article in PDF format - Zeszyty Naukowe Instytutu

article in PDF format - Zeszyty Naukowe Instytutu

PROCEEDINGS OF THE INSTITUTE OF VEHICLES 4(104)/2015
Zbigniew Lozia1
EXAMPLES OF AUTHORIAL MODELS FOR THE SIMULATION OF MOTOR
VEHICLE MOTION AND DYNAMICS
1. Introduction
In motor vehicle research, analyses carried out with the use of simulation models are
an element of great importance. Some of them are related to the motion and dynamic
properties of a vehicle. The tools of this type have become more and more commonly
used in engineer’s environment for the recent three decades. Previously reserved for
universities and research institutes, such tools have now become helpful for specialists
directly searching for practical solutions.
The author presents here examples of the simulation models of motor vehicle
motion and dynamics that he built during 39 years of his work at the Warsaw University
of Technology and during his guest-researcher stays at VTI (The Swedish National Road
and Transport Research Institute) in Linköping, within numerous research, purposeoriented, and development projects. He has paid special attention to highlighting the
practical applications of the models developed. Mostly, the models are characterized by
unique solutions; in many cases, they have been presented with specifying their coauthors or the persons for whom the models were developed with an intention of using
them for joint applications.
The author would like to emphasize the great importance of the people and
institutions he collaborated with when developing the models presented (see the attached
list of publications). It is symptomatic that the number of people and institutions
involved in practical application of the tools developed as aids to support the
examination of motor vehicles and other engineering works steadily grew with time.
Noteworthy is the considerable influence of the literature available to the author in
the period covered here, dedicated to analytical mechanics and vibration analysis
(authors: R. Gutowski, J. Maryniak, J. I. Nejmark and N. A. Fufajew, J. W. Osiecki,
Z. Osiński) and to the theory of vehicle motion and dynamics (authors: S. Arczyński,
E. Kamiński
and
J. Pokorski,
J. W. Osiecki,
T. Kasprzyk,
L. Prochowski,
R. Andrzejewski,
A. Kleczkowski,
J. Knapczyk,
T. L. Stańczyk,
J. Wicher,
J. Lanzendoerfer, C. Szczepaniak, J. Kisilowski, A. Chudzikiewicz, R. S. Sharp,
H. Pacejka, D. A. Crolla, P. S. Fancher, L. Segel, J. R. Ellis, R. R. McHenry,
N. J. De Leys, S., W. R. Garrot, K. M. Captain, D. N. Wormley, W. R. Allen,
D. H. Weir, D. T. McRuer, S. Nordmark, M. Mitschke, A. Zomotor, G. Rill, K. Rompe,
B. Heissing, P. Lugner, R. W. Rotenberg, A. Litwinow, A. A. Chaczaturow).
It would be difficult to imagine that the work on the issues presented here could be
successfully done without knowledge of the publications issued by such organizations
and publishers operating in Poland (as WNT, WKŁ, PWN, ZNIPPW, PNPW-Transport,
AMot, ATr) and abroad (as VSD, SAE Paper, SAE SP, SAE Transactions, IJofVD,
IJofSV, Swets & Zeitlinger Publishers, John Wiley&Sons Inc.). The benefits gained
1
Prof. Zbigniew Lozia, D.Sc., Ph.D. – Warsaw University of Technology, Faculty of Transport,
ul. Koszykowa 75, 00-662 Warsaw, Poland. [email protected]
9
from the participation in seminars and conferences held in Poland (BwPS Warszawa,
BwPS Kielce, BSwTS Kazimierz Dolny, AUTOPROGRES, KONMOT Kraków, KHiB
Łódź, IES Kraków) and abroad (SAE, IAVSD, DSC) cannot be ignored, either.
Very much inspiration was also drawn from collaboration with colleagues working
on similar issues, who in many cases were also co-authors of publications or
implementations
(P. Zagrodzki,
G. Marcinkowski,
M. Guzek,
I. Stegienka,
W. Mackiewicz, P. Zdanowicz, W. Pieniążek, J. Pokorski, T. L. Stańczyk, D. Żardecki,
L. Prochowski, W. Luty, J. Jackowski, G. Ślaski, J. Unarski, W. Wach, A. Gajek,
A. Reński, J. Wicher, D. Więckowski, S. Nordmark, O. Nordström).
2. Models for the research on low-velocity vehicle motion
Such models are used for the assessment of vehicle agility. The simplest of them are
based on the principles of plane motion (Figs. 1 and 2). When building them, the author
(together with co-authors of the models) used the known patterns, e.g. those presented in
[1, 6], describing the vehicle motion, in most cases with ignoring the tyre sideslip angles,
i.e. built with using the Ackermann model [1]. In [33] (Fig. 1), the agility of two-axle
and three-axle city buses operated in Warsaw was assessed. Based on analyses carried
out, the values of turning radii and swept path widths were determined. These
calculations provided grounds for evaluating the method of dimensioning various
transport infrastructure elements. Dimensional incompatibility between street
intersections in towns and city buses was shown to be quite frequent. This
incompatibility may pose a hazard to the road traffic safety. In [35] (Fig. 2), calculations
were carried out for model data corresponding to specifications of the Mercedes Benz
Actros 4148 AK truck. The most favourable and unfavourable configurations of the
steered and non-steered wheels were indicated.
The vehicle agility was also assessed with the use of models where tyre sideslip was
taken into account as well. Fig. 3 shows a model of motion of a two-axle motor vehicle
with 10 degrees of freedom (DoF): coordinates xO1, yO1, zO1 of point O1 (centre of
vehicle mass) in inertial coordinate system Oxyz, vehicle body yaw (heading) angle ψ 1,
pitch angle φ1, and roll angle 1, and steering angles φ5, φ6, φ7, φ8 [22]. An authorial
simulation program named ZL_FL_3D determines them with rough methods but with
high accuracy of calculations. A model of the steering system has been presented in
Fig. 4, with solutions typical for motor trucks being used as an example. In this model,
the geometric and spring characteristics of the system are taken into account.
