1 Introduction In common products like a tail gate of a car tuned mass dampers are used to reduce noise causing vibrations. They are often heavy, weighing around 1.5 kg. The aim of this project is to replace those heavy dampers with new damping elements. The elements will use friction to dissipate energy. Experiments were carried out to compare materials with suitable damping properties. Then FEM-simulations are carried out to simulate the damping behaviour. The simulations should represent the damping properties of a suitable material to later use them for simulation and design of whole structures of cars. For the experimental part of this paper, different material combinations were compared in terms of their damping ability. Materials that are suitable must have low wear but still dissipate energy. The energy wear approach [1] is used to evaluate this property. Previous papers that reported on the wear behaviour in correlation with the dissipated energy often investigate the behaviour of different coatings [2-6]. Some also investigate a steel- [4-7] or titanium-alloy [6-10]. In these papers the counter body is alumina or a self-mating contact. In the application of the tail gate the counter body could be steel. That is why in this paper, steel was tested against a nickel alloy, a lead-free brass alloy, and an anodised aluminium alloy. In the simulative part of the paper, a numerical model is developed based on the experiments. This model provides energy dissipation through numerical calculation. In a FE environment, intermediate elements are placed in a joint, which are implemented with the material law found from the experiments. This can help to consider the damping properties of a joint much earlier in the design process. For the application it is planned to produce bolted joints out of a material that has good damping behaviour. A bolted joint offers the advantage that the desired contact pressure can be set precisely. The FE model would allow to search for the ideal position for energy dissipation in a complex structure. 2 Experiment 2.1 Test setup For the experiments, a self-built fretting tester, shown in Figure 1, is used. It moves a sample, which is mounted on a ball-bearing stage with adjustable frequency and amplitude, with a shaker. The amplitude is measured via Science and Research 5 Tribologie + Schmierungstechnik · volume 71 · issue 4/ 2024 DOI 10.24053/ TuS-2024-0018 Damping behaviour of different materials in fretting contact - Experiment and simulation using finite element method Marion Kugler, Silas Rödiger, Carsten Könke, Martin Dienwiebel* submitted: 18.09.2023 accepted: 27.09.2024 (peer-review) Presented at the GfT Conference 2023 The fretting behaviour of three different material pairings was investigated, to compare their suitability for the application as a damping-element. The transition from partial to gross slip occurs at different amplitudes and friction forces depending on the pairing. The experimental data were used to derive a material law that can be implemented in thin film elements in a finite element environment. The simulation model can be adapted to different materials. Keywords fretting, energy wear approach, friction, damping, finite element method (FEM), numerical model Abstract * M.Sc. Marion Kugler (corresponding Author) Fraunhofer-Institute for Mechanics of Materials, MicroTribology Center µTC, 79108 Freiburg M.Sc. Silas Rödiger Weimar Institute for Material Research and Testing at Bauhaus-University Weimar (MFPA Weimar), 99423 Weimar Prof. Dr.-Ing. habil. Carsten Könke Weimar Institute for Material Research and Testing at Bauhaus-University Weimar (MFPA Weimar), 99423 Weimar Institute of Structural Mechanics (ISM), Bauhaus-University Weimar, 99423 Weimar Prof. Dr. rer. nat. Martin Dienwiebel Fraunhofer-Institute for Mechanics of Materials, MicroTribology Center µTC, 79108 Freiburg; Karlsruhe Institute for Technology, Institute for Applied Materials - Reliability and Microstructure (IAM-ZM), 76131 Karlsruhe the beginning of all experiments. The experiments are conducted with different frequencies f, normal forces F N and amplitudes a. The parameters used for the experiments, can be seen in Table 1. An amplitude in the grossslip regime was chosen for all experiment. During the experiments, the fretting hysteresis of two consecutive cycles are recorded at regular intervals, usually every 10 s. From these hysteresis, the dissipated energy E Diss was then calculated [5]. The experiments were interrupted after a different number of cycles (see last column of Table 1), the samples with holders were removed, and the wear volume was determined by white light interferometry before the experiment was continued. On both samples the volume of removed and added material is measured. To calculate the wear volume of the whole system V W (System) the two wear volumes are summed up while the volume of the material added is subtracted from that result. 