9354 [l/m] Flow Down = 8.5192 [l/m]
40
30
20
10
0
-10
-20
0
2
4
6
8
10
12
14
Time [s]
Figure 66
Valve test with a 70% command input.
60
Experimental Work and Results
Height Adjustment for Right Rear with Valve 80 % open
120
Displacement
Displacement
Displacement
Displacement
Displacement [mm]
100
left front
right front
left rear
right rear Flow Up = 21.86 [l/m] Flow Down = 11.6847 [l/m]
80
60
40
20
0
-20
0
2
4
6
8
10
12
14
Time [s]
Figure 67
Valve test with a 80% command input.
Flow vs  P
24
60%
70%
80%
22
20
Flow [l/m]
18
16
14
12
10
8
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
 P [MPa]
Figure 68
4.4
Flow vs Pressure curve obtained for different valve openings.
PID Control Algorithm
Initially when the control algorithm was first implemented (Par. 3.5) the PID controller was averaged
over 5 terms. However, the derivative term gave erroneous values due to the noise present in the
displacement signals, a typical signal is shown in Figure 69 where the noise is visible in the detail section.
In Figure 70 the drift on the PID signals for a static test can be seen in the left figure. Therefore the
displacement signals were filtered by taking the average over 5 terms. The derivative was then calculated
from the filtered displacement and this was found to improve the results substantially as can be seen in the
right figure of Figure 70.
61
Experimental Work and Results
Suspension Displacement
Detail Section
-30
-41
-41.1
-41.2
Displacement [mm]
Displacement [mm]
-40
-50
-60
Displacement
Displacement
Displacement
Displacement
-70
left front
right front
left rear
right rear
-41.3
-41.4
-41.5
-41.6
-41.7
-41.8
-80
-41.9
-90
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
-42
5
2
2.1
2.2
2.3
2.4
Figure 69
-0.005
-8
-0.01
-8.5
-0.015
2.7
2.8
2.9
3
-9.5
-0.025
-10
0
2
4
6
8
10
12
14
16
18
20
x 10
PID Signal for Averaged Displacement
-9
-0.02
Time [s]
4.5
-4
-7.5
PID
PID
Averaged PID Signal
Figure 70
2.6
Noise on the displacement Signals
0
-0.03
2.5
Time [s]
Time [s]
-10.5
0
1
2
3
4
5
6
7
8
Time [s]
PID signals for the averaged PID (left) and for the averaged displacement (right)
Volume Estimation
The amount of oil in the suspension units are estimated to prevent the control algorithm from pumping
out too much oil from the suspension, as this can have a negative effect on the suspension response. In
order to estimate the amount of oil in each suspension unit the equation for the bulk modulus of fluid is
used in combination with the ideal gas equation. The volume of the nitrogen is estimated using the ideal
gas law while the compression of the oil is calculated using the bulk modulus equation (See Appendix C).
In order to get a better estimation the input signals to the volume equation is filtered with a low pass finite
impulse response filter in real time. The filter has a pass frequency of 8 Hz and a stop frequency of 25
Hz. The filter is of the order 14 and has a step response of about 90 ms. This results in a delay of about
90 ms on the estimated volume signal. In order to get a minimum volume value where the algorithm
should stop the outflow the volume of oil in the suspension is calculated while the vehicle is standing still
and the roll control is active, the vehicle is left until the suspension settles and then the average of the
predicted volume is obtained. Twice the standard deviation of the signal is taken and subtracted from the
average to get a value that will include 97.8% of the signal values at the desired amount of oil. In the
control algorithm of the suspension no more oil is pumped out of the suspension once the predicted
62
Experimental Work and Results
amount of oil in the suspension reaches this value. In Figure 71 it can be seen that the suspension has
settled by the time it reaches 8s therefore the value is calculated from 8s to the end of the signal and is
shown in Figure 72. To test if the estimation prevents the suspension from pumping out too much oil the
vehicle was lifted at the front with a hydraulic jack and then dropped. The same was then done with the
rear as is shown in Figure 73. The results look relatively good but there is some error in the prediction of
the volume, possibly due to the friction in the suspension strut. The effect can be seen in Figure 74 at the
right front and left rear wheels where the volume settles to a different value even though the displacement
is at zero in both cases as can be seen in Figure 73. In a controlled environment like this it is expected
that the suspension will settle close to the same value each time but due to the friction this is not the case
in reality. It is however expected that during actual driving of the vehicle, the effect of friction will be
less due to continuous suspension movement and the dynamic friction is significantly lower than the static
friction. In Figure 74 one can see that the Left front and Right Rear had a large and definitive reaction to
the suspension being extended, it was later found that these two suspension units had very little gas in
their accumulators. Thus pressures nearing zero were measured and this gave the large change in the
estimated volume.
