Jtam.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

46, 1, pp. 205-221, Warsaw 2008

VIBRO-IMPACTS INDUCED BY IRREGULAR ROLLING
SURFACES OF RAILWAY RAILS AND WHEELS

Zofia Kowalska

Institute of Fundamental Technological Problems PAS, Warsaw, Poland

e-mail: zkowal@ippt.gov.pl

Irregularities on rolling surfaces of deformable compact bodies induce
normal contact vibrations and vibro-impacts in particular. Modelling,
simulation and analysis of such an excitation and the system dynami-
cal response are the objects of the study. Parameter analysis of transient
vibro-impacts inducedbya single irregularity is helpful in theunderstan-
ding of dynamical properties of the system.Moreover, the analysis may
be helpful in experiment design for detecting defects of rolling surfaces
and faults of neighbour structures suspending/supporting the rolling bo-
dies. Simulations performedwith very simplemodels are next compared
with results obtained from simulations of thewholewagonperformed by
using the Adams/Rail software.

Key words: unilateral contact, contact vibration, wheel-rail contact

1. Introduction

Two compact hard bodies in unilateral rolling contact constitute the core of
the studied systems. Dynamical behaviour of the core system depends on its
parameters, rolling surface geometry and also on dynamical properties of the
adjoining structures. A simple example shown in Fig.1a consists of a flexibly
suspended rolling body m pressed against an elastic half-space with an addi-
tional external force P. Under certain conditions, such a system is a reduced
model of the wheel/rail system. Normal contact vibrations and vibro-impacts
excitedwith irregularities on the rolling surfaces are of interest. The systems of
this type are also encountered in other engineering systems.Examples include:
a cam and a roller, a ball and its race in rolling bearings.



206 Z. Kowalska

Fig. 1. Simple models: (a) unsprungmass m of the wheelset and its primary
suspension k-c on a stiff foundation, (b) the same system rolling over the floating

deck of the railroad scale

The main objective of the investigation is to gain a better insight into
the system dynamics, in particular to understand how the adjoining structu-
res, namely the suspension and support, influence the dynamics of the above
described core system. The practical objective is to investigate via computer
simulation the possibility of wayside detection of wheelset defects in trainmo-
tion. Particular defects are of interest, for example: a broken spring in the
primary suspension, bad fixing of ends of the springs or dampers.

2. Modelling and simulation

The main assumption in the modelling is that the bodies are infinitely rigid,
only afinite contact compliance of curved rolling surfaces is taken into account.
The systemstructure changeswhenever the sign of indentation δ changes from
positive to negative or vice versa. At every step of numerical integrations the
current value of indentation is computed. The systems of this type are very
sensitive to errors in values of times at which the structure of the system
changes (Bogacz andKowalska, 2001).
In the case of the system m-c-k rolling over the floating deck M, the

indentationδ is a sum of the rolling body displacement −yC and the floating
deck displacement yM as well as the constraint y

k
C

δ=−yC +ykC +yM ­ 0 (2.1)

The constraint yk
C
(x) is a trajectory of the centre C (see Fig.1) in the case

whenbothbodies are in contact andare infinitely rigid. In the two-dimensional
(plane) problem, for a given profile of the surface yr(x), the value of constraint
at a given abscissa yk

C
(x0) is calculated from the formula



Vibro-impacts induced by irregular... 207

yk
C
(x0)=

√

R2− (x−x0)2+yr(x) for x=xc (2.2)

where xc denotes the horizontal coordinate of the contact point of the circle
of radius R and the profile. The value xc is numerically determined bymaxi-
mizing the sum in formula (2.2) with respect to x. It is a sum of a half of the
vertical chord on the line x= xc and the value of the profile height yr(x) at
x=xc. In other words, we look for the pointwhere the gap between the circle
and the profile is minimal, and is equal to zero (Bogacz andKowalska, 2001).
When the bodies are in contact, their vertical motion is governed by equ-

ations

mÿC =−P −mg−kyC − cẏC +N(δ)cosα
(2.3)

MÿM =−N(δ)cosα−Mg−KyM

In the systems being considered, the angle α is very small and cosα≈ 1.
The relationship N(δ) is referred to as a static contact model. In the elastic
range, a Hertzian model is used, that is N(δ) =C

√
δ3, and the coefficient C

changes with the curvature of the irregularity yr(x). Thus, two types of exci-
tations take place, a displacement excitationmodelledwith the constraint and
a parametric excitation due to changes in the contact stiffness. In the elastic-
plastic range, Johnson’s indentation model is used (Johnson, 1985; Stronge,
2000); the loading characteristic to computemotion and theunloading charac-
teristics to compute permanent patterns left on the rolling surfaces in result
of vertical oscillations (Kowalska, 2004).

