A proposal of a unique formula for computing compliance in bolted joints

The connection system between mechanical parts with the greatest advantages in terms of production is the threaded connection. This type of connection has considerable stiffness but also high weight. Often the search for the reduction of the masses clashes with the limits dictated by production needs. A considerable effort has been made in making screws with higher performance materials and therefore guaranteeing greater tightening forces with smaller cross sections, but there have not been as many notable developments on the method of determining the compliance of tightened elements. The classical theory identifies three different conditions for calculating deformability, which are sometimes not easy to interpret and implement. The use of numerical techniques such as finite elements allows designers to be very precise, but requires a great deal. To facilitate the work of the designers and provide them with a more manageable tool to better understand the type of threaded connection to be designed, the present work proposes an analytical formulation that allows a quick assessment of the compliance value of the clamped elements, regardless of the geometric relationships and materials. To achieve this, starting from a literature analysis, a parametric finite element model was developed and, based on the results obtained, a formula is proposed that covers all the possible scenarios for determining compliance. The results were compared with the classical theory in order to verify the correctness and applicability of the formulation. At the moment the formulation is valid for screws whereas for the bolts with nut unified formula is under investigation.