A finite element formulation for coupled rigid and flexible dynamic analysis of an internal combustion engine crankshaft system.

摘要

A coupled rigid and flexible body dynamics formulation is developed for analyzing, at a system level, the dynamic behavior of a flexible engine block and a rotating, flexible crankshaft. Both the flexible deformation of the crankshaft and the block are computed by finite elements. A new rigid and flexible body dynamics algorithm is developed for coupling the rigid-body rotation and the dynamic flexibility of the crankshaft. The flexible DOF for both the crankshaft and the block are represented as a set of retained and internal DOF of a Craig-Bampton formulation. The coupling matrices between the rigid-body rotation and the flexible DOF are adopted accordingly. The nonlinear effects from the work done by the centrifugal forces are included in the formulation. Finite element shape functions for solid elements are employed for deriving the coupling terms between the rigid-body DOF and the physical DOE Since the rigid-body DOF is coupled with the internal and the retained DOF of a Craig-Bampton formulation, an additional transformation is performed. A NASTRAN DMAP program is developed for extracting the Craig-Bampton DOF for the flexible block and the flexible crankshaft along with coupling matrices between the rigid and flexible DOF for the crankshaft. The interaction between the rotating crankshaft and the block at the bearings is modeled by either linear or nonlinear springs distributed around the circumference of the crankshaft. The coupling between the flexibility of the crankshaft and the flexibility of the block is accomplished through the equilibrium conditions at the bearings. The coupled system of equations is solved in the time domain using the Newmark method for time integration. The Newton-Raphson method is used for solving the nonlinear system of equations within each time step. Analyses are performed to validate the new development for several configurations. Finally, the dynamic response of a V6 gasoline engine is computed in order to demonstrate the simulation capabilities of the new algorithm.