ANALYSIS OF VEHICLE BOGIE EFFECTS ON TRACK STRUCTURE – NON-STATIONARY ANALYSIS OF DYNAMIC RESPONSE ANALYSIS OF VEHICLE BOGIE EFFECTS ON TRACK STRUCTURE – NON-STATIONARY ANALYSIS OF DYNAMIC RESPONSE

The present paper is concentrated on the analysis of in situ vibration measurements during operating conditions in the track structure for loading by current passenger trains at the new built up railway corridor in the section Bratislava – Trnava. Tests were carried out to determine the dynamic track behaviour and relative dynamic effects between the track components – the rails, the sleepers, and the ballast bed during the passage of characteristic passenger trains moving at the operating speeds 70 ÷ 130 km/h. Experimentally obtained signals of the dynamic response of track components – measured as vertical accelerations and displacements of the rails, sleepers, and ballast bed are analysed in detail as the nonstationary random signals corresponding passages of characteristic vehicle bogies (locomotives, coaches). Vertical dynamic response of these components were measured at two different locations of this section and the vertical dynamic behaviour of track components were investigated in the time


Introduction
Dynamic phenomena in the track structure are associated with the operating conditions and are in the direct relation with the vehicle-track dynamic interaction. Field tests were carried out to determine the dynamic behaviour and relative vertical dynamic effects between the track components -the rails, the sleepers, and the ballast bed during the passage of characteristic passenger and freight trains moving at the operating speeds. In concentrating on the track structure the dynamic effects may be divided into two groups: 1. The vibration of the track structure -the vibration of rails, sleepers, and the ballast layer and the wave propagation in the track structure. 2. The wave propagation in the surrounding of the track which can produce vibrations to adjacent structures and radiated noise.
This paper is focused on the first area of the dynamic response. The dynamic phenomena in the track structure are caused by several mechanisms which are well known: -the quasi-static excitation due to the moving axle load of trains, -the wheel and the rail roughness and their defects, -the type of trains loading the track and their composition and speed, -the excitation due to discrete supports of the rail by sleepers, etc.
When the frequencies of interest are low, we speak about "structural vibration" and for higher frequency components about "structural-borne sounds" and "air-borne sounds". Their origin of sound emission, however, is always in structural vibration of track components. One effect of the moving load is associated with the wave propagation in the rails and in the subsoil which is presented at the higher speed train. Another phenomenon is linked to the Doppler effect which forms two peaks in the frequency spectrum for any frequency component.
All these dynamic phenomena are analyzed in particular through the theoretical -simulation approaches, such as in Refs. [1,2,5,6]. One simulation model developed at the Department of Structural Mechanics [5], was addressed to the study of dynamic behaviour of the track structure, especially the evaluation of the dynamic behaviour and the response of track components (rails, sleepers, the ballast bed) due to variability in the vertical stiffness of rail supports [5,6]. In fewer cases the experimental approach is applied, especially focussed on the free field vibration measurements during the passage of train [3,4,7]. In addition to analytical models for the dynamic train-track interaction the experimental analyses are needed for the validation and appreciation of these vibrations. Experimental results have also important place in dynamic tuning of the moving vehicle -track. The three most common approaches to detect dynamic response of track components are based on the use of either: (a) Deflections measurement w x (t) using the displacement transducers DR, DS imbedded in a fixed reference datum at a position x to measure the response, see Figs. 3, 4. (b) Acceleration measurements wЉ x (t) using the accelerometers x ϭ A R , A S , A B that are glued on the rail web or on the sleeper and which require no fixed datum to measure the response at a position x, see Figs. 3, 4. (c) Strain measurements ε x (t) using the strain gauges T R that are glued on the rail web (R) or on the sleeper (S) at a position X to measure the response.
This contribution is devoted right to experimental measurements and the detailed analyses of in situ measured signals in the frequency domain up to 500 Hz. The paper is focused on the analysis of the track response of passenger trains only. The frequency composition of the vibration is measured as vertical accelerations wЉ x (t) for track components X at the position x on the track: x → the rail / accelerometer A R , sleepers / the accelerometer A S , and the ballast bed / the accelerometer A B . Displacement amplitudes can be calculated from measured accelerations. Displacement amplitudes w x (t) were measured also direct by displacement transducers D R , D S .

