## 4 Conclusions  
In this paper, the stress distributions and stress concentration factors at the shaft-hub interface in interference fits with a chamfer hub were analyzed. This modified hub only requires two parameters for defining the hub geometry for a given hub thickness: the chamfer angle, \(\alpha\), and the dimensionless chamfer height, \(\beta\). According to the obtained results the following conclusions can be drawn:  
* Full-chamfer hubs caused a progressive reduction of the radial stress at the hub edge as the chamfer angle increased, reaching an almost uniform distribution of radial stress (or in other words, of contact pressure) for medium chamfer angles (\(\alpha\) = 15\({}^{\circ}\)).
* Although radial stress was reduced at the hub edge, the tangential stress was slightly increased. Nevertheless, the von Mises stress was also reduced at the hub edge, reaching a more uniform distribution at the shaft-hub interface than conventional hubs.
* The use of chamfer hubs with high chamfer angles causes a loss of contact pressure because of a high reduction of the radial stress nearby the hub edge and a soft reduction of radial stress at the hub center. This loss produces a reduction of the maximum transmitted torque and, hence, high values of chamfer hubs are not suitable.
* A curve of recommended chamfer angles to be selected in the design of full-chamfer hubs for different hub thicknesses \(\gamma\) is proposed. Taking this into account, the optimal chamfer angles are within the interval 13\({}^{\circ}\) \(<\)\(\alpha\) \(<\) 15\({}^{\circ}\) for commonly used hub thicknesses 0.375 \(<\)\(\gamma\) \(<\) 0.5.
* By using full-chamfer hubs with the proposed chamfer angles, a complete removal of radial stress concentration was achieved with a slight increment of tangential SCF and a reduction of the von Mises SCF. In this way, a more accurate estimation of the stress fields at the hub-shaft interface can be obtained by using the design equations given by theory.
* Partial-chamfer hubs with a hub height higher than \(\beta\) \(>\) 0.4 and chamfer angles \(\alpha\) \(>\) 15\({}^{\circ}\) exhibited a significant reduction of radial SCF with a slight increase of tangential SCF and a decrease of the von Mises SCF similar to the ones obtained by using full-chamfer hubs.
* Curves of recommended chamfer angles to be selected in the design of partial-chamfer hubs for different chamfer heights \(\beta\) and hub thicknesses \(\gamma\) were proposed. According to the results, the optimal values to be used for designing partial-chamfer hubs are chamfer heights higher than \(\beta\) \(>\) 0.5, hub thicknesses \(\gamma\) = 0.5, and chamfer angles \(\alpha\) = 15\({}^{\circ}\).
* By using the proposed optimal values, the same reductions on stress concentrations observed for full-chamfer hubs were obtained in partial-chamfer hubs and, consequently, the design equations can be used for estimating the real stress state at the shaft-hub interface.  
Conceptualization, M.L.; Data curation, M.L. and E.I.; Formal analysis, M.L., E.I. and R.G.-M.; Funding acquisition, M.L.; Investigation, M.L., E.I., M.R.-M. and R.G.-M.; Methodology, M.L.; Software, M.L., E.I. and R.G.-M.; Supervision, M.L., M.R.-M. and R.G.-M.; Validation, M.L.; Writing--original draft preparation, M.L. and E.I.; Writing--review and editing, M.L., E.I, M.R.-M. and R.G.-M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Fundacion Memoria D. Samuel Solorzano Barruso, grant numbers FS/32-2017 and FS/12-2021 and MCIN/AEI/10.13039/501100011033, grant number PID2020-119003 GB-I00