 
Summary: R Present address: Department of Mathematics, University of Manchester, Oxford Road,
Manchester M13 9PL, England.
Journal of Sound and
doi:10.1006/jsvi.1999.2510, available online at http://www.idealibrary.com on
CURVE SQUEAL OF TRAIN WHEELS, PART 1:
MATHEMATICAL MODEL FOR ITS GENERATION
MARIA A. HECKL AND I. D. ABRAHAMSR
Department of Mathematics, Keele ;niversity, Keele, Sta+ordshire Są5 5BG, England
(Received 25 August 1998, and in ,nal form 5 August 1999)
A mathematical model is presented for the squeal noise generated by trains when
traversing tight curves. Curve squeal is presumed to arise from lateral crabbing of
the wheels across the rail head. This induces a lateral friction force acting at the
contact of each wheel with the rail. An individual wheel then performs outofplane
oscillations which are radiated and heard as squeal. This phenomenon is modelled
by considering a #at round disc, with several outofplane modes, excited at one
point along the edge by a dryfriction force (typically a stick/slip force) which is
dependent on the disc velocity. An iteration scheme is developed which gives the
time history of the disc velocity. The iteration is straightforward and only requires
the impulse response (or the Green's function) of the disc and the functional
dependence between friction force and disc velocity (friction characteristic). The
