Unlike the surface roughness or waviness, the wavelength of height waviness is larger than the pin size, which makes it inconspicuous as the pin is expected to self-align to the disk surface profile. However, a recent study [9] reported waviness profile impacted friction and wear behavior under slurry lubricated conditions. It was found that the surface deviations can significantly affect the friction coefficient. As the height waviness is inevitable for all experiments, it is necessary to understand how it would influence the frictional performance. In this work, a pin-on-disk set-up was used to investigate the effect of height waviness on friction between surfaces in conformal contact. We vary the height waviness to test the friction reduction efficiency at different speed. Aus Wissenschaft und Forschung 4 Tribologie + Schmierungstechnik · 70. Jahrgang · eOnly Sonderausgabe 2/ 2023 DOI 10.24053/ TuS-2023-0040 1 Introduction Engineering applications involving frictional activities can cause energy consumption and CO 2 emissions, and bring challenges for achieving sustainability and environmental goals [1]. One of the effective approaches to reduce friction-induced energy losses is altering surface contacts. Literature shows how the surface roughness [2,3], coatings [4] or texturing [5,6] can dramatically influence the frictional behavior of the contacting surfaces. However, controlling the surface contacting condition is always a difficulty as it’s affected not only by the inherent characteristic of surface profile, but also by the mounting error or deformations, especially for the conformal contact set-ups. For a common pin-on-disk tribo-system as shown in Figure 1, when the disk rotates around the spindle, the pin will vibrate perpendicular to the contacting surface. The height waviness of pin vibration reflects the real height form of disk surface during sliding. It may be caused by the height profile (Figure 1b), misalignment (Figure 1c) and deformation (Figure 1d). It should be emphasized that the height waviness under consideration in this paper are the measured results of the fluctuation of height which is the mixture of inherent surface profile, misalignment of surfaces and the warpage due to deformation. It’s different from the surface waviness defined by standards, which is larger than the roughness sampling length but small, short, and regular enough that they are not considered flatness defects and may result from such factors as machine or work deflections, vibration, or chatter [7,8]. Effect of height waviness on the friction behavior of 100Cr6 steel under mixed or hydrodynamic lubrication Hongzhi Yue, Gerda Vaitkunaite, Yulong Li, Johannes Schneider, Christian Greiner, Peter Gumbsch* Friction can indeed have a significant impact on energy consumption and CO 2 emissions. Height waviness changes depending on the fabrication, mounting or deformation due to high load. This can be an important factor in determining the friction performance of many engineering systems that involve contact and sliding between two surfaces. However, the relation between height waviness and friction remains for a further investigation. In this work, a pin-on-disk setup was used to investigate the effect of height waviness on friction between surfaces in conformal contact. The tribological system was lubricated with FVA2 oil with the contact load of 150 N. Friction was measured at different speed steps ranging from 0.04 to 2 m/ s for acquiring the Stribeck curve. Screws on the back of the disk were used to control the height waviness of the disk surface. The results show up to 60 % friction reduction for high waviness surface. The findings of this study suggest a potential that the reduction in friction for high waviness surfaces could be exploited to enhance the performance of engineering systems. Keywords Mixed or Hydrodynamic Lubrication, Stribeck Curve, Height waviniess, Friction Abstract * Dr. Hongzhi Yue Dr. Gerda Vaitkunaite Mr. Yulong Li Dr.-Ing. Johannes Schneider Prof. Dr. Christian Greiner Prof. Dr. Peter Gumbsch Institute for Applied Materials - Reliability and Microstructure (IAM-ZM) and MicroTribology Center µTC, Karlsruhe Institute of Technology (KIT), Karlsruhe, 76131, Germany 2 Experiments The rotational experiments were conducted in a tribometer (Plint TE-92 HS, Phoenix Tribology, Kingsclere, UK) using a pinon-disk set-up. The cylinder pins of 8 mm diameter were made from 100Cr6 with an average hardness of ~700 HV. The 70 mm diameter disks with 7 mm thickness were also made out of 100Cr6 with an average hardness of ~ 800 HV. The averaged sample roughness before the tests was Ra = 0.2 µm and Ra = 0.07 µm for the pin and disk samples, respectively, measured by a stylus profilometer (Hommel T8000, Jenoptic, Jena, Germany). As shown in Figure 2a, the pin sample was fixed on a self-aligned