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There are several commercial off-the-shelf software available to study transmission and driveline dynamics. Many of these software require a faithful representation of the transmission topology in order to carry out the analyses. These modeling techniques utilize several redundant degrees of freedom which may not be necessary for studying low frequency (< ~30 Hz) dynamics and may be computationally inefficient. The dual-clutch model has been proposed as a generic 2-DOF model that overcomes some of these drawbacks. In this paper, the dual-clutch model is initially derived from first principles, starting with the equations of motion for a planetary automatic transmission. The model coefficients - the inertia matrix and the matrix of clutch coefficients - are then derived using a more intuitive approach based on energy considerations.

All-wheel Drive (AWD) is a mature technology and most automobile manufacturers offer this feature on their vehicles. Improved traction, enhanced vehicle stability, and better handling are some of the key characteristics of AWD vehicles which are achieved by distributing the appropriate level of torque to the front and rear axles. Accurately capturing the torque split between the two axles is essential for sizing of driveline components like gears, bearings, and shafts. Traditionally, the torque split is considered to be either 50-50%, or solely proportional to the static weight distribution between the two axles. Design decisions are made based on historical test data. In this paper a longitudinal vehicle dynamics model for AWD systems is proposed to understand the influence of various key factors such as dynamic weight transfer, compliance of driveline components, and changing tire radius on the torque split.

Understanding planetary gear efficiency is more involved than understanding efficiency of external gears because of the recirculating power that is inherent in planetary gear operation. There have been several publications going back several decades on this topic. However, many of these publications are mathematical in their approach and tend to be overlooked by practicing engineers. This paper brings a new, more visual and more intuitive approach to the problem. It uses lever diagrams, which have been a standard tool in the transmission engineer’s arsenal for almost four decades, to visualize the power flow and develop analytical expressions for the efficiency of simple and compound planetary gears. It then extends the approach to more complex gear trains.