E. S. Lyuminarskaya - Post-graduate Student, Moscow State Industrial University. E-mail: lyuminarskaja.caterina@yandex.ru
V. N. Dianov - Dr.Sc. (Eng.), Professor, Moscow State Industrial University. E-mail: vyacheslav-dianov@yandex.ru

One way to improve the reliability of the electrical contacts is the timely detection of failures in their work. Refinement of existing and development of new methods for the detection of failures requires the creation of a mathematical model of the electrical contact on failure . The paper proposes a mathematical model of low-voltage electrical contacts on failure. Error conditions and failures in such contacts occur mainly due to falling into intercontact space dust , a sudden change in contact force contacts , educational films , non-destructive when the contacts. The proposed article mathematical model allows to determine the electrical contact resistance change in the transition zone in the failed state. The calculation is based on the representation of rough surfaces contact spherical random roughness height. All microprojections divided into three groups: interacting microprotrusions noninteracting microprojections and microprojections, between which there is a speck of dust. If the mean contact pressure at the surface microasperity first group σт, its deformation obeys Hooke's law. Here σт - the yield stress. When σт elastoplastic deformation occurs microasperity in which one part of its volume is elastic deformation, and the other portion of the volume - plastic. When σт comes the development of plastic for microscopic. Joint deformity motes and two micropoints obeys Hooke's law. In determining the transition resistance accounted for resistance and resistance to contraction micropoints not destroyed films. The calculations of transient resistance electrical contact in the absence of failure showed satisfactory agreement between the results of calculation and experiment.