翻译原文--通过采用有限元模拟来优化运货车辆的车轮阻尼器

B. Schulte-Werning et al. (Eds.): Noise and Vibration Mitigation, NNFM 99, pp. 334340, 2008. Springer-Verlag Berlin Heidelberg 2008 Optimization of a Wheel Damper for Freight Wagons Using FEM Simulation W. Behr1 and S. Cervello2 1 Deutsche Bahn AG, DB Systemtechnik, TZF12, Voelckerstr. 5, D-80939 Muenchen, Germany Tel.: +49 (0)89 1308 7344; Fax: +49 (0)89 1308 2590 wolfgang.behrbahn.de 2 LucchiniSidermeccanica, Railway Product, Lovere Plant,Via G. Paglia 45, I-24065 Lovere (BG), Italy Tel.: +39 035 963483; Fax: +39 035 963488 Summary Within the EU-Project SILENCE a new approach was followed to develop a wheel absorber which is suitable for freight trains with block-brakes. Lucchini has devel- oped an absorber made exclusively out of steel consisting of various plates connected to each other while sliding is possible. In order to evaluate the effect of the absorber, FEM simulations have been performed in addition to measurements in the laboratory. The results of the simulations of a wheel with and without the absorber device are given, including the modelling of the absorber using the FEM technique. Also a com- parison between calculated and measured results is presented. 1 Introduction The growing railway traffic causes increasing sound emission. Therefore Deutsche Bahn AG makes every effort to reduce the sound emission, especially of K-block- braked freight trains, even if the requirements of operation make it difficult to develop a new wheel design regarding the acoustical needs by meeting the given structural and thermal properties. A good possibility to reduce the sound radiation is to fix absorbers to the wheel. In contrary to disc-braked wheels used in conventional rolling stock, freight trains are mostly equipped with brakes acting on the running surface. So, absorbers for block- braked wheels have not only to withstand high temperatures up to 450C but they have to be functional despite such temperatures. Within the EU-Project SILENCE 1 LucchiniSidermeccanica developed in coop- eration with Deutsche Bahn the absorber system “Hypno” which consists only in steel components in order to withstand the thermal loads. This paper presents the working mechanism of the damping device as well as the calculations performed using the Finite Element Method (FEM) tool Ansys to estimate the acoustical effects due to this absorber. Since measurements on the first prototype of this absorbing system showed good damping and noise reduction effects, calculations performed with the finite ele- ment method concentrate on the particular case that the absorbing plates are rigidly coupled which may describe a certain kind of dysfunction due to extreme weather Optimization of a Wheel Damper for Freight Wagons Using FEM Simulation 335 conditions in winter like ice, or rusty surfaces of the absorbing plates. That condition can be handled as a worst case state of the damping system on which the investiga- tions are focused. First the damping system “Hypno” and its function will be presented. In the next section the finite element model of the wheel with mounted damping system will be described. The major part afterwards is focused on the calculations performed with the finite element method especially for the condition of rigidly coupled absorber plates. The possibility of calculating the damping effect of the device with working absorber plates gliding against each other will be discussed in the outlook. 2 The Damping System “Hypno” (prototype 1) The main parts of the damping system are two thin plates made out of steel resting on each other without a rigid connection so that sliding is possible. Due to this sliding, vibration energy can be transformed into friction energy. The absorbing plates cover the complete rear face of the wheel. Therefore they are slitted to allow heat transfer from the back of the wheel during braking. Each absorb- ing plate is fixed to a mounting ring. One large ring is arranged at the inner side of the rim, a second small ring is arranged at the hub. For the arrangement of the mounting rings there are grooves milled into the wheel body in which the rings are clamped. So sliding is possible between each mounting ring and the wheel body. But due to the prestress effect of the clamping the rings can be handled as nearly rigidly fixed, espe- cially the small ring. The single parts of the damping device and a cross section view of the wheel with mounted absorbers are shown in Fig. 1. Also shown is the computer model described in section 3. The wheel BA004 manufactured by Radsatzfabrik Il- senburg was used for the investigations of the damper device. Fig. 1. The damping system “Hypno”: single parts (left), a cross section view (middle) and the computer model (right) 3 Description of the Finite Element Model The finite element model shown in Fig. 1 consists out of solid elements which are sorted in five groups: the wheel BA004, the large mounting ring, the small mounting 336 W. Behr and S. Cervello ring, the large absorbing plate and the small absorbing plate. For these elements the material parameters for steel have been used, which are a density of 7700 kg/m3 and an elastic modulus of 214 GPa. The large absorbing plate is