A pin is to be inserted into a collar using an expansion fit. Properties of the pin and collar metal are: coefficient of thermal expansion is 12.3 × 106 m/m/ °C, yield strength is 400 MPa, and modulus of elasticity is 209 GPa. At room temperature (20°C), the outer and inner diameters of the collar = 95.00 mm and 60.00 mm, respectively, and the pin has a diameter = 60.03 mm. The pin is to be reduced in size for assembly into the collar by cooling to a sufficiently low temperature that there is a clearance of 0.06 mm.
(a) What is the temperature to which the pin must be cooled for assembly?
(b) What is the radial pressure at room temperature after assembly?
(c) What is the safety factor in the resulting assembly?