3. Systems properties

The systems under consideration are inherently non-linear and show, in ge-
neral, very complex dynamical behaviour. Herein, the analysis is focused on
transient vibro-impacts excited with a single irregularity of a cosine profile.
Figure 2a presents an exemplary transient dynamical response N(t) of a he-
avily damped rolling system on a stiff foundation. The time history N(t) of
the normal contact force shows two phases: the initial phase of vibro-impacts,
and the phase of subsequent normal contact vibrations.
In dynamical analysis, the level surfaces of chosen scalar features of a

dynamic response were used. Such an analysis helps to improve the parame-
terisation of the model, in particular helps to avoid parameter redundancy,
and to find measurable features which are the most sensitive and specific for



208 Z. Kowalska

Fig. 2. Transient responses: (a) exemplary time history N(t); (b) level curves of the
time distance ∆t; (c) level curves of the normal forces ratio rN

a chosen parameter. In turn, the parameter estimation is helpful in defects
diagnostics. For example, Figs. 2b and 2c show the level curves of two scalar
features on the xy-plane, where x = c/c0, y = m/m0 and m0, c0 denote
the nominal values of the damping coefficient c andmass m. Thementioned
features are: the time distance ∆t between two subsequent impacts (Fig.2b)
and the ratio rN of the maximum normal forces at two subsequent impacts:
Nmax(i−1)/Nmax i (Fig.2c). In the first case, the gradient vectors on the level
curves are almost parallel to the m/m0-axis, which indicates that the time
period ∆t is a very specific feature for the mass m. In a relatively large ne-
ighbourhood of the point (1,1), the ratio rN is also specific for the damping
coefficient c in the suspension.
In the system with the floating deck (Fig.1b), vibrations induced with

irregularities on the rolling surface are sensitive to parameters of the rolling
system: m-c-k. In particular, a fundamental frequency of transient vibrations
is sensitive to m and the rate of decrease of the amplitude of oscillations is
sensitive to the damping coefficient c. Generally, the tendency of the rolling
body to bounce after the excitation with irregularity of a given amplitude
decreases with a decrease of the dynamic stiffness of the foundation. The
magnitude of the dynamic stiffness equals: Mω2 +Cω+K, where C and
K denote damping and stiffness of the floating deck bearing. Moreover, the
maximum normal force Nmax decreases with the dynamic stiffness decrease.

4. Simulations with Adams/Rail software

Since several years, owing to rapid development of computer technology, the so
called ”computational railwaydynamics”hasbeendevelopingvery fast aswell.
Presently, many research groups investigate numerous important theoretical



Vibro-impacts induced by irregular... 209

andpractical problemsusingvery complex computermodels of railwaywagons
and tracks.TheAdams/Rail software is oneof themostpopularmodelling tool
in which well-established models of sub-systems are implemented. However,
thequestion ofunilateral dynamical contact hasnotbeen sufficiently examined
yet.

One of the reasons of this state of art is that it is easy to overlook short
loses of contact when inappropriate numerical integrators are used in simu-
lations. According to Bogacz and Kowalska (2001), the loses of contact are
very likely at high train speeds in the case of short periodic rail irregulari-
ties, which are called corrugations. In a few earlier publications, for example
Nielsen and Igeland (1995), Ilias (1996), Igeland and Ilias (1997), the authors
explored problems of modelling and computational analysis of the dynamic
contact of a railway wheel with a corrugated rail. However, they dealt with
bilateral contact. On the other hand, it is worth tomention the paper byNay-
ak (1972), who more than thirty years ago noticed the problem of unilateral
wheel/rail contact. He investigated the dynamics of the core system shown
in Fig.1a using analytical but approximate methods of non-linear vibration
analysis.

