Ulrich Becker

Dynamic simulation of electromechanical systems: from Maxwell's theory to common-rail diesel injection.

Abstract. This paper describes the state-of-the-art of dynamic simulation of electromechanical systems. Electromechanical systems can be split into electromagnetic and mechanical subsystems, which are described by Maxwells equations and by Newtons law, respectively. Since such systems contain moving parts, the concepts of Lorentz and Galilean relativity are briefly addressed. The laws of physics are formulated in terms of (partial) differential equations. Numerical methods ultimately aim at linear systems of equations, which can be solved efficiently on digital computers. The various discretization methods for performing this task are discussed. Special emphasis is placed on domain decomposition as a framework for the coupling of different numerical methods such as the finite element method and the boundary element method. The paper concludes with descriptions of some applications of industrial relevance: a high performance injection valve and an electromechanical relay.

Development of a submodel technique for the simulation of solder joint fatigue of electronic devices mounted within an assembled ECU.

The thermomechanical fatigue of solder joints on the system level is more complex to predict than on the board level. The damage of the solder joints of an electronic device in an ECU (Electronic Control Unit) depends on the thermal expansion mismatch between the materials of the device and the PCB (Printed Circuit Board), so called local mismatch, as well as on the global deformation of the PCB induced by the casing of the ECU. Therefore we have performed a transient sequentially coupled thermal-mechanical simulation on the system level. We used a two-step submodel approach. In the first step the electronic device with a PG-LQFP package was included in the entire ECU model, though the creep behaviour of its SnAgCu solder joints was omitted. In the second step the simulation of the solder joints fatigue was carried out with the help of the submodel. The submodel technique allowed to reduce the simulation model of a system to the electronic device model with a piece of the PCB underneath and at the same time maintain realistic PCB deformations and the realistic temperature field in the entire submodel during the temperature cycle. The simulation is validated with the temperature and strain gage measurement. The simulation predicts a loss of the life time by a factor of 0,5 for the solder joints in the ECU compared to the the board level tests.

The role of stress state and stress triaxiality in lifetime prediction of solder joints in different packages utilized in automotive electronics

This work presents an overview on the role of the stress state and stress Triaxiality Factor (TF, see Eq.1) in lifetime prediction of solder connections. According to various literature sources, the TF is one of the most important factors influencing initiation of ductile fracture [5, 16]. It is widely reported that lifetime of the ductile materials decreases under hydrostatic tension when combined with high TF-values. Recent investigations report that the compressive hydrostatic stress state combined with a high shearing load and low (or even zero) TF-values also contributes to failure [4,5]. Two package types, the Loss Free Packaging (LFPAK) and the Plastic Ball Grid Array (PBGA), were investigated by means of FE-simulation on Board- and System-Level, and presented damage prediction will be compared with experimental data. In the LFPAK and BGA solder joints the regimes of hydrostatic tension and compression during temperature cycles are evaluated and compared with distribution of equivalent von Mises stress, stress intensity (maximum shear stress) and triaxiality. The increments of damage related variables, inelastic strain and energy density, were modified in a postprocessing routine according to the current state of hydrostatic stress and TF for each time increment. Further, using a simplified simulation approach, the path of the crack propagation was calculated according to the distribution of the modified and non-modified inelastic strain. It is shown that when including multiaxial effects by modification of damage related variables a better correlation between calculated and experimentally observed crack path is achieved.