Suspension Displacements
5
Displacement
Displacement
Displacement
Displacement
4
left front
right front
left rear
right rear
Displacement [mm]
3
2
1
0
-1
-2
-3
0
2
4
6
8
10
12
14
16
18
Time [s]
Figure 71
Suspension displacements
63
Experimental Work and Results
Estimated Volume of Oil in Supension
Left Front
-4
1.3
1.25
1.2
1.15
8
10
12
14
16
1.38
1.36
1.34
1.52
Estimated Volume [m3]
3
Estimated Volume [m ]
1.4
8
1.56
1.55
1.54
1.53
1.52
1.51
8
1.42
measured
mean
+-2 
Left Rear
-4
1.44
18
Time [s]
x 10
10
12
14
Right Front
-4
x 10
Estimated Volume [m3]
x 10
3
Estimated Volume [m ]
1.35
16
12
16
18
16
18
Right Rear
-4
x 10
1.48
1.46
1.44
1.42
1.4
8
10
12
Time [s]
Figure 72
14
Time [s]
1.5
1.38
18
10
14
Time [s]
Estimated volume of oil in suspension
Suspension Displacements
70
Displacement [mm]
60
50
40
30
Displacement
Displacement
Displacement
Displacement
20
left front
right front
left rear
right rear
10
0
-10
0
10
20
30
40
50
60
70
Time [s]
Figure 73
Suspension displacements during fall test
64
Experimental Work and Results
Estimated Volume of Oil in Suspension
Let Front
-4
x 10
2
0
-2
-4
-6
-8
0
10
20
30
40
50
60
1.4
1.35
1.3
Estimated Volume [m ]
3
1.55
1.5
1.45
1.4
0
10
20
30
40
0
10
50
60
70
30
40
50
60
70
50
60
70
Time [s]
Right Rear
x 10
14
12
10
8
6
4
2
0
-2
0
10
Time [s]
Figure 74
20
-5
16
3
Estimated Volume [m ]
1.45
+-2 
1.6
1.35
1.5
measured
mean
Left Rear
-4
x 10
x 10
1.55
70
Time [s]
1.65
Right Front
-4
1.6
Estimated Volume [m3]
Estimated Volume [m3]
4
20
30
40
Time [s]
Estimated volume of oil in suspension during fall test
4.6
Vehicle Implementation and Experimental Results
4.6.1
Initial problems and modifications
4.6.1.1 Battery Power
The initial test setup used a 2 ℓ accumulator to store the oil and the pump was switched on when the
pressure dropped below a certain value. It was however found that the current drawn by the 12V Direct
Current (DC) motor, used to pump the oil, drops the voltage of the batteries to such an extent that the
directional valves cannot function. Extra batteries were added but this did not solve the problem and the
2 ℓ accumulator was replaced with a larger 10 ℓ accumulator (see Figure 75), to enable a DLC without
using the pump. This solution (not using the pump while performing a DLC) however limits the duration
that the suspension can be controlled and it also limits the maximum oil flow. From the valve
characteristics for the FPPC valve in Figure 30 it can be seen that sufficient flow (more than 14 ℓ/min) is
still possible with a ΔP of 2 MPa. During an experimental DLC at 80 km/h a maximum pressure in the
suspension of less than 5 MPa was reached and therefore the accumulator was charged to 7 MPa (this
means that the gas pressure will be 7 MPa when the gas volume is 10 ℓ), which allows the accumulator to
65
Experimental Work and Results
store about 3 ℓ of oil at 12.5 MPa, which is close to the maximum pressure the pump would deliver with
the battery setup.
