###### Abstract
The test outcomes illustrated that the best thresher operation occurred at a feed rate of 180 kg/h, a cylinder rotational speed of 500 rpm and a crop moisture content of 9-13%. The authors in [12] examined some engineering parameters (concave hole size, concave clearance and roller speed) to evaluate a rasp-bar thresher used in the sunflower threshing process. The authors of [13] designed and tested the performance of a pedal-operated sunflower thresher according to its threshing efficiency, cleaning efficiency, damaged seed quantity, machine productivity and the consumed specific energy under three levels of the pressure surface pressing on the friction roller (2.0, 4.0 and 6.0 kg/cm\({}^{2}\)), four levels of the friction roller speed (2.8, 3.7, 4.9 and 6.9 m/s), different radial curves of the pressure surface (330, 345 and 365 mm) and different resting times of the sunflower heads inside the threshing chamber (5, 10, and 15 s). The authors in [14] designed and fabricated a sunflower seed extraction machine to separate the seeds from the sunflower heads in order to overcome the problems faced by farmers during the manual threshing process. Many studies revealed that the broken grain percentage was increased with the increase in the thresher roller rotational speed while it was decreased with the increasing grain moisture content as well as unthreshed grains [15; 16; 17]. For axial flow threshers, about 80% of the crops are threshed in the first half of the threshing area, whereas just 20% of the crops are threshed in the other half [15], which may lead to decreased threshing efficiency and increased threshing power requirements, in addition to blockages and the machine sometimes ceasing to work. The authors of [18] evaluated the screw conveyor performance through its output productivity, volumetric efficiency, seed damage percentage and specific conveying energy. Their results concluded that some operation parameters affect the performance efficiency of conveyors, like the transported materials' properties, the difference between conveying place levels, conveyor size, conveyor screw speed, conveyor length and the distance between the ends of the screw and the inner diameter of the conveyor cylinder. The authors of [19] investigated the effect of the transport distance on the power requirements for screw conveyors at various speeds., while in [20], the authors developed a sunflower threshing device to separate seeds under the influence of centrifugal and gravitational forces. Meanwhile, the authors of [21] tested the air-jet effect on a sunflower seed separating from its head in static conditions. Despite China having an advanced place between other countries in sunflower planting, however, the mechanization of sunflower treatment in China is not at the desired level [22,23]. This research was conducted to design an axial flow sunflower threshing machine attached with a screw conveyor and study the effect of the roller rotational speed and feeding rate to evaluate its performance and select the optimal operation conditions. A mathematical equation was developed to simulate and predict the threshing efficiency of the machine, which helped to save time and other resources by reducing the number of field experiments.