# Mathematical Modeling of the Manufacturing Sector's Dominant Part as a Base for Automation
## 2 Materials and Methods  
Mathematical modeling represents a core for many empirical studies. The versatility of the mathematical methods and tools is indisputable. A huge application area is posed by the manufacturing field. An irreplaceable role of the mathematical modeling within manufacturing processes is highlighted [18]. Experimentations, investigations, and numeric simulations are stated as reasons for which the mathematical model's elaboration is required. In fact, it signifies the thoughtful comprehension of the main mechanism belonging to such processes. What is more, mathematical models are a basis for the improvement of computational models. Mathematical modeling in the manufacturing sphere can be found in [19]. The electrochemical micro additive manufacturing technology grounded on the fluidic force microscope was constituted there. The particle conversion process manifested the mathematical modeling. The suggestion of the mathematical model concerned the species flux under the action of pulsed pressure in a newly localized liquid feeding procedure. Another empirical study from this domain is the work in [20], where additive manufacturing is also the principal topic. The authors proposed a universal method for setting up the mathematical spatial uncertainty model. Its fundamentals were based on the gauged geometry of additive manufacturing microstructures. The benefit of this lies in the universal utilization--possible use for parts fabricated by different manufacturing methods or different additive manufacturing processes. There was also uncertainty in [21]. The automobile segment was under scrutiny. The paper dealt with mathematical analysis to the modeling of automobile engine remanufacturing with regard to optimization. The uncertainty mentioned referred to market demand and procurement. Furthermore, solving the practical problems on the subject of automobile engine remanufacturing was integrated into the paper. The next example, where the mathematical modeling is implemented in manufacturing, is the work compiled in [22]. This research was targeted at the needs of the manufacturing companies' leaders. A multi-product fabrication-distribution issue signified the key matter. The survey offered a two-stage single-machine manufacture scheme. Naturally, an application of the mathematical modeling was important in proceeding with the chosen experimental idea. Manufacturing in the context of environmental concerns and sustainability is an increasingly intense topic nowadays. It is an area with potential for the implementation of mathematical modeling. The capital objective established in [23] reflected discovering the finest product mix of a manufacturing device to maximize its sustainability. A mixed integer nonlinear programming model was designed. Thus, a mathematical programming technique found its use. A mathematical model appeared in [24], where attention was paid to the oscillations of a boring mandrel with a vibration damper connected to the mandrel with a viscoelastic coupling. This model was constructed through differential equations. The fact was underlined that the drafted mathematical model and algorithms for the numeric answer to the particular differential equations gave the possibility for the selection of the most suitable parameters of the boring mandrel damping element. A strategic part of the manufacturing sector is deputized by the machinery and electrical machinery segment. Many scientific works are dedicated to this segment at different levels and take it as a subject for analysis. The overview involving electrical machinery with the emphasis on optimization was pursued in [25]. Prospects of the technology that have recently appeared, as well as various questions, tasks, or calls from practice, were discussed. The other study dedicated to the disputed sector is that in [26], where fractional-slot surface permanent-magnet machines were analyzed. Their multiple usage was highlighted, for instance, industrial automation or electrical traction.