Within works reported in [39, 40], a model of a two-axle motor truck was tested to
find out how strong effect on the turning radius value is produced by asymmetric
operation of the braking system and power transmission system. Prior to this, the
simulation model was verified experimentally. The test results obtained confirmed the
preliminary hypothesis as regards the expectation that the agility of a two-axle vehicle
can be thus improved.
In study [10], the agility of a passenger car moving “forwards” was compared with
that of the same car moving “backwards”. This was done with the use of a vehicle model
presented in Fig. 3 and a steering system model similar to the one shown in Fig. 4, but
with a parallel structure typical for passenger cars and delivery vehicles (see also
Fig. 18). The vehicle manoeuvres simulated during the tests included vehicle drive along
a path with a constant curvature radius (steady-state curvilinear motion) on a road
surface affording good adhesion, vehicle drive with a “saw-tooth” input applied to the
steering wheel, and vehicle pulling-in to a parking place parallel to a roadway edge. The
vehicle speed was limited to 40 km/h. The results obtained have shown significant
10
differences in the vehicle behaviour when it moved “forwards” and “backwards”. Some
of them are known to every experienced driver and this fact may rather be considered
just confirmation of the usefulness of the simulation method adopted.
The models presented in Figs. 3 and 4 were used at simulation testing of motor
vehicles Fiat CC, Daewoo FSO***, Star 1142, and MAN-Star.
L
L1
LZP
LZT
L4
L2
L3
ß4
ß2
b2
B
OS
OP
b3
b4
CO
b1
ß1
ß3
r1
r2
r3
r4
rCO
O
Fig. 1. Model of low-velocity motion of a
three-axle articulated bus [33]
Fig. 2. Model of low-velocity motion of a
four-axle vehicle, with 8W/4WS wheel
configuration taken as an example [35]
Fig. 3. Model of motion of a two-axle
vehicle [22]
Fig. 4. Model of a steering system, motortruck version taken as an example [39, 40]
3. Models for the research on vehicle dynamics in frequency domain
The vehicle testing in frequency domain provides information different from that
obtainable from the testing of vehicle motion in space or in time domain. In this case, the
matter of particular interest is the susceptibility of mechanical systems (with motor
vehicles being counted among them), to phenomena related to oscillations. The models
used for this purpose may be linear or non-linear. The former, in spite of simplified
description of vehicle properties, make it possible to carry out analyses of more general
nature, including the application of one-dimensional or multidimensional (transmittance
matrix) notation based on operational transmittance (transfer function) of selected
quantities. Theoretical fundamentals for such an approach to dynamics of mechanical
11
systems, especially including vehicles, may be found in publications [1, 6, 43, 44, 45]. In
most cases, “quarter-car” models are used, including strongly non-linear models as well
(e.g. [11]).
Figs. 5 and 6 show two linear models used for examining selected vehicle features
in frequency domain. The model presented in Fig. 5 with the accompanying simulation
program named SIDYSL [11] were employed by the author for comparative
examinations, in frequency domain, of models used at many universities and research
centres and representing the radial characteristics of a pneumatic tyre, referred to as
PCTM (point contact tyre model) and FFTM (fixed footprint tyre model). At the
examinations, the road surface was assumed to have random irregularities. The
examinations confirmed the opinion, expressed also by other authors in their
publications, about the superiority of the latter model. In turn, the model presented in
Fig. 6 with the accompanying simulation program named ZLCT1 [12] were used to
assess the impact of flexible fastening of the tow hook (elements kc and cc) on the
dynamics of a motor vehicle with a trailer in constant-velocity rectilinear motion. Such a
design solution was the subject of a more extensive research carried out at VTI (The
Swedish National Road and Transport Research Institute) in Linköping. The calculations
carried out by the author revealed that the vertical dynamic loads of the hook would be
considerably reduced, by 10 % to almost 40 % depending on the road class and vehicle
speed, thanks to the application of the flexible fastening of the tow hook. This would
lead to a reduction in the probability of separation of the trailer being towed from the
towing vehicle. Such cases took place in Sweden when tow hooks of traditional design
were used.
Fig. 5. Model of a system used for comparative examinations of the PCTM and FFTM
pneumatic tyre models in frequency domain [11]: road surface with random
irregularities; 4 DoF: zM, α, wP, wT; vehicle velocity V = constant;
vehicle modelled: Fiat 125p
12
Fig. 6. Model of constant-velocity (V = const) rectilinear motion of a two-axle motor
vehicle with a one-axle trailer: road surface with random irregularities;
4 DoF: zF, zR, zT, zBw; vehicle modelled: Mercedes 508 D (delivery vehicle) [12]
4. General-type models for the research on vehicle motion and dynamics in time
domain and in space
These models were built by the author for research purposes and as tools used at
works carried out to support design engineers or specialists working on motor vehicle
safety issues.
A model of rectilinear motion of a two-axle motor vehicle on an uneven road
surface has been presented in Fig. 7. The model shown in Fig. 7a, incorporated in the
simulation program ZLS2D, is the basic version [7, 11], used at author’s work on his
doctoral dissertation and at other studies. The model shown in Fig. 7b, associated with
the simulation program ZLS2D(MK), constitutes a version expanded by adding a
representation of the possible movements of the cargo transported on the load bed [8].
