# Mathematical Modeling of Screw Press Configuration for Processing Safflower Oil
## 1 Introduction  
The oil and fat industry takes one of the leading positions in the food complex of Kazakhstan, which is associated with both the diversity and uniqueness of oil and fat raw materials and the important role of oils in human nutrition. Today, the oil and fat industry complex of the Republic of Kazakhstan is an integrated system of technologically and economically interconnected industries of the agro-industrial complex [1, 2].  
The technology of producing vegetable oils consists of various processes of oil raw material treatment. Mechanical processes are a significant part of this technology. Processes such as the cleaning of seeds from impurities, the destruction and separation of fruit and seed shells from the embryo and endosperm-kernel, and the grinding of the kernel and intermediate products of its processing are mainly mechanical processes, preparing the material for intensive physical and chemical transformations [3, 4].  
Recently, there is an increased interest in the use of new types of cultivated plants, which differ from traditional ones in the complex of features and useful properties. Safflower has an important role among the perspective of plant food resources, which in the future can compete with the traditionally known oil-bearing crops [5, 6].  
Safflower is a crop with a long history: for many centuries, this plant has been used to produce both dye from its petals and oil from its seeds. Safflower oil is a unique product of plant origin, the chemical composition of which allows it to be used for medical and cosmetic purposes, and for the production of food products. Taking into account itsbiological values and rich composition of vitamins and phospholipids, the production of safflower oil is currently an urgent task [7; 8; 9].  
One of the main methods in the production of vegetable oil is the pressing method. Most modern presses are constructed for pressing specific oils from individual crops. Therefore, it is very difficult to readjust this equipment for another crop, because the oil would then be pressed less efficiently. This is unacceptable for small-capacity facilities. A universal press for pressing oil from both low- and high-oil-bearing crops is needed [10; 11]. The screw press is the most universal and low-cost process. However, screw presses are low-productivity machines compared to solvent extractors and consume more power and energy per ton of oil extracted than solvent extractors. The oil obtained by screw pressing is used either as a food product or as an industrial product [12; 13; 14]. Screw units are used in the oil industry and are one of the most efficient working elements of press machines. Screw units are used as versatile work tools for the simultaneous and continuous operation of multiple processes [15; 16].  
Modern methods of analysis of oil pressing processes are based on complex mathematical descriptions expressed by differential equations. This causes complexity in solving and obtaining information about the technical parameters of the described processes. Mathematical modeling can be an effective way to calculate the technological parameters of pressing [17; 18].  
The development of modern high-efficiency pressing equipment for pressing vegetable oils requires the use of more advanced calculation methods, as well as mathematical modeling of the influence of various design parameters, considering the change in the properties of the pressed material. The purpose of this work is to mathematically calculate the pressing process depending on the configuration of the screw and the pressing cage.