The paper considers applying the residue theory in obtaining mathematical models for autocorrelation functions of vibroacoustic oscillations in a machine dynamic system during the cutting process. It shows that these models are analogous to experimental data and reflects their practical application for assessing the dynamic quality of machine tools and setting a processing mode. Calculating the dynamic system stability margin is carried out automatically according to the oscillation index obtained from a real amplitude-frequency characteristic of the dynamic system. This characteristic, in its turn, is determined from the identified transfer function. The article considers the construction of a theoretical model for the autocorrelation function of vibroacoustic oscillations of a grinding machine dynamic system, that would be equivalent to the autocorrelation function obtained from experimental data. Such a model would be feasible to use to calculate the dynamic system transfer function of the machine with a subsequent evaluation of its stability margin. It substantiates applying the dynamic system stability margin of the machine as an informative characteristic based on measuring vibroacoustic oscillations during the cutting process to evaluate the technological system quality and stating an appropriate processing mode to achieve the required part surface quality. It is shown that the identification of transfer function under the established conditions by the autocorrelation function of vibroacoustic oscillations during cutting enables us, based on the maximum stability margin of the dynamic system, to determine the machine with the highest dynamic quality and set the cutting mode, which ensures high processing quality and reduces tool wear.
When modeling a jet during hydroabrasive processing of structural materials, we will represent it as a heterogeneous environment. And accordingly, the hydroabrasive flow will be considered as a heterogeneous flow. The equations describing the formation of a heterogeneous flow are based on the equation of conservation of momentum of the total movement and allow for the interaction of the background flow and particles of the abrasive. A mathematical model of a heterogeneous flow, reveals the mechanism of formation of a waterjet jet. Based on the mathematical model, the hydrodynamic forces and surface stresses acting between the abrasive and the liquid can be taken into account. It also takes into account speed, concentration, mass, density of the fluid and abrasive. Knowing these parameters, it is possible to use the mathematical model of a heterogeneous flow to find the optimal conditions for the formation of a waterjet flow and the processing of structural materials.
To increase the durability of the bearing, it is necessary to achieve a profile shape of the groove of the bearing close to that obtained during running-in. This effect allows you to achieve a method of non-abrasive tuning of the raceways of the rings of roller bearings. To study the effectiveness of this method, it is necessary at the initial stage to build a mathematical model of metal removal from the treated surface. To derive the mathematical model, we used the energy theory of friction, the theory of elasticity, and the physical theory of similarity. After the conclusion of the model, you can see which factors have the greatest impact on the efficiency of the process of non-abrasive tuning of the raceways of the roller bearing rings.
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