connected to the large mounting ring, the small ab- sorbing plate is fixed to the small mounting ring. Between the two absorbing plates there are contact-/target elements which enable the sliding of the two plates against each other 2. The energy loss due to friction damping is modelled with additional damping elements between the damping plates (combin elements 2). The strength of this damping of the plates can be adjusted with the damping factor Cv1. In the same way there are contact-/target elements modelled between each mounting ring and the wheel body to allow sliding. To model the prestress effect of each ring and also its participating damping effect there are damping elements between both ends of each ring. Again the strength of that damping effect due to the mounting rings can be adjusted with the damping factor Cv2. Constraints are set to the hub which is realistic for the wheel connected to an axle. 4 FEM Calculations 4.1 Modal Analysis of the Wheel BA004 In a first step a modal analysis of the wheel BA004 without the damping device was performed. Each wheel radiates sound only at specific frequencies which can be ob- tained performing a modal analysis. Whether a specific modal frequency will be ex- cited depends on the location and direction of excitation, the strength of the vibration amplitude (in case of excitation) depends on the exciting force itself which is fre- quency dependent due to the surface conditions of the wheel and the track. The result- ing mode shapes for the frequency range 900 Hz 2200 Hz are shown in Fig. 2. 01 02 03 04 05 06 07 08 936 Hz 1201 Hz 1528 Hz 1705 Hz 1745 Hz 1894 Hz 2123 Hz 2190 Hz Fig. 2. Modal shapes of the wheel BA004 in the frequency range between 900 - 2200 Hz (arbi- trary numbering) 4.2 Harmonic Analysis and Validation of the FE Model To determine the vibration behaviour of a wheel only a few different frequency trans- fer functions (FRF) are sufficient. Common excitation points are shown in Fig. 3. An excitation on the running surface in radial direction (e.g. at 2X or 3X) simulates the behaviour of running on a straight track while an excitation on the rim (e. g. at 1Y) simulates the behaviour running in curves. Transfer functions like 3X-1Y or 2X-1Y can give a first hint of the sound radiation even though only one point of the front of the wheel is used for analysis. Optimization of a Wheel Damper for Freight Wagons Using FEM Simulation 337 2x 3x 4x 1y x y 6x -35,00 -30,00 -25,00 -20,00 -15,00 -10,00 -5,00 0,00 5,00 10,00 110012001300140015001600170018001900200021002200 Frequency / Hz FRF modulus dB ref 1 BA004 measured frequency response function 2X - 2X BA004 calculated frequency response function, wheel without constraints: 2X - 2X Fig. 3. Location of common excitation and analysis points used to obtain a set of FRF (left). Comparison of measured (dark) and calculated (light) FRF of the wheel BA004 without con- straints excited on the running surface at location 2. A set of transfer functions has been measured in the test lab of Lucchini where the wheel was mounted on rubber blocks so that no constraints influence the vibration behaviour of the wheel. Therefore the FE model without any constraints was used to calculate that transfer functions. The comparison between measured and calculated data show good agreement for all transfer functions. For example, the transfer func- tions 2X-2X is shown in Fig. 3. It can be seen that the natural frequencies agree well. The maxima levels which are relevant for sound radiation differ only by a few decibel which may be caused by the individual modal damping of each mode. The structural behaviour indicates that the FE model can be considered to be validated. 4.3 Determination of the Sound Power Performing a harmonic analysis gives the vibration velocity n at each point of the wheel surface. Averaging over all points n of the wheel surface A using Eq. (1) gives the sound power with P0 = 10-12 W, A0 = 1 m2, 0 = 510-8 m/s, = 1.225 kg/m3 and c = 340 m/s 3. Thereby the radiation efficiency is set to unity which is a good approxi- mation for the wheel for frequencies above 1 kHz. + = 2 0 2 00 2 00 0 log10log10log10 log10 n P A A P cA P P dBL (1) 15 25 35 45 55 65 75 50010001500200025003000 Frequency / Hz Sound Power / dB Wheel BA004 without damping device, excitation at 2X, front side Wheel BA004 without damping device, excitation at 1Y, front side 1 2 3 4 5 6 7 8 Fig. 4. Sound Power of the wheel BA004 for excitation on the running surface at 2X (dark) and at the rim at 1Y (light) 338 W. Behr and S. Cervello The radiated sound power of the wheel shown in Fig. 4 was calculated for excita- tion locations on the running surface and the rim. It can be seen that the vibration modes shown in figure 2 are excited differently in dependence of the radial or tangen- tial excitation direction. It should be noted that an excitation force of 1 N was used for the harmonic analysis. Therefore the absolute values of the sound power displayed in Fig. 4 do not represent the real radiated sound power of a wheel, but they do enable a quantitative comparison of different set-ups 4. 