A time-dependent parametric model order reduction technique for modelling indirect bearing force measurements

• Extension of a novel parametric model order reduction strategy to 3D systems
• Full derivation of parametric load dependency for a linear tetrahedron mesh
• Analytical formulation for the parameter derivatives for application to bearings
• Considerable reduction of the number of equations for multiple load locations
• Results show the accuracy of the method with respect to standard techniques.

Model order reduction is frequently used to keep computational effort affordable at the expense of a minimal loss of accuracy. One particularly challenging problem that yet needs to be solved satisfactorily in this regard is the efficient treatment of time-varying multiple-input/multiple-output behaviour. Recent developments in the field of parametric model order reduction have led to a novel method that deals with moving loading or boundary conditions, but only a few of them are active at a certain time. This work extends the novel method, named static modes sliding, to deal with time-varying multiple-input/multiple-output behaviour for use in dynamic simulation of three-dimensional models. A parametric relationship which describes the location of externally applied loads on a linear tetrahedron mesh has been described to form a continuously time-varying reduction space. A mode tracking technique is inherently incorporated in this method by interpolating among the correct modes. The dynamic simulation of an indirect dynamic bearing load measurement setup serves as a technically relevant case-study. Moreover, the viability of the proposed strategy in an industrial environment with respect to conventional reduction techniques is discussed. The numerical results demonstrate the potential in the development of dedicated reduction schemes for bearings and gears.