Systematic modeling of complex time-variant gear systems using a Power-Oriented approach

This paper addresses a methodology for the systematic modeling of complex gear systems. The methodology is based on the use of a unified general model, working for all complex gear systems: time-variant as well as time-invariant, having parallel or oblique rotation axes. The model equations are automatically written following the outlined procedure and applying the presented algorithms, making this approach less prone to mistakes with respect to other approaches. Next, a reduced model assuming rigid gear connections and introducing no loss of information is proposed, which directly gives the kinematic relations between the gears angular speeds and input torques. In order to show some case studies, the proposed methodology is applied to three systems of interest for vehicle dynamics and powertrain modeling. The considered case studies are a differential structure having a bevel gearing system with non-perpendicular gear shafts, a vehicle differential and a full toroidal variator, which is suitable for applications such as KERS (Kinetic Energy Recovery System) and IVT (Infinitely Variable Transmission). Furthermore, the control of a full toroidal variator acting as a KERS with reference to an automotive case study and the comparison of the proposed modeling methodology with two other approaches are addressed.