2.2 Materials The spherical segments (TIS Wälzkörpertechnologie GmbH, Gautingen) were made of 100Cr6 and had diameters of 38, 50, and 70 mm. A nickel alloy, a brass alloy, and an anodised aluminium alloy is tested. The counter-bodies were grounded for final finishing. The surface roughness and hardness is summarised in Table 2. Science and Research 6 Tribologie + Schmierungstechnik · volume 71 · issue 4/ 2024 DOI 10.24053/ TuS-2024-0018 a glass scale and controlled during the test. The counter sample is fixed in the head of the device. Here, the frictional force is measured with a piezoelectric sensor. The head can be adjusted in height and thus apply a different normal force. The normal force is controlled during the experiment and thus kept as constant as possible. The contact geometry consists of a flat sample in contact with a spherical segment. Depending on the material, the sphere diameter was chosen in such a way that a Hertzian pressure of 325 MPa (F N = 20 N) is obtained at head with F R measurement ball-bearing stage displacement measurement direction of movement sample bottom sample top F N Figure 1: Setup of the fretting test rig. Table 1: Parameters for all experiments. First letter indicates the material combination. A: anodised aluminium-steel, I: Inconel-steel, B: Brass-steel. Material 100Cr6 Inconel 718 CuZn37Mn3Al2Si AlSi1MgCuMn (anodised) Table 2: Hardness and Roughness of the samples. Hardness 768 HV5 426 HV5 209 HV5 450 HV (converted from HM) R a [nm] 21 52 127 470 2.3 Results For a frequency of 30 Hz and a normal force of 20 N, the transition from partial to gross slip is considered for the different materials. The hysteresis changes its shape during the transition. In the partial slip range, the hysteresis is an ellipse and after the transition, it is the typical parallelogram-shaped friction loop. To define the boundary between the regimes, the loss factor A can be calculated. This is the coefficient of dissipated energy and mechanical work. Theoretically, the transition to gross slip occurs at a value of A = 0.2 [11]. In Figure 2, the loss factor is plotted against the displacement amplitude for the three materials against steel. The transition-amplitude from partial to gross slip can be determined. For brass and Inconel, the transition occurs at an amplitude of approximately 8 µm, while for the anodised aluminium alloy, the amplitude is 13 µm. The different hystereses obtained in these experiments are later used to identify boundary forces and stiffnesses for the implementation in the FE-Model. In further experiments, the dissipated energy and the corresponding wear volumes were determined for different test durations. The evaluation follows the energy wear approach [1]. The materials show different wear behaviours (Figure 3). The wear is not distributed evenly on the two counter bodies. In most case one mating material shows a significantly higher wear. For example, the steel does not wear when run against brass. Indeed, there is material transferred to the steel surface. The opposite is true for the experiments with Inconel. Here, only the steel wears, and some material transfer accumulates on the Inconel. In the experiment with the anodised aluminium samples, the steel wears less than against the Inconel samples. Both material transfer and wear occur on the aluminium sample. There is a huge scattering of the datapoints in Figure 3. To better understand the scattering, comparison of Figure 3 and Figure 4 is needed. In Figure 3 all the experiments are plotted, but in Figure 4 only the experiments with the same parameters (f = 30 Hz, F N = 20 N, a = 30 µm) are displayed. The scattering of the