On the efficient simulation of pass-by noise signals from railway wheels

The article presents an approach for calculating pass-by sound pressure radiated from railway wheels in the time domain using moving Green's functions. The Green's functions are obtained by using Finite Element (FE) and Boundary Element (BE) methods in the frequency domain, subsequent inverse Fourier transform, followed by convolution with a time series of rolling contact forces to obtain the pass-by time signals. However, traditional BE methods are computationally expensive due to the low structural damping of the wheel, necessitating a high frequency resolution. To overcome this issue, a modal approach is introduced in which the pass-by sound radiated by each wheel mode is calculated separately. This approach incorporates the dynamic response of the wheel in the time-domain processing and thus reduces the cost of the BE solution. A modal source signal is introduced to describe the excitation of each mode at each time step. The sound field radiated by unit modal amplitudes is calculated in BE and subsequently approximated by spherical harmonic (SH) equivalent sources, which allows for efficiently calculating acoustic transfer functions for varying relative positions of the wheel and a stationary receiver. Convolution of the source signal with the moving acoustic transfer function produces the pass-by pressure signal. The article investigates the directivity of the radiation from each mode and finds that most modes, including those with dominant radial deflection, radiate in mostly axial direction at high frequencies. Modes that dominate the pass-by pressure level are identified, both in frequency bands and with respect to the relative positioning of the wheel to the receiver. Finally, it is found that an SH expansion order of approximately 30 is required to satisfy the employed error measures, although lower orders may suffice for an auralisation of the signal.