Figure 75
10 l bladder type accumulator being charged to 7 MPa
4.6.1.2 Volume Limit
As mentioned in par. 4.5 the amount of oil in the suspension units are estimated to prevent the control
algorithm from draining too much oil from the suspension, as this can result in a negative effect on the
suspension response. Although the signals are filtered there is still a substantial amount of noise present,
because filtering out lower frequencies will cause an excessively large delay. Due to the change in
volume of oil in the suspension being relatively small, the noise on the measured signals has a severe
effect on the accuracy of the volume estimation. The volume estimation is shown in Figure 76 where one
can see the substantial amount of noise present, also note the small change in volume relative to the noise.
Friction affects the estimated volume to some extend as well, but the effect seems relatively small during
actual driving as expected due to the constant movement of the strut. During earlier tests an improvement
in the results was obtained by reducing the limit by 10% from the limit obtained in par. 4.5. After testing
it was found that the new limits were set too low as can be seen in Figure 76, and that it never stopped the
algorithm from draining too much oil. The improvement was likely due to the lower limit preventing the
66
Experimental Work and Results
volume algorithm to make any decisions and thus it also prevented it from making erroneous decisions
caused by the noise.
Estimated Volume of Oil in Suspension Units
-3
1.6
1.5
Estimated Volume [m3]
Estimated Volume [m3]
x 10
Left Front
-3
1.45
1.4
1.35
Right Front
x 10
1.55
1.5
1.45
1.4
1.35
1.3
0
x 10
4
6
8
Time [s]
10
1.3
0
2
Estimated Volume
Limit
-3
x 10
1.65
12
Left Rear
-3
1.6
Estimated Volume [m3]
Estimated Volume [m3]
1.65
2
1.55
1.5
1.45
1.4
1.35
0
5
10
15
6
8
Time [s]
10
12
14
Right Rear
1.6
1.55
1.5
1.45
1.4
1.35
0
Time [s]
Figure 76
4
5
10
15
Time [s]
Estimated Volume during a DLC at 60 km/h
4.6.1.3 Valve Response
During the characterisation of the FPCC valve shown Figure 77, a single proportional valve was
characterised to determine the flow rate across the valve as a function of the input voltage (See par. 4.3).
It was assumed that all valves will share the same characteristics. However it was found during field
testing that all the valves do not respond the same, and some adjustments had to be made in the field with
limited success due to the limited information available at the time. In Figure 80 (Par. 4.6.2) it can be
seen that the flow of the left suspension units were too low, but there is a significant improvement in the
displacement of the right suspension units were the flow was somewhat higher.
67
Experimental Work and Results
FPCC
Proportional
valve
PC104
SV12-33
Directional valve
Figure 77
4.6.2
Valves for the rear suspension unit during characterisation
Experimental Results
Experimental testing was done by performing a DLC on a level concrete straight track at Gerotek near
Pretoria in South Africa (Gerotek, 2012). A total of 31 DLCs were done at different speeds (50, 60, 70
and 80 km/h) over two testing sessions. After looking at the results of the initial tests it was decided to do
the tests at 60 km/h on the stiff suspension setting due to the flow constraints on the system. The Land
Rover Defender test vehicle (see Figure 78) was equipped with a VBOX III GPS (Racelogic, 2012) to
record the path and speed of the vehicle. String displacement sensors were used to measure the
suspension displacements, laser displacement sensors were fixed to each side of the vehicle to measure
the roll angle as can be seen in Figure 79. Pressure transducers were used to measure the pressure of the
accumulator as well as the pressures in the suspension struts. To link the GPS data with the data recorded
on the PC104 (Diamond Systems, 2012) an optical trigger was fixed to the rear of the vehicle and it was
68
Experimental Work and Results
triggered by a reflective strip placed on the track before the vehicle enters the DLC. An accelerometer
was used to measure the lateral acceleration. In total 15 measured channels were used to perform the
experimental tests. The control algorithm made use of a PID controller to control the suspension
displacement by opening or closing the proportional valves while the magnitude of the valve opening was
determined by the amount of lateral acceleration that the vehicle experiences (Table 3). The PID value
was calculated digitally using the PC104.