dissipated energy over the number of cycles (Figure 3 and 4 right) can be explained by the variation in normal force and amplitude of the experiments. Taking the energy wear approach into account, one should expect that the wear volume should change in the same order of magnitude. Figure 4 left shows that even for experiments with the same parameters, surprisingly this is not the case. Further analysis of additional influencing factors is necessary. Nevertheless, the three material pairings can be compared to identify a suitable material for the application. When only the non-steel counter-bodies are compared, Science and Research 7 Tribologie + Schmierungstechnik · volume 71 · issue 4/ 2024 DOI 10.24053/ TuS-2024-0018 Figure 2: A-a diagram with transition from partial to gross slip at A = 0.2. Figure 3: Overview of the wear data form all experiments. Left: Wear volume of both counter bodies over the cumulated dissipated energy. Right: cumulated dissipated energy over the number of cycles. the constitutive model from an example hysteresis. The rheological model visualises the interaction of the components of the differential equation of motion when force is applied. The constitutive model consists of nonlinear stiffness and velocity-proportional components for energy dissipation. If the force is sufficient, F R is exceeded and the friction component according to Coulomb is added to the viscous damping component. The transition from partial-slip to gross-slip takes place with increasing energy dissipation. To adapt the simulation model for different friction materials, the parameters can be adjusted. The constitutive model is implemented in an interface element to transfer the energy dissipation of local damping effects in a joint to the vibration behaviour of a global structure. Science and Research 8 Tribologie + Schmierungstechnik · volume 71 · issue 4/ 2024 DOI 10.24053/ TuS-2024-0018 Inconel has the lowest wear volume and would thus be the most effective. The anodised aluminium is less effective, and the brass has the worst damping property when also considering wear. 3 Simulation 3.1 Parameter Identification for Constitutive Model To be able to represent the effects of joint damping, interface elements are implemented in the FE model with the constitutive model obtained from the experiments. Although no new material can be found there, in reality, this allows calculating energy dissipation numerically. Figure 5 shows the identification of the parameters for Figure 4: Data from experiments A1, A2, A3, I2, I5, M1, M2 with f = 30 Hz, F N = 20 N, a = 30 µm. Left: Wear volume of both counter bodies over the cumulated dissipated energy. Right: cumulated dissipated energy over the number of cycles. example hysteresis of experiments friction force in N relative displacement in μm rheological model equation of 1-DoF system in decay test Figure 5: Parameters from experiment for interface elements with constitutive model. 3.2 FEM-Modelling For the interface elements, thin-layer-elements (TLE) and zero-thickness-elements (ZTE) were compared in 3D structures [12]. With TLE, the large thickness-width ratio can lead to numerical problems, as the Jacobian determinant approaches 0 for d, i.e. the Jacobian matrix is no longer regular and can no longer be inverted. This is why ZTE are used [13]. These have no thickness. In the normal direction, the stiffness of a joint is many times higher compared to the tangential direction. In the normal direction, a pure linear-elastic behaviour can be assumed, in the tangential direction, the constitutive model found, which represents energy dissipation, is effective. The ZTE are integrated via contact connections such as bonding (the node of one component has the same displacement as the node of the other component). In the practical application of the bolted joint, it must be noted that over time the bolts exhibit settling behaviour when subjected to vibration. Large relative movements are needed to maximise dissipation. Low preload forces are needed, or other constructive ways must be found to make this possible. The FEM allows finding places of large relative displacements before manufacturing the part and thus considering the energy dissipation early in the development process. To validate the simulation model experiments