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Rolling radii and moment arm of the wheel load for pneumatic tyres

Heinz Dieter Kutzbach, Alexander Bürger, Stefan Böttinger,

Journal of Terramechanics, Volume 82, 2019, Pages 13-21, ISSN 0022-4898,

Abstract: Tractors and self-propelled harvesters are equipped with high volume pneumatic tyres with a low tyre inflation pressure. The contact patch can shift forwards or backwards in reference to the wheel centre as reaction on traction or brake forces because of the elastic tyre wall. Theoretical investigations – as necessary for modelling and simulation of dynamic vehicle behaviour – are complicated, since important tyre metrics cannot directly be measured based on the large deformations. Additionally, different definitions are often used. This is especially valid for the conversion of a drive torque into a traction force. In this context, the moment arm of the wheel load and the rolling radius of the tyre at zero slip condition are especially important. In contrast to the hitherto existing perception, the magnitude and position of the moment arm of the wheel load in reference to the wheel centre is dependent on traction and brake forces in addition to the motion resistance. The rolling radius of an elastic pneumatic tyre can be interpreted as radius of a fictitious rigid substitute wheel. This contribution emphasizes the outstanding importance of the rolling radius rdyn for all calculations on pneumatic tyres and the important roll of the variable moment arm of the wheel load for the moment compensation on the wheel.

Keywords: Pneumatic tyres; Rolling radius; Moment arm of the wheel load; Kinetic radius; Kinematic radius; Torque radius; Inner tyre ratio