Improvements to torque versus tension relationship considering nut dilation effects

Torque as a tightening method is a simple technique that can be used to tighten a bolt to a given pre-load. Therefore, it is important to theoretically derive an accurate torque vs tension relationship for threaded fasteners as this would enable the industry to achieve a reliable pre-load. Various attempts were made to develop a complete theoretical relationship between torque and tension. Due to the thread angle there exists a nut dilation force causing the nut to expand radially out wards. This effect is more prominent in nuts with smaller height (Style 0 hex nut, refer ISO 4035 1 ). This nut dilation force creates a combined frictional effect with the drive torque thus affecting the torque tension relationship. This paper proposes a novel 3D formulation for torque tension relationship taking into consideration the nut dilation effect. This paper further develops new formulae for tightening and loosening torque, retaining torque, tension vs nut rotational angle relationship as well as formula for nut dilation force for both tightening and loosening.

Effect of Dynamic Contact Angle on Spontaneous Capillary-Liquid-Liquid Imbibition by Molecular Kinetic Theory

Summary Imbibition is one of the most common physical phenomena in nature, and it plays an important role in enhanced oil recovery, hydrology, and environmental engineering. The imbibition in a capillary is one of the fluid transports in porous media, and the effect of a dynamic contact angle that changes with the imbibition rate on liquid-liquid imbibition is not clear. In this paper, the molecular kinetic theory (MKT) is used to study the effect of a dynamic contact angle on spontaneous capillary-liquid-liquid imbibition at a micrometer scale. The results show that: Using a scaling time, the effects of various forces in different imbibition systems can be compared, the influence of a dynamic contact angle on imbibition can be characterized by a frictional effect of the three-phase contact line, and the proposed model considering the effect of a dynamic contact angle is better than the model neglecting the effect of a dynamic contact angle. As the displacing phase viscosity increases, the influence of a dynamic contact angle on imbibition strengthens, which is attributed to a decrease in the viscous effect and an increase in the frictional effect during the imbibition process; as the displaced phase viscosity increases, the influence of a dynamic contact angle on imbibition weakens, which is attributed to an increase in the viscous effect and a decrease in the frictional effect during the imbibition process. As the interfacial tension increases, the frictional effect increases, with the result that the effect of a dynamic contact angle on imbibition increases. As the capillary becomes more hydrophilic, the effect of a dynamic contact angle on imbibition becomes stronger because of a decreasing viscous effect and an increasing frictional effect. As the capillary length increases, the viscous effect increases, whereas the frictional effect decreases, leading to a decrease in the dynamic contact angle effect. As the capillary radius increases, the frictional force decreases, whereas its proportion in total resistance or the frictional effect increases, resulting in an increase in the effect of a dynamic contact angle. This work sheds light on the effect of a dynamic contact angle on capillary-liquid-liquid imbibition, including displacing phase viscosity, displaced phase viscosity, interfacial tension, capillary wettability, length, and radius. It will provide new insights into manipulating a capillary imbibition process and provide a fundamental theory for enhanced oil recovery by imbibition in conventional or unconventional reservoirs. Supplementary materials are available in support of this paper and have been published online under Supplementary Data at https://doi.org/10.2118/205490-PA. SPE is not responsible for the content or functionality of supplementary materials supplied by the authors.