EVALUATION OF THE EFFECTS OF TEMPERATURE ON RAILPAD PROPERTIES, RAIL DECAY RATES AND NOISE RADIATION

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1 EVALUATION OF THE EFFECTS OF TEMPERATURE ON RAILPAD PROPERTIES, RAIL DECAY RATES AND NOISE RADIATION R. A. Broadbent, D. J. Thompson and C. J. C. Jones ISVR, University of Southampton, Southampton, SO7 IBJ, UK Rolling noise is one of the main sources of railway noise. It is a broadband source covering the frequency range to 5 Hz and is caused by the interaction between the wheel and the rail as a train runs on the track. The track can be the major contributor to the radiated noise up to around khz. The decay rate of vibration along the rail has an important influence on the noise from the track. The decay rate is particularly affected by the dynamic properties of the railpad, which is a 5- mm thick elastomeric pad located between the rail foot and the top of the sleeper. The stiffness and damping of an elastomeric material are known to be sensitive to temperature, but the implications for the noise from a railway track have not previously been quantified. The work described here investigates the significance of these variations in railpad properties over a temperature range 4 o C to - o C. Laboratory measurements are presented of the dynamic shear stiffness of samples of railpad materials. The dependence of the railpad stiffness and loss factor on temperature as well as on frequency has been determined from these measurements. Using TWINS (Track-Wheel Interaction Noise Software), the sound power emitted by the track has been predicted for the range of temperatures measured in the laboratory considering only the vertical motion of the rail. It is shown that the temperature dependence can be considerable.. Introduction When a train wheel runs over a rail the roughness on each surface will result in vibrations being generated in, and sound radiated from, both structures,. This phenomenon is known as rolling noise. Jones et al 3 showed that the decay rate of the rail is an important factor in predicting this noise behaviour of a track. It has also been found that the railpad plays a key role in determining the decay rate along the rail, and the ratio of noise radiated by the rail and sleeper 4. The railpad consists of a thin layer of elastomeric material located between the rail foot and the sleeper. The railpad stiffness, K, determines the frequency above which the rail and sleeper vibration decouple (typically around -4 Hz) and free wave propagation occurs along the rail 3,5. Below this frequency the decay rate is very high and vibrations are transmitted with little attenuation through the railpad to the sleepers and ballast. The railpad can be represented by a hysteretic damping model with a complex stiffness, K(+iη), where η is the damping loss factor of the material. The corresponding damping force is proportional to Kη. ICSV6, Kraków, Poland, 5-9 July 9

6 th International Congress on Sound and Vibration, Kraków, Poland, 5 9 July 9 Vincent et al 4 found that to obtain the lowest noise level from a track the pad stiffness should be chosen such that

2 6 th International Congress on Sound and Vibration, Kraków, Poland, 5 9 July 9 Vincent et al 4 found that to obtain the lowest noise level from a track the pad stiffness should be chosen such that the rail and sleeper noise components are equal, this optimal stiffness being dependent on roughness spectrum and train speed. However, the stiffness values found were higher than the current railpad stiffness values used on European railways. The effect of the railpad damping was also considered. It was found that by increasing the damping loss factor both the lateral and vertical vibration of the rail was reduced. This made a larger impact on the overall track noise when a soft railpad was used, as the sleeper contribution is then lower; the increase in damping was found not to affect the sleeper vibration significantly. The stiffness and damping loss factor of an elastomer vary with frequency and temperature. While the frequency dependence of railpad stiffness has been investigated 6,7,8, little is known about the temperature dependence and its effect on the decay rate of the rail and the sound radiated by the track. Two samples of railpad material have been investigated, a 5 mm thick sample from a thicker studded natural rubber pad and a 6 mm thick medium stiffness cork rubber pad. The frequency and temperature dependence have been found for small samples of each material as this can be achieved much more easily than for a whole railpad. Laboratory experiments have been undertaken in a temperature chamber to measure dynamic stiffnesses of the test material up to 5 Hz over a temperature range of - o C to 4 o C. These are used to determine the temperature and frequency dependence of the shear modulus and thus the stiffness. The temperature dependence of the loss factor is also determined. The vertical track decay rates and resulting sound radiation of a typical European track are predicted using TWINS (Track-Wheel Interaction Noise Software), accounting for the temperature dependence of the railpads.. Laboratory measurements. Method The rig used to determine the temperature dependence and frequency dependence of elastomeric materials is shown in Fig.. Four separate samples (approximately x5x5 mm) of the material are mounted in a sample holder, and are excited in shear by a coil and magnet exciter. The base is attached to a seismic mass to provide a blocked termination. A force transducer measures the force transmitted to the seismic mass while the input vibration on the source side is measured using an accelerometer. Figure. Experimental set up used for the laboratory experiments to determine the railpad shear modulus and damping loss factor at different temperatures and close up of sample holder The rig was located inside a temperature chamber. A thermocouple located close to the samples was used to record the temperature during measurements. From initial experiments a period of 5 minutes at constant temperature (±.5 o C of the desired temperature) was found to be sufficient to allow the sample material to reach the required temperature. The samples were tested in shear and the transfer function, H, between the input acceleration, a, and the transmitted force, F, can be converted to the dynamic shear stiffness (K d = force/displacement) by,

