  The noise generated by the friction of two rough surfaces under weak contact
pressure is usually called roughness noise. The underlying vibration which
produces the noise stems from numerous instantaneous shocks (in the microsecond
range) between surface micro-asperities. The numerical simulation of this
problem using classical mechanics requires a fine discretization in both space
and time. This is why the finite element method takes much CPU time. In this
study, we propose an alternative numerical approach which is based on a
truncated modal decomposition of the vibration, a central difference
integration scheme and two algorithms for contact: The penalty algorithm and
the Lagrange multiplier algorithm. Not only does it reproduce the empirical
laws of vibration level versus roughness and sliding speed found experimentally
but it also provides the statistical properties of local events which are not
accessible by experiment. The CPU time reduction is typically a factor of 10.
