# Dependence of the Preload on the Tightening Torque for Hydraulic Plugs
## 1 Introduction
Due to the complex contact and tribological conditions in bolted connections, especially between the threads (uneven pressure distribution, high pressures [23], deformation of the threads, etc. [8; 24; 25]), the coefficients of friction given in the literature are often inadequate and their ranges are given too wide for precise calculations of preload. Also, in the case of threaded plugs, which differ from ordinary bolts in their design, it turned out that the friction and torque coefficients given in the literature for bolts inaccurately described their preload-torque relationship. Thus, for a more accurate description of this relationship, the thread and underhead friction coefficients should be measured as standardized [20; 21]. Since the measurement of both friction coefficients requires a demanding measurement setup, often only the overall friction coefficient \(\mu_{m}\) (uniform thread and underhead friction coefficient) is determined. In [16; 18], for example, the tightening torque and preload were measured in different bolted joints of the front motorbike suspensions and the overall friction coefficients were calculated as follows [19]:  
\[\mu_{m}=\frac{T/F_{V}-0.16\cdot p}{0.58\cdot d_{2}+0.5\cdot d_{u}} \tag{4}\]  
The aim of these two studies was to provide an experimental methodology useful to determining the overall friction coefficients in bolted joints and to precisely relate the tight ening torque to the preload. They found that surface finishing, lubrication, the interaction between these two parameters and the number of repeated tightenings were the most influential parameters on the overall friction coefficient. [PERSON] and [PERSON] [26] investigated the effect of joint friction on wheel bolt preload in heavy commercial vehicles. They reported that repeated tightening caused up to a 50% reduction in preload, while a constant state was reached when the bolts were relubricated with engine oil. [PERSON] and [PERSON] [27] investigated the friction coefficients of fasteners used in preloaded zinc-coated bolted connections in vehicle chassis after repeated tightening. They emphasized the importance of friction coefficient accuracy for determining the preload-torque relationship of bolted connections. Likewise, as in [16; 18], they found that the friction coefficients increased with repeated tightenings, which they attributed to the worn coating material. [PERSON] et al. [19] investigated the relationship between tightening torque and preload in extended hollow-bolt blind bolted connections with concrete-filled steel hollow sections by experimental and numerical analyses. They found that the nut factor of these bolts was higher (\(K\) = 0.37) than the suggested typical value (\(K\) = 0.2) and determined the belonging friction coefficients (\(\mu_{t}\) = 0.04, \(\mu_{u}\) = 0.3). Other studies investigated the preload-torque relationship of preloaded bolted connections (e.g., [11; 25; 28]), but none of them were performed on hydraulic plugs. The main aims of the present study were (1) to determine the preload-torque relationship of two non-standard threaded hydraulic plugs under lubricated and unlubricated conditions by determination of their overall friction coefficient \(\mu_{m}\) and torque coefficient \(K\), (2) to analyze the influence of repeated tightening on these two coefficients and (3) to analyze the possible error made in the plug preload in case friction coefficients from the literature would be used for calculation of the necessary tightening torque.