# Dependence of the Preload on the Tightening Torque for Hydraulic Plugs
## 5 Conclusions  
The study investigated the preload-torque relationship of two non-standard threaded hydraulic plugs under lubricated and unlubricated conditions. The tightening torque and preload were measured, and the overall friction and torque coefficients were calculated. (1) Despite the plug-valve connections having a similar geometry with the same surface roughness of the contacting surfaces, the average overall friction coefficient and torque coefficient differed by 16% and 18% between the two plug-valve connections in the unlubricated and lubricated conditions, respectively, indicating that even small geometry differences between the plug-valve connections can have considerable influence on these coefficients. The overall friction and torque coefficients were from 8% to 17% higher in the unlubricated condition than in the lubricated condition but were not statistically supported. (2) The overall friction and torque coefficients decreased degressively with repeated tightening. (3) Consideration of the minimum and maximum thread and underhead friction coefficients given in the literature would result in a large error in the estimated preload (\(-\)15% to +86% of the actual preload).  
This study has shown that the preload-torque relationships of non-typical bolted connections cannot be accurately determined from the friction coefficients given in the literature. Thus, for accurate determination of these relations, tightening torque and preload must be measured. The results also show that it is not possible to demonstrate a systematic relationship between the size of the plugs and the preload-torque relationship, which makes it necessary to treat the subsequent sizes and different types of plug-valve connections separately. To ensure stabilie preload-torque relationships of the plug-valve connections, it is recommended to tighten and loosen the plugs a few times before they are placed on the market.  
Conceptualization, B.J., A.C. and F.M.; methodology, B.J., A.C., J.H. and F.M.; validation, B.J. and J.H.; analysis, B.J., J.H. and F.M.; investigation, B.J., J.H. and F.M.; resources, B.J., A.C. and F.M.; data curation, B.J. and J.H.; writing--original draft preparation, J.H.; writing--review and editing, B.J., A.C., J.H. and F.M.; supervision, B.J. and F.M.; project administration, B.J. and F.M.; funding acquisition, B.J. and F.M. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by Poclain Hydraulics d.o.o., Slovenia, Ziri [grant numbers 20100109631, 2021].  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
**Acknowledgments:** The authors acknowledge [PERSON] for providing help in the construction and assembly of the hydraulic test rig. The authors also acknowledge the financial support provided by the Slovenian Research and Innovation Agency (ARIS) for the open access publication of this scientific article.  
**Conflicts of Interest:** Author [PERSON] was employed by the company Poclain Hydraulics d.o.o. 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. The sponsors had no role in the design, execution, interpretation, or writing of the study.