# Mathematical Modeling of Screw Press Configuration for Processing Safflower Oil
## 3 Results and Discussion
### Mathematical Modeling of the Separation and Output Dependence during the Pressing Process
 \tag{8}\]  
where \(F\) is the cross-sectional area of the selected layer, \(\text{m}^{2}\); \(S_{H}\) is the perimeter of the layer along the inner cavity of the pressing cage, m; \(dz\) is the length of the elementary layer, m; and \(d\) is the screw shaft diameter, m.  
In this equation, the first term characterizes the forced flow generated by the moving walls, and the second term characterizes the velocity distribution in the flow (Figure 7). If we introduce the coefficients of the geometry of the pressing screw of forced flow \(K_{\text{BII}}\) and reverse flow \(K_{\text{OII}}\), then we determine the capacity of the pressing screw as follows (Equation (9)):  
\[Q_{\Pi}=K_{B\Pi}n-\frac{K_{\text{OII}}}{\eta_{\ast\phi}}\Delta p, \tag{9}\]  
where \(Q_{\Pi\Pi\Pi}\) is the capacity of the pressing screw, kg/h; \(K_{B\Pi}\) is the forced flow coefficient; \(K_{\text{OII}}\) is the reverse flow coefficient; \(\Pi\) is the screw rotation speed, rpm; \(\eta_{\ast\phi}\) is the effective viscosity, Pa\(\cdot\)s; and \(\Delta\rho\) is the pressure drop in the matrix forming device, Pa. Figure 8 shows the volumetric flow rate of total oil passing through the holes of the pressing cage at the smooth movement of the screw, \(\text{m}^{3}/\text{s}\). This equation (Equation (10)) describes the geometric shape of the holes of the pressing cage. \[Q=K\frac{\Delta p_{\text{max}}}{\eta_{M}}, \tag{10}\]  
where \(Q_{3\Pi}\) is the volumetric flow rate, \(\text{m}^{3}/\text{s}\); and \(K\) is the geometric coefficient of the pressing cage. Figure 7: Drawing of the total speed diagram over the height of the screw channel (**a**) and the performance of the press screw for two values of speeds (**b**). \(v_{B\Pi}\)—direct flow rate; \(v_{O\Pi}\)—back flow rate; \(v_{z}\)—sum of speeds. The pressure difference on the longitudinal axis of the screw for oil separation during pressing is determined by the expression (Equation (11)):  
\[\Delta p_{\rm max}=q_{\rho}\frac{Q_{\rm TI}}{K_{3}}\eta_{\rm\phi}, \tag{11}\]  
where \(\Delta p_{\rm max}\) is the pressure difference, Pa; and \(q_{p}\) is a qualitative indicator of the extraction of a certain amount of oil. For the determination of the material flow rate of oil production, this equation describes the narrowing of the screw channels as a result of the geometric shape of the holes of the pressing cage and the mechanism of the pressure regulator (Equation (12)). \[Q_{M}=\frac{K_{\rm IIK}K}{K_{\rm IIK}+K}n, \tag{12}\]  
where \(Q_{M}\) is the oil capacity, kg/h; \(K_{\rm IIK}\) is the pressing channel coefficient; \(K\) is the pressing cage cylinder coefficient; and \(n\) is the screw rotation speed, rpm. From here, we determine the material flow rate of the productivity of the cake (Equation (13)):  
\[Q=\frac{K_{\rm BII}K_{\rm IIK}}{K_{\rm OII}+K_{\rm IIK}}n, \tag{13}\]  
where \(Q\) is the cake yield, kg/h; \(K_{\rm IIK}\) is the pressing channel coefficient; \(K\) is the pressing cage cylinder coefficient; and \(n\) is the screw rotation speed, rpm. Using the obtained equations and nomograms, according to the figure below, we draw a nomogram determining the productivity of the cake and separated oil, depending on the geometric features of the oil press equipment (Figure 9). Study on the Dependence of the Oil Content of Safflower on Various Parameters in the Pressing Process  
The main purpose of the work is to determine the optimal ways of safflower oil production to improve the oil press. Pressing the product by screw alone cannot provide the optimal pressure required for the process. Therefore, the press is additionally equipped with a regulating mechanism that creates pressure in the pressing chamber. Figure 8: Dependence of pressing cage coefficient on capacity and pressure. Figure 10a shows a schematic diagram of the pressure control mechanism for a traditional press. When this mechanism is adjusted, additional pressure is created in the press chamber by narrowing the size of the outlet slot.