a)
b)
tyre model
tyre model
tyre model
tyre model
Fig. 7. Model of rectilinear motion of a two-axle motor vehicle on a rough road surface:
a) basic version [7,11]; 7 DoF: xM, zM, α, ζP, ζT, φP, φT; vehicles modelled: Fiat 125p,
Zastava 110, Berliet PR110;
b) version expanded by adding a representation of the cargo transported on the load
bed [8]; 8 DoF: xM, zM, α, ζP, ζT, φP, φT, ξQ; vehicle modelled: FSO 1500 pick-up
13
A three-dimensional 14-DoF model of a two-axle motor vehicle has been presented
in Fig. 8. Fig. 8a shows its basic version, which is used in a simulation program named
SYMRU14 [13, 30, 31]. A developed version of this model, covering a wider range of
model properties, can be seen in Fig. 8b; it is used with the simulation program
ZL3DSYM [14, 15, 19]. These models were employed to assess the effects of
asymmetric operation of vehicle brakes [31] (at this work, a model representing the
controlling properties of the driver, drawn from the US literature – see [18], was used as
well), to assess the impact of random irregularities in the road surface on the course of a
single lane-change manoeuvre [13], and to assess driver’s activities when the vehicle
moved on an even (smooth) and uneven (rough) road surface [15]. A next version of this
model, developed again and related to the simulation program ZL3D_SYM [18], has
been presented in Fig. 9. It was used to assess the impact of suspension roll stiffness and
distribution of this stiffness between the front and rear suspension system on the
transverse stability of the vehicle, which was a prototype design of a DAEWOO delivery
vehicle [5]. The primary objective of the design changes was to reduce vehicle’s
propensity to rollover.
a)
b)
Fig. 8. Three-dimensional model of a two-axle motor vehicle;
14 DoF: xO1, yO1, zO1, ψ1, 1, 1, ζ1O2, ζ1O3, ζ1O4, α4, 5, 6, 7, 8 (or 5, 6, 7, 8);
vehicle modelled: FSO Polonez 125PN:
a) basic version [13, 30, 31]; b) modified version [14, 15, 19]
14
Fig. 9. Three-dimensional model of a two-axle motor vehicle;
14 DoF: xO1, yO1, zO1, ψ1, 1, 1, ζ1O2, ζ1O3, ζ1O4, α4, 5, 6, 7, 8;
vehicle modelled: a prototype DAEWOO motor vehicle [18]
A three-dimensional 14-DoF model of a two-axle motor truck has been presented in
Fig. 10. It is related to a simulation program ZL_STAR [18, 34]. This model was used to
assess the propensity of a motor truck to rollover [17, 18, 34]. At the work described in
[21], it was used to analyse the impact of damping in vehicle suspension system,
especially the dry friction, on the values of the dynamic normal reactions at the tyre-road
contact area during motion on an uneven road surface with random irregularities.
The models shown in Figs. 9 and 10 were also used at works being done to assess
the impact of simplifications in the construction of automotive “black boxes”, referred to
as event data recorders (EDR) or accident data recorders (ADR), on road accident
reconstruction results, especially with respect to the assessment of pre-accident
situations [2, 3]. The models representing the operation of automotive EDR and ADR
units were made by M. Guzek.
Fig. 10. Three-dimensional model of a two-axle motor truck;
14 DoF: xO1, yO1, zO1, ψ1, 1, 1, ζ1O4, 4, ζ1O9, 9, 5, 6, 7, 8;
vehicles modelled: Star 1142, and MAN-Star [18,34]
15
This group of models includes the one the use of which for the vehicle agility
assessment purposes has been described in a previous section and which has been shown
in Fig. 3. The model was used [9] for simulation calculations, carried out to compare the
characteristics of steerability (ease of steering) of a specific motor vehicle when moving
“forwards” and “backwards”. The vehicle velocity was limited to 40 km/h because it
would be difficult to achieve higher velocities when “reversing” in real conditions and it
would not be possible then to consider the results obtained in relation to actual
manoeuvring. The steerability characteristics were more favourable when the vehicle
moved forwards: the vehicle remained understeering over the whole range of lateral
accelerations under consideration; the understeering is considered better than the varying
characteristics observed at “reversing”, when the vehicle may be understeering or
oversteering depending on the value of its lateral acceleration and, in result of this, the
vehicle behaviour becomes unpredictable and requires higher psychomotor capabilities
of the driver.
Fig. 11 shows a three-dimensional 14-DoF model of a Light Tactical Vehicle (LTV)
Dzik, a patrol and intervention motor vehicle, which was manufactured at AMZ-Kutno
Sp. z o.o. The model is associated with a simulation program named ZL_Dzik [24].
Publication [41] includes results of calculations carried out to assess the impact of the
position of the centre of mass of this vehicle on its behaviour in curvilinear motion. The
assessment was based on results of an analysis of uniform vehicle motion along a circle
(steady-state curvilinear motion) and on determining the maximum velocity at which the
steering wheel may be rapidly turned by 90 ° without vehicle rollover. The model used
for this purpose was previously verified experimentally, with carrying out the typical
tests recommended by ISO. Furthermore, results of simulation tests carried out to assess
the impact of immunity of the LTV Dzik to tyre sideslip and of the stiffness of its antiroll bar on the vehicle behaviour in curvilinear motion have been presented in [42].
Fig. 11. Three-dimensional model of a two-axle motor vehicle;
14 DoF: xO1, yO1, zO1, ψ1, 1, 1, ζ1O4, 4, ζ1O9, 9, 5, 6, 7, 8;
vehicle modelled: LTV Dzik [24]
16
Fig. 12 shows a three-dimensional 22-DoF model of a four-axle vehicle KTORosomak, associated with a simulation program ZL_KTO1 [26]. Publications [4, 27, 28,
29] include results of experimental verification of the model and the simulation program,
providing grounds for using this tool at vehicle stability tests, inclusive of tests carried
out under tyre blow-out conditions.
The simulation test results having been published were obtained from tests
performed with simulating the conditions in which experimental tests are difficult or
impossible for being carried out. They confirmed good properties of the object under
test, even at high velocities of vehicle motion. The tests revealed a visible impact of the
failure of a vehicle tyre (or tyres) on vehicle characteristics in rectilinear and curvilinear
motion. The testers also managed to identify specific situations where the object under
test showed a tendency to lose its stability.