3 6 th International Congress on Sound and Vibration, Kraków, Poland, 5 9 July 9 K d ω H ω F = = () 4 4 a where ω is the angular frequency and the factor 4 in the denominator occurs as there are four samples held in the test rig. The loss factor is determined from the phase of the dynamic stiffness using, Im( Kd ) η = Re( Kd ) The shear modulus, G, is determined, accounting for the size of the samples, () hk G = d (3) A where A is the shear area of the sample and h is its thickness. Results from the rig are known to be unreliable at low frequencies for high stiffnesses and at high frequencies for low stiffnesses 9. Therefore, from each measurement, results in the vicinity of khz have been used to determine the temperature dependence. This is calculated from the shear modulus and loss factor values by averaging the values between 9 Hz and khz to obtain single values at each temperature. The resulting dependence is expressed relative to the value at one temperature, 5 o C for the natural rubber pad and o C for the cork rubber pad. Although the loss factor will show a dependence on frequency, by assuming a constant loss factor understanding can be gained of the frequency dependence of the stiffness. The frequency dependence of the shear modulus for each temperature can be calculated using η G( f) f = π G( f) f where f and f are different frequencies. For each temperature the average shear modulus values between 9 Hz and khz are taken as the reference G(f ), where f is 95 Hz. This can be compared to the measured frequency dependence. For a given railpad geometry, the stiffness of the railpad will be proportional to the shear modulus. Therefore the temperature dependence of the pad stiffness can be determined from that of the shear modulus. Measured values of railpad stiffness at a reference temperature are used to convert from shear modulus to pad stiffness.. Temperature Dependence The real part of the shear modulus along with the temperature dependence of both the real part of the shear modulus and the loss factor are shown in Fig. and Fig. 3 for the natural rubber and cork rubber railpads respectively. Note that the frequency range is not the same for the measurements of each pad; the natural rubber sample produced reliable data over a larger frequency range. A pronounced increase in shear modulus with decreasing temperature is exhibited in both railpad materials. The natural rubber pad has a relatively low loss factor at high temperatures, increasing at lower temperatures. The stiffness increases by a factor of 3 over this range. A larger increase in stiffness is seen for the cork rubber pad, reaching a plateau at -5 o C. In this case the loss factor has its maximum value at around o C, corresponding to the steepest part of the stiffness curve. The dip seen in the data at approximately Hz is likely to be due to a feature of the rig and cannot be attributed to a property of the material. (4) 3

4 6 th International Congress on Sound and Vibration, Kraków, Poland, 5 9 July 9 a) 7 b) 6.9 Shear Modulus (Pa) 6 Dependence factor of shear modulus re:5oc Loss Factor 5 5,5 3, Figure. a) Real part of the shear modulus for the natural rubber railpad over the temperature range 4 o C to - o C, b) Temperature dependence of the loss factor (--) and shear modulus (-) based on reference temp 5 o C a) 7 b) 6 Shear Modulus (Pa) Dependence Factor of shear modulus re:oc Loss Factor Figure 3. a) Real part of the shear modulus for the cork rubber railpad over the temperature range 4 o C to - o C, b) Temperature dependence of the loss factor (--) and shear modulus (-) based on reference temp o C Reference stiffness values for each pad are derived from decay rate measurements on the ISVR test track, Chilworth, UK. The natural rubber pad stiffness at 5 o C is approximately MN/m. The cork rubber pad stiffness at o C is approximately 55 MN/m. Using these reference values, the stiffness of the railpads at each temperature is determined using the dependence from Fig. b) and Fig. 3b). Loss factor values are taken directly from the test rig measurements. The resulting stiffnesses and loss factors for the two railpads can be seen in Fig. 4. a) 4 b) natural rubber pad cork rubber pad.9.8 natural rubber pad cork rubber pad Stiffness (MN/m) 3 Loss Factor Figure 4. a) Stiffness and b) Loss factor of the two railpads over the temperature range - o C to 4 o C.3 Frequency Dependence The frequency dependence of the shear modulus of the two railpads for each temperature, assuming a constant loss factor, is shown in Fig. 5. These predicted values from Eq. (4) have been 4

