Mathematical description of the probability of capturing rod-shaped stepped blanks in hopper feeding devices with an inclined disk and tangential pockets

In this work, we present a mathematical model of the capture probability of rod-shaped stepped blanks in mechanical disk hopper feeding devices with an inclined disk and tangential pockets. The model must take into account the influence of the design and kinematic parameters of the device on its performance, as well as those of the workpieces. The object of the research was a mechanical disk hopper feeding device having an inclined rotating disk and pockets tangentially located along its periphery, whose active orientation of the mentioned blanks is implemented by overturning them on special supports placed under the rotating disk. The tipping action is carried out under the action of gravity. For the construction of mathematical models, methods based on probability theory, analytical spatial geometry, theoretical mechanics, and general physical laws were used. The methodology for constructing a mathematical model of the probability of capture of rod-shaped step blanks of bodies of revolution in the studied devices with an inclined disk and tangential pockets is described. Algorithms for determining each coefficient of the developed model are presented. The developed model is a product of the probability of finding the rod blanks in a position favorable for their gripping in the direction of the tangentially located pocket, the probable absence of encumbrance during gripping of the blank due to its interlocking with other blanks, and the probable absence of encumbrance as a result of the peripheral speed of the gripping organs of the device. Thus, the developed mathematical models for calculating the capture probability of rod-shaped step blanks of rotational parts can be used at early design stages to estimate with high accuracy the actual productivity of mechanical disk hopper feeding devices with an inclined rotating disk and pockets tangentially located along their periphery.

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