The final setup comprised of the following:
Table 3
Valve opening commands for different lateral accelerations
| |
Lateral Acceleration ( )
% Valve Opening Command
(
| |
| |
| |
)
∫
Suspension Extended
(Outflow Control)
Suspension Compressed
(Inflow Control)
|
|
It was found during the testing that the results improved when the integral component was excluded and
effectively using a Proportional Derivative (PD) controller. This is likely due to the noise present on the
signals, which was not present in the simulations. Due to a limit on the size of the variables, the noise on
the signals and the fact that simulations showed that the response is not sensitive to changes in the gains
above the limit value the gains were chosen as
,
and
and the limit was set as 0.5,
this will start countering displacement the moment it passes 0.5mm which is sufficiently sensitive relative
to the sensitivity of the displacement sensors and the magnitude of the noise. The valve opening
command for the left front valve was multiplied with 1.3 and right rear with 1.2 in an attempt to get the
same flow at all the suspension units. Afterwards it was however found that these adjustments were not
sufficient. The volume limit was also deactivated here due to the reasons explained in section 4.6.1.2.
69
Experimental Work and Results
Figure 78
Land Rover Defender test vehicle being prepared for testing
Laser
Displacement
Sensor
Figure 79
Laser displacement sensor on the side of the vehicle
70
Experimental Work and Results
Figure 80 shows the suspension displacement of Run 1 for a DLC at 60km/h and an overall improvement
is visible in the displacement of the right suspension units. Improvement in the RMS of the displacement
as high as 56% is obtained as can be seen in Table 4. The left front suspension‟s valve allowed too little
flow and therefore it can be seen that the reaction of the control is slower than that of the left rear unit.
This added with the volume algorithm not stopping the oil draining resulted in the excessive compression
of the suspension around 10s on the x-axis. On the left rear one can see that the system had a faster
response due to higher oil flow but here similar to the left front unit too much oil was drained and this
resulted in an excessive compression around 10s as well. The body roll angle shown in Figure 81 was
improved overall even with the volume estimation and oil flow not optimal. A maximum improvement of
0.9˚ is found just after 5 seconds for run 1, where the roll angle is improved from 1.85˚ to 0.95˚ giving a
49% improvement. In Table 5 it can be seen that the RMS of the roll angle was improved by as much as
30%. Figure 82 shows the vehicle‟s path and speed during the baseline and controlled runs and the
consistency between the two runs is very good.
RMS of the displacement for run 1
Table 4
RMS of the displacement during a DLC at 60km/h for Run 1
Baseline [m]
Controlled [m]
Left Front
3.22
3.16
Right Front
4.73
2.09
Left Rear
3.61
3.08
Right Rear
2.35
1.90
Difference [m]
0.068
2.64
0.52
0.45
% Improvement
2.10
55.75
14.50
19.19
Suspension Displacement
Left Front
Right Front
10
Displacement [mm]
Displacement [mm]
10
5
0
-5
-10
0
2
4
6
8
10
12
Left Rear
-10
0
2
4
6
8
10
12
14
10
12
14
Time [s]
Right Rear
6
Displacement [mm]
Displacement [mm]
-5
Baseline
Controlled
15
10
5
0
-5
-10
0
-15
14
Time [s]
5
0
2
4
6
8
10
12
14
4
2
0
-2
-4
-6
0
2
4
Time [s]
Figure 80
6
8
Time [s]
Suspension displacements for Run 1 during a DLC at 60km/h
71
Experimental Work and Results
Table 5
RMS of the roll angle for two different runs
RMS of the roll angle during a DLC at 60km/h
Baseline [˚]
Controlled [˚]
Run 1
0.81
0.57
Run 2
0.81
0.61
% Improvement
29.6
24.7
Difference [˚]
0.24
0.2
Roll Angle Run 1
1.5
1
Vehicle Path
Roll Angle [deg]
2
1
0
-1
-2
0.5
0
-0.5
-1
-1.5
-3
-4
-2
0
0
1
2
50
3
4
5
Time [s]
100
6
7
150
8
9
200
X [m]
Baseline
Controlled
Vehicle Speed
Roll Angle Run 2
59
1.5
58
Roll Angle [deg]
1
57
56
55
0
-0.5
-1
-1.5
0
50
-2
0
Figure 81
100
1
2
150
3
X [m]
4
200
5
6
7
8
9
Time [s]
Body roll angle for DLC’s at 60km/h
Vehicle Path
2
1
Y [m]
0
-1
-2
-3
-4
0
50
100
150
200
X [m]
Baseline
Controlled
Vehicle Speed
59
Speed [km/h]
54
0.5
58
57
56
55
54
0
50
100
150
200
X [m]
Figure 82
Vehicle path and speed for the baseline run and controlled run1
72
Experimental Work and Results
4.7
Simulation Verification
After experimental data was obtained the simulation model was updated and compared to the
experimental data. The results correlated well and using this model the effects of some system changes
were investigated.
