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In this paper, a method is presented to determine the vibrational behavior of an electric motor and the associated structure. Therefore, a holistic simulation approach is used, which takes into account the mutual influence of structural mechanics and electrodynamics. For this purpose, a multi body simulation (MBS) is extended so that electromagnetic loads can be considered, which are calculated by using the finite element method (FEM). In electric machines an undisturbed and constant magnetic field is of great importance. Even small variations of the air gap lead to changes in the magnetic field compared to the ideal geometry, which cause a change in the resulting torque and vibration excitation. Especially local and global asymmetric air gap changes due to load‐ and operation‐dependent deformations of the stator and rotor are problematic. Such deformations result on the one hand from the electromagnetically excited structural vibrations and on the other hand from the rotordynamic loads. For these reasons, it is necessary to consider the electro‐ and structural‐dynamic effects together. The developed method is presented on a simple generic motor to show the influence of the coupling. [ABSTRACT FROM AUTHOR]

In this paper, a method for vibration analysis of electric engines and associated structure is presented. For this purpose, a multi‐body simulation (MBS) is extended in such a way that electromagnetic loads can be considered using the finite element method (FEM). Subsequently, the determined loads lead to an excitation of the structural vibrations and a sound radiation of the engine, which is analyzed at selected operating points. A test rig will be used to validate the implemented method. Finally, different design variations of the engine are evaluated with respect to their acoustic behavior. The developed method is not limited to the presented application, but it can be applied to any system with electric drives. [ABSTRACT FROM AUTHOR]

Numerically stable and accurate time integration methods are important in structural dynamics. We propose such a method based on a mixed variational formulation of the underlying semi‐discrete equations of motion. The newly developed scheme relies on a specific combination of the so‐called continuous Galerkin (cG(k)) method and the discontinuous Galerkin (dG(k)) method. We refer to [2] for an introduction of the original cG(k) and dG(k) methods for ODEs (see also [1]). The mixed approach relies on polynomial approximations of degree k on the level of each time finite element. In particular we make use of hierarchical interpolation polynomials. The present approach is closely related to Hellinger‐Reissner type mixed variational formulations for elastodynamics. The mixed method yields implicit time‐stepping schemes with order of accuracy equal to 2k for the displacements and velocities. In addition to that, the method is capable of conserving the energy in the case of conservative mechanical systems. Numerical examples are presented which highlight the numerical properties of the newly proposed mixed approach. [ABSTRACT FROM AUTHOR]

Disc brakes convert kinetic energy into thermal energy in order to slow down vehicles. During the braking process enormous heat flows and temperature gradients occur in the system. Because heating leads to a change in shape for most materials, it is important to take the temperature and its influence into account during the design process. The interaction between the structure and the heat in disc brakes can be described with methods from thermoelasticity. To simulate thermoelastic behaviour the Finite Element Method is commonly used. The thermal and mechanical domain are taken into account by coupling the equation of motion and the heat equation. However, in transient analysis often the problem occurs of different time scales of the structural and thermal dynamics for many technically relevant materials, like steel. For metallic materials the time constant of structural dynamics is much smaller than those of thermal dynamics. This complicates an efficient transient simulation. In the present work the implementation of a Finite Element Method in thermoelasticity and associated investigations are shown. The method is applied to various parts and load cases. Also different approaches to deal with the different time scales will be shown. Heuristic methods like mass‐scaling as well as more mathematically oriented approaches like model order reduction are presented. [ABSTRACT FROM AUTHOR]

Abstract: We apply a multipreconditioned domain decomposition method based on Finite Element Tearing and Interconnecting to linear structural dynamics with highly heterogeneous material properties. A recently published method to build and select the multiple directions is presented and applied. We hint at possible problems when localized phenomena are considered and present a new simple measure that extends the selection process in existing algorithms. We show numerical results and conclude how to effectively prevent a possible degeneration of the minimization space basis. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Computational costs for detailed Finite Element approximations can be reduced by using reduced-order models instead. In this contribution, four subspace-based reduced-order modeling methods are compared. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In structural dynamics the initial boundary-value problem has to be solved in the space and time domain. The spatial discretization is done using finite elements yielding systems of differential equations of second-order. Incorporating inelastic material properties, thermo-mechanical coupling and particular Dirichlet boundary conditions essentially changes the underlying mathematical problem. The main goal is to provide higher-order time integration schemes using diagonally-implicit Runge-Kutta methods (DIRK) and the Generalized α-method consistently applied to the semi-discretized ODE-system comprising the semi-discretized equations of motion, the unsteady semi-discrete heat equation and constitutive equations of evolutionary-type. Furthermore, we want to show the applicability of time-adaptivity by embedded schemes so that step-sizes are chosen automatically. The inelastic constitutive equations are given by a thermo-viscoplasticity model of Perzyna/Chaboche-type with non-linear kinematic hardening. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In the present paper we consider structure-preserving integration methods in the context of mixed finite elements. The used low-order mixed finite elements typically exhibit improved coarse mesh accuracy. On the other hand energy-momentum (EM) consistent time-stepping schemes have been developed in the realm of nonlinear structural dynamics to enhance the numerical stability properties. EM schemes typically exhibit superior robustness and thus offer the possibility to use large time steps while still producing physically meaningful results. Accordingly, combining mixed finite element discretizations in space with EM consistent discretizations in time shows great promise for the design of numerical methods with superior coarse mesh accuracy in space and time. Starting with a general Hu-Washizu-type variational formulation we develop a second-order accurate structure-preserving integration scheme. The present approach is applicable to a large number of mixed finite element formulations. As sample application we deal with a specific mixed shell element. Numerical examples dealing with large deformations will show the improved coarse mesh accuracy in space and time of the advocated approach. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Computational resources can be used more efficiently by introducing reduced-order models, instead of solving large systems of equations of the original model. In this contribution, the Krylov subspace method, a reduced-order modeling method, is studied and compared to the modal decomposition for a rubber wheel model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Explicit time integration has proven to be highly suitable for the simulation of very fast processes and highly nonlinear applications. As is well known the time integration algorithm is only stable if the Courant-Friedrichs-Lewy criterion is fulfilled leading usually to very small time step sizes. As a result the efficiency of the time integration algorithm is dictated by the computational time of element operations. In structural mechanics low order finite elements are attractive due to their efficiency but introduce artificial stiffness effects. To resolve the so-called locking effects a transient description - suitable for the solution in the context of explicit time integration - of the method of enhanced assumed strains (EAS) is formulated utilizing a generalization of the method of incompatible modes (IM). The element routines are computationally realised applying symbolic programming. The functionality and achieved efficiency are demonstrated on a numeric example. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]