5 6 th International Congress on Sound and Vibration, Kraków, Poland, 5 9 July 9 compared with the measured data of Fig. a) and Fig. 3a) and have been found to give good agreement. The predicted values are used in preference as they are smoother and allow extrapolation. It can be seen that there is a clear, fairly linear, increase in stiffness with frequency at all temperatures. The natural rubber railpad exhibits a clear trend with temperature, the frequency dependence being more pronounced at lower temperatures/higher stiffnesses. The cork rubber railpad does not exhibit such a simple trend with temperature due to the peak in the loss factor at about o C (see Fig. 3b)). a) b) Dependence Dependence Figure 5. Dependence of a) natural rubber and b) cork rubber railpad stiffness with frequency for each temperature (4 o C to - o C), reference frequency 95 Hz The calculated railpad stiffnesses are shown in Fig. 6 from which it can again be seen that at higher temperatures there is a negligible variation of stiffness with frequency for both railpads. The cork rubber railpad exhibits a different dependence at the two lowest temperatures than the natural rubber railpad. The stiffnesses are very similar at these two temperatures and overlap at higher frequencies. This is due to the reduction in loss factor as temperatures decrease below o C. a) b) 3 3 Stiffness (MN/m) Stiffness (MN/m) 3 3 Figure 6. Calculated stiffness over the frequency range, for each temperature (4 o C to - o C) reference frequency 95 Hz, for a) natural rubber and b) cork rubber railpad It is expected that at the higher temperatures (above o C) the frequency dependence will have little effect on the decay rates as the stiffness is fairly constant across the frequency range. For the natural rubber railpad at temperatures below o C the frequency dependence becomes significant and is expected to produce a more pronounced effect on the decay rates, while a wider temperature range (below o C) will be affected for the cork rubber railpad. 3. Noise Predictions The TWINS model for rolling noise was developed in the 99 s by Thompson,3. Using the railpad stiffnesses determined in this work TWINS is used to predict the vertical rail decay rates 5

6 6 th International Congress on Sound and Vibration, Kraków, Poland, 5 9 July 9 and the sound power level in db(a) due to a single wheel of a freight train travelling at km/h on conventional track with UIC 6 rails. 3. Decay rates Using the stiffnesses and loss factors from Fig. 4 the vertical decay rates shown in Fig. 7 have been calculated using TWINS. The track used in the prediction consists of UIC 6 rail, monobloc sleepers, and ballast with a frequency dependent stiffness. a) b) Vertical Decay Rate (db/m) Vertical Decay Rate (db/m) 3 3 Figure 7. Vertical decay rates along a UIC 6 rail with continuous two layer support a) natural rubber railpads, b) cork rubber railpads The initial high decay rate at low frequencies corresponds to a region of blocking where waves do not propagate along the rail. This occurs as vibration at these frequencies is transmitted to the sleepers, ballast, and ground with little attenuation. There is therefore no significant effect of changing the railpad stiffness. The dip in the decay rate around Hz is caused by the sleeper and rail vibrating in phase on the ballast stiffness. When the railpad stiffness increases, the rail and sleeper are more strongly coupled and vibrate in phase over a larger frequency range. This results in an increase in size and a shift to higher frequencies of this dip with decreasing temperature. The following peak in decay rate is due to the sleeper and railpad acting as a vibration absorber to the rail. As the railpad stiffness increases, the natural frequency of this absorber system increases, shifting this peak to higher frequencies. Propagation of free waves occurs when the rail and sleeper vibrate out of phase on the railpad stiffness and results in a sharp decrease in decay rate. This cuton frequency of the track increases as the railpad stiffness increases. Finally the decay rate begins to increase again at high frequencies. This is linked to cross-section deformation of the rail, foot flapping, increasing the damping effect of the railpad, but is included in the model by adding damping to the rail. The same trends are exhibited in the decay rates for tracks containing both railpads; a decrease in temperature increases the cut-on frequency and the decay rate of propagating waves above cut on. This is due to the increased damping force provided by larger values of Kη. The additional peaks which can be seen in the decay rates at the higher railpad stiffnesses are due to sleeper modes of vibration. These only appear when the railpad stiffness is very high since the vibration of the sleeper and the rail will be more closely coupled when the pad between them is stiffer. The cork rubber pad is significantly stiffer below o C than the natural rubber pad at any temperature, resulting in higher decay rates and a higher cut-on frequency. The higher the decay rate, the lower the sound level radiated from the rail. Therefore it is expected that the cork rubber railpad will result in a lower noise level. However, due to the increased sleeper-rail coupling the sleeper will add to the overall noise level over a larger frequency range for the cork rubber pad. 6

