Project: Traction modelling for a toroidal CVT.
Client: Torotrak (Development) Ltd (UK)
Sponsor: Department of Trade and Industry (UK) via the Foresight Vehicle project LAMTRAK
Researcher: Dr George K. Nikas (under contract with IC Consultants Ltd (UK))
Dr Richard Sayles (Imperial College London, Mechanical Engineering Department).
Dr Jonathan Newall (Torotrak (Development) Ltd).
Project duration: 18 months (2000-2002).
Project cost: £51,000.
Technical report: A technical report was written by Dr Nikas for the sponsoring company and the Department of Trade and Industry. The 77-page report contains 29 figures and 46 detailed equations.
TORO. Elastohydrodynamic lubrication,
three-dimensional stress analysis, and contact fatigue
analysis of toroidal Infinitely Variable Transmissions. Compiled in
Code length: 2241 lines. Latest version: 2.2.3. Registered user:
(Development) Ltd (UK).
The Torotrak variator on which the modelling of this project is based is shown in the following figure.
The variator of Torotrak's Infinitely Variable Transmission.
The objectives of the project were as follows.
Development of a generalized Reynolds equation to describe the lubrication of a typical elliptical rolling-sliding-spinning toroidal CVT type contact.
Numerical solution of the developed generalized Reynolds equation to compute the traction coefficient and contact efficiency of the CVT contact.
Computation of the resulting subsurface stress fields and incorporation of residual stresses.
Computation of the life expectancy of the CVT contact and study of the effects of the residual stresses.
This project was preceded by an 18-month project by Dr G. Nikas for Torotrak, aimed at modelling the contact fatigue of CVTs, which involved traction modelling but without spin effects in the analysis. "Spin effects" refers to the spin velocity (angular velocity vector perpendicular to the tangent plane of the contact), which is inherent in typical toroidal CVT contacts. It has been found that this spin can cause increased wear and affect both traction and efficiency; hence, its modelling and incorporation in a complete mathematical formulation via the solution of the appropriate form of the Reynolds equation is essential.
A computer algorithm was developed to solve a generalized Reynolds equation for elliptical mixed rolling-sliding-spinning toroidal CVT contacts. It includes:
Roughness effects (surface roughness simulated mathematically or measured with a Talysurf device).
Newtonian and non-Newtonian analysis with any rheological model (4 rheological models have been pre-programmed).
A generalized treatment of the traction-fluid limiting-shear-stress constraint in the contact (the limiting shear stress varies spatially and is a function of pressure and temperature).
Roughness asperities elastoplastic interactions and subsequent modification of the profiles of the contacting surfaces.
Computation of the contact pressure, film thickness, traction map and overall traction coefficient.
Computation of the contact efficiency.
Three-dimensional subsurface elastic stress analysis, including residual stresses.
Computation of the fatigue life of the CVT components (roller and toroidal disk) using the Ioannides-Harris model.
Evaluation of the effect of residual stresses on the contact fatigue life.
Maximum Hertzian contact pressures in the range of 0.8 to 2.0 GPa have been studied using the compiled computer program and the results of the program validated both theoretically and experimentally via comparison with published studies and through the traction rigs and Torotrak's own experimental results. Some figures from the author's simulations based on Torotrak's data are presented below.
Fig. 2. Normal stress in the rolling direction, 6 microns below the surface of the roller.
Fig. 3. Shear stress "xy", 6 microns below the surface of the roller.
Fig. 4. Distribution of the "Mises" stress, 55 microns below the surface of the roller. The Mises stress takes into account all 6 components of the stress tensor.
Publications of the author related to this work
Nikas, G. K. Miscalculation of film thickness, friction and contact efficiency by ignoring tangential tractions in elastohydrodynamic contacts. Tribology International, 2017; in press.
Nikas, G. K. Fatigue life and traction modeling of continuously variable transmissions. ASME Journal of Tribology, 2002, 124(4), 689-698.
Nikas, G. K. Boussinesq-Cerruti functions and a simple technique for substantial acceleration of subsurface stress computations in elastic half-spaces. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2006, 220(1), 19-28.
Finally, a photograph with the research teams from one of the meetings at Torotrak's premises, circa 2001-2002, in front of an American SUV equiped with Torotrak's Infinitely Variable Transmission. Pictured from left to right: Mr Robert Dunlop (Department of Trade and Industry); Dr Jonathan Newall (Torotrak); Professor Ray Snidle (Cardiff University); Torotrak member (?); Dr George Nikas (Imperial College London); Dr Valeria Anghel (Imperial College London); Professor Pwt Evans (Cardiff University); Professor Hugh Spikes (Imperial College London); Dr Adrian Lee (Torotrak); Dr Kayri Sharif (Cardiff University).
Homepage of Dr Nikas