The work aims to determine the friction effect and change the velocity and kinetic energy during the movement of solid particles along the rotating machine's radial blade surface. It has been previously shown that the influence of the frictional forces of the particle against the rotor disc is negligible compared to the influence of the centrifugal force and the friction force of the particle against the rotor blade. Based on the analysis of the differential equation solution for particle motion along the surface of the blades, it was established that the total sliding velocity of a particle increase intensively in the initial period of motion and approaches asymptotically to the values described by a linear function, practically independent of the initial position of the particle. The obtained analytical expressions enable the determination of change in the relative and total velocity of the particle, the angle between the respective velocity vectors and its kinetic energy. Changes in the values of these parameters were also estimated for a wide range of variability of the friction coefficient.
The introduction substantiates the relevance of research. The purpose of the work is to create and approbate a methodology for calculating the speed mode for movement of coarse solid particles along the radial blades of turbomachines. In the methodological part an analysis of the forces acting on a solid particle when sliding along the radial blades of turbomachines is carried out. A differential equation for motion of solid particles has been compiled and options for its solution have been considered. Analytical dependencies have been obtained that make it possible to determine the values of the relative and total velocities, as well as the angle between the corresponding vectors for the velocities of the particle as a function of time when it moves along the radius of the blade. A calculated estimate of the change in these parameters for a wide range variation of the friction coefficient of a particle on the rotor blade is carried out. It is shown that the total sliding velocity of the particle as well as its radial and transport components intensively increasing in the initial time range, asymptotically approach the linear functions of the particle coordinate, practically independent of its initial position, but linearly dependent on the angular velocity of the rotor rotation and nonlinearly – on the coefficient of friction of the particle on the blade. In this case, the exit angle of the particle does not depend on the radius and rotor angular velocity, but depends on the friction coefficient of the particle against the rotor blade. With an increase in the friction coefficient the relative and total velocities of particle motion decrease which leads to a decrease in the kinetic energy accumulated by the particles. Conclusions are drawn from the results of the study. It is noted that the results obtained can be used by design engineers when designing turbomachines with radial blades, as well as in the educational process when training mechanical engineers and process engineers.
Shot blasting consists in hardening of the parts surface layer or workpieces with a stream of solid particles, mainly in the form of hardened steel balls. The purpose of the work is to develop and test a method for calculating the parameters of an elastic-plastic dynamic contact during shot blasting of parts based on mathematical modeling. The research technique is based on the consideration of a three-stage model of workpiece deformation under elastic-plastic impact by a steel spherical indenter. At the initial stage, the deformation is carried out elastically. Then, under some dynamic load, in the near-surface layer of the impacted body, a region of plastic state is generated, surrounded by an elastically deformable material. With a further increase in the dynamic load above a certain characteristic value, the region of the plastic state comes to the surface of the impacted part. Subsequently, the process is characterized by elastic-plastic indentation of the indenter (shot) into the impacted part. A method for upper calculating estimate the parameters of the dynamic contact of steel shot with parts based on the energy theory of elastic-plastic impact has been developed. To separate the elastic and plastic components of the deformation energy, the velocity recovery factor upon impact was used. The deformable material is accepted at the final stage of deformation as an ideal elastic – plastic material obeying the Prandtl’s scheme. Analytical dependencies convenient for practical use are obtained, which allow one to make calculating estimate of the depth and diameter of the imprint. Estimated calculations of the depth of the indentation depending on the speed of exposure to steel shot for shot blasting of a number of structural carbon steels have been performed. The results of the research can be used in the educational process in the preparation of engineering personnel of the machine-building profile, as well as in engineering practice.
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