Development of a mathematical model of stationary processes in tribosystems under boundary lubrication conditions

Abstract

The methodical approach in modeling stationary processes in tribosystems under boundary lubrication conditions is substantiated., where the input flows are: tribosystem quality factor, which characterizes the input flow - matter; the speed of dissipation in tribosystem, which characterizes the input flow - energy; the stability limit of the tribosystem, which characterizes the input stream - information. The target simulation function is the volumetric wear rate. I, м3 /hour and friction losses, which are determined by the friction coefficient f. Mathematical model - exponential dependence, which connects the input stream - matter, energy and information with an output stream - wear rate and friction coefficient. Mathematical expressions are obtained for modeling the volumetric wear rate and friction coefficient for stationary modes of operation of tribosystems (after completing the run-in). An experimental assessment of the adequacy of the developed mathematical models to experimental results has been performed. A three-factor experiment was carried out with an assessment of the compliance of the experimental data array with the normal distribution law. The values of the Cochren criterion are calculated, which confirm the reproducibility and repeatability of the experimental results from experience to experience. Using the Fisher criterion, the assessment of the adequacy of the results of mathematical modeling of experimental data was made, it was shown that the results of modeling the volumetric wear rate and friction coefficient are adequate to the experimental results with a confidence level 0,9. A simulation error was calculated for each series of experiments; it was shown that when modeling the volumetric rate of wear, the error does not exceed 10,3%, when modeling friction coefficient – 11,5%. Mathematical expressions are obtained that allow modeling the fluctuations of the wear rate and the friction coefficient during the operation of the tribosystem in the stationary mode. This allows us to take into account the formation and wear of surface films on friction working surfaces and to improve the accuracy of calculations for friction and wear, which is a distinctive feature of the model being developed from previously known. The simulation results obtained with regard to the oscillatory component were checked for compliance with the normal distribution law, reproducibility and adequacy, which allows to conclude that the resulting model can act as a tool in tribosystem calculations at the design stage. Accounting for the oscillatory component to improve the accuracy of modeling after completion of the run-in.