Article 7 #1'2024

© Vitaliі Krivda, Ph. D. in Technical Sciences, Associate Professor, ORCID: 0000-0002-8304-2016, e-mail:, (Dnipro University of Technology) © Serhii Fedoriachenko, Ph. D. in Technical Sciences, Head of the Department, ORCID: 0000-0002-8512-3493, e-mail: (Dnipro University of Technology)

Principles of Mathematical Simulation of Mining Vehicles Using Applied Mathematical Software

Abstract. The transportation of rock mass and coal in mining operations relies heavily on the efficiency and reliability of mining transport systems. This study delves into the intricate dynamics of chassis functions during transportation, emphasizing the critical role of transmitting dynamic stresses and mass to the road or rail structures. With a focus on increasing productivity, modern mining locomotives and heavy dump trucks now carry substantial adhesion adhesive weights, allowing for the hauling of heavier loads even on steep slopes. The integration of scientific simulations and research-based design methods aids in identifying and managing dynamic loading effects within mining vehicle chassis. This approach minimizes the transfer of dynamic loads onto the bolster structure, enhancing system reliability and operational efficiency. Computer-aided software plays a vital role in stream-lining the development process, reducing the need for costly physical prototypes and extensive testing in challenging mining environments. The study outlines simplified calculation schemes for mining transport utilities, balancing the need for accuracy with computational efficiency. By utilizing mathematical models and simulation techniques, the dynamics of mine locomotives and dump trucks can be accurately evaluated, guiding design decisions and operational strategies. The application of Lagrange equations and software tools like “Wolfram Mathematica” facilitates the generation of differential equations for dynamic analysis, providing insights into vehicle dynamics and road interactions. Overall, this research underscores the importance of advanced modeling and simulation techniques in optimizing mining transport systems, enhancing safety, productivity, and reliability in demanding mining environments. Purpose. To highlight the application of mathematical software as an instrument for mechanical system dynamics study, that allows scientifically substantiate the usage of new technical solutions during their development. Method. Development a system of differential equations using Lagrange equations of the 2nd order, which are solved in Wolfram Mathematica. Preparation of initial conditions and mass-inertia data can be done by any known software. The generalized mathematical model can be used for any vehicle suspending unnecessary coordinates. Results. Implementation of new technical solutions without scientific ground could be resulted in difficulties while exploitation. For its removal necessary to receive dynamical characteristics. Existing engineering calculation methods are not suitable, especially because of tight time and limited financing. The customized mathematical models can be developed and solved on demand using available software. A scientific novelty. Enhancement of theoretical and experimental research become possible owing to the usage of mod- ern approaches of dynamic systems simulation using applied mathematical software Wolfram Mathematica. Obtained model can be modified in few operation from one mass task into multibody system with maximum 69 free displacements (coordinates). Practical value. The possibility to receive customized simulation model fast, verified with increased quality for scientific purposes. Keywords: dynamics, simulation, rail-wheel interaction, dynamical stress, mining rolling stock research. References 1. Ziborov, K. A. (2013). On formation of kinematic and dynamic parameters of output elements of the mine vehi-cles in transient motion / V.V. Protsiv, S.O. Fedoryachenko // Science Newsletter of NSU, No. 4. – P. 65–70. 2. Krivda, V. V. (2014). Planar and spatial mathematical motion simulation of open pit mining vehicles/ К. М. Bas, S. M. Kuvayev, V. V.Plakhotnik, V. V. Krivda // Science Newsletter of NSU, No 3, 60-65. [in Ukrainian]. 3. Zibirov, К. А. (2013). Applicability of computer simulation while designing mechanical systems of mining rolling stock / К. А. Ziborov, V. V. Protsiv, S. E., Blokhin, S. О. Fedoriachenko // Science Newsletter of NSU, No 6, 55–59. [in Ukrainian]. 4. Matsyuk, I. N., Shlyahov, E. M. (2015). The research of plane link mechanisms of a complicated structure with vector algebra methods. Eastern-European Journal of Enterprise Technologies, 3 (7 (75)), 34–38. doi: 10.15587/1729-4061.2015.44236. 5. Kravets, V. V., Kravets, T. V. (2009). Kinetic energy of an asymmetric rigid body moving around a fixed point: Invariant representation in terms of quaternion matrices, International Applied Mechanics. 6. Bas, K. M., Kravets, V. V., Ziborov, K. A, Fedoriachenko, D. A., Krivda, V. V., Fedoriachenko, S. A., Kornilenko, I. O. (2016). Mathematical Models of Hybrid Vehicle Power-train Performance. Mechanics, Materials Science & Engineering, Vol 7. doi: