24th International Colloquium Tribology - January 2024 265 Modeling of Shape Deviations for the Development of Predictive Models of TEHD Contacts Klara Feile 1* , Marcel Bartz 1 , Sandro Wartzack 1 1 Friedrich-Alexander-Universität Erlangen-Nürnberg, Faculty of Engineering, Department of Mechanical Engineering, Engineering Design, Martensstraße 9, 91058 Erlangen, Germany * Corresponding author: feile@mf k.fau.de 1. 1 Introduction The reduction of frictional losses in lubricated contacts of machine elements provides a significant contribution towards the development of energy-efficient and wear-resistant technical products and thus to the preservation of resources [1]. Manufacturing-related shape deviations, which are e.g. caused by tool vibrations [2], have a significant influence on the film formation in elastohydrodynamic (EHD) contacts, synonymous with influencing the friction and wear behavior [3,4]. A numerical consideration of shape deviations within the calculation of contact pressures and lubricant film heights in thermo-elastohydrodynamic (TEHD) contacts is complex, time-consuming and therefore not application-oriented. An approach for a comparatively simple consideration is, e.g., the extension of the widely used analytical approximation equations to determine the central and minimum lubricant film heights in EHD contacts developed by Dowson/ Higginson [5,6] and further evolved by other authors [7]. Due to additional correction factors, it is possible to consider different boundary conditions regarding thermal effects, fluid behavior and surface deviations [7]. Kumar et al. [8] developed a correction factor for 2D line contacts depending on the mean square surface roughness to extend the approximation equations of Dowson/ Higginson. However, this approach assumes a constant wavelength and neglects transient effects. The central and minimum lubricant film heights of elliptical contacts considering stochastic surface roughness can be approximated with the correction factors of Masjedi and Khonsari [9]. To date, there are no known research results regarding comprehensive, simple predictive models, such as correction factors, to complement established analytical approximation equations with respect to the consideration of manufacturing-related shape deviations of the surface topography in 2D and 3D TEHD contacts. The present work aims to provide the prerequisites to close this research gap. The development of predictive models requires the generation of comprehensive databases for 2D line and 3D point contacts, enabled by the application of simulative calculation methods. For this purpose, simulation models considering shape deviations have to be defined. Within the scope of this work, manufacturing-related shape deviations of 2 nd and 3 rd order of magnitude describing waviness and surface roughness were mathematically defined and integrated into TEHD simulation models. 2. Procedure and results In Figure-1, the conceptual approach of this work (dark blue) is shown in the context of further prospective research steps (light blue). Fig. 1. Overall conceptual approach. 2.1 Mathematical description of shape deviations Waviness and roughness were each mathematically modeled and superimposed using sinusoidal functions. Within the parametric description of the two orders of magnitude, in order to ensure a differentiated consideration of the shape deviations, the amplitudes- a 2 and a 3 as well as the wavelengths-λ 2 and λ 2 listed in Table 1 were selected as parameter limits. The limiting wavelengths were defined in accordance to [2]. The minimum and maximum amplitude of the manufacturing-induced wavi-ness was chosen according to [10]. The limits of the roughness amplitude caused by the tool cutting edge or feed, e.g. [2], were based on arithmetic mean roughness values-(R a ) between 1.6 and 6.3-µm which can be typically measured in this context. Table 1. Defined parameter limits of shape deviations. Order of magnitude a min a max λ min λ max 2 nd 10-µm 30-µm 100a 2 1000a 2 3 rd 2.5-µm 10-µm 10a 3 100a 3 Modeling of Shape Deviations for the Development of Predictive Models of TEHD Contacts 266 24th International Colloquium Tribology - January 2024 2.2 Integration into TEHD simulation model The mathematically defined shape deviations were integrated into the TriboFEM simulation tool, which allows 2D line and 3D point contacts to be simulated. The numerical modeling was based on a fully coupled finite element approach following-[11] and-[12] and a generalized, modified Reynolds equation-[13] in its weak form considering a mass conserving cavity model-[14]. The isothermal EHD equations were further coupled with thermodynamics, as described in detail in [15]. More-over, non-Newtonian fluid properties were considered by integrating rheological models according to Roelands-[16], Dowson/ Higginson-[17] and Eyring-[18]. The TEHD contacts were simulated transiently, with an initial smooth contact and shape deviations moving into the contact. By screening, the limits of the following parameter sampling were verified using 2D simulations of line contacts. In addition to the shape deviation limits listed in Table-1, the parameter values defined included limits regarding the temperature and fluid properties, a maximum elastohydrodynamic pressure of 4-GPa, a minimum and maximum slip-roll ratio of -2 and 2 as well as a minimum and maximum cumulative velocity of 10 -1 and 10 2 -m/ s, respectively. To ensure thermo-elastohydrodynamic full-film lubrication, fully filled lubrication gaps in the deviated contacts were ensured. 2.3 Data generation and development of predictive models Within the defined parameter limits, this work will be followed by the generation of test plans using Latin-Hypercube-Sampling to generate a database for both line and point contacts using the developed deviated TEHD models. By deriving correlations between input and output variables, models such as correction factors to extend the approximation equations of Dowson/ Higginson can be developed in order to predict the central and minimum lubricant film heights as well as the maximum contact pressure in contacts subject to manufacturing deviations. The prediction models depend on the amplitudes and wavelengths of the 2 nd and 3 rd order of magnitude shape deviations, which are easy to measure in reality. 3. Conclusion In this work, transient TEHD models have been developed to determine lubricant film heights, pressures, and maximum temperatures of line (2D) and point (3D) contacts with manufacturing-related shape deviations of 2 nd (waviness) and 3 rd order (roughness). The models represent a wide range of load, speed, geometry, lubricant and temperature parameters. Thus, a basis for the development of simple but comprehensive predictive models of deviated TEHD contacts was established. References [1] Woydt, M. Material efficiency through wear protection - The contribution of tribology for reducing CO2 emissions. Wear, 2022, 488-489. [2] DIN 4760: 1982-06, Form deviations, Concepts, Classification system. [3] Simon, V. Influence of machine tool setting pareters on EHD lubrication in hypoid gears. Mech. Mach. Theory, 2009, 44, 923-937. [4] Simon, V.V. Improved mixed elastohydrodynamic lubrication of hypoid gears by the optimization of manufacture parameters. Wear, 2019, 438-439. 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