Dynamic characteristics of railway concrete sleepers using impact excitation techniques and model analysis
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1 Dynamic characteristics of railway concrete sleepers using impact excitation techniques and model analysis Akira Aikawa *, Fumihiro Urakawa *, Kazuhisa Abe **, Akira Namura * * Railway Technical Research Institute Hikari-cho, Kokubunji, Tokyo, , Japan ** Niigata University 85 Igarashi 2-nocho, Nishi-ku, Niigata, 95-28, Japan SUMMARY A concrete sleeper transmits an impact load to ballast grains through multicontact loading conditions within the boundary layer separating a sleeper and ballasts. The occurrence of plastic deformation in the ballasted track is affected by characteristics of dynamic loads on sleeper bottoms. The sleeper, which has several natural frequencies in frequency bands up to khz, vibrates sympathetically with dynamic loads of a running train. Such vibration of concrete sleepers is an important factor giving rise to track deterioration. As described in this paper, field measurements and experimental modal analysis of dynamic characteristics of concrete sleepers were conducted based on an impact excitation technique. Key Words: Ballasted track, Load on sleeper bottom plane, Sleeper deformation. INTRODUCTION Dynamic load transmission to the ballast layer through the bottom plane of the sleeper causes track settlement. To identify effective measures against track bed deterioration and to perform more effective maintenance, it is important to understand the mechanisms underlying track deterioration by identifying the characteristics of load transmission to the ballast layer. Measurements of the load exerted on the bottom plane of sleepers are therefore necessary. The load on the sleeper bottom results from vibrations of the track and sleeper caused by passing trains. A key assumption is that track settlement is worsened not only because of resonance caused by the sleeper vibrating at a frequency close to its natural frequency, but also because of the uneven distribution of that load on the sleeper bottom, which can occur because of sleeper deformation. Moreover, past research [] has demonstrated that concrete sleepers have several normal modes in the frequency range below khz. In this research, the normal mode for a 3PR-type mono-block concrete sleeper was determined through experimental modal analyses to identify the relation with the characteristics of load transmission to the ballast layer. Sleeper vibration, the vibration load on the ballast, and the ballast layer response were measured dynamically on the existing track using an impulse hammer and during the actual passage of trains. The measurement results were discussed through comparison with the experimental and numerical results related to the sleeper's normal mode.
2 2. MEASURING THE NORMAL MODE FOR A SINGLE SLEEPER One property of a structure with a defined set of conditions (shape, material and bearing conditions) is that the structure vibrates at a given frequency (its natural frequency) when it is in a normal state: this is called its normal mode. The number of normal modes agrees with the value of the structure's degrees of freedom. Arbitrary structural deformation can be shown by overlapping linearly normal modes. After analyzing the vibration test data of the vibrational force and response, experimental modal analysis was adopted to measure the set of normal modes for a sleeper. Experimental modal analysis can identify individual modes by disassembly of the overlapped modes. Figure portrays the experimental setup of a sleeper in a free free condition. To reproduce the free free condition, the sleeper was placed on a 6-mm-thick extremely soft urethane mat. When an excitation impulse was applied to one end of sleeper edge, accelerance (acceleration/excitation force) at 22 points located along the sleeper, as well as excitation load, were measured simultaneously. Experimental modal analysis software ME scope VES (Vibrant Technology Inc.) was used to analyze the measurement data obtained for.6 khz or less. Measurement points of accelerance (22point,3 direction) Sleeper(3PR) Urethane mat Excitation(3 direction) Fig. Sleeper excitation test of experimental modal analysis. Table and Fig. 2 present the six normal modes identified in the frequency range below khz through this process. The sleeper vibration on existing track will correspond to each of the mode shapes with a response showing a peak at a value that is close to the natural frequencies. However, in a similar experiment where the sleeper is placed on a ballast layer, Remennikov et al. [] showed that the natural frequency of the sleeper in the in situ condition increases by a maximum of about 4 Hz in comparison with the sleeper in the free free condition. In addition to the ballast layer support, the stiffness and mass of the rail and the rail fastening system were added. Table Measurement result of 3PR-sleeper s natural modes N o. m ode shape natural frequency [Hz] st vertical bending 48 2 st horizontal bending nd verticalbending st tw isting nd horizontal bending rd vertical bending 825
3 () First vertical bending (4) First twisting (2) First horizontal bending (5) Second horizontal bending (3) Second vertical bending (6) Third vertical bending Fig. 2 Mode shapes of 3PR-sleeper. 3. DYNAMIC SLEEPER CHARACTERISTICS UNDER REAL TRACK CONDITIONS A vibration test was conducted using an impulse hammer under existing track conditions to examine the relation among sleeper vibration, the excitation load acting on the ballast, and the ballast response. 3. Experimental conditions The vertical response was measured for the three following parameters: sleeper vibration acceleration, load exerted on the sleeper bottom, and vibration acceleration of the ballast. Figure 3 shows the measurement points. For measurements up to the vertical third bending mode, the sleeper vibration acceleration was measured in eight places (see Fig. 3). The load exerted on the sleeper bottom was measured using a specially developed sensing-sleeper [2]. The sensing-sleeper is a sleeper fitted with 75 force impact force sensors (25 columns 3 rows) designed to measure the load distribution on its bottom plane. To compare the average load distribution by location along the bottom plane of the sleeper, the sleeper was divided into five sections: SM, SM2, SM3, SM4, and SM5 (each section having 5 sensors) as portrayed in Fig. 4. Then a total measurement value was calculated for each section. As presented in Fig. 4, in the test, the left rail head was excited with a force of about 2 kn in the Z (vertical) direction and Y (horizontal) direction with five times in succession. The transfer function (response/excitation force) was measured each time. The measurement value attributed to each measurement point was assumed as the mean of five measurements.
