IEXPERIENCE IN RAILWAY TRACK TESTING FOR VALIDATION OF THEORETICAL DYNAMIC ANALYSIS Z TESTOVANIA TRATE PRE OVEROVANIE TEORETICKÝCH MODELOV EXPERIENCE IN RAILWAY TRACK TESTING FOR VALIDATION OF THEORETICAL DYNAMIC ANALYSIS

vehicle/track interaction analyses. results of dynamic analyses of the track structure verified compared with obtained experimental herein presented track testing for validation of


Introduction
The commercial necessity for higher speed and greater axle loads has been established and this trend will probably continue. In this context, close cooperation between civil and mechanical engineers is essential. Track must have a high standard of alignment and maintenance quality must be improved accordingly. New vehicles, particularly those for high-speed operation, must not generate excessive track forces. These high speeds or heavily laden vehicles must operate with high levels of safety and with existing or improved standards of comfort.
The basic step for solving the indicated problems is identification of dynamic interaction vehicle and track structure and a prediction of the dynamic behaviour of the track components (rails, sleepers, ballast, fastening systems etc.) and their long term behaviour. With this purpose a program of theoretical and experimental works in our workplace studying the interaction of vehicle and track has been undertaken and it comprises: Obr. 1. Výpočtové modely trate vo vertikálnom smere Fig. 1 Models of track structure in vertical direction G Statické a dynamické testovanie prvkov konštrukcie trate (podvaly, systémy pružného upevnenia, pružné podložky pod koľajnice, interakciu podval/štrkové lôžko atď.).
Vyvinuli sa viaceré kvázistatické a dynamické výpočtové modely pre posudzovanie vertikálnych a horizontálnych silových účinkov, v ktorých vystupujú jednak charakteristiky komponentov -koľajnice, podvaly, štrkové lôžko, podložie, alebo celkové charakteristiky konštrukcie trate. V štandardnej analýze konštrukcie trate bola koľajnica modelovaná ako pružný nosník na pružnom Winhlerovskom podklade. V súčasnosti sa aplikuje Metóda konečných prvkov (MKP) a trať (koľajnica) je modelovaná ako pružný nosník na diskrétnych pružných podperách (v miestach podvalov). Výsledné pohybové rovnice koľajnice vo vertikálnom smere môžu byť zapísané v tvare: A number of quassi-static and dynamic computer models have been developed for the track structure behaviour under vertical and horizontal loads which include either separate components representing rails, fasteners, sleepers, and subgrade or total characteristics of the track. In the standard track analysis, the rail has been modelled as an elastic beam on an elastic Winkler foundation. At present, the Finite Elements Approach (FEA) is applied and the track (rail) is modelled as an elastic beam on the discrete supports. The resulting equations of motion of rail are are the mass, damping and stiffness matrices, and {v} is the nodal displacement vector.
In this notation a general set of equation for the description of the response of a track structure may be written analogous of those of a single-degree of freedom structure. Time domain solution of the problem is presented in [4,5], where the numerical algorithm consisting of the finite element procedure to model the track structure and the time-step integration to calculate the response. Figure 1 shows the used physical modelling of the track component in vertical direction corresponding to the application of the FEA, Eq. (1). The mechanical properties of track structure are modelled by a set of springs and dampers in one or two layers, see Fig. 1.
The characteristics of springs and dampers can be determined by the laboratory load tests of track components, or the field measurement in the typical track condition. The load -deflection track characteristics are particularly important in the design, use of modern concrete-sleepers track, and to provide data for computer modelling of the track dynamic behaviour and the dynamic vehicle/track interaction. Thus, the theoretical dynamic analyses of track structure can be compared with the gained experimental results. The track testing presented herein for validation of theoretical dynamic analysis can give many useful indications concerning the evaluation of superstructure performances.
The objective of this study is just the signal analysis of track structure at passing trains and investigation of what information can be obtained from the measurement and analysis of response analysis. The dynamic deflection and vertical acceleration time histories give a base information about overall characteristics of dynamic response of the track. The frequency analysis gives the additional helpful and comprehensive information about a vibration of track. The paper presents just some approaches and results in the vertical dynamic testing of railway track, both the mid frequency domain and a higher frequency domain, 0 -800 Hz.
In this section, some experimental practices and some obtained results will be shown to demonstrate the dynamic behaviour of track structurethe rails, the sleepers, and ballast respectively, at passages of trains. Results of these measurements may be used to assess the short-term dynamic behaviour of the track at an observed section and to give the state parameters of the vehicle/track system in certain time.
In our workplace two techniques for the dynamic response measurement of the track structure are applied: G The deflection measurement of the rail, the sleepers using the displacement transducers set with the rail and the sleepers. G The acceleration measurement using accelerometers set with the rail, the sleeper and with the ballast.
Arrangement of the vertical displacement transducers of Bosh type and accelerometers of KS 50, BK 4500, and BK 3806 type and the corresponding block diagram are shown in Fig. 3.
Moving vehicles generate deflection, stresses, and forces in the track components (rails, sleepers, ballast) that are generally greater than those caused by the same vehicle load applied statically or moving at low speed. The dynamic amplification ␦ generally has a stochastic character and can be defined as a ratio of the maximum dynamic deflection of a quantity Y dyn , (Y = rail deflection v R , sleeper deflection v S ) to the static deflection of a quantity Y st .
The passage of each wheelset induces a peak of the observed quantity Y dyn and the results may be treated statistically. Thus, histograms can be constructed and exploited for statistic expected values of the dynamic coefficient for the rail deflection v R and the sleeper deflection v S . Accuracy of measurement of the relative deflections (transducers D R and D S in Fig. 2) of the rail and the sleepers in practice is not easy. The fundamental difficulty is fixed datum against which the deflections are measured. When a train passes the measured place, the ballast and ground nearby the track deflects and vibrates, so that we do not have a stable platform for measurement. Acceptable results have been obtained using the displacement measuring transducers of

