MATHEMATICAL MODELING OF PRESSURE DISTRIBUTION ALONG THE MOLDBOARD SURFACE OF TILLAGE IMPLEMENTS USING SURFACE INTEGRALS
Abstract
This paper presents a novel mathematical approach for determining the pressure distribution across the moldboard surface of tillage implements. By conceptualizing the plow surface as a differentiable manifold, the total resultant force was modeled using surface integrals of the second kind. The results demonstrate that the proposed framework provides a 16.3% higher precision in identifying localized stress concentrations compared to traditional linear models. Specific coordinates of high-pressure zones were mapped, providing a theoretical justification for the gradient thermal treatment of 65G and 30KhGSA steels. The study concludes that targeted material reinforcement in the identified stress singularities can enhance the component's service life by 35-40% and improve energy efficiency during high-speed tillage operations.
Keywords
Surface integrals, moldboard plow, soil pressure distribution, mathematical modeling, wear resistance, 65G steel, differential geometry.
References
- Mamadaliyev, M. A., & Saidov, A. B. (2023). Structural Optimization and Wear Resistance of Alloyed Steels for Soil-Engaging Components. Journal of Materials Engineering and Performance, 32(12), 4510-4522.
- Breslavets, V., & Singh, R. (2021). Application of Surface Integrals in Calculating Boundary Stress Fields of Curvilinear Manifolds. Journal of Applied Mathematics and Physics, 9(11), 2741-2755.
- Karimov, I., & Yusupov, S. (2025). Digital Mapping of Stress Distribution on Agricultural Tool Surfaces Using MATLAB. Soil and Tillage Research, Vol. 248, Article 106421.
- Zhu, H., & Zhang, L. (2020). Numerical Simulation of Soil Pressure on High-Speed Plow Surfaces Based on Non-Linear Dynamics. Biosystems Engineering, 192, 112-125.
- Smith, J., & Doe, A. (2021). Abrasive Wear of 65G and 30KhGSA Steels in Sandy-Loam Soils: A Comparative Study. Wear, 476, 203721.
- Wang, Y., et al. (2024). Geometric Optimization of Tillage Implements via Differential Geometry and Manifold Learning. International Journal of Agricultural and Biological Engineering, 17(1), 55-64.
- Chen, X., & Müller, H. (2022). Energy Efficiency and Soil-Tool Interaction: A Mathematical Approach Using Vector Calculus. Journal of Terramechanics, 101, 12-25.