A series of simulations of the whole wagon were performed using the
Adams/Rail program. The practical aim and motivation of simulations was
to find those measurable signals whose properties are sensitive and speci-
fic for particular defects of a wheelset or its suspension, and for that re-
ason the signals could be useful in dynamical diagnostics performed in train
motion.

In the Adams/Rail program, motion of the whole ERRI virtual wagon is
simulated. The ERRI stands for European Rail Research Institute, and the
ERRI wagon was developed as a benchmark for evaluating computer softwa-
re. It has a structure and parameters of a common modern railway passenger
wagon. The car body of the ERRI wagon is supported by two bogies (Fig.3).
Springs and dampers between the car body and frame of the bogie create
the secondary suspension. Both rear and front bogies consist of two wheel-
sets. Each wheelset is connected with a frame through dampers and springs
that constitute the so-called primary suspensions. The original ERRI wagon
is equipped with dampers whose parameters and characteristics can be easily
changed. Results given herein are obtained for damping-free wagon; therefo-
re we can observe long-lasting transients. The only sources of damping are
frictional damping, calculated by Kalker theory (Kalker, 1991), and material
damping in the contact zones. In this Section simulations of transients induced
by single short irregularities are discussed.



210 Z. Kowalska

Fig. 3. Side and rear view of the bogie supporting a car body of the ERRI wagon

Simulations performedwith the Adams/Rail software generally confirmed
that a simple model consisting of an effective mass m and a damper c is a
good approximate model to simulate transient vertical vibro-impacts in the
case of an impulse excitation with identical vertical irregularities on both rails
or wheels. The spring representing the stiffness k of the primary suspension is
of lesser importance. In other words, the transients are almost insensitive to
the spring stiffness k due to its relatively low value.

Figure 4 shows a response to the step excitation of the front and rear
wheelset of the samebogie.Thenotation is as follows: N denotes normal force,
T denotes lateral force. The letters ’f’ and ’r’ stand for front and rear, and the
letters ’R’ and ’L’ stand for right and left. First, the front wheelset is excited,
next the rear one. It can be seen that vertical motion of the front wheelset
is not affected by the excitation of the rear wheelset. Other simulations also
confirm that vertical motion of the wheelset is practically uncoupled with
vertical motion of the second wheelset of the same boogie. Contact vibrations
of a frequency about 200Hz are not transmitted through the sub-system of a
heavy mass of the wheelset and its soft primary suspension.

For comparison, the lateral forces are shown in Fig.4 as well. Despite
a symmetrical excitation, the lateral forces do not equal zero because the
wheel and rail profiles are designed so that the normal force has a very small
component directed toward the centre line of the track, and some frictional
forces are also involved.

The situation is a bit different in the case of irregularities on one rail or
onewheel. In such a case, vertical oscillations of thewheelset are coupledwith
angular oscillations around its mass centre, and due to higher frictional forces
both lateral and vertical oscillations are more strongly damped. Moreover,
transient normal forces on the right and left site are not in phase.

Figure 5 shows the normal contact forces and the acceleration of themass
centre of the floating deck (see Fig.1b). The vibro-impacts are excited with



Vibro-impacts induced by irregular... 211

Fig. 4. Normal and lateral forces resulting from a step excitation on both rails

flats on the wheels of a depth (strictly speaking – a sagitta) 0.1mm. The
flats on the wheels usually result from sliding of the wheels on rails, which is
caused by an emergency over-brakingwith blockedwheels. The flat is a source
of a displacement excitation expressed with the constraint yk

C
. In this case,

the constraint means a change in the relative vertical distance between two
points of a rigid wheel rolling on the rigid floating deck. The contact stiffness
changeswhen the flattenedwheel rolls along a rail. This additional parametric
excitationhasbeenneglectedbecause theAdams/Rail softwaredoesnotmodel
such an excitation yet.However, simulations of transientswith the core system
model show that this parametric excitation is much less significant than the
displacement excitation and, therefore, can be neglected.