4 cm S S3 S2 B B 2 B 3 Sleeper vibration acceleration(s-s8) S4 S 6 S 5 B 4 Sensing sleeper S8 Left S7 B 5 Ballast vibration acceleration (B-B5) () Overall X Z Right S S3 S6 S8 S4 S2 S5 S7 4m m 57m m 57m m 4m m (2) Sleeper vibration acceleration Fig. 3 Measurement points. Y vertical Z excitation horizontal Y excitation Left Right Z SM SM 2 SM 3 SM 4 SM 5 Fig. 4 Impulse hammer test. X Y 3.2 Experimental results for the transfer function Figure 5() shows the transfer function for total load values for SM SM5 and for the entire sleeper bottom plane for the Z direction; Fig. 6() shows that for the Y direction. The transfer functions for sleeper vibration acceleration for vertical Z excitation and for horizontal excitation Y are shown in Figs. 5(2) and 6(2). The transfer functions ballast vibration acceleration for vertical Z and horizontal Y excitation are presented respectively in Figs. 5(3) and 6(3). The transfer function for load on the sleeper bottom is greatest in the range of frequencies between and 2 Hz. It decreases as the frequency increases above 2 Hz, up to 7 Hz, at which point it once again begins to increase. The transfer functions for sleeper vibration acceleration increase with frequency up to about 2 Hz, after which they level off. Regarding comparison of the peak frequencies obtained for each measurement value, the load on the sleeper bottom, sleeper vibration acceleration, and ballast vibration acceleration reach peak values at around 8 Hz, 4 Hz, 6 Hz, and 86 Hz for excitation in both vertical Z and horizontal Y directions. In the range of 8 Hz and Hz, the load on the sleeper bottom reaches a peak under vertical Z excitation and the transfer functions for sleeper and ballast vibration acceleration are small. At around 3 Hz, when the load on the sleeper bottom reaches a peak, the sleeper and ballast vibration acceleration (B, B5) at each extremity of the sleeper also register small peaks.
5 Load on sleeper bottom plane [kn/kn] Sleeper vibration acceleration[m /s 2 /kn] Balast vibration acceleration [m /s 2 /kn ].. SM SM 2 E-3 SM 3 SM 4 SM 5 Entire E Load on sleeper bottom plane [kn/kn].. E-3 S M S M 2 S M 3 S M 4 S M 5 Entire E () Load on the sleeper bottom plane () Load on the sleeper bottom plane. S 2 S 4 S 5 S 7 S S3 S6 S Sleeper vibration acceleration[m /s 2 /kn]. S2 S4 S5 S7 S S 3 S 6 S (2) Sleeper vibration acceleration (2) Sleeper vibration acceleration B. B 2 B 3 B 4 B Ba last vibration acceleration[m /s 2 /kn] B. B2 B3 B4 B (3) Ballast vibration acceleration (3) Ballast vibration acceleration Fig. 5 Transfer functions for vertical Z excitation. Fig. 6 Transfer functions for horizontal Y excitation. 3.3 Comparison with normal sleeper mode Transfer functions of the load on the sleeper bottom, sleeper vibration acceleration, and ballast vibration acceleration registered several peaks at frequencies of less than khz; these peak frequencies were almost identical. The results suggest that the normal mode of the sleeper is situated in the region close to the frequency at which the transfer function shows a peak. To identify which normal mode causes transfer function peaks, sleeper responses on existing track were compared with the normal mode of the sleeper described previously in Chapter 2. Figure 7(a) 7(f) present the transfer function distribution of load on the sleeper bottom and the shape of its deformation under vertical Z excitation at the peak frequencies of load on the sleeper bottom. The acceleration measurements of the measuring points S S8 of the sleeper were integrated twice in the frequency domain. The sleeper deformation is calculated by converting acceleration measurements S S8 into time-dependent displacement data of t =, t = T/4, and t = T/2 (where T: Period). This figure clearly illustrates the vibration mode, t = is adjusted to each frequency. The distribution of the load on the sleeper bottom is presented with a color-coded load, where the load is converted into a time-dependent series for each sensor, in the same way as deformation measurements were converted above for each sensor. Moreover, because the load and displacement values differ greatly at each frequency, figures are arranged according to the frequency range.
