Theoretical study of the motion of material particles in centrifugal devices with curved blades and variable angle of their rise

<ns0:p>In centrifugal scattering devices, the blades provide the necessary trajectory and speed of the particle in relative motion. The operation of scattering devices with straight blades has been sufficiently studied. From a theoretical point of view, it seems interesting to study the motion of a particle along a curved blade, when the angle of elevation of the particle increases from zero to a given value at the moment of its descent from the blade.The purpose of the study is to perform a comparative analysis of the motion of a particle along straight and curved blades, which provide a given angle of elevation of the particle at the moment of its descent from the blade.When a disk with a curved blade rotates, the particle performs a complex motion: translational due to the rotation of the disk and relative along the blade. To compile the differential equations of motion, it is necessary to find the absolute acceleration vector, which includes three components: acceleration in translational motion, acceleration in relative motion, and Coriolis acceleration. This vector is conveniently searched for in the projections onto the orthogonal surfaces of the accompanying trihedron of the translational motion curve, which for the rotational motion of the disk will be a circle.Generalized differential equations of particle motion in centrifugal devices along a curved blade with a variable lift angle have been derived. A comparative analysis of the kinematic parameters of motion for straight and curved blades has been performed.A comparative analysis of particle motion along straight and curved blades of a centrifugal scattering device has shown that a particle along a curved blade in the form of an arc of a circle of the specified length accelerates faster than along a straight one. Thus, replacing straight blades with curved ones allows achieving the same effect while reducing the angular velocity of disk rotation from 25 rad/s to 23 rad/s, i.e., the reduction is 8%.With an unlimited length of the blade in the form of an arc of a circle, the particle performs an oscillatory motion along it up and down with damping until it comes to a complete stop in the presence of friction.</ns0:p>