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Statens v g- och trafikinstitut (VTI) - Fack ~ 581 01 Linkiiping
Nr 138A ° 1978
National Road & Traffic Research Institute Fack - S-581 01 Linképing - Sweden ISSN 0347-6030
Lateral Stability of Road Tankers
Volume I. Main report
(with Swedish summary:
1 3
Tankfordons sidstabilitet)
PREFACE
This report presents a survey on the project "The overturning tendency of road tankers". It contains previously unpublished results together with further evaluations of data presented in earlier reports from the National Swedish Road and Traffic Research Institute
(VTI). The investigation methods, results and conclu-sions in chapter 1-4 are aiming at a creative discussion on countermeasures, developing and substituting the
suggestions in chapter 5 into successful actions for safer road tankers. Appendices are collected in a separate volume where appendix B-E contain specific
technical details.
The project has been sponsored by the National Swedish Road Safety Office with partial contribution from
funds available by the budget of the Transport
Research Delegation.
Thanksanxadue to several Swedish companies for supplying
valuable information on vehicles and tank containers.
Contributions in several technological activities has been given by Mats Lidstrom, M.Sc.Eng., during the la-ter stages of the project. Bengt-Goran Bergdahl, M.Sc. Eng. and Goran Palmkvist M.Sc.Eng., solved problems with servo control and electronic measurements during the initial phases. Chief engineer Olle Nordstrom, M.Sc. Eng., has contributed during numerous discussions on the guidelines of the project where also Staffan Nordmark. D.Eng. participated in the later phases.
CONTENTS
ABSTRACT
REFERAT
SUMMARY
SAMMANFATTNING
THE ROAD SAFETY PROBLEM
Passive and active safety for heavy vehicles
Common primary differences between light and heavy vehicles
Space demand paradox with articulation and axle steering
Aggravation due to load motions
Lateral compared to longitudinal liquid motions
LITERATURE ON LIQUID LOAD MOTIONS IN VEHICLES
Natural frequencies in partially filled containers Sloshing forces
Damping of liquid motions in a container Road tanker oriented investigations
INVESTIGATION PROCEDURE
Investigation phases
Computer evaluated measurements on scale models - benefits and drawbacks
Vehicle and tank configurations
Manoeuvres and risk criteria Validation
INFLUENCE ON OVERTURNING AND SKIDDING TENDENCY
Manoeuvre peak acceleration Manoeuvre oscillation frequency
VTI REPORT NO. 138A
Page II III l3 16 18 23 23 28 3O 35 4O 41 41 43
w 1 5 1 0 0 Page
Tank cross section. baffles
Liquid forces and motion in half fikled tanks
Shape, walls,
Load volume percentage Roll stiffness
DISCUSSION ON COUNTERMEASURES
Discussion and interdisciplinary solutions needed
Priority to performance demands and to trailers
General tilting test for overturning limit
Slosh load definition Maximum compartment width
REFERENCES
VOLUME II NOTATION
CONDITIONS FOR DYNAMIC SIMILARITY BETWEEN MODEL AND FULL SIZE TANK
TANK MODEL AND LIQUID FORCES
MATHEMATICAL DESCRIPTION OF THE SIMULATION MODELS COMPUTER PROGRAMS FOR PHASE II
RESULTS FROM PHASE II
Appendices
VTI REPORT NO. 138A
47 52
56
59
64 64 65 65 67 68 70Lateral Stability of Road Tankers by Lennart Strandberg
National Swedish Road and Traffic Research Institute Fack
8-581 01 LINKGPING SWEDEN
ABSTRACT
The influence from large amplitude sloshing on the overturning and skidding stability of road tankers has been experimentally quantified. Liquid force measure-ments in laterally oscillated model tanks were evalua ted by simplified vehicle models in a hybrid computer.
The experimental technique is described in detail.
Re-markable deteriorations of the cornering capacity due to dynamic liquid motions were found for partly loaded tanks. A short lateral distance between vertical cross walls is recommended: 0.6 m or less. A previous sugges tion on a steady-state overturning limit of minimum
4 m/s2 tested in full scale by static tilt - is
discussed for road tankers as well.
VII
Tankfordons sidstabilitet
av Lennart Strandberg
Statens vag- och trafikinstitut (VTI) Fack
581 01 LINKUPING
REFERAT
Inflytandetanzstora vatskerérelser pa tankfordons
valt-nings och sladdningsstabilitet har kvantifierats ex
perimentellt. Matningar av vatskekrafter i sidledes oscillerade modelltankar utvarderades med férenklade fordonsmodeller 1 en hybriddator. Experimenttekniken beskrivs i detalj. Anmarkningsvarda farsamringar av kurvtagningsférmagan pgya dynamiska vatskerbrelser
kon-staterades fér dellastade tankar. Litet sidoavstand
mellan vertikala mellanvaggar rekommenderas: 0,6 m eller mindre. Ett tidigare férslag om en stationar valtnings-grans p5 minimum 4 m/s2 - prévad i full skala genom
sta-tisk lutning diskuteras aven fér tankfordon.
lll
SUMMARY
Articulation, high centre of gravity, and load motions
cause the overturning and skidding stability of road
tankers to be comparatively poor. The problem is parti-cularly serious for trailers being subjected to the most violent motions in the vehicle combination during
dynamic manoeuvres. Further reduction of the overall safety is caused by the lack of lateral force
feed-back cues from the trailer to the driver.
Liquid load relative motion in vehicles has been
investigated for decades with different methods. For
conventional,partly loaded road tankers the liquid's
resonance frequency may coincide with the peaks in an
emergency manoeuvre's spectral distribution. It has
also been shown that resonance forces from a small
amplitude sloshing load are much larger than if the load were rigid. Though being qualitatively well known, the large amplitude sloshing effect on lateral stability
of road tankers required further experiments to be quantified.
This investigation was based on measuring liquid force in laterally oscillated model tanks - with or without baffles/cross walls. The effects of liquid forces on overturning and skidding tendency were evaluated from simplified vehicle models (no roll, no yaw) in a hybrid computer. Comparisons were made with the effects from liquid motion during steady-state cornering and with roll influence. The experimental technique is described in detail in an appendix volume.
The poorest lateral stability was found for tank cross sections and load volume percentages with large lateral distance between tank walls at the liquid surface
height. The deterioration seems to be due to a combina-tion of:
a) dynamic forces from the sloshing liquid values above twice the rigid load force were found
b) lateral displacement of the liquid's centre of
gravity values about 0.4 m should be expected.
The overturning limit during steady state cornering with
a 50% volume loaded rectangular tank can be improved
from-3.1 m/s2 to 3.8 m/s2 by increasing roll stiffness
100% and to 5.2 m/s2 by adding three longitudinal cross walls. Adding the same number of cross walls in a 50%
load elliptic like tank on a non-rolling vehicle impro
ves the overturning limit during a dynamic manoeuvre from 2.4 m/s2 to 6.3 m/sz. In the last case the
over-turning limit with 100% load volume is 5.4 m/s2 illu-strating the distinct deterioration (to 2.4 m/sz) when unloading an uncompartmented tank.
Suggested countermeasures in vehicle design are most
urgent for trailers and should have priority over trucks
and tractors in legislation. The static tilting test
- corresponding to 4 m/s2 lateral acceleration is
outlined for type approval of road tankers in order to
complete previous suggestions for rigidly loaded vehicles.
The maximum width 0.6 m for partly loaded major compart-ments would make the dynamic manoeuvre performance less dependent of steering frequency and load volume
percen-tage.
