VOSSLOH has been working on dynamic wheel-rail forces along track discontinuities for some time. Track discontinuities determine the overall vehicle-track-interaction for safety, ride quality and maintenance.
In general, the behaviour of a railway and the maintenance strategy depend on the overall track quality, which includes track geometry, track stiffness and damping.
Track quality can be evaluated by measurements taken along track sections. Together with a co-simulation model based on the Finite Element Method (FEM) and Multi-Body Simulation (MBS) it is now possible to validate different scenarios using measured data and dynamic wheel-rail forces along sections of high-speed lines without simplifying the track structure into interconnected single elements.
This co-simulation was examined intensively to optimise Vossloh’s rail fastening systems and particularly for the development of new tension clamps which must be insensitive to moderate external vibrations in order to reduce the risk of possible track faults.
Until now, fastening systems have been designed according to technical specifications such as fatigue strength and creep resistance and normally using CAD geometry simulations which allow a 3D representation. FEM also includes material parameters in the simulation. For fastening systems or angle guide plates, for example, conclusions can be drawn about elasticity, clamping force, fatigue strength, load and possible failure. MBS also considers the time factor using a 4D representation. Already used in the automobile industry as a standard, Vossloh has now applied this to railways. Taking rail maintenance and wheel quality into account, the use of safety factors can provide even more precise information about which tolerances in the track are still safe.
In addition, FEM and MBS save a lot of time and money since all solutions are developed on a computer. Reconciliation with reality takes place only after a certain degree of design maturity, after pre-conversion to the computer, prototyping and subsequent laboratory tests.
MBS also allows the investigation of the natural frequency or vibrations of a component, which is difficult to determine in reality using amplitudes only.
In order to ensure durability and safety, the different damping behaviour, which can raise problems depending on the softness of the subsoil structure and the rigidity of the superstructure, must be considered.
If a train excites the track through the wheel we consider this a rail contact mechanism. Under certain track conditions, such as uneven track settlement or corrugation, the train load can be significantly higher than the static value. In addition, the vehicle can contribute to dynamic loads, for example through wheel flats.
This excitation is not only important due to its magnitude, but also due to its characteristic frequency. This frequency fext can be calculated as follows: fext = V / (3.6 x L), where fext is the excitation frequency (Hz), V stands for speed in km/h, and L represents the characteristic wave length in metres.
With vehicle-driven excitation, such as polygonised wheels, this excitation frequency is constant during the entire passage of the vehicle. There are also many characteristic frequencies from the track structure, the so-called natural frequencies. If the natural frequencies of the tension clamp happen to be identical to the excitation frequency from the vehicle, the tension clamp will be in resonance vibration.
Exceptional, high additional loads occur, particularly with high-speed trains, in the form of high-frequency vibrations at the same time which, under certain circumstances, can overload a conventional fastening system.
With this background, Vossloh and its partners have carried out intensive examinations to optimise rail fastening systems and, in particular, for the further development of tension clamps.
FEM analysis is performed using an Ansys-Workbench as a coupled analysis. The first step involves calculating the preload status using static analysis. This corresponds to the tension clamp assembly process. The tension clamp is fastened by tightening the screw, resulting in preload in the component. The characteristic curve represents the relationship between the preloading path and the resulting force.
The second step entails performing a modal analysis based on the imposed load calculated in the first step. In this analysis, not only are the natural frequencies determined but also the associated modes of the tension clamp (Figure 1). Depending on the component’s symmetry, it is common practise in FEM analysis to represent only 50% of the tension clamp geometry as this reduces the calculation time with sufficient accuracy.
Various calculation models, such as full or symmetric, are considered and evaluated in terms of their suitability. In any case, linear modal analysis does not consider material and geometric non-linearities. The determined natural frequencies exhibit a significant sensitivity to the definition of the boundary conditions (Figure 2).
MBS is designed to produce time-dependent simulations. By using elastic bodies, the FEM model is condensed and used as the starting point for the MBS calculation, and this coupling of both methods is called co-simulation.
However, the time-consuming simulation of an FEM model is still necessary, since element cross-linking and finite element meshing reflects local strengths and stiffnesses. This accuracy is necessary to create the best possible representation of the structure’s bending behaviour. Co-simulation therefore achieves the highest degree of accuracy at a reasonable cost, taking the time factor into account.
A time-dependent sinusoidal loading, which has a constant load amplitude and an increasing frequency up to 1000Hz, is applied to both spring arms to illustrate the time-dependent movement of the spring arm. Under its natural frequency, this movement can be considerably higher than normal.
The co-simulation of FEM and MBS shows that the natural frequency vibration can be theoretically up to 50 times higher than other vibrations. In addition, evidence shows that neighbouring frequencies can also cause a high amplification.
A systematic investigation program is used to analyse the natural frequency of the tension clamps. First, this involves measuring the natural frequencies of the tension clamp in a laboratory. Accelerometers are placed on the rail and tension clamp, to measure the vibration acceleration of the track. The measured raw acceleration level of the track was used to analyse track quality and the respective vibration level.
Specially-made accelerometers are used to record and convert the physical acceleration into electronic signals with an upper frequency limit of more than 10kHz.
An impulse hammer was used to extract a standard impulse load on the rail head in order to calibrate the track vibration behaviour. The contact head is made of metal.
Eight accelerometers are installed on the rail, sleepers and in the trackbed of each test section to provide the exact information regarding the elements which are excited the most. Fast Fourier Transformation (FTT) allows a translation of all functions from the time to the frequency domain. With the aid of suitable data preparation, the component or system’s natural frequencies can be determined from the transmission function.
At the indicated natural frequency of the tension clamp, the mode shape can be estimated by combining the amplitude and phase values from different measurement channels. The mode shape is a combined movement in longitudinal and vertical directions of the spring arm.
All natural frequency results gathered from FEM, co-simulation and measurements (Table 1) focus only on the natural frequency, which is excited through vertical excitation at the spring arm.
The numerical simulation of the single tension clamp analyses the natural frequency and mode shape. The resulting deviation between simulation and measurement is sufficient for further simulation needs.
For the construction or interpretation of new tension clamps these results are particularly important since with new developments the tension clamp is only available in CAD, and an eigenfrequency analysis by FEM is strongly dependent on the contact definition. By combining FEM and MBS, more accurate predictions can be made:
- the simulation of natural frequencies by excitation from other directions will be supplemented
- the whole hammer test method can be simulated with co-simulation to produce a verified model for both natural frequency and amplitude
- measurement in operational track with impulse hammer and trains, and
- guidlines for the development of new tension clamps.