Weight Optimization of Transmission Housings

The Finite Element Analysis (FEA) of many solid structures like transmission housings, combustion engines, or brake systems have to take contact into account for stress simulation due to a prestressed state by bolting, gasket sealing, or braking pressure. Beyond stress simulation, all kinds of vibrational behaviour like eigenfrequencies and modes, up to sound radiation from the surface of the structures are very important to be calculated for prestressed structures. Due to developing low noise products, an optimization procedure has to be applied on top of stress and dynamic analysis to reduce the sound radiation while keeping stress values below certain limits. The path to achieve sound and stress optimized products has to combine stress analysis, dynamic analysis, and shape optimization of the structural surface in one simulation process. While contact in stress analysis is a nonlinear phenomenon, vibrational analyses methods are typically linear, which requires a practical linearization of the contact state after stress analysis to continue with the dynamic analysis. The linearization will be based on the contact pressure calculated during stress analysis. In this way, stress analysis, linearization, and sound radiation analysis (e.g. in frequency domain) can be combined in one optimization loop, where the shape of the structural surface is modified to reduce sound radiation and to keep the stress values (e.g. principal stresses) below given limits. One effective method to optimize shapes is a freeform optimization using a non-parametric approach, which also allows to control the weight of the structure. The paper will use an industrial example of a transmission housing to demonstrate the above outlined optimization procedure. Key results of stress analysis and sound radiation analysis as well as from the optimization are presented. In addition, the computation times are analysed to demonstrate the feasibility of the described process for practical applications in research and industry. All simulations will be performed with the commercial FEA software PERMAS, which beside contact analysis also supports the linearization process and the sound radiation analysis. In addition, it also integrates optimization solvers in order to perform all simulation steps of this project with one software in one single computation.