SAMMANFATTNING
Leder i fordonskombinationen, hog tyngdpunkt och rorel ser i lasten ar faktorer, som gor att stabiliteten mot valtning och sladdning for tankfordon ar jamforelsevis délig. Problemet ar sarskilt allvarligt for slapvagnar,
som utsatts for de haftigaste rorelserna i
fordonskom-binationen under dynamiska manovrer. Systemsakerheten forsamras ytterligare pQJa bristande informationsater-foring till foraren om de sidkrafter, som verkar pa slapvagnen.
Vétskelastens relativa rorelse i fordon har undersokts under artionden med olika metoder. For konventionella, dellastade tankfordon kan vatskans resonansfrekvens sammanfalla med maxima i spektrum for en undanmanover. Det har ocksa framkommit att resonanskrafterna vid sma vatskerorelser ar mycket storre an om lasten vore fixe-rad. Fastan inverkan av stora vatskerorelser pa_tank
fordons sidstabilitet kvalitativt sett ar valkand,
krav-des ytterligare experiment, for att den skulle kunna
kvantifieras.
Denna undersokning har grundats pa matningar av vatske-krafter i modelltankar som oscillerats i sidled - med eller utan skvalpskott/mellanvaggar. vatskekrafternas inverkan pa valtnings- och sladdningsbenagenheten ut-varderades med hjalp av forenklade fordonsmodeller
(ingen krangning, ingen girning) i en hybriddator. Jam forelser gjordes med inverkan av vatskerorelse under stationar kurvkorning och med inverkan av krangning. Experimenttekniken beskrivs detaljerat i en separat bilagedel.
Den samsta sidostabiliteten upptradde med tanktvarsnitt och lastvolymer som hade stort sidoavstand mellan
tank-vaggarna i hojd med vatskeytan. Forsamringen forefaller
bero pa en kombination av:
VI
a) dynamiska tillskottskrafter i sidled fran den
rorli-ga vatskan varden patraffades, som var mer an
dubbelt sa stora som med fixerad last.
b) sidoforskjutning av vatskans tyngdpunkt - varden
omkring 0,4 m kan forvantas.
valtningsgransen under stationar kurvkorning med en rektangular tank fylld till 50% volym kan forbattras
fran 3,1 m/s2 till 3,8 m/s2 med fordubblad
krangstyv-het och till 5,2 m/s2 med tre langsgaende mellanvaggar.
Samma antal mellanvaggar 1 en till 50% fylld elliptisk tank, monterad pa ett icke krangande fordon, forbattrar valtningsgransen under en dynamisk manover fran 2,4 m/s2 utan mellanvaggar till 6,3 m/SZ. I det senaste fallet ar valtningsgransen for 100% lastvolym 5,4 m/s2, vilket visar den tydliga forsamringen (till 2,4 m/sz) vid av-lastning av en tank utan skiljevaggar,
Foreslagna motatgarder i fordonsutformning ar sarskilt
angelagna for slapvagnar, som bor fa prioritet over
lastbilar och dragbilar i lagstiftningene Det statiska valtningsprovet - motsvarande 4 m/s2 sidacceleration ~ skisseras har for typgodkannande aven av tankfordon som komplement till tidigare forslag for fordon med fixerad
last, Maximibredden 0,6 m for storre dellastade fack
skulle medfora att de dynamiska manoverprestanda blir mindre beroende av styrfrekvens och lastvolym.
THE ROAD SAFETY PROBLEM
Passive and active safety for heavy vehicles
The consequences of heavy vehicle overturning and skid-ding accidents are often serious with severe human
in-juries and considerable economic losses.
If the accident causes a poisonous or concentrated
chemical load to escape from its container, the envi
ronment as a whole may be damaged and threatened. Of course, this is likely to occur when road tankers are
involved (Kuhn and Isermann, 1966, found liquid pour
out in 126 out of 1288 road tanker accidents that were sufficiently reported by the police during 1964).
Therefore one should expect the manoeuvre performance and the active safety of heavy vehicles to be at least as good as for other road vehicles. But unfortunately this is generally not the case due to some particular
designcharacteristics-listed below found in the
major part of the heavy vehicbefleet.Ebllowing points are discussed more in detail by Strandberg et al (1975).
Common primary differences between light and heavy
vehicles
The ratio between centre of gravity height and effec tive track width is often much higher for heavy than for light vehicles. This results in poor lateral sta bility and less capacity to perform escape manoeuvres
than for automobiles.
The corresponding difference in handling performance is probably not well-known to the road user in common. For example the out of control criterion for an automo-bile is often connected to skidding. The corresponding limit can always be roughly estimated for light and
heavy vehicles from the road friction icy, wet or
dry road surface. However, the heavy vehicle will often overturn for a less severe manoeuvre than what is ne-cessary for skidding¥ (Among 1288 accidents classified by the police and with some kind of road tanker in
volved, Kuhn and Isermann, 1966, reported overtur ning of a road tanker in 145 cases).
In addition, there is a large variation in handling performance - due to the major influence from load condition and articulation (see chapter 1.3 below).
This uncertainty makes it even more difficult to pre dict the heavy vehicle manoeuvre limit prOperly for the driver - as well as for other road users in the
Vicinity.
Space demand paradox with articulation and axle
steering
The heavy vehicle space demand is generally larger than for automobiles. At low speed and in urban traf fic this is a well-known safety problem in itself.
However, the most common countermeasures in vehicle design (i.e. articulation and axle steering) will
cau-se the high speed space demand to increacau-se and the la teral stability to decrease. Figure 1.1 shows that the
X In fact poor overturning stability contributes to the skidding tendency due to lateral load transfer
and nonlinear tyre characteristics see Strandberg
(1974).
COURSE
COURSE
COURSE
8
SECTION
SECTION
SECTION
A
B
C
'
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ONCOMING TRAFFIC
I. u. I. .. .- < f "
-- Inc--bun .-- III III Ilsilu III
OBSTACLE
DOUBLE-ARTIC TRIPLE-ARTIC[R
WISE
[2
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AX LE CE NT RE LA TE RA L D E V I A T I O N F4 no 111 Ae===__. 100(
1501
200Figure 1.1 a) The double lane change manoeuvre. See appendix D.9.
b) Corresponding trajectories for leading vehicle c.g. and rear axle centre at
70 km/h. The two vehicles carry comparab-le loads but differ in number of articu
lations. Simulation results from
Strandberg et a1 (1975).
rear axle trajectory deviation from the leading ve hicle can be larger with three articulations than with two. This is contrary to the common description
of offtracking, based on low speed behaviour. Then -by neglecting side forces and sideslip angles
(kinematic instead of dynamic analysis) - the rear
axle deviation occurs inwards and is decreased by
articulation.
The dynamic analysis show that the high speed manoeuv-re manoeuv-response in general- and probably the braking manoeuv- re-sponse, as well- is most severe for the rear units in an articulated vehicle combination. Thus the trailer is more close to overturning and skidding than the
truck. See figure 1.2. This is particularly serious
as it is impossible for the driver to be aware of the trailer s dynamic state continously. The inertia and steering wheel forces in the truck (most important cues for overturning avoidance according to driver interviews by Tydén, 1975) are namely often unaffected by the lateral motions of the trailer.
25 MPH 43 MPH 56 MPH 25 MPH 43 MPH 56 MPH 40 KM/H 70 KM/H 90 KM/H 40 KM/H 7O KM/H 90 KM/H O V E R T U R N I N G R I S K PE AK S
Rv 14: TRUCK RV 16: TRACTOR + SEMITRAILER Rv 58: TRAILER RV 710: FULL TRAILER
D O U B L E A R T I C T R I P L E-A R T I C
Figure 1.2 Overturning factor peaks-seeappendix[h3.
