## Mathematical Modeling of Continuous Tossing of the Brush with the Gap from the Commutator

Andrey V. Eliseev 1, Alexey I. Orlenko 2, and Sergey V. Eliseev 1
1. Irkutsk State Transport University, Irkutsk, Russia
2. Krasnoyarsk Institute of Railway Transport, Krasnoyarsk, Russia

Abstract—The proposed study is related to the development of the theoretical foundations of the dynamics of the contact group of the elements of the brush-commutator unit. Dynamic interactions of the brush with the commutator under the vibration applying from the side of the corpus of traction motor are considered. A special feature of the study is the possibility of breaking the not-holding brush-commutator contact as a result of the vibrational effects of internal and external force factors. A method is proposed for constructing mathematical models based on the use of the generalized gap function, which represents the analytical apparatus for accounting for unilateral constraints. The construction of the mathematical model assumes, at the primary stage, the permissibility of reducing the design scheme to the interaction of a material particle with a vibrating surface in a gravitational field. Within the framework of the model under consideration, non-standard force factors are taken into account by introducing an additional quasi-constant force applied to the brush. The influence of force factors on the modes of continuous tossing of the brush is shown. Peculiarities of the interaction of the brush on the interval of ascent and fall on the commutator surface are obtained in analytical form

Index Terms—the brush-commutator unit, traction motor, not-holding ties, unilateral constraints, the gap of contact, the function of the gap, continuous tossing

Cite: Andrey V. Eliseev, Alexey I. Orlenko, and Sergey V. Eliseev, "Mathematical Modeling of Continuous Tossing of the Brush with the Gap from the Commutator," International Journal of Electrical and Electronic Engineering & Telecommunications, Vol. 8, No. 2, pp. 72-77, March 2019. Doi: 10.18178/ijeetc.8.2.72-77