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STATENS VAG- OCH TRAFIKINSTITUT National Swedish Road and Traffic Research Institute

THE DYNAMIC STABILITY OF HEAVY VEHICLE COMBINATIONS by

Olle Nordstrom and Lennart Strandberg

A paper presented at the

Third International Conference on Vehicle Systems Dynamics August 12-15, 1974. Blacksburg, Virginia, USA

REPORT No. 67 A

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STATENS VAG- OCH TRAFIKINSTITUT

National Swedish Road and Traffic Research Institute

THE DYNAMIC STABILITY OF

HEAVY VEHICLE COMBINATIONS

by

Olle Nordstrém and Lennart Strandberg

A paper presented at the

Third International Conference on Vehicle Systems Dynamics August 12 15, 1974. Blacksburg, Virginia, USA

REPORT No. 67 A Linkbping 1975

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IO I] I2 I3 I4 0 d wi g -. d. is ?» CONTENTS Abstract Introduction Test method Test manoeuvre

Dynamic stability criteria

Main structure of mathematical vehicle. model and computer program Tyre-road contact forces

Side forces Traction forces

Wheel loads and overturning risk Inverse steering procedure

Mathematically defined test course

Validation of the mathematical model Full scale tests

Validation

Single vehicle parameter variation

Comparative studies of I8 m truck-full trailer and tractor-semi trailer-full trailer combinations with different length distribution

Comparison, between truck-full trailer combinations

Comparison between tractor-semitrailer-full trailer combinations Comparison between truck-full trailer and

tractor-semi trai Ier-full trailer combinations Influence of load distribution and weight

Axle load distribution of the trailer in a 24 m truck-full trailer Load location on the semitrailer of a

24 m tractor semitrailer-full trailer

Load location on the full trailer at a tractor-semitrailer full trailer Load Weight and load distribution between

semitrailer and full trailer in a 24m combination Influence from speed

Influence from number of articulations

I4 I9 I9 20 20 22 22 22 23 24 26 3O

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15 16 17 18 19 20 21

.3?

3 ;

Proposed demands on dynamic stability of heavy vehicle combinations 3] Measurements of static overturning limits

High speed off-tracking

Proposed complementary demands on overturning stability and high speed off-tracking

Test methods

Discussion on demands on dynamic stability during braking Suggestions for Future research

Notation References

Appendix

General vehicle data

Tyre side force measurement

32 34 34 35 35 35 37 38 4O 4O

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ABSTRACT

The object of the investigation was to develop criteria suitable for regulations on the dynamic stability of heavy vehicle combinations. Demands for type approval are proposed in this paper.

A double lane change manoeuvre was chosen as critical for evaluating the dynamic beha-viour. ltwas carried out on a seven metres wide road with the lane off-set being three

metres .

The investigation included digital computer simulations and ful scale field tests. The field test recordings are used for validation of the simulation model. The vehicle model has non-linear tyre characteristics and includes roll but not pitch motions. By an inverse method the appropriate steering angle is computed in order to give the tractor a prescribed lateral acceleration time history .

For the evaluation the Following risk variables are chosen: 1) The slip angle maximum for each axle, 2) The lateral deviation maximum for each axle, and 3) The overturning risk maximum for each axle or vehicle unit. The simulation results show the influence from speed and. from a number of vehicle parameters . They are also used for comparing different types of combinations .

The dynamic behaviour ofthe tractor+ semitrailer+ full trailer combination is found to be speed dependent'and inferior to comparable truck + full trailer and tractor +

semitrai-ler combinations .

The double lane change is proposed as a test procedure for the dynamic stability of heavy vehicle combinations. The manoeuvre should be performed at 70 km/h with full load, and maximum allowed center of gravity height. Certain maximum values on the mentioned risk variables must not be exceeded for approval.

The problem of off-tracking towards the outside of a curve due to the side slip angles is also discussed, and a steady state test is proposed to assure that this off-tracking is kept within safe limits.

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In addition to these studies a full scale investigation was made of the static overturning stability of some heavy trucks, tractor+ semitrailers and full trailers at maximum allowed weight and varying centre of gravity height. As a result of this investigation a full scale static overturning stability test is proposed.

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THE DYNAMIC STABILITY OF HEAVY VEHICLE COMBINATIONS

By OIIe Nordstr oml) and Lennart Strandbergz)

National Swedish Road and Traffic Research Institute 5-114 28 Stockholm Sweden

INTRODUCTION

At the moment no regulations concerning the dynamic behaviour of heavy vehicle combinations exist in Sweden. With increasing traffic density and the development of longer and heavier vehicle cornbina tions the need of such regulations has become

more and mo re obvious.

In I970 the Swedish Department of Transportation contracted the National Swedish Road and Traffic Research Institute to make the necessary investigations to develop a test procedure for control of the dynamic stability of heavy vehicle combinations and to propose demands which have to be fulfilled for type approval. Furthermore the dynamics of the vehicle combination tractor-semitrailer-full trailer was to be studied with respect to speed dependance and to be compared to truck-full trailer

combinations .

The scope of the investigation was mainly restricted to manoeuvres not involving braking and only three types of vehicle combinations were taken into account, namely

I Tractor-semitrailer 2 Truck-full trailer

3 Tractor-semitraiIer-full trailer (double bottom)

Some general discussions Concerning braking problems based on literature studies were included in order to complete the picture of the problem area.

I)

2)

[M Sc, Chief Engineer M Sc, Senior Engineer

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TEST METHOD

Full scale field tests were performed for validation purpose. Digital computer simulation was used as the primary test method because of Following reasons.

l . This method offers easy variation and control of vehicle and environment data compared to full scale or physical model test.

2. Analytical stability analysis based upon linearizing was not considered appropriate as the nonlineari ties are important in severe manoeuvres .

3. Apart from local or global stability, also response time and handling qualities, etc. should be investigated. lhus, simulation of some severe manoeuvres with close

connection to real traffic situations was selected.

TES T MAN OEUVRE

A double lane change manoeuvre was chosen as most suitable for the investigation . Other possible manoeuvres under consideration were

J-turn

single lane change

slalom course

J-turn and single lane change were considered less severe and the slalom course to

far from a real traffic situation.

DYNAMIC STABILITY CRITERIA

In this investigation it has been the aim to study the dynamic stability of the combination: in terms which have as close relation to the accident risk in a real traffic situation as possible. Typical accidents caused by the dynamic behaviour of a vehicle combination may be defined as

l . Skidding accidents such as iack-knifing and trailer swing accidents with excessive side slip angles.

2. Overturning accidents due to low overturning stability often in combination with acceleration or side slip angle amplification towards the rear end of the combination. 3. Accidents caused by excessive space demand due to the geometrical dimensions in

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The following variables have close connection to these accident definitions and they are generally referred to as risk factors.

