Calculation of the Wheel Rolling Radius at Design Modeling of a Wheeled Vehicle

Abstract

AbstractWhen design mathematically evaluating of a wheeled car properties as stability, controllability and braking dynamics, a modeling of the machine movement is performed. This movement is most affected by the interaction of the elastic wheel with a solid support surface. When describing the wheel movement, it is required to know its rolling radius with minimal initial data. The rolling radius is necessary to calculate the longitudinal slip in the wheel contact spot with the support surface, to calculate the moment from the longitudinal reaction in the wheel rotation plane, etc. The moment from the longitudinal reaction in the wheel rotation plane determines the wheel angular velocity and also affects the amount of longitudinal slip in contact. An expression is obtained for calculating the relative rolling radius depending on the relative tire radial deformation. Developed and realized a methodology for the study of mathematical relationships of the physical quantity «rolling radius» on the example of “Continental” tires. It is shown that the dimensionless value «relative rolling radius» does not depend on the load capacity and tire dimensions. It is determined only by the relative tire radial deformation. Its value is close to 1. It can be calculated from the obtained dependence with an error not exceeding 4.5% for radial tires and not exceeding 1…2% for diagonal tires.KeywordsWheeled vehicleDesign modelingElastic wheelRolling radiusMathematical relationships