A model of a¯exible wheelset running on¯exible rails is presented which demonstrates the growth of out-of-round pro®les of the wheels. This process of growing is called polygonalization. We divide the model into two parts. One part describes the oscillations of the wheelset and the rails. The excitations, which are a result of the out-of-round wheels, are due to geometrical terms, while excitations of unsprung masses are not considered. The second part describes the development of the wheel pro®les and the wear rate due to wear and hardening, respectively. The two parts can be coupled by means of perturbation theory with multiple-time scales, [4], [10] as a wear-feedback loop proposed in [6]. As the calculation show, the greater is the phase shift between the-out-of-round pro®les of the right and the left wheel the faster the wheels become out-of-round. Furthermore, it is shown, that the ®rst and the second bending modes of the wheelset play an important role in the growth of polygonized wheels. It should be emphasized that other reasons for polygonalization may exist too, e.g. excitations due to unsprung masses, [14].

The discrete element method (DEM) is frequently used to investigate the behaviour of granular media (Bravo in Simulation of soil and tillage-tool interaction by the discrete element method, 2013; Tijskens et al. in J Sound Vib 266:493–514, 2003; Langston et al. in Chem Eng Sci 50:967–987, 1995; Kohring et al. in Comput Methods Appl Mech Eng 124:273–281, 1995; Stahl et al. in Granul Matter 13:417–428, 2011). The parameter calibration is a challenging task due to the large number of input parameters and the computational effort. Sometimes, this is performed with a trial-and-error approach as mentioned in Roessler et al. (Powder Technol 343:803–812, 2019), Rackl and Hanley (Powder Technol 307:73–83, 2017) based on laboratory tests, e.g. the pile experiment, the oedometer experiment and the shear test. To achieve a more suitable calibration, a better model understanding is necessary in which the influence of the DEM parameters is analysed. Consequently, the calibration can be focused on specific parameters, which have a significant influence on thef model response. If parameters with a negligibly small influence exist, the number of calibration parameters can be reduced. On this basis, it is possible to decide whether the laboratory test is suitable for the calibration of specific parameters or not. This is demonstrated with a sensitivity analysis based on Sobol’ indices for the oedometer laboratory test. In order to reduce the computational effort, the sensitivity analysis is performed with different metamodels of the oedometer simulation. The metamodels are fitted and validated with two separate sampling point sets. It is shown that the Young’s modulus for the investigated input space is the most significant parameter. This knowledge can be used to only focus the calibration on this significant parameter which enables an easier calibration and makes clear that for calibrating of other parameters this laboratory test is inappropriate. An algorithm of a force-driven plate is developed and shown which prevents non-physical states in which the interaction force between the particles and the loadplate exceeds the applied force.

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In this paper a method is presented to predict the ride comfort of passenger cars for single-obstacle crossings based on measured acceleration data and airborne sound. The method takes advantage of applying the continuous complex wavelet transform to the signals using specially adapted Gabor wavelets. Through an innovative approach, the comfortrelevant features are extracted to describe the geometric properties of the transformed data and to predict the ride comfort using artificial neural networks with a feedforward structure. In order to avoid overfitting, basic data division is applied to the available training data and the networks are trained using Bayesian regulation.

In the case of full vehicle models, the technique of multi-body simulation (MBS) is frequently used to study their highly non-linear dynamic behaviour. Many non-linearities in vehicle models are induced by force elements like springs, shock absorbers, bushings and tires. Commonly, spline functions are used to represent the force responses of these components. If the non-linear relationships are more complicated, the spline approximations are no more accurate. An alternative approach is based on empirical neural networks which are based on the mathematical approximation of measured data. It is well known that neural networks are able to represent and predict complex component responses accurately. The aim of this paper is to perform a dynamic full vehicle simulation using a thermomechanically coupled hybrid neural network shock absorber model. In this shock absorber model, the spline approach is combined with a temperature-dependent neural network. Based on a displacement-controlled excitation on a four post test rig in the ADAMS/Car MBS software, a rugged test track is simulated. In this way, the front and rear shock absorbers are dynamically loaded with comfort-relevant frequencies in the range of 0.75-30 Hz and velocity amplitudes up to 2 m/s. By the simulation, stability of the hybrid neural network model is demonstrated. Furthermore, the damping force, the vertical acceleration of the chassis and the required simulation times are compared. The standard spline approach is used as a reference.