Lateral acceleration (SA) for the centre of gravity (c.g.) of each vehicle unit is a measure of the manoeuvre violence and of the tyre road friction necessary to perform

the manoeuvre .

Side slip angle (5) for each axle is a measure of the use of available friction. Above a certain side slip angle the maximum cornering capacity is reached and the vehicle goes more or less out of control . In other words the vehicle is skidding .

Overfuming risk (RV) describes the overturning" risk in term S'Qf relatiyefwheel load change on individual axles or all axles of a vehicle unit. This risk variable is defined in chapter 6.3 .

Lateral deviation of the vehicle axles was used for destcri'p tion'df'the-space demand Yaw angle and angles between the vehicle unitshave been used to measure iack-knifing tendency and oscillatory stability of the units in the combination.

The wheel steer angle of the leadinivehicle indicates the difficulty for the driver to per-form the manoeuvre. However, easy steering combined with high rearward risk factor amplification (see below) Was considered as dangerous.

Rearward risk factor amplification defined as the ratio between the risk factor maxima of the semitrailer or trailer axles and the corresponding mean value of the risk faCtor maxima for the leading vehicle axles. High amplification is. judged as dangerous

be-cause the feed back to the driver of the behaviour from the rear units is very weak. This is especially true for the full trailer.

The double lane change manoeuvre can be Separated in sections, the entry section A, the middle section B and the departure section C.Most. riskfactors have one maior extrem value in each of these sections. The dynamic behaviour of many vehicle combinations have been summarized only by these values. Of course this was preceeded by a thorough examination of the time historiesforevery variable in the computer output.

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MAIN STRUCTURE OF MATHEMATICAL VEHICLE MODEL AND COMPUTER PROGRAM

The mathematical vehicle model permitted the study of three different heavy vehicle

combinations

l . Tractor and semitrailer. One articulation. 2. Truck and full trailer. Two articulations.

3. Tractor-semitrailer-full trailer (double bottom). Three articulations.

The moving coordinate system was fixed to the sprung mass of the tractor (truck) but did not roll. The system was right hand carthesian with vertex in the centre of gravity of the total mass of the tractor. The x-axis was horizontal in the plane of symmetry of the tractor with positive direction Forward. The z-axis was positive upwards.

The most important of the simplifying assumptions in the mathematical model are listed

below .

l . Roll axes were horizontal and the centres of gravity of the unsprung masses were located on the roll axes. Thus the centre of gravity of the total mass was fixed to the sprung mass

2. Pitch motion was neglected 3. Roll angles were considered small 4. Camber angles were neglected

5. Roll and compliance steering effects were neglected

6. The road was considered flat and horizontal,and no vertical movement was included 7. The principal axes of inertia of the tractor coincided with the vehicle fixed

coordinate system. The principal axes of inertia of the other units in the combination were located analogously

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8. The tyres were considered to be rigid. Consequently the unsprung masses had no

freedom to roll.

9. The side slip angle for all wheels on one axle were regarded as equal and calculated at the axle centre. The lateral movement of the axle in the centre of gravity

system,due to roll, was neglected in these calculations. l0. Bogie axles were substituted by single axles.

For the vehicle combination tractor-semitrailer-full trailer the program was based upon l7 basic equations. For the truck-full trailer the number of equations were l3. The tractor-semitrailer combination required 8 basic equations. The following variables were solved from these equations by matrix inversion .

l . Longitudinal and lateral acceleration of the leading vehicle c.g. 2. Yaw angle acceleration for each unit in the vehicle combination 3. Roll angle acceleration for each unit in the vehicle combination 4. Horizontal coupling forces in each articulation point

5. Roll torque transmission in the full trailer turntable

(In order to avoid numerical oscillations, caused by small inertia and large forces, the dolly roll movement was attached to the rear trailer movement. So, the original number of equations - l6, l2 and 8 respectively - might have been reduced - to l5, ll and 8 respectively. However, programming efforts were less with the solution mentioned above - i.e. l7, l3 and 8 equations respectively).

Subsequent to the matrix inversion, integration and a number of subroutines were performed for evaluation of sideslip angles tyre forces (chapter 6), steering angle (chapter 7 and 8) ,output variables etc .

The pragram structure was according to the IBM 360 CSMP translator but most

statements were written in FORTRAN IV. The computer cost was approximately 6 US dollars per real time second when about 50 variables were printed (5 times per real time second) and when about30 diagrams were plotted.

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6.l

6.2

6.3

TYRE ROAD CON TAC T FORCES

Side forces

Tyre side forces for different wheel loads and side slip angles were entered into the simulation program in tabular form. Table data originated from measurements according to appendix .

Linear interpolation between table data was used when side force and wheel loads were computed by an iterative procedure for each axle. The side slip angle for each time step was solved in advance outside the iterative loop.

Traction forces

The only traction forces involved were the rolling resistance and the forces on the rear wheels of the tractor necessary to keep the speed constant. These forces were

comparatively small, and their effect on the side forces was not considered. Wheel loads and overturning risk

The dynamic wheel loads (i teratively computed, according to section 6.1) were used for calculation of the overturning risk (RV) defined by

Dynamic wheel load on left side _ I Static wheel load on left side

RV =

RV was always calculated for each axle. When appropriate,RV was also eValuated-for all axles together on a trud<, on tractor+ semitrailer, and on full trailer.

lNVERSE STEERING PROCEDURE

An inverse steering procedure was developed in order to get comparable simulation

results for the investigated vehicle combinations. Theprocedure made the leading vehicli in every vehicle combination fallow the same trajectory and lateral acceleration time history, independent of vehicle parameters, load or load distribution .

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Of course, certain conditions concerning tyre characteristics and trajectory design (see next chapter) had to be satisfied. In these simulation runs the steering angle output from the inverse steering procedure subroutine was reasonable and similar to the full scale test. See Figure 9.3.

The steering angle demand was calculated at each time step from the equations of motion for the leading vehicle. Inputs to the subroutine in question were:

predetermined lateral acceleration for the centre of gravity of the leading vehicle, current values ofstate variables for the leading vehicle necessary in calculation of steering angle demand . ,

The output from the subroutine - i.e. the steering angle necessary to achieve the desired lateral acceleration - acted as input to the vehicle model outlined in chapter 5. In this way no "railway-effects" were introduced by the inverse steering procedure. Other methods of steering along a predetermined path have been found in the literature beforeaand aftersthis investigation. However, this procedure seems promising and the development will continue .

MATHEMATICALLY DEFINED TEST COURSE

Preinvestigations of the inverse steering procedure in an analogue computer indicated that some specific constraints had to be put on the test course. Unreasonable steering movements appeared if the third order derivative (V) of the lateral deviation was

discontinuous .