4.4 Simulation of the Absorbing System with Rigidly Coupled Absorber Plates In order to estimate the quantitative effect of the sound radiation of the wheel with damping system for rigidly coupled absorber plates compared with the wheel without damping device, the sound power has been calculated for both options. Fig. 5 shows that sound power of the front side of the wheel when excited on the running surface (at location 2) compared with the corresponding sound power of the undamped wheel. It can be seen that there is a damping effect for roughly all modes, even for the damp- ing device with rigidly coupled absorber plates. 15 25 35 45 55 65 75 50010001500200025003000 Frequency / Hz Sound Power / dB Wheel BA004 without damping device, excitation at 2X, front side Wheel BA004, damped, with rigidly connected absorbing plates, front side 1 2 3 4 5 6 7 8 Fig. 5. Sound power of the wheel body (dark) compared with the wheel with rigidly coupled absorber plates (light) 1201 Hz 1291 Hz 1291 Hz Fig. 6. Comparison of the mode shape of the undamped wheel (left) with the mode shape of the wheel with rigidly coupled absorber plates (middle. front view, right: back view) for the mode shape numbered 2 The total level of the sound power over the frequency range 500 3000 Hz is 83.9 dB for the undamped wheel. For the damped wheel with rigidly coupled absorber plates the corresponding sound power level is 82.6 dB. That reduction of the sound radiation may be caused by the stiffening of the wheel. Fig. 6 demonstrates the effect of the rigidly coupled absorber plates for the mode numbered 2 as an example. As the rigidly coupled absorber plates without the possibility to slide can be stated as the Optimization of a Wheel Damper for Freight Wagons Using FEM Simulation 339 worst case of damping, the sound radiation of the wheel with damping system can be assumed at least 1.3 dB less. Consequently, for a working absorbing system more reduction of the sound radiation can be expected. But that calculated changes in sound radiation for a constant force excitation will possibly not produce any difference when rolling damping is included. 4.5 Sound Radiation of the Damping System Itself The calculations described in section 4.4 demonstrate the effect of the damping sys- tem on the wheel when the absorber plates are rigidly coupled. Due to reduced vibra- tion levels on the front of the wheel, the resulting sound radiation caused by the wheel will be less. Nevertheless the absorbing plates themselves also vibrate and therefore radiate sound. Like the wheel, the absorbing plates also have certain vibration modes which will be excited when the wheel is excited. That source on the back of the wheel may contribute to the noise emission from the train due to reflection from the wagon body and the track. To get an estimation of the maximum possible amount of that sound level caused by the absorbing plates, the sound power from the back of the wheel was calculated and compared with the sound power from the front. That comparison is shown in Fig. 7 for the worst case (rigidly coupled absorber plates) using equation (1). Since the radiation efficiency is smaller than 1 for thin plates, the sound radiated by the plates may be over-estimated (for frequencies 2 kHz in the specific case due to the combined thickness of 6 mm of the plates). Fig. 7 shows that the sound power of the absorbing plates compared to the front side is more, equal or less depending on the mode. Also there are additional mode shapes of the absorbing plates which count only for the sound radiated backwards. The highest sound power backwards results at the mode numbered 2 which splits into the two frequencies 1292 Hz and 1417 Hz. The sum level of the sound power radiated from the front gives 82.6 dB and for the back side 87.2 dB (for the wheel with rigidly coupled absorbing plates). Therefore the sound radiation backwards due to the rigidly coupled absorber plates is nearly 5 dB more compared to the sound radiation to the front. Due to absorption and reflection from the wagon body and the track a reduction of that radiated sound can be exspected and so this effect can be assumed as not rele- vant within the calculated values. 15 25 35 45 55 65 75 50010001500200025003000 Frequency / Hz Sound Power / dB Wheel BA004, damped, with rigidly connected absorbing plates, back side (damping plates) Wheel BA004, damped, with rigidly connected absorbing plates, front side Fig. 7. Sound power of the front (light) of the wheel with rigidly coupled absorber plates com- pared with the sound power of the back which are the absorber plates (dark) 340 W. Behr and S. Cervello 5 Outlook Simulations demonstrated in sections 4.4 and 4.5 have been focussed on calculations of the wheel with the damping device with rigidly coupled absorber plates in order to in- vestigate the worst case of dysfunction of the absorber system. As described in section 3 the FE model includes damping elements between the absorber plates. First calculations with that model with a working absorber device show a damping effect and will allow an optimization of the specific design of the different parts of the device. 6 Conclusion The paper presents calculations of the effect of the damping device “Hypno prototype 1” developed by LucchiniSidermeccanica in cooperation with Deutsche Bahn AG wh