Model Reduction Of Flexible Multi-body Dynamics Based On Krylov Subspce Method

The floating frame method is most commonly used in flexible multi-body systems, in which the flexible body's motion is subdivided into two parts: a large overall reference motion and elastic deformations with respect to the floating frame. The finite element method is widely used to describe the elastic deformations of flexible bodies, which leads to a large number of elastic coordinates and large computational burden. Thus, model reduction is investigated in this paper to improve the computational efficiency of flexible multi-body dynamic simulations. Moreover, it makes control easier to be designed and implemented.Inspired by balance truncation method, this dissertation proposes a new automatic order control algorithm based on Hankel singular value. The existing model reduction methods of flexible multi-body system, especially modal reduction method and Krylov subspace method are comprehensively reviewed. Furthermore, both first order Krylov subspace equations and second order Krylov subspace equations are derived systematically. The existing automatic reduction algorithms are introduced in detail. Then, inspired by balance truncation method, this dissertation proposes a new automatic order control algorithm based on Hankel singular value. The critical projection angle algorithm is usually used to implement order control of Krylov subspace method. However, the size and accuracy of the reduced model are sensitive to the value of critical projection angle, and comparing with the existing critical projection angle method, the physical meaning of the new method which is proposed in this dissertation is clear. In addition, it's easier to realize order control.Research on model reduction of flexible multi-body dynamic systems is carried out based on Krylov subspace method. Compared with the existing modal reduction method such as modal truncation method, modal cost analysis method and balance truncation method, with the Krylov subspace method smaller orders are needed whether the influence of large overall reference motion is taken account or not, which is in good agreement with that of the finite element method. It means that Krylov subspace method can keep both low frequency characteristics and high frequency characteristics of flexible dynamic systems and its simulation efficiency is higher. Combined with multi-variable method, Krylov subspace method is successfully applied to model reduction of multi-body system's contact-impact area. The contact-impact process is discontinuous, high transient and high nonlinear, model cannot be reduced directly. Multi-variable method divides the flexible body into two parts: impact area and non-impact area. The deformations of impact area are described by finite element coordinates and the deformations of non-impact area are described by modal coordinates. And the subarea description makes model reduction possible. The numerical simulations show that Krylov subspace method can reduce more degrees-offreedom of the non-impact area and the simulation efficiency is improved a lot.