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Abstract.The article gives an analysis of the influence of technological factors on the parameters of the surface roughness during the machining of workpieces with the abrasive tools, based on the use of the modern mathematical apparatus of the theory of probability. It is shown that when processing with abrasive tools, the formation of surface microrelief is directly related to the mechanism of material removal in the area of contact between the workpiece and the tool. The main parameters of the contact zone are its dimensions and parameters of the material removal processes, which are characterized by the probabilities of removal or non-removal of the material. The obtained dependences take into account the parameters of the state of the working surface of the tool and can be used to calculate the basic parameters of the surface roughness in round external grinding. The made estimation of the influence of technological factors on the roughness of the surface of the workpiece being processed allows for the selection of the most significant ones, the changes of which must be taken into account when designing grinding operations.Microroughness of the surfaces of the parts have a significant effect on their performance properties. In this regard, the provision of roughness parameters is provided for the treatment of all surfaces. Criteria for roughness are very diverse. The most frequently used are the arithmetic mean deviation of the Ra profile, the largest height of the roughness of the Rmax profile, the height of the unevenness of the profile at ten Rz points, and the parameters of the reference surface curve.When developing a machining operation, the problem arises of predicting the parameters of roughness, which provides a more reasonable choice of tools, cutting modes and other conditions for its implementation. This task is especially important in the design of operations with abrasive tools, which often result in technological processes [1,2,3]. The complexity of the problem lies in the fact that the process of interaction between the abrasive tool and the workpiece is stochastic and requires special approaches in the study. Nevertheless, at the present time the system principles of analysis based on the theory-probabilistic approach, system principles of analysis and possessing sufficiently high adequacy of the model, allowing to take into account at designing a large number of technological factors are developed [3,4,5,6]. They are the basis for creating techniques, algorithms and programs and can be included in modern CAD systems.The purpose of the article is to substantiate the method and sequence of solving the problem of predicting surface roughness parameters when machining parts with abrasive tools based on the use of modern mathematical models.

The article shows that during the grinding of complex profile blades of metal cutting tools from tool steels, unfavorable thermodynamic conditions are created in the cutting zone and, as a result, grinding burns and cracks occur on the surface of the polished workpiece. One of the methods of controlling the temperature in the cutting zone at the final grinding operations is the use of grinding wheels with a discontinuous surface. The method of calculating the profile of the discontinuous surface of the grinding wheel presented in the article makes it possible to determine its geometric parameters taking into account the wear resistance of the grinding wheel and the heat stress of the process of treatment. The results of the verification of the proposed technique in the production conditions are given which showed that the treatment of the teeth of the broaches with a grinding wheel with a discontinuous profile, in comparison with the machining of broaches according to the traditional technology, provides a higher quality of blade surfaces, while the process productivity, compared with the factory technology, increased by 20...26%.

The article analyzes the influence of the structural crack-like defect in the girth weld root welding the bottom to the collector body on the crack growth resistance. A mathematical model has been developed to estimate the residual life resource of welded joints with an internal crack-like defect in the root of the weld under creep. Results of metallographic studies of bench tests results for the welded joints long-term strength formed the basis of the calculation model. In all tested models the cracks start at the top of the narrow structural gap in the weld root and develop along almost the entire weld axis, perpendicular to the wall of the pipe and have a discrete growth pattern. As a result, discrete rupture of material occurs on a length of rc, and the initial crack is incremented by this length. After that, a “plastic core” of rc length is formed in the newly formed crack tip, additional damage is accumulated, and the crack development process continues until the stress level in the section weakened by the crack reaches a critical value. The obtained dependence characterizes the crack growth time from the initial crack-like defect to its critical length.

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