Although the results correlate well, there are some known shortcomings to the model. The model under
estimates the suspension force when it is being drained down into the negative and this can cause quite
significant deviations as can be seen in par. 4.1. The suspension does however never compress more than
10mm (due to the control) and therefore the effect of this shortcoming is very small. The valve flow
during opening and closing is not modelled. The valves are modelled as if they open fully immediately
but this is not the case in reality. The model compensates for this to some extend by using a sample time
of 60ms. The effect of this does however seem small and it does make the model less computationally
expensive. The road input in reality is not 100% smooth as it is in the simulations. Taking into account
that the control system will react differently to different inputs and that these reactions will influence the
rest of the decisions still to be made the correlation of the model with the measured is satisfactory. Figure
83 shows the roll angle results of the experimental run and the BWR simulation. These simulations were
done by giving the actual speed and path of the experimental run to the model. A major deviation occurs
at the right rear unit around 8 s in Figure 84. This might be due to some unknown input that is not
modelled into the simulation or due to the mentioned shortcomings of the model.
To see how the system would perform if a larger oil flow was possible and the volume in the suspension
could be determined accurately a few different scenarios were simulated. Suspension displacement and
roll angle for different flow magnitudes with and without a minimum volume limit is shown in Figure 85
to Figure 89. The flow stated in Figure 85 to Figure 89 is the total average flow for all four suspension
units. From these simulation results it becomes visible that the volume limit does not always have a
positive effect. But the volume limit does reduce the maximum roll angle in almost all the runs. It also is
more advantageous in the case of low oil flow where the flow is not sufficient to counter the quick
compression, as was also seen in the experimental data. The left front displacement is not significantly
influenced by adjusting the volume limit and this is because of the suspension being compressed initially
and a relatively large amount of oil is pumped into the suspension so that the limit of -5 ml is not reached
again in some of the cases. These results have also been obtained using the experimental speed and
vehicle path and should give an indication what the results would have been if the volume control was
successfully implemented during the experimental testing.
73
Experimental Work and Results
Roll Angle
1.5
Controlled (Measured)
Controlled (Simulated)
Roll Angle [deg]
1
0.5
0
-0.5
-1
-1.5
0
1
2
3
4
5
6
7
8
9
10
Time [s]
Figure 83
Simulated and experimental roll angle for a controlled DLC at 60 km/h
Suspension Displacements
Left Front
Right Front
6
Displacement [mm]
Displacement [mm]
10
5
0
-5
-10
0
2
4
6
8
10
12
Time [s]
2
0
-2
-4
-6
14
0
2
4
Left Rear
6
8
10
12
14
10
12
14
Time [s]
Experimental (Controlled)
Simulated (Controlled)
8
Right Rear
4
6
Displacement [mm]
Displacement [mm]
4
4
2
0
-2
-4
2
0
-2
-4
-6
-8
0
2
4
6
8
Time [s]
Figure 84
10
12
14
-6
0
2
4
6
8
Time [s]
Simulated and Experimental controlled suspension displacement for a DLC at 60km/h
74
Experimental Work and Results
In = 0.54 [l/m]
4
6
2
Displacement RF [mm]
