Structural identification of the mathematical model of the functioning of tribosystems under conditions of boundary lubrication

Abstract

In the work, a methodological approach to obtaining mathematical models was further developed, which describe the functioning of tribosystems in stationary and transient modes under boundary lubrication conditions.The structural identification of the tribosystem as an object of modeling the functioning of tribosystems in the conditions of boundary lubrication is performed. It is established that the operation of tribosystems is described by a third-order differential equation and, in contrast to the known ones, takes into account the function of changing the quality factor of the tribosystem during running-in. It is shown that the nature of the functioning of tribosystems under conditions of ultimate lubrication depends on the gain and time constants included in the differential equation. It is shown that the coefficient К1 takes into account the degree of influence of the input signal (load, sliding speed, tribological characteristics of the lubricating medium), on the value of the output signal (quality factor of the tribosystem). Coefficient К2 takes into account the magnitude of the change of the output parameters (volumetric wear rate and friction coefficient) when changing the values of the input parameters (load, sliding speed, quality factor of the tribosystem. Coefficient К3 takes into account the degree of influence of the input signal on the restructuring of the material structure in the surface layers of the triboelements.The time constants of the tribosystem characterize the inertia of the processes occurring in the tribosystem, during running-in, or during changes in operating modes. Increasing the time constants makes the process less susceptible to changes in the input signal, the running-in process increases over time, and the tribosystem becomes insensitive to small changes in load and slip speed. Conversely, the reduction of time constants makes the tribosystem sensitive to any external changes.

Parametric identification of the mathematical model of the functioning of tribosystems in the conditions of boundary lubrication

“…According to the principle of Le Chatelier -Brown, any physical system that was in equilibrium is exposed to an outrageous factor, the equilibrium in the system is shifted so that the effect of this factor is weakened. Therefore, the inertial link 3 G in work [1] included in the scheme of the second block in the form of negative feedback and takes into account the ability of the tribosystem to weaken the perturbing force, by rearranging the surface layers of materials from which the triboelements are made during secondary running-in. Outrageous forces include load, sliding speed, tribological characteristics of the lubricating medium, quality factor of the tribosystem.…”

“…To substantiate the methodological approach in research, we use the equation of the dynamics of the functioning of the tribosystem, which is given in [1]. The third-order differential equation is written in operator form:…”

“…Obtaining such models is associated with the stages of structural and parametric identification. Structural identification of the tribosystem is carried out in the work [1], where the third-order differential equation is obtained. The obtained equation can be used provided that all the parameters that are included in the left and right sides of the equation are determined.…”

“…This work is a continuation of work [1], where a third-order differential equation is obtained for modeling the boundaries of stable operation of tribosystems under boundary lubrication conditions. To use this approach, it is necessary to obtain expressions for calculating all the coefficients and time constants that are included in the left and right sides of the equation.…”

Experimental verification between the functioning of tribosystems in the conditions of boundary lubrication

“…To substantiate the methodological approach in research, we use the equation of the dynamics of the functioning of the tribosystem, which is given in [8]. The third-order differential equation is written in operator form:…”