For design purposes the stresses and deformations in elastic plastic form for a thin ring disk shrink-fit as- sembly have been analysed and a graph of interface pressure in the disc with respect to interference was gi- ven by Gamer and Lance [17]。 In another work [18], the stress and displacement in a rotating shrink-fit for an elastic disc were evaluated and it was shown that the stresses in the elastic region of the hub were not de- pendent on the hardening law。 Guven [19] worked on the state of plane stress in shrink-fit with an elastic– plastic hub with various thicknesses and it was reported that the elastic–plastic interference radius is influenced by the hardening parameter and that the stress distri- bution in a fully plastic hub with variable thickness is also influenced by Poisson’s ratio。

Antman and Shwartsman [20] presented work on solving the problems in a shrink-fit of acolotropic non- linear elastic bodies with arbitrary axisymmetric boundary  conditions on  the  outer  edge  of the annulus。

Satish Kumar et al。 [21] developed a finite element contact stress algorithm with linear elastic assumptions to deal with varying partial contact/separation at the pin–plate interface using a marching solution。 Zhao Hua [22] developed a virtual contact loading method to simulate the contact phenomena on the interference fitting surfaces between wheel hub and shaft。 The in- fluence of some structural parameters, interference tol- erance and structural geometry, on the contact stress distribution has been presented。

In a recent work presented by Juuma [23,24], the torsional fatigue strength of shrink-fitted shaft couplings was estimated by experiments by varying the geometry of the assembly, the load and the contact pressure for only shaft and for both shaft and grooved hub, respec- tively。 In another work undertaken by Chen et al。 [25], the minimisation of die-design component errors caused by die elasticity, secondary yielding, springback and temperature in cold forging was analysed。 The rigid- plastic FE analysis of elastic deformation of dies in backward extrusion has been performed by Hur et al。 [27]。 Results showed that the use of high stiffness ma- terials to the first stress ring forging dies can reduce the elastic deformation of the insert without failure。 In a work presented by Besterfield et al。 [26] the causes of failures were analysed。 It was concluded that the de- velopment of high stresses at low temperatures during assembly while fracture toughness of trunnion-hub-gir- der materials decreased with temperature and alterna- tive assembly procedure that nearly doubles allowable crack length, and that lowers cooling temperature to avoid trunnion sticking in the   hub。

In this work, the stress distribution for a shaft–hub system along the interference-fit contact line in the plastic zone for various interference fitting    dimensions

S。 Sen, B。 Aksakal / Materials and Design 25 (2004)   407–417 409

was investigated by, depending upon shaft diameter and the contact length using finite element program, ANSYS 5。6 [28]。

2。Description  of  the problem

In general when two solid surfaces contact  each other, due to the natural roughness of any real mate- rial, actual physical contact takes place only at some projecting asperities of the surfaces。 Conduction takes place at these points of contact while heat is  trans- ferred across the gaps by radiation and conduction [5]。 Despite empirical generalisations and simplifications of the analytic heat transfer formulations and because of unsteady boundary conditions,  the  complete  solution of the interference-fit problems appears to be extremely difficult and therefore nowadays numerical methods such as the finite element method have become wide spread in use in order to evaluate stresses  on  the contact surfaces。