Extended Computational Module for Tractive Effort at Rolling and Spinning Point Contacts
Doktorsavhandling, 2001

One category of mechanical systems that contains power-transferring point contacts is traction drive variators. These variators can be used in different concepts for Continuously Variable Transmissions (CVTs) and in vehicle applications, in order to achieve optimum engine operating conditions leading to improved driveability, reduced fuel consumption and an increase in overall vehicle performance. The purpose of this work is to present an efficient computational module which generates the tractive forces occurring at the point contact and to show how it can be used within modern simulation software to enable fully dynamic analysis of mechanical traction drive systems. The constitutive relationship between traction and motion is based on a simple concept of dry friction and Hertzian pressure distribution. The relative motion is described by using the fundamental form of the pole concept which requires the presence of rotational motion (spin). This relationship can also be used to display the isothermal behaviour of contacts, where a solidified oil film is present. The present work is general in the sense that it can handle bi-directional slip conditions, i.e., slip along and perpendicular to the direction of rolling. Earlier efficient methods of analysis only considered slip in the rolling direction. A close study of different numerical methods has been conducted to find the most efficient methods for computation of the general relationships between traction and motion. This has resulted in the following three groups of methods: low slip conditions with fully analytical solutions, moderate slip conditions with partially analytical solutions, and large slip conditions with fully numerical solutions. The required input parameters are the relative motion, the shape of the elliptical contact and the accuracy requested. The corresponding output parameters are the equivalent tractive force and spin torque at the theoretical point of contact. To cover thermal effects at high slip conditions, the isothermal coefficient of friction can be corrected by means of an extension of a simple method by Tevaarwerk for the correction of large spin traction curves to cover the bi-directional slip conditions. This method is verified against experimental data produced by Gaggermeier. Experimental investigations have been conducted on a modified KOPP type traction drive variator to investigate the robustness of the contact module under operating conditions where thermal effects are apparent and the slip conditions are bi-directional. An important finding was that the torque losses are underestimated with the contact model. To cover that a simple formula for rolling resistance was included into the analysis. The contact module comprises general functions for calculation of the contact properties, relative sliding conditions, rolling resistance and tractive effort. It can also be customized with specific functions for detection of the point of contact. This has resulted in a contact module that can be used either in simple simulation software for analysis of simple applications, or in powerful Multi-Body System simulation packages for analysis of more complex applications. Both simple and complex implementations are presented. The new computational module efficiently evaluates the tractive forces for a given arbitrary relative sliding motion as well as the existing rolling resistance in a Hertzian point contact. This has not been available until now. By combining this contact subroutine with a powerful simulation tool such as ADAMS, DADS, Mechanica/MOTION, etc., the mechanical systems investigated can now be modelled in a more realistic way than before. This enables also an introduction of virtual prototyping into the product development process since the iteration between modelling and simulation is fast and the overview of the system is good in spite of the complexity.


thermal effects

Hertzian contact

continuously variable transmission

rolling resistance

speed pole

traction drive

multi-body system

efficient numerical procedure


Mikael Törmänen

Institutionen för maskin- och fordonskonstruktion





Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 1763

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