Theoretical studies of physical processes and phenomena in the zone of physical interaction of nanoinstruments with the surfaces of elements of microsystem technology are carried out in work. Based on the conducted research, mathematical models of energy heat exchange in the zone of physical contact of nanometric dimensions were compiled, and their analytical solution was obtained using the Fourier method of separation of variables and Goodman’s integral method. Simultaneously, the energy components of the processes in the nanocontact zone were considered. The numerical solution of the mathematical model of energy heat exchange in the zone of physical nanocontact was carried out using a software application based on the finite element method. The results were checked according to the equivalent thermal scheme to confirm the adequacy and accuracy of the obtained models. As a result, the mechanisms of energetic interaction of the nanoinstrument with the surfaces of the elements of microsystem technology devices were clarified. It is shown that the use of the proposed method of equivalent thermal circuits for the evaluation of mathematical models of the energy interaction of nanoinstruments with the surfaces of microsystem technology device elements, as well as the further study of the distribution of thermal fields in the nanocontact zone, differs from other numerical and analytical methods in terms of sufficient accuracy and speed of calculations. At the same time, it was established that the discrepancy between the results of mathematical modeling and the results obtained according to the equivalent thermal scheme does not exceed 5-8 %.

To ensure the reliability and accuracy of products, an automated construction method for the assembly sequence of high-precision axisymmetric products is presented. The work purpose is to verify the acceptability of using an oriented assembly graph, which includes adjacency and incidence matrices, for structuring and planning the theoretical schematization of the assembly technological process. The considered method coincides with a possible mathematical implementation of the problem. The specifics of structural modeling and the assembly process using mathematical methods were assessed. The technique of creating graphs reflecting the relationship between details and the assembly process is considered. Solving the tasks of the automated assembly process is performed using algorithms and computer software based on graphs constructed in matrix form. The achieved results make it possible to adjust the sequence of products assembly in real-time mode, based on which it becomes possible to monitor parameters and control decision-making when planning assembly processes.

The subject of this study is the quality indicators (geometric accuracy, roughness, cylindricity and taperness) of holes obtained by drilling in aircraft structures (AS) made of polymeric composite materials (PCM). The quality indicators of holes in AS made from PCM were studied by using kinematic schemes across and along the direction of drilling. A kinematic scheme of formation of the predicted surface roughness of the hole in AS made from PCM has been built. The calculation of the predicted roughness of PCM holes taking into account the geometry of the drill and drilling modes has been proposed. Experimental studies have been implemented to establish the parameters of predicted roughness, geometric accuracy, taperness, as well as deviations from cylindricity. The methods used were the method of expert assessments and experimental studies of quality indicators of PCM openings. The following results were obtained: the roughness in full-scale experiments turned out to be lower than the theoretical calculated values with a difference of not more than 10...15 %. It was found that roughness, taperness, deviations from geometric precision and cylindricity differ in characteristic rotation zones of the drill from 0° to 360° and depend on the drilling parameters and PCM properties. It was found that the deviation from the hole cylindricity is affected by the shrinkage of the material. The appearance of ovality in the holes of prototypes was established. The results of experimental studies of measurements of hole diameters to establish deviations from cylindricity, geometric accuracy, and taperness met the production requirements for the accuracy of their manufacture. For geometric precision and deviation from cylindricity, the results ranged from 7 to 12 IT grades, and for taperness, from 0.083 to 0.28 % per a hole in AS made from PCM and 9–10 IT grades