The test course illustrated in figure 8.l was selected as input for the inverse steering and has been used in all simulations except some validation runs. The acceleration peak

2 C O C C O C

values were l .75 m/s and Its time history was composed by harmonic and linear functions of time. The lateral deviation peak value was 3.0 m.

At none of these simulations the difference between desired test course and simulated trajectory exceeded 0.05 m. This error was regarded as negligible compared totthe-desired lateral deviation peak value (3.0 m). The comparison indicates a satisfactory effectiveness of the test course and inverse steering subroutines.

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Figure 8.2 Read oriented 1aferal- accelera on (V) as function of Hm in thedcsfred

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9.I

VALIDATION OF THE MATHEMATICAL MODEL

Full scale tests

In order to validate the mathematical model full scale field tests have beenperformed. The following configurations were tested

Vehicle combination Load condition

Truck Semitrailer Full trailer

Tractor-semi trailer Full load

. * Full load Full load

Truck-full trailer , Unleaded FU Ioad

. . . Full load Full load

Tractor-semltraIIer-full trailer unloaded FU load

The test manoeuvre represented a real traffic situation where the vehicle combination is driven on the right hand side of a road of seven metres width. Suddenly the driver discovers an obstacle of ten metres-length blocking the righjL hand side of the road. In orde to avoid a collision the driver starts steering over to the left hand side 40 m in front of the obstacle. Because of oncoming traffic the driver has to be back on the right hand

side 40 metres behind the obstacle.

For the tests the road edges, road centre line and obstacle were marked by rubber

COI I es .

The driver kept the speed as constant as possible. The test was carried out at several speeds between 40 and 80 km/h . The test course was not" changed for different speeds like in chapter l3.

Recorded data were steering wheel angle, road distance, yaw angle of the tractor, lateral acceleration for all vehicle units, angles between the different vehicle units and the roll angle for one vehicle unit selected differently on repeated runs.

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9.2

10.

Validation

At the validation simulations the mathematical vehicle model has been steered either according to recorded steering wheel angle time history or by the inverse steering routine along a test course closely corresponding to the course performed during the field test. See appendix, table A] for vehicle data.

Figure 9.l a-c shows a comparison between lateral accelerations achieved at field test and simulation. Only one of the field test curves was measured by a roll stabilized accelerometer. For the other curves a correction for the roll angle influence has been indicated for the peak values. As the simulation accelerations were horizontal this was necessary for a fair comparison . The result is considered as satisfactory.

In figure 9.] d the front axle courses of the tractor from field tests and simulation are compared. The course achieved at the simulation deviates from the field test course. It must be noted however that a change of the initial direction as slight as 4 m rad

(~0.23°) corresponds to the shown deviation at the end of the course. If this correction is made the two curves coincide~quite well.

Figure 9.2 shows a comparison between courses from a field test and from a simulation where the inverse steering routine .has' been used. Figure 9.3 shows the corresponding wheel steer angles. The field test wheel steer angle has been calculated from recorded steering wheel angle. No correction for steering compliance, roll steering etc. has been made why the similarity probably is better than shown.

Figure 9.4 a-c show comparisons of lateral accelerations. The similarity is regarded as satisfactory .

The validation tests show that the mathematical vehicle, model gives simulation results well coinciding with field test results.

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LA TE RA L AC CELE RA TI ON LA TE RA L AC CE LE RA TI ON ll. m'x's l m/s ll

---- Field test Field

test-) - '» Simulation 2:0 " - Simulation

ms t 3 Correction for roll 1.5 ~ A] Correction for roll

I Z i l,0 2. 1,0 t 0,5 a 0,5

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a LateraLaccelemtion of the tractor c..g . b Lateral camelerati-orrcnc the semi trailer

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c.g.~. A" the tractor W

Comparison between simulation and Field test results for a tractor-semitrailer full trailer combination . The steering function measured at

the field test was used as steering input in the simulation. Figure 9.1 a-c

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LA TE RA L DE ViAT lO N l2. 2 m

9

t 31 g i _____._ Field test > . . Lu 2~ Simulation 0 _.I 5 11 IE

3

:

LONGI TUDINAL ROAD COORDINATE a) Lateral deviation of tractor front end

m ll 3« 2. _ ._ _ Field test 1 . "Simulation ° NE"? W ' 'de m

-1. LONGlTUDlNAL ROAD COORDINATE

b) Lateral deviation of full trailer rear end

Figure 9.2 Comparison between front and rear end traiectories of a tractor-semitrailer-full trailer combination in field test and simulation.

lnverse steering procedure'and mathematically defined test course were used in the simulation.

mrad ll l-J-IJ 80 o o 60 . __ _ Field test. Z 40 - \ ' A Simulation

<

/ \

/ \

log-Ll / 4 \ '.\\ . 4 TE 0 I 2' 3 4 7 3 5 3 9 16 i m "l \ ~ . TIME s d 40 \ g 60« V 3

80-Figure 9.3 Comparison between wheel steer angles in field: test and

simulation. Tractor-semitrailer-full trailer combination.

Inverse steering procedure and mathematically defined test

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i3.

Z m

.9 :l

' ! - Field test é Simulation» '11" LL, \ U \W4A\ L_ U 5'wa 10 75 < . l < c: LL]

3

a. Lateral acceleration of tractor c.g.

Z * fl

9

l- e , é __ _ Field test LLI Simulation _| LLI U e U T < _l

5%

3

__ _. _ Field test Simulation -2+ LA TERA L AC CE LE RA TI ON

c. Lateral acceleration ofrrear trailer c.g.

.Figure <9.4.a-c Comparison between simulation and Field test results For a tractor-semitrailer-full trailer combination. Inverse steering

procedureand mathematically defined test course were used

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'-i4. SINGLE VEHICLE PARAMETER VARIATTON

The influence from changes in single vehicle-parameters was studied for a tractor-semitrailer-full trailer combination. The aim was to get an idea of the relative importance of different design parameters. The basic vehicle data conformed to the fully loaded field test combination except for the tyre-road study where the law c.g. truck-full trailer was used. See appendix for vehicle data. Each parameter was assigned three different values according to the table below. Basic data are in the middle column of test values. Best value is indicated by +.

Parameter ' Test values

+

T. Tractor wheel base (m) 2.5 3.4 6.0

2. Fifth wheel position in front +

of rear axle (m) 0 0.60 2.23

3. Roll torque stiffness of the 3000 30000 300 000

fifth wheel - kingpin (Nm/rad)

4. Roll stiffness of the semitrailer 850 000 l 700 000 3400 000 rear suspension (Nm/rad)

5. Yaw moment of inertia of the T20 000 236 000 350 000

semitrailer (l<gm2)

6. Distance between semitrailer + +

axle and trailer drawbar tow 0 l .94 3.9

Pin (m)

7. Drawbar length of the full + +

trailer (m) l.72 3.34 4.5

8. Viscous yaw velocity damping of the articulation ioints

(Nm/rad) 7 +

8.] Kingpin 0 1:00 000

8.2 Tow pin 0 50000

+

8.3 Turntable 0 50000

9. Tyre road characteristics. 3 + + +

standard cornering stiffness:S~ S T .5 S

(Low c.g. truck-full trailer) best value, small effect

+ 5:

++ = best value, medium effect = best value, large effect

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15.

