Problem #1 (75 Points): A single-stage gear reduction system is shown in the schematic below representing drive to a pulley using belt-drive transmission. The goal here is to find the minimum diameter of the transmission shaft. The material to be considered is AISI 1050 cold-drawn steel. The reliability goal for the endurance limit is 0.99. The force transmission from the driving gear to driven gear is occurring at a pressure angle of 20 (both the gears are spur gears). The size of the driven gear is specified as 100 mm. Consider diameter of the pulley as 60 mm, width as 20 mm, and weight of the pulley as negligible compared to the belt tensions on two sides of the pulley as shown in the schematic. a) Draw the shear force diagram, bending moment diagram and torque diagram representing how each of these quantities would vary along the shaft axis. b) Determine minimum diameter of the transmission shaft using modified Goodman failure criteria with a fatigue factor of safety (n = 1.5). c) Determine the factor of safety against static yielding. d) Determine rotational speed of driving gear mounted on the electric motor shaft if the motor is delivering constant power output of 1 hp. e) Select a 02-series single-row deep-groove ball bearing at the two bearing location ('A' and 'B') with the following conditions: Desired Life - 50 million revolutions Outer Ring Rotating (V) - 1.2 Load Application Factor (af) - 1.5 Desired Reliability (RD) - 0.99 Electric Motor Transmission Shaft driving a belt-driven pulley Z y x Driving Gear, 12T Bearing A Bearing B Pulley driving a load using belt-drive transmission T = 200 N Driven Gear, 50T T = 1000 N 100 mm 75 mm 50 mm