Computation of the Negative Damping Associated to the Hunting Motion of the Railway Wheelset, without Using Geometrical or Tribological Restrictions into the Model

Recently, analytical expressions for the damped natural frequency and damping ratio were proposed for the so-called dynamical hunting, either by assuming that the wheel conicity can be neglected, or by imposing restrictions on the ratio between the lateral and longitudinal creep coefficients, and also, on the ratio of the track span to the yawing diameter. However, instead of a pair of complex conjugate roots, and two real roots, of opposite sign, two pairs of complex conjugate roots were obtained for the characteristic equation. Purpose of this work is to achieve accurate expressions for the damping associated to the hunting motion, without imposing geometrical or tribological limitations into the vibration model, and to evaluate the error on the damping ratio, introduced by the simplified models. Also, nature of the roots of the characteristic equation is discussed, relative to the critical speed of the railway vehicle.