Displacement LF [mm]
Suspension Displacements With Average Flow
8
4
2
0
-2
-4
Out = 0.34 [l/m]
0
-2
-4
-6
-8
-10
-6
0
2
4
6
8
10
12
-12
14
0
2
4
Time [s]
6
8
10
12
14
10
12
14
Time [s]
Min Volume Limit = 5 ml
No Min Volume Limit
8
8
6
Displacement RR [mm]
Displacement LR [mm]
6
4
2
0
-2
4
2
0
-2
-4
-6
-4
-8
-6
0
2
4
6
8
10
12
14
-10
0
2
4
Time [s]
6
8
Time [s]
Suspension displacement for average total inflow of 0.54 l/m during a DLC at 60km/h
Figure 85
3
6
2
5
Displacement RF [mm]
Displacement LF [mm]
Suspension Displacements With Average Flow
7
4
3
2
1
0
-1
Out = 0.8 [l/m]
1
0
-1
-2
-3
-4
-5
-2
-3
In = 1.35 [l/m]
0
2
4
6
8
10
12
-6
14
0
2
4
Time [s]
6
8
10
12
14
10
12
14
Time [s]
Min Volume Limit = 5 ml
No Min Volume Limit
8
8
Displacement RR [mm]
Displacement LR [mm]
6
6
4
2
0
4
2
0
-2
-4
-2
-6
-4
0
2
4
6
8
Time [s]
Figure 86
10
12
14
-8
0
2
4
6
8
Time [s]
Suspension displacement for average total inflow of 1.35 l/m during a DLC at 60km/h
75
Experimental Work and Results
Suspension Displacements With Average Flow
6
Displacement RF [mm]
Displacement LF [mm]
Out = 2.3 [l/m]
3
5
4
3
2
1
0
2.5
2
1.5
1
0.5
0
-0.5
-1
-2
In = 3.37 [l/m]
3.5
-1
0
2
4
6
8
10
12
14
-1.5
0
2
4
Time [s]
6
8
10
12
14
10
12
14
Time [s]
6
8
5
6
Displacement RR [mm]
Displacement LR [mm]
Min Volume Limit = 5 ml
No Min Volume Limit
4
3
2
1
0
2
0
-2
-4
-1
-2
4
0
2
4
6
8
10
12
-6
14
0
2
4
Time [s]
Figure 87
6
8
Time [s]
Suspension displacement for average total inflow of 3.37 l/m during a DLC at 60km/h
7
5
6
Displacement RF [mm]
Displacement LF [mm]
Suspension Displacements With Average Flow
6
4
3
2
1
0
-1
-2
In = 6.75 [l/m]
Out = 4.5 [l/m]
5
4
3
2
1
0
-1
0
2
4
6
8
10
12
-2
14
0
2
4
Time [s]
6
8
10
12
14
10
12
14
Time [s]
Min Volume Limit = 5 ml
No Min Volume Limit
6
8
7
Displacement RR [mm]
Displacement LR [mm]
5
4
3
2
1
0
-1
-2
5
4
3
2
1
0
-1
0
2
4
6
8
Time [s]
Figure 88
6
10
12
14
-2
0
2
4
6
8
Time [s]
Suspension displacement for average total inflow of 6.75 l/m during a DLC at 60km/h
76
Experimental Work and Results
Roll Angle With Average Flow In = 1.35 [l/m] Out = 0.8 [l/m]
1
1
0.5
0.5
Roll Angle [deg]
Roll Angle [deg]
Roll Angle With Average Flow In = 0.54 [l/m] Out = 0.34 [l/m]
0
-0.5
-1
-1.5
0
2
4
6
8
10
12
Time [s]
0
0.8
0.6
0.6
Roll Angle [deg]
Roll Angle [deg]
1
0.8
0.4
0.2
0
-0.2
-0.4
6
8
10
12
12
0
-0.4
-0.8
Time [s]
10
-0.2
-0.6
4
8
0.2
-0.8
2
6
Time [s]
0.4
-0.6
0
4
Roll Angle With Average Flow In = 6.75 [l/m] Out = 4.5 [l/m]
1
-1
2
Min Volume Limit = 5 ml
No Min Volume Limit
Roll Angle With Average Flow In = 3.37 [l/m] Out = 2.3 [l/m]
4.8
-0.5
-1
-1.5
Figure 89
0
-1
0
2
4
6
8
10
12
Time [s]
Roll angle for different total flow magnitudes during a DLC at 60km/h
Conclusion
The experimental results show that a significant improvement in the body roll angle is possible with
relatively low flow requirements. The average flow for the experimental runs is estimated to be around
3.5 l/min (without losses). The average flow out of the accumulator during the DLC test run shown was
6.1 l/min. The large amount of losses is primarily due to the leakage of the solenoid operated valves and
expansion of the rubber pipes. It might be possible to reduce the losses and then the system will be even
more effective. An accurate method of determining the volume of oil in the suspension will also improve
the results. But even with the mentioned shortcomings a significant improvement was obtained using
slow active suspension control. The simulation model also correlates well with the experimental results.