and simulations of a Brake-Reuss-Beam will be conducted. Figure 6 shows the vibration modes of the simulated model. With the help of the Brake-Reuss-Beam [14], the question of whether the joint damping is also relevant for vibration modes in, which the vibration maxima do not occur in the joint, is investigated. The oscillating movements are the greatest for modes 1 and 2 within the joint, i.e. the potential for a relative movement is the highest. On the other hand, the oscillating movements for modes 3 and 4 are lowest within the joint. From the previous investigations, an amplitude-dependent damping factor is evident. This shows that at the maximal relative displacements the damping factor is the largest. In a construction the position with the greatest relative displacement can be identified using a simulation. Also the damping elements need to be designed in a way to allow for this. 4 Conclusion The fretting behaviour of three different material pairings is investigated. The transition from partial to gross slip occurs at different amplitudes and friction forces depending on the pairing. The wear volume of the material parings does not increase linearly with the cumulated dissipated energy as it would be expected according to the energy wear approach. For example, a reduced frequency leads to a decrease in the wear volume of the anodised aluminium. More investigations on the factors influencing the wear volume need to be done. Against Inconel only the steel wears of. The opposite behaviour can be observed for steel against the brass alloy. The experimental data, especially the friction hystereses, is used to derive a material law. This law can be implemented in thin-layer elements in a finite element environment. The simulation model can be adapted to different materials and can also simulate the transition from partial to gross slip regime. The model still needs to be validated by experiments with the Brake-Reuss-beam. Science and Research 9 Tribologie + Schmierungstechnik · volume 71 · issue 4/ 2024 DOI 10.24053/ TuS-2024-0018 mode 1 total deformation f=137,9 Hz mode 2 total deformation f=214,2 Hz mode 3 total deformation f=568,3 Hz mode 4 total deformation f=652,3 Hz Figure 6: Brake-Reuss-beam and his modes. [4] S. Fouvry, V. Fridrici, C. Langlade, P. Kapsa, L. Vincent, Tribology International 2006, 39, 1005. [5] S. Fouvry, P. Kapsa, H. Zahouani, L. Vincent, Wear 1997, 203-204, 393. [6] S. Fouvry, C. Paulin, T. Liskiewicz, Tribology International 2007, 40, 1428. [7] T. Liskiewicz, K. Kubiak, T. Comyn, Tribology International 2017, 108, 186. [8] R. S. Magaziner, V. K. Jain, S. Mall, Wear 2008, 264, 1002. [9] C. Mary, S. Fouvry, Wear 2007, 263, 444. [10] S. Fouvry, P. Duó, P. Perruchaut, Wear 2004, 257, 916. [11] S. Fouvry, P. Kapsa, L. Vincent, Wear 1995, 35. [12] S. Bograd, A. Schmidt, L. Gaul, Proceedings of IMAC XXVI: A Conference and Exposition on Structural Dynamics 2008. [13] J. Geisler, Numerische und experimentelle Untersuchungen zum dynamischen Verhalten von Strukturen mit Fügestellen, Dissertation, Friedrich-Alexander-Universität 2010. [14] P. Reuß, Dynamische Substrukturtechnik unter Berücksichtigung nichtlinearer Interfacekomponenten. Universität Stuttgart 2020. Science and Research 10 Tribologie + Schmierungstechnik · volume 71 · issue 4/ 2024 DOI 10.24053/ TuS-2024-0018 Further research must be done to investigate if enough energy per cycle can be dissipated for the real-life application and if such contact would maintain its dissipative properties for the lifetime of a whole car. For a better understanding of the fretting mechanism, investigations on the hardness and chemical composition of the third body can be done. Acknowledgement Funded by the German Federal Ministry for Economic Affairs and Climate Action (BMWK) under the “Technologietransfer-Programm Leichtbau” (TTP LB) FKZ 03LB2027D. Literatur [1] S. Fouvry, T. Liskiewicz, P. Kapsa, S. Hannel, E. Sauger, Wear 2003, 255, 287. [2] T. Liskiewicz, S. Fouvry, Tribology International 2005, 38, 69. [3] H. Mohrbacher, B. Blanpain, J. P. Celis, J. R. Roos, L. Stals, M. van Stappen, Wear 1995, 188, 130. \ Gesundheit \ schaft \ Linguisti schaft \ Slawisti \ Sport \ Gesun wissenschaft \ L wissenschaft \ philologie \ Spo Fremdsprachend \ VWL \ Maschi schaften \ Sozi Bauwesen \ Fre