The most important effect on the risk factors was achieved from the following changes 1 . Distance between semitrailer axle and trailer drawbar tow pin. The shortest

distance was most favourable (see fig . l0. 1).

2 . Drawbar length of the full trailer. Contrary to reported<5 results from step steering tests the shortest drawbar was considered as the best alternative. Though the longer drawbars were superior in the first part of the manoeuvre the ranking order was

reversed in the middle part which was the most critical (see fig. 10.2) .

3 . Tyre-road characteristics. Tyres with 50 % higher cornering stiffness and friction compared to standard tyres had considerably lower risk factor values (see fig. l0.3) .

Less important,but worth mentioning,are the following indications from the simulation

results .

Short tractor wheel base was favourable.

Viscous kingpin and tow-pin damping were-favourable.

Viscous turntable damping was unfavourable compared to no damping .

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Maximum absolute values of different risk factors. Field test combination with different distance between axle and tow pin (q56- I56) forvthe semltraller.

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0,4 0,3 0,2 0,1 Co ur se se ct io n A O V ER T U R N I N G RI SK M A X I M A Co ur se se ct io n C Co ur se se ct io n B b) ,Overtu-ming risk ~.

D standard high coming

cornering stiffness (1.5 S) - stiffness (S)

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c) Lateral deviation

Maximum absolute values of different risk factors. Low c.g . truck-trailer combination with different cornering stiffness.

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II

I9.

COMPARATIVE STUDIES OF I8 M TRUCK-FULL TRAILER AND TRACTOR-SEMI-TRAILER-FULL TRAILER COMBINATIONS WITH DIFFERENT LENGTH DISTRIBUTION Three different ratios between the length of front and rear load carrier were investigated. In all cases the total length of l8 m and the Swedish weight limit were almost reached. As the comparisons were primarily to be made between truck-full trailer and tractor-semitrailer-full trailer combinations the total mass of the loads has been equal for both combinations in each length distribution. However, the difference in total mass between the different length distribution variants of one type of combination was very small. Thus a comparison also within one type of combination is possible. See appendix fig A2 for further data .

Shortenings will be used in the following sections. For the tractor-semitrailer-full trailer(T ST FT) they are:

I short semitrailer and long full trailer - short-long combination

2 semi trailer and full trailer of equal length - equal length combination 3 long semitrailer and short full trailer - long-short combination

The same shortenings will be used for the corresponding truck-full trailer (T-F T) combinations .

Comparison between truck-full trailer combinations

Every risk criterion based upon side slip angles, overturning risk, lateral side deviations, - rearWard amplification of risk factors etc, showed that theshort-long combination was

better than the others. Seefigure II .I

Usually, the equal length combination had smaller risk factor values in course section C. However, these maximum values were smaller than in course section B where the short-long combination was more favourable. In addition the short-short-long combination has better oscillatory damping . This is also the case for rearward amplification of the risk factors.

Similar results have been found from other investigations. The short-long combination is therefore to be recommended.

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ll.2

11.3

20. Comparison between tractor-semitrailer full trailer combinations

The largest risk factor values were found for the long-short combination (see figure ll.l). The comparison between the short-long and the equal length combination showed that the short-long combination generally seen was more favourable in terms of risk factor maxima and rearward amplification of the risk factors. However, the overturning risk of the semitrailer axle was larger on the short-long combination to such an extent that the equal length combination is iudged to be safer.

Comparison between truck-full trailer and tractor-semitrailer full trailer combinations In this comparison (see figure ll .1) it can be noted that the tractor-semitrailer-full trailer combinations show the largest risk factors in the critical middle part (B) of the manoeuvre and at least incase of the side slip angles have a larger rearward amplification .

It is noteworthy that the time histories of lateral accelerations, side slip angles, over-turning risk factors, side deviations and in some cases even the angles between the vehiclr units are very similar for the rear units and axles with the same index number independent of the type of combination. This supports the hypothesis that the number of foregoing articulations is of significant importance for the behaviour of the vehicle unit. See chapter l4 for further discussion .

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21.

SHORT-LONG

EQUAL LENGTH

LONG-SHORT

T-FT

T ST FT

T FT

T-ST FT

T FT

T-ST-FT

q O. 5? (I ) O % L O N O Co ur se sect io n A SIDE SL IP AN G L E FO R E A C H AXLE Co urse se ct ion C Co urse se ct ion B 12 34 '56 78 910 333? Axleno 238:? I2 34 56 78 12 N 000 3

. §tni\ 2&838 Axleno

a) Sideslip angle

SHORT LONG

EQUAL LENGTH

LONG-SHORT

T-FT

T-ST-FT

T--FT

T-ST-FT

T-FT

T-ST-FT

12 34 56 78 12 34 56 LA TERA LD EV IA TI ON FO R EACH AX LE 91 0 5. CD 3 O 12 34 56 78 12 34 56 78 91 N . 3383 SEREE'Axle noA b) Lateral deviation '

Figure H .l Maximum absolute values of sideslip angle and lateral deviation for each axle in different 18 m combinations. T-FT is short for truck-Full trailer and T ST-FT means tractor-semitrailer-full trailer.

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I2

_12.1

12.2

22.

INFLUENCE OF LOAD DISTRIBUTION AND WEIGHT

Vehicle and load data concerning this chapter are summarized in appendix, table AI and figure AI .

Axle load distribution of the trailer in a 24 m truck-full trailer

In order to study the influence of load magnitude and distribution,three load configura-tions were compared .

I . Truck and trailer fully loaded

2. Truck fully loaded and trailer with full load on the front axle and empty axle

load on the rear axle

3. Truck fully loaded and trailer with full load on the rear axle and empty axle

load on the front axle

The greatest side slip angle appeared for the front loaded combination at the trailer front axle. The skid motion was similar to the start of a front end trailer swing . The overturning risk was smallest for the front loaded trailer and greatest for the fully loaded trailer. It has to be observed however that the rear end ,IoadWas much larger than the front end load. Thus, the size of the loads was possibly more important to this result than the position of the loads.

It should be noted that the trailer frame has been considered as rigid. Thus, the effective roll-stiffness was higher than what can be expected in reality.

