Nonlinear finite element analysis of TWEEL geometric parameter modifications on spoke dynamics during high speed rolling.

摘要

The acoustic signature and noise produced by non-pnuematic wheels such as the Michelin TWEEL(c) is a critical design criteria for automotive and other mobility applications. The TWEEL(TM) structure consists of three basic parts: (1) a circular deformable "shear beam", (2) collapsible spokes and (3) a rigid hub. During high speed rolling the Tweel(TM) produces acoustic noise which is hypothesized to be due to resonant vibration of the Tweel(TM) spokes 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 TWEEL a nonlinear two-dimensional finite element model using ABAQUS has recently been developed by a research team at Clemson and Michelin. The Tweel(TM) model consists of a shear beam modeled as two inextensible membranes with high circumferential modulus separated by a relatively low modulus elastic material. The temporal variation in spoke length as the spoke passes through the contact zone is extracted and used as input to a 3-D model of a single spoke. The 3-D spoke model is able to capture more complex vibration modes of the spoke, including out-of-plane "flapping" behavior that are thought to be a primary source of acoustic excitation. The original model studied changes in uniform spoke thickness and wheel rolling speeds on amplitude and frequency of spoke vibrations.;The TWEEL model used in this work is a continuation and expansion of this model; additional geometric parameters of the spokes are examined including edge scalloping, reduced width with scalloping, curvature change, and variable thickness. In addition, modal frequencies and 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 do not have a strong effect on frequency peaks. An optimal amount of scalloping was determined which reduces maximum vibration amplitude to an asymptotic value. Changes in spoke thickness do not significantly affect the frequency, but can affect the amplitude of vibration. Changes in spoke width do not appear to affect either frequency or amplitude significantly. Spokes with smaller curvature resulted in a load-displacement curve which indicates higher wheel stiffness and produced higher vibration frequencies but with lower amplitude when compared to spokes with bigger curvature.;In previous models, the dynamic loading and rolling steps where performed using ABAQUS/Explicit with a restart from a steady-state cooling analysis performed in ABAQUS/Standard. In this work, additional models are developed and compared where the dynamic loading and rolling steps are performed with restart from a transient cooling analysis using ABAQUS/Explicit and an analysis with no cooling step but an initial defined pre-tension. Results obtained from these alternative methods for modeling pretension produced a spoke-length profile with reduced amplitude high-frequency oscillations.