MATHEMATICAL MODELS OF PROBABILISTIC CHARACTERISTICS OF TRACTION RESISTANCE OF TILLAGE WORKING BODIES
Mathematical modeling of surface tillage by different working bodies with due account for the probabilistic and statistical characteristics of their energy parameters is an urgent task as it allows to design more advanced and energy-efficient tillage tools. The aim of research was to create the mathematical models and to estimate the effect of travelling speed and soil tilling depth on the probabilistic and statistical characteristics of the traction resistance of dynamic and typical (non-dynamic) tilling tools. The study objects were the regularities in variation of the average value, mean square deviation, and the coefficient of variation of the traction resistance of dynamic and typical (non-dynamic) tilling working bodies. The study subject was the practice of ploughless surface soil tillage. Mathematical modeling methods, based on the study of physical regularities occurring during the tillage process by dynamic and typical (non-dynamic) tilling working bodies, were applied. The energy consumption by tilling tools was estimated in the experimental study. Experimental data obtained were analysed and integrated. The scientific novelty of the work was manifested in created mathematical models, which described the functional dependence between the average value, mean square deviation, and the coefficient of variation of the traction resistance of dynamic and typical (non-dynamic) tilling tools and the tilling depth and travelling speed. The article presents graphical dependences (response surfaces) of probabilistic and statistical estimates of traction resistance of dynamic and standard (non-dynamic) tilling tools. The determination coefficient for the functional dependences of the average traction resistance of dynamic and non-dynamic working bodies on the tilling depth H and the travelling speed V in the form of a regression equation ranged from 0.959 to 0.970. The determination coefficient for the functional dependences of the mean square deviation of traction resistance of dynamic and non-dynamic working bodies on the tilling depth H and the travelling speed V in the form of a regression equation ranged from 0.784 - 0.877. The determination coefficient for the functional dependences of the coefficient of variation of traction resistance of dynamic and non-dynamic working bodies on the tilling depth H and the travelling speed V in the form of a regression equation ranged from 0.898 - 0.937. The established values of the determination coefficient indicate a high accuracy in the selection of regression equations of the probabilistic and statistical characteristics of traction resistance of the working bodies under consideration.