6 Figures 8() 8(6) portray corresponding data for horizontal Y excitation. At 8 Hz, where the load on the sleeper bottom reaches a peak under vertical Z excitation, the shape in Fig. 7() shows that high-level vibration is only visible around the excitation point. Nevertheless, there is no normal mode at which the sleeper undergoes deformation corresponding to that occurring around this frequency. Moreover, the load only reaches a peak value for vertical Z excitation, which engenders the assumption that this peak results from the vertical or rotational rigid body mode because of the ballast layer rigid support. Under horizontal Y excitation, the waveform representing the load on the sleeper bottom shows a sharp peak at 8 Hz (Fig. 6(2)). By examining deformation of the sleeper at this frequency (Fig. 6()), it can be concluded that this peak is caused by a first bending mode. The fact that this peak frequency is higher than the natural frequency of a sleeper unit is probably attributable to the influence of the support stiffness of the ballast. No normal mode or specific sleeper deformation appears to correspond to the peak reached for 3 Hz. The assumption therefore is that the peak here results from some other track material or element other than the sleeper, such as the rails. At 435 Hz in the region of 4 Hz, the sleeper unit normal mode appears to be a second bending mode. Deformation of the sleeper and the load exerted on the sleeper bottom are both larger close to the regions around the left and right rails (deformation is shown in Figs. 7(5) and 8(5), and the load is shown in Figs. 5() and 6()). The normal mode for vertical vibration around 6 Hz is a single torsion mode (538 Hz). Under horizontal Y vibration, a twisting vibration that shifts the phase at the front and back is apparent in the sleeper deformation mode (Fig. 8(5)). Furthermore, second and third bending deformation is apparent under vertical Z excitation. Therefore, the assumption is that these modes strongly influence the response around 6 Hz. At 86 Hz, sleeper deformation under vertical Z excitation (Fig. 7(6)) and the normal mode for this frequency range indicate clearly that the sleeper vibrates in a third bending mode.
7 Load on sleeper bottom Deformation shape Load large t = t = T/4 t = T/2 ()8Hz t = t = T/4 t = T/2 - ()8Hz small vertical downward t = t = T/4 t = T/2 - (2)8Hz t = t = T/4 t = T/2 - (2)8Hz t = t = T/4 t = T/2 - (3)3Hz t = t = T/4 t = T/2 - (3)3Hz t = t = T/4 t = T/2 - (4)4Hz t = t = T/4 t = T/2 (4)4Hz t = t = T/4 t = T/2 (5)6Hz t = t = T/4 t = T/2 (5)6Hz t = t = T/4 t = T/2 - (6)86Hz Fig. 7 Load on the sleeper bottom plane and the shape of its deformation under vertical Z excitation. t = t = T/4 t = T/2 (6)86Hz - Fig. 8 Load on the sleeper bottom plane and the shape of its deformation under horizontal Y excitation. 4. MEASURING DYNAMIC RESPONSE UNDER TRAIN OPERATION 4. Frequency response measurement results The dynamic response was measured during train operation. The train speed was 25 km/h. The Fourier amplitude spectra for loads exerted on the sleeper bottom, sleeper vibration acceleration, and ballast vibration acceleration are shown, respectively, in Figs. 9(), 9(2), and 9(3). The values were obtained by application of FFT to data collected during 6.55 s (65536 points) as the train passed, and smoothed through a Parzen window of 2 Hz bandwidth. The load exerted on the sleeper bottom decreases rapidly as the frequency rises above Hz, then it dips at around 45 Hz; it then increases again gradually up to Hz. After reaching a peak at Hz, the load decreases rapidly again to
