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In our study, we develop a finite element model based on Archard's wear law to predict the cumulative wear and the evolution of the tool profile in friction stir welding (FSW) applications. Our model considers the rotational and translational behaviors of the tool, providing a comprehensive description of the wear process. We validate the accuracy of our model by comparing it against experimental results, examining both the predicted cumulative wear and the resulting changes to the tool profile caused by wear. We perform a detailed comparison between the predictions of the model and experimental data by manipulating non-dimensional coefficients comprising model parameters, such as element sizes and time increments. This comparison facilitates the identification of a specific non-dimensional coefficient condition that best replicates the experimentally observed cumulative wear. We also directly compare the worn tool profiles predicted by the model using this specific non-dimensional coefficient condition with the profiles obtained from wear experiments. Through this process, we identify the model settings that yield a tool wear profile closely aligning with the experimental results. Our research demonstrates that carefully selecting non-dimensional coefficients can significantly enhance the predictive accuracy of finite element models for tool wear in FSW processes. The results from our study hold potential implications for enhancing tool longevity and welding quality in industrial applications.