Torsional finite elements and nonlinear numerical modelling in vehicle powertrain dynamics

Torsional finite elements for direct, branched and grounded (boundary) connections and geared connections with rigid or elastic tooth mesh are presented. The use of these elements for developing dynamic models of various passenger vehicle powertrains is illustrated and discussed. A six-degree-of-freedom dynamic model for clutch engagement is used to investigate the effect of low-frequency transients on clutch engagement stick–slip and gear backlash in powertrains. Results for free vibration analysis and transient vibration numerical simulations are presented. Attention is paid to the algorithms used in the piecewise nonlinear transient analysis and the method of numerical simulation. The methodology is thoroughly detailed and is discussed for application to higher degree-of-freedom powertrain models.