One of the three-dimensional models of motion of a two-axle motor vehicle, with a
complex model of the steering system, has been presented in Fig. 13. The models of this
family have 14 degrees of freedom. They are related to programs ZL_DZ*** [36, 37,
38]. They were built in order to incorporate two formal descriptions of the phenomena of
friction (tar(…)) and freeplay (luz(…)), formulated by D. Żardecki, into a program for
the simulation of motion and dynamics of a motor vehicle. In [36], the authors presented
results of testing the susceptibility of the lateral dynamics of a two-axle vehicle (at tests:
parking manoeuvre to standard ECE 79; combination of two tests, i.e. transient test to
ISO 7401 and steady-state circular driving test to ISO 4138; test with steady sinusoidal
input applied to the steering wheel to ISO 7401) to changes in the freeplay and friction in
the steering system. In [37], the authors presented results of a typical open-loop test
(combination of three tests, i.e. transient test to ISO 7401, steady-state circular driving
test to ISO 4138, and “let-go-of-the-steering-wheel” test) for vehicles provided with
2WS and 4WS systems, for different levels of dry friction and freeplay in the steering
system. It was ascertained that both of these phenomena have a significant impact on the
motion and dynamics of a motor car. In [38], the authors presented the influence of
various formalisms in the description of dry friction on the course of vehicle tests
(combinations of the said open-loop manoeuvring tests recommended by ISO). It was
found that in spite of using three different descriptions of dry friction, recommended in
various publications, the mutually corresponding results of the simulation tests carried
out were very similar to each other.
Fig. 12. Three-dimensional model of a four-axle special vehicle;
22 DoF: xOC, yOC, zOC, ψC, C, C, ζCOi, i, i=1,…,8;
vehicle modelled: KTO-Rosomak [26]
17
Fig. 13. One of the three-dimensional models of a two-axle motor vehicle, with
a complex model of the steering system. The models of this family have 14 degrees of
freedom: xC, yC, zC, ψ, , , 1, 2, 3, 4, αk, αp, α2, α3.
Vehicle modelled: Fiat Seicento [36, 37, 38]
5. Models for the simulation of vehicle motion and dynamics in time domain and in
space, dedicated to driving simulators
A separate group may be formed from models intended for being used in driving
simulators. Apart from high accuracy of mapping real vehicle properties in various
conditions of motion, these models should make it possible to carry out “real-time”
calculations and this, for the usually adopted time sharing for simulator computers
(regardless of series or parallel configuration of the software operation system), leads to
a requirement that the computer system should operate with a speed higher by more than
an order of magnitude (calculations for one second of motion and dynamics of a motor
vehicle should be carried out within less than 0.1 second). The growth in computation
speed is fostered by ongoing improvements in computer performance and appropriate
construction of algorithms of the vehicle motion and dynamics simulation programs.
Fig. 14 shows a 2-DoF “bicycle model” of a four-wheel vehicle [46]. The
accompanying program ZL-IP was used for the simulation of curvilinear motion of a
motor vehicle on a drum-type test rig. Therefore, this model may be said to be a
precursor of a motor vehicle driving simulator, implemented in a joint effort by the
teams of the Institute of Vehicles and the Faculty of Transport of the Warsaw University
of Technology.
Fig. 14. “Bicycle model” of a four-wheel vehicle; 2 DoF: yO1, ψ1 (V = const);
vehicle modelled: Fiat 125p [46]
18
Fig. 15 shows a 7-DoF model of a two-axle vehicle for “real-time” simulation of
motion and dynamics of a motor vehicle [20, 23]. This model is associated with a
simulation program ZL_RTS3; it has been successfully used since 1998 in the first
Polish driving simulator named “autoPW”, built at the Faculty of Transport of the
Warsaw University of Technology in cooperation with colleagues from the Institute of
Vehicles of the same University, Institute of Automobiles and Internal Combustion
Engines of the Cracow University of Technology, and Grapolelectronic (Krzysztof
Grąziewicz).
Fig. 15. Model of a two-axle vehicle for “real-time” simulation of motion and dynamics
of a motor vehicle [20, 23], used in the “autoPW” driving simulator;
7 DoF: xO1, yO1, ψ1, 5, 6, 7, 8; vehicles modelled: Fiat CC, Chrysler Neon, Daewoo
FSO***, Ford Transit, Star 1142, and MAN-Star
Since 2008, a team of specialists from the Department of Vehicle Maintenance and
Operation of the Faculty of Transport of the Warsaw University of Technology, assisted
(within the scope of experimental testing of tyres and vehicles) by partners from Institute
of Automobiles and Internal Combustion Engines of the Cracow University of
Technology, Vehicle Tests Laboratory (BLP) and Simulation Tests Laboratory (BLY) of
PIMOT (Automotive Industry Institute), and Division of Construction and Safety of
Motor Vehicles of the Institute of Motor Vehicles and Transportation of the Military
University of Technology, has been collaborating with ETC-PZL Aerospace Industries
Sp. z o.o. in the field of the construction of dynamic simulators of motor vehicle driving.
The simulators covered by the scope of this cooperation include devices meeting the
minimum requirements for the “top-of-the-range simulators” and are intended for being
used in the process of training and examining of drivers for the purposes of initial
qualification of drivers, according to provisions of EU Directive 2003/59/EC. A 12-DoF
model of a three-axle bus or motor truck for “real-time” simulation of motion and
dynamics of the vehicle, used in the SYM-SAM driving simulator developed by ETCPZL Aerospace Industries Sp. z o.o., has been presented in Fig. 16. Fig. 17, in turn,
19
shows a 29-DoF model of a tractor-and-bus-semitrailer unit for “real-time” simulation of
motion and dynamics of the vehicle, used in the same driving simulator.
