# Parametric Optimization of a New Gear Pump Casing Based on Weight Using a Finite Element Method
## 1 Introduction  
This article is a study of the design of a five-gear pump and includes the modeling of its strength in ABAQUS 2020, the subsequent development of recommendations for the optimization of the geometric dimensions, the casing, and the front and rear covers, and the choice of material to reduce the weight of the entire pump structure. Gear pumps are widely used in many industries due to their reliability, simplicity of design, compactness, and efficiency [1, 2]. Gear pumps are positive displacement type pumps. Gear pumps are generally used to pump liquids with high viscosity: fuel oils, oils, lubricating oils, paints, acids and alkalis, alcohols, and solvents [3, 4, 5]. In a gear pump, the rotation of the pump is transmitted by the drive gear [6]. The drive gear rotates through contact with the drive gear. The liquid is transported from the suction side to the discharge side of the pump (from the input port to the outlet port) [7]. A gear pump moves fluid by repeatedly enclosing a fixed volume within interlocking gears, mechanically transferring it to provide a smooth, impulse-free flow proportional to the speed of rotation of its gears [8]. In this case, a tight contact is formed between the teeth, as a result of which the reverse transfer of liquid from the discharge cavity to the suction cavity is impossible [9]. There are several types of external gear pump designs. These designs differ due to the presence of two, three, or four driven gears located on one axis (Figure 1) and the presence of three or four driven gears located around the drive gear (Figure 2). External gear pumps with three gears are advantageous for use in hydraulic drives in which it is necessary to have two hydraulic lines with independent pressure [14]. The design of an external gear pump with four gears on one axis increases the pump energy intensity [15]. Depending on the location of the gears, the shape of the casing is selected when designing a gear pump and the material from which it will be made. To facilitate the design of the gear pumps, the casings are usually made of aluminum [18]. Gray cast iron is also used for gear casings [19]. Reducing the weight of a gear pump greatly affects the geometry of the structure [20]. However, if the hull geometry is reduced too much, it will reduce the structural strength below the limiting value. Therefore, it is necessary to determine the optimal geometry of the gear pump casing with small dimensions and the appropriate strength criteria. In view of this, gear pump casings often have irrational designs in terms of material consumption [21]. When obtaining the geometric dimensions of the gear pump casing, the designers try to obtain a less labor-intensive method to manufacture the structure, even one which is universal with respect to the operating modes of the pumps [22]. Also important in the design of gear pumps is the identification of dangerous sections of the structure in areas of stress concentration [23]. The key design stage in the determination of the optimal dimensions of the casing is the calculation of static strength [24]. This calculation is limited to the use of empirical dependencies and is labor-intensive [25]. The complexity of the calculations is explained by the large volume of analytical loads that act on the body. Furthermore, the difficulty of the calculations is due to the fact that the analytical methods for determining the stress-strain state of a structure are limited to simple load diagrams and primitive geometry [26]. Figure 1: Designs of external gear pumps with different numbers of driven gears on the same axis [10; 11; 12; 13]. Figure 2: Designs of external gear pumps with driven gears around the drive axis [16; 17]. For newly created structures, it is difficult to immediately select the optimal dimensions; therefore, after obtaining a calculation model and identifying its shortcomings or potential capabilities, the designers resort to optimization.