Load location on the semitrailer of a 24 m tractor-semitrailer-full trailer

To study the influence of load location on the dynamics of the vehicle,a specific load was located in three different positions on the semitrailerwhilethe trailer was fully loaded.

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12.3

23.

The three load positions were

1 . Load centre of gravity at the fifth wheel kingpin

2. Load centre of gravity between kingpin and semi trailer axle with the same load distribution as when fully loaded

3. Load centre of gravity at the semitrailer axle

The rear loaded combination showed the poorest course tracking, jerky steering and the highest risk factor values.

The middle loaded combination generally had the best perfon'nance except in the initial section A of the test course. As the highest risk factor values occur in the middle section B the middle load location can still be said to be the best one. It should be noted that the judgements were based upon the fUll trailer behaviour as it had the largest risk factors of the combination.

Load location on the full trailer of a tractor-semitrailer-full trailer

Simulations were also made with a fully loaded semitrailer and a partly loaded full trailer with a specific load which was located in three positions:

1 . Load centre of gravity at the front axle

2. Load centre of gravity between front and rear axle with the same load distribution as when fully loaded

3. Load centre of gravity at the rear axle

The behaviour of the tractor and the semi trailer was not affected by the load distribution onthe trailer. Thus the behaviour of the trailer was closely related to

the load location.

The rear loaded combination behaved worseithan theTrQn r loaded and the middle loaded combination was the most favourable of the three configurations.

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12.4

24.

Load weight and load distribution between semitrailer and Full trailer in a 24 m

combination

Fig l2.l shows some results from four simulations that were carried out with the Following load configurations.

l . Semitrailer partly loaded

Full trailer partly loaded SYmbOI DD

2. Semitrailer fully loaded

Full trailer partly loaded

57mm FD

3. Semitrailer partly loaded

Full trailer partly loaded SymbOI DF

4. Semitrailer fully loaded

Full trailer Fully loaded stbo' FF

It is noteworthy that the FD combination behaved better than the DFcombi nation although the FD load was clearly heavier than the DF load. Therefore, unloading

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a) Load con guration and axle loads

Combination symbol 00 FD 0F FF (see text) Load weight (kg) Totally 15200 26510 20850 32160 Semi trailer 8360 19670 8360 19670 F011 trailer 6840 6840 12490 12490 Weight of complete 34100 45410 39750 51060 combination (kg) Loads (N) Fifth wheel 54550 96900 54550 96900 Axle no 12 53800 63480 53800 63480 34 64390 97030 64390 97030 56 88790 157380 88790 157380 78 63610 63610 90900 . 90900 1710 63950 63950 921 10 921 10

OV

ER

TU

RN

IN

G

RI

SK

MA

XI

MA

Co ur se se ct io nC Co ur se se ct io n-B Co ur se se ct io nA Tmctor+ semi- Eyll mile: trailer (Rv16) (RV 710) 0,5 0,3 0,2. 0,1 0,2 0,1 0 9) vgtEmingriSk -Co ur se se ct io n A S-ID ES LI P A N G L E FO R E A C H AX LE Co ur se se ct io n C Co ur se 's ec lt iO n B LA TE RA L DE VI AT IO N FO R EA CH AX LE m rod 25. 80 60

100 r) 80 60 _4 40 H 2° af- 88:? q 5 0 100 80 60 40 2° TM 8 831: t 00 7 _ 7 , 12 364.9 78 910

b) sfde sitp angle

L,

5

WE

-35; 13 p E _%3 0 St E ' F. - +-__ F.__v __ _. __ FM) d) Lateral deviation

Figure'TZtl absolute values of different risk factpr5,

semitrailer-ful'l trailer 24 m combinatizoagf "differentioads according to the table (a).

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13

26.

INFLUENCE FROM SPEED

In this study the lateral movement as a function of time was kept unchanged and

independent of speed. This means that the centre of gravity in the leading vehicle was exposed to the same road oriented lateral acceleration - time function at all speeds. It also means that the test course was expanded longitudinally with increasing speed. The following combinations were studied. Vehicle data appear in appendix table Al .

1 . The field test combination i.e. the tractor-semitrailer full trailer combination used

at the validation simulations.

2. A typical Swedish 24 m truck-full trailer combination, fully loaded (fig A1). 3. A typical Swedish 24 m tractor-semitrailer-full trailer combination, fully loaded

(fig Al).

Compared to combination 1, combination 2 and 3 have higher centre of gravity and slightly higher tyre cornering stiffness.

For combination l simulations were made at 40, 70, 90 and 110 km/h. With combina tions 2 and 3 simulations were made at 40, 70 and 90

Some of the simulation results for combination 1 are shown in figure 13.1. The risk factor amplification at the rear end of the combination was negligible at 40 km/h, quite important at 70 km/h and then successively increasing at higher speeds. At

110 km/h, wheel lift and severe rear end skid Occurred for the full trailer at the end of the manoeuvre .

The comparative simulations with vehicle combination 2 and3 are illustrated by figure 13.2 and 13.3. Figure 13.4 shows the speed dependency of the steer angle for the full trailer in combination 3. Noteworthy is the great increase in amplitude

between 70 km/h and 90 km/h.

The simulations showed that increased speed has a strong negative effect on the dynamic behaviour of vehicle combinations with more than one articulation point.

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Vt HI CLI: U N I l4 Co ur se se ct io n C Co u rs eS ec ti on B TP: center of gravity TP1234 TP56 TPI78 TP 910 : 1 PMDA Co E 1 / .1 l g "1/52 < C O 2 O: U 0 V I d) 32 D O 0 U Co ur se se ct io n C Co urs e se ct io n B 40 km/b 70 w» 90km/b a) Lateral acceleration Co ur se se ct io n A 0,5 40 km/h 70 Ian/1n c) Overturni ng risk Figure 13.1 90 km/h HOkm/h ilOkm/h a.

Maximum absolute values of different risk factors.

LA

TE

RA

LD

EV

IA

nO

N

FO

R

EA

CH

AX

LE

27. Lot o 12 34 is 910 Co ur se se ct io n A SI DE SL IP A N G L E F O R EA CH AX LE Co ur se se ct io n C Cour se se ct io n B 40 km/h 70 km/b l 10 km/b B) Sideslip angle 90km/h > w 40 km/b 7O km/b 90 km/h d) Lateral deviation ' Mom/h

Field test combination at

four different speeds. Lack of values for HO km/h in course section C is due to overturning of the full trailer. Graphical interpolation between speeds is

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.nrcd Co ur se sect io n A SlDE SL lP AN G L E FOR EA CH AX LE Cour se se ct ion C Co urse se ct ion B Co ur se se ct iO nA

OV

ER

TU

RN

IN

G

RI

SK

MA

XI

MA

Co ur se sect io n C Co ur se se ct ion B Figure i3.2 80 60 40 20 40 km/h 70 km/h 70 km/h O 90 km/h 40 lun/h 70 km/h Axl e T TF T-ST- FT a) Sideslip angle 40 km/h 70 km/h 90 km/h 40 km/h 70 km/h 90 km/h 0,5 0,4 0,3 0,2 RV 71 0

*T ra ctoH -se mi tr ai le r: Ful l tr ai le r /

.T-ST-FT

T-FT b) Overtuming risk

Maximum absolute values of sideslip angles for each axle and overturning riskmaxima for each vehicle unit. Fully loaded 274m combinations at different speeds. Graphical interpolations is pOssible like in figure l3. la.

