(a) Figure 1 shows a rotor assembly consisting of three components: shaft, hub a

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(a) Figure 1 shows a rotor assembly consisting of three components: shaft, hub and disc, all made of steel. The assembly is to be fabricated using multi-step shrink fit process. (S1) First the shaft is cooled while the hub is heated to expand. The shaft is inserted onto the hub. The subassembly is placed in a room until it returns to the normal temperature. (S2) The subassembly is kept at a room temperature due to its rigidity and the disc is heated. The shrink fit is performed for the subassembly and the disc. We wish to know the residual stress in the hub in S1 and in the disc in S2. Determine the most proper two-dimensional finite element models one can use for the two steps S1 and S2. Provide explanations for your answers, and, if a suitable plane elasticity model exists, sketch its mathematical model.

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