| Multibody models are often constructed with moving intermediate reference frames to characterize critical forces and moments. Ideally, these reference frames would be described by rigid bodies with zero inertia. However, existing equation formulation methods require that the accelerations of all bodies be resisted by inertia; singularities result otherwise. Thus, models are often given bodies with “small” inertias to serve as such reference frames. In these cases, small inertias contribute high-frequency dynamics to the system that are not of interest. The high-frequency dynamics are undesirable because they require the use of small integration time steps or sophisticated numerical integration methods.; This dissertation presents a new method of model reduction for multibody systems that allows masses and rotational inertias of the bodies to be set to zero. The method forms constraint equations that are solved to eliminate singularities, due to the zero inertias by eliminating the degrees of freedom with which the singularities are associated. A computer program, based on the AutoSimTM multibody program, called “AutoSimIR” (the “IR” denotes “inertia removal”) was created to implement the new formulation method. Procedures and data structures developed for AutoSimIR are presented. The method is demonstrated for two example multibody models: (1) a four-body heavy-truck suspension, and (2) a twelve-body three-dimensional vehicle model of a 5-axle tractor-semitrailer, similar to the one in the TruckSimTM software package. For each system, the equations of motion are formulated for the full model (small inertias are kept in the model) and for the reduced model (small inertias are removed).; The example simulations show that the modeling assumption of removing inertias is sometimes beneficial, and sometimes detrimental. The reasons for this are shown to be related to the amount of rate-dependent damping in the system. A “rule of thumb” is proposed for predicting whether removing a small inertia from a system will be beneficial or detrimental. For systems for which removing small inertias is beneficial, the new method proves to be a valuable modeling tool, enabling simulation times to be significantly reduced with little effort on the part of the modeler. |
