23rd International Colloquium Tribology - January 2022 425 Preparation of measured engineering surfaces for digital twins in tribology Yuechang Wang Institute of Functional Surfaces, University of Leeds, Leeds, UK Corresponding author: y.wang1@leeds.ac.uk Abdullah Azam Institute of Functional Surfaces, University of Leeds, Leeds, UK Mark C.T Wilson Institute of Functional Surfaces, University of Leeds, Leeds, UK 1. Introduction Digital twins in tribology are precise, virtual copies to predict the tribologcial performance, e.g., friction, wear, and tribofilm formation of laboratory apparatus, machine components. or even engineering systems. Surface topography, evolving during the tribological processes, plays an essential role in building digital twins in tribology. Although measurement, characterization, and modeling of surface topography have been well studied, the application of surface topography in constructing digital twins in tribology is still rudimentary. Some published works only use several classic roughness parameters to incorporate the surface topography. Although many researchers report that measured surface topography is used, the necessary preparation of measured engineering surfaces is rarely mentioned. As yet there appears to be no general guidance on preparing measured engineering surfaces for digital twins in tribology. Therefore, the authors attempt to establish such a framework by the latest progress of surface modeling in this report. 2. Proposed framework The proposed framework consists of characterization, filtration and resampling, and reconstruction of rough surfaces. The three parts are not independent but related to each other. This framework aims to generate rough surfaces that contain the surface features of interest and are ready to use in further numerical models. 2.1 Characterization of rough surfaces Unlike other works on characterizing rough surfaces by various roughness parameters, the current study considers them based on the reconstruction requirements of rough surfaces. The recent work of Pérez-Ràfols and Almqvist provided a new technique to generate rough surfaces with a given surface height probability distribution (HPD) and power spectral density (PSD). Following their method, the current study proposes to use the HPD and PSD to characterize the measured rough surfaces. For the HPD, the empirical cumulative distribution function (CDF) with generalized Pareto distributions (GPDs) in the tails is used to estimate the CDF of measured surfaces. The Pareto tails can improve the smoothness of the distribution in the tails where data might be sparse. The PSD is directly calculated from the surface heigh matrix z by the following equation. (1) The S z is a real centrosymmetric matrix, which illustrates the double-sided power spectrum. 2.2 Filtration and resampling of rough surfaces The size and resolution of the measured rough surfaces are determined by the specific measurement equipment and corresponding measurement settings. Thus, the measured surface data usually cannot be directly input into numerical models of specific tribology systems. According to the specific application scenarios, the measured surfaces usually need to be filtered or decomposed to specific frequency ranges. Moreover, the measured surfaces usually have dense mesh grids, such as 1024×1024 points. Such grid sizes result in substantial computational cost in running numerical models of tribological problems. Therefore, after the filtration of measured surfaces, it is necessary to resample the surfaces to coarse grids while keeping the essential roughness features. The current work proposes a solution for resampling the filtered rough surfaces based on the characterization and reconstruction of rough surfaces. The HPD and PSD of the filtered rough surfaces are calculated. Then the PSD is resampled. The resampled PSD and the HPD are used 426 23rd International Colloquium Tribology - January 2022 Preparation of measured engineering surfaces for digital twins in tribology to reconstruct rough surfaces, which can be directly used in subsequent numerical simulations. 2.3 Reconstruction of rough surfaces The reconstruction procedures developed by Pérez-Ràfols and Almqvist are used. Random series following the estimated HPD of rough surfaces and the target PSD are the inputs of the reconstruction method. Then the simulated rough surface is iteratively updated to approach the desired HPD and PSD until the predetermined criteria are reached. Detailed descriptions of the reconstruction procedures can be seen in Ref [1]. In summary, the proposed framework to prepare the measured rough surfaces for tribological digital twins can be illustrated by the schematic diagram Figure 1. Figure 1: Schematic diagram of the proposed framework 3. Results and discussions In this extended abstract, measured honing and lapping surfaces were used to illustrate the proposed framework. The size of measured surfaces is 833mm×833mm with grid size 1024×1024. Figure 2 shows the results for a measured honing surface. 23rd International Colloquium Tribology - January 2022 427 Preparation of measured engineering surfaces for digital twins in tribology Figure 2: (a) Measured honing surface, (b) Simulated honing surface, (c) HPD, (d) PSD It can be seen that the simulated honing surface has similar patterns to the measured one. The HPD and PSD of the simulated surface agree with the measured one. Figure 3 shows the results for a measured lapping surface, which has filtered out the high-frequency components and resampled to 256×256 grids. The simulated surface is based on the filtered lapping surface and is resampled to 256×256 grids. 428 23rd International Colloquium Tribology - January 2022 Preparation of measured engineering surfaces for digital twins in tribology Figure 3: (a) Measured lapping surface, (b) Filtered lapping surface, (c) Simulated surface with resampling (256×256 points), (d) HPD, (e) PSD The results show that the simulated one has similar features to the filtered one. Moreover, the HPD and PSD curves show a good match between the simulated and filtered surfaces, although they have different grid sizes. The preliminary results above prove that the proposed framework can characterize and reconstruct the measured rough surfaces with different features by HPD and PSD. Moreover, the resampling procedures are also proved preliminarily. One interesting finding is that the simulated honing surface does not show the significant grooves in the measured one, although the HPD and PSD of the measured surface are kept in the reconstruction. This result indicates that HPD and PSD cannot fully characterize some features, and other characterization methods should be used. 4. Conclusion A framework for preparing the measured engineering surfaces for digital twins in tribology is proposed. The framework includes characterization, filtration, resampling, and reconstruction procedures, which have been proved to be valid preliminarily. Reference [1] Pérez-Ràfols F, Almqvist A. Generating randomly rough surfaces with given height probability distribution and power spectrum. Tribology International. 2019; 131: 591-604.