Centrifugal Spreading of Fertiliser : Deducing Three-Dimensional Fertiliser Velocities from Horizontal Outlet Angles Using Computer Vision

The quality of the deposit pattern produced by centrifugal spreaders is known to depend on many parameters, making its prediction using models based on fertiliser properties and disc settings difficult. An alternative approach consists of measuring the initial conditions of the ballistic flight of the fertiliser particles as they leave the disc, thus avoiding the use of on-spinner dynamic models. Measurement methods need to be developed to determine the outlet velocity vector of the particles in three dimensions. Using kinematic analysis of the mechanical system, this paper establishes that the three-dimensional velocity components of the particles are functions of the horizontal outlet angle, the disc configuration and the rotational speed. The theoretical relationship between the vertical and the horizontal outlet angles was also derived from this analysis. A digital imaging system was developed to measure the horizontal outlet angle and thus estimate the velocity components. In order to avoid any bias regarding the angle determination, special attention was paid to image acquisition and measurement corrections. Experiments have been carried out to assess the technique. / Les disques d'épandage utilisés dans la pratique étant de forme "tronconique", les particules qui sont accélérées par ce disque acquièrent une vitesse total qui présente 3 composantes, l'une radiale au disque, l'autre tangentielle, et la dernière verticale. L'article propose une méthode de calcul de ces trois composantes qui repose sur l'acquisition d'une seule photographie numérique prise dans un plan donné, et utilisant les caractéristiques géométriques du disque.