Fig. 16. Model of a tree-axle bus or motor truck for “real-time” simulation of motion and
dynamics of a motor vehicle, used in the SYM-SAM driving simulator developed by
ETC-PZL Aerospace Industries Sp. z o.o.;
12 DoF: xO1, yO1, zO1, ψ1, 1, 1, 5, 6, 7, 8, 51, 61;
vehicles modelled: MAN- Star 1142, Mercedes Atego, Autosan Lider A1012T
Fig. 17. Model of a tractor-bus-semitrailer unit for “real-time” simulation of motion and
dynamics of the vehicle, used in the SYM-SAM driving simulator developed by ETCPZL Aerospace Industries Sp. z o.o.; 29 DoF: xO1, yO1, zO1, ψ1, 1, 1, ζC1, ζC2, ζC3, ζC4,
1, 2, 3, 4, ψN, N, N, ζN1, ζN2, ζN3, ζN4, ζN5, ζN6, 7, 8, 9, 10, 11, 12;
vehicle modelled: Mercedes Actros 1841
20
Within one of the projects carried out, a model and a simulation program for driving
simulators for special vehicles were built for ETC-PZL Aerospace Industries Sp. z o.o.
Such simulators are used by the Police Academy in Szczytno and by the Republic of
Poland’s Government Protection Bureau. Figs. 18 and 19 show 14-DoF models of a
passenger vehicle and a light-duty vehicle for both the carriage of goods and passengers,
respectively [25]. The related simulation programs have been named ZL_SPC1 and
ZL_SPC2, respectively.
Fig. 18. Model of a passenger car for “real-time” simulation of motion and dynamics of
a motor vehicle, used in the driving simulator developed by ETC-PZL Aerospace
Industries Sp. z o.o. [25]; 14 DoF: xOC, yOC, zOC, ψC, C, C, ζCo1, ζCo2, ζCo3, ζCo4, 1 2,
3, 4; vehicle modelled: KIA cee’d SW
Fig. 19. Model of a light-duty vehicle for both the carriage of goods and passengers for
“real-time” simulation of motion and dynamics of a motor vehicle, used in the driving
simulator developed by ETC-PZL Aerospace Industries Sp. z o.o. [25]; 14 DoF: xOC,
yOC, zOC, ψC, C, C, ζCo1, ζCo2, ζCo3, ζCo4, 1 2, 3, 4; vehicle modelled: Fiat Ducato
21
6. Conclusion
Examples of authorial models of motor vehicle motion and dynamics, used at the
“off-line” and “real-time” simulation, have been presented. Almost all of them
successfully passed experimental verification, which has been more comprehensively
described in monographs [4, 18, 23, 26, 28, 29] and other publications [3, 16, 19, 32].
Some of the results of the successful verification of the simulation models, especially
those of commercial importance, have the nature of industrial secret.
The models were developed during the recent period of 39 years. They are still used
at author’s own work, at research works carried out by his younger co-workers, or at
research, purpose-oriented, development, and commercial projects.
References:
[1]
Arczyński, S.: Mechanika ruchu samochodu (Mechanics of motion of a motor
vehicle). WNT, Warszawa 1993.
[2]
Guzek, M.; Lozia, Z.: Possible Errors Occurring during Accident Reconstruction
Based on Car “Black Box” Records. 2002 World SAE Congress and Exposition.
Detroit, Michigan, USA, March 4–7 2002, SAE TP 2002-01-0549 (also in
Special Publication SP-1666 “Accident Reconstruction 2002”).
[3]
Guzek, M.; Lozia, Z.; Pieniążek, W.: Accident Reconstruction Based on EDR
Records – Simulation and Experimental Study. SAE TP 2007-01-0729, separate
booklet, 12 pages (also in Special Publication SP-2063 “Accident Reconstruction
2007”).
[4]
Guzek, M.;
Lozia, Z.;
Pieniążek, W.;
Zdanowicz, P.:
Weryfikacja
eksperymentalna modelu symulacyjnego ruchu i dynamiki wieloosiowego pojazdu
specjalnego (Experimental verification of a simulation model of motion and
dynamics of a multi-axle special vehicle). Chapter 8 in the monograph “Badania
eksperymentalne i symulacyjne dynamiki pojazdu wieloosiowego w warunkach
uszkodzenia ogumienia” (“Experimental and simulation research on the
dynamics of a multi-axle special vehicle under tyre failure conditions”).
Wydawnictwo Politechniki Krakowskiej (Publishing House of the Cracow
University of Technology), 2012, ISBN 978-83-7242-674-1, pp. 110–136.
[5]
Guzek, M.; Lozia, Z.; Reński, A.: Wpływ sztywności kątowej zawieszeń na
stateczność poprzeczną pojazdu dwuosiowego na przykładzie samochodu
dostawczego (The influence of suspension roll stiffness on the lateral stability of a
two-axle vehicle, for a delivery motor vehicle taken as an example). Zeszyty
Instytutu Pojazdów Politechniki Warszawskiej, No. 3(29)/98, Warszawa 1998,
pp. 17–29.
[6]
Kamiński, E.; Pokorski, J.: Teoria samochodu. Dynamika zawieszeń i układów
napędowych pojazdów samochodowych (Motor vehicle theory. Dynamics of
motor vehicle suspension systems and drivelines). WKŁ, Warszawa 1983.
[7]
Kisilowski, J.; Lozia, Z.: Modelling and Simulating the Braking Process of
Automotive Vehicle on Uneven Surface. The Dynamics of Vehicles on Roads and
on Tracks – Supplement to Vehicle System Dynamics, Vol. 15, Swets &
Zeitlinger B. V. Lisse and IAVSD, 1986, pp. 250–263.
[8]
Kozyra, M.; Lozia, Z.: Analiza numeryczna procesu hamowania samochodu w
ruchu prostoliniowym z uwzględnieniem oddziaływania ładunku (Numerical
analysis of the process of motor vehicle braking in rectilinear motion with the
load impact being taken into account). International Conference “Transsystem
22
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'89”, Warszawa, 21–23 Sept. 1989, Conference proceedings, Section C, pp. 75–
78.