Fig. 5. Dynamical response to an excitation with flats of the sagitta 0.1mm on both
wheels at the velocity 5m/s: 1 – dynamical component of the normal force,

2 – acceleration

In this example, the mass M of the floating desk is ten times larger than
the mass m of the wheelset, and m = 1500kg. The first observation, which



212 Z. Kowalska

is not illustrated herein, is that for such a big mass M and for frequencies
of 100-200Hz – that is frequencies of contact vibrations and transient vibro-
impacts – the normal forces are practically identical as for the stiff track. In
Fig.4,we can see that theacceleration ÿM(t) of theheavyfloatingdeck reflects
the time history of the normal force N(t) very well. In fact, in this case, the
acceleration is almost linearly proportional to the force.

Figure 6 illustrates how the step irregularity of a depth 0.1mm affects the
ride comfortmeasuredwith the acceleration of themass centre of the car body.
In the case of a damping-free wagon without any dampers or other sources of
damping in the primary or secondary suspension, the step irregularity excites
non-damped oscillations of very low amplitudes. In the case of the original
ERRIwagon, the impulse excitation causes a short jerk the amplitudeofwhich
is even higher thanwithout the damping.Despite a small velocity V =5m/s,
for short irregularities the dampers are harmful. However, in both cases, the
vertical accelerations are very small and we can say that short irregularities
do not affect the ride comfort but they may cause very high contact forces
which badly affect wear of the wheels and rails.

Fig. 6. Dynamical response to an excitation with a step irregularity of the depth
0.1mm at the velocity 5m/s: 1 – ERRI original wagon, 2 – ERRI damping-free

wagon

5. Vibro-impact induced by periodic irregularities

In this Section, thedynamical response of the rearwheelset of the rear bogie of
the ERRI wagon to excitations with a harmonic rail irregularity is discussed.
Simulations with sinusoidal excitations are intended to get a better insight
into the dynamics of the system. Moreover, they are helpful in the analy-



Vibro-impacts induced by irregular... 213

sis of damage mechanism leading to corrugations on rail and wheel surfaces.
Corrugations are periodic irregularities of a period of several centimetres.

The irregularity is given in the form: yr(t) = −asin[(x− x0)2π/λ] for
x­ x0. The simulations were performed with the Adams/Rail software. The
sinusoidal irregularity starts at a distance x0 from the beginning of a virtual
track, at the pointwhich is between the front and the rear wheelset of the rear
bogie at the time t=0.

Typical results of simulations are given in Fig.7. Values of parameters of
the sinusoidal excitation are as follows: the amplitude a is 50µm, the period
λ is 5cm and the velocities V of the ERRI wagon are: 2.25m/s, 9m/s, and
36m/s, that is, respectively: 8.1km/h, 32.4km/h and 129.6km/h. When the
period λ = 5cm and the amplitude 50µm or less, then the constraint yk

C
(t)

is almost identical with the rail irregularity yr(t). Therefore, for simplicity,
in the text and in the graphs, the two terms, i.e. irregularity and constra-
int, are used synonymously. The frequency of the harmonic excitation equals
fs =V/λ.

Each of the three graphs in Fig. 7 illustrates different operational condi-
tions. The upper one – a very low velocity V of the wagon and fs far below
the contact resonance region, the middle one – a low velocity of the wagon,
the contact resonance region, and the lower graph –mediumand high velocity
and far above the resonance region.

There are three curves in each graph: 1 – the irregularity yr(t), 2 – the
variable component of the vertical displacement of the centre ofmass (CM) of
the rear wheelset in the rear bogie yC(t), 3 – the normal force N(t).

For a low velocity and a low frequency of excitation, after transientmotion
decays, the variable component ofCMdisplacement yC(t) has almost identical
amplitude as the irregularity yr(t) and is in-phasewith the irregularity. In the
uppergraph, after some time fromthebeginning of excitation, the curve yC(t)
overlays the curve yr(t). The variable component of the normal force is small,
harmonic and is in anti-phase with the irregularity. Physically, it is better to
say that the acceleration of CM is in-phase with the normal force. Thus, in
this region of frequency, the bodies in contact behave similarly to the rigid
ones.

