# Modeling of Dry Clutch Wear for a Wide Range of Operating Parameters
## 9 Conclusions  
Experimental characterization and data-driven modeling of dry clutch friction lining wear has been presented in the paper. The experiments were performed on a custom-made disk-on-disk tribometer mimicking real clutch operation with clutch temperature, initial slip speed, clutch torque, and closing time as closed-loop controllable operating parameters resulting in 121 static operating points. The clutch friction interface temperature was identified to be most influential parameter input, with correlation index of 0.744. The  
Figure 20: Absolute (**a**) and relative (**b**) width of 95% CI with respect to clutch plate wear level for modeling points. correlation indices with respect to initial slip speed, clutch torque and closing time were 0.295, 0.210 and 0.173, respectively. The developed data-driven model predicts the friction lining worn volume and is organized around three distinctive submodels, providing wear rate expectation, standard deviation and weighting function accounting for run-in effect. The wear rate expectation is described by a cubic model with three inputs: temperature, torque, and a surrogate distance combining initial slip speed and closing time. The optimal model structure has been selected via best subset selection, leave-one-out cross-validation, and least squares parameterization. The final model, maximizing the cross-validation index \(R_{p}^{2}\) includes 10 out of 20 possible parameters. The \(R_{p}^{2}\) value of 0.841 demonstrates a significant improvement over the common, baseline model having the temperature as the only input which is characterized by the \(R^{2}\) value of 0.583. On a separate validation dataset, the \(R^{2}\) index still has relatively high value of 0.721, compared to 0.462 for the baseline model, confirming the modeling consistency. The wear rate variability model was developed by the maximum likelihood approach and its validity was confirmed by the statistical Kolmogorov-Smirnov test, both for modeling and validation datasets. The overall wear model has been experimentally validated throughout the wear depth under randomly varying operating parameters mimicking real driving conditions. Prediction error of worn volume at the end of friction lining life was 3.8% and 6% for plates experiencing floating and constant clutch temperature, respectively. The model-predicted 95% confidence interval (CI) embraces well the recorded worn volume samples throughout the wear depth, except at the very early stage of run-in phase. The 95% CI decreases in relative sense as the friction plate is wearing down. For the worn-out level of 10% the relative width of 95% CI ranges from 7 to 33% depending on the operating conditions, while it reduces to the range from 3 to 10% for the fully worn-out plate. Conceptualization, B.S., M.H. and J.D. ; methodology, B.S., N.K. and A.T.; software, K.H. and B.S. ; validation, K.H. ; formal analysis, K.H., M.H. and J.D. ; investigation, K.H., B.S., M.H., N.K. and J.D. ; resources, A.T.; data curation, M.H. ; writing--original draft preparation, K.H. and M.H. ; writing--review and editing, B.S. and J.D. ; visualization, K.H. ; supervision, B.S., N.K., J.D. and A.T.; project administration, J.D. ; funding acquisition, J.D. and A.T. All authors have read and agreed to the published version of the manuscript. This research was funded by the Ford Motor Company under the internal funding program number DEPT2019-075.6. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy issues. Author [PERSON] was employed by the company Ford-Werke GmbH. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. List of Mathematical Symbols and Abbreviations