T-FT is short for truck-Full trailer and T ST FT means tractor-semitrailer-full trailer.

(35)

LA TE RA L DE VI AT ION 29. 70 km/h 90 km/b 4O Kmluh m 40 "Km/b 70 km yr 90 ml'h FO R EA CH AX LE T-FT T-ST.-FT

Figure Sgeedinfluenceion-lateral deviaTio TfruTi-y loaded 24 m combinations. Graphical nterpolation possible like in figure l3.l .a. T-FT is short for truck-full trailer and T-ST-FT means tractor semitrailer-full trailer

40 km/h - -__ 70 km/h 90km rad ' 0 . 0 5 1 L RF IU -o .0 3 0. 01 1 1 1 1 ~p . 0 7

' 2100 3200' «100' siog mg'mo' oo 3100 9100 {0.00' 1'1.oo' 5

Figure l3..4 Steer angleofthefull ailerKAFlglizsfunctmf. , a . e of time. Fully loaded 24m tractoresemitrail-er-fuil-f '

(36)

14

30.

INFLUENCE FROM NUMBER OF ARTICULANONS

The possibility for vehicle movements that are uncontrollable for the driver, will increase with the number of articulations and degrees of freedom. In addition, all simulations at high speed showed the largest risk factor values for the highest

articulation number among comparable vehicle combinations. See figures ll. 1 , 13.2

and 13.3.

Another argument against articulation concerns the driver's perception of the rear vehicle unit dynamic behaviour. Although the rear unit appears to be the most critical unit at high speed, it offers the poorest sensory feedback to the driver.

Rearward risk factor amplification due to added articulations may occur even in steady-state cornering. This phenomenon is indicated by fig 14.] where the outWards off-tracking increases when one articulation is added. If the side forces and the sideslip angles (a) are unchanged the outer track radius (Ry) will increase when the rigid trailer (a) is substituted by an articulated trailer

Thus, it must be emphasized that the number of free articulations should be minimized for vehicle combinations operating at high speed.

Figure 14.1 Outwards off-rtracking increase .when. a rigid vehicle unit (a) is substituted by an articulated unit (b). See text.

(37)

IS

31.

PROPOSED DEMANDS ON DYNAMIC STABILITY OF HEAW VEHICLE COMBINATIONS

The following test procedure and demands are proposed on basis of the theoretical and experimental investigations. These demands are considered to be minimum performance regarding dynamic stability during non-braking conditions. The vehicle combination has to carry out a double lane change manoeuvre with specifications according to the simulations of this investigation. The test is to be done with maximum load and maximum load centre of gravity height at a constant speed of at least 70 km/h . For acceptable performance the following limit values must not be exceeded.

I . The side slip angles of any axle except the front axle of the leading vehicle must not exceed I50m rad (8.6 degrees)

2. The side slip angle maxima for all axles must not exceed '20 m rad 75 metres after the point where the first axle of the combination has returned to straight

COU rse

3. The amplification of the axle side slip angle maxima relative to the mean value of the side slip maxima of the axles of the leading vehicle must not exceed 2. 4. The maximum space requirement during the manoeuvre must not exceed the limits

defined by side deviation limits for the axle centres according to figure l4.I . This corresponds to the requirement that the combination must stay whi thin the road limits of a seven meter wide road, typical for Swedish conditions, and not touch an obstacle, ten metres long and occuping the righthand side of the road. 5. During the manoeuvre the overturning risk (RV, see chapter 6.3) for any axle

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I6 AX LE CENT RE LA TERA L DE VI ATI O N l 3,2.

Curved parts of the test course (standard at 70 km/h)

L , I . l 25m_ 50m J r .. _ 2 ,5 m 4 A A n A I A L A I I T V j V f V I V 1' f r v T 1 IO 20 '30 40 so 200

Figure I5.T Lateral deviation limits for axle centers.

MEASUREMENTS OF STATIC OVERTURNING LIMITS

In order to get empirical data on the overturning stability for heavy vehicle combina-tions, static tests were carried out. The full scale, loaded vehicles were inclined until the gravity force (m 29) caused overturning. An inclination angle a

' {corresponds to steady state cornering. at the lateral acceleration g - tan a with the vehicle real mass reduced to m 0 cos a. Themeasurements were perfonnedon a tilting device consisting of a number of wheel support beams, one for each axle. The beams are tilted by hydraulic jacks.

Subiectfor investigation were two tractor-semitrailer' combinations, two full trailers and one truck. All vehicles were maximum loaded at different centre ofgravity

heights. The tested vehicles were considered as representative for modern heavy

vehicles in Sweden. However, the roll stiffness was comparatively high especially for the semitra-ilers and trailers. Results are shown in figure 16.I .

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33.

foadc.g.above Load Gross

m/fé Symbol Vehicle load platform weight weight

.21:

(m)

(k9)

(k9)

+ Truck

0.24 0.97 1.71 10600 21000

A

ea Tractor-semitrailer 0.27 0.94 1.62 6600 16000

Z B O Tractor-semitrailer 0.26 0.97 1.64 18000 31000

g

EB F011 trailer

0.27 0.94 1.62 6600 10000

g 5-

O

1:] F011 trailer

0.15 -

1.681330019300

E

U

<

E

3' 4~

12

+6

0

3

m

0

Z

3-E

a "l" 9 Cl M -' O > ..

O 2

p

z

53

_>_

1-D.

0

LL! 4/: f 11 y w l 2 3 m

VEHICLE CENTRE OF GRAVITY HEIGHT

Figure l6.l Static overturning stability limit as a function of c.g. height.

A demand on minimum static overturning stability has been proposed. It is

regarded as a complement to requirements at the dynamic, computer simulation test. It is alsosimple to supervise. The proposed limit value was assessed with the aid of . experimental results according to Fig 16.l .

(40)

I7

TB

34.

HIGH SPEED OFF TRACKING

Low speed off-tracking is a wellknown problem for long vehicle combinations in sharp

curves .

At high speed and large sideslip angles off-tracking towards the outside of the curve will occur. This phenomenon is probably less known to the drivers than the "classic", low speed off-tracking . Furthermore it is often impossible for the driver to observe the outer track of the rear vehicle. Accidents have occurred in Sweden that seem to be caused by this kind of off tracking .