Kulma, J.; Lozia, Z.: Simulation Method of Comparative Evaluation of the
Steerability of a Passenger Car when Moving Forwards and Backwards /
Symulacyjna ocena porównawcza kierowalności samochodu osobowego w ruchu
„do przodu” i „do tyłu”. The Archives of Automotive Engineering – Archiwum
Motoryzacji, Vol. 63, No. 1 (2014), pp. 51–70 (in English) / pp. 157–176 (in
Polish).
Kulma, J.; Lozia, Z.: Simulation Method of Comparative Evaluation of the Agility
of a Passenger Car When Moving “Forwards” and “Backwards” / Symulacyjna
ocena porównawcza zwrotności samochodu osobowego w ruchu „do przodu” i
„do tyłu”. The Archives of Automotive Engineering – Archiwum Motoryzacji,
Vol. 64, No. 2 (2014), pp. 49–64 (in English) / pp. 149–164 (in Polish).
Lozia, Z.: Wybrane zagadnienia symulacji cyfrowej procesu hamowania
samochodu dwuosiowego na nierównej nawierzchni drogi (Selected problems of
digital simulation of the process of braking a two-axle motor vehicle on uneven
road surface). Doctoral dissertation defended at the Faculty of Automotive and
Construction Machinery Engineering of the Warsaw University of Technology on
26 March 1986.
Lozia, Z.: Analiza wpływu podatnego zamocowania haka holowniczego na
dynamikę zestawu samochód – przyczepa w ruchu prostoliniowym ze stałą
prędkością (Analysis of the impact of flexible fastening of the tow hook on the
dynamics of a motor vehicle with a trailer in constant-speed rectilinear motion).
The 5th Scientific Conference of the Institute of Transport of the Warsaw
University of Technology “Science and Practice in Transport”, Warszawa, 19–21
Sept. 1990, Conference proceedings, pp. 116–123.
Lozia, Z.: An Analysis of Vehicle Behaviour during Lane-Change Manoeuvre on
an Uneven Road Surface. Supplement to Vehicle System Dynamics, Vol. 20,
Swets & Zeitlinger B. V. Lisse and IAVSD, 1992, pp. 417–431.
Lozia, Z.: ZL3DSYM. Program do symulacji ruchu samochodu dwuosiowego.
Możliwości i ograniczenia (ZL3DSYM. Program for the simulation of motion of a
two-axle motor vehicle). Autoprogres’93. Conference organized by PIMOT
Warszawa, WITPiS Sulejówek, SIMP (Association of Polish Mechanical
Engineers) – Automotive Section, Jachranka 11–13 May 1993, Papers, Vol. III,
pp. 51–62.
Lozia, Z.: A Comparison of Driver Steering Activity during Motion on an Even
and Uneven Road Surface. The Dynamics of Vehicles on Roads and on Tracks –
Supplement to Vehicle System Dynamics, Vol. 23, Swets & Zeitlinger B. V.
Lisse and IAVSD, 1994, pp. 322–333.
Lozia, Z.: Weryfikacja modelu dynamiki samochodu z nadwoziem furgonowym.
Ruch krzywoliniowy (Verification of a model of dynamics of a motor vehicle with
a van-type body. Curvilinear motion). Biuletyn Wojskowej Akademii
Technicznej (Bulletin of the Military Academy of Technology), Year XLV, No. 4
(524), Warszawa 1996, pp. 37–53.
Lozia, Z.: Ocena możliwości wywrotki bocznej samochodu ciężarowego na
równej nawierzchni drogi (Assessment of the possibility of motor truck rollover
on a road with even surface). Biuletyn Wojskowej Akademii Technicznej
(Bulletin of the Military Academy of Technology), Year XLV, No. 4 (524),
Warszawa 1996, pp. 55–71.
23
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[21]
[22]
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[24]
[25]
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[28]
Lozia, Z.: Analiza ruchu samochodu dwuosiowego na tle modelowania jego
dynamiki (Analysis of biaxial car motion based upon dynamic models). A
monograph, Prace Naukowe Politechniki Warszawskiej – Transport, Vol. 41.
Warszawa 1998.
Lozia, Z.: Vehicle Dynamics and Motion Simulation versus Experiment. 1998
SAE International Congress and Exposition, Detroit, Michigan, USA, February
23–26, 1998, SAE TP 980220 (also in Special Publication SP-1361 “Vehicle
Dynamics and Simulation, 1998” and in SAE 1998 Transactions – Passenger
Cars, Section 6, Vol. 107, pp. 341–360, 1999).
Lozia, Z.: Model symulacyjny ruchu i dynamiki samochodu dwuosiowego,
wykorzystywany w symulatorze (Simulation model of motion and dynamics of a
two-axle motor vehicle, used in a real-time simulator). Zeszyty Instytutu
Pojazdów Politechniki Warszawskiej, No. 4(34)/99, pp. 37–51.
Lozia, Z.: Vehicle Dynamics Model as Road-pavement Load Generator.
Engineering Transactions (Rozprawy Inżynierskie), Polish Academy of Sciences,
Vol. 48, No. 3, 2000, pp. 243–259.
Lozia, Z.: Symulacja testów otwartych układu kierowca-pojazd-otoczenie
(Simulation of open-loop tests of the driver–vehicle–environment system). Teka
Komisji Naukowo-Problemowej Motoryzacji (Files of the Scientific and Problem
Committee of the Automotive Industry), Polish Academy of Sciences, Division in
Cracow, Vol. 26–27, Kraków 2003, pp. 229–234.
Lozia, Z.: Symulatory jazdy samochodem (Motor vehicle driving simulators).
WKŁ Warszawa 2008, ISBN: 978-83-206-1663-7, a monograph.
