Aerospace systems are built up from many individual parts, e.g., using screws or rivets. At the joints, the components never slide completely over each other. On the other hand, the surfaces do not stick completely either. This is directly related to the fact that real technical surfaces have a topography with shape deviations, waviness, and roughness. As a result, even under high squeezing forces, the actual contact area accounts for only a small fraction of the apparent contact area, and the pressure distribution is highly non-uniform. When vibrations occur, parts of the contact area slide locally on each other while the contact is still in a macroscopic stick state. This state is also referred to as partial sliding or micro-slip. Damping due to micro-slip cannot be predicted using the methods available today.
We develop methods to make damping predictable even in the case of micro-slip. The challenge: Local sliding distances are often only in the sub-micrometer range, whereas component vibration is in the range of several millimeters. We are developing suitable multi-scale methods for this challenge. The structural dynamics of the components are described using a finite element model, while the contact mechanics are described using a boundary element model. This means that a relatively coarse finite element mesh is sufficient, both at the contact interface and inside. In the boundary element model, the actual contact topography is resolved with sufficient precision. The two submodels are coupled by means of compatibility and equilibrium conditions. Using special algorithms, the handling of contact conditions is numerically robust and efficient. Compared to conventional, full finite element analysis, the computational effort is reduced by several orders of magnitude. Only with this reduced effort, scenarios with multiple or larger contact interfaces become computationally feasible and still open, fundamental research questions can be addressed:
- Which length scales of the technical surface (shape deviation, waviness, roughness) must be resolved in order to accurately predict damping?
- How do uncertainties in the alignment of contact partners, material properties, and the manufacturing process affect structural dynamics?
- Can targeted modifications to the shape or waviness have positive effects on the dynamics?
The basis for contact models is the measurement of friction force-displacement curves for given material samples. However, the measuring devices (tribometers) available today are only suitable for larger sliding distances and full-surface sliding (gross slip). With the “Black Metal Tribometer” developed by us, we can record force-displacement relations for both normal contact and friction (tangential to the surface) with milli-Newton and nanometer resolution, enabling us to investigate micro-slip. For comparison: a human hair is approximately 60 micrometers thick. In addition to state-of-the-art measurement equipment, the key to this precision is the play-free and friction-less guidance of movement thanks to flexures.
Selected publications
- Linder, H. D., Gross, J., & Krack, M. (2025). A coupled FE-BE multi-scale method for the dynamics of jointed structures. https://arxiv.org/abs/2501.12833
- Fochler, D., Schwarz, S., Kohlmann, L., & Krack, M. (2025). The Black Metal Tribometer: High-resolution measurement of normal load-indentation curves and partial slip hysteresis cycles. Tribology International, 206, 110560. https://doi.org/10.1016/j.triboint.2025.110560
Malte Krack
Prof. Dr.-Ing.Head of Structural Mechanics / Dynamics Group