2. A gearbox containing steel gears is currently being used in an application where it is driven by a 5-hp motor at 900 rpm. Tests indicate that the gearbox will last

500 hours under these conditions, with failure due to fatigue of the gear teeth. The capacity of the system is to be increased; a 6-hp motor will now be required and the rpm value will be decreased 10%. What effect will this have on the life (in hours) of the gearboxes? For the steel, since we do not know anything else of the specific steel used for the gears, just assume the generalized S-N curve in the finite life regime is given by (Eq. 1.7 in BCH book): Sa=AN 1.62SuNf Hint: This problem requires a relative life calculation (as opposed to absolute), so parameters that will not change between the current and new application will cancel out in the end. -0.085 One additional consideration: The parameter b in the S-N equation above for steel can range from -0.06 to -0.12 depending on the steel and its heat treatment. How much will this affect your answer?