When the frequency of sinusoidal excitation fs = V/λ is about the con-
tact resonance frequency fr, then high bounces of the wheelset are observed.
Maximum values of the normal force N(t) are several times greater than the
normal static load.Maximumvalues of the vertical displacements yC(t) of the
wheelset CM are also very high, as high as 1mm and even more. It is seen in
Fig.7 that at resonance, the vertical position yC(t) of CM rises very quickly.



214 Z. Kowalska

Fig. 7. Dynamical response of the rear wheelset to an excitation with a sinusoidal
irregularity on both rails of the amplitude 50µmand the period 5cm: upper – below
the resonance regime at velocity 2.25m/s; middle – close to the resonance frequency
at velocity 9m/s; lower – above the resonance regime at the velocity 36m/s



Vibro-impacts induced by irregular... 215

For an amplitude of 50µm within only a half of the period of excitation, the
wheelset bounces off the rails. The time distance between subsequent impacts
of the wheels on rails depends on the bounce height, but generally is longer
than the period λ/V . For a given irregularity, the height of bounces depends
on the wheelset mass m and the static normal load P. At resonance, time
histories yC(t), N(t) are complex mainly due to the unilateral type of con-
tact. The non-linearity of contact stiffness is of lesser importance. After a long
time period since the beginning of sinusoidal excitations, limiting cycles are
observed, but they have not been fully examined yet.

At higher velocities or higher frequencies of the excitation, that is far above
the resonance region, different time patterns of oscillations are observed. The
amplitude of displacement of the wheelset CM is significantly less than the
amplitude of the irregularity. Thewheel compresses the irregularity peaks and
does not go into its valleys. Physically, it can be explained as follows: at high
frequencies of the excitation, the wheelset is too heavy (its mechanical impe-
dance is too high) to follow the irregularities. However, in the post-resonance
regime, instantaneous values of normal forces are high, much higher than the
static load, although the amplitude of thewheelsetCMdisplacement decreases
in time for a given velocity V and also decreases with the velocity increase.
High instantaneous values of the normal force are at peaks and low or zero at
valleys.

Notice that the simulations performed with the core system model reve-
aled the same oscillatory time patterns in three frequency ranges (Bogacz and
Kowalska, 2001). In other words, dynamical properties of the core system are
preserved in the complex system. This means that dynamical couplings be-
tween the core system and the adjacent dynamical structures are weak.

The weakness of dynamical coupling between vertical oscillations of two
wheelsets of the same boogie has been already illustrated with the step re-
sponse of the system in Fig.4. Generally, a dynamical response to periodic
excitation gives more information of any system dynamics than the impulse
or step response. Therefore, another simulation experiment was performed.
Figure 8 presents vertical oscillations of the rear wheelset and the bogie frame
at the velocity V = 18m/s. The front wheelset encounters first sinusoidal
irregularities on both rails at the time t≈ 0.1s. Vertical motion of the front
wheelset also slightly excites the bogie frame. Its motion is normally damped,
but in this simulation experiment all damping sources were deactivated in
order to better grasp the inertial couplings. After some time, the rear wheel-
set encounters the beginning of sinusoidal irregularity, and then transients of
high amplitude are observed.We can see that oscillations of the rearwheelsets



216 Z. Kowalska

start before it encounters the beginning of the sinusoidal irregularity, but the
amplitude of these oscillations is very small, almost unnoticeable. Generally,
contact vibrations or vibro-impacts excited with surface irregularities are ef-
fectively filtered out by a heavy mass of the wheelset suspended by means of
a relatively soft primary suspension.

Fig. 8. Vertical vibrations of the rear wheelset CM and the bogie frame point above
the wheelset CM

At the end, let us consider the case when the sinusoidal irregularity is ap-
plied to the right rail only. When comparing the graph of the right normal
force in Fig.9 with the graph of the force in the post-resonance regime in
Fig.7, we can see that time histories of the forces are very similar. The re-
ason of such conformity is as follows. In both considered cases, motion of the
wheel centre is smooth in comparison with harmonic constraints. Therefore,
the normal force time pattern results primarily from the elastic pressing of si-
nusoidal irregularities by the smoothly rolling wheel. In the second case, only
the right wheel rolls over irregularities. It presses the peaks, and it is seen in
the normal force time history, which contains a frequency component equal to
the frequency constraints. The left normal force in Fig.9 contains only a lower
frequency component of a smaller amplitude.