Vehicles and manoeuvres as in figure
1.1. The lateral acceleration peak of the leading vehicle c.g. is 1.75 m/s2 indepen dent of speed. Thus the road length demand is prOportional to the speed.
Similar tendencies should be expected in light automo bile trailer vehicles. So their lower speed limit
com-pared to single automobiles may be justified until the
destabilizing effects from articulation etc. can be
eliminated.
Aggravation due to load motions
Every problem mentioned above may be seriously aggra vated if the load is allowed to move relative to the vehicle. Normally the load should be tightened to the vehicle and this is even stated by law in Sweden. De tails on fastening methods are given in order to keep the load tight at least for accelerations ofluCkyrear-wards 0.5g forofluCkyrear-wards and 0.5g laterally (g==gravity:
9.81 m/s2).Se National Swedish Road Safety Office vehicle regulations F44 for further information.
However, legislation for liquid load is not that well
defined. For lateral liquid motions within the tank, no valid regulations at all are known to the author.
Of course, the phenomenon of lateral sloshing and cer-tain countermeasures have been well-known, for a long
time. But no datalunnebeen found where the influence
of sloshing on overturning or skidding tendency has been quantified for VLL (road yehicles with liquid load, sometimes called road tankers in this report). This investigation and reportxmaxaprepared to cover a part of this gap in our knowledge of road vehicle pre-crash (active) safety.
In addition to the braking and handling stability problem, sloshing may cause high local pressures and dangerous stress on the tank structure. This subject is not treated in this report but the reader may
ini-tialize further studies from Irrgang (1960), Dalzell
(l966b),Hagiwara and Tani (1968), Schonig (1971) or
Faltinsen et al (1974). The conclusions drawn by Irrgang are worth mentioning as he finds that ".... though there are certain differences between tank cars with and without wash plates, these provide no advan tages with regard to holding power (danger of
derai-ling), running characteristics, braking and shunting.
Consequently because of their disadvantages they are
not to be required in future for new stockor for
exi-sting cars...." Irrgang points at the aggravation of
structure stresses when certain baffles are introduced,
but his recommendation to avoid baffles concern rail-way cars and should not be generalized to other
vehic-les with different motion characteristics.
Lateral compared bolongitudinalliquid motions
In conventional VLL tanks the internal liquid motions
can be more severe longitudinally than laterally if
no transversal walls or baffles are dividing the tank cylinder. Apart from simple geometrical reasons (most tanks are longer than wide) the longitudinal accelera tion peaks are larger than the lateral ones. Due to the common tank shape (sharp corners at the transver-sal walls in contrast to the rounded cross section)
the liquid impact is probably much more severe to the
structure for longitudinal sloshing than for lateral sloshing.
These phenomenological differences justify that
legislation has been concentrated on decreasing
longitudinal slosh and that different authorities re-quire only transversal walls or baffles. However, the manoeuvre stability might be more sensitive to lateral
.sloshing:
Tyre load transfer and overturning tendency can be more pronounced laterally than longitudinally
(compare e.g. the liquid motions in the tank to
track width and wheel base respectively).
Longitudinal sloshing in itself is more abrupt and easily perceivable to the driver even if it occurs in the trailer. Lateral sloshing is less abrupt and more difficult to perceive - especially sloshing in the trailer. Thus it is unlikely that the driver
-by learning at low risk levels can adapt his
steering behaviour in severe manoeuvres to avoid
frequencies that are particularly dangerous due to lateral sloshing.
LITERATURE ON LIQUID LOAD MOTIONS IN VEHICLES
The influence of steerability from liquid load motions in various vehicles has been treated by many
investi-gators. A small sample of reports, with contents that
may be significant to the road tanker application, will be reviewed below. Road vehicles are not always touched upon in these references. The need of know-ledge in liquid sloshing was apparently urgent during the initial phase of space exploration. Therefore many reports are based on space vehicle applications.
However, the basic problems, methods and results can often be extended to all kinds of vehicles.
Natural frequencies in partially filled containers Budiansky (1960) presented a hydrodynamic theory and mathematical analysis of small-amplitude sloshing in circular canals and Spherical tanks. His evaluation of natural frequencies for different liquid depths was verified eXperimentally by McCarty and Stephens
(1960). Figure 2.1 and 2.2 show some of their results
of specific interest to our application.
From figure 2.1a (or from Budiansky s table 1, p.
169) we find the fundamental natural frequency for 50%
load volume (i.e. h/2a==0.5) in a horizontal circular
cylinder to be
_ l.l7 radians
wn C50 _ a second (2'1)
9.81
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If we assume that the tank diametre is 1.9 m (a==0.95) according to the vehicle example in appendix D.8.l -the natural frequency for lateral liquid motion is:
wn C50
fn c50 =
2n
==O.60 HZ (2.2)This frequency is low enough to coincide with major
frequency components in an unfortunate cornering or escape manoeuvre (0.5 Hz corresponds to one steering reversal per second in a slalom course). The studies with restricted preview by McLean & Hoffmann (1973)
support that drivers really are able to impose a lar ge portion of their steering spectral density within this critical frequency range. It should be remembered
too (Abramson et a1, 1966) that real sloshing exhibits
lower resonance frequencies than indicated by this
linear theory.
For comparison the corresponding values with longitu-dinal sloshing, upright cylinders, rectangular cylin-ders and spherical tanks as well are given in figure 2.3. In every of these cases the load volume is 50% of the tank volume which is held equal to the volume of a sphere with radius 0.95 m. Thus the tank volume
3.59 m3 demands the circular cylinder (a==0.95 m as
well) to be 1.27 m in length (Q).
As indicated above, Budiansky analyzed theoretically transversal liquid motions and presented e.g. the natural frequency in mathematical expressions. But no such well defined algebraic expressions has been found for longitudinal sloshing in circular cylinders.
How-ever, McCarty and Stephens nondimensionalization in
figure 2.1b seems successful in making the results in dependent of the experimental geometry. So, their fi-gure was used with confidence for evaluationof1 uacorre-sponding natural frequency in figure 2.3b.
ll 1
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;____-1.9 m l 9 m{ t
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it,
e-l
a
d
L \ <:; 0.64 Hz ;:>Figure 2.3 Fundamental natural frequencies of liquid slosh in
half filled tanks with inner width l.9 m. The sphere (f) volume 3.59 m3 is duplicated for the cylinders
if their length is 1.27 m (a,b,c) and 0.99 m {d,e)
provided that the liquid level is 0.95 m above bottom for the rectangular tanks as well.
12
The upright circular cylinder natural frequency in
fi-gure 2.3f has been expressed by Silverman and
Abram-son (1966 - equation 2.58c)
= a. .
£1.
rm
wnCZUpright //a 8n tanh(a 8n) second (2'3)
where an is the n th zero of Ji (en) (i.e. first
de-rivative of the Bessel function of the first order and the first kind). According to interpolation from tab-les e.g. by Lofgren (1963) or directly from Roberts
(1966, table A-3): el==l.84l
This value, a= 0.95 m and h= 0.5-1.27 mwere used in (2.3) for calculation of fn==0.64 Hz in figure 2.3c. From the tangent hyperbolic function it is apparent that this frequency is almost independent of the li-quid height h if h:>a (tan h (l.84l)==0.951 and 0.990
<<tan h (d)<<l.0 ifcx>2.65). Of course this statement as well as the formulas (2.3) above and (2.4)below -- is based on no contact between the liquid and the upper boundary of the tank cylinder.
