In this study, the contact between fitted hub and solid shaft was modelled through the finite element method as schematically illustrated in Fig。 1。 Due to symmetry only one quarter of the assembly was considered。 In order to transfer the torque via the hub–shaft system, the re- quired pressure is produced by a diameter difference between the shaft and hub。 For this, either the shaft is machined to a greater diameter than the hub’s internal diameter, or hub’s internal diameter is machined to a smaller one than the shaft diameter。 After shrink-fitting, pressure occurs at the contact surfaces between the mating parts。 The relevant theoretical equations can be found in [1–5]。

2。1。The model and material   properties

The process of assembly was based on heating the outer part, the hub, and then shrink-fitting it to the inner part,  the shaft, and  finally  slow-cooling  the whole sys-

Fig。 1。 Schematic illustration of the full shaft–hub   assembly。

tem。 The materials of the shaft and hub are assumed to be the strain hardening material where the dimensions are given in Fig。 1 and mechanical/thermal properties in Table 1。 For heating and cooling the transient conduc- tion heat transfer state was considered。 During cooling of the hub, it was assumed that there exists a heat transfer between the shaft and hub along the interfer- ence-fit surfaces。 Furthermore, an overall energy bal- ance was also considered for the solid assembly which relates the rate of heat loss at the surface to the rate of change of internal energy。The solution was conducted for four l=d ratios of 0。5, 0。75, 1。0 and 1。25 and again

Table 1

Thermal and mechanical properties of the material used in the    analysis

Shaft diameter, d  (mm) 200

Hub outer diameter, D  (mm) 400

Convection heat transfer coefficient for  hub 16742。2

Convection heat transfer coefficient, h for shaft (W/m2    °C) 16742。2

Specific heat capacity, cp  (W s/kg °C) 579。7

Thermal conductivity, k (W/m °C) 43。124

Thermal expansion coefficient, a (°C—1 ) 12:10—6

Poisson’s ratio, m 0。3

Density, q (kg/m3 ) 7800

Other properties with temperatures (°C) 20 100 200 400 600

Yield strength, rY (MPa) 256 221 216 157 73

Modulus of elasticity, E  (MPa) 210 × 103 206 × 103 200 × 103 181:5 × 103 165 × 103

Modulus of plasticity, ET    (MPa) 3:63 × 103