Figure 10 compares vertical motion of the left and right wheel CM in
the case of excitation on the right rail only. The amplitudes at the velocity
V = 36m/s are very small in comparison with the amplitude of irregularity
a = 50µm. In the time history of motion of the centre of the right wheel,
the component of corrugations is seen, which is entirely filtered out on the left
side.After a short time from the beginning, the centres of bothwheelsmove in
phaseupwards anddownwards.Thismodeof vibrations dominates inwheelset
motion, despite the unsymmetrical excitation. Other possible modes of the



Vibro-impacts induced by irregular... 217

Fig. 9. Right and left normal forces in the post-resonance regime for an excitation
with a sinusoidal irregularity on the right rail

Fig. 10. Displacements of the centres of the left and right wheel for an excitation
with a sinusoidal irregularity on the right rail

wheelset oscillations, that is lateral motion or angular oscillations around the
wheelset CM, are damped by tangential frictional forces. Moreover, angular
oscillations of the wheelset in the ERRI wagon are very much constrained by
itsmechanical structure: thewheelset together with parallel rigid links joining
the axle boxes with the bogie frame, form the so-called trailer.

6. Conclusions

In addition to the results discussed and illustrated above, the simulations
performedwith theAdams/Rail software and the simplemodels given inFig.1
have revealed some dynamical properties of the considered system and have
lead us to the following conclusions.



218 Z. Kowalska

The simple models shown in Fig.1 and discussed in Section 1 and 2 are
appropriate for basic analysis of vibro-impacts induced by short single or pe-
riodic irregularities, particularly in cases when the irregularities are the same
on both wheels or rails. This is because the properties of isolated sub-systems
determine dynamical behaviour of the whole system. Vibro-impacts of a re-
latively high frequency excited in the wheel/rail contact zone are effectively
filtered out by the mechanical filter consisting of a wheelset and its soft pri-
mary suspension. A small amount of vibration energy can be transmitted to
the bogie frame but practically is not transmitted to the car body through
the secondary suspension. That is why the simple model (see Fig.1a) can be
accepted as a reducedmodel of a complex system in the case of a stiff railway
track.

A disadvantage of the Adams/Rail model of the wheel/rail contact is the
fact that the contact compliance does not depend on the profile yr(t) – it is
always the same as for a smooth rail and wheel. In fact, the model involves
only the displacement excitation with the constraint and neglects parame-
tric excitation due to changes in the contact stiffness. The advantage of the
Adams/Rail model as comparedwith the simplemodels given in Fig.1 is that
it comprises the model of frictional contact forces based on Kalker’s theory
(Kalker, 1991). This is particularly important in simulations of the dynamical
response to the excitation with the irregularity on one rail or wheel only. In
such cases, transients are usually shorter due to higher frictional forces in the
contact zone.

Let us consider practical aspects of dynamical properties discussed above
in respect of damage of the wheel and rail.

For the wheelset mass equal to 1500kg the contact resonance frequency
fr is about 180Hz. Hence, for a sinusoidal irregularity of the period λ =
5cm, the velocity V at which the contact resonance occurs is slightly above
30km/s, whereas for the period 10cm, the relevant velocity is about 60km/s.
It means that practically in normal straight-line motion all modern trains
operate in post-resonance conditions. The resonance conditions also occur,
but less frequently, when accelerating or slowing down.

In simulationswith theAdams/Rail themodel of the contact zone is purely
elastic, however at forces as high as twice greater than the static load the
limits of elastic behaviour are exceeded and some permanent deformations
due to plastic flow are unavoidable. Thus, it can be expected that the wheel
rolling or bouncing over a smooth or corrugated rail can change the rail and
wheel profiles due to plastic deformations.Moreover, it can initiate or develop
cracking.



