Abstract In general the stress calculations in interference-fit designs are estimated by using conventional equations。 In the event that the parts show an elastic–plastic behaviour the process becomes more complicated。 In this study, the stress distribution in interference fitted shaft–hub assembly was investigated in relation to the ratio of contact length-shaft diameter using the finite element method。 During heating and cooling the transient conduction heat transfer state was considered in which the boundary conditions of the system are continuously changed。 In such interference fitted connections the occurrence of plastic deformation zone and its dis- tribution was evaluated。 It was shown that the current results will certainly help the designer in force in transferring assemblies such as shaft–hub fitting coupled with pulley and gear systems in terms of dimensional analysis, tolerance and controlling the cooling conditions。83180

Keywords: Interference fits; Transient heat transfer; Finite element method; Elastoplastic deformation

1。Introduction

Interference fitted connections are widely used in transmitting motion via two cylindrical parts。 Such ap- plications are; crank shaft-belt, shaft-bearing and shaft bearing assemblies。 These kinds of assemblies create a complicated contact problem between the two cylindri- cal parts。 In practice, contact stresses in such designs are generally estimated using some equations, e。g。 Lame’s equation [1]。 Due to the reasons such as; the finite extent of the contact surface area, local variations in thermal gradient, even if having slow cooling rate of the heated hub during shrink-fitting process, dimensional changes take place。 Also because of thermal variations in the neighbouring parts and friction between the contact surfaces, such equations fail to describe the process adequately。

The analytical solutions also appear to be quite com- plicated even for idealised interference fitted assemblies。 Lame’s equations are still used very commonly for the assemblies such as cylindrical shaft-ring applications [1–

5]。 However nowadays some numerical methods such as the finite element method have become popular for using such systems by considering the real geometry and working conditions。 Cangming and Yongie [6] investi- gated a mathematical programming-finite element meth- od for the frictional contact problem。 A finite element method formulated by Daniel [7] was applied to inter- ference fitted applications by Prasad et al。 [8]。 In their analysis a hollow shaft and hub system was considered and the stress distribution was presented for various val- ues of l=D and D=d ratios。 The stress distribution was investigated for the elastic steady state along the shrink- fitted region。 Zhang et al。 [9] analysed the selective as- sembling of the shrink-fitted ring gear and wheel system, and the stresses at the interface were calculated using structural static analysis with the effects of thermal strains included。 Parson and Wilson [10] suggested a method for determining the contact stresses between any two elastic bodies but ignoring the effects of friction at the contact surface。 Mack and Bengeri [11,12] investigated the influ- ence of temperature dependence of the yield stress on the stress distribution in an elastic–plastic shrink-fit analyti- cally and it was reported that the unloading process due to

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

the temperature dependence of the yield stress had only a minor influence on the stress distribution。 Later on they made another attempt to solve a transient elastic–plastic thermal stress problem for a shrink-fit with solid inclu- sions [13]。 Tsuta and Yamaji [14] found irreversible non- linearity caused by frictional forces at the contact surfaces and proposed a new method based on incremental theory。 Ohte and Zhang [14] extended this method to a contact problem by including friction。 Oh et al。 [15] analysed the stress patterns resulting from high temperature and pressure in a shrink-fitted linear-steel sleeve under high pressure and temperature in manufacturing of an alumina tube using the finite element method。 Okomoto and Nakawaza [16] worked on a simplified algorithm based on the finite incremental contact analysis with different fric- tion conditions。