Separation of reference motions and elastic deformations in an elastic multi-body system

摘要

The computational simulation of multi-body dynamics (MBD) of moving structural components is one of the most challenging objectives in the design analysis work of automotive engineers. These simulations are a need to assess the vibro-acoustic quality of new products in the early development stage and can reduce development time and costs significantly. The concept of elastic MBD is based on dividing the non-linear mechanic system into subsystems with linear elastic behaviour (bodies) and non-linearities occurring only at the connections (joints) between these subsystems. Because of the non-linear characteristic of the system, the dynamic simulation has to be solved in time domain via numerical time integration. Both the necessary small time-step sizes and the iterative solution scheme within one time step imply large computational effort. Thus, the improvement of the efficiency and the stability are main targets for the software development. This article presents two variants of modelling linear elastic components via a multi-body model. The main difference between the two variants is in the strategy used for the separation of reference (global) motions and elastic deformations (small motions). The first variant applies a projection strategy, whereas the second variant considers reference conditions that are based on a minimum relative kinetic energy or on a minimal square average displacement approach. This article describes the mathematical modelling of the two variants, which based on the floating frame of reference formulation. On the basis of the theoretical formulation, a comparison of the two strategies from application as well as numerical and algorithmic point of view is presented. Consequently, the advantages and the disadvantages of the two approaches will be analysed. The results section compares the two presented methods, which were applied for the simulation of the dynamics of two crankshaft models. First, a crankshaft of a five-cylinder combustion engine is analysed. The second investigated example is a crankshaft of a one-cylinder engine with special consideration of different strategies for the applied reference conditions. Both the obtained calculation results and the computational performance in terms of CPU time are discussed.