Measured track structure
The in situ measurements were made on the newly built up railway corridor in the line Bratislava -Žilina at the two locations at the straight section track Cífer -Trnava,

Experimental setup
The vertical vibrations of rails (R), sleepers (S) and ballast layer (B) between the sleepers were measured as the vertical acceleration wЉ x (t), x ϭ (R, S, B), the vertical relative displacement w x (t), x ϭ (R, S), and the strain measurement ε x (t) at a position x ϭ (R, S) on the rail or on the sleepers. The B&K piezoelectric accelerometers A R , A S , of the type BK 4500 were glued to the rail and the sleeper. The BK 8306 seismic accelerometer A B was embedded into the plaster bed in ballast layer between the sleepers at the depth of placing sleepers, see Figs. 3 and 4. The vertical displacements w R (t) of the rail and the sleeper w S (t) were measured by the relative displacement transducers of the type Bosh mounted on the fixed reference datum (displacement transducers D R , D S ). The direct dynamic strain ε(t) of the rail was measured by the Kistler piezoelectric tensiometer T R mounted on the rail flange.
Direct dynamic deflection measurements using the displacement transducers D R , D S provide a frequency response limited. Using accelerometers A R , A S , A B gives the response in the broad frequency range and is attractive since no fix datum is required.
Measured quantities -deflections w x (t), vertical accelerations wЉ x (t), and strains ε x (t) were recorded as electrical signals and transformed by means of the analogy-digital convector of the type 32-channel NI CompactDAQ data acquisition. The A/D device records the signals with the chosen sampling frequency f s ϭ 1000 Hz directly into the computer memory. The NI DIAdem interactive software for managing and analysing the data was applied.

The characteristics of the measured passenger trains
The measured track section was loaded by the passenger and freight trains running in operational conditions. As the paper is devoted to the analysis of passenger trains only, the typical configuration of a passenger train is shown in Fig. 5. They consist of a locomotive and 5÷10 carriages of a similar composition. The speed of passenger trains in the measured section varies between 90 km/h ÷ 130 km/h. The locomotives of passenger trains (types EL350, EL150, EL263) are supported by 2 bogies, equally as the coaches, see Fig. 5 and Tab. 1.
The basic spatial and mass characteristics of locomotives and coaches for the passenger transport are the coach total length L t , the distance between bogies L b , the wheelset distance in a bogie L a , the total vehicle mass M t , the bogie mass m bog , and the one axle mass (the unsprung mass of the one wheelset) m 1,uns . and they are summarised in Table 1. While the quasi-static contribution in the track response depends on the total mass of vehicles M t , the dynamic load contributions depend dominantly on the unsprung mass of wheelsets m1,uns.

Measured time history during the passage of trains
In Fig. 6 are presented characteristic time histories of the rail deflection w R (t), the rail acceleration wЉ R (t), and the sleeper acceleration wЉ S (t) corresponding to the passage of the passenger train EL 350ϩ8 carriages, speed c ϭ 32.9 m/s ϭ 119 km/h. The bogie passages of a locomotive and coaches next the locomotive form a characteristic load of the track -impulse load activated by vehicle bogies.

Time histories of the track response and their analysis -Nonstationary signals
The obtained time histories of the vertical acceleration (measured signals) wЉ R (t), wЉ S (t) and wЉ B (t) represent generally random functions of time t describing the track response. In the full sense of the word they represent the generally nonstationary random   The geometrical and mass characteristics of vehicles for the coaching traffic in ŽSR Table 1 Locomotives Axles processes with the time-varying mean square value corresponding to the passage of bogies of coaches through the measured place. In the broader sense they may be considered as the stationary processes [8]. Then, the frequency analysis of obtained time signals can be applied as: (1) The analysis of whole passage of the train -the measured signal is considered as a stationary one (the passage of the whole train over the measured site).
(2) The analysis of selected stationary parts of the signal and use the technique of window function (considering the short section as a stationary process). This is applied to the passage of locomotive bogies, characteristic coach bogies (couple of bogies), or the passage of characteristic parts of the train (the passage of characteristic coaches).
Then, the passage of the coach bogies over a measured place constitutes characteristic cyclic signals that in the long term they may be considered stationary, but in the short term they are nonstationary ones. The NI DIAdem interactive software for managing and analysing the measurement data [9] was applied for the spectral analyses of these signals.

