Generalized analytical model for optimal design of hollow shaft–hub shrink-fit joints under torsional loading

Interference-fit joints are widely used in lightweight and high-speed transmission systems due to their ability to transmit high torque, resist fatigue and maintain compact geometry. However, most prior studies focused on solid shafts and similar materials overlooking the combined influence of torsion, friction and geometry in hollow shaft shrink-fits with dissimilar materials. This limitation restricts their applicability to modern engineering systems. This work presents a generalized analytical model for optimizing shrink-fit joints under torsional loading. Closed-form solutions are derived for the optimal hub and shaft aspect ratios, interference value, contact pressure as well as torque capacity ensuring balanced effective stress in both shaft and hub while minimizing material usage. A main contribution of the model is the identification of threshold conditions: (i) a lower limit of the joint strength factor, below which no feasible solution exists, and (ii) upper and lower bounds for the shaft aspect ratio depending on design scenarios. These thresholds provide clear criteria for determining whether a given material combination and geometry can support the required torque transmission. The results showed that increasing friction will reduce the necessary interference while demanding a thicker hub to withstand shear stresses, whereas the contact pressure remains unaffected and depends only on geometry and material properties. Case studies with steel, aluminum, and brass demonstrated the differences between high-strength homogenous joints and low-strength or dissimilar material pairings, with the latter requiring more significant geometric adjustments. Three-dimensional finite element analysis validated analytical predictions within deviations ranging from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mn>10</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> . This work provides direct design formulas useful for aerospace and automotive lightweight transmission systems. It provides theoretical understanding and practical tools, including closed-form formulas and design charts for efficient, reliable shrink-fit joint design without iterative simulations.