# Mathematical Modeling of Screw Press Configuration for Processing Safflower Oil
## 3 Results and Discussion
### Determination of Safflower Cake Density  
In the next stage, we determined the density of the cake depending on the change in the gap and screw speed. It should be noted that with an increase in the number of screw revolutions, there is a slight increase in the density of the cake. Therefore, if, at a revolution of 5.2 rad/s and a gap of 1 mm, the cake density was 1097 kg/m\({}^{3}\), increasing to 7.3 rad/s leads to an increase in density to 1120 kg/m\({}^{3}\) (Figure 11). The same tendency is observed with increasing the rotation of the screw. Increasing the speed of the screw leads to an increase in the press throughput. However, the residual oil content in the cake will be higher because less time is spent on squeezing oil from the safflower seeds [29; 30]. Figure 9: Graph of determining the capacity of a screw press for oil (**a**) and cake (**b**) depending on the press channel and pressing cage. At a constant rotation of the screw, but changing the diaphragm gap from 1 mm to 7 mm, the density of the cake increases significantly. However, it should be noted that at a gap of 3 mm, the density of the cake decreases in comparison with a gap of 1 mm. Therefore, if we consider the option at which the screw rotation is constant (6.2 rad/s), then, at a gap of 1 mm, the cake density was 1105 kg/m\({}^{3}\), and, at 3 mm, it decreased to 1057 kg/m\({}^{3}\). However, at gaps of 5 mm and 7 mm, the density increased to 1162 kg/m\({}^{3}\) and 1218 kg/m\({}^{3}\), respectively. When the gap is reduced (the size of the nozzle), the pressure in the press chamber increases, which leads to an increase in oil yield. The increase in pressure is because more force is required to overcome the smaller gap [31; 32]. Figure 10: Design of the traditional press screw (**a**) \(\delta\)—output slit; \(p\)—the longitudinal pressure generated by the output slit; 1—regulating mechanism; 2—pressing screw; 3—pressing cage and the experimental screw (**b**) \(P\)—lateral pressure resulting from the narrowing of the gap; \(\theta\)—back-and-forth movement of the screw; \(\delta_{H}\), \(\delta_{K}\)—initial and final gap between the screw and the pressing cage; 1—pressing cage; 2—pressing screw. Change of Rheological Properties Depending on Oil Content and Temperature of Safflower Cake  
The rheological characteristics of the raw material, which depend on such factors as the fat content of the initial product and the temperature of pressing, are a determining parameter in the pressing process [33; 34]. An analysis of the dependence of the rheological characteristics on the temperature and oil content of the safflower cake will allow us to consider the behavior of oil-bearing raw materials inside the screw press, and the impact of the temperature gradient on oil yield. The rheological properties of the oilcake were studied within the temperature range of 20 to 80 \({}^{\circ}\)C. The temperature of 80 \({}^{\circ}\)C was taken as the upper investigated limit, which approximately corresponds to the beginning of the denaturation of proteins and the oil raw material from the viscoplastic state to the elastic state. The effect of the beginning of protein denaturation is expressed in the breaking of the solidity of the oil-bearing raw material [35; 36]. In the process of pressing, the yield stress was measured depending on the cake's temperature and oil content. It was found that the yield stress index decreases as the temperature of the raw material increases. Thus, if, at 20 \({}^{\circ}\)C, the yield stress of the cake was 18,200 Pa, when increasing the temperature to 80 \({}^{\circ}\)C, the yield stress decreased to 18,100 Pa, with a fat content of 30%. It should be noted that the lower the oil content of the product, the higher the yield stress. At 15% oil content, the yield stress was 18,430 Pa, while at 30% oil content, the yield stress decreased to 18,200 Pa (Figure 12). The same trend is observed for plastic viscosity. The lower the raw material's temperature and oil content, the higher the plastic viscosity.