The model can be used to predict the effect of changes to the system with good accuracy.
77
Conclusion
5.
Conclusion
Slow active suspension control has been successfully modelled and implemented on a test vehicle. Both
the simulation and experimental results show that a significant improvement in body roll angle is possible
by actively controlling the amount of oil in each of the hydropneumatic suspension struts. This also
provides the possibility to cancel out squat and pitch. This setup will either utilise or enable height
adjustment on the vehicle. The average flow out of the accumulator during a DLC test run was 6.1 l/m
including the leakage of the valves which can easily be obtained with an engine driven pump.
The suspension displacements on the right were improved in all aspects and similar results should be
possible for all the suspension units. A more accurate method of determining the volume of oil in the
suspension and a rigid algorithm to adjust the volume limit for the specific situation is also expected to
improve the results. The correlation between the experimental data and the simulation data is satisfactory
and different setup configurations can be modelled with good certainty. This will allow for faster further
development of this system. Better improvement might also be possible on a softer suspension where
there are larger displacements but due to oil flow limitations this was not tested.
Using slow active suspension control will enable one to use, with some minor changes, the height control
on vehicles to replace the anti-roll bar. Individual suspension control will also give the possibility of
changing the handling characteristics while driving to suit the specific situation best. Thus, this method
of roll control is feasible with added advantages over that of an active anti-roll bar.
78
Recommendations for future work
6.
Recommendations for future work
During opening and closing phase of a valve a complex flow phenomena takes place. Some work on
modelling the flow through a valve in these phases has been done at the University of Pretoria. Including
these phases in the model might improve the results. The model also makes many ideal assumptions
which make it more effective computationally, but better correlation might be possible if the losses in the
system is determined and modelled in.
When the directional valves were chosen the flow was expected to be much higher than it was found to
be. The result is that these valves are larger than necessary, this result in slower response times and more
leakage than with smaller valves. The solenoid operated valves were chosen for their fast response times
and ease of controllability but their leakage does have a detrimental effect on the energy requirements and
if a better solution could be found it would increase the effectiveness of the system drastically.
Characterising of each of the proportional valves individually is required. To obtain the flow relative to
the other valves will allow one to control the flow of each suspension unit to be the same. This can
increase the effectiveness of the control significantly and should be investigated.
Further work can be done on finding a better method to determine the volume of oil in the suspension and
an algorithm that will decide what the volume limit should be for certain driving situations. The PID
controller and the proportional control can also be optimised some more.
Currently a 12V DC electrical motor drives the pump that supplies the oil. This is an ineffective setup
due to the many losses associated with an electrical system. A pump driven directly from the engine of
the vehicle can solve the oil flow problems and should be investigated. With an engine driven pump it
might also be possible to test the system on a softer suspension.
A theoretical study looking at rollover and not just at the body roll angle can be investigated, to determine
the improvement in the rollover threshold.
79
Bibliography / References
7.
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D
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F
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G
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I
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M
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85
Appendix ADerivation of the differential equation used to calculate the gas temperature in the suspension
Appendix A
Derivation of the differential equation used to
calculate the gas temperature in the suspension
The first law of thermodynamics (Energy Equation) is:
̇
̇
̇
or
̇
̇
̇
(1)
With:
̇
̇
̇
̇
In order to apply the method used by Otis and Pourmovahed (1985) to a hydropneumatic suspension,
Els (1993) makes the following assumptions:




The system is a closed system.
