Water hydraulic components and systems play pivotal roles in the development of modern hydraulics. Sustainable development and environmental protection cannot be imagined without the use of water as a working medium in modern hydraulic systems. An axial piston pump is the main component of these systems. This paper presents analytical and experimental methods for the development of an axial piston pump. The presented mathematical model is rooted in numerous research results in the literature and in our own experience. It is based on mathematical modelling of hydrodynamic processes of a water hydraulic axial piston pump which, combined with experimental research, provides a great tool to analyse the influence of different factors on the operating process and to optimise the pump parameters. The experimental equipment used in our tests simulates a real hydraulic installation, and the obtained results are very close to the actual operating parameters. This research included a modification of the swash plate in order to achieve ideal operating parameters and, thus, extend the service life of the pump. Water has a number of advantages over conventional hydraulic oils. It is a sustainable, environmentally friendly resource, more readily available than oil (lower transportation costs), cheaper to dispose of, non-flammable and non-toxic, and its high thermal conductivity aids in cooling.

Symmetry plays a key role in the study of stress and strain analysis of spherical tanks, as described in detail in the main text. The inherent geometric symmetry of a spherical tank–being uniform in all directions from its center–allows for significant simplification of finite element models. This radial symmetry means that the stress and strain fields under uniform internal pressure are also symmetrical, reducing the computational domain to a small, representative portion of the tank rather than the entire structure. By using these symmetry principles, the study not only ensures the accuracy of its predictions but also achieves a high degree of computational efficiency, making complex engineering problems easier and more accessible. The application of symmetry, therefore, is not just a theoretical concept but a practical tool that underlies the methodology and success of this analysis. This study investigates the mechanical behavior of a spherical tank subjected to internal fluid pressure, utilizing the finite element method (FEM) as a primary analytical tool. Spherical tanks are widely used for the storage of various fluids, including liquefied natural gas (LNG), compressed gases, and water. Their design is critical to ensure structural integrity and safety. This research aims to provide a comprehensive stress and strain analysis of a typical spherical tank, focusing on the hoop and meridian stresses, and their distribution across the tank’s geometry. A 3D finite element model of a spherical tank will be developed using commercial FEA software. The model will incorporate realistic material properties (e.g., steel alloy) and boundary conditions that simulate the support structure and internal fluid pressure. The analysis will consider both linear elastic and potentially non-linear material responses to explore the tank’s behavior under various operational and overpressure scenarios. The primary objectives of this study are as follows: (1) determine the maximum principal stresses and strains within the tank wall, (2) analyze the stress concentration at critical points, such as support connections and nozzle penetrations, and (3) validate the FEM results against classical analytical solutions for thin-walled spherical pressure vessels. The findings will provide valuable insights into the structural performance of these tanks, highlighting potential areas of concern and offering a robust numerical approach for design optimization and safety assessment. This research demonstrates the power and utility of FEM in engineering design, offering a more detailed and accurate analysis than traditional analytical methods.

In the development of applicative software for mathematical modelling, identification, and optimization of parameters of axial piston pumps, special attention is paid to the real need of the engineers' practice. We used the original graphical 2D and 3D software for the application in real-time with a simultaneous presentation and processing in 24 windows of high resolution. Here it is mentioned that during optimization and identification of axial piston pump's parameters, we automatically form and present several hundreds of the complex 2D diagrams, which enables to intervene at any point in the study of hydrodynamic processes by the change of input data, where the following flow of identification and optimization is changed.

The article presents a mathematical model for pressure growth in the line supplying the engine KAMAZ with cryogenic fuel under specific insulation conditions. By using the heat balance equation the model in a simple linear form is obtained. This makes the model suitable for use in solving practical tasks related to the design of a liquefied natural gas engine fuel system. According to the above-mentioned method, the geometric parameters of the section of the main elements are determined under different external conditions and the boundary parameters of the gas fuel (maximum and minimum values of pressure, temperature, and flow). These data are necessary to determine the consumption, hydraulic and project features of the project. Fuel pipes are optimized (for hydraulic resistance, pressure and flow impulses, structural strength) to improve the accuracy of fuel dosing. The adequacy of the model was tested on a special modified test stand.

Spherical tanks represent key infrastructure in the petrochemical industry, playing a vital role in the safe and efficient storage of a wide range of products. These products can range from highly volatile hydrocarbons such as liquefied petroleum gas (LPG) and liquefied natural gas (LNG) to various other chemicals essential for industrial processes. The very geometry of a sphere offers inherent advantages for such applications. Its uniform curvature allows for even distribution of internal pressure across the entire surface, making it an inherently strong and stable shape for containing pressurized fluids. This optimal stress distribution leads to the need for a thinner shell compared to other tank geometries for the same volume and pressure, potentially leading to material savings. Loads can arise from the internal pressure of the stored liquid, external factors such as wind and seismic activity, thermal gradients, and even localized loads at support points or connections. However, despite these advantages, spherical tanks are still susceptible to various external and internal loads that can cause stress and deformation.