Model Order Reduction Of Flexible Multibody System Based On Physical Subspace Method

Flexible multibody systems are needed for accurate multibody system simulation,because it considers the flexibility of the component.The scale of the system increase sharply with the elastic coordinates.Which reduce the computational efficiency for dynamic simulation.Model order reduction is an important issue for flexible multibody systems dynamics.The generalized elastic coordinates reside on a non-physical subspace after reduction by traditional component mode synthesis and Krylov subspace methods,which limit the use of the model in such area of structure optimization and damage identification.Model condensation by Guy an method,Dynamic condensation method and IRS method not only decreased the number of elastic coordinates,the reduced coordinates also lied on physical subspace.So this kind of condensation method can be call as physical subspace method.At present,this kind of method is mainly used in the field of structural dynamics.In this work,physical subspace method is adopted to reduce the flexible body's degrees of freedom.First,the developing history and current state of the dynamics modeling and model order reduction of the flexible multibody system are summarized and analyzed.Second,the modeling and reduction processes are deduced in detail for the planar motion using Floating Frame of Reference.The planar flexible multibody system is reducing by physical subspace method.Third,physical subspace method such as Guyan method,Dynamic condensation method,IRS method,IIRS method and IOR method are introduced in detail.Component Mode Synthesis as comparison is describes briefly.Fourth,selection of master DOFs(degrees of Freedom)is an important issue for model condensation,several qualitative guidelines and quantitative algorithms of selection masters are described.A two-level condensation scheme for minimum reduced model is proposed.Several assessment criteria and error estimation method are discussed based on the intrinsic properties of the flexible components.At last,verification numerical examples and applied example are shown.Computational algorithms for the dynamic analysis are briefly reviews.The modelling process,model order reduction and dynamic analysis are accomplished by MATLAB program.And some problems in the programming are discussed.Two numerical examples are shown in this work to validate the proposed method.The rotating beam model is present to show the effect of Sequence of reduction and constraint,and different boundary condition.Sequence of reduction and constraint has an effect on accuracy of reduced model,'constraint first' is recommended during the modeling process.Flexible slider crank mechanism is another example to illustrate the efficiency and effectiveness of the proposed physical subspace based reduction method with comparison to the well-known modal reduction and modified Craig-Bampton methods.Finally,a frame assembly of commercial vehicle model is reduced by the proposed method,and assess by relative error and MAC values.Physical subspace method decreases the scale of the model and improves calculation efficiency.Which also has good approximation accuracy to the original model compared to those two reduction methods.One of the greatest strengths of the physical subspace based model order reduction method is that all the reduced coordinates are in physical base,which makes it easier to couple with other substructures than non-physical subspace based reduction methods.Two-level condensation scheme can achieve a minimum reduced model,under precondition of assuring precision requirement.