No Inertia effects are present during the gas compression.
The process is seen as a homogeneous, quasi-static gas compression process.
The effect of the thermal capacity of the piston rod and that of the cylinder wall is seen as
negligibly small.
The convective heat transfer between the suspension and the environment can be approximated by:
̇
(
)
(2)
With
Where
86
Appendix ADerivation of the differential equation used to calculate the gas temperature in the suspension
And the rate of the piston work is given by:
̇
̇
(3)
With
̇
(In terms of the piston movement or the oil flow)
The internal energy per unit mass is given by the thermodynamic relation
*
(
)
+
(4)
With
Replace (2),(3) and (4) into (1)
*
*
(
)
+
*
(
)
+ ̇
(
+
)
̇
Simplify:
̇
Divide with
(
)
̇
Knowing that ̇
(
)
)
̇
:
̇
̇
(
̇
(
̇
)
̇ the differential equation simplifies to:
(
) ̇
(5)
The BWR Equation is used to represent the
(
relationship:
)
(6)
Differentiate (6) in terms of T:
(
)
(
)
(7)
87
Appendix ADerivation of the differential equation used to calculate the gas temperature in the suspension
Replace (7) into (5)
(
̇
)
̇
)
̇
(
[
)
]
Regroup:
(
̇
*
(
)
(
(
)
)
+
(Otis and Pourmovahed, 1985) and (Els, 1993)
This equation can be solved numerically. The ode45 in MATLAB (MathWorks, 2012), which is based
on the 4th order Runge Kutta method, can be used but this method is computational expensive due to
additional features in the code. A basic 4th order Runge Kutta function was written as recommended by
Otis and Pourmovahed (1985) and it solves in significantly less time.
The 4th order Runge Kutta method formula is as follows:
(
)
( )
(
)
Where:
(
)
(
)
(
)
(
)
(Cheney and Kincaid, 2004)
The ideal gas specific heat is given by:
*
(
)
(
)
+
Where:
88
Appendix ADerivation of the differential equation used to calculate the gas temperature in the suspension
Knowing
the specific heat for the real gas can be calculated:
(
)
(
)
(
)
(Otis and Pourmovahed, 1985)
The constants for the BWR equation and
Constants
can be found in Appendix B
BWR and Nitrogen
89
Appendix B
Appendix B
BWR and Nitrogen Constants
BWR and Nitrogen Constants
Constants for the BWR equation
[(
)
]
[(
)
]
[(
) ]
*
+
[(
)
]
[(
)
]
[(
) ]
[(
) ]
*
+
Constants for the calculation lf the ideal gas specific heat capacity (Temperature in Kelvin)
(Els, 1993)
90
Appendix C
Appendix C
Equation for volume estimation
Equation for volume estimation
In order to estimate the volume of oil in the suspension units, the compressibility of the gas and oil is
taken into account using the ideal gas law and the bulk modulus of the oil. The pressure of the gas and oil
is assumed to be the same.
The Ideal gas law is stated as:
(1)
Assuming an isentropic relationship the ideal gas law can be written in the following manner:
( )
⁄
(2)
The following values are obtained from Els (2006):
(pressure at which the gas was charged)
(volume at which the gas was charged)
And the heat capacity ratio for nitrogen is
.
Bulk modulus equations as found on P 4.21 (Els, 2006)
(
(3)
)
(3) can be rearranged to get (4)
(
(
)
)
(4)
In this case the displacement of the suspension and the compression of the nitrogen in the accumulator
need to be taken into account. The compression of the nitrogen is taken into account using the ideal gas
law and the compression of the oil using the bulk modulus. The change in the height due to oil being
91
Appendix C
Equation for volume estimation
added or removed is taken into account by multiplying the change in the displacement of the suspension
unit with the piston area as shown in (5) and (6).
(
)
(5)
But
(6)
Thus by placing (2) and (6) into (4) we get the amount of oil in the suspension that can be compared with
the original amount of oil in the suspension.
(
) (
(
)
(
(
⁄
)
(
)
⁄
)
)
(7)
Where:
(Rear)
(Front) (50mm less travel)
(Atmospheric Pressure)
(Bulk Modulus)
92
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