Knowledge of the forces at the wheel}rail contact is fundamental to estimate the consequences in terms of noise and vibration. The traditional use of strain gauges mounted on the wheel web and axle is not capable of determining the high-frequency content of the contact force. Measurements made on the rail are characterized by the spatial variability of input}output transfer functions which makes it di$cult to estimate the contact force by simple inversion of the point frequency response function. In this study the problem of rolling contact force reconstruction has been approached through the following steps: (i) the track has been characterized precisely for a "nite length by the analysis of the time series of several impacts supplied with an instrumented hammer by using an ARMAX model that proved to be capable of modelling the vertical dynamics of the rail up to 5 kHz; (ii) the response of the rail has been simulated with a random force acting on the system, and the variability of the transfer function has been taken into account by distributing the force on adjacent elements; (iii) the simulated response has been compared with the rail acceleration measured for the passage of several trains; (iv) the wheel}rail contact force has been estimated with a closed-loop algorithm. It has thus been possible to reconstruct the octave power spectrum of contact forces with a simple and stable iterative procedure. Forces reconstructed from di!erent sensors were found to be practically the same for a given wheel; forces from nominally similar wheels are statistically examined and partial results of comparisons made on di!erent rolling stock are shown.
2000 Academic Press