Lozia, Z.: Model symulacyjny ruchu samochodu LTV Dzik (Simulation model of
Light Tactical Vehicle Dzik). Zeszyty Naukowe Instytutu Pojazdów / Politechnika
Warszawska (Proceedings of the Institute of Vehicles / Warsaw University of
Technology), No. 3(70)/2008, pp. 17–24.
Lozia, Z.: Modele symulacyjne ruchu i dynamiki dwóch pojazdów
uprzywilejowanych (Vehicle dynamics simulation models of two emergency
vehicles). Czasopismo Techniczne. Mechanika / Technical Transactions.
Mechanics, Cracow University of Technology, 3-M/2012, pp. 19–34.
Lozia, Z.: Model symulacyjny ruchu i dynamiki wieloosiowego pojazdu
specjalnego (Simulation model of motion and dynamics of a multi-axle special
vehicle). Chapter 7 in the monograph “Badania eksperymentalne i symulacyjne
dynamiki pojazdu wieloosiowego w warunkach uszkodzenia ogumienia”
(“Experimental and simulation research on the dynamics of a multi-axle special
vehicle under tyre failure conditions”). Wydawnictwo Politechniki Krakowskiej
(Publishing House of the Cracow University of Technology), 2012, ISBN 97883-7242-674-1, pp. 91–109.
Lozia, Z.; Guzek, M.; Pieniążek, W.; Zdanowicz, P.: Metodyka i przykładowe
wyniki badań symulacyjnych ruchu wieloosiowego pojazdu specjalnego w
warunkach eksplozyjnego uszkodzenia opon (Methodology and exemplary results
of simulation research of multi-axle special vehicle under tire blow-out
condition). Zeszyty Naukowe Instytutu Pojazdów / Politechnika Warszawska
(Proceedings of the Institute of Vehicles / Warsaw University of Technology),
No. 4(90)/2012, pp. 19–42.
Lozia, Z.; Guzek, M.; Zdanowicz, P.: Wyniki symulacji ruchu wieloosiowego
pojazdu specjalnego w przypadku eksplozyjnego uszkodzenia ogumienia (Results
of simulation research on motion of a multi-axle special vehicle under tyre blow24
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
out conditions). Chapter 9 in the monograph “Badania eksperymentalne i
symulacyjne dynamiki pojazdu wieloosiowego w warunkach uszkodzenia
ogumienia” (“Experimental and simulation research on the dynamics of a multiaxle special vehicle under tyre failure conditions”). Wydawnictwo Politechniki
Krakowskiej (Publishing House of the Cracow University of Technology), 2012,
ISBN 978-83-7242-674-1, pp. 137–156.
Lozia, Z.; Guzek, M.; Zdanowicz, P.: Wpływ zachowania kierowcy na
bezpieczeństwo ruchu wieloosiowego pojazdu specjalnego w przypadku
eksplozyjnego uszkodzenia ogumienia (Impact of driver’s behaviour on the safety
of motion of a multi-axle special vehicle under tyre blow-out conditions).
Chapter 10 in the monograph “Badania eksperymentalne i symulacyjne dynamiki
pojazdu wieloosiowego w warunkach uszkodzenia ogumienia” (“Experimental
and simulation research on the dynamics of a multi-axle special vehicle under
tyre failure conditions”). Wydawnictwo Politechniki Krakowskiej (Publishing
House of the Cracow University of Technology), 2012, ISBN 978-83-7242-6741, pp. 157–173.
Lozia, Z.; Marcinkowski, G.: Model samochodu dwuosiowego do badań
symulacyjnych ruchu nieustalonego (Model of a two-axle motor vehicle for
simulation research on unsteady motion). International Scientific Seminar
“Steerability and modelling of the dynamics of motion of vehicles and
construction machinery”, Radziejowice, 4–6 May 1988, Prace PIMB, Nos. 1, 2,
3/1988.
Lozia, Z.; Marcinkowski, G.: Zagrożenie bezpieczeństwa ruchu samochodu
wynikające z asymetrycznego rozdziału sił hamowania na koła strony prawej i
lewej (Hazard to the safety of motor vehicle motion arising from asymmetric
distribution of braking forces between the wheels of the right and left vehicle
side). Proceedings of the Brake Conference ’91, Łódź, 3–5 Sept. 1991, Vol. 2,
pp. 122–132.
Lozia, Z.; Pieniążek, W.: Real Time 7DOF Vehicle Dynamics Model and Its
Experimental Verification. 2002 World SAE Congress and Exposition, Detroit,
Michigan, USA, March 4–7 2002, SAE TP 2002-01-1184 (also in Special
Publication SP-1656 “Vehicle Dynamics and Simulation 2002”).
Lozia, Z.; Pudło, J.: Niekompatybilność wymiarowa elementów infrastruktury
drogowej miast i autobusów, jako możliwe zagrożenie bezpieczeństwa ruchu
pojazdów (Dimensional incompatibility of urban road infrastructure elements
and buses). Paragraf na drodze, special issue, October 2011, Wydawnictwo
Instytutu Ekspertyz Sądowych (Institute of Forensic Research Publishers),
Kraków, ISSN 1505-3520, pp. 283–297.
Lozia, Z.; Stegienka, I.: Biaxial Vehicle Motion Simulation and Animation. The
Dynamics of Vehicles on Roads and on Tracks (ed. L. Segel) – Supplement to
Vehicle System Dynamics, Vol. 25, Swets & Zeitlinger B. V., Lisse, 1996,
pp. 426–437.
Lozia, Z.; Turski, K.: Analiza zwrotności pojazdu czteroosiowego (Analysis of
four-axle road vehicle manoeuvrability). Autobusy: technika, eksploatacja,
systemy transportowe, No. 6/2014, page 3 + a text file *.pdf on a CD, pp. 179–
184.
