Design and optimization of shaft–hub hybrid joints for lightweight structures: Analytical definition of normalizing parameters Dario Croccolo n , Massimiliano De Agostinis, Nicol  o Vincenzi University of Bologna—DIEM, Viale Risorgimento 2, 40136 Bologna, Italy article info Article history: Received 22 November 2010 Received in revised form 6 October 2011 Accepted 4 January 2012 Available online 18 January 2012 Keywords: Lightweight structures Interference-fit Design optimization Normalizing parameters abstract This paper addresses the design and optimization of interference-fit and adhesively bonded joints (hybrid joints) in lightweight structures. These types of joint involve a hub and a solid or hollow shaft, locked together by a frictional force (based on the radial pressure and the Coulomb friction law) and an adhesive strength generated at the coupling surfaces. The total strength of the joint allows the transmission of axial forces or torque moments. This paper amply investigates the optimal combina- tions of the hub aspect ratio (ratio between internal and external diameters) in order to maximize the axial (or torque) load transmitted by the joint as well as to reduce the weight of the structure. Derived from an analytical approach, two normalizing parameters are employed which are able to take into account the simultaneous effect of the materials density, the shaft aspect ratio, the hub yield strength, the coefficient of friction between the mating parts and, finally, the adhesive mean strength. Some design formulae and charts, based on the maximum shear yield criterion (Tresca), are proposed as a function of such normalizing parameters. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction Interference-fitted and adhesively bonded joints are assembly systems that transmit an axial force or a torque moment by means of the frictional force (based on the radial pressure and the Coulomb friction law) and of the adhesive strength acting at the interface (coupling diameter D C ) of their constituent parts, called shaft and hub. They provide a low cost joining method that is widely used in industrial applications [1–3]. Interference-fitted joints basically involve a pressure generated between the inside diameter of the hub (D Hi ) and the external diameter of the shaft (D Se 4D Hi ) by means of a nominal interference U ¼ D Se  D Hi at their interface, as shown in Fig. 1. The assembly can be realized in two ways: (i) with the male component at room temperature whereas the female is heated sufficiently to ensure free assembly with no need for force (shrink-fit assembly technique); (ii) by pushing the male component into the female at constant speed using a hydraulic press (press-fit assembly technique). In case of shrink-fit, the actual interference Z coincides with the nominal one U, whereas in case of press-fit the actual interference Z is equal to the nominal U decreased by a G contribution. G is normally related to the roughness of the hub (R zH , R aH ) and the shaft (R zS , R aS ), as suggested by some Standards [4,5] and by Yang et al. [6], because the amounts of roughness are partially erased by the under-pressure sliding of components: its value can be calculated by means of Eq. (1) Z ¼ UG, G ¼ 3ðR aS þ R aH Þ 0:8ðR zS þ R zH Þ ( ð1Þ Stress and strain distributions in interference-fitted components, both in elastic [7] and in elastic–plastic field [8–10], have been extensively developed in over fifty years of studies that have brought to increasingly complex theoretical elaborations, rather than to innovative design applications. All the proposed and devel- oped models start from a known geometry (i.e. diameters reported in Fig. 1 are completely defined), which is a suitable situation to define the tensile state accurately but does not supply any guideline in order to select an appropriate configuration. As a matter of fact, engineers establish, at first, the coupling diameter D C (and the ratio Q S , related to the shaft design) or the external diameter of the hub D He (related to space constraints), than they define the other geometric parameters, in particular the coupling length L C , the aspect ratio Q H and, eventually, the actual interference Z necessary to transmit the required load: the basic involved parameters are usually related each other, as reported, for example, in Eq. (2) [11]. Unfortunately, this consolidated design process does not allow the geometrical optimization of the coupling that could maximize the axial load or the torque transmitted by the joint as well as could Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ijmecsci International Journal of Mechanical Sciences 0020-7403/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmecsci.2012.01.007 n Corresponding author. Tel.: þ39 051 2093413. E-mail address: dario.croccolo@unibo.it (D. Croccolo). International Journal of Mechanical Sciences 56 (2012) 77–85