24th International Colloquium Tribology - January 2024 111 Thermal-Elasto-Plastic Hydrodynamic Contact Between Rough Surfaces M. J. Montenegro Cortez 1 , P. Correia Romio 1 , C. M. da Costa Gomes Fernandes 1 , P. M. Teixeira Marques 2 , S. Portron 2 , J. H. O. Seabra 1 1 Universidade do Porto, Faculdade de Engenharia, Departamento de Engenharia Mecânica, Porto, Portugal, 2 INEGI - Universidade do Porto, Unidade de Tribologia Vibrações e Manutenç-o Industrial, Porto, Portugal 1. Introduction Machine elements often operate under a wide range of conditions, leading to significant variations in interfacial friction due to changes in the lubrication regime. The Stribeck curve provides a comprehensive overview of friction variance across the boundary, mixed, and full-film lubrication [1]. This study used a commercial ISO VG150 polyalphaolefin gear oil in friction measurements to determine the influence of the temperature, Slide-to-Roll Ratio (SRR), and surface roughness on the Stribeck curve. It was observed that all three factors influence the coefficient of friction (CoF) and the lubrication regime. It was observed that the temperature does not significantly impact the lubrication regime when keeping the remaining factors constant, but the surface roughness and SRR do. Using the Stribeck curves resulting from the Ball-on-Disc friction tests and the roughness parameters obtained from the surface roughness assessment, a new parameter was proposed to evaluate the influence of these factors on the Stribeck curve in opposition to the traditional Hersey number [2]. 2. Materials and Methods The Stribeck curves presented in this study were obtained using an EHD2 Ball-on-Disc apparatus (PCS Instruments, England, 2014). One chose a commercial ISO VG150 polyalphaolefin oil for this evaluation, with properties summarized in Table 1 [2]. The balls (19.05 mm diameter) and discs are made of 100Cr6 steel with a measured hardness of 820-HV. For discs and balls, two different isotropic surfaces were chosen, with average roughness (Ra) of 0.02 mm and 0.30 mm, which allows three different roughness combinations (0.02-mm, 0.16-mm and 0.30 mm). The roughnesses were acquired using 3D Optical Profilometer equipment (Bruker NPFLEXTM, Germany, 2013), with acquisitions before and after each test. For this campaign, two different SRRs were applied (0.5 and 1) and three oil temperatures (65-°C, 80-°C and 120-°C). The entrainment velocity ranged between 50- mm/ s and 2500- mm/ s, while the applied load was kept constant and equal to 50 N. Table 2 summarizes the whole campaign based on a factorial Design of Experiments. 3. Stribeck curve results Figure 1 presents the Stribeck curves from the experimental campaign using the Hersey (H) number, Eq. (1), for the horizontal axis. The H number aims to distinguish the three lubrication regimes, promoting a better distribution of the curves. However, it becomes evident from this analysis that the parameter used does not allow a complete differentiation between boundary, mixed, and full-film lubrication. (1) Where, v e is the entrainment velocity in m/ s; h is the viscosity in Pa s; R x is the equivalent radius of curvature in m; and F is the normal load in N. Table 1: ISO VG150 polyalphaolefin oil properties Property Unit Method Value Density @ 27-°C kg m -3 ASTM D 4052 849.8 Thermal expansion °C-1 - 7.53 3 10 -4 Viscosity @ 65-°C Pa s ASTM D 2983 0.0457 Viscosity @ 80-°C Pa s ASTM D 2983 0.0282 Viscosity @ 120-°C Pa s ASTM D 2983 0.0101 Viscosity Index / ASTM D 2270 150 Piezoviscosity @ 65-°C Pa -1 Gold 1.26 3 10 -8 Piezoviscosity @ 80-°C Pa -1 Gold 1.19 3 10 -8 Piezoviscosity @ 120-°C Pa -1 Gold 1.04 3 10 -8 Table 2: Stribeck curves campaign Test ID Roughness [mm] * Temperature [°C] SRR 1 0.02 65 0.5 2 0.02 80 1 3 0.02 120 0.5 4 0.16 65 1 5 0.16 80 0.5 6 0.16 120 1 7 0.30 65 0.5 8 0.30 80 1 9 0.30 120 0.5 * Composite roughness from disc and ball roughness combination 112 24th International Colloquium Tribology - January 2024 Thermal-Elasto-Plastic Hydrodynamic Contact Between Rough Surfaces On the other hand, Figure 2 presents the CoF curves using the proposed dimensionless New Parameter (NP), calculated with Eq. (2) and its constants in Eqs. (3) to (7) [2]. (2) (3) (4) (5) (6) (7) Where, E 9 is the Equivalent Young Modulus in Pa; α Gold is the piezoviscosity in Pa-1; is the composite reduced peak height roughness obtained from the surfaces after the friction tests; and α is a lubricant-dependent exponent, equal to 0.40 at 65-ºC, 0.39 at 80-ºC, and 0.37 at 120-ºC [2]. Figure 1: Stribeck curves with Hersey parameter Figure 2: Stribeck curves with New Parameter (NP) Based on Figure 2, the following limits are proposed to separate the lubrication regimes: NP > 0.15 for full-film, 0.015 < NP < 0.15 for mixed, and NP < 0.015 for boundary. The only exception in this approach is the test condition 8. A practical result from this analysis is that the CoF in the mixed lubrication regime can be estimated as a function of NP, as indicated in Eq. (8). The constants used in Eq. (8) are oil-dependent and valid for the ISO VG150 polyalphaolefin gear oil utilized in this study. (8) 4. Thermal-Elasto-Plastic Hydrodynamic lubrication model (TEPH) Finally, a TEPH model [3] was used to analyze the contact between rough surfaces under full-film, mixed, and boundary lubrication conditions. The CoF predictions by the TEPH model were correlated with the experimental Stribeck curves, as illustrated in Figure 3 for test condition 1. Figure 3: Stribeck curve test 1 versus TEPH model prediction 5. Conclusion Using Stribeck curves from the friction tests and the roughness parameters obtained from the surface roughness measurements after the frictional tests, a new parameter (NP) was proposed to evaluate the Stribeck curve lubrication regimes in a more practical way. A crucial aspect of this approach was using the roughness parameters after the tests to account for the surface modifications during the CoF measurements. Complementary, a numerical model was validated using the experimental results from this study. 6. Acknowledgements National Funds through Fundaç-o para a Ciência e a Tecnologia (FCT) under the PhD grant 2021.05562.BD; - LAETA under project UID/ 50022/ 2020. References [1] Dong Zhu, Jiaxu Wang and Q. Jane Wang. On the Stribeck Curves for Lubricated Counterformal Contacts of Rough Surfaces. ASME. J. Tribol. 2015; 137(2), 021501. DOI: https: / / doi.org/ 10.1115/ 1.4028881 [2] Maria J. M. Cortez, Thermal-Elasto-Plastic-Hydrodynamic Contact Between Rough Surfaces: Influence of Surface Roughness, MSc Dissertation, Engineering Faculty, University of Porto, Portugal, July 2023. [3] P. C. Romio, P. M. T. Marques, C. M. C. G. Fernandes and J. H. O. Seabra, A Simplified Thermal Plasto-Elastohydrodynamic Lubrication Model for Circular Contact With Real Surface Roughness, J. Tribol. Dec 2023, 145(12): 124102. DOI: https: / / doi.org/ 10.1115/ 1.4062898