7 6 th International Congress on Sound and Vibration, Kraków, Poland, 5 9 July 9 3. Track sound power level The total sound power level and separate contributions of the wheel, rail and sleeper are determined using TWINS. The wheel contribution is not significantly affected by changes made to the track structure and so, while the total sound power level includes the wheel contribution, only the rail and sleeper contributions are displayed separately here. Fig. a) shows results for the natural rubber railpad and Fig. b) for the cork rubber railpad. As expected as the temperature increases the overall sound power level of the track increases. Only the vertical component from the rail is shown as the effects on the lateral railpad stiffness have not yet been determined. However the lateral component will be less significant especially for softer pads. This will be included in future work. a) b) 5 5 Sound Power Level db rex-w 5 95 Sound Power Level db rex-w Figure 8. Variation of total sound power level radiated, due to vertical rail vibration, from the track (-), and the rail (--) and sleeper ( ) contribution, with temperature for the a) natural rubber railpad and b) cork rubber railpad There is an increase of 6.7 db(a) in the sound power level of the track with natural rubber railpads between - o C and 4 o C. As the railpad stiffness increases (decreasing temperature) the rail contribution drops and the sleeper contribution increases, resulting from the higher cut-on frequency produced by a stiffer railpad. From Fig. a) it can be seen that the lowest sound power level is produced when the rail and sleeper components are closest in magnitude. It is also seen that only at the lowest temperatures does the sleeper affect the total sound power level significantly; above approximately o C the sleeper contribution is more than db below the rail contribution. The variation in total sound power level over the temperature range for the cork rubber railpad is less than for the natural rubber railpad due to the greater contribution of the radiation from the sleepers; the level increases by 3. db(a) between - o C and 4 o C. As a result of the higher stiffness of the cork rubber railpad the sleeper contribution affects the total sound power level at all temperatures and produces a higher sound power level than the vertical rail motion at low temperatures/high pad stiffnesses. The sleeper and rail (vertical vibration) produce equal sound power levels at approximately 5 o C. 4. Conclusions The two railpad materials display similar trends with temperature and frequency. The main difference between them is in the loss factor which peaks below - o C for natural rubber and at around a temperature of o C for cork rubber. It is seen that there is an effect on overall noise radiated by the track due to the temperature of the railpad. The stiffness of both railpads can be seen to have a considerable temperature dependence which has a clear effect on the rail vertical decay rate, and translates to between 3 and 7 db(a) difference in track sound power level over the measured temperature range. From the current data it appears that the extent of the change in sound power level depends on the stiffness of the railpads; softer railpads display a larger variation. 7

8 6 th International Congress on Sound and Vibration, Kraków, Poland, 5 9 July 9 However only two materials are tested here, a wider range of railpad materials needs to be tested before this could be confirmed. It has also been shown that there is a small frequency dependence of the railpad stiffness, although the effect of this on the decay rate of the rail and the sound radiation of the track has not yet been investigated in the current work. It is also important to consider the frequency dependence of the loss factor in predictions. Further work will include measurements of track decay rates on a test track fitted with these pads for a range of environmental temperatures. Additionally lateral rail decay rates are to be considered in both measurements and predictions. REFERENCES P. J. Remington, Wheel/rail rolling noise, I: Theoretical analysis. J. Acoust. Soc. Am, : p D. Thompson, Railway Noise and Vibration: Mechanisms, modelling and means of control, Elsevier, London, 9. 3 C. J. C. Jones, D. J. Thompson, and R.J. Diehl, The use of decay rates to analyse the performance of railway track in rolling noise generation. J. Sound Vib, 6. 93: p N. Vincent, et al., Theoretical optimisation of track components to reduce rolling noise. J. Sound Vib, (): p D. J. Thompson, Experimental analysis of wave propagation in railway tracks. J. Sound Vib, (5): p D. J. Thompson et al, Developments of the indirect method for measuring the high frequency dynamic stiffness of resilient elements, J. Sound Vib., (): p Å. Fenander, Frequency dependent stiffness and damping of railpads, Proc. Instn. Mech. Engrs., Part F: J. Rail and Rapid Transit, 997. (): p D. J. Thompson and J. W. Verheij, The dynamic behaviour of rail fasteners at high frequencies, Applied Acoustics, (): p-7. 9 N. Ahmad, A methodology for developing high damping materials with application to noise reduction of railway track, PhD Thesis, ISVR, University of Southampton, 9. N. Ahmad, et al, Predicting the effect of temperature on the performance of elastomer-based rail damping devices, J. Sound Vib, 9. 3: p G. De France, Railway track: effect of rail support stiffness on vibration and noise. Master of Science Dissertation, ISVR, University of Southampton, 998. D. J. Thompson, et al, Experimental validation of the TWINS prediction program for rolling noise, part : Description of the model and method, J. Sound Vib, (): p D. J. Thompson, et al, Experimental validation of the TWINS prediction program for rolling noise, part : Results, J. Sound Vib, (): p

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