Steven M. Cron

On the Effects of Edge Scalloping for Collapsible Spokes in a Non-Pneumatic Wheel During High Speed Rolling

The acoustic signature produced by non-pneumatic wheels with collapsible spokes is a critical design criterion for automotive and other mobility applications. During high speed rolling, acoustic noise may be produced by the interaction of vibrating spokes with a shear deformable ring as they enter the contact region, buckle and then snap back into a state of tension. In order to identify and help understand the causes of acoustic noise for a rolling non-pneumatic wheel, a two-dimensional finite element model with geometric nonlinearity has been utilized. The model consists of a shear ring modeled as two relatively inextensible membranes with high circumferential modulus separated by a hyper-elastic material. The temporal variation in spoke length as the spoke passes through the contact zone is extracted and used as input to a three-dimensional (3-D) model of a single spoke. The 3-D spoke model is able to capture out-of-plane vibration modes of the spoke which may contribute as a source of acoustic excitation and allows for modeling of edge scalloping. Natural frequencies and mode shapes of the various spoke design strategies are computed and correlated with the frequency response of the out-of-plane spoke vibrations. Results indicate that scalloping the edges of the spoke can dramatically reduce the amplitude of vibration, but does not have a strong effect on location of frequency peaks in a FFT of the time-signal. An optimal amount of scalloping was determined which reduces maximum vibration amplitude to an asymptotic value.Copyright

Tire Energy Loss from Obstacle Impact3

Abstract Tires in actual service conditions operate on rough roads with a random distribution of obstacles. Rolling resistance, however, is typically measured on smooth surfaces. This paper considers the nature of tire energy loss when impacting obstacles. It is demonstrated by a simple example that translational energy can be “lost,” even in purely elastic impacts, by trapping energy in structural vibrations that cannot return the energy to translation during the restitution phase of the impact. Tire simulations and experiments demonstrate that this dynamic energy loss can be very large in tires if the impact times are short. Impact times indicating the potential for large energy loss are found to be in the range of normal highway speeds.