Interpolation-based parametric model order reduction for material removal in elastic multibody systems

One essential step in the simulation of elastic multibody systems is the model order reduction of the elastic degrees of freedom. For simulations of material removal, the system matrices can be described as parameter dependent. In this contribution, parametric model reduction methods based on interpolation are applied for this type of problem. Thereby, the interpolation of the reduced system matrices, interpolation of projection matrices, interpolation of subspaces and the interpolation of the transfer functions are investigated. The advantages and disadvantages of these techniques, especially for the application in elastic multibody systems are carved out and illustrated for the manufacturing of a T-shaped workpiece which varies in its thickness due to material removal. In this contribution, we focus on the investigation of the methods in the frequency domain.

[1]  Peter Benner,et al.  Modellreduktion für parametrisierte Systeme durch balanciertes Abschneiden und InterpolationModel Reduction for Parametric Systems Using Balanced Truncation and Interpolation , 2009, Autom..

[2]  Peter Eberhard,et al.  Simulation of Moving Loads in Elastic Multibody Systems With Parametric Model Reduction Techniques , 2014 .

[3]  Ortwin Farle,et al.  Order-Reduction of Fields-Level Models with Affine and Non-Affine Parameters by Interpolation of Subspaces , 2015 .

[4]  Karen Willcox,et al.  A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems , 2015, SIAM Rev..

[5]  Boris Lohmann,et al.  Parametric Model Order Reduction by Matrix Interpolation , 2010, Autom..

[6]  Peter Eberhard,et al.  Application of parametric model reduction with matrix interpolation for simulation of moving loads in elastic multibody systems , 2015, Adv. Comput. Math..

[7]  C. Farhat,et al.  Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity , 2008 .

[8]  Boris Lohmann,et al.  Parametric Model Order Reduction by Matrix Interpolation (Parametrische Ordnungsreduktion mittels Matrixinterpolation). , 2010 .

[9]  Jr. Roy Craig,et al.  Coupling of substructures for dynamic analyses - An overview , 2000 .

[10]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[11]  P. Eberhard,et al.  Time-Dependent Parametric Model Order Reduction for Material Removal Simulations , 2017 .

[12]  Charbel Farhat,et al.  An Online Method for Interpolating Linear Parametric Reduced-Order Models , 2011, SIAM J. Sci. Comput..

[13]  R. Schwertassek,et al.  Dynamik flexibler Mehrkörpersysteme , 1999 .

[14]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .