The prospects and novelty of using the expression of Lame's superellipse for approximating the curvature of shells in superplastic forming (SPF) and for predicting the geometry of a product are shown. Different versions of the SPF facilitate the realization of different radii of curvature of the shell contours, which differ significantly from the radius of the spherical segment. The regularities of the change in the radius of conjugation of the bottom and the wall of the spherical shell for various SPF variants are established.

The criteria for the assessment of the form change in the process of direct profiling of workpieces , applying the stretching method with a rupture are developed, methods for their calculation are proposed with allowance for the volume of the redistributed metal and energy costs for deformation. The nature of the functional connection of these criteria of shape change assessment with the work of deformation is determined.

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Radial gas bearings with one line for supplying compressed gas to the working gap with blind microgrooves of constant width and variable depth of the different profiles are considered. Such as with constant depth microgrooves; triangular or stepwise with decreasing depth of grooves along the course of compressed gas. For them, the radial lifting force, the recovery moment for angular displacements of shaft in the range of constancy of radial and angular stiffness and consumption of compressed gas for the bearing’s work are found. Calculations and studies have shown that a radial bearing with longitudinal microgrooves whose depth decreases linearly in the direction of gas flow has a large radial lifting force and a recovery moment for angular displacements of shaft compared to a bearing with microgrooves of constant depth. Bearings with stepped longitudinal microgrooves with greater depth at the entrance to working gap are operable in the range of practical use of bearings and have greater dimensionless radial and angular stiffness and are more economical compared to bearings with microgrooves of constant depth. In practical activities (when designing spindle units), it is not recommended to use gas bearings with a variable depth of microgrooves having a minimum depth at the entrance to working gap. With optimal design parameters, the flow rate of compressed gas for bearings with longitudinal microgrooves of different transverse profiles with alignment of shaft and sleeve is almost the same (the difference is about 7, 8%).

The use of internal combustion engines increase environmental pollution and dependence on fossil fuels. The biodiesel fuel, which is renewable, more environment friendly, and cheaper, is a good alternative for diesel engines. The use of biodiesel fuel leads to a drop in diesel power and an increase in fuel consumption. To prevent these shortcomings, it is proposed to use dynamic regulation of the percentage composition of a mixture of diesel and biodiesel fuel. The modernization of diesel engines for their transfer to work on a mixture of fuels with a dynamic regulation of its percentage composition is possible at service stations serving diesel engines.