Slip Analysis on a Non-holonomic Continuously Variable Transmission Using Magic Formula

Non-holonomy in input-output systems can be characterized by a reachable space whose dimension is larger than that of its input space. Among the various mechanical examples of non-holonomy, we have dealt with the friction drive type semi-spherical continuously variable transmission (SS-CVT) in this paper. SS-CVT transmits power by rolling friction and realizes the neutral, forward and reverse states of output shaft without any additional devices. A spherical shaped variator in SS-CVT transmits power and changes its gear ratio keeping contact with an output disc. It is necessary to consider the friction forces along with in two-directional slip on the contact point, because the directions of friction forces to transmit power and to change gear ratio are perpendicular to each other. For this, the friction forces must be analyzed by using the slip ratio and slip angle on the contact patch. Therefore, we have determined the planar friction variables by the dimensional analysis, and the SS-CVT test bench. Finally, the empirical formula for evaluating the two friction forces has been proposed based on the experimental results. And the numerical results regarding the dynamics of SS-CVT have been addressed.