The formula for the lowest natural frequency in a
rectangular cylinder has been deduced from Lamb (1945) by e.g. Silvermann and Abramson (1966 - equation
2.130):
=
EM
wnRectangular
//%_ tan}1( a)
second
(2.4)
where a is the distance between the vertical tank walls perpendicular to the oscillation direction. Keeping h==0.95 m gives the frequencies fn==0.61 Hz and fn==0.89 Hz for a==l.9 m and a==0.99 m respecti-vely. Here the independence of liquid height occurs
13
for a slightly higher ratio between liquid height and tank width (notation h/a for rectangular and h/2a for circular cylinders).
Assuming that the tank is a 50% filled sphere (i.e. h/2a==0.5) with radius a==0.95 m, figure 2.2 (or Budiansky s table 2, p 170) gives the fundamental natural frequency:
fnsphere 50: =O.64 Hz (2.5)
Sloshing forces
The theory, applied above, is based on small amplitu-des and linearized equations. Therefore, the sloshing force from the liquid on the tank is not defined when the tank oscillation frequency is equal to the natu-ral frequency. So, the expressions given by Budiansky '(page 168, 169) for circular canals and spherical
tanks are of limited use for estimations of sloshing
force peaks in our application.
Nonlinear analysis allows calculation of sloshing
forces close to and at resonance. However, "the theory is quite complex in its analytical details and conse-quently good agreement with experimental data at.and beyond resonance is hardly to be expected" (quoted
i xnnAbramson,( ui & Kana 1966, page 781) which is
illustrated by figure 2.4.
The mechanical model approach see Dodge (1966) for
an extensive survey and Fontenot (1968) for an
analy-tical review is based on linear liquid motions.
Nevertheless,sloshing force calculation is possible at resonance. The slight damping, normally present in sloshing, can be treated by adding linear dashpots
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3
10 \'3 i
_ | 7Non - linear theo L X Non - linear theor
% 8 i )ix I ry 4% 8 T XXX /7 y S I E I % 5 i f A 8 I Ox E? 6 I f V § 6 a \ 2 | If 0 «9- O y 0K g A
3 .§\
g 43%
2 t g C 2 t 2 X C 8 .E 9. 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0Frequency parameter wzd/g Frequency parameter wzd/g
h/d = 1.0
0 Increasing frequency
x Decreasing frequency
Excitation
----/\mplitudc of liquid form: response in half-vylindrival tank for various excitaliun nmpiitmir s
Figure 2.4 Lateral force peaks in an upright circular
VTI REPORT NO.
cylinder with vertical splitter plate
parallel to excitation. From Abramson, Chu and Kana (1966) reproduced from Abramson, Chu and Dodge (1966).
15
to the spring-mass or pendulum elements. This method
is quite straightforward too, for an investigator
used to conventional road vehicle models. The compila-tion of models by Dodge or Roberts et al (1966) illu strates the influence from tank geometry on the mecha nical model parameters such as pendulum length, equi-valent masses, Spring and damping constants etc. How-ever, these parameters may be functions of the actual type of tank motion and have to be varied when oscil lation frequency or amplitude is changing.
Experimental verificationc fdestabilizing sloshing
forces, calculated by linear, nonlinear or mechanical
models at resonance, has been found only for accelera-tion amplitudes far below the overturning limit for
a road tanker but probably sufficiently large to be
pertinent for the stabilization of a rocket or space-craft . In figure 2.4a these sloshing forces are more than seven times larger at resonance than the inertia
force calculated for the same mass if it were rigid (index R) or "frozen" and fixed to the tank:
Using the symbols in figure 2.4, Newton s law yields
|F|==w2 XO-p1Th d2/4 (2.6)
and if the liquid height (h) is equal to the tank
diametre (d)
[F] =w2d
(2.6a) pgd3 g ol e M :with oscillation amplitude (XO/d) 0.00547 and
fre-quency parameter (wzd/g) 2.9, equation (2.6a) shows
that the frozen mass force parameter (lFl/pggd3) is
1.25-10 2. Corresponding sloshing force parameter is
approximately 9-10 2 according to the figure 2.4a.
16
Even larger force ratios between sloshing and frozen
masses are reported for spheres by Abramson, Chu and
Dodge (1966, fig 3.10). However, larger oscillation
amplitudes imply smaller force ratios, which is
apparent already for the comparatively small ampli tudes in figure 2.4, where the sloshing force para-meter peak is almost insensitive to the amplitude in contrast to equation (2.6a).
This limitation in known data - together with the lack of comprehensive and general results for horizontal cylinders - supported the decision to put emphasis on
model experiments in our main investigation, described
in chapter 3.
Damping of liquid motions in a container
In an extensive survey of liquid motion damping, Silverman and Abramson (1966b) stated that: "The
term damping is generally employed to describe the fact that some energy dissipation always occurs du ring fluid oscillations". One way to quantify damping is by measuring the decrement per cycle of sloshing
amplitude (e.g. liquid surface level or sloshing for-ce). However, Abramson, Chu and Dodge (1966) pointed out that overzealous attempts to introduce damping or decrease structural weight by perforation of existing cross walls can easily negate the upward shift in re-sonance frequency, otherwise provided by compartmen tation. Thus, the efficiency of damping devices should not be characterized by the amplitude decrement only. In our application it is also necessary to know about the sloshing force peaks during forced oscillations -e.g. their duration, amplitude and phase.
Some favourable effects from compartmentation in gene-ral are illustrated by Bauer (1972) for a rectangular
l7
cylinder: Subdivision of the container by cross walls increases the fundamental natural frequency - see fi-gure 2.5a and equation (2.4) - and reduces the so called sloshing mass, thereby enhancing the vehicle stability.
Another survey on anti slosh devices in upright cir-cular cylinders has been compiled by Roberts et a1
(1966). Apart from the references above, a sample of model experiments with general interest may include the works of Silveira et a1 (1961 - upright circular
cylinder), Stofan and Sumner (1963 - sphere with
diaphragm) and Sumner (1964 - sphere with ring baff-les). u(%)1.0 w¢m 5 >
.e
a
4 _ u t 34-/El]}]
\ L.- a c4 1 1 l 4 l 2 3 .4 5 "Fundamental natural frequency for compartmenth tanks
m r_______ -45.,____
"'5 1 tanh a-___.,=1
Elal 1+ tanh [1m
u = NUMBER OF COMPARTMENTS 0 4 J J l l l .4 .5 .5 .3 '1 a
Reduction of fundamental sloshmasy by additional cross walls
Figure 2.5 Effects of compartmentation for varying
liquid height (h). COpied from Bauer
(1972) by kind permission from Swets &
Zeitlinger.
18
Road tanker oriented investigations
Apart from the references given in chapter 1, a few reports will be mentioned below dealing particularly with the lateral stability of road tankers.
Gustafson and Gustafsson (1969) presented an extensive practically oriented survey of the overturning problem for heavy vehicles in general. They pointed at several
countermeasures with emphasis on vehicle design and confirmed some of their theory by brief reviews from
five overturning accidents with road tankers. Steering wheel motions and rolling resonance were supposed to
coincideai11cnm3 roundabout. accident. However, no
attempts were made to quantify the contribution from liquid motions. Their conclusions on lateral acce-leration ratio between truck and trailer must not be regarded as general (sideslip angles neglectable only for low speed and small curve radii).
Isermann (1970) computed the overturning limit for
some tank semitrailers during steady state cornering. Full scale measurements with static g-simulation were used for validation. Emphasis was put on improved overturning stability by prOper adjustments of the spring characteristics for each individual axle. The
evaluation included other technical measures too,
and the report is a valuable review indicating how much the overturning limit can be increased by reason able improvements in vehicle design. The mathematical
models of liquid centre of gravity deviations see
figure 2.6 etc might as well be of interest in
cer-tain applications. However, Isermann treated steady state conditions only and he did not analyze the in-fluence of tank compartmentation or similar counter-measures against lateral load transfer due to liquid
motions.
