Abstract. The article considers the wireframe-kinematic method of hydrodynamic simulation of surfaces presented by the example of marine craft's bottom structure. The motion trajectory for the variable shape generator is normally set by a single or a number of directing lines. The law of shape variations of the generator is represented by the graphical or analytical display, or by a set of directing lines. All of these make up the so-called determinant of the surface, which includes the geometry component, or a certain initial position of the generator, and the algorithm component, i.e. the algorithm of the wireframe sealing. The directing line may be simple, described by a single equation, or compsite piecewise-smooth. In this situation, they are commonly modelled using splines, which results in piecewise-smooth surfaces.
For the design of surfaces in architecture, as a rule, universal techniques developed for other technical industries are used. First of all, these are general kinematic surfaces and interpolation cubic splines for modeling complex piecewise smooth surfaces. The authors propose to use the fourth degree inerodifferential spline developed by them for problems of geometric modeling of architectural forms. For calculations and constructions on a computer, the proposed spline is not much more complicated than traditional cubic splines, since it has one additional parameter - a coefficient. However, this allows you to locally control the shape of a curve or surface during design, that is, to change the shape in individual areas without affecting other areas. The article proposes a method for constructing a geometric model of the kinematic surface of dependent sections with a fourth degree parabola as a generator. When using cubic splines as a guide, the surface is a 3 × 4 non-uniform (heterogeneous) spline. The article shows that the surface on the basis of the proposed mathematical apparatus can be composite piecewise-smooth. A particular case of surface design is considered on the example of creating a model of the surface of the facade of a residential building according to the existing concept. The algorithm can be easily programmed and added as a tool to existing CAD systems.
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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