holder, while the disk sample was mounted on the rotating spindle. Three screws were used to adjust the height waviness. The height profile of the disk was measured using a capacity distance sensor (AW 210-52-1, E+H Metrology, Karlsruhe, Germany) before the test. During the test, a normal load of 150 N was applied from the pin side. The disk started rotation from 2 m/ s and gradually decreased to 0.04 m/ s in 12 steps for each speed ramp. Five repetitions were conducted for the speed ramps and only the last three ramps were calculated to avoid the running-in effects. Each speed step last for 5 mins for averaging friction using 10 Hz sampling rate. The capacity distance sensor was also used to measure the pin height variation in-situ (Figure 2b). After each speed step, the pin height variation in three revolutions were recorded at a high sampling rate triggered by the encoder of 2048 ppr. The z signal of encoder was used to mark the zero point of the disk. The experiments were conducted at oil temperature of 50 °C. An additive-free FVA 2 oil was used in the test. The oil viscosity value was 0.024 Pa·s at 50 °C, measured by a rheometer (DHR series, TA instruments, New Castle, USA) at a shearing rate of 500 s-1. The oil was supplied to merge the contact surface, with a constant oil flow rate of 5 ml/ min during whole test. Each test was repeated 3 times with new samples and fresh oil in the system. 3 Results and discussions 3.1. Height waviness due to disk alignment The typical disk height waviness profiles of disk surfaces are as shown in Figure 3. Different disk height waviness was built by adjusting the screws, with peak-to-peak amplitude ranging from 15 µm to 45 µm. The profiles exhibit a quasi-sinusoidal form, but distortions can be observed especially for the low waviness profile. The distortions mainly occurred at screw support position, Aus Wissenschaft und Forschung 5 Tribologie + Schmierungstechnik · 70. Jahrgang · eOnly Sonderausgabe 2/ 2023 DOI 10.24053/ TuS-2023-0040 Figure 1: Schematic representation of the pin-on-disk set-up (a) and the potential sources for height waviness (b, c, d). Figure 2: Schematic representation of height waviness measurement. (a) Pre-test, (b) In-situ. Figure 3: Pre-test height waviness profile plot against rotation angle. Aus Wissenschaft und Forschung 6 Tribologie + Schmierungstechnik · 70. Jahrgang · eOnly Sonderausgabe 2/ 2023 DOI 10.24053/ TuS-2023-0040 which suggests the height waviness is a result of disk misalignment and disk warpage due to screw force. Obviously, the height profile of the reference disk also shows a certain height waviness as the results of the manufacturing flatness error and mounting error. 3.2. Height waviness in-situ Surface warpage occurs when the contacting part is subjected to force resulted from mounting, loading or sliding. In this study, the normal load for the experiment is 150 N. As the disk was supported by 3 screws on the back, disk warpage was observed when pin load was applied on the contacting surfaces. Figure 4 shows the comparison of pre-test steady state height waviness profile and the in-situ height variation at 0.05 m/ s for a 30 µm peak-to-peak amplitude test. The highest deformation of up to 7 µm was observed between the supporting screws, while the height at screw position remains the same. Similar behavior was observed for all tests. Figure 5 shows the height waviness for the reference test (Figure 5). In this case the highest waviness difference is about 4 µm. The disk warpage might be different depending on the initial waviness profile and supporting location. It should be noticed, in this study, the in-situ height waviness was acquired indirectly by measuring the vibration of pin and supporting parts. Hence, compared to the height waviness of the real disk profile, there might be errors related to the surface contact, such as oil gap height variation. 3.3. Friction behavior Figure 6 demonstrates the frictional performance of tests for different disk height waviness. The reference disk had the highest friction coefficients. The transition points of hydrodynamic and mixed lubrication are similar for all the disks at around 0.15 to 0.2 m/ s. However, the friction values vary for different height waviness. The 30 µm test has the best friction behavior, with a friction reduction up to 60 % at 0.05 m/ s. The friction results of 45 µm height waviness is slightly higher but very close to the 30 µm test. The friction for 15 µm waviness is even higher than 45 µm test but still much lower than the reference test. Figure 4: Comparison of Pre-test and in-situ profile at 0.05 m/ s for a 30 µm height waviness test. Figure 5: Comparison of Pre-test and in-situ profile at 0.05 m/ s for a reference test. Figure 6: Friction coefficient for different height waviness plotted against sliding speed. Figure 7 gives the variations