Spectra of the vertical acceleration of the track components due to passenger trains
While the dominant frequency composition of the deflection w x (t) of rails and sleepers (measured by displacement transducers D R , D S ) present a low frequency range only, the frequency content of acceleration wЉ x (t) of these motions gives a wide range of frequencies. At the same time we have to keep in view the relations between the displacement amplitude w ៣ o (f) and the acceleration amplitude w ៣ o Љ(f ) at a given frequency component fi.
Frequency analyses performed from the time signals were focused just to the frequency content of the vertical acceleration of the track component response during the passage of trains. However, for the train speed lower than the wave speeds propagating in the ground, the measured quantities may be considered as a dynamic component of the response that strongly dominates over the quasi-static axle loads response.
In the track response measurements the sampling frequency f s of the measured signal (the discrete sampling of a measurement time signal) plays an important role because of speedy processes (the quasi impact processes). An analysed record {x(t)} of the total length T r is divided into nd segments of the length T -the record length T. Then, the one-side auto-spectral density function G XX (f k ) for a arbitrary frequency component f k is given [8,9]: , k ϭ 1, 2, 3, … N/2 (2) where: N is the sample size (the block size) → N ϭ 128, 256, 512, 1024, 2048, 4096. where: G XY (f k ) is cross-spectral density function. The important step in the frequency analysis of the time signals is the choice of a time window function. The Hanning weighting was applied in the analyses. For the applied sample frequency f s ϭ 1000 Hz, and a chosen sample size N the resolution frequency β is (5) The Hanning weighting to "the quasi-stationary time record of the train passage" with the adequate overlapping 50% of the record length T and the averaging of these signals was applied. The spectral analyses were displayed as the Power spectrum (PWS), or the Power spectral density (PSD).

The spectral analysis of the whole train passage -analysis of a stationary signal
The passage of the train (EL 350ϩ8 coaches) over the measurement site is considered and analysed as a stationary time record, as shown in Fig. 7. This approach does not take account of the non-stationary of signal.
Considering to option of the block size (N), option of the overlap (%) and averaging obtained PVS the resulting mean power spectrum (PVS) gives a gross picture of frequency composition of the response. This analysis averages the frequency composition of the response.

Spectral analysis for the locomotive EL350 passage -analysis of segmented stationary part
The passage of locomotive EL 350 bogies over the measurement site evidently differs from the coach bogies -it is considered as a non-stationary signal with the variable mean square value. This signal can be segmented into stationary parts which can be analysed as a stationary signal, as is shown in Fig. 8.

Spectral analysis for the passage of coach bogies -analysis of segmented stationary part
The passage of coach bogies over the measurement site evidently differs from the passage of the locomotive as showed the time histories, Fig.9. Then the extract part of signals can be analysed as a stationary signal (cyclic signals), as is shown in Fig. 9. The Hanning weighting to the passage of coach bogies (a quasi-stationary time record) was applied.