19 "I (3 <3
tn vvv I Y T I l a), I 0.21 9°/ 5° , ' Fallungsgrad 013 --A---1 mm Fullungsgrad E: 0.137] - mm 0.7!_._° ._
; 04° Me/onrro . l :. _ .: Aus leichskurvon i ; 500 Bohdlterdurchmessor: 503 g , I / ; 2100 mm l J to. I I I ~ l Bend/pernqgung; 9°/ Bohdlrerbreife: 2330mm / g u n . -~ I : / E '7: m 6. ,t I . 99 z 3 I g 'lhl'l . A/ G .D U" z, ' m . B x 5°/ be 0 (a A ,/ C k go 3 I, / I» / LL / I ! % 5° 5 N " / on d w / gt a / b 300 I I ,I . o, E c / r// I I w 00 E / / of / a, / A [/g 3 5. / I / o > L I /\ / v, o 5/ 3 2200 ,i. ' Inf /_1 / C ° " / . o a E y x/4'/.) .¥-/"°r Ao/ . ' u ." 3 ° . E ,4/ i/ .2 k m /_/y . / s " / 4% x (n U)u :00 . / ' /
0 0,! 0,2 0,3 0 0,5 0 0,] 0,2 0,3 0,1 0,5
B z°g°" Querbescmeunigung 7-0/9 Bezogene Ouerbeschleunigung q- a/g
Bild 13. Querschnittsformen der untersuchten Fl ssigkeitsbehélter Bild 14. Horizontale und vertikale Schwerpunktverlagerung der Bild 15. HorizontaIe und vertikale Schwerpunktverlagerung im
sowne Bezeichnungen zur Kennzeichnung der Lage der Schwer- Fliissigkeit in Behéltern mit kreisférmigem Querschnitt bei ver- Behélter mit einem Ouerschnitt entsprechend Bild 13 b bei
ver-Punkte V0" Flilssigkeit und Behélter schiedenen Neigungswinkeln der Behélter schiedenen Neigungswinkeln des Behélters
Figure 2.6 Horizontal and vertical c.g. displacement
during constant lateral acceleration
(a,m/s2). COpied from DEUTSCHE
KRAFTFAHRT-FORSCHUNG UND STRASSENVERKEHRSTECHNIK Heft 200 (paper Isermann) by kind permission from VDI-Verlag GmbH D sseldorf.
The same limitations - steady state and no compart
mentations applies to the analysis of Guerin (1975).
Guerin reports overturning limits - as maximum lateral acceleration and maximum speed at different curve
radii - for different vehicles and load volumes.
Bauer (1972), on the contrary, made a thorough
mathe-matical analysis for different container geometries with oscillating liquid load. Natural frequencies,
forces and moments are presented in generalized mathe-matical expressions based on the theory of liquid mo-tion with a free surface and on a mechanical model. The improvements from compartmentation are illustra-ted and explained - see chapter 2.3 above for further details. However, the analysis is valid for small oscillations only, and further work is necessary to
2'0
interpret the results in terms of road vehicle over-turning stability.
Slibar and Troger (1975,76) oriented their paper towards
road vehicle behaviour. They even present lateral wheel load transfer ratio which is synonymous to our overturning factor (see appendix D.3 or e.g.
Strand-berg, 1974). Their mathematical analysis concern a
tractor semitrailer with different load distribution
among the five chambers in the tank conventionally
separated by vertical transversal walls. The forces and moments from the liquid load for harmonic oscilla-tion steeringenxaintroduced by the mechanical model approach ~ whichanxaintended mainly for small ampli-tudes. Each chamber has one rigid and one laterally
moving load mass. The moving masses being restrained
by linear springs and dashpots. Slibar and Troger found large influence from load conditions and di-stinct load transfer peaks for steering frequencies about 0.3 0.4 Hz. The high dependance on speed is not astonishing as the steering amplitude (and not the manoeuvre lateral acceleration peak) seemingly was kept constant. Unfortunately their quantitative re sults must be questionned as the printed mathematical expression for semitrailer roll motion lacks terms for gravitational force moment about the roll axis from the liquid load masses. These moments seem to be very important according to our model experiments -see chapter 4.
Full scale dynamic experiments were performed using a
truck with outrigger in a double lane change manoeuvre.y See figure 2.7 euui Jansson (1973). The purpose of
the experiments was to investigate the overturning stabilizing effects from anti-roll bars compared to baffles. The results should contribute to the details of a legislation prOposal in Norway.
21
Figure 2.7 Full scale double lane change experiments.
3 and 8 m3 water load
The tests were performed with 6 m
occupying 50% and 75% respectively of the tank volume. The vertically mounted longitudinal baffles covered 50% of the longitudinal section area at both sides 0.4 m from the symmetry axis of the tank. The cross-section contour was similar to the so called "elliptic" tank model mentioned in the following chapters. The roll
stiffness without anti roll bars was l.l-lO5 Nm/rad in the front and 3.0-105 Nm/rad in the rear. With
ri-gid fitting the anti-roll bars would have increased the roll stiffness with 3.6-105 Nm/rad in the front and 2.9-105 Nm/rad in the rear.
The trajectory was defined according to figure l.la
or D5 with the lateral translation peak 8.8 m and
with the manoeuvre length 80 m. Thus variation of speed caused variations of lateral acceleration peaks and oscillation frequency. Unfortunately the real manoeuvre frequencies seem to have been too low for
22
liquid resonance and low enough to make high roll re-sistance and anti-roll bars favourable. This evidence is supported by the results from our scale model simu-lations performed later and reviewed in the following chapters.
These frequency relations and the uncertainty in Opti-mal baffle design must be kept in mind when
interpre-ting the results in the table below from Jansson (1973).
Load Anti_roll Overturning speed
km/h
volume bars
% No baffles With baffles
50 No 33 38
50 Yes 45 Not tested
75 No 32 35
75 Yes 42 45
23
INVESTIGATION PROCEDURE Investigation phases
Even if the main method will be outlined below, some other methods have been used and will be referred to in the result chapters 4 and 5. Thus the
investiga-tion history is overviewed here - see figure 3.l.
Eb§§§_£
After the problem statement and a primary literature
survey - see chapters 1 and 2 - some preliminary
scale model experiments were performed.
The tank motion system was almost identical to the
one used later in phase II and III. See figure 3.2
and 3.3. However, the power source was a lathe
instead of the computer controlled hydraulic servo. This allowed only discrete oscillation frequencies and stroke lengths for the sliding platform. As the tank motions had to be reproducible, only stationary quasi-harmonic motions were possible. Unfortunately the mechanical arrangement could not produce suffi-ciently symmetric motions. This drawback was serious as the tank was suspended by only two force
trans-ducers (outputting FA and FB in figure Cl). Therefore,
the interesting forces and moments from the liquid
could not be evaluated. In addition, this phase offered
only diagram recording on paper not compatible to
computers. So, the equipment had to be completed to
allow easy and continous evaluation of important
variables - like time overturning risk; factor' for
example. Anyhow approximate evaluations indicated sloshing effects that were large enough to support
further work.