8 5 Hz. Then it peaks at 2 Hz, 28 Hz, 34 Hz, 43 Hz, 55 Hz, and 67 Hz, after which it begins once again to decrease. The load reaches a minimum at around 7 Hz, increasing again thereafter, and peaks again at around 9 Hz. The Fourier amplitudes of the sleeper and ballast vibration acceleration reach their respective peaks at around the same time as the sleeper bottom plane frequency reaches its peak (Figs. 9(2) and 9(3)). Load on sleeper bottom plane [kn s] Sleeper vibration acceleration [m /s 2 s] Ba last vibration acceleration [m /s 2 s].. E-3 SM SM 2 SM 3 SM 4 SM 5 Entire E () Load on sleeper bottom plane. S S 2 S 3 S 4 S 5 S 6 S 7 S (2) Sleeper vibration acceleration. B B2 B3 B4 B Frequency [H z] (3) Ballast vibration acceleration Fig. 9 Fourier amplitude spectrum under train operation. 4.2 Sleeper deformation and load distribution on the bottom plane of the sleeper Figures () (8) show the load distribution on the sleeper bottom and sleeper deformation at the point where the frequency shows a peak on the load on the sleeper bottom plane spectrum. The FFT and smoothing processes described above were applied to data collected for the load on the sleeper bottom and sleeper vibration acceleration in order values within the frequency limit. Subsequently, the values were converted into time series by application of the Fourier amplitude to the vibration amplitude and S5 phase difference to the phase to obtain t =, t = T/4, and t = T/2 (where T: Period), which were then shown. At Hz, both ends of the sleeper undergo large vibration in phase, although the center vibrates less, in similar fashion to vibration under the first bending mode (Fig. ()). However, in the impulse hammer tests under real track conditions, the first bending mode appears at 8 Hz. Therefore, in this
9 case, the load peak seems to correspond to that of the rigid vertical body mode obtained in the region of 8 Hz in the same test. At 2 Hz, both ends of the sleeper vibrate strongly with a 9 phase difference (Fig. (2)). At 28 Hz, only the right side of the sleeper vibrates strongly (Fig. (3)). At 34 Hz, the form of vibration becomes very complex, with the previously only slightly vibrating center part of the sleeper beginning to vibrate strongly, together with both extremities (Fig. (4)). At 43 Hz, close to where vibration is strong under the rail, vertical second bending also appears. At 55 Hz and 67 Hz, vertical second and third bending appear. Moreover, within this frequency range, which is the sleeper s normal mode, the single torsion mode which occurs here is not apparent because of deformation of the sleeper. At 9 Hz, third bending appears where the center and both ends of the sleeper vibrate strongly in phase (Fig. (8)). Load on sleeper bottom Deformation shape Load large t = t = T/4 t = T/2 ()Hz t = t = T/4 t = T/2 - (5)43Hz small vertical downward t = t = T/4 t = T/2 (2)2Hz t = t = T/4 t = T/2 (6)55Hz t = t = T/4 t = T/2 (3)28Hz t = t = T/4 t = T/2 (7)67Hz t = t = T/4 t = T/2 (4)34Hz t = t = T/4 t = T/2 - (8)9Hz Fig. Sleeper deformation and under sleeper load distribution under train operation. 5. CONCLUSION The six normal modes of a 3PR-sleeper were identified for frequencies of khz or less using experimental modal analysis to clarify the relation between the sleeper s normal mode and load transmission characteristics to the ballast layer. Impulse hammer test results showed that the sleeper s normal modes existed in the region where the load on the sleeper bottom plane and sleeper vibration acceleration frequencies reach a peak. Test results also showed that deformation corresponded to the specified normal modes. Furthermore, results showed that the load distribution on the sleeper bottom became uneven, depending on the sleeper deformation. Moreover, despite
10 being less obvious than in the impulse hammer tests, under actual track conditions with the passing of a train, it was possible to identify vibration characteristics influenced by the sleeper s normal mode from various frequencies at which the load on the sleeper bottom plane reached a peak. REFERENCES [] Remennikov, A., Kaewunruen, S., Investigation of vibration characteristics of prestressed concrete sleepers in free free and in-situ conditions, Australian Structural Engineering Conference 25 (ASEC 25), Newcastle, Australia, 4 September, 25. [2] Aikawa, A., Urakawa, F., Kono, A., Namura, A., Sensing sleeper for dynamic pressure measurement on a sleeper bottom induced by running trains, Railway Engineering 29, CD-ROM, University of Westminster, London, UK, 29.
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