The outside off-tracking can be reduced by shortening the combination, reducing the number of free articulations, using tyres with high cornering stiffness etc. Unfortunately the common method to reduce low speed off-tracking (i .e. articulation) will also

increase the high speed off-tracking. See fig I4.I .

PROPOSED COMPLEMENTARY DEMANDS ON OVERTURNING STABILITY AND HIGH SPEED OFF- TRACKING

Overtuming stability

. . . 2

As a complement to the dynamic overturning stability requurement,4 m/s was proposed as the minimum static overturning stability. In fact, this means a limitation of the load and its c.g. height, to be'specified for each vehicle.

High speed off- tracking

The proposed limitation of dynamic space requirements in the double lane change manoeuvre (fig 15.1) was completed by following demand. Off-tracking towards the

outside of the curve must not exceed 0.5 m in a curve defined by a speed of 70 km/h

and a lateral acceleration 2 m/s2. The lateral acceleration should be maintained during five seconds. During the test, the vehicles should carry maximum load with c.g. at maximum height.

(41)

I9

20

2]

35.

TEST METHODS

The following test methods were suggested for type approval

I . Mathematical simulation of the double lane change manoeuvre and the off-tracking

test

2. Full scale static overturning test

DISCUSSION ON DEMANDS ON DYNAMIC STABILITY DURING BRAKING Following demands on braking behaviour of heavy vehicle combinations have been

considered desirable .

The vehicle commnation must not loose stability and manoeuvrability when maximum pedal force is applied . At the same time good braking efficiency should be maintained. This must be fulfilled. in empty and full load condition, on high and low friction surfaces

and on even and uneven roads.

It can directlybe stated that antiIock braking systems will be needed to fulfill these demands. Thereby the longitudinal slip distribution between the axles during braking can be expected to be a major design problem for these systems. Further research in

. 5 7 8

I'I IIS area seems to be needed. However, important. investigations ' 'héve been performed. SUGGESTIONS FOR FUTURE RESEARCH

The relatively poor overturning stability for heavy vehicles and the rearward risk factor amplification in articulated vehicles are the maior problems, that are revealed in this

0 I I O 9 I O 0 O 0

paper, In the mam report and IIS summary1 . Novel design pruncnples have been

suggestedH The compromise between low speed and high speed handling requirements

A may be fulfilled by speed-dependent braking of relative motions in articUlations and by unconventionally steered axles. In order to develop these ideas, following investigations are now active at the institute.

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36.

Handling characteristics of articulated-heavy vehicles. The mathematical model mentioned in this paper will be expanded for steering axles. Low speed and high speed off-tracking as well as different steering strategies for the-axles will be considered.

Overturning risk for heavy vehicles. Measurements in vehicles used in real traffic and driver interviews have been performed. Driver estimated overturning risk will be compared to the measurements.

Overturning risk due to sloshing in vehicles with liquid loading. The overturning risk for a simple vehicle model is calculated in an analogue computer. Liquid force input is fed to the computer from a laterally moving physical tank scale model.

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RV SA

T-FT

T-ST-FT

Y

12,:yL.56;;uL 910

14, L6,: L 710

37. NOTATION

Fifth wheel or tow pin distance behind c.g. of the leading vehicle Forward articulation point distance in front of c.g. of indexed vehicle

unit

' Distance from rearaxle to c.g. of the leading vehicle Centre of gravity

Distance from c.g. to front axle of the leading vehicle Acceleration of gravity (9.81 m/sz)

Distance from foremost articulation point to the axle for a trailer or a dolly

Mass of vehicle unit

Distance between articulation points for a semitrailer or dolly Overtuming risk

Lateral acceleration (with index according to vehicle unit). Direction is perpendicular to the longitudinal symmetry plane of the unit

Abbreviation for truck-full trailer

Abbreviation for tfactor semitrailer-full trailer

Road fixed coordinate perpendicular to the initial velocity vector of the vehicle

Side slip angle Index

Axle index or vehicle unit index

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38.

REFERENCES

Backman, C3,, C.A. Jonsson, O. Nordstrom and A. Pelliieff (1972): The dynamic stability of heavy vehicle combinations etc. (in Swedish). Swedish Department of Transportation, Ds K 1972:10.

Bernard, J.E., C.B. Winkler, P.S. Fancher (1973): A computer based Mathematical method for predicting the directional response of trucks and tractor-trailers. Phase II technical report. Highway Safety Research Institute.

Chiesa, A and L. Rinonapoli (1969): A new loose inverse procedure for matching tyres and car using a mathematical model. Proc Instn Mech Engrs Vol. 183, Part3H.

Dugoff, H. and R.W. Murphy (1971): The dynamic performance of articulated highway vehicles - A review of the state-of-the-art. SAE Paper 710080. Eshleman, R.L., and S.D. Desai (1972): Articulated vehicle handling. Final

report, DOT Contract DOT-HS-105 1-151, IlTRl proiect no. J6255. Jindra, F. (1965): Handling Characteristics of tractor-trailer combinations.

SAE Paper 650720 .

. Mikuleik, E.C. (1971): The dynamics of tractor-semitrailer vehicles: The iackknifing problem. SAE Paper 710045.

Murphy, R.W., J.E. 'Bemard and C.B. Winkler (1972): A computer based

mathematical method for predicting the braking performance of trucks and tractor-trailers. Phase I report. Highway Safety Researchlnstitute. Nordstr m, 0., G . Magnusson and L. Stmndberg (1972): The dynamic stability of

heavy vehicle combinations (in Swedish). National Swedish Road and TrafficResearch Institute, report no. 9.

(45)

39.

10 Schmid, l. (1966): Dos Fohrsfobilit fsverholfen zwei-und dreigliedriger Fohrzeugkeffen. Deufsche Krofffohrfforschung und Sfrossenverkehrsfechnik, heft 182.

i i Sfrondberg, L. (1974): The dynamics of heavy vehicle combinations. Translation of orficle in Teknisk Tldskriff no. 3, 1974. National Swedish Road and

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A.2

40. APPENDIX A

General vehicle data

Every vehicle parameter necessary for simulation was measured on the vehicle

combina-tions that were used in the field tests. Special were for

Wres-ment of moWres-ments of inertia, c.g. height, roll stiffness , roll damping,effective track width etc. Almost every parameter connected to roll dynamics was evaluated from experiments in the tilting device mentioned inchapter l6.

Experience from these measurements was valuable for the assessment of reasonable

parameter values to the 18 m and 24 m combinations . Specific formulas were developed where all parameter values could be calculated from the desired design parameters.

Table Al, figures Al and A2 show someparameters for the investigated vehiCle

combinations .