24
PROBLEM STATEMENT Ch 1
LITERATURE SURVEY Ch 2
PRELIMINARY SCALE Unpublished
H MODEL MEASUREMENTS data
a - Power source: Lathe ggmpare
< igure 3.2
{I}
m Only two force transducers - Circular tank only
MATH MODEL, METHOD & Figure 3.2 & 3.3 EQUIPMENT DEVELOPMENT App B, C, D
ANALOGUE COMPUTER App E
PROGRAMMING
MEASUREMENTS, EVALUATION & Ch 4 PRELIMINARY SUGGESTIONS App F : Lateral harmonic or DAVIS motion
m Strandberg,
g ' Three tank cross sections NordstrOm &
m Nordmark (1975)
m - Frequency and load volume varied
- Overturning but not skidding risk evaluated - Countermeasures in vehicle design suggested - Continued experiments outlined
IMPLEMENTATION ON HYBRID COMPUTER. Lidstrém COMPLETION OF METHOD AND EQUIPMENT (1977b) MEASUREMENTS, EVALUATION OF Ch 4 BAFFLE INFLUENCE, CHECK OF
PHASE II
. . . . LidstrOm
. Harmonic motion, Ielliptic tank onlyI (1977a)
H 3 4 cross wall/baffle configurations
H
H - Frequency, acceleration peak and load volume varied
m
2 - Overturning and skidding risk factors evaluated
m _
0.4
STEADY STATE OVERTURNING Ch 4 LIMIT CALCULATION
- Circular and rectangular cross sections LidstrOm (1976) Compartmentation, load volume and roll resistance varied'
SUMMARY OF PHASE II & III Ch 4 >> RESULTS
H
gg CONCLUSIONS, SUGGESTIONS Ch 5
d .
33 DISCUSSION, MODIFICATIONS Initialized
RECOMMENDATIONS by sponsor
Figure 3.1. Investigation phases
25
Figure 3.2. Laboratory equipment with circular tank
model.
Eh§§§£l
The figure 3.2 3.3 equipment and computer programs,
develOped after phase I, will be treated below. During the development stage it was not decided whether our
analogue computer EAI 680 shouldlme expanded to the
hybrid system EAI Pacer 600 which is available now at the institute. So, phase II was prepared and completed when the computer was a pure analogue.
Three different tank cross sections were investigated with different liquid load levels and different
oscillation frequencies. The motion was either harmonic oscillations or a double lane change manoeuvre - called
VTI REPORT NO . 138A / FO RC E TR AN SD UC ER S A C C E L E R O M E T E R J
LA
BO
RA
TO
RY
\
I
E Q U I P M E N T * 4% "m H Y D R AU L I C "" J Hz;
A
'6
K
//
//
//
//
//
//
//
//
//
//
//
/
/
/
/
/
/T
//
//
//
(-Ii 7 EL IM IN AT IO N OF : LI QU ID FO RC ES AND MO ME NT IN TE RFAC E TA NK IN ER TI A FO RC ES RE FE RR ED TO TA NK CE NT REA}
S C A L I N G S C A L I N GU
A N A L O G U E V E H I C L E M O D E L V E H I C L E M O D E L C O M P U T E R { I N D E X 0R " I N D E X OS O P E RA T I O N SU,
[
I V E H I C L E M O D E L / IN DE X P R Z ) E V A L U A T I O N P R E D E T ER M I N E D M A N O E U V R E D A V I S O R H A R M O N I C R E C O R D I N GK
V
e
F i g ur e 3. 3 E xp e r i m e n t a l c o n f i g ur a t i o n a n d c o m p ut i n g s c h e m e in p h a s e II 2627
DAVIS motion according to appendix D.9. For comparison the overturning risk factor was computed for a rolling
vehicle with the same load rigidly fixed to the tank.
The results - see appendix F - indicated that the liquid motions can increase the overturning risk more
than what was expected according to previous studies.
Some countermeasures were suggested, but it was agreed that further studies were desired before final
recommendations could be given. So, the efforts were
concentrated on the phase III program and conversions
for the now available hybrid computer. Thus only the
main conclusions were published at that stage Strand
berg et al (1975, chapter 4.4).
Phase III
The phase II results and conclusions were similar for
both DAVIS and harmonic motion. Thus it was decided to use only harmonic motion in phase III in order to allow the scale model measurements to be performed
off-line with input from a sine wave generator.
Force and acceleration (analogue) data were recorded on magnetic tape for processing later in the hybrid computer. This processing included the same computer
operations as before - see figure 3.3 - even if they
were facilitated and speeded up by the new digital/ hybrid equipment installed at the institute at that
time. The computer equipment improvements made it
possible to put additional parameters and variables into the analysis.
Apart from checking previous experiments on the
influence from oscillation frequency and load volume, the effect from acceleration peak value and cross
wall/baffle configuration were investigated. In addi
tion the skidding risk factor was introduced as another
28
dependent variable, thereby expanding the study from pure overturning problems. See Lidstrom (1977a, b)
for further details.
Bauer's (1972) results on compartmentation of
rectangular tanks see figure 2.5 - were supported
with lower risk factors and higher resonance frequen-cies even for the "elliptic" tank cross section,
which was the only one used in the phase III laboratory
experiments. However, it was not perfectly clear how
much the centre of gravity shift in itself contributed to the overturning risk factor compared to the dynamic
sloshing forces.
Therefore, this phase was terminated by computer
calculations of the steady state overturning limit for circular and rectangular tanks with different compartmentation. The load volume and roll resistance were varied, as well. Results have been reported by Lidstrom (1976).
Phase IV
The conclusions and suggestions in this report are
based on the mentioned investigations and have been
treated as a separate phase.
Computer evaluated measurements on scale models
- benefits and drawbacks
The critisism in chapter 2.4 indicate why we found it necessary to complete the pioneer works of the referred authors with scale model measurements evaluated by computer.
29
Compared to mathematical model investigations the scale model technique:
a) allows studies of tank cross sections with specific
complicated bwundaries and v i m baffles or
walls to prevent sloshing
b) enhances the application area due to the absence
of certain assumptions such as non-viscous
fluid, small amplitudes etc
c) requires data storage or a fast on-line computer
- in addition to the computer for evaluation of how the liquid forces affect the vehicle (which is a prerequisite for mathematical model investi
gations, as well)
d) restrictst madegrees of freedom if not the tank suspension and motion system can be very sophisti cated and expensive
The possibilities a) and b) have not been utilized to their full extent in our investigations. But the
methods and computer programs are completely presented
in the appendices and by Lidstrom (1977a, b). Hope-fully this will facilitate further studies on new tank geometries, longitudinal slosh suppression, and
on more viscous liquids.
It seems reasonable qrconscious.tank manufacturers
to use this method for optimizing the tank design.
Our hydraulic servo can be substituted by much more
simple mechanical oscillators (compare our phase I
lab equipment described in chapter 3.1). In addition our analogue/hybrid computer is unnecessarily flexible and expensive for this application. The vehicle models
and evaluation circuits or programs in the computer
(appendix E) may be substituted by micro computer
30
components or electronic circuitry. Or - if there is no requirement on immediate results - data storage and off-line computer evaluation can be used: see Lidstrom (1977b).
The drawback d) above is most serious for the roll degree-of-freedom and its interaction with sloshing, which could not be studied simultaneously due to
servo accuracy limitations. Even yaw, pitch, vertical and longitudinal motions of the tank were neglected, but thisxwuson purpose for isolation of the lateral sloshing and overturning problem. Anyhow, these limitations and their consequences for the results will be touched upon page 38 and 40.
Vehicle and tank configurations
The cross sectional shapes of the three model tanks used in phase II are drawn in figure 3.7 below. The tanks will be called for short
C - circular (full scale inner diametre 1.9 m) E - "elliptic" (do. width 2.3 m & height 1.5 m)
S - "superelliptic" (do. width 2.4 m & height 1.1 m)
even if the E and S tank contours are not exactly
elliptic or superelliptic in the mathematical sense. During computation - see figure 3.3 - the liquid
forces were modified to represent tank lengths giving identical inner volumes for all three tanks.
