Rolling Resistance Model for Deformable Bodies With No Slip

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Abstract
Rolling contact is a complex phenomenon that is dependent on a host of physical properties, as well as relative motion. Simplified treatments of rolling often rely on point or line contact and use nonslip kinematic constraints to treat rolling. However, during rolling motion, the deformation of the contacting bodies leads to energy dissipation and contact forces that oppose the rolling motion. Given the importance of rolling contact in mobile and multibody systems, the problem has received considerable attention over the years and has motivated a number of different modeling approaches. This paper examines rolling from a macroscopic perspective that accounts for the deformed area and presents an approach for defining the resultant tangential and normal reaction forces under the assumption of no-slip. Deformations in the normal direction are modeled using bilinear springs and dampers, while the forces in the tangential direction are calculated using reaction forces computed from a constrained Lagrangian approach. One particular motivation for the development of the model in this paper is for the prediction of how multiple payloads being lifted by a single crane can roll relative to each other. The modeling approach is applied to the planar case of a disk rolling under conditions of acceleration, deceleration, and constant speed. Results are also presented for the application of the model to a planar disk-on-disk rolling system.

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