Tyre side force measurement

The side forces as a function of Wheel load and side slip angle have been measured for the tyres on the vehicles used in the field test. The measurements were carried out on wet asphalt at low speed (m 10 km/h) by a special technique. Two trucks were driven,laterally interconnected by a cable and a force transducer. The method is

(47)

41

Table A1 . Vellicle combinations tested in simulations

Refer to :".'et:icle l Distances according to fig Al (m) Truck or semi trailer Full trailer load confi- Gross Load c.g.

text car-bination C 7b a_ b I _' I | load configuration (fig guration (fig A1) and weight above load chapterna. notation t 56 056 56 78 910 A1)and load weight load weight . (kg) platform (m

275' "0 'lf Sdeg ]; 2132346 -0.66 9.09 1.94 334* 4.15 Fully loaded 17680 kg Fully 166866 13660 kg 50530 ~0.15 10 11570526 +2.95 3.34 - 4.15 - Fully loaded 11435 kg Fully loaded 13660 kg 4.1405 1~0. 15 ll 318 m 15.3] Six different configurations according to fig A2 0.50 4__

.' Front loaded 12.1 3 683mg 37680 Rear loaded 12.1 :m T-FT 19.77526 +2.55 2.90 - 9.06 - Fully loaded 13250 kg 10820 kg :3 41670 0-50 T Fully loaded 12.1.13 ; _ 17540 kg 48390 _

.j ' Partial load, Partial load,

24le ddle. 836qu [:3 middle. 6840 kg :3 34100

""_' " ' Partial load .

12.3 t . front. 6840 kg '1

.._._.._._..

t' ll d

£263,121: Fully loaded 19670 kg [gage . (2°84?) kg 45410

g Partial load,

12.3 2 ! P | 1 rear. 6840 kg

' f t' d

12.2 2.1.5141 pl.803.20 -0.73 6.68 1.90 3.20 7.55 11321? 83°20 kg 0.50

o t P . I

1 . ,12.4:i ggqéfe ggb k9 Ci Fully loaded 12490 kg 39750.

___..'2'2l rgdr..ab§g8<l<'g i' =

Jul-4 ( 1511 . Fully loaded 19670 kg Fully loaded 12490 kg 1060

. Different values in chapter 10

TRUCK -, FULL TRAILER (T-FT)

Y . C

. I ' "a: g

)4

34 . .

-

I

y 6 1 b - a ' - t . " ' - 1 A -- q -.1 1 4 1 5+ 5 L: 56 V 56 56v: jB 910 J T C

Fig Al . Scale drawings of the .24 m combinations with different load configurations.

(48)

circa «(am 30905 to V - ' 1334-4159-GM 10194 wolqht 25074 109

E,

.1 ! mL - 3173099-J00

Gm wolghf 40530 kg Gtoulood weight 25074 kg '

ml.- 13344 kg l: / \ \ A (

\:e >4--%-

L mL-11330Lg "(93 3.90 (0&9 .9 .

_(

plea 30'00 N (5920 kg) 9. 152900 N ((5590 up) -vu. _ 18.00 03000 N (0540 kp) T

Grost 0901913! 38905 kg Gran load weight 24695 kg

5 1.- (2905 kg 86900 N (8860 kp) mL- 11730 kg A a N 3.20 3.90 _ 113 15,80 I4-.- H-.-3!.?.2~H~. 47300 N (4830 kp) 86700 N(0040 kp) 10,00 92900 N (9450 kp) GrossWolght 40805 kg G \

(7*

mLa 12955 kg 03000 N (8540 kp) mlood weight 24695 1:9 L m 173099 3,63 4,90 92 1 F !

(4,90-15,00 10L00 03700 N 87000 N 53300 N (5950 .kp) (15550 kp)unmN cm weight 30905 kg RL._1_2585 kg ' J \ ' L 1 \f j\] ( (0530 kp) Grassland 59.191151240150109 (0070 kp) mL- 117301<a

5,50 , 1,04f 3,90 8 1 15,00 10,00 83700 N 87000 N (8860 kp) 58200 N (5930 kp) (15570 kp)152800 N F19 A2, (8540 kp) /1

r

\l 12l ._ w L20 15,80 47500 N (4840 kp) 00300 N(9000 kp) 10,00 93900 N (9570 kp) .Grou ' weight 30905 kg 03700 N (0530 kp)

Gross load weight 24315 kg

073037 ? (0070 kp) m II 12585 kg vm " 11730 kgL v

N

\J 20 1. 5.60 35.30 18,00 94000 N 83700 N 8700 N 47500 N (4840 kp) 00500(9030k9)N (9590 kp) (0540 kp)

'Moosum,.wolghfs and axle 1000!: for 18 m combinations according to chapter 11. a: Short-long" 13: Equal length" c: Long short

11!: load m are 13mm,~widd\: 2,4 «3.1305951! (obdvo load p1arform) : 1.0 m.

. (9360 kp)

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Direction of motion Force transducer

r

0

Test wheels

Side slip angle transducer

Side slip angle

Figure A3. Tyre side force measurement

10 N 10' Wheel load 9220 N 0 22200 N I 34800 N

/ A

Direction of A motion

Side slip angle 94

i A t .l A, 33 80 :! 30 |S Axle I S, 1 .. A/ Side force o 1 . 1 0,1 0.2

SIDE SLIP ANGLE (6)

/

ll

?

\

Fig A4. Example of measured side force characteristics. Radial tyre,

0' Dimension ll.OO-20. Tyre pressure 6 bar. Wet asphalt.

(50)

Figure

Figure 84 Lagrajfpad positjon (Y) as fgnc on of time fqr fhe #65 ?
Figure 9.2 Comparison between front and rear end traiectories of a tractor- tractor-semitrailer-full trailer combination in field test and simulation.
Figure H .l Maximum absolute values of sideslip angle and lateral deviation for each axle in different 18 m combinations
Fig l2.l shows some results from four simulations that were carried out with the Following load configurations.
+7

References

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This lack of appropriate quantitative palaeotemperature data, especially for the Southern Hemisphere, together with the inability of state-of-the-art General Circulation Models and

The simulations show that 802.11p is not suitable for periodic position messages in a highway scenario, if the network load is high (range, packet size and report rate) since

We present conditional immediate transmission, a packet forwarding abstraction that achieves a data throughput of 97% of the theoretical upper bound and reaches a raw

Svar: Det f¨ oljer fr˚ an en Prop som s¨ ager att om funktionen f (t + x)e −int ¨ ar 2π periodisk, vilket det ¨ ar, sedan blir varje integral mellan tv˚ a punkter som st˚ ar p˚

In the showroom visits and in the free trials, which both gave subjects hands-on experience with a specific EV, the Renault Clio Electrique, it was shown that the subjects did