In phase III the E tank was equipped with different longitudinal cross walls/baffles without perforation according to figure 3.4
31
A
m
1.05m
(j 2.26 m :3 1.12 m 1. 471E. "Elliptic" tank without Vl. One vertical wall
baffles or cross walls
I *s
E
.48m4.55m
\
1.13 m a .55m .55m
_.
J
'
\____,/
H. Horizontal baffle V3. Three vertical walls
Figure 3.4 Longitudinal Cross walls and baffles in
the E-tank during phase III. Tank for 50% and 75% load volume.
Because only lateral tank motions were applied, no model tank was compartmented longitudinally with
lateral-vertical walls and the length was kept constant. However, the full scale length could be varied in
the computer by calculation of liquid. forces etcetera
per length unit of the tank. So, in phase III
longitudinal compartmentation was investigated by the
computer without additional lab experiments at least
from one point of View: What is the difference bet-ween an uncompartmented tank with 75% liquid load volume and a longitudinally compartmented tank with the same total load filling one compartment to 100% and the other to 50%? Answer is given in figure 4.12
and hinted in figure 3.5.
32 lOO+-0% lOO+-50% m o G o
8
MORE UNSTABLE 3 (see chapter 4) H .pB
<At resonanceFigure 3.5 Schematic liquid volume distribution with
longitudinal compartmentation in phase III. Viscosity scaling rules tell us that the model liquid being used (water) represent a wide area of full
scale liquids in this application, as viscous forces are very small compared to inertia forces. Appendix B.4 explains why these results are representative for most road tanker transported liquids,having their
-3 m /s.2
Examples with viscosity at normal transportation viscosity in a range up to 100 c St = 10
temperature increasing from 1.12 c St to 900 c St are: mercury (Hg), condensed oxygen and nitrogen (02 and N
water (H20), ethanol (CZHSOH), gasoline, diesel oil,
2)!
fuel oil.
The results are independent of liquid density if the tank length is regarded to give 100% load volume for
20 000 kg load mass for every liquid. For example
33 7.7 m Circular tank 3.8 m 7.9 m "Elliptic" tank 3.9 m / 9.5 m "Super- 1 4.7 m \ elliptic" _1:;:)_r~ g Kg tank 4]
Figure 3.6 Examples of vehicle configurations
repre-sented by the simulations. The indicated tank inner lengths correspond to liquid
density 920 kg/m3 and gross weight 10000
kg per axle at 75% load volume.
fuel oil with density 920 kg/m3 requires 21.6 m3 tank
volume and 7.9 inner length for the E tank see
table D2 and figure 3.6.
The data and computer programs for the tank carrying vehicle was outlined from previous experience and
measurements on heavy vehicles in general. As no yaw
motions or wheel steering were simulated,t
m2mathema-tical model can represent either a truck or a semi trailer as well as a full trailer. Anyhow, data were selected for a typical full trailer with two axles carrying 10 000 kg each when the liquid load occupied
34
75% of the tank volume. The empty trailerweight was
assumed to be 5 000 kg. However, the results are valid even for e.g. aone axle trailer if its gross weight is 2 500 kg empty and 10 000 kg with 75% load volume - providing its c.g. and tank centre height, track
width etc is the same as for the bigger trailer.
As the following data are very important for the over turning stability, the selection of their numeric values is discussed somewhat more in detail. See appendix D.8 for further data.
The effective track width (2c) has been found by
Nordstrom et al (1972) to be remarkarkably small
(hereik:= 1.8 m) compared to maximum allowed vehicle width (2.5 m in Sweden).
The tank centre height above the road surface was assumed to be 2.0 m for the circular tank. Keeping the circular and the "elliptic" tank bottoms at the same height caused the E tank centre height to be 1.8 m above road level. With the same condition the "super elliptic" tank centre would be even lower. But due to its possible need for a supporting frame structure it was assumed to have the same centre height as the E tank. 2.3 m 2.4 m 2.1 m E 4 § 7 2.3 m E Area % A Z go 2 I . rea . m a
F;
_L
C-circular E-"elliptic" S-"superelliptic"
8
Figure 3.7 Tank inside cross sectional shapes and
centre heights. Liquid free surface widths indicated for 75% load volume.
35
The centre of gravity for the empty vehicle was
assumed to be 1.17rnabove road level. However,
deviations from reality for the empty vehicle mass and its c.g height is of minor importance in a loaded vehicle as the product of mass and c.g. height is much larger for the load than for the empty vehicle.
Roll resistance, roll axis location,roll moment of inertia, and other roll motion characteristics could
not be combined with sloshing force computations. And even if they are important for the overturning stability, the discussion on their selection from appendix D will not be reviewed here.
Manoeuvres and risk criteria
As mentioned above,harmonic oscillation H or a double lane change manoeuvre D (see figure 1.1 and D5) were used as inputs to the tank motion platform. These in-puts were considered to be sufficiently revealing when the lateral stability with sloshing load or a rolling vehicle should be compared to that with a nonrolling vehicle with rigid load. The term 'lateral stability'
is used in a nonmathematical sense, more connected to
the real-life overturning or skidding problem than e.g. to damping of small oscillations in the liquid. The so called overturning factor (R) is defined by
l__Instantaneous wheel load on left Slde) (3 l)
R::ABS(
Static wheel load on left Side
When R approaches unity, the vehicle is close to inner wheel lift and overturning. In some figures R is used without the absolute value Operation. Then R < 0 usually corresponds to a right hand turn.
36
Of course R is dependent of the lateral acceleration amplitude. Thus it was necessary to find some kind of
normalized measure of the overturning stability.
Therefore we defined the overturning limit (SALIM) as
the lateral acceleration when the vehicle overturns,
i.e. when R = 1.0.
In phase II,when the lateral acceleration interval was
small, normalization was made by computing a corre Spondence to the overturning limit from the formula:
Sl naj<
SALIM : 12
Ina):(3'2)
where SAmax is the lateral acceleration peak during the same manoeuvre where the overturning factor peak Rmax was measured. A more precise method to find SALIM was used in phase III by Lidstrom (l977a)- see figure 3.8.
Overturning limit SAL IM
4 m/s 1. / O. // Harmonic oscilla-//7 tion frequency m g3 As0.3 Hz H 00.4 Hz 0 0 HZ 4; ' 00.6 Hz 3 V0.8 Hz U J @ c H 0. E / 3 /// 3 // > O O. 4 m/s2 Lateral acceleration SA
Figure 3.8. Determination of the overturning limit for different harmonic oscillation frequencies.
50% liquid volume in "elliptic" tank
with-out baffles or cross walls. Filled symbols from Lidstrom (1977a). Unfilled symbols
co-ver results from phase II see table F5.
37
The demand on side force in the tyre/road contact areas was evaluated in phase III and normalized by division with the simultaneous vertical force. Thus
the expression for the demand on side force coefficient (SC) yields:
m ' SA - F Y
SC (m+ml) g _ de (3.3)
where
g is the gravitational acceleration 9.81 m/s2 m is the empty vehicle mass
ml is the load mass
Fy is the resultant force to the left from the liquid load
de is the resultant upwards force from the load after subtraction of gravity force
SA is the lateral acceleration
As the ayailable sideiknxxacoefficient depends mainly on the road surface the SC values have not been norma-lized to any kind of skidding risk factor. Thus
SC-peaks are always presented together with the SA peak from corresponding manoeuvre. Thus increased skidding
tendency due to sloshing can be identified for every experiment where the SC value is above SA/g, which is the nominal demand on lateral friction coefficient in the actual manoeuvre without sloshing.
