In a well-known test machine, the "four-ball machine", an upper steel ball is loaded and rotated against three lower balls so that the four form a close-packed tetrahedron. The whole system is immersed in lubricant. The balls are normally 535A99 steel, with; E = 210 GPa, Poisson's ratio, v= 0.3 diameter = 0.0254 m. a) b) c) If the lubricant is gear oil, kinematic viscosity 19 cSt at 100C, pressure- viscosity coefficient, a = 15 GPa and the system is initially at 40C. Assume the density of the oil is 880 kg/m. What would this testing machine be used for? J What is the Hertz contact diameter at 1200 N load? What is the minimum film thickness just after starting a test at this load and at 1000 rpm? Hints: a) use your judgement, based on the type of contact between the balls, the relative motion and on the contacts of various machine componets we studied during the module; e.g. lubrication and fatigue in rolling element bearings, etc. b) the 1200N load is resolved in three directions along the sides of a regular tetrahedron. Find the force in one direction (this is the force between the top and any of the bottom balls) then use Hertz' formula for conatct radius. Note that the centres of the balls form a regular tetrahedron and that the forces between balls are directed along the sides of this tetrahedron. c) Calculate the peripheric velocity of the top ball, at the contact with any of the lower balls; use Hamrock & Dowson formula for film thickness.