A Finite Element Method for the Dynamic Analysis of Automatic Transmission Gear Shifting with a Four-Degree-of-Freedom Planetary Gearset Element

Abstract

A dynamic model of a passenger car automatic transmission and driveline is developed for simulating transient torsional vibration in gearshifts. A finite element method is proposed for presenting the transient dynamics of the parametric system, element matrices are defined and then global inertial, stiffness and damping matrices are formulated corresponding to the defined global coordinate vectors. A four-degree-of-freedom matrix element is developed that describes the rigid body dynamics of the planetary gear set and is then integrated with the driveline system; this element captures the parametric change while the transmission speed ratios vary over gearshifts. Free vibration analysis and a transient 2-3 upshift simulation are discussed and results presented.