Determination of analytical dependencies of distributed forces in a deformable wheel – deformable surface contact zone - Kovbasa, Volodymyr; Priliepo, Nataliia (Technology audit and production reserves, 2025)
The object of this study is the contact interaction of two deformable bodies of inconsistent geometric shape, in particular, change in the stress-strain state of the wheel and the supporting surface. The significance of this topic arises from growing demands for vehicle mobility in difficult terrains, the necessity of minimizing environmental impact, and the need to optimize the design of mobile machinery components. A major challenge lies in developing a suitable analytical solution to define the stress-strain state variations within the contact zone between the wheel and soil or other surfaces. This study employs an approach grounded in the fundamental principles of mathematical physics applied to elasticity theory problems. This enabled the derivation of analytical equations that describe the absolute deformations of both the surface and the wheel (tire), along with the contact pressure distribution. The pressure distribution within the contact zone was determined using the properties of surface integrals of the second kind. Concentrated forces, when related to the contact area, were equated to the integral value of this surface integral. The values of these distributed forces were then incorporated into the transformed Boussinesq and Cerruti potential equations. The resulting analytical relationships can be utilized to determine the relative deformations of the contacting bodies and the stress distribution within them. Crucially, these relationships also serve as a basis for deriving equations that define the contact zone boundaries and the rolling resistance coefficient for deformable bodies. These derived relationships are general and presented in a form applicable to loads on both driving and passive (driven) wheels. This proposed model offers substantially improved analytical accuracy over existing empirical methods. Moreover, these analytical dependencies help circumvent the computationally intensive calculations typically required by FEM (Finite Element Method) or DEM (Discrete Element Method) simulations for every unique loading scenario and material property set.