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Koronatov V.A. The presentation of a new rolling theory with reference to the description of motion of the driven wheel of the locomotive (automobile). Modern technologies. System analysis. Modeling, 2018, Vol. 57, No. 1, pp. 49-60. DOI: 10.26731 / 1813-9108.2018.1 (57).49-60

Journal number: 
531: 534.013: 622.24: 622.23.01


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This article proposes a new qualitative method that makes it possible to take into account the dynamics of processes in the contact spot of the wheel with the roadway without determining the contact stresses. The latter means that it is not necessary to use semi-empirical relations in the form of the Hertz law, which is customarily introduced for normal stresses when establishing the law of their distribution. The method allows us to establish analytical dependencies for the force components through kinematic quantities. The following results are obtained: a) the rolling resistance depends directly on the sliding speed and vice versa ‑ on the angular speeds of rolling and spinning; b) the moment of rolling resistance depends directly on the angular velocity of the rolling and vice versa - on the speed of sliding and the angular velocity of rotation; c) the moment of resistance to rotation depends directly on the angular velocity of rotation and vice versa ‑ on the angular velocity of rolling and the speed of sliding.

These dependences qualitatively coincide with the results of V. V. Kozlov, the member of the Russian Academy of Sciences, which were obtained with the use of Lagrangian formalism, when, in contrast to conventional mechanics, a generalized law of dry friction was postulated. In mechanics of V. V. Kozlov, there are difficulties in the physical interpretation of such results. But there are no difficulties in a new theory constructed within the existing laws of mechanics. The new method made it possible to construct a new rolling theory different from the existing ones, which makes it possible to establish qualitative features in the wheel motion. For example, to determine the critical sliding or rolling speeds at which the possible modes of wheel motion change: pure rolling, rolling with slippage or pure sliding. The possibilities of the new theory are shown on the example of the description of the motion of the driven wheel of a locomotive (automobile).

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