Approximate Closed-Form Solutions for the Shift Mechanics of Rubber Belt Variators

The mechanical behavior of V-belt variators during the speed ratio shift is different from the steady operation as a gross radial motion of the belt is superimposed to the circumferential motion. The theoretical analysis involves equilibrium equations similar to the steady case, but requires a re-formulation of the mass conservation condition making use of the Reynolds transport theorem. The mathematical model of the belt-pulley coupling implies the repeated numerical solution of a strongly non-linear differential system. Nevertheless, an attentive observation of the numerical diagrams suggests simple and useful closed-form approximations for the four possible working modes of any pulley, opening/closing, driver/driven, whose validity ranges over most practical cases. The present analysis focuses on the development of such simplified solutions, succeeding in an excellent matching with the numerical plots, and on the comparison of the theory with some experimental tests on a motorcycle variator, revealing a very good agreement.