Mathematical models of strengthening ground compaction for rutting estimation eliminated in elementary functions

Mathematical models and scientific basics of the theory of forestry machines locomotion, revealing the nature of interaction of forestry vehicles with strengthening soils, have been poorly developed. In practice, the lack of a complete scientific description complicates substantiation of the parameters and operating modes of the vehicles compatible with strengthening soil and ground conditions and makes it difficult to select passable forestry equipment. The objective of the article is to develop and study mathematical models of rutting that take into account the variable nature of the mechanical properties of soils under the influence of movers of forestry machines. The study bases on the provisions of soil mechanics and the theory of locomotion of forestry machines. In the development of mathematical models classical methods of mathematical analysis and approximation of functions were used. Based on the solution of the rutting equation analytical expressions in elementary functions were obtained for the first time, taking into account both gradual and possible more abrupt changes in the mechanical properties of the soil with depth. The obtained expressions will allow conducting computational experiments with a mathematical model of the interaction of the machine propeller with the soil in particularly difficult conditions represented by sodded soils (a stronger upper layer on a weakly bearing underlying layer). Also, as a result of solving the rut formation equation, expressions were obtained in elementary functions, taking into account the increase in the estimates of the mechanical properties of the bearing surface under the influence of the vehicle (strengthening). The formulas were obtained for the first time and are intended for calculating the indicators of the interaction of forestry machine vehicles operating in especially difficult conditions with bearing surfaces of linearly hardening peatlands and quadratically strengthening loose snow. The models were implemented in Python programming language. The results of calculating the rut depth formed on loose snow when a wheeled forestry machine is moving, as well as estimates of the coefficient of the rolling resistance are presented.

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