A generalized model of stationary turning of any vehicle

The article discusses a method of building a mathematical model of the curvilinear motion of an arbitrary vehicle. The proposed approach allows us to describe the turn of a vehicle with any transmission layout moving along any ground. We ignored vertical oscillations of the frame at this stage and confined our research to consideration of plane motion. Therefore, the motion equations are algebraic. The unknown ground reactions included therein are recorded based on the mathematical theory of friction. In this case, the pulling force, the lateral shearing force, and the stabilizing moment in wheel-to-ground contact are a function of unknown coordinates of the instantaneous slip center. This reduces the power problem to wheel movement kinematics and allows them to be solved simultaneously, considering their interconnection and interdependence. Then, the article considers the kinematics of wheel movement on the vehicle turn and derives the missing equations of holonomic and non-holonomic constraints placed on the unknown coordinates of the instantaneous slip centers. The equations of holonomic (geometric) constraints reflect the position of the wheel and its installation angle relative to the vehicle frame. The equa-tions of non-holonomic (kinematic) constraints describe the type of transmission and the wheel movement mode (driving, driven, braking). The article gives examples of non-holonomic constraint equations for various types of transmissions. As a result, the description of each wheel individually, considering its contact size and normal load, allows us to receive the developed traction force and the value of slipping. To illustrate the implementation of the proposed methodology, the article presents an example of building a mathematical model for the Uralets compact wheeled tractor manufactured by Chelyabinsk Tractor Plant with an unconventional turn control scheme. This model has been tested experimentally, which confirms the applicability of the offered approach.