Vibro-impacts induced by irregular... 219

In respect of fatigue damage, the fact that trains normally operate in post-
resonance conditions is disadvantageous becausehighnormal forces are impos-
sible to avoid. The consequences of these dynamical properties depend on the
quality of steel that is on the main failure mechanism of wheels and rails. It
seems that a ductile rail with a hard surface layer of high fatigue strength be-
ars such dynamical loadingwell and plastic deformations due to high forces at
peacksmay even help to smooth irregularities. However, whenmechanical fati-
gue is themainmechanism of failure, high normal forces in the post-resonance
region accelerate damage of wheels and rails.

Dynamical response N(t) to a single irregularity on a stiff track consists
of a long series of impacts. So, a long section of the rail undergoes hammering
and is prone to fatigue damage. In this respect a flexible track is better than
a stiff track. However, it is impossible to attenuate even on a flexible track
the first and the highest impulse of the normal force induced by a short irre-
gularity.

Let us sumup themain resultswhich consist the basis for design of railway
diagnostic systems. Time histories of normal forces N(t) on a stiff track are
sensitive to different defects of wheelsets and their primary suspension. Some
faults generate transients or periodic signals N(t) of a specific time pattern.
Other faults can be detected from transients excited with specially designed
irregularities put purposely on the rails of the test track. The frequency of
transientvibro-impacts stronglydependson the effective value of theunsprung
mass m. Somedefectsmay change the effective unsprungmass. For instance, a
broken spring of the primary suspensionmay result in a quasi-rigid connection
between thewheelset and thebogie frame, and it canbedetectedbymeasuring
the frequency of a transient vibro-impact.

Easy measurable vertical acceleration ÿM(t) of the heavy ’floating deck’,
which is supported on relatively soft bearings of the stiffness K, imitate very
well the time-history of normal contact forces N(t), therefore measurements
of the acceleration can be used for diagnostic purposes.

Directmeasurements of the contact forces are nowadays impossible.Howe-
ver, the signal of vertical forces can be extracted from the acceleration signal
of a heavy floating deck. Note, that the elastic support of the floating deck
should be pre-stressed with a load equal to the vertical static force, when the
wheelset of interest approaches the floating deck.

In general, the simulations prove the possibility to develop a test railway
track for efficient diagnostics of wheelsets in train motion. Different technical
problems need to be solved, but they are solvable at the present stage of
measuring technology.



220 Z. Kowalska

In regards of diagnostic systems for detection of track faults, in particular
for detection of short irregularities on rails, dynamical properties of the system
under study are not advantageous. Short irregularities do not affect the bogie
ride quality much, but profoundly affect the contact forces and noise. The
main component of motion yC(t) with bounces has a lower frequency than
the irregularity yr(t). Bouncesmay also contain higher components, which do
not exist in the spectrumof irregularity. Thedifferences in timehistories yr(t),
yC(t) andtheir spectraare importantwhendesigninga trackdiagnostic system
based on measurements of accelerations ÿC(t). Such a diagnostic assessment
can bemisleading or limited.

Acknowledgements

This workwas supported by the PolishMinistry of Scientific Research and Infor-

mation Technology (MNiI Grant No. 5T12C01924).

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Vibro-impacts induced by irregular... 221

Wibro-uderzenia wywołane przez nieregularne powierzchnie toczne szyn
i kół kolejowych

Streszczenie

Nierówności na powierzchniach tocznych zwartych, lokalnie odkształcalnych ciał
powodują drgania kontaktowe, w szczególności tak zwane wibro-uderzenia. Modelo-
wanie, symulacja i analiza takiego wymuszenia oraz dynamicznej odpowiedzi na nie
są przedmiotembadań.Analiza parametrycznaprzejściowychwibro-uderzeńwywoła-
nych przez pojedynczą nierówność szyny jest pomocna w zrozumieniu dynamicznych
własności układu. Ponadto,może być przydatna w projektowaniu eksperymentu dia-
gnostyki defektów powierzchni tocznych oraz sąsiednich struktur dynamicznych, tj.
zawieszenia i/lub toru. Symulacjewykonane zwykorzystaniemprostegomodelu o jed-
nym stopniu swobody zostały następnie porównane z symulacjami ruchu całego wa-
gonu za pomocą programuAdams/Rail.

Manuscript received February 21, 2007; accepted for print April 4, 2007