Dynamické priehyby koľajnice a podvalu
Skutočné prevádzkové zaťaženie trate zahŕňa postupnosť opakovaných dynamických impulzov, ktoré všeobecne závisia od Bosh type that made measurement against a fixed 6 m long console beam imbedded in 2 m long sand bed. The obtained values of the vertical displacements can be used to determine the dynamic amplification ␦ resulting from the passage of railway vehicles (locomotive and characteristic coach bogies) over the tested track section.
Using accelerometers (transducers A R , A S , A B in Fig. 3) to measure the dynamic track response (vibration of the track components) is very attractive, since no fixed datum is required and different frequency response can also be measured.

Rail and sleeper dynamic deflections
The actual loading of a track line section will consist of a mix of many different wheel loads, which are defined by the individual Dynamické priehyby koľajníc a podvalov priamo súvisia s ich dynamickým zaťažením. Aplikáciou základných postupov lineárnej mechaniky možno získať približné hodnoty dynamických síl P dyn : kde: P st ϭ k.v st k je vertikálna tuhosť trate (N/m 2 ) v sledovanom úseku.
The dynamic deflections have direct relation to the dynamic load of rails, sleepers and ballast. Applying linear mechanics theory can be roughly estimated the dynamic interaction forces wheel/rail P dyn : where: P st ϭ k.v st k is the vertical track stiffness (N/m 2 ) at the track line section.
Generally, we can say that in service conditions each rail cross-section or each sleeper is loaded by a sequence of impacts or shocks of the wheel load of the passing trains. This dynamic load induces a dynamic deflection of rails and sleepers having a characteristic shape in time domain, see Fig. 4. Amplitudes of these vertical dynamic rail and sleeper deflections for known track stiffness can be exploited to assess: G the dynamic amplification ␦ applying the relation (2) G the vertical rail and sleeper forces applying the relation (3) G the degree deterioration and degradation of the permanent way structure G the effect of train speed on the dynamic track response G the function of resilient fastenings in the track structure.

Rail and sleeper accelerations
Track vibrations measured under train load may be described in terms of force, acceleration, velocity and displacement and for a complete description it is obtain a time history record of the quantity in question. The measured vertical dynamic response of rails and sleepers has a characteristic shape in time domain, see Figs. 6 -9. They represent typically non-stationary random signals with time-varying mean square value.
Transformation of these signals to the frequency domain yields the acceleration spectrum that gives the additional helpful information about the vertical vibration of track. The spectrum shows concentration of the energy and its distribution in a signal as a function of frequency. Our measurements show that the spectra of vertical rail and sleeper acceleration cover a wide range of frequencies.

