Joints of high quality can be formed by friction welding. Consider the friction welding of two 40-mm-diameter Inconel rods. The bottom rod is stationary, while the top rod is forced into a back-and-forth linear motion characterized by an instantaneous horizontal displacement, d(t) = a cos(ωt) where a = 2 mm and ω = 1000 rad/s. The coefficient of sliding friction between the two pieces is μ = 0.3. Determine the compressive force that must be applied to heat the joint to the Inconel melting point within t 3 s, starting from an initial temperature of 20°C.
