Geodesy

Ellipsoid method

Engineering

Convex combination

Ellipsoid

Geotechnical engineering

Agricultural engineering

Computer science

Sphericity

Geology

Physics

Mathematics

Astronomy

Angle of repose

Process engineering

Environmental science

Geometry

Convex optimization

Regular polygon

Powder Technology

To build a general modelling method for wheat seed particles, based on the analysis of wheat seeds from different regions in mainland China, twelve representative varieties of wheat seeds were selected as the research objects. Through an analysis of the size and shape of wheat seeds, it can be seen that the seed thickness has a certain functional relationship with the seed length and width for each variety of wheat seeds, and the shape of wheat seeds can be approximated as a double ellipsoid or a single ellipsoid. The radial difference, mass error and moment of inertia error between these two shapes and the actual wheat seeds were analyzed, and the results showed that the shape accuracy of the double ellipsoid is higher than that of the single ellipsoid. The 13-, 17-, 25- and 33-sphere models based on the double ellipsoid and the 5-, 9-, 13-, 17- and 21-sphere models based on the single ellipsoid were built using the multi-sphere method. Meanwhile, the ellipsoid models were built using the ellipsoid equation for a comparison with the other models. Based on the above work, the particle models of wheat seeds proposed in this paper were verified by comparing the experimental data and the simulation results in terms of the static angle of repose test, "self-flow screening" test and dynamic angle of repose test. These results showed that the 33-sphere model based on a double ellipsoid is suitable for modelling of the wheat seeds with a length-thickness ratio smaller than 2.05. The 17- and 25-sphere models based on a double ellipsoid are suitable for modelling wheat seeds with a length-thickness ratio larger than 2.05. In addition, the 5-sphere model based on a single ellipsoid is also suitable for modelling wheat seeds with a length-thickness ratio greater than or equal to 2.38. The results indicated that the shape of the double ellipsoid is more accurate and applicable than that of the single ellipsoid and can be used as a general particle size model to represent wheat seeds. Moreover, the multi-sphere model is superior to the ellipsoid model built by an ellipsoid equation.

A DEM-based general modelling method and experimental verification for wheat seeds