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The problem of linear dynamic thermoelasticity in Kirchhoff–Love-type circular cylindrical shells having properties periodically varying in circumferential direction (uniperiodic shells) is considered. In order to describe thermoelastic behaviour of such shells, two mathematical averaged models are proposed—the non-asymptotic tolerance and the consistent asymptotic models. Considerations are based on the known Kirchhoff–Love theory of elasticity combined with Duhamel-Neumann thermoelastic constitutive relations and on Fourier’s theory of heat conduction. The non-asymptotic tolerance model equations depending on a cell size are derived applying the tolerance averaging technique and a certain extension of the known stationary action principle. The consistent asymptotic model equations being independent on a microstructure size are obtained by means of the consistent asymptotic approach. Governing equations of both the models have constant coefficients, contrary to starting shell equations with periodic, non-continuous and oscillating coefficients. As examples, two special length-scale problems will be analysed in the framework of the proposed models. The first of them deals with investigation of the effect of a cell size on the shape of initial distributions of temperature micro-fluctuations. The second one deals with study of the effect of a microstructure size on the distribution of total temperature field approximated by sum of an averaged temperature and temperature fluctuations.

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Observing the latest manufacturing processes, the following tendencies can be noted: the gain of the energetic efficiency and shortening of the processing time with parallel preservation of the dimensions tolerance, shape tolerance and outer layer quality of the processed workpiece. Also the possibilities of gaining efficiency by rising criteria for process parameters are limited. It is mainly observed in the processing of hard machinable materials like titanium alloys or sintered carbides. Problems related to poor machinability were revealed during the final manufacturing processes using abrasive grinding [1,2]. In this work the results which have been presented are related to the influence by selected electrical parameters of the Abrasive Electrodischarge Grinding (AEDG) on the surface layer temperature of machined samples, in comparison to conventional grinding. Also the change in temperature during the AEDG has been depicted. The basis of this work is similar to the investigations of the deep grinding of surfaces of the titanium alloy Ti6Al4V using CBN and a diamond grinding wheel. For the comparative evaluation of the conventional grinding and AEDG, measurements of the specific grinding energy, energy of the spark discharge and internal stresses in the surface layer have been used.

In this work the results related to the influence of selected electrical parameters of the abrasive electrodischarge grinding process on the surface layer temperature and morphology of machined samples in comparison to the conventional grinding method are presented. The basis of this work has been investigations of the deep grinding of surfaces of the samples made of titanium 5553 β, Inconel 617, Hastelloy X and magnesium AZ31 using a cubic boron nitride (CBN) grinding wheel with metallic binding agent. For the comparative evaluation of the conventional grinding and abrasive electrodischarge grinding, measurements of the specific grinding energy, temperature on the surface layer (at the contact of the grinding wheel‐workpiece) and geometric structure of the surface layer have been used.