В.В. Лапшин, Е.А. Юрин
10
Nonlinear model of blow with dry friction
© V.V. Lapshin, E.A. Yurin
Bauman Moscow State Technical University, Moscow, 105005, Russia
According to the Hertz model of absolutely elastic impact, the contact force of interaction of
the bodies depends on deformation as well as it is in statics. K.H. Hunt and F.R.E. Crossley
suggested that at collision there arises not only an elastic force, but also viscous friction be-
tween particles of the colliding bodies. Thus the restoration coefficient monotonously de-
creases with increasing impact velocity. A nonlinear elastic-plastic model of collinear impact
of a body about a fixed obstacle is based on the Hertz and Hunt — Crossley models of impact,
in which it is assumed that the friction between the particles of colliding bodies is not viscous,
but dry. We obtained the first integrals of the equations of the movement in phases of defor-
mation and restoration. The coefficient of restoration and its dependence on a friction con-
stant was defined. We obtained a solution of equations of motion of the body in quadrature;
presented the results of mathematical modeling. In the paper we show that absolutely inelastic
impact is possible in this model, while elastic collision restitution coefficient does not depend
on the speed of the collision.
Keywords:
collinear impact, the coefficient of restitution, nonlinear dynamics.
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