Results of dynamic analyses
The measured time histories of the vertical rail acceleration wЉ R (t), sleeper accelerations wЉ S (t), and ballast bed acceleration wЉ B (t) and corresponding spectra PSD or PWS give the principal picture of the dynamic behaviour of the track structure for passages of the characteristic passenger trains. G The amplitudes of the vertical acceleration of track componentsthe rail wЉ R (t), wЉ S (t), and wЉ B (t)) are gradually damped in the vertical direction. The standard acceleration rail peaks for locomotives occur up to 300 m/s 2 and for coaches up to 50 ÷ 100 m/s 2 . These peaks are reduced on the sleepers up to 30 m/s 2 and on the ballast bed to 8 ÷ 10 m/s 2 , as can be seen in Fig. 6.   The frequency content of the vertical acceleration on the track components -rails, sleepers, and ballast bed differs: -The frequency spectrum for a rail acceleration is a broadband spectrum in the frequency range f ϭ 0-500 Hz, without any sharp spectral components. The frequency component content at the frequency area f Ϸ (0÷150 Hz) has the dominant signification on the rail response. -The frequency spectrum for a sleeper acceleration is a broadband spectrum too, but two marked frequency areas be detected: f (1) Ϸ 0 ÷ 100 Hz, and f (2) Ϸ 280 ÷ 320 Hz. They present two characteristic damped resonant areas occurring in all the measured signals: a/ In the first area the frequency range f (1) ϭ (55 ÷ 90 Hz) with a max. f (1) Ϸ 60 Hz is dominant -the rails, sleepers, and ballast layer vibrate together and constitute dominant effect on the sleeper response. b/ In the second one the frequency range f (2) ϭ (280 ÷ 320 Hz) with a max.f (2) Ϸ 280 Hz is dominant -the rails vibrate on sleepers. -The frequency spectrum for ballast bed is narrow-band and always is concentrated about frequencies f ϭ 80 ÷ 120 Hz.
The presented spectra of vertical accelerations of track components can be considered as characteristic, occurring in all the analysed passages of the passenger trains, because the dynamic loading is similar. The characteristic and important spectral components are appeared in the frequency range f ϭ (0 ÷ 150 Hz) in all the track components when the rails, sleepers, and ballast bed vibrate together. A gradual damping of frequency components in the vertical direction is apparent in all spectral analyses in Figs. 7 ÷ 10.
-The spectra corresponding to passages of heavy freight trains are different in comparison of passenger trains, because the frequency of loading, the speed of freight trains, the mass of carriages are different from passenger trains, and a quasi-static preloaded of the track is higher. -The comparison of the measured amplitudes of the vertical acceleration of track components (rails, sleepers and the ballast bed) indicates the proper damping and filtration of the frequency components at the transmission of dynamic loading from the rail to the substructure and to the subgrade as the consequence of the resilient rail fastening (Vossloh Skl 14), the resilient pads, and the generally proper function ballast bed and subgrade. -A very negative impact of coaches with some defective wheels (the out-of-round wheels) to the vertical track acceleration was indicated. Peaks reached up to a double higher value of the response than the coaches with smooth wheels.  f (1) = 13, 51, 92, 123 Hz f (1) = 13, 39, 55, 78,

Conclusions
Dynamic behaviour of the track structure during the passage of passenger trains was investigated as the vertical acceleration of the track components -the rails wЉ R (t), the sleepers wЉ S (t), and the ballast layer wЉ B (t) at the depth of placing sleepers. The frequency analysis was made for the mid frequency range f ϭ (0 ÷ 500 Hz). Measured signals include a large number of excitation sources -geometrical errors, or irregularity on the rails, wheel out-of-roundness, irregular track stiffness, etc. The selected stationary part of the measured signals considered as a stationary process (the passage of locomotive bogies, characteristic coach bogies or couple of bogies, the passage of characteristic coaches) were analysed by the time window technique. The spectrum changes corresponding to characteristic bogie passages were evaluated.
The presented experimental analyses for the new construction of the track structure are complementary to the other data setsthe measurement of the passage of freight trains, or the measurement of the response on other types of ballasted tracks. Frequency analyses of time histories of the vertical rail acceleration wЉ R (t), the sleeper accelerations wЉ S (t), and the ballast bed acceleration wЉ B (t) provide the principal picture of the dynamic behaviour of the track structure, the transmission and the damping of frequency components through the track components under the passage of the characteristic passenger trains. Although they moderately differ under the passage of different trains the main features and the character of the response is maintained.