Construction and testing of an empirical model for calculating the tumbled range of dry prickly ash particles on the separation belt

•The tumbled trajectories of particles were extracted using the Kalman filter.•The correlation between the tumbled range and the working parameters was analyzed.•A theoretical method for optimizing belt separation was proposed. In this paper, an empirical model is proposed for calculating the tumbled range of dry prickly ash particles on the separation belt to provide a method for obtaining the individual tumbled ranges of pericarp, closed exocarp, and seed particles to achieve the dry prickly ash transverse inclined belt separation mechanism. First, a single-factor test was conducted of the belt separation mechanism, and the movement trajectories of the pericarp, closed exocarp, and seed particles on the separation belt surface were extracted based on Kalman filtering and a high-speed camera system. Then, the trajectories of dry prickly ash particles during tumbling were simplified through regression analysis, from which an empirical model for calculating the tumbled range was derived. Furthermore, the ranges of X-axis acceleration and Y-axis velocity were determined for the empirical model by combining kinetic analysis and a normal distribution test. Finally, the proposed empirical model was used to derive the individual pericarp particle tumbled range at the optimal inclination and belt velocity of the separation mechanism, and the lateral end of the separation belt was divided into the collecting area, reseparating area, and wasting area. After validation, it was shown that the average mass proportion of pericarp particles in the collecting area was 97.3%, which agrees with the empirical model calculations. The empirical model is instructive for the separation process of dry prickly ash and can be applied to the study of spherical particle tumbling on a motional inclined surface.