Torque Transmission by Friction in a Keyed Shaft-Hub Press-Fits

Interference fits are widely employed to semi-permanently connect gears, pulleys, flanges, wheels, disks, rotors, and similar mechanical components, to a shaft. The stress state along the hub central portion may be thoroughly predicted by modelling the press-fit problem as plane and by employing the Lamé equations for thick-walled cylinders, and the transmissible torque may be confidently estimated by relying on the Lamé predictions, since they are valid along most of the contact axial length. Often a key is added to the press-fit, to secure the torque transmission and to prevent any relative rotation between the shaft and the hub. Both parallel and tapered keys are employed in practical applications. With respect to their tapered counterparts, parallel keys possess the advantage that they do not cause any eccentricity. This study considers parallel keys only. The presence of the keyseat increases the compliance of the hub and the shaft, thus producing a diminution of the contact pressure between the hub and the shaft, which results in a similar diminution of the transmissible torque. In this paper, a preliminary Finite Element analysis is carried out to quantify the above diminution of the contact pressure in the assumption of frictionless contact. The analysis is carried out for a solid shaft and for a practically relevant selection of ratios between the hub inner and outer radii. A preliminary development is presented of an analytical approach based upon the classical Michell polar solution, which is particularly suitable to mimic rings. The diminution of the transmissible torque with respect to a keyless shaft-hub press-fit is quantified, and the results are presented in a design diagram.