Mathematical model of electrical contact bouncing

Abstract

Mathematical model of a contact bouncing takes into account elastic-plastic and electrodynamic forces, phase transformations during interaction of electrical arc with the contact surface as a result of increasing temperature. It is based on the integro-differential equations for the contact motion and Stefan problem for the temperature field. These equations describe four consecutive stages of the contact vibration from the impact at contact closing up to opening after bouncing including effects of penetration and restitution. The new method for the solution of the Stefan problem is elaborated, which enables us to get the information about dynamics of zones of elasticity, plasticity and phase transformations during contact vibration. It is shown that the decrement of damping depends on the coefficient of plasticity and the moment of inertia only, while the frequency of vibration depends also on the hardness of contact, its temperature, properties of contact spring, and geometry of rotational mechanism. It is found also from the solution of Stefan problem that the relationship between dynamical zones of plasticity and melting explains the decrease of current density and contact welding. The results of calculations are compared with the experimental data.