Paper: Fatigue life and traction modeling of continuously variable transmissions.
Author: George K. Nikas
Published in: Transactions of the American Society of Mechanical Engineers (ASME), Journal of Tribology, 2002, 124(4), 689-698
Abstract
A model was developed to study the elastohydrodynamics and contact mechanics of toroidal Continuously Variable Transmission (CVT) type contacts. The aim is to predict the fatigue life, traction and efficiency of such contacts with the intention of making optimisations based on design criteria and constraints. A generalized Reynolds equation was developed for isothermal, transient lubrication of elliptical rough contacts with mixed rolling, two-dimensional sliding, and spinning conditions, incorporating any non-Newtonian model, roughness asperity isothermal elastoplastic interactions, and a three-dimensional subsurface stress analysis. The output is in the form of film thickness and traction maps, including contact efficiency, three-dimensional stress fields, and, finally, the predicted fatigue lives of CVT contacts, based on the Ioannides-Harris life model. A parametric study reveals the effect of surface roughness, lubricant bulk temperature, contact ellipticity ratio, slide-roll ratio, and contact load on the fatigue life, traction and contact efficiency of CVTs, and allows for design optimisations based on a compromise between life, traction and efficiency.
Some figures from this work
The configuration on which this model is based is shown in Fig. 1. This is part of the variator, which is the core of a toroidal CVT. Power is transmitted from an input toroidal disk through a roller to an output toroidal disk. Both the input and the output toroidal disks rotate about axis AA'. The roller rotates about axis BB' and the transmission ratio is altered continuously by varying the angle j of the roller (Fig. 1).
Fig. 1. Basic geometry and kinematics of the toroidal CVT variator.
An example of the effect of the contact load on fatigue life, traction and contact efficiency is shown in Fig. 2 below.
Fig. 2. Effect of contact load.
The "relative life" in Fig. 2 is the absolute fatigue life of the roller (and that of the output disk - they are indistinguishable in that figure) divided by a reference life (the latter defined here as the fatigue life for maximum Hertz pressure of 1.6 GPa). "E.I.T." stands for "Efficient Input Torque" and is the product of roller input torque (constant) and contact efficiency (variable). The computed central film thickness (hc) and the minimum film thickness (hmin) correlate generally well with those predicted by the widely used Hamrock-Dowson regression formula for elliptical contacts for the explored range of operating conditions, even though the present model includes non-Newtonian and spin effects in the analysis. However, there exists an interval of low slide-roll ratio where the minimum film thickness is significantly overestimated by regression formulae that ignore contact spin; this has been thoroughly analysed by the author in a later study.
Similarly to Fig. 2, there are four other figures in the paper showing the effect of surface roughness, lubricant bulk temperature, contact ellipticity ratio, and slide-roll ratio on the fatigue life, traction and contact efficiency.
For more information, please see the author's related CVT project.