| This thesis details an investigation into the modeling and simulation of vehicle powertrains and powertrain components. The work expands on previous studies in three areas; the derivation of powertrain component models, the formulation of mixed planar and spatial dynamic equations of motion, and lastly, the development of an implicit, stiffly-stable integration technique.; Planar models are used to represent components, such as gearing, clutches and differentials, along the power-transmission path of the powertrain. While many of these models have been formulated and presented in previous studies; some, such as the differential and tire models are either newly derived or enhanced in this work. The planar component models are each referenced to a three-dimensional component body, such as the engine block or transmission casing, for the purpose of defining their spatial orientation and dynamic characteristics. Dynamic and constraint equations are formulated, based on the Euler-Lagrange technique, allowing a powertrain to be viewed as a locally-planar, three-dimensional system.; The use of the Euler-Lagrange formulation results in a mixed system of differential and algebraic equations (DAE) which are difficult to solve numerically. An implicit, stiffly-stable integration algorithm is developed and applied to directly integrate the DAE system and simultaneously satisfy the kinematic constraints. The algorithm includes both variable-order and variable-stepsize techniques to control the error accrued in the state variables.; The powertrain component models and the integration algorithm are incorporated into a computer program, allowing simple and flexible powertrain system model formulation and solution. |