Analysis of the vertical track acceleration
The core of the analysis of the track vibrations records rests on the frequency analysis of these records. In a broad sense, the frequency analysis is an extraction of useful information from measured acceleration and estimation of certain properties or measures of the signals.
In the vertical track acceleration measurements we obtained a real-valued time records where the sequence of N discrete samples is a length of record.
The used BK Analyser Type 2032 [3] develops Fast Fourier Transformation (FFT) as a calculation procedure for obtaining the Discrete Fourier Transformation (DFT). The advantages of the FFT can be achieved in a variety of ways but a particular version of a Radix 2 algorithm (N ϭ 2 m ) is used in BK Analyser, where m ϭ 7, 8, 9, 10, 11, and corresponding number of discrete samples N ϭ 128, 256, 512, 1024, 2048. As has just been shown, the FFT algorithm produces identical results to direct application of the DFT and thus, the analysed record and results are a finite number N representing one period of an infinitely long periodic signal.
For each signal, the time function is first transformed to a complex spectrum. The squared amplitudes of a number of such instantaneous spectra are next averaged to give the autospectrum for that particular signal. All other functions in the diagram are calculated on these two autospectra (channel "A" and channel "B") and the cross spectrum: G Instantaneous spectrum G Enhanced spectrum G Frequency and impulse response G Coherence G Correlation, etc. Figures 6 -10 show examples of more comprehensive analysis by using the B&K Analyser Type 2032 [3]. Probably the most important function of these is Frequency Response Function (FRF), that represents the ratio of output b(t) to input a(t) in the frequency domain, and thus characterise physical system. In our case it is a resilient fastening system Keď mechanický systém je charakterizovaný funkciou impul- Aplikáciou konvolučného teorému dostaneme kde: H(f) je Fourierová transformácia h(t). FRF potom získame za pomeru V praktickej analýze sa vyššie uvedené vzťahy využívajú aj v modifikovanej forme: : V zosilnenom analytickom signále H 1 sa získa ako pomer zosilnených signálov G B ෆ (k) a G A ෆ (k): Príklady analýzy vertikálneho zrýchlenia kmitania koľajníc a podvalov s využitím B&K analyzátora typu 2032 [3]. sú ukázané na obr. 6 -10.
When the system is characterised by its impulse response h(t), and the output signal b(t) is the convolution of the input signal a(t) with function h(t), thus: By the convolution theorem, it follows that where H(f) is the Fourier transform of h(t). Thus, the FRF can be obtained from: In practice, there are found to be advantages in modifying Eqn. (7) in various ways, for example: or a version known as H 2 (f): In Dual Signal Enhancement mode, H 1 is the complex ratio of the Enhanced Spectra G B ෆ (k) and G A ෆ (k), that is:

Conclusions
The dynamic behaviour of rails and sleepers under passage of the trains has been analysed in time and frequency domain. It is a process of determining the response of the track structure as a mechanical system due to same generally unknown excitation at passing trains. It enables distinct frequency components to be related to the rails, the sleepers, and the ballast and thus identify the dynamic structure of the track vibration and sources of the vibration, respectively. The major causes of increases in the vertical force between the rail and the wheel and the major dynamic sources are generally known. These dynamic forces are transmitted to the track structure, damage its components and can be appreciated indirect just by the dynamic response under passage of trains.
The measured vertical acceleration represents typical nonstationary signals with the time-varying mean square value that must be adequately analysed. The corresponding spectra of these signals cover a wide range of frequencies. Dominant frequencies are depending in general on: G the track characteristics (track geometry, quality, stiffness, and track structural components). Výsledky našich meraní preukázali, že celkové hodnoty hladín zrýchlenia sa pohybujú v medziach: G na koľajniciach 0 -400 ms -2 a v extrémnych prípadoch aj viac G na podvaloch 0 -60 ms -2 .