of the efficiency of friction reduction against sliding speed. The efficiency of friction reduction was calculated according to the equation: efficiency = (μ μ reference ) / μ reference × 100 %. Highest friction reduction can be observed for 30 µm test at whole speed range, with an average efficiency of 54 %. In the hydrodynamic lubrication regime (speed > 0.2 m/ s), the efficiency decreases with increasing speed. Several factors might be responsible for this behavior (Figure 8). As the pin and its support parts are in vibration with the height waviness, the inertia or damping may play an important role, leading to variations in contacting pressure (Figure 8a). Second, the contacting surfaces speed steps ranging from 0.04 to 2 m/ s. Different height waviness was built by adjusting the screws behind the disk. Surface warpage up to 7 µm was observed during sliding with the contact load of 150 N. The results show larger height waviness is beneficial for friction reduction. Up to 60 % friction reduction was achieved in for tests with 30 µm height waviness. Acknowledgements The authors would like to acknowledge funding by the German Research Foundation (DFG) Project Number 438122912. References [1] Holmberg, K. and Erdemir, A., 2017. Influence of tribology on global energy consumption, costs and emissions. Friction, 5, pp.263-284. [2] Bhushan B. Introduction to tribology. John Wiley & Sons. 2013. [3] Chen, L., Liu, Z., Wang, X., Wang, Q. and Liang, X., 2020. Effects of surface roughness parameters on tribolo- Aus Wissenschaft und Forschung 7 Tribologie + Schmierungstechnik · 70. Jahrgang · eOnly Sonderausgabe 2/ 2023 DOI 10.24053/ TuS-2023-0040 Figure 7: Efficiency of friction reduction for different height waviness plotted against sliding speed. Figure 8: Schematic representation of potential effect of height waviness on friction. may move close to or far away from each other, resulting in gap height variation (Figure 8b). Meanwhile, the uphill or downhill movement might affect the inclination building up (Figure 8c). Obviously, all the factors might be detrimental or beneficial during rotation. There is not much literature about this behavior. Some studies reported the rotating cycle-based friction fluctuation [10,11]. Li et al. [9] reported a “hill” along the sliding track can lead to significant increase the friction compared to the valley area. In this study, the large height waviness disks bring friction reduction comparing to the low waviness references. It should be noticed that the friction value in this study was an average of the whole height waviness revolution. Hence, it’s possible that the waviness brings both hills and valleys, which results in both negative and positive effects. As long as the positive effects are dominant, friction reduction can be achieved. 4 Conclusions The effect of height waviness on friction was investigated using a pin-on-disk set-up under lubricated condition. The frictional performance was recorded at different Engineers, An American National Standard; 2002. p. 1- 98. 2002. [8] Iso 13565-2. Geometrical Product Specifications (GPS) - Surface texture: profile method; Surfaces having stratified functional properties - Part 2: height characterization using the linear material ratio curve. 1996. [9] Li, Y., Garabedian, N., Schneider, J. and Greiner, C., 2023. Waviness affects friction and abrasive wear. Tribology Letters, 71(2), p.64. [10] Godfrey, D., 1995. Friction oscillations with a pin-ondisc tribometer. Tribology International, 28(2), pp.119- 126. [11] Prost, J., Boidi, G., Lebersorger, T., Varga, M. and Vorlaufer, G., 2022. Comprehensive review of tribometer dynamics-Cycle-based data analysis and visualization. Friction, pp.1-15. Aus Wissenschaft und Forschung 8 Tribologie + Schmierungstechnik · 70. Jahrgang · eOnly Sonderausgabe 2/ 2023 DOI 10.24053/ TuS-2023-0040 gical performance for micro-textured eutectic aluminum- silicon alloy. Journal of Tribology, 142(2), p.021702. [4] Cheng, Y.H., Browne, T., Heckerman, B. and Meletis, E.I., 2010. Mechanical and tribological properties of nanocomposite TiSiN coatings. Surface and Coatings Technology, 204(14), pp.2123-2129. [5] Rosenkranz, A., Grützmacher, P.G., Gachot, C. and Costa, H.L., 2019. Surface texturing in machine elements − a critical discussion for rolling and sliding contacts. Advanced Engineering Materials, 21(8), p.1900194. [6] Gropper, D., Wang, L. and Harvey, T.J., 2016. Hydrodynamic lubrication of textured surfaces: A review of modeling techniques and key findings. Tribology international, 94, pp.509-529. [7] Standard A. B46. 1. Surface Texture, surface roughness, waviness and lay. The American Society of Mechanical \ Gesundheit \ schaft \ Linguisti schaft \ Slawisti \ Sport \ Gesun wissenschaft \ L wissenschaft \ philologie \ Spo Fremdsprachend \ VWL \ Maschi schaften \ Sozi Bauwesen \ Fre