Development of an analytical model for predicting the trajectory and energy dissipation of bee bread granules in a rotary impact separator

The object of this research is the impact interaction between a bee bread granule and a hammer-type working element in a rotary separator. The practical relevance of the research arises from the need to ensure reliable release of granules while preventing their mechanical damage, since even partial destruction leads to deterioration of product quality and a decrease in its commercial value. Such an approach does not allow reliable prediction of energy transfer during impact or the subsequent trajectory of the granule. As a consequence, rotor speed and hammer mass are often selected without sufficient theoretical justification, which limits the efficiency and controllability of the separation process. To overcome these limitations, an analytical model describing granule impact and its post-impact motion in a rotating reference frame was developed. The mathematical formulation accounts for the combined action of centrifugal, Coriolis, gravitational, and friction forces, which made it possible to derive parametric relationships for velocity and displacement as functions of time. It was established that the post-impact motion follows a damped pattern, with the displacement amplitude decreasing by more than 60% within the first 0.02 s and exceeding an 80% reduction after 0.05 s. It was also found that energy transfer efficiency strongly depends on hammer mass. At a mass of 5 g, the efficiency reaches approximately 0.7–0.8%, whereas at 100 g it decreases to about 0.1%, and at 200 g it falls below 0.05%. These trends are explained by increasing dissipative losses within the rotating system. The proposed model enables prediction of granule trajectory, velocity, and energy dissipation under different operating conditions. Its practical value lies in providing a scientifically grounded basis for selecting hammer mass and rotor speed to achieve efficient and gentle separation of bee bread granules.