Lozia, Z.; Żardecki, D.: Vehicle Dynamics Simulation with Inclusion of Freeplay
and Dry Friction in Steering System. 2002 World SAE Congress and Exposition,
Detroit, Michigan, USA, March 4–7 2002, SAE TP 2002-01-0619, separate
25
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
booklet, 17 pages (also in Special Publication SP-1654 “Steering and Suspension
Technology Symposium 2002” and in SAE Transactions 2002, Section 6, Vol.
111, pp. 907-923).
Lozia, Z.; Żardecki, D.: Dynamics of Steering System with Freeplay and Dry
Friction – Comparative Simulation Investigation for 2WS and 4WS Vehicles.
SAE TP 2005-01-1261, separate booklet, 10 pages (also: in Special Publication
SP-1915 “Steering and Suspension, Tires and Wheels”).
Lozia, Z.; Żardecki, D.: Friction and Stick-Slip Phenomena in Steering system –
Modeling and Simulation Studies. SAE TP 2007-01-1153, separate booklet,
13 pages (also in Special Publication SP-2128 “Steering & Suspension
Technology Symposium”).
Lozia, Z.; Zdanowicz, P.: Ocena możliwości zwiększenia zwrotności
dwuosiowego samochodu ciężarowego (Assessment of the possibilities of
improving the agility of a two-axle motor truck). Zeszyty Instytutu Pojazdów
Politechniki Warszawskiej, No. 2(49)/2003, pp. 5–20.
Lozia, Z.; Zdanowicz, P.: Assessment of Possibilities of Increasing
Manoeuvrability of Heavy Biaxial Commercial Vehicle. 19th IAVSD Symposium,
Milano, Italy, 29 Aug. – 2 Sept. 2005; shotgun presentation and poster, 8 pages,
on CD-ROM.
Lozia, Z.; Zdanowicz, P.: Wyniki symulacyjnej oceny wpływu masy i położenia
środka masy samochodu LTV Dzik na jego wybrane własności w ruchu
krzywoliniowym (Results of simulation study of the influence of LTV vehicle CG
position on its curvilinear properties). Zeszyty Naukowe Instytutu Pojazdów /
Politechnika Warszawska (Proceedings of the Institute of Vehicles / Warsaw
University of Technology), No. 3(70)/2008, pp. 47–66.
Lozia, Z.; Zdanowicz, P.: Wyniki symulacyjnej oceny wpływu odporności na
boczne znoszenie ogumienia i sztywności stabilizatorów przechyłu samochodu
LTV Dzik na jego wybrane własności w ruchu krzywoliniowym (Results of
simulation study of the influence of LTV vehicle tire cornering stiffness and antiroll bars stiffness on its curvilinear properties). Zeszyty Naukowe Instytutu
Pojazdów / Politechnika Warszawska (Proceedings of the Institute of Vehicles /
Warsaw University of Technology), No. 3(70)/2008, pp. 67–86.
Mitschke, M.: Teoria samochodu. Dynamika samochodu (Motor vehicle theory.
Motor vehicle dynamics). WKŁ, Warszawa 1977.
Mitschke, M.: Dynamika samochodu. Tom 2: Drgania (Motor vehicle dynamics.
Vol 2: Vibrations). WKŁ, Warszawa 1989.
Osiecki, J.; Gromadowski, T.; Stępiński, B.: Badania pojazdów samochodowych i
ich zespołów na symulacyjnych stanowiskach badawczych (Testing of motor
vehicles and their components on simulation test stands). Wydawnictwo Instytutu
Technologii Eksploatacji – PIB, Radom-Warszawa 2006, ISBN 83-7204-510-0.
Reński, A.; Pokorski, J.; Lozia, Z.; Stegienka, I.: Symulacja krzywoliniowego
ruchu samochodu na stanowisku bębnowym (Simulation of curvilinear motion of
a motor vehicle on a drum-type test rig). Zeszyty Instytutu Pojazdów Politechniki
Warszawskiej, No. 2(14)/95, pp. 29–46.
26
Abstract
The author has presented examples of the simulation models of motor vehicle
motion and dynamics that he built during 39 years of his work at the Warsaw University
of Technology and during his guest-researcher stays at VTI (The Swedish National Road
and Transport Research Institute) in Linköping, within numerous research and
development projects. The models are characterized by various degrees of complexity;
they describe the vehicle motion and its dynamics on the road surface plane, in
frequency domain as well as in time and in space. Some of them were intended for
driving simulator applications. Mostly, the models are characterized by unique solutions;
in many cases, the models have been presented with specifying their co-authors or the
persons for whom the models were developed with an intention of using them for joint
applications. Special attention has been paid to highlighting the practical applications of
the models developed.
Keywords: model, simulation, motor vehicle motion, motor vehicle dynamics
PRZYKŁADOWE AUTORSKIE MODELE DO SYMULACJI RUCHU
I DYNAMIKI SAMOCHODU
Streszczenie
Autor przedstawia przykładowe modele symulacyjne ruchu i dynamiki samochodu,
które zbudował w okresie 39 lat swej pracy na Politechnice Warszawskiej, w trakcie
pobytów w Szwedzkim Narodowym Instytucie Badań Dróg i Transportu w Linköping
(VTI – The Swedish National Road and Transport Research Institute) oraz w trakcie
realizacji projektów badawczych, celowych i rozwojowych. Są to modele o różnym
stopniu złożoności, opisujące ruch pojazdu i jego dynamikę na płaszczyźnie drogi, w
dziedzinie częstotliwości oraz w czasie i w przestrzeni. Część z nich była dedykowana
zastosowaniom w symulatorach jazdy samochodem. Większość z nich ma autorski
charakter. Część ma wskazanych współautorów lub osoby, na rzecz których powstała z
myślą o wspólnej aplikacji. Autor szczególną uwagę zwraca na wskazanie praktycznych
zastosowań zbudowanych modeli.
Słowa kluczowe: model, symulacja, ruch samochodu, dynamika samochodu
27