According to next chapter different tank designs,
load percentages and manoeuvre parameters were compared
- primarily with the aid of the mentioned SALIM and SC values. In addition the sloshing effect on Rmax was quantified by the so called sloshing factor:
38
R
SFAC = _2§_B§EE (3.4)
OR peak
where the peaks are from the same part of the manoeuvre
but do not necessarily occur at the same time. The
indices refer to different vehicle models - see figure 3.3.
OR - Zero roll angle. Rigid load
OS Zero roll angle. Sloshing load
TR - Rolling vehicle. Rigid load
Apart from the ratio between the peaks of the
overtur-ning factors (ROS and ROR) also the instantaneous
ratio and the time lag between successive peaks are
S OR and that the
driver adjusts the steering according to the vehicle's
of interest. Assume that RO lags R
response and behaviour without perceptible sloshing effects (probably corresponding to the perception of ROR - synchronous stimuli from the driver s seat). Then the real overturning risk peak occurs unpredicted and maybe during a more severe manoeuvre than what the drivers unfuihave initialized with predictable sloshing effects. Compare the phase portraits a and
c in figure 3.9.
Unfortunately it was not possible to simulate a rolling
vehicle with sloshing load. For comparability - and
sometimes for computing stability the predetermined
lateral acceleration (SAL in figure Dl) had to refer to a part of the vehicle that was not rolling. Then
the lateral acceleration of the tank centre (SAO)
- which included a roll component - would not be independent of the vehicle model and the sloshing forces. This made closed 100p computation necessary - figure D2. However, the accelerometer feedback to the hydraulic servo was not a successful strategy and
these simulations had to be cancelled.
VTI REPORT NO. 138A R V OS ] -F i g ur e 3. 9. O ve r t ur n i ng r i s k f a cto r wi t h slo s h i n g l o ad (R o f a) b) c) '0 Po 0 V O O N O O do. 50 % 75 % 50 %
__1P.
wit h c o r r esp o n d i n g r i g i d l oad (R OR ). C i r c ul a r t a n k , h a r m o n i c m ot i o n " E l l i p t ic" ta nk , D A V I S m o t io n " S up er e l l i p t i c " ta nk , h a r mon i c m o t i o n OS ) as a f un c ti o n O sc i l l a t i o n f r e q ue n c y 0. 4 Hz. 3940
In simulations with @R-models, the peaks of SAO were sometimes more than twice as large compared to the SAL peaks. Therefore Open loop computation, based upon the approximation SA sSAL, is not an acceptable way to simulate rolling vehicles with sloshing load. It is also apparent that the overturning factors and side force coefficients evaluated from these experi-ments are smaller than in reality when rolling and
sloshing interact. Thus the overturning and skidding limits presented in next chapter should be regarded as Optimistic for the vehicles and manoeuvres in
question. Anyhow the rolling effect on Rmax was
quantified by the rolling factor:
R
KFAC = 33
(3.5)ROR
evaluated in the same way as the sloshing factor in eXpression (3.4) above.
The absence of yaw in the simulations may cause too Optimistic conclusions, as well. In a real road tanker with conventional compartmentation (transversal walls), yaw motions can increase the lateral acceleration in one compartment above the value for the vehicle's centre of gravity. Then the elasticity of the vehicle struc
ture may contribute to cause wheel lift on one axle, skidding and overturning - even if the remaining
com-partments are empty and our simulations indicate a safe reSpons for the actual manoeuvre.
Validation
Magnetic tape recordings were kindly supplied by AB Volvo from the full scale experiments mentioned on page
20 22 for validation of our modeling technique.
Un-fortunately their double lane change lateral amplitude had to be so large (because of limitations in power and forward speed) that it was not achievable in our tank motion system. SO, the validation procedure had to be
limited to resonance frequency comparisons from slalom driving in these full scale experiments and similar data
from the references.
4l
INFLUENCE ON OVERTURNING AND SKIDDING TENDENCY
Manoeuvre peak acceleration
Of course, the overturning factor (R) as well as the
side force coefficient demand (SC) are directly pro-portional to the lateral acceleration (SA) for a non rolling vehicle with rigid load (index 0R). See
equations (D.4), (D.ll), (D.lZ) and (3.3).
PrOportionality for R and SC in relation to SA exists even for the rolling vehicle with rigid load (index WR) - provided the oscillation frequency is unchanged.
However, the prOportionality constants are usually
larger i.e. R and SC are larger with roll than
with-out for a certain SA. This is illustrated by table F4 page 2 where the rolling factor - column KFAC==RPR/ROR according to equation (3.5) - exceeds unity for every experiment. See also figure 4.13-4.16.
Controlling the risk factors in a somewhat prOportional manner from the perceived acceleration amplitude is
probably a well established behaviour among drivers
-provided speed and oscillation frequency are kept constant. Compensation for the quite linear rolling
behaviour seems to be possible, as well, for a
skil-full driver. But the sometimes extremely nonlinear
- sloshing effects will require superhuman predictions
and efforts in certain cases.
The frequency dependence may be the most serious irre gularity, but nonlinearities occur even in the R(SA)
diagrams - see figure 3.8 and 4.1. Compare the linear
behaviour for 0.3 and 0.8 Hz with the nonlinear for 0.5 and 0.6 Hz. Similar nonlinearities for frequencies close to resonance are present for most of the tank configurations and load conditions investigated by
Lidstrom.
42
A 50% Load 75% Load 4 - 4. .5 Hz 3_ 3-m Of. 0 O B j 8 E 2 E (.9 L9 2 . 2 H H II: :I. 8 8 A l - a U) U) 0 I I l > 2 I I l t 1.0 2.0 3.0 m/s 1.0 2.0 3.0 m/s2
LATERAL ACCELERATION LATERAL ACCELERATION
Figure 4.1 The sloshing factor - see expression
(3.4) - as a function of the lateral
acce-leration peak level. "Elliptic" tank in different harmonic oscillation frequencies. From phase III and Lidstrom (1977b).
:1
il.
,a$a% fi
Figure 4.2 Paper records from harmonic oscillation
with 50% liquid volume in circular tank. a) 0.3 Hz (experiment no. 65 in appendix
F tables).
b) 0.4 Hz (experiment no. 63 in appendix F tables), phase portrait in figure 3.9a.
may be seen as irregularities in R 43
The nominal manoeuvre peak acceleration for the roll axis in a rolling vehicle is amplified if we move to the tank centre. See figure 4.14 or SAFAC in the 2nd page of table F4. Therefore the sloshing load in a
(real) rolling vehicle is subjected to more severe mo tions than what could be consistently applied to the tank model in these experiments. Thus the real (roll and slosh combined) overturning stability - and proba-bly the skidding stability as well, according to
Lidstrom's data (1977b) - must be even more poor than what is evaluated below for the nonrolling vehicles with sloshing load.
'Manoeuvre oscillation frequency
The vehicle behaviour is highly dependent on the oscillation (steering) frequency components of the manoeuvre - especially if the load can move relative to the vehicle. Partly loaded road tankers manoeuvering with comparatively low frequency components - or cor-nering with constant radius and speed (zero frequency) - will be subjected to lateral liquid motions within
OS) to
see fi-the tank, causing fi-the overturning risk factor (R be larger than if the load were rigid (ROR)
gure 4.2. In our diagrams the spontaneous sloshing
OS superimposed on the fundamental oscillation excited by the tank motion and illustrated by ROR.
When the steering frequency is close to the natural oscillation frequency, the liquid mass will act like a
pendulum swinging with the vehicle. This will result in a distinct increase in load transfer and overtur-ning risk factor as well as sideforce cOefficient demand. Compare a and b in figure 4.2 where b would
have shown larger ROS peaks if the frequency had been
