This data article comprises experimental data acquired to investigate the critical angular clamping speeds for fasteners by the use of design of experiments methodology (DOE) and analysis of variance (ANOVA). The stick-slip phenomenon is considered as a critical factor limiting the angular speed. The stick-slip was quantified using the stick-slip factor as a function of the amplitude ratio by the frequency of the friction force time series. An investigation was carried out involving the influencing variables on the stick-slip factor, on torque, and on clamping force (preload): friction coefficient, clamping angular velocity, cathodic electrodeposition, hardness of the bolt